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Remote Sensing and Simulation to Estimate Forest Productivity in Southern Pine Plantations

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PAGE 1

REMOTE SENSING AND SIMULATI ON TO ESTIMATE FOREST PRODUCTIVITY IN SOUTHERN PINE PLANTATIONS By DOUGLAS A. SHOEMAKER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Douglas A. Shoemaker

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This research is dedicated to my mother and father.

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iv ACKNOWLEDGMENTS I am grateful for the opportunity to work with Dr. Wendell Cropper who was generous with his knowledge, which is substa ntial, and patience. I also thank committee members Tim Martin and Michael Binf ord for access to valuable data. I am obliged to Dr. Jane Southworth w hose unbiased eye and fearless commentary kept me honest. I want to acknowledge individuals who contri buted in large and small ways to this work including Dr. Timothy Fik for inspira tion in statistics; Alan Wilson and Brad Greenlee of Rayonier Inc., landholder of the st udy site and member of the FBRC; Greg Starr for helping review this manuscript; a nd Dr. Loukas G. Arvanitis who kept me on task. Special thanks go to fellow students L ouise Loudermilk and Brian Roth who remain steadfast allies.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT....................................................................................................................... ix CHAPTER 1 BACKGROUND..........................................................................................................1 Modeling and Leaf Area Index......................................................................................2 Use of Remote Sensing Data.........................................................................................4 Scale and Resolution......................................................................................................5 2 PREDICTION OF LEAF AREA INDEX FOR SOUTHERN PINE PLANTATIONS FROM SATELLITE IMAGERY.....................................................7 Introduction................................................................................................................... 7 Methods......................................................................................................................10 Study Sites...........................................................................................................10 Remote Sensing Data..........................................................................................11 Seasonal LAI Dynamics and Leaf Litterfall Data...............................................14 Integration of Ground Referenced LAI and Remote Sensing Data.....................16 Climate variables..........................................................................................17 Statistical analysis........................................................................................18 Regression Techniques........................................................................................18 Linear regression..........................................................................................18 Multivariate regression.................................................................................18 Artificial neural network..............................................................................19 Use of ancillary data to specify model sets..................................................19 Results........................................................................................................................ .20 Linear Models......................................................................................................21 Multiple Regression Models................................................................................21 ANN Multiple Regression Models......................................................................21 Discussion...................................................................................................................22

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vi OLS Multiple Regression Models.......................................................................28 ANN Models.......................................................................................................28 Fertilization..........................................................................................................29 Suggestions for Future Effort..............................................................................29 Conclusions.................................................................................................................32 3 REMOTE SENSING AND SIMULA TION TO ESTIMATE FOREST PRODUCTIVITY IN SOUTHERN PINE PLANTATIONS.....................................34 Introduction.................................................................................................................34 Methods......................................................................................................................37 Study Area...........................................................................................................37 Integration of Remote Sensi ng and Ground Referenced Data............................39 Processing Data with the GSP-LAI and SPM-2 Models.....................................39 Results........................................................................................................................ .39 Discussion...................................................................................................................40 Conclusions.................................................................................................................44 4 SYNTHESIS...............................................................................................................46 Results and Conclusions.............................................................................................46 Further Study..............................................................................................................47 APPENDIX A VARIABLES USED IN MODELS............................................................................48 B GSP-LAI CODE.........................................................................................................51 LIST OF REFERENCES...................................................................................................62 BIOGRAPHICAL SKETCH.............................................................................................67

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vii LIST OF TABLES Table page 2-1. Catalog of images used in study.................................................................................13 2-2. Summary of linear mode ls fitted to dataset................................................................24 2-3. Summary of OLS multiple regre ssion models fitted to dataset..................................25 2-4. Summary of ANN models fitted to dataset................................................................26 2-5. ANOVA analysis of significant vari ables in OLS multiple regression......................30 2-6. Significance and ranking of variab les used in ANN multiple regressions.................31

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viii LIST OF FIGURES Figure page 2-1. Map of the Intensive Management Prac tices Assessment Center, Alachua County, Florida, USA.............................................................................................................12 2-2. Characterization of nor th-central Florida climat e during study period 1991-2001....15 2-3. Annual cycle of variation in leaf phenology illustrating two populations of needles.......................................................................................................................1 6 2-4. Comparison of the range of LAI va lues for slash and loblolly pine...........................23 2-5. Differences in effect of fertilizer treatment on slash and loblolly pine......................23 3-1. Predicted LAI values for closed canopy slash and loblolly pine. Bradford FL..........41 3-2. Predicted NEE values for closed canopy slash and loblolly pine. Bradford FL........41 3-3. Predicted LAI values for southern pine plantations in north-central Florida.............42 3-4. Predicted NEE values for southern pine plantations in north-central Florida............43 3-5. Effect of variable FERT on LAI prediction................................................................45

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ix Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science REMOTE SENSING AND SIMULATION TO ESTIMATE FOREST PRODUCTIVITY IN SOUTHERN PINE PLANTATIONS By Douglas A. Shoemaker August, 2005 Chair: Wendell P. Cropper, Jr. Major Department: Forest Resources and Conservation Pine plantations of the Sout heastern United States consti tute one-half of the world’s industrial forests. Managing these forests fo r maximum yield is a primary economic goal of timber interests; the rate at which thes e forests remove and sequester atmospheric carbon as woody biomass is of interest to climate change researchers who recognize forests as the only significant human -managed sink of greenhouse gases. To investigate a given pine plantation’ s productivity and corresponding ability to store carbon two significant parameters were predicted: net ecosystem exchange (NEE) and leaf area index (LAI). Measurement of LAI in situ is laborious and expensive; extraction of LAI from satellite imagery would have the advantages of making predictions spatially explicit, scalable, and would allow for sampling of inaccessible areas. Consequently the study was conducted in three steps: 1) the development of an LAI extraction model using satellite imagery as a primary data source, 2) application of the model to a study extent, and 3) determin ation of NEE using derived LAI values and Cropper’s SPM-2 forest simulation model.

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x We derived several models for extracti ng LAI values using various prediction techniques. Of these a best model was sele cted based on performance and potential for operational application. The generalized sout hern pine LAI predictive model (GSP-LAI) was developed using artificial neural network (ANN) multivariate regression and incorporating important local information in cluding phenological a nd climatic data. In validation tests the model expl ained > 75% of variance (r2 = 0.77) with an RMSE < 0.50. The GSP-LAI model was applied to Lands at ETM+ image recorded September 17, 2001, of the Bradford forest, north of Waldo, FL Within the extent are substantial slash ( Pinus elliottii ) and loblolly ( P. taeda ) pine plantations. Based on image and stand data projected LAI values for 10,797 ha (26,669 acres) were estimated to range between 0 and 3.93 m2 m-2 with a mean of 1.53 m2 m-2. Input of slash pine LAI values into SPM-2 yielded estimates of NEE for the area ranging from -5.52 to 11.06 Mg ha-1 yr-1 with a mean of 3.47 Mg ha-1 yr-1. Total carbon sequestered fo r the area analyzed is 33,920 metric tons, or approximately 1.4 tons per acre. Based on these results a map of the Bradfo rd forest was drawn locating areas of carbon loss and gain and LAI values for indi vidual stands. Ownership and accounting of carbon stores are prerequisites to anticipated carbon trading schemes. The availability of stand-level LAI values has si gnificance for forest managers seeking to quantify canopy response to silvicultural treatments. Effici encies may be realized in management practices which optimize leaf growth based on site potenti al rather than focusing on resource availability.

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1 CHAPTER 1 BACKGROUND The monitoring of forest biological proce sses has become increasingly important as nations seek to control th eir outputs of carbon dioxide (CO2), the primary component of climate-changing greenhouse gasses, in the face of global climate change. Forests in general and trees specifically provide the essential service of removing CO2 from the atmospheric reservoir of carbon through phot osynthesis, where carbon is fixed as energy-storing sugars. The metabolic processe s of the tree respire carbon back to the atmosphere but a portion is isolated from environment in the durable biomass of the plant, namely wood. Carbon will re-enter th e atmosphere when wood decomposes or burns, however the period of carbon sequestra tion is on the terms of decades, perhaps longer if that wood is built into a stru cture or buried as waste in a landfill. Carbon sequestration via forestry is currently the only means by which mankind can significantly remove carbon from the at mosphere; agricultural plantings are not counted as the carbon returns to the environm ent too quickly to have an appreciable effect (Tans & White 1998). The Kyoto Protoc ol of 1997, an international accord which seeks to reduce the emissions of greenhouse ga sses, calls for the cooperation of nations in finding and maintaining sinks or reservoirs, of greenhouse gases. This language lays the foundation for the trade in carbon credit s, whereby a nation exceeding its emissions of CO2 could pay another nation to sequester carbon, e.g. let stand a forest scheduled for harvest. The emissions trading scheme (ETS) identifies value (and a potential new revenue source) from what was previously an un-valued, non-marke t services provided

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2 by the forest. Carbon credits are not simp ly economic talk—on October 1, 2003, carbon credits traded for the first time in an international market, the Chicago Climate Exchange, for $.98 per metric ton (Doran, 2003). Modeling and Leaf Area Index Economists and ecologist want to better understand the flow of carbon in and out of forests on a regional and global scale. Fo rest ecosystems are complex, and systems ecologists use models to analyze the responses and productivity of fore sts, especially the movements of carbon (Waring & Running 1998) Models such as SPM-2 aim to characterize the flows of carbon between the atmosphere, the trees and the soil (Cropper 2000). This model, specific to coastal plain slash pine ( Pinus elliottii ) forests, uses dozens of input parameters ranging from rainfall a nd humidity to wind sp eed; outputs include carbon assimilation (g CO2 m-2 d-1 and Mg C ha-1 yr-1) and annual stem growth (g m-2). In forest system models the complexities of leaf area, incl uding canopy structures and geometry, may be simplified into a ratio of total leaf area to unit ground area known as the leaf area index (Wari ng & Running 1998). This leaf area index (LAI) composes the most basic input into current fo rest system models (Stenberg et al 2003). Unfortunately LAI is notoriously difficult to determine for a number of logistical reasons to be illustrated and for many speci es it changes within the growing season. In the subject species P. elliottii LAI varies seasonally because trees bear two age classes of leaves through most of the year. A maxi mum LAI occurs around mid-September when last year’s leaf class has not yet senesced and the new leaves have reached their maximum elongation. Workers thus need to be aware of the time-of-year when the sample is taken and account for th is seasonal variation (Gholz et al 1991). The climatic

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3 conditions at time of sampling are also importa nt, as drought or leaf loss due to storms can depress the index. LAI is measured in situ three distinct ways: the areaharvest method, th e leaf litter collection method, and the canopy transmitta nce method. A fourth indirect method involves the use of satellite imagery to m easure electromagnetic energy reflected from the forest canopy at specific indicative wavelengths. T hough laborious and limited in spatial extent, in situ methods provide important ground tr uth estimates for validating and training remote sensi ng techniques (Stenberg et al 2003). The area-harvest method involves ra ndomly choosing a tree in a forest community similar to that of the study, measuring the footprin t of the tree, harvesting it, and giving each leaf collected a specific leaf area (SLA), whic h is the ratio of fresh leaf area to dry leaf mass. Age cl ass of leaves should be accounted for as SLA can differ by a factor of two between old and new foliage. The number of trees measured in this fashion should reflect a sample size sufficient to repr esent the spatial heterogeneity of community studied (Stenberg et al 2003). The leaf litter collection method involves a sample selection process similar to the area-harvest method, however l eaves are continuously collected in leaf traps and each assessed as to area and age class. Extrapol ation techniques then extend the information along a timeline to determine LAI at a given time (Stenberg et al 2003). Field determinations of LAI may also be made without laborious collection using the canopy transmittance method. Optical sensors that measure light not intercepted by leaves, or canopy gap, are placed beneath th e canopy. The amount of light recorded is then compared with a model of canopy archit ecture, and from there an LAI is derived (Stenberg et al 2003). This method assumes the distribut ion of leaves in the canopy to be

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4 random; thus it is invalid for open-canopy fore sts, such as coniferous forests (Gholz et al 1991). In situ LAI determinations are the standard of comparis on for all new techniques, and are currently the most re liable data available. Area-ha rvest methods a nd leaf litter collection are assumed to be more accurate than canopy transmittance methods, however Gower reports that all in situ methods are within 70% to 75% accurate for most canopies, exceptions being non-random leaf di stributions and LAI > 6 (Stenberg et al 2003). Use of Remote Sensing Data Because of the arduous nature of determining LAI in situ there has been emphasis on developing new methods which use remotely se nsed data captured by sensors on airborne or satellite platforms (Gholz et al. 1991; Sader et al. 2003). These methods take advantage of the fact that photosynthetic ally active vegetation absorb specific wavelengths of the incident electromagne tic (EM) spectrum and reflect others. Specifically, blue (0.45-0.52 m) and red (0.63-0.69m) are absorbed, green (0.530.62m) and near infrared (0.7-1.2 m) are re flected (Jensen 2000). Reflectance of green wavelengths creates the green a ppearance of foliage, while re flected NIR is invisible to the human eye. Measurements of absorban ce and reflectance comprise unique spectral signatures that disti nguish between vegetation and othe r ground features, or between different genera of plants. The reflectance of NIR bandwidths are of part icular interest as they are indicative of the amount of leaves within the canopy at the time of imaging. Reflected wavelengths consist of EM energy the plant cannot use whic h leaves reflect or allow to pass through (transmit). Transmitted radiation falls incident on a leaf below, which in turn reflects

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5 50% and transmits 50%. This characteristic is cal led the leaf additive reflectance, and it is indicative of amount of leaves within a canopy. Several remote sensing indices have been created to classify and measure foliage from space using the differential reflectance and absorption characteristics of red and near infrared bandwidths. The most wi dely used algorithms (Trishchenko et al 2002) include Simple Ratio (Birth & Mcvey 1968) and Normalized Difference Vegetative Index (Eklundh et al 2003). The formula for Simple ratio (SR) is described as: SR = NIR/red Normalized Difference Vegetative Index (NDVI) is described as: NDVI = (NIR – red) / (NIR + red) The ratios have the advantage of using tw o of the seven or more bands typically collected, and requiring no other auxiliary data for calculatio n. However, they require calibration from in situ reference locations in order to produce secondary data, such as physical measurements of biomass (Wood et al 2003). Additionally, variability is introduced to the index by soil reflectance, atmospheric effects, and instrument calibration (Holben et al. 1986; Huete 1988). Of these thr ee soil reflectance is pervasive and its contribution to vegetati on indices is ideally subtracted using a two-stream solution developed by Price (Soudani et al 2002). A Leaf area index is a sec ondary datum produced by linking in situ reference data with a vegetation index, typically NDVI (Sader et al 2003). The data are connected through regression analysis resulting in a linear relationship (R amsey & Jensen 1996). Scale and Resolution The use of satellite imagery has also brought the issue of scale to the forefront. The spatial extent of forest systems modeled has typically been limited to a stand or woodlot

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6 scale due to the restrictive nature of in situ LAI sampling. Estimates of LAI from satellite imagery may be the only way to measure vegeta tive processes of forest at a regional or larger scale (Sader et al 2003). A fundamental question in choosing a data source is one of resolution. In remotely sensed data, a pixe l, or picture element, represents a spatial extent on the ground that is the minimum ar ea capable of resolution by a particular sensor. For the Thematic Mapper (TM) carried by the satellite platfo rm Landsat the pixel size is a 30 meter by 30 meter square. Thus the resolution of Landsat TM is said to be 30 meters. Different sensors have different reso lutions. The French SPOT satellite carrying the High Resolution Radiometer (HRR) ha s a 10 meter resolution (Jensen 2000). In working with vegetation, resolution should ma tch the size of the f eature-of-interest as closely as possible.

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7 CHAPTER 2 PREDICTION OF LEAF AREA INDEX FOR SOUTHERN PINE PLANTATIONS FROM SATELLITE IMAGERY Introduction Pine plantations of the Sout heastern United States consti tute one-half of the world’s industrial forests. In Florid a alone annual timber revenue exceeds $16 billi on and is the dominant agricultu ral sector (Hodges et al 2005). Managing these forests for maximum yield is a primary economic goal of timber in terests; the rate at which these forests remove and sequester atmospheric carbon as woody biomass is of interest to climate change researchers who recognize forests as the only significant human-managed sink of greenhouse gases. Leaf area index (LAI) is a ke y parameter for estimation of a given pine plantation’s productivity or net ecosystem exchange of carbon (NEE). In this study we focus on the estimation of LAI, a primary biophysical para meter used in forest productivity modeling, carbon sequestration studies, and by fore st managers seeking to quantify canopy responses to silvicultural treatm ents (Cropper & Gholz 1993; Sampson et al. 1998; Gower et al. 1999; Reich et al. 1999). LAI is the ratio of leaf surface area supported by a plant to its corresponding hor izontal projection on the gr ound, and it is difficult and expensive to assess in situ resulting in sparse sample sets that are necessarily localized at a stand scale and thus difficult to ex trapolate to larger extents (Fassnacht et al 1997). Determination of LAI from remotely sens ed data would have the advantage of being spatially explicit, scaleab le from stand to regional or larger extents, and could

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8 sample remote or inaccessible areas (Running et al 1986). An ideal empirical model linking ground-referenced LAI to remote sensin g data would make reliable predictions at various extents and image dates and be ge neral enough to incorporate important local information such as climatol ogical and phenological data. As Gobron et al (1997) point out the ra nge of variation that exists in vegetative biomes of interest worldwide preclude th e likelihood of a single universal relationship between LAI and remote sensing products; bu t regional prediction of LAI in important subject systems such as the extensive and ec onomically important holdings of industrial pine plantations across the southeastern U. S. should have important applications. There have been previous attempts to remotely estimate LAI for this specific forest system. Industrial plantations in the south typi cally consist of dense plantings of loblolly ( Pinus taeda ) and slash ( Pinus elliottii ) pine (Prestemon & Abt 2002). Gholz, Curran et al (1991) studied a north-central Florida ma ture slash pine plantation where they evaluated LAI determination techniques and related those to remote sensing data collected by Landsat TM. Flores (2003) looke d at loblolly pine in North Carolina and related ground-based indirect LAI values to hyperspectral remote sensing data. These studies used ordinary least squares (OLS) regression analys is to establish an empirical relationship between vegetative i ndices (VI) and ground-referenced LAI. The best understood VIs are the normalized di fference vegetative index (NDVI) (Rouse et al 1973) and the simple ratio (SR) (Birth & Mcvey 1968) both of which make use of recorded values for red and near infrar ed wavelengths. In the case of Gholz et al (1991) three predictive equations were produced us ing NDVI. Flores used SR in his predictor. We evaluated these models using a new da taset assembled for this study and found none

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9 exhibited significant predictive ability (see Ta ble 2-2 in results). While linear regression remains a popular approach, variations in su rface and atmospheric conditions as well as the structural considerations of satellite remo te sensing have foiled attempts to establish a universal relationship between LAI and VIs (Gobron et al. 1997; Fang & Liang 2003). Perhaps this failure is due to underor misspecification of the models. The biochemical and structural component of th e forest canopy is complex, varying in both time and locale (Raffy et al 2003). Cohen et al (2003) suggest that the incorporation of other recorded spectra and the use of data from multiple dates as predictive variables as a way to improve regression analysis in remote sensing. Multivariate regression techniques allow for the incorporation of more type s of data, including important locational information such as climate or categorical stand data. When OLS regression is used variable selection technique s permit the exploration of a wide range of data for significance. Despite these advantages many of the a ssumptions necessary for OLS regression are violated by remote sensing data which characteristically exhibits non-normality and tends to suffer multicollinearity and autocorr elation. For these reasons a nonparametric technique, regression with artific ial neural networks, was inves tigated as an alternative to OLS regression. Artificial neural networks ( ANN) are loosely modeled on br ain function: a series of nodes representing inputs, output s and internal variables ar e connected by synapses of varying strength and connectivity (Jensen et al 1999). The network architecture is typically oriented as a per ceptron which ‘learns’ by passing information from inputs to outputs (forward propagation) and from output to inputs (back propagation) to optimize

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10 the accuracy of prediction by adjusting wei ghts. The ability to accommodate complexity can be made by altering the construction of the network to include multiple layers of internal nodes. These networks are attractively robust in th at many of the assumptions needed for OLS regression are relaxed, including requirements of normality and independence. In this study our objective was to deve lop a single ‘general’ empirical model capable of producing reliable LAI predictions at various extents and image dates. We hypothesized that such a solution would requir e multivariate statistics to incorporate important local information such as c limatological and phenological data. Three regression techniques, linear OLS, multiple OLS and ANN, were applied to a large dataset constructed from data acquired by Lands at sensors over a 10 year period and the resultant models evaluated for performance using a validation process. Models were developed in strata of incr easing complexity to identif y high performing yet simple solutions. Methods Study Sites Two plantations of southern pine were used in this study: the Intensive Management Practices Assessment Center (IMPAC) operated by the Forest Biology Research Cooperative (FBRC) and the Donaldson tract, part of the Bradford forest owned by Rayonier, Inc. and site of a Florida Am eriflux eddy covariance monitoring station. Both sites are planted with sout hern pine species loblolly ( Pinus taeda L.) and slash ( Pinus elliottii var. elliottii ) which have similar physiol ogy and seasonal foliage dynamics (Gholz et al 1991).

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11 The IMPAC site is located 10 km nort h of Gainesville, Florida USA (29 30 N, 82 20 W, Figure 2-1.) The site is flat with elevation vary ing < 2 m and experiences a mean annual temperature of 21.7 C and 1320 mm annual rainfall. Soils are characterized as sandy, siliceous hyperthermic Ultic Alaquods (Swindle et al 1988). The stand was established in 1983 at a stoc king rate of 1495 seedlings pe r hectare, a dense planting typical of industrial pine plantations. The site was surveyed using a differentially corrected global positioning syst em (DGPS) in February, 2004. The site consists of 24 study plots, each 850 m2, exhibiting factorial combinations of species (loblolly and slas h pine), fertilization (annua l or none) and control of understory vegetation (sustained or none) in three replicates Fertilization of respective plots occurred annually for ages 1-11, was ceased for ages 12-15, and resumed at age 16. The Donaldson tract is located 12 km east of the IMPAC site (29 48 N, 82 12 W) the stand was established in 1989 and stocke d at a rate of 1789 slash pine seedlings per hectare. The site is flat and well drained. Within the stand are four 2,500 m2 plots from which leaf litterfall wa s collected starting at age 10 (1999). Plots were surveyed with GPS May, 2002. Estimates of LAI based on needlefall from 10 randomly located traps were collected by Florida Ameriflux aver aged into a single valu e for all four plots beginning April, 1999. Remote Sensing Data The study acquired 18 cloudless images r ecorded of the st udy area between 1991 and 2001 by the Landsat 5 and 7 satellite platfo rms (Table 2-1.). This series of images contain examples of each of the four phenol ogical categories and is concurrent with cycles of dry and wet periods for the region (Figure 2-2).

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12 Figure 2-1. Map of the Intensive Manageme nt Practices Assessment Center, Alachua County, Florida, USA.

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13 Table 2-1. Catalog of images used in study. Number Image Date† Sensor Phenological period PHDI‡ 1 1/17/91 TM Declining LAI -1.75 2 3/22/91 TM Minimum LAI -0.63 3 10/16/91 TM Declining LAI 2.63 4 1/20/92 TM Declining LAI 1.59 5 8/31/92 TM Maximum LAI 1.22 6 3/27/93 TM Minimum LAI 1.85 7 8/18/93 TM Maximum LAI -2.76 8 1/25/94 TM Minimum LAI 2.78 9 9/6/94 TM Maximum LAI 1.3 10 6/7/96 TM Expanding LAI 0.83 11 9/30/97 TM Maximum LAI -0.86 12 6/29/98 TM Expanding LAI 0.59 13 1/7/99 TM Minimum LAI -1.9 14 9/4/99 TM Maximum LAI -2.38 15 1/2/00 ETM+ Declining LAI -2.29 16 4/7/00 ETM+ Minimum LAI -2.71 17 8/13/00 ETM+ Maximum LAI -4.02 18 1/4/01 ETM+ Declining LAI -3.05 † All images are Path 17N, row 39. Datum NAD83/ GRS 80. Georectification error 0.5 pixels ‡ Palmer hydrological drought index: negativ e values indicate dry conditions, positives wet, normal 0. National Climatic Data Center. Images were captured with the both the Thematic Mapper (TM) sensor aboard Landsat 5 and the Enhanced Thematic Mappe r Plus (ETM+) aboard Landsat 7. These sensors are functionally identical for the ba ndwidths used in the study: visible spectra blue (0.45 – 0.52 m, band 1), green (0.52 – 0.60 m, band 2) red (0.60 – 0.63 m, band 3) and infrared spectra: near (0.69 – 0.76 m, band 4) mid (1.55 – 1.75 m, band 5) and reflected thermal (2.08 – 2.35 m, band 7). Spatial resolution for these bands is 30m. Band 6, which detects emitted thermal radiance between 10.5 – 12.5 m, has a resolution of 120 m for TM and 60m for ETM+. Brightness values (BV) were recovered from the data ba sed on the center point of each study plot. All images were individuall y rectified using a second order polynomial equation with between 30 and 40 ground contro l points; while the im ages maintained the

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14 accepted rectification accuracy of 0.5 pixels the overlay with study plots varied from image to image. Seasonal LAI Dynamics and Leaf Litterfall Data P. taeda and elliottii are evergreen trees that mainta in two age classes of leaves throughout much of the year, needles from bot h the previous and current growing seasons (Gholz et al. 1991; Curran et al. 1992; Teskey et al. 1994). In north Florida these classes overlap between July and September, establis hing a period of peak leaf area categorized as maximum LAI. As such the phenological year is typically categorized into four periods: minimum LAI, leaf expansion, maxi mum LAI and declining LAI (Figure 2-3). This dynamic must be well understood to inte rpret LAI from remotely sensed data.

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15 Figure 2-2. Characterization of north-central Florida climate during study period 1991-2001 (National Climatic Data Center 2005). -5 -4 -3 -2 -1 0 1 2 3 4 5 6Jan-91 Jul-91 Jan-92 Jul-92 Jan-93 Jul-93 Jan-94 Jul-94 Jan-95 Jul-95 Jan-96 Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Palmer Hydrological Drought Index DRY WET

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16 Mid-rotation Pinus elliottii OVERALL NEW OLD JAN FEB MAR APR MAY JUN JULY AUG SEP OCT NOV DEC 0 100 200 300 400 500 600Canopy foliage biomass (g/m2) MAXIMUM LAI EXPANSION MINIMUM DECLINE Figure 2-3. Annual cycle of variatio n in leaf phenology illustrating two populations of needles (Cropper and Gholz, 1993). In situ estimates of LAI were calculated by le af litterfall collection. Needlefall was collected monthly from six 0.7m2 traps distributed randomly within each of the 24 IMPAC study plots from year 8 (1991) w ith the assumption of closed canopy through 2001. A similar method was used at the Donalds on site’s four study pl ots, the results of which were aggregated into a single value for the tract. LAI from litterfall was estimated using foliage accretion models (Martin & Jokela 2004). LAI results were presented as hemi-sur face leaf area and converted to projected leaf area for integration w ith remote sensing data. Integration of Ground Referenced LAI and Remote Sensing Data LAI data based on monthly leaf litterfa ll collection from all 24 study plots was ground referenced to plot centroids based on GPS survey. Data from IMPAC ranged in date from January 1991 with the assumption of canopy closure at age 8 to February 2001,

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17 the latest calculations available. Data fr om the Donaldson Tract ranged from April, 1999 with a similar assumption of ca nopy closure, to February 2001. Landsat images were overlaid with plot locations within a ge ographic information system (GIS). Surface reflectance data and ground referenced LAI were related by a point method which joined LAI values to pixels based on the presence of a plot centroid. LAI data, aggregated monthly, were matched with image date based on proximity. The integration resulted in a dataset based on the point method of 453 samples which linked 28 locations with their respectiv e surface reflectance va lues at specific times over a period of 11 years. All rows we re randomized within the table and 51 cases were extracted and withheld for external validation. The data were densified with vegetative indices including normalized difference vegetative index (Birth, 1968), simple ratio (Rouse et al. 1973; Crist & Cicone 1984) and tasseled cap analysis components (Crist and Cicone 1984). Ancillary data were incorporated into the set including climate i ndexes and categorical plot data representing species type, plot treatment and phenological period. The comp lete list of va riables used in modeling is included in Appendix A. Climate variables Local climatic conditions were repres ented by the Palmer Hydrological Drought Index (PHDI), a monthly index of the severity of dry and wet spells used to access longterm moisture supply (Karl & Knight 1985). Th e variety of indexes developed by Palmer and others standardize climatic indicators to allow for comparisons of drought and wetness at different times and locations. The PHDI was used instead of the better known rainfall-based Palmer Drought Severity Inde x (PDSI) because it accounts for site water balance, outflows and storage of water based on short-term trends.

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18 The time scales at which climate infl uences leaf area are unknown. Therefore several variables were developed to expl ore specific lags: a simple annual lag, a summation of PHDI values during the leaf expansion period, that summation with an annual lag and finally a summation for PHDI during leaf expansion for current and previous growing years. This la st variable is an attempt to capture the cumulative effect of climate when represented by two age clas ses of needles present during the maximum LAI period. Correct chronologi cal sequence between phenology and climate indicators was maintained by interacting lagged variab les with appropriate phenological periods. Statistical analysis Statistical analysis was performed on the integrated data set including descriptive, principle component and autocorrelation analys is using NCSS statisti cal software (Hintze 2001). The likelihood of spatial autoco rrelation was explored using GEODA 0.9.5 geostatistical software (Anselin 2003). Regression Techniques Three types of regression processes were evaluated; two based on ordinary least squares (OLS), the third artifi cial neural networks (ANN). Linear regression Linear regression represents the simple form of OLS regression where a single independent variable, often a vegetative index, was regressed against the dependent variable LAI. Linear regression has been the typical approach in previous studies including Gholz and Curra n (1991) using NDVI and Fl ores (2003) using SR. Multivariate regression In the multiple form of OLS regressi on, many independent variables, including surface reflectance data, vegetative indices, climate data and categorical data were

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19 regressed against the dependent LAI. Stepwise variable se lection was used to identify variables significant at p-value < 0.05. Artificial neural network Construction and processing of ANNs was accomplished with the neural network module of Statistica statistical software (S tatSoft 2004). Architectures were limited to Multilayer Perceptron with a maximum of four hidden laye rs as suggested by Jensen et al (1999). A back-propagation trai ning algorithm was used to train the network with a sigmoidal transfer function activating nodes. Sample sets were bootstrapped based on available cases. One hundred architectures we re evaluated per model, with the top 5 retained based on the lowest ratio of st andard deviation between residuals and observation data. From these five a ‘best’ model was selected based on the relationship between predicted and observed values from the training and validation set (r2, RMSE). Use of ancillary data to specify model sets An advantage of multiple regressions (including ANN) over linear regression is the ability to include important locational information that is available but outside of the primary data source through the use of additiona l continuous or categor ical variables. In particular the incorporation of categoric al variables specifying phenological periods, species and treatments allow the relationshi p between LAI and its predictors to be generalized to a single model. Three classes of multiple regression models are evaluated in this work: (1) simple models whose constituent vari ables are generated solely fr om remote sensing data and corresponding vegetation indice s only; (2) intermediate models that additionally incorporate image date (and therefore phenologi cal information) and climate data: (3) the most complex models that add stand level da ta such as species and treatment. Following

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20 precedent set by Gholz and others the simple and intermediate models sets were developed for single species and single phenological periods. Results LAI values from leaf litterfall collecti on vary from just under 0.5 to 4.5 with a mean of 2.38 m2 m-2.There is considerable overlap in LAI for slash and loblolly (Figure 2-4.). There is a disproportio nate effect of fertilization on species, with loblolly exhibiting an increase of 1.0 in mean LAI as compared to 0.56 for slash (Figure 2-5.). One of the limitations of relating LAI to remote sensing data is spatial autocorrelation. Band 6, which detects emitted thermal radiation, exhibited significant spatial autocorrelation (Moran’s I = 0.53) lik ely due to its coarse resolution of 120m (Landsat TM), an extent which overlays seve ral plots at once. Spa tial autocorrelation was not indicated for the reflectance values of the other 5 bands and LAI (Moran’s I =0.03 and -0.02 respectively). When two or more of the independent variables of a multiple regression are correlated, the data is said to exhibit mu lticollinearity. Multico llinearity may result in wide confidence intervals on regression coeffi cients. Principle component analysis of spectral variables used revealed eigenvalues near 0.0 for 5 of the 9 resultant components, indicating multiple collinearity. There was, however, little correlation between regional climate conditions, as indicated by the Pa lmer hydrological drought index and LAI for both species. In general, the simplest possible predictive model is desirable. Simpler models are easier to apply to new cases because of the reduced requirements for input data. Complex environmental systems with multiple inter acting biological and physical components are

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21 however not likely to be adequately modele d by the simplest models. In this study we have examined a range of models from simple linear models through non-linear ANN multiple regression models. Our goal was to find a model that was a good predictor for separate validation data. Th e latter requirement was necessary as a guard against “overtraining” (Mehrotra et al 2000). Linear Models For comparison purposes previously publishe d models are listed above new models (Table 2-2). Of the 20 models tested 16 failed to reject the null hypothesis 1= 0. No model exceeded an r2 >0.12. These simple models were not adequate predictors of LAI for the training data. Even the published models with a history of useful predictors of southern pine LAI failed for this dataset. Multiple Regression Models All models tested statistically significan t for slope representing improvement over linear models. r2 values ranged from 0.31 to 0.70. In validation testing, increasingly complex models accounted for greater variation in LAI for training data, but performance with testing data was mixed. (Table 2-3) ANOVA analysis of significant variables appear in Table 2-5. Signifi cant variables include presence or absence of fertilization treatments and phenological periods. ANN Multiple Regression Models The ANN predictions improved on OLS multiple regressions at each class strata. r2 values ranged from 0.4 to 0.85 in training validation, and from 0.02 to 0.77 in testing (Table 2-4).

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22 The generalized southern pi ne LAI predictive model (G SP-LAI) was selected as the top performing model (Figure 2-6). In valid ation tests the model explained > 75% of variance (r2 = 0.77) with an RMSE < 0.50. Discussion In this study we created GSP-LAI, a m odel which effectively predicted LAI for a managed southern pine forests system of two species, multiple management treatments and climate variability on annual and seas onal scales. The model’s development was guided by three major factors: 1) a focus on a relatively simple and well understood forest system for which there was ample data, 2) a desire to create an operational solution with wide applicability, a nd 3) the willingness to empl oy sophisticated regression techniques. The intensively managed pine plantation is a simple system compared to natural regrowth forests or mixed coniferous/deciduous forests in terms of the presence of evenaged stands and the reduc tion of canopy layers (Gholz et al 1991). Although seemingly an ideal system for LAI pred iction, previously published so uthern pine LAI predictors applied to new remote sensing data lead to results so inaccurate as to be unusable as inputs for forest productivity modeling. New simp le linear regression models constructed using single vegetative indi ces and trained on the study’s large database offered no improvement.

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23 SLASH LOBLOLLY 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8LAI ABSENCE (0) OR PRESENCE (1) OF FERTILIZATION TREATMENTLAI SLASH 01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 LOB 01 Figure 2-4. Comparison of the range of LAI values for slash and loblolly pine fo r all sites, 1991-2001. Figure 2-5. Differences in effect of fertilizer treatment on slash and loblolly pine.

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24 Table 2-2. Summary of linear models fitted to data set. First two models are previously published. Model Spp. Phenological category n a Intercept b Slope r2 RMSE T Value Prob. Level Reject H0 END 79 -14.31 32.25 0.03 1.50 20.80 <0.001 yes MAX 74 -20.02 43.62 <0.01 6.66 37.7 <0.001 yes Gholz (1991) † LAI = a + b (NDVI) S MIN 36 -10.80 26.29 <0.01 3.59 -0.21 0.8344 no Flores (2003) ‡ LAI = a + b (SR) L EXP/END 139 -0.83 0.56 0.01 1.75 0.25 0.2487 no MIN 36 1.65 -0.15 <0.01 0.43 -0.2 0.9821 no EXP 20 3.76 -3.70 0.03 0.46 -0.72 0.4762 no MAX 73 2.54 -0.12 <0.01 0.59 -0.21 0.8356 no S END 79 0.85 1.95 0.02 0.54 1.40 0.1652 no MIN 31 1.61 0.82 0.02 0.75 0.68 0.5018 no EXP 21 3.54 -1.57 <0.01 0.97 -0.15 0.8805 no MAX 68 2.95 0.49 <0.01 1.02 0.46 0.6468 no LAI = a + b (NDVI) L END 74 -0.60 6.05 0.12 0.80 3.20 0.0020 yes MIN 36 1.67 -0.01 <0.01 0.43 -0.08 0.9353 no EXP 20 4.03 -0.75 0.03 0.46 -0.79 0.4308 no MAX 73 2.55 -0.3 <0.01 0.59 -0.21 0.8320 no S END 79 1.15 0.22 0.02 0.54 1.18 0.2397 no MIN 31 1.53 0.17 0.02 0.75 0.69 0.4928 no EXP 21 3.58 -0.29 <0.01 0.97 -0.16 0.8779 no MAX 68 2.83 0.13 <0.01 1.02 0.62 0.5375 no LAI = a + b (SR) L END 74 -0.19 0.87 0.12 0.80 3.12 0.0025 yes †Based on surface reflectance values ‡ Base d on exoatmospheric reflectance values

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25 Table 2-3. Summary of OLS multiple regression models fitted to dataset Validation Training Testing Class Label Model† Spp. Phenolo gical category n r2 RMSE n r2 RMSE PASEND LAI = -0.54+ 5.70E-02(B1)5.27E-02(B5)+ 8.08E02(TCA-2) S END 79 0.31 0.459 130.51 0.37 Remote sensing data only PALEND LAI = -2.48 + 1.23(SR)+ 0.11(TCA-3) L END 74 0.33 0.707 8 0.05 1.05 PBSTOT LAI = 2.350.79(EXP) – 0.045(LAG-PHDI) – 0.63(MAX) – 0.40(MIN) – 6.32(NDVI) + 0.06(PHDI) + 1.20(SR) + 0.06(TCA-3) S ALL 208 0.42 0.497 270.02 1.40 Include Categorical and Climate Variables PBLTOT LAI = 2.04 -1.03(EXP) 0.74(MAX) -0.68(MIN) 14.78(NDVI) + 3.02(SR)+ 0.09(TCA-3) L ALL 194 0.43 0.794 200.17 0.92 General Model PCTOT LAI = 4.48-1.038(EXP).902(FERT)-.508(HERB).835(MAX)-.515(SPP)+ 0.0308(TCA-3) ALL ALL 402 0.70 0.49 47 0.63 1.97 †B1= Band 1; B5= Band 5; TCA-2, 3= Tassel cap analysis component 2, 3; SR= Simple ra tio vegetative index; MIN, EXP, MAX= phenol ogical period: minimum LAI, expanding LAI, maximum LAI; PHDI= Palmer hydrologic al drought index; LAG-PHDI= PHDI one year previous; NDVI= Normalized differe nce vegetative index; FERT= Fertilization; HERB= Herb icide application; SPP= Species of tree. Details about variables are contained in Appendix A.

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26 Table 2-4. Summary of ANN m odels fitted to dataset Validation Training Testing Network architecture: Class Label Inputs Hidden Layers Nodes per Layer Spp. Phenolo gical category n † r2 RMSE n r2 RMSE ASEND5 6 2 16, 12 S END 79 0.40 0.422 260.02 1.10 Remote Sensing data only ALEND9 7 1 4 L END 74 0.40 0.650 180.26 1.30 BSCLIM10 14 2 16, 6 S ALL 213 0.42 0.490 270.39 0.52 Include Categoric al and Climate Variables BLCLIM5 15 2 16, 7 L ALL 190 0.49 0.784 240.12 0.94 General Model GSP-LAI 18 2 16, 7 ALL ALL 402 0.85 0.347 51 0.77 0.40 † Number of cases available for bootstrap sampling.

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27 GSP-LAI = 0.3675+0.8406*x 0.00.51.01.52.02.53.03.54.04.55.0 OBSERVED LAI 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 PREDICTED LAI GSP-LAI: r2 = 0.8506 Figure 2-6. Plot of LAI values pred icted by GSP-LAI for training data. It is unclear if the previo usly published models were ever intended for use outside of the image from which they were created ; they were developed with relatively few samples and with few sample dates. Climate history and leaf phenology would necessarily differ from remote sensing data used for model calibration. These shortcomings lead to a crite rion that LAI estimation should not be limited to a single image, location, phenological period or satell ite sensor. The poor performance of linear regression techniques applied to a robust dataset lead us to th e conclusion that even this simple system was too complex to be predicted by a single variable.

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28 In addition to the remote sensing data ther e are many variables that might be useful predictors of the system, including climate variables, management treatments such as fertilization, the presence and/or cont ribution of understory, phenological period, and others. To incorporate these variables multivar iate regression techniques were necessary. The availability of ANN regression functions in modern statistical software allowed for the quick explorations of predictive netw orks to compare to OLS regressions. In both OLS and ANN regression the highest performing models were the most general, capable of incorporat ing both continuous and categoric al variables into a single solution. The assignment of cate gorical variables is a useful and underexploited technique permitting the development of models with wide domains of application. OLS Multiple Regression Models OLS regression revealed some of the probable drivers of this system, namely phenological period and management treatmen t. Tassel cap component 3 was the only consistent remote sensing va riable used between models (Table 2-5). This component, also known as “wetness”, is typically associ ated with evapotranspi ration (ET) which is expected to increase with increased LAI. Tassel cap components are the product of coefficients for all 6 bands of reflected radi ation that TM and ETM+ record and as such exploit more spectra than the commonly used NDVI and SR (Cohen et al 2003). ANN Models The best general model was the produc t of ANN regression. This non-parametric technique was able to incorporate climate data as represented by PHDI and its lagged derivatives. Climate, while assumed to be important, is typically absent in the development of these sorts of empirical models. It is a difficult problem: eligible satellite images are all captured on sunny days, and th e various temporal scales on which local

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29 climate influences vegetation is mostly unknown and likely to be species and site specific. Typical data used in multitemporal analyses exhibit serial autocorrelation, necessitating transformations in order to become valid OLS inputs. The improved performance conveyed by the ANN regression su ggests that 1) climatic variables are significant and 2) OLS regression was una ble to use the variables as employed. The GSP-LAI model is deterministic and easily implemented. Code for the model is detailed in Appendix B. Fertilization In the OLS and ANN generalized models fertilization repres ents a significant variable (Tables 2-5, 2-6). This result supports observations (Figure 25) and also Martin and Jokela’s (2004) analysis of IMPAC leaf litterfall data. Ferti lization is a focal treatment in intensive management practices and indications of canopy response in the form of LAI assessment could direct the location and frequency of application. The availability of reliable LAI data could l ead to a paradigm change in management practices were the goal becomes optimizati on of leaf growth based on site potential. Suggestions for Future Effort The improved performance of increasingl y complex models provides insight into variables which drive or improve the predictability of LAI. Of these climate variables are particularly interesting in that they ar e widely assumed to play a role in canopy appearance and yet are rarely incorporated in empirical analysis. Difficulties exist in how to characterize climate, i.e. in terms of rainfall or temper ature, and on what temporal scales it operates. Climate data necessarily suffers serial autocorrelation, a violation of assumptions required for OLS regression.

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30Table 2-5. ANOVA analysis of highly significan t variables in OLS multiple regression. Ot her, less significant variables not sho wn. Model Variable Df r2 Sum of Square Mean Square F-ratio Prob. levelPower (5%) FERT 1 0.22 69.48608 69.48608 286.143 <0.0001 1 MAX 1 0.1612 50.91658 50.91658 209.674 <0.0001 1 PCTOT EXP 1 0.1053 33.25625 33.25625 136.949 <0.0001 1 MAX 1 0.149 12.7119 12.7119 51.476 <0.0001 1 PBSTOT TCA-3 1 0.0902 7.697152 7.697152 31.169 <0.0001 0.9998 TCA-3 1 0.1572 32.37256 32.37256 51.311 <0.0001 1 PBLTOT MAX 1 0.0818 16.85336 16.85336 26.713 <0.0001 0.9993 PASEND TCA-2 1 0.2165 4.925346 4.925346 23.39 <0.0001 0.9976 SR 1 0.2191 11.53746 11.53746 23.087 <0.0001 0.9973 TCA-3 1 0.2065 10.87232 10.87232 21.756 <0.0001 0.9959 PALEND B1 1 0.1444 3.284696 3.284696 15.599 0.0002 0.9737

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31 Sensitivity analysis of the GSP-LAI mode l indicates that a non-parametric, nonlinear technique can make use of that data at various lags, a tantalizing clue which should inspire additional research (Table 2-6). Table 2-6. Sensitivity analysis of vari ables used in ANN multiple regressions. Model Label Rank ASEND ALEND BSCLIM BLCLIM GSP-LAI 1 TCA-1 B2 B1 END END 2 B5 TCA-3 B4 MAX FERT 3 B4 TCA-1 EXP-PHDI B7 B2 4 B2 SR TCA-3 LAG1-PHDI B5 5 TCA-2 TCA-2 SUM-EXP-PHDI B1 SPP 6 B1 B4 B5 NDVI HERB 7 B1 MIN MIN PHDI 8 EXP B3 TCA-1 9 LAG-PHDI SR MIN 10 TCA-2 PHDI B3 11 SR EXP-PHDI EXP 12 B7 TCA-3 EXP-PHDI 13 PHDI B2 SUM-EXP-PHDI 14 B2 TCA-2 LAG1-PHDI 15 B4 B7 16 LAG-PHDI 17 TCA-2 18 TCA-3 Variable codes appear in Appendix A. The effectiveness of LAI predictions woul d be enhanced with a reduction of time between the acquisition of re mote sensing data and its analysis. The use of ground referenced LAI from litterfall necessitates an 18 month lag in processing from collection to value. Using optical methods to indirectly measure LAI in situ would likely reduce this lag provided corrections as suggested by Gower et al (1999) were in corporated to maintain accuracy. With minor modification the GSP-LAI model can be adapted to new remote sensor that share ‘legacy’ characteristics with TM and ETM+. Due to mechanical malfunctions

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32 the ETM+ sensor has become an unreliable sour ce of remote sensi ng data. Data captured by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is particularly interesting for this applica tion. Aboard the TERRA platform, ASTER flies the same orbit as Landsat and shares similar spectral, radiometric and temporal resolution as ETM+ with recording at additional bandw idths. Integrating ASTER data into GSPLAI would allow for continuous anal ysis into the reasonable future. The substantial LAI data collected by th e researchers at IMPAC and other sites should be maintained and expanded if possible. These sites should be oriented to Landsat legacy coordinates, and a minimum size is recommended at 1.5 times the 30 m pixel resolution, which would allow for the 0.5 pixel georectification e rror. Designed in this fashion sites could serve to train and ‘calibrate’ existi ng and future LAI predicting models. Conclusions The development of empirical models re lating ground-referenced parameters to remote sensing data may be greatly facilitated using multivariate regression techniques. The specification of ancillary variables are an effective way to in clude the unique biology of a given system, in this study represented by seasonal leaf dynamics variation in local climate and influential management practi ces. The use of these local variables was essential for developing a model which met the objectives of multitemporal and spatial applicability. The evaluation of increasingly complex re gression models was designed to expose simple solutions to the problem of LAI predic tion if they existed. In this study none were found, and instead advanced non-linear tec hniques were requir ed to incorporate

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33 important data with non-normal distributions and multicollinearity such as serially correlated climate data.

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34 CHAPTER 3 REMOTE SENSING AND SIMULATION TO ESTIMATE FOREST PRODUCTIVITY IN SOUTHERN PINE PLANTATIONS Introduction Pine plantations of the Sout heastern United States consti tute one-half of the world’s industrial forests and account fo r 60% of the timber products used in the United States (Prestemon & Abt 2002). In Florida alone indu strial timber is the leading agricultural sector, generating $16.6 billion in revenues in 2003 (Hodges et al 2005). Almost half the State’s land area is in forest s concentrated in northern a nd central counties where this study is centered. Managing these forests for maximum yiel d is a primary economic goal of timber interests; the rate at which these forests remove and sequester atmospheric carbon as woody biomass is of interest to climate change researchers who recognize forests as the only significant human-influenced sink of greenhouse gases (Tans & White 1998). Sequestered carbon is likely to become another revenue source as the global community endeavors to limit CO2 emissions through cap-and-trade carbon exchange schemes such as those outlined by the Kyoto Protocol of 1997. The net ecosystem exchange of carbon (NEE) in a landscape may be estimated through simulation given the system is somewhat homogenous, well understood and important biophysical parameters are known (Turner et al. 2004b). The SPM-2 model (Cropper & Gholz 1993; Cropper 2000) estimates NEE for slash pine ( Pinus elliottii ) plantations, a dominant plantati on type in Florida and the subject of several studies

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35 (Gholz et al. 1991; Teskey et al. 1994; Clark et al. 2001; Martin & Jokela 2004). SPM-2 simulates hourly fluxes of CO2 and water, and accounts for th e contributions of typical understory components including saw palmetto ( Serenoa repens ), gallberry ( Ilex galabra ) and wax myrtle ( Myrica cerifera ). Annual estimates of net ecosystem carbon exchange simulated by SPM-2 matched measured values from an eddy covariance flux tower site (Clark et al. 2001). Although SPM-2 was originally designed to simulate individual stand dynamics it may be scaled to broad biogeogr aphical extents with inputs of spatially referenced leaf area index (LAI) and stand age. LAI is the ratio of leaf su rface supported by a plant to its corresponding horizontal pr ojection on the ground; as such LAI has direct correspondence with the ability of the canopy to absorb li ght to conduct photosynthesis (Asner & Wessman 1997). LAI’s contribution as a primary biophysic al parameter in NEE simulation also makes it an important indicator of productivity for land mana gers. Current silvicultural practices focus on improving the availability of resour ces, through fertilization and herbicidal control of understory, to increase stem growth. Sampson et al (1998) suggest management for increased leaf growth could in troduce efficiencies related to site growth potential that would otherwise be missed. LAI is difficult and expensive to assess in situ resulting in sparse sample sets that are necessarily localized at a st and scale and thus difficult to extrapolate to larger extents (Fassnacht et al 1997). A model which determined LAI from remotely sensed data would have the advantage of being spatially ex plicit, scaleable from stand to regional or larger extents, and would sample remote or inaccessible areas (Running et al 1986). An

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36 ideal empirical model linking ground-referenced LAI to remote sensing data would be make reliable predictions at various extent s and image dates and be general enough to incorporate important local information su ch as climatological and phenological data. The generalized southern pine LAI pr edictive model (GSP-LAI) described in Chapter 2 satisfies many of these criteria in that it uses Landsat Thematic Mapper (TM) and Enhanced Thematic Mapper Plus (ETM+) imagery to make high resolution (30 m) estimates of LAI for slash and loblolly pl antations captured within the image’s 185 km wide swath. Climate variables are incorporat ed in the form of Palmer’s Hydrological Drought Index (Karl & Knight 1985) at image date and in various lags; categorical variables representing phenologi cal period and stand data such as age and silvicultural treatments are also included. With the input of spatially explicit LAI va lues NEE may also be simulated for the same extent and resolution. Previous studies have estimated components of NEE with coupled remote sensing and simulation model a pproaches for diverse forest stands with multiple dominant species (Lucas et al. 2000; Smith et al. 2002; Turner et al. 2004a). The GSP-LAI model was developed for loblolly and slash pine plantations and the SPM-2 models is limited to closed-canopy slash pine forests (age 8 or older). Slash pine plantations are an important forest type in northern Flor ida, and the simple forest ecosystem provides the potential for greater precision and for outputs relevant to commercial forestry. Objectives In this study we apply the GSPLAI model to a Landsat ETM+ image of an extensive pine plantation holding in North-Central Florida and estimate 1) Leaf Area Index and 2) NEE based on inte gration with the SPM-2 model.

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37 Methods Spatially explicit LAI values were estimated for the plantation pine within the study extent using the GSP-LAI model and brig htness values recorded by the Landsat 7 Enhanced Thematic Mapper Plus sensor on September 17, 2001. LAI values and stand age were used to generate estimates of NEE using the sl ash pine specific forest productivity model SPM-2. Study Area The study extent is comprised of a 1 78,655 ha (441,467 acre) landscape centered at 29 51.5 N, 82 10.7 W near Waldo, Florida USA (Figur e 3-1). This extent contains many classes of land cover/ land use includi ng open water, urban and agricultural. Of specific interest are 11,142 ha (27,520 acres) of intensively managed slash and loblolly plantation forests which as of image date were closed canopy (8 year s old or older). Of this 83% was planted in slash and 17% lobl olly pine. Other classes of forest were excluded from analysis includi ng natural regrowth areas, rece ntly cut or planted stands, and stands which contained other species of pine, such as longleaf pine ( Pinus palustris ), or hardwoods. Stand data was provided by Rayonier, Inc. and indicated date of establishment, planting density and silvicultural treatments, including date of fertilization or herbicide application.

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38 372214.519365 372214.519365 377214.519365 377214.519365 382214.519365 382214.519365 387214.519365 387214.519365 392214.519365 392214.519365 397214.519365 397214.519365 402214.519365 402214.519365 3287449.128450 3287449.128450 3292449.128450 3292449.128450 3297449.128450 3297449.128450 3302449.128450 3302449.128450 3307449.128450 3307449.128450 3312449.128450 3312449.128450 3317449.128450 3317449.128450 3322449.128450 3322449.128450 3327449.128450 3327449.128450 Landsat ETM+ Imagery: UTM 17N Resolution 30m, RGB=4,3,2 Scale Units: Meters I Figure 3-1. Map of the Bradford Forest, Flor ida, USA. Yellow indicates forest extent; background is a false color mosaic from Landsat ETM+.

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39 Integration of Remote Sensin g and Ground Referenced Data The study extent was imaged by Landsa t 7 Enhanced Thematic Mapper Plus (ETM+) on September 17, 2001 at approxima tely 11:00 am on a cloudless day. The image was geographically rectified using a second order polynomial equation with between 30 and 40 ground control points Rectification error reported as < 0.5 pixels. Vector-based stand data was converted to raster format and matched to remote sensing data in an overlay procedure w ithin image processing software (Leica Geosystems GIS and Mapping 2003). Ancillary information such as climatic and phenological data was incorporated in the sa me manner. The resultant layer stack was reported as a text file with over 150,000 rows of pixel information including coordinates and imported into a Statistica spreadsheet (S tatSoft 2004) where it was densified with tassel cap components 1-3 (Huang et al 2002). Processing Data with the GSP-LAI and SPM-2 Models The GSP-LAI model was employed within th e Statistica neural network interface. Resultant LAI values were reported in spr eadsheet format and made ready for SPM-2 by 1) masking of non-forest pixel anomalies co mprised of negative LAI values, and 2) extraction of slash-only values. Processing of LAI values and stand age resu lted in an estimate of NEE in Mg ha-1 yr-1 for each pixel defined by coordinates. Both NEE and LAI results were imported into a geographic information system (ESRI 2003) and projected as a map. Results The GSP-LAI model estimated LAI fo r 10,797 ha (26,700 acres) of slash and loblolly pine plantations. Values ranged from 0 to 3.93 with a mean of 1.06 (Figure 3-1).

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40 Approximately 1% of the area analyzed exhibited very lo w LAI values (< 0.1) which were associated with forest edges. The SPM-2 model estimated NEE for pl antation slash pine totaling 9,770 ha (24,131 acres). Values ranged from -5.52 to 11.06 Mg ha-1 yr-1 with a mean of 3.47 Mg ha-1 yr-1 (Figure 3-2). As with the LAI values very low NEE was exhibited at forest edges. Approximately 1.6% of the area analy zed exhibited NEE values greater than 8.0 Mg ha-1 yr-1, a maximum value reported by Starr et al (2003) from a Florida Ameriflux study of slash pine in north-cen tral Florida. Total carbon bala nce for the area analyzed is 33,920 metric tons representing 87,243 tons of CO2 or about 9 tons per acre. By means of associated map coordinate s these values were categorized and displayed on a map along with the Landsat imag e used as the primary data source (Figure 3-3, 3-4). Discussion The feasibility of estimating forest produc tivity in terms of NEE was demonstrated using empirical and simulation models based on remotely sensed data. Despite our inability to ground-truth the resultant values for LAI and NEE are plausible and in the realm of expected values. Th e utility of these estimates is enhanced by their landscape scale and that carbon gain and loss are attributed to specific stands and ownership. These results offer proof of concept and further work is encouraged. Based on the May 27, 2005 pr ice of $1.30 per 100 T CO2 the estimated value of carbon sequestered in this analysis is $102,891.10 or $4.26 per acre (Chicago Climate Exchange 2005).

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41 0.00.51.01.52.02.53.03.54.0 LAI 0 5000 10000 15000 20000 25000 30000 35000No of obs Figure 3-1. Predicted LAI values for closed canopy slash and loblolly pine. Bradford FL -4-2012345678910 NEE 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000No of obs Figure 3-2. Predicted NEE values for closed canopy slash and loblolly pine. Bradford FL

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42 372214.519365 372214.519365 377214.519365 377214.519365 382214.519365 382214.519365 387214.519365 387214.519365 392214.519365 392214.519365 397214.519365 397214.519365 402214.519365 402214.519365 3287449.128450 3287449.128450 3292449.128450 3292449.128450 3297449.128450 3297449.128450 3302449.128450 3302449.128450 3307449.128450 3307449.128450 3312449.128450 3312449.128450 3317449.128450 3317449.128450 3322449.128450 3322449.128450 3327449.128450 3327449.128450 Leaf Area Index 0.0 0.5 0.6 1 1.1 1.5 1.6 2 2.1 2.5 2.6 3Landsat ETM+ Imagery: UTM 17N Resolution 30m, RGB=4,3,2 Scale Units: MetersIFigure 3-3. Predicted LAI values for southern pine plantations in north-central Florida for September 17, 2001

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43 379093.685084 379093.685084 380593.685084 380593.685084 382093.685084 382093.685084 383593.685084 383593.685084 385093.685084 385093.685084 386593.685084 386593.685084 388093.685084 388093.685084 389593.685084 389593.685084 391093.685084 391093.685084 3308911.733893 3308911.733893 3310411.733893 3310411.733893 3311911.733893 3311911.733893 3313411.733893 3313411.733893 3314911.733893 3314911.733893 3316411.733893 3316411.733893 3317911.733893 3317911.733893 3319411.733893 3319411.733893 3320911.733893 3320911.733893 3322411.733893 3322411.733893 Negative values indicate loss to atmosphere <= -3.0 -1.0 to -3.0 -1.0 to 1.0 1.0 to 3.0 3.0 to 5.0 5.0 to 8.0Landsat ETM+ Imagery: UTM 17N Resolution 30m, RGB=4,3,2 Scale Units: MetersNet Ecosystem ExchangeIFigure 3-4. Predicted NEE values for southe rn pine plantations in north-central Florida for September 17, 2001.

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44 Visual analysis of the map (Figure 34.) reveals low LAI and NEE values along logging roads and for other mixed pixels repr esenting partial contri butions of forest. These values were not masked as they represen t valid data and offer some confidence that the models are selective and appropriate. The bimodal distribution of LAI values in Figure 3-1 can be traced to the effect of the variable fertilizer on the model (Figure 3-3). Fertilization is known to increase LAI in slash and loblolly (Martin & Jokela 2004); however ground truthing is needed to assess how close model predictions are to observati ons. Fertilization is a focal treatment in intensive management practices, and indi cations of canopy response could lead to efficiencies in the location a nd frequency of application. The availability of reliable LAI data could lead to a paradigm change in management practices were the goal becomes optimization of leaf growth based on site potential. The conceptual framework presented he re represents one way by which carbon sequestration may be monitored and invent oried, providing necessary underpinning for carbon trading schemes. Landscape-scale valu ations of carbon sinks could lead to a revaluation of ecosystem services as na tions acknowledge the benefits of removing greenhouse gases from the atmosphere. Conclusions This work provides a conceptual mode l whereby forest productivity may be estimated for a forest system using an em pirically derived LAI prediction model and a process simulation model. Spatially explic it results of LAI and NEE values relate important forest attributes to specific ow nership creating new oppor tunities for improved management.

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45 LAINo of obs Absence of Fertilization 0.00.51.01.52.02.53.03.54.04.55.0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 Presence of Fertilization 0.00.51.01.52.02.53.03.54.04.55.0 Figure 3-5. Effect of variable FERT on LAI prediction.

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CHAPTER 4 SYNTHESIS Results and Conclusions In this study we developed an LAI prediction model which was novel in many respects: it used an advance regression tec hnique to establish a non-linear relationship between the dependent and independent vari ables; the independent variables included important local information, an example being climate data, which is a widely recognized yet seldom employed driver of all things vegetative; models underwent a validation process. The GSP-LAI model represents an improvement over previous efforts in our study system. The requirement of stand data by GSP-LAI may be criticized researchers desirous of LAI determination without a priori knowledge. The stratified model methodology illustrated that only tenuous relationships were established with remote sensing data only; furthermore significant explanatory improvements (r2> 0.1) are realized simply through the incorporation of basic phenol ogy as indicated by image date. The visualization of net ecosystem exch ange of carbon via a map represents an advance in our management of slash pine car bon sequestration. It is noteworthy that these carbon totals are linked to specific ownership. It is foreseeable that industry rather than academia will advance carbon seque stration research once the pe rceived values of forest properties adjust to these new appraisals. Pragmatically the availability of timely LA I data might influence a paradigm shift among forest managers away from current goals emphasizing res ource availability

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47 through fertilization and herbicid e application, to an integrat ed approach that considers canopy response to treatments in the context of site potential and biological potential. Management approaches of this type are likely to improve yield while decreasing expense and impact on the environment. Further Study The substantial LAI data collected by the IMPAC and other sites should be maintained and expanded if possible. These si tes should be oriented to Landsat legacy coordinates, and a minimum size is recommended at 1.5 times the 30 m pixel resolution, which would allow for the 0.5 pixel georectification error. Designed in this fashion sites could serve to train and ‘calibrate’ ex isting and future LAI predicting models. As technology advances higher quality remo te sensing data is becoming available. Data from the Advanced Spaceborne Ther mal Emission and Reflection Radiometer (ASTER) sensor integrates well with Landsat legacy operations yet offers an additional 7 bandwidths for analysis. Physi cal tree structure below the canopy is being recorded with light detecting and ranging (LIDAR) sensors. Many of the techniques presented in this study are able to integrate da ta from disparate sources.

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APPENDIX A VARIABLES USED IN MODELS

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49Variable Tag Type Equation/ Bandwidth Range Notes Band 1 B1 Continuous 0.45 – 0.52 m Blue 0 – 255 Surface reflectance, 8-byte Band 2 B2 Continuous 0.52 – 0.60 m Green 0 – 255 Band 3 B3 Continuous 0.60 – 0.63 m Red 0 – 255 Band 4 B4 Continuous 0.69 – 0.76 m Near infrared 0 – 255 Band 5 B5 Continuous 1.55 – 1.75 m Mid infrared 0 – 255 Band 6 B6 Continuous 10.5 – 12.5 m Emitted thermal 0 – 255 Variable not used due to severe spatial autocorrelation Band 7 B7 Continuous 2.08 – 2.35 m Mid infrared 0 – 255 Surface reflectance, 8-byte Normalized Difference Vegetative Index NDVI Continuous (B4 – B3)/(B4 + B3) -1.0 – 1.0 Vegetation index Simple Ratio SR Continuous B4/B3 0 – 255 Vegetation index Tasseled Cap Analysis Component 1 TCA-1 Continuous 0.2043(B1) + 0.4158(B2) + 0.5524(B3) + 0.5741(B4) + 0.3124(B5) + 0.2303(B7) n-space vegetation index: “Brightness” Tasseled Cap Analysis Component 2 TCA-2 Continuous (-0.1603(B1)) + (-0.2819(B2)) + (-0.4934(B3)) + 0.7940(B4) + 0.0002(B5) + (-0.1446(B7)) n-space vegetation index: “Greenness” Tasseled Cap Analysis Component 3 TCA-3 Continuous 0.0315(B1) + 0.2021(B2) + 0.3102(B3) + 0.1594(B4) + (0.6806(B5)) + (-0.6109(B7)) n-space vegetation index: “Wetness” Species SPP Categorical Loblolly = 1 Slash = 0 N/A Type of tree Fertilizer FERT Categorical Fertilized = 1 Not Fertilized = 0 N/A Based on previous season Herbicide HERB Categorical Treated = 1 Untreated = 0 N/A Maintained understory control

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50Minimum LAI period MIN Categorical Within Minimum = 1 Other periods = 0 N/A Minimum leaf biomass; spans March through April in region Expanding LAI period EXP Categorical Within Expansion = 1 Other periods = 0 N/A Increasing leaf biomass; spans May through June in region Maximum LAI period MAX Categorical Within Maximum = 1 Other periods = 0 N/A Maximum leaf biomass; spans July through September Declining LAI period END Categorical Within needlefall = 1 Other periods = 0 N/A Minimum leaf biomass; spans October through February in study area. Implicit in multiple regressions Palmer Hydrological Drought Index PHDI Continuous Values generated by NOAA -7.0 – 7.0 Monthly: indicates severity of dry and wet spells; dry negative values, wet positive values, norms zero One year lag PHDI LAG_PHDI Continuous Monthly PHDI – 1 year -7.0 – 7.0 Previous year’s PHDI Expansion period PHDI EXP_PHDI Continuous Interactive Average PHDI for March, April, May -21.0 – 21.0 PHDI during leaf expansion; interacts with phenological period. Previous season expansion period PHDI LAG1_PHD I Continuous Interactive Lagged Average PHDI for March, April, May -21.0 – 21.0 PHDI during leaf expansion; interacts with phenological period. Two consecutive years expansion period PHDI SUM_PHDI Continuous Interactive Sum Lagged Average PHDI for March, April, May -42.0 – 42.0 PHDI during leaf expansion; interacts with phenological period.

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51 APPENDIX B GSP-LAI CODE Note: this code written in python. from Numeric import import math class Predict_LAI: ''' prediction of LAI by Artifical Neural Network model GSP-LAI model is 18:16:7:1 18 in puts, 2 hidden layers and 1 output Doug Shoemaker and Wendell Cropper June, 2005''' def __init__(self): self.pattern = [25.0, 24.0, 48.0, 14.0, 101.1557, 9.9365, 4.0215, -0.63, -1.25, -4.94, -4.94, -4.94, 0, 1, 1, 1, 0, 0] self.in_labels = ['B2 ','B3 ','B5 ','B7 ','TCA1 ','TCA2 ','TCA3 ','PHDI ','LAG_PHDI', 'EXP_PHDI','LAG1_PHDI','SUM_EXP_PHDI','SPP','FERT','HERB','MIN_LAI ', 'EXP_LAI ', 'END '] self.N_hidden = [16, 7] #number of nodes in each hidden layer; in order # e.g., [4, 6, 9] for three layers self.N_input = 18 self.N_layers = 2 # number of hidden layers self.afunc = [self.activ, self.act iv] # each layer may have a separate activation function # [self.activ, self.activ, self.a2] for example self.W = zeros((self.N_i nput + 1, self.N_hidden[0]), Float32)

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52 self.W2 = zeros((self.N_hi dden[0] + 1, self.N_hidden[1]), Float32) self.WO = zeros((s elf.N_hidden[1] + 1), Float32) #weights from input to hidden self.W[0][0] = -0.68070867581967331; self.W[1][0] = -0.47077273479909026 self.W[2][0] = -0.85230477952479411; self.W[3][0] = 0.33897992017428513 self.W[4][0] = 0.27701895076167499; self.W[5][0] = -1.0572088503393293 self.W[6][0] = 0.36528134122444544; self.W[7][0] = -0.99617510476443649 self.W[8][0] = -0.50428492164536609; self.W[9][0] = -0.18280550315894767 self.W[10][0 ] = -0.94167697838932418; self.W[11][0] = 0.98202982430634478 self.W[12][0 ] = 0.61440222032592962; self.W[13][0] = 1.1844340063249028 self.W[14][0 ] = -0.25002768723088353; self.W[15][0] = 0.63030042820138565 self.W[16][0 ] = 0.51299032922949417; self.W[17][0] = 0.44325306956489968 self.W[18][0] = 0.2248803488147274 #bias weight input should be 1.0 # NOTE: the bias (Threshold weight signs have been reversed (* -1) # from the Statistica program c code to match the algorithm in SNNCode.cc self.W[0][1] = 0.51346930771036581; self.W[1][1] = -0.82554800347023094 self.W[2][1] = 0.90426603023396934; self.W[3][1] = 0.58889085506156402 self.W[4][1] = -0.95958368729266708; self.W[5][1] = -0.90469199829822045 self.W[6][1] = -0.14307625257737089; self.W[7][1] = -0.20554967720687164 self.W[8][1] = -0.21554929367886586; self.W[9][1] = -0.34579555496400843 self.W[10][1 ] = 0.83046571076512765; self.W[11][1] = 0.32340290066403304 self.W[12][1] = -0.18118559428067804; self.W[ 13][1] = -0.75238704258583811 self.W[14][1 ] = -0.37747431711820228; self.W[15][1] = 0.85923511162687338 self.W[16][1] = 0.39065411751788415; self.W[17][1] = -0.20355515889674639 self.W[18][1] = 1.0246810022363515 #bias weight input should be 1.0 self.W[0][2] = -0.35311763505484994; self.W[1][2] = -0.4386456022349271 self.W[2][2] = -0.87637948900026352; self.W[3][2] = -0.72428696217924937 self.W[4][2] = -0.31671942062831882; self.W[5][2] = 0.05527068372351699 self.W[6][2] = 0.56535409825860228; self.W[7][2] = 0.51021420192585065 self.W[8][2] = 0.016770303367016015; self.W[9][2] = 0.34584426212393066 self.W[10][2] = -0.2487170315158326; self.W[11][2] = -0.10550485203992196 self.W[12][2] = -0.48798944879736178; self.W[ 13][2] = -0.6190887070661879 self.W[14][2 ] = -0.22993121833505939; self.W[15][2] = 0.50627708251063963 self.W[16][2] = -1.0785292527624635; self.W[17][2] = 0.033937996367607123 self.W[18][2] = 0.65202105499593555 #bias weight input should be 1.0 self.W[0][3] = -1.0409218053604059; self.W[1][3] = -1.0248054352063849 self.W[2][3] = 0.33260785739356169; self.W[3][3] = -0.26650614694911684 self.W[4][3] = -0.64306159332498813; self.W[5][3] = -0.59743303482074173 self.W[6][3] = -0.78619166931548001; self.W[7][3] = 0.45658535946357542 self.W[8][3] = -0.30551820237080174; self.W[9][3] = 0.99383562833852823

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53 self.W[10][3 ] = 0.58314990180960924; self.W[11][3] = 0.37535417400887111 self.W[12][3] = -0.28530757703577508; self.W[ 13][3] = -0.090269033578186067 self.W[14][3 ] = 0.064328952896598818; self.W[15][3] = 0.97787174712308034 self.W[16][3 ] = 0.19248517688726832; self.W[17][3] = 0.33429026289740676 self.W[18][3] = -0.035729304447247368 #bias weight input should be 1.0 self.W[0][4] = -0.69171961247455427; self.W[1][4] = -0.19318811287043236 self.W[2][4] = -0.24535334151780164; self.W[3][4] = 0.83124440482653728 self.W[4][4] = -0.25125881212500051; self.W[5][4] = 0.67654822161911254 self.W[6][4] = 1.1935093304341891; self.W[7][4] = -0.1061578514825464 self.W[8][4] = 0.97769969375119914; self.W[9][4] = -0.62531219673983507 self.W[10][4 ] = 0.44887478855493629; self.W[11][4] = 0.25089122271948444 self.W[12][4] = 0.39739937692561506; self.W[13][4] = -0.11329258567683172 self.W[14][4 ] = -0.58529954873398038; self.W[15][4] = 1.0085035066605659 self.W[16][4 ] = 0.16742174428496126; self.W[17][4] = 0.58995422198121061 self.W[18][4] = 0.3348083808274705 #bias weight input should be 1.0 self.W[0][5] = -0.77429576139488687; self.W[1][5] = -0.15475931985401509 self.W[2][5] = 0.73579372223419681; self.W[3][5] = 0.1381863709121455 self.W[4][5] = 0.6873206129011652; self.W[5][5] = 0.46745295715611929 self.W[6][5] = 0.41009374571990187; self.W[7][5] = -0.87188230719585069 self.W[8][5] = -0.72335484095791835; self.W[9][5] = -0.91529433041239316 self.W[10][5] = -0.58370952581324753; self.W[ 11][5] = -0.67397946658272845 self.W[12][5] = -0.34210837715877956; self.W[ 13][5] = -0.41773337644458219 self.W[14][5 ] = 0.47038952274991436; self.W[15][5] = 0.093448267923307141 self.W[16][5 ] = 0.26835793839884453; self.W[17][5] = 0.22325046302604781 self.W[18][5] = -1.0210341534849725 #bias weight input should be 1.0 self.W[0][6] = 0.080858496314387546; self.W[1][6] = 0.0084803147734866177 self.W[2][6] = -0.45972948915316991; self.W[3][6] = -1.0221823283337763 self.W[4][6] = -0.011916970527570785; self.W[5][6] = 0.2898749572896876 self.W[6][6] = -0.70301410605914416; self.W[7][6] = -0.96795643773447171 self.W[8][6] = 0.19725907114720687; self.W[9][6] = 0.20975438358448029 self.W[10][6] = 0.36924810928999657; self.W[11][6] = -0.10139479969175098 self.W[12][6] = -0.060662670497412904; self.W[13][6] = -0.34857292408604584 self.W[14][6] = -0.58353859501523964; self.W[ 15][6] = -0.41258775067250342 self.W[16][6] = 0.91182517839270993; self.W[17][6] = -0.56916166564089354 self.W[18][6] = -1.0285604223454949 #bias weight input should be 1.0 self.W[0][7] = -0.32865925594153583; self.W[1][7] = 0.04942365443898445 self.W[2][7] = 0.94576664098391583; self.W[3][7] = -0.52058188611049716 self.W[4][7] = 0.34173019628887918; self.W[5][7] = 0.23316279649833077 self.W[6][7] = 0.93354218924489529; self.W[7][7] = -0.3672399273616016 self.W[8][7] = 0.24492040865298623; self.W[9][7] = 0.62309764743750939 self.W[10][7 ] = -0.31738646556078642; self.W[11][7] = 0.49240143356911215 self.W[12][7 ] = -0.63613804743008662; self.W[13][7] = 0.27255090370977308

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54 self.W[14][7 ] = -0.077490270085429441; self.W[15][7] = 0.03996644688196864 self.W[16][7 ] = -0.42607929700787811; self.W[17][7] = 0.070260106536832997 self.W[18][7] = 0.68278617148868181 #bias weight input should be 1.0 self.W[0][8] = -0.5203133183715809; self.W[1][8] = 0.76526828167302097 self.W[2][8] = 0.11362124877625604; self.W[3][8] = 0.93936007101853969 self.W[4][8] = -0.32325776716962157; self.W[5][8] = -0.50373426830327472 self.W[6][8] = -0.61124578984982036; self.W[7][8] = -0.55151966342108183 self.W[8][8] = -0.50104432378214458; self.W[9][8] = -0.30459007736977906 self.W[10][8] = -0.3159522940418959; self.W[11][8] = -0.065342188976498211 self.W[12][8 ] = 0.39061159628437425; self.W[13][8] = 0.59170422967153369 self.W[14][8 ] = -0.16956740248484886; self.W[15][8] = 0.18794488956438776 self.W[16][8 ] = -0.34436713394629842; self.W[17][8] = 0.63513932853507671 self.W[18][8] = 0.30307186938747249 #bias weight input should be 1.0 self.W[0][9] = -0.8275124467384023; self.W[1][9] = -0.11677639936330871 self.W[2][9] = -0.1251652096057006; self.W[3][9] = -0.34447644211000494 self.W[4][9] = 0.44231016923933497; self.W[5][9] = -0.67835978699981769 self.W[6][9] = 0.10671669828894725; self.W[7][9] = 0.052493351739184235 self.W[8][9] = -0.13220081875069595; self.W[9][9] = -0.37290173453154851 self.W[10][9] = 0.037026514129265595; self.W[ 11][9] = -0.38829556664334314 self.W[12][9 ] = -0.41969064484146179; self.W[13][9] = 1.0370135682327706 self.W[14][9] = 0.72233117331089669; self.W[15][9] = -0.26787152887521748 self.W[16][9] = -0.032418233516579437; self.W[17][9] = -0.47082294426757276 self.W[18][9] = 0.58984303347455413 #bias weight input should be 1.0 self.W[0][10] = 0.99545420020183517; self.W[1][10] = 0.40670899831678181 self.W[2][10] = 0.11853073510231668; self.W[3][10] = 0.58812453777427598 self.W[4][10] = -0.79645600422265672; self .W[5][10] = 0.25972144416010789 self.W[6][10] = -0.74823811652818473; self .W[7][10] = 0.60024217417752057 self.W[8][10] = -0.0073119157875114237; self.W[9][10] = 0.84124958610319833 self.W[10][10] = -0.2617949002805095; self.W[11][10] = 0.64006977894777428 self.W[12][10] = 0.9477926706115315; self.W[13][10] = -0.29951602470691668 self.W[14][10] = 0.30016030289901718; self.W[15][10] = -0.83346922323500006 self.W[16][10] = 0.17169493427772073; self.W[17][10] = 0.40107106183219271 self.W[18][10] = 0.70903533284002751 #bias weight input should be 1.0 self.W[0][11] = -1.142759022542396; self.W[1][11] = 0.44985414251574563 self.W[2][11] = 0.3895513876502969; self.W[3][11] = -1.226383084875748 self.W[4][11] = -0.92868023640950426; self.W[5 ][11] = -0.49184381233707225 self.W[6][11] = 0.17925844190885934; self.W[7][11] = -0.20505890929724421 self.W[8][11] = 0.64675932461962349; self.W[9][11] = 0.14682528315075502 self.W[10][11] = 0.035955907391130484; self.W[11][11] = -0.24746822575992516 self.W[12][11] = -0.50773043572067322; self.W[13][11] = 0.24967556622437737 self.W[14][11] = 0.80942581518738244; self.W[15][11] = 0.69574565324455129 self.W[16][11] = 0.23778917275425218; self.W[17][11] = 0.89204034325895742

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55 self.W[18][11] = 0.2218448568058044 #bias weight input should be 1.0 self.W[0][12] = -0.35511846140043241; self .W[1][12] = 0.70733180758484104 self.W[2][12] = -0.83165126184425742; self.W[3 ][12] = -0.83504960919917026 self.W[4][12] = -0.13755256747487241; self.W[5 ][12] = -0.52966103620956229 self.W[6][12] = 0.25071078472815855; self.W[7][12] = -0.35216098305186072 self.W[8][12] = 0.088542557230076688; self.W[9 ][12] = -1.1040221735380804 self.W[10][12] = 0.79594009769706098; self.W[11][12] = -0.73714848198026295 self.W[12][12] = -0.18180847746449641; self.W[13][12] = 0.41331841770555355 self.W[14][12] = 0.41428659784606314; self.W[15][12] = -0.4290960896492258 self.W[16][12] = -0.98897305155024584; self.W[17][12] = 0.78215239795834623 self.W[18][12] = -0.44364199938191162 #bias weight input should be 1.0 self.W[0][13] = 0.79858959493477089; self.W[1][13] = 0.10650095639849158 self.W[2][13] = 0.41879177374855703; self.W[3][13] = 1.0263932028577394 self.W[4][13] = 0.189570080155397; self.W[5][13] = -0.44376619219939994 self.W[6][13] = -0.60203148870373557; self .W[7][13] = 0.74519204084468549 self.W[8][13] = 0.20937947312546459; self.W[9][13] = -0.73403570501855497 self.W[10][13] = 0.030778866771470657; self.W[11][13] = 0.28322753361566022 self.W[12][13] = 0.92880385369204232; self.W[13][13] = 0.1644240293137085 self.W[14][13] = -0.21608287824017328; self.W[15][13] = -0.2904478515294443 self.W[16][13] = -0.41154041855238949; self.W[17][13] = 0.90293535522249624 self.W[18][13] = 0.97015377694600791 #bias weight input should be 1.0 self.W[0][14] = -1.0325407768158865; self.W[1][14] = -0.84527794204417972 self.W[2][14] = -0.25248895386672582; self .W[3][14] = 0.47151219855652071 self.W[4][14] = -0.94815743730612323; self .W[5][14] = 0.067206226767283619 self.W[6][14] = 0.54728649621049807; self.W[7][14] = -0.87468384013164791 self.W[8][14] = -0.0083579697762564686; self.W[9][14] = 0.74901199144024511 self.W[10][14] = -0.63222006168505462; self.W[11][14] = -0.87475753047840932 self.W[12][14] = 0.9016299328644094; self.W[13][14] = -0.11257067471748695 self.W[14][14] = -0.27838527717268613; self.W[15][14] = 0.95224921487717162 self.W[16][14] = 0.50084256089794099; self.W[17][14] = -0.71743881771230811 self.W[18][14] = -0.02701900591046871 #bias weight input should be 1.0 self.W[0][15] = 1.0437741273389674; self.W[1][15] = -0.45408494721878151 self.W[2][15] = 0.96511020810437909; self.W[3][15] = -0.30063151326050935 self.W[4][15] = -0.071082781756073923; self.W[5][15] = 0.2447287444213701 self.W[6][15] = -0.24195063780165757; self .W[7][15] = 0.98824904641780897 self.W[8][15] = 0.74073183617769423; self.W[9][15] = 0.43863706340778019 self.W[10][15] = -1.0108726386238427; self.W[11][15] = -0.79646911633394357 self.W[12][15] = -0.36001428038607081; self.W[13][15] = 0.17255191773894921 self.W[14][15] = -0.16546627399110897; self.W[15][15] = -0.3996833211136836 self.W[16][15] = -1.2185776823559316; self.W[17][15] = -0.1455316758747702 self.W[18][15] = 1.1403808043303105 #bias weight input should be 1.0

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56 self.W2[0][0] = -0.84028171889997116; self.W2[1][0] = -0.43346076499958708 self.W2[2][0] = -0.43557589480677411; self.W2[3][0] = -0.42513219690958287 self.W2[4][0] = 0.54188493979188723; self.W2[5][0] = -0.046737792182397153 self.W2[6][0] = -0.80478664818881229; self.W2[7][0] = -0.678851216176377 self.W2[8][0 ] = 0.71149222702874249; self.W2[9][0] = 0.68341599319600177 self.W2[10][0 ] = 1.0328752945835469; self.W2[11][0] = 0.24740667798727475 self.W2[12][0] = -0.2469023592420069; self.W2[13][0] = 0.508095168051796 self.W2[14][0] = -0.69387411534727783; self.W2[15][0] = 0.19338083305716081 self.W2[16][0] = 0.18211612650330075 #bias weight input should be 1.0 self.W2[0][1] = 0.2859958155039441; self.W2[1][1] = 0.24091476574654414 self.W2[2][1 ] = 0.91115699781689941; self.W2[3][1] = 0.48388496460003888 self.W2[4][1] = -0.68637080910887738; self.W2[5][1] = 0.61678116159010321 self.W2[6][1] = 0.071795625009126882; self.W2[7][1] = -0.73207375760099258 self.W2[8][1] = 0.6556064256037778; self.W2[9][1] = -0.44088680852652473 self.W2[10][1] = -0.20501788340358035; self.W2[11][1] = -0.4010598542444288 self.W2[12][1] = -0.45119284181746144; self.W2[13][1] = 0.52587578563884863 self.W2[14][1] = -0.22088901355724097; self.W2[15][1] = 0.2495482636642444 self.W2[16][1] = -0.60347877573598951 #bias weight input should be 1.0 self.W2[0][2 ] = 0.42336720355483193; self.W2[1][2] = 0.50245942687953626 self.W2[2][2 ] = 0.21654723337885157; self.W2[3][2] = 0.70531360649670838 self.W2[4][2] = 0.093535694516742818; self.W2[5][2] = -0.21420036356255232 self.W2[6][2] = -0.012639507473030611; self.W2[7][2] = 0.31554596948648805 self.W2[8][2] = -0.0040929337148137854; self.W2[9][2] = -0.17044839540087706 self.W2[10][2] = 0.46951908908293116; self.W2[11][2] = -0.66754027180472342 self.W2[12][2] = 0.82473208826382194; self.W2[13][2] = -0.1571156431250397 self.W2[14][2] = -0.42213152740242382; self.W2[15][2] = 0.79329857749148425 self.W2[16][2] = 0.80557575135338377 #bias weight input should be 1.0 self.W2[0][3] = -0.13255563062284348; self.W2[1][3] = 0.37810476302366636 self.W2[2][3] = 0.21070959566965541; self.W2[3][3] = -0.89366749130281953 self.W2[4][3] = 1.0078487477830862; self.W2[5][3] = 0.42900826466769421 self.W2[6][3] = 0.39769863416066875; self.W2[7][3] = -0.49379617511626256 self.W2[8][3] = 0.26323002509449323; self.W2[9][3] = -0.37429078671305493 self.W2[10][3] = 0.86815937993400716; self.W2[11][3] = -0.59414843110057125 self.W2[12][3] = 0.51956225729714856; self.W2[13][3] = -0.34767642086198647 self.W2[14][3] = -1.0664791956925401; self.W2[15][3] = 0.81194836042924168 self.W2[16][3] = 0.38600602910012766 #bias weight input should be 1.0 self.W2[0][4] = -0.7852457933457988; self.W2[1][4] = 0.67182369199536496 self.W2[2][4] = 0.11976172539016033; self.W2[3][4] = -0.35345828007455571 self.W2[4][4] = -0.75884001297513415; self.W2[5][4] = -0.68270928953850274 self.W2[6][4 ] = 0.039984026585529499; self.W2[7][4] = 0.1324556886239189 self.W2[8][4] = -0.42219247413963362; self.W2[9][4] = 0.76451311676056533 self.W2[10][4] = 0.67287618465966093; self.W2[11][4] = 0.17620257431174735

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57 self.W2[12][4] = -0.37423290298627587; self.W2[13][4] = 0.15449217725083536 self.W2[14][4] = 0.15546713985527782; self.W2[15][4] = 0.94462533981671326 self.W2[16][4] = 0.52053670319683165 #bias weight input should be 1.0 self.W2[0][5] = -0.11383317674524207; self.W2[1][5] = 1.093880403742064 self.W2[2][5] = 0.48574982685208123; self.W2[3][5] = -0.36562169083116408 self.W2[4][5] = 0.8476825029450753; self.W2[5][5] = -0.2273487774476374 self.W2[6][5] = -0.84103370298577607; self.W2[7][5] = -0.47561685116962277 self.W2[8][5 ] = 0.76334113447610374; self.W2[9][5] = 0.5048639068148526 self.W2[10][5] = -0.53656874325571335; self.W2[11][5] = -0.33513742916677347 self.W2[12][5] = -0.28172906506309481; self.W2[13][5] = -0.76272398129498198 self.W2[14][5] = -0.66025788802885732; self.W2[15][5] = 0.95701289266244449 self.W2[16][5] = -0.3592191351002838 #bias weight input should be 1.0 self.W2[0][6] = -0.21764607397928706; self.W2[1][6] = 0.75056281843678718 self.W2[2][6] = -0.55413003683237416; self.W2[3][6] = -0.13285829175998887 self.W2[4][6] = 0.58529457481651215; self.W2[5][6] = -0.7624180695963737 self.W2[6][6] = 0.31736963218013603; self.W2[7][6] = -0.9402512575105112 self.W2[8][6] = -0.67112980522916854; self.W2[9][6] = -0.7235067875934823 self.W2[10][6] = -0.26022571343166184; self.W2[11][6] = -0.43886863821482747 self.W2[12][6] = 0.3063464033973422; self.W2[13][6] = -0.58939225217425462 self.W2[14][6] = 0.45724366645921521; self.W2[15][6] = 0.5685444957630944 self.W2[16][6] = -0.88450826792892168 #bias weight input should be 1.0 self.wts = [self.W, self.W2] # list of weight arrays for each layer; in order # [W, W2, W3] for three hidden layers #weights from hidden to output self.WO[0] = -0.26706611706223854 self.WO[1] = -0.42003016388263759 self.WO[2] = 0.72028255111376516 self.WO[3] = 0.28335883323926864 self.WO[4] = -0.89717920199668166 self.WO[5] = -0.49025758877601794 self.WO[6] = -0.38930986874947926 self.WO[7] = 0.30361700984309659 #bias sign change to subtract threshold def scaler(self): ''' linear scaling of input values; -9999 is missing value ''' missing = [0.27413464591933939, 0.30335820895522386, 0.31809701492537301,

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58 0.26026119402985076, 0.37654065907577805, 0.65600816582363053, 0.65964013022874357, 0.50367098331870064, 0.37765094021418316, 0.4680048264547062, 0.50156899600184768, 0.58077275397528705 ] # slope and intercept for scaling inputs linear_eq= {0:(0.021276595744680851, -0.34042553191489361), 1:(0.025, -0.3), 2:(0.020833333333333332, -0.4375), 3:(0.03125, -0.125), 4:(0.011224516139170531, -0.67367525454396482), 5:(0.027361802376646153, 0.50862854437947536), 6:(0.028418294561306793, 0.30574390569673132), 7:(0.14705882352941174, 0.5911764705882353), 8:(0.14124293785310735, 0.43926553672316382), 9:(0.053361792956243326, 0.50266808964781207), 10:(0.053361792956243326, 0.50266808964781207), 11:(0.033355570380253496, 0.59239492995330223) } categ_eq = {0:0.45149253731343286, 1:0.39925373134328357, 2:0.48134328358208955, 3:0.15298507462686567, 4:0.089552238805970144, 5:0.55970149253731338} lineqs = len(missing) for i in range(lineqs): if self.pattern[i] == -9999: self.pattern[i] = missing[i] else: self.pattern[i] = self.pattern[i] linear_eq[i][0] + linear_eq[i][1] for i in range(len(categ_eq)): if self.pattern[i + lineqs] == 0: self .pattern[i + lineqs] = categ_eq[i] elif se lf.pattern[i + lineqs] == 1: self.pattern[i + lineqs] = 0 else: self.pattern[i + lineqs] = 1

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59 #print self.pattern def activ(self, x): ''' sigmoidal activation: inputs to hidden ''' if x > 100.0: x = 1.0 if x < -100.0: x = -1.0 e1 = math.exp(x) e2 = math.exp(-x) #print x, e1, e2 return (e1 e2) / (e1 + e2) def layerX(self, nh, invalues, W, activ): #number hidden nodes in layer, # of inputs, Wt matrix, activation func ''' from inputs to hidden layer ''' hidden = matrixmultiply(invalues, W) #print hidden for i in range(len(hidden)): hidden[i] = activ(hidden[i]) #print hidden[i] hidden2 = zeros((nh + 1), Float32) hidden2[nh] = 1.0 #bias or threshold input for i in range(nh): hidden2[i] = hidden[i] return hidden2 def layer_out(self):

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60 self.pattern.append(1.0) #bias or threshold input inputs = self.pattern for i in range(self.N_layers): inputs = self.layerX(self.N _hidden[i], inputs, self.wts[i], self.afunc[i]) return matrixmultiply(inputs, self.WO) def out_scale(self, x): ''' inverse scaling to get LAI output ''' self. prediction = (x + 0.099788683247846094)/ 0.23868893546020067 def predict(self): self.scale r() # scale i nput pattern x = self.layer_out() #a pply weights and activation function self.out_scale(x) # predict LAI (s elf.prediction) if __name__ == '__main__': test = Predict_LAI() test.predict() print "LAI for test pattern should be 1.41547" print "This program calculates: print test.prediction print ' test.pattern = [] for i in range(18): x = raw_input(test.in_labels[i]) x = float(x) test.pattern.append(x) print '

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61 test.predict() print 'LAI = ',test.prediction zzz = raw_input('DONE')

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62 LIST OF REFERENCES Anselin L. (2003) GEODA 0.9 User's Guide. University of Illinois, Urbana-Champaign, IL Asner G.P. & Wessman C.A. (1997) Scaling PAR Absorption from the Leaf to Landscape Level in Spatially Heterogeneous Ecosystems. Ecological Modelling 103 81-97 Birth G.S. & Mcvey G.R. (1968) Measuring Color of Growing Turf with a Reflectance Spectrophotometer. Agronomy Journal 60 640-649 Chicago Climate Exchange (2005) Carbon Financial Instrument Market Data http://www.chicagoclimatex.com /trading/stats/daily/index.html : May 30, 2005 Clark K.L., Cropper W.P. & Gholz H.L. ( 2001) Evaluation of Modeled Carbon Fluxes for a Slash Pine Ecosystem: SPM2 Simulations Compared to Eddy Flux Measurements. Forest Science 47 52-59 Cohen W.B., Maiersperger T.K., Gower S. T. & Turner D.P. (2003) An Improved Strategy for Regression of Biophysical Variables and Landsat ETM+ Data. Remote Sensing of Environment 84 561-571 Crist E.P. & Cicone R.C. (1984) A Physically-Based Transformation of Thematic Mapper Data the Tm Tasseled Cap. IEEE Transactions on Geoscience and Remote Sensing 22 256-263 Cropper W.P. (2000) SPM2: A Simulation Model fo r Slash Pine (Pinus elliottii) Forests. Forest Ecology and Management 126 201-212 Cropper W.P. & Gholz H.L. (1993) Simulation of the Carbon Dynamics of a Florida Slash Pine Plantation. Ecological Modelling 66 231-249 Curran P.J., Dungan J.L. & Gholz H.L. (1992) Seasonal LAI in Slash Pine Estimated with Landsat Tm. Remote Sensing of Environment 39 3-13 Doran, J. 2003. Landmark Emissions Exchange Launched in Chicago. The Times London. Oct. 1, pg 75 Eklundh L., Hall K., Eriksson H., Ardo J. & Pi lesjo P. (2003) Investigating the Use of Landsat Thematic Mapper Data for Estim ation of Forest Leaf Area Index in Southern Sweden. Canadian Journal of Remote Sensing 29 349-362

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63 ESRI (2003) ArcMap 8.3. ESRI. Redlands CA. Fang H.L. & Liang S.L. (2003) Retrieving Leaf Area Index with a Neural Network Method: Simulation and Validation. IEEE Transactions on Geoscience and Remote Sensing 41 2052-2062 Fassnacht K.S., Gower S.T., MacKenzie M.D ., Nordheim E.V. & Lillesand T.M. (1997) Estimating the Leaf Area Index of Nort h Central Wisconsin Forests Using the Landsat Thematic Mapper. Remote Sensing of Environment 61 229-245 Gholz H.L., Vogel S.A., Cropper W.P., McKelvey K., Ewel K.C., Teskey R.O. & Curran P.J. (1991) Dynamics of Canopy Structure and Light Intercepti on in Pinus-Elliottii Stands, North Florida. Ecological Monographs 61 33-51 Gobron N., Pinty B. & Verstraete M.M. (1997 ) Theoretical Limits to the Estimation of the Leaf Area Index on the Basis of Vi sible and Near-infrared Remote Sensing Data. IEEE Transactions on Geoscience and Remote Sensing 35 1438-1445 Gower S.T., Kucharik C.J. & Norman J.M. ( 1999) Direct and Indirect Estimation of Leaf Area Index, f(APAR), and Net Primary Pr oduction of Terrestrial Ecosystems. Remote Sensing of Environment 70 29-51 Hintze J. (2001) Number Cruncher Statsti tical Systems (NCSS). Kaysville, UT Hodges A.W., Mulkey W.D., Alavalapati J. R., Carter D.R. & Kiker C.F. (2005) Economic Impacts of the Forest Indu stry in Florida, 2003. In, p. 47. IFAS, University of Florida, Gainesville, FL Holben B., Kimes D. & Fraser R.S. (1986) Directional Reflectance Response in AVHRR Red and Near-Ir Bands for 3 Cover Type s and Varying Atmospheric Conditions. Remote Sensing of Environment 19 213-236 Huang C., Wylie B., Yang L., Homer C. & Zy lstra G. (2002) Deri vation of a Tasselled Cap Transformation Based on Lands at 7 At-satellite Reflectance. International Journal of Remote Sensing 23 1741-1748 Huete A.R. (1988) A Soil-Adjusted Vegetation Index (SAVI). Remote Sensing of Environment 25 295-309 Jensen J.R. (2000) Remote Sensing of the Environmen t : An Earth Resource Perspective Prentice Hall, Upper Saddle River, N.J. Jensen J.R., Qiu F. & Ji M.H. (1999) Pred ictive Modeling of Coniferous Forest Age Using Statistical and Artifi cial Neural Network Approaches Applied to Remote Sensor Data. International Journal of Remote Sensing 20 2805-2822

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64 Karl T.R. & Knight R.W. (1985) Atlas of the Palmer Hydr ological Drought Indices (1931-1983) for the contiguous United States National Environmental Satellite Data and Information Service, Asheville, N.C. Leica Geosystems GIS and Mapping. (2003) ERDAS IMAGINE 8.7. Atlanta, GA Lucas R.M., Milne A.K., Cronin N., Witte C. & Denham R. (2000) The Potential of Synthetic Aperture Radar (SAR) for Qu antifying the Biomass of Australia's Woodlands. Rangeland Journal 22 124-140 Martin T.A. & Jokela E.J. (2004) Developmen tal Patterns and Nutrition Impact Radiation Use Efficiency Components in Southern Pine Stands. Ecological Applications 14 1839-1854 Mehrotra K., Mohan C.K. & Ranka S. (2000) Elements of Artificial Neural Networks MIT Press, Cambridge, MA. National Climatic Data Center (2005) Pa lmer Hydrological Dr ought Index FloridaDivision 2: 1895 2005 Monthly Averages http://climvis.ncdc.noaa.gov/cgibin/ginterface : May 12, 2005 Prestemon J.P. & Abt R.C. (2002) Timber Products: Supply and Demand. In: Southern Forest Resource Assessment (eds. Wear DN & Greis JG), pp. 299-325. Southern Research Station, USDA Forest Service, Asheville, N.C. Raffy M., Soudani K. & Trautmann J. (2003) On The Variability of the LAI of Homogeneous Covers with Respect to the Surface Size and Application. International Journal of Remote Sensing 24 2017-2035 Ramsey E.W. & Jensen J.R. (1996) Remote Sensing of Mangrove Wetlands: Relating Canopy Spectra to Site-specific Data. Photogrammetric Engineering and Remote Sensing 62 939-948 Reich P.B., Turner D.P. & Bolstad P. (1999) An Approach to Spatially Distributed Modeling of Net Primary Production (N PP) at the Landscape Scale and its Application in Validatio n of EOS NPP Products. Remote Sensing of Environment 70 69-81 Rouse J.W., Haas R.H., Schell J.A. & D eering D.W. (1973) M onitoring Vegetation Systems in the Great Plains with ERTS. In: 3rd ERTS Symposium NASA SP-351, Vol 1, pp. 48-62 Running S.W., Peterson D.L., Spanner M.A. & Teuber K.B. (1986) Remote-Sensing of Coniferous Forest Leaf-Area. Ecology 67 273-276 Sader S.A., Bertrand M. & Wilson E.H. (2003) Satellite Change Detection of Forest Harvest Patterns on an Industrial Forest Landscape. Forest Science 49 341-353

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65 Sampson D.A., Vose J.M. & Allen H.L. (1998) A Conceptual Approach to Stand Management Using Leaf Area Index as the In tegral of Site Structure, Physiological Function, and Resource Supply. In: Proceedings of the ninth biennial southern silvicultural research conference (ed. Waldrop TA), pp. 447-451. U. S. Department of Agriculture, Forest Service, Southe rn Research Station, Clemson, S. C. Smith M.L., Ollinger S.V., Martin M.E., Aber J.D., Hallett R.A. & Goodale C.L. (2002) Direct Estimation of Above Ground Forest Productivity Thro ugh Hyperspectral Remote Sensing of Canopy Nitrogen. Ecological Applications 12 1286-1302 Soudani K., Trautmann J. & Walter J.M.N. (2002) Leaf Area Index and Canopy Stratification in Scots pine (P inus sylvestris L.) Stands. International Journal of Remote Sensing 23 3605-3618 Starr G., Martin T.A., Binford M.W., Ghol z H.L. & Genec L. (2003) Integration of Carbon Dynamics From Leaf to Landscape in Florida Pine Forest. ESA Report #140. Ecological Society of America, Savannah, GA StatSoft Inc. (2004) STATISTICA. Tulsa, OK Stenberg P., Nilson T., Smolander H. & Voip io P. (2003) Gap Fraction Based Estimation of LAI in Scots Pine Stands Subjected to Experimental Removal of Branches and Stems. Canadian Journal of Remote Sensing 29 363-370 Swindle B.F., Neary D.G., Comerford N.B ., Rockwood D.L. & Blakeslee G.M. (1988) Fertilization and Competition Control Accel erate Early Southern Pine Growth on Flatwoods. Southern Journal of Applied Forestry 12 116-121 Tans P.P. & White J.W.C. (1998) The Global Carbon Cycle—In Balance, With A Little Help From the Plants. Science 281 183-184 Teskey R.O., Gholz H.L. & Cropper W.P. (1994) Influence of Climate and Fertilization on Net Photosynthesis of Mature Slash Pine. Tree Physiology 14 1215-1227 Trishchenko A.P., Cihlar J. & Li Z.Q. ( 2002) Effects of Spectral Response Function on Surface Reflectance and NDVI Measured With Moderate Resolution Satellite Sensors. Remote Sensing of Environment 81 1-18 Turner D.P., Guzy M., Lefsky M.A., Ritts W.D., VAN Tuyl S. & Law B.E. (2004a) Monitoring Forest Carbon Sequestration wi th Remote Sensing and Carbon Cycle Modeling. Environmental Management 33 457-466 Turner D.P., Ollinger S.V. & Kimball J.S. (2004b) Integrating Remote Sensing and Ecosystem Process Models for LandscapeTo Regional-Scale Analysis of the Carbon Cycle. Bioscience 54 573-584 Waring R.H. & Running S.W. (1998) Forest Ecosystems : Analysis At Multiple Scales. Academic Press, San Diego

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66 Wood G.A., Taylor J.C. & Godwin R.J. (2003) Calibration Methodology for Mapping Within-field Crop Variability Using Remote Sensing. Biosystems Engineering 84 409-423

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67 BIOGRAPHICAL SKETCH Douglas Allen Shoemaker was born in Washington, DC, on August 26, 1962, first of three sons to Wayne B. and Joanne S hoemaker. Raised in the nearby suburbs of Maryland, Douglas cultivated a love for th e outdoors on frequent hunting, hiking and fishing trips with his father and brothers. On his entry to the University of Maryland in 1980, he brought with him college credits earned through advanced placement English and biology testing while still in high school Originally a zoology major, his interests changed and after two years he left UM to drift through a series of jobs including elephant keeper, construction worker and se miprofessional bicycle racer. Douglas was nearly killed in a 1988 boating accident off of St. Croix, U.S.V.I., an experience that dramatically changed his life. Returning to the U.S.A. he promptly undertook a career in retail sales, an occupation he maintained for the next 12 years. During this period Douglas married Kathryn Jean Goody of Andove r NH and had the first of two daughters, Brook Hanna. In 2001 Douglas left his position and returned to finish his education, entering the University of Massachusetts ma joring in biology and geographic information science. Graduating with a Bachelor of Science degree summa cum laude Douglas arrived at the University of Florida’s School of Forest Resources and Conservation in 2003 to work with Dr. Wendell Cropper, Jr. modeling forest processes using remote sensing


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REMOTE SENSING AND SIMULATION TO ESTIMATE FOREST
PRODUCTIVITY IN SOUTHERN PINE PLANTATIONS















By

DOUGLAS A. SHOEMAKER


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Douglas A. Shoemaker
































This research is dedicated to my mother and father.















ACKNOWLEDGMENTS

I am grateful for the opportunity to work with Dr. Wendell Cropper who was

generous with his knowledge, which is substantial, and patience. I also thank committee

members Tim Martin and Michael Binford for access to valuable data.

I am obliged to Dr. Jane Southworth whose unbiased eye and fearless commentary

kept me honest.

I want to acknowledge individuals who contributed in large and small ways to this

work including Dr. Timothy Fik for inspiration in statistics; Alan Wilson and Brad

Greenlee of Rayonier Inc., landholder of the study site and member of the FBRC; Greg

Starr for helping review this manuscript; and Dr. Loukas G. Arvanitis who kept me on

task.

Special thanks go to fellow students Louise Loudermilk and Brian Roth who

remain steadfast allies.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ....................................................... ............ .............. .. vii

L IST O F FIG U R E S .............. ............................ ............. ........... ... ........ viii

ABSTRACT ........ .............. ............. ...... .......... .......... ix

CHAPTER


1 B A C K G R O U N D ............................................. ......... .... ... .......... ....1

M odeling and L eaf A rea Index ......................................................................... ...... 2
U se of R em ote Sensing D ata ........................................................................... .... ... 4
Scale and R solution .......... ............................................................... ......... .... .5

2 PREDICTION OF LEAF AREA INDEX FOR SOUTHERN PINE
PLANTATIONS FROM SATELLITE IMAGERY.........................................7

Introduction ....................................................................................................... 7
M e th o d s ..............................................................................1 0
Stu dy Sites .................................................................................................. 10
Rem ote Sensing D ata ..................................................... ... ...............1
Seasonal LAI Dynamics and Leaf Litterfall Data .............. ............................14
Integration of Ground Referenced LAI and Remote Sensing Data.................... 16
Clim ate variables ...... ........ ...... ................. .. .... .... ......... ....17
Statistical analysis ...................... ...... ...... .. .............. ..18
R egression T echniqu es ......... ................. ........................................................18
Linear regression ..................... .................. .. .... .... ........... ..18
M ultiv ariate regression ....................................................... ..................... 18
A artificial neural netw ork .................................. ................. ................ .... 19
Use of ancillary data to specify model sets. ..............................................19
R e su lts ...................................... .......................................................2 0
L in e ar M o d e ls .................................................................................. 2 1
M multiple R egression M odels.......................................... ........... ............... 21
ANN Multiple Regression Models .......................................... ...............21
D isc u ssio n .................................................................................. 2 2


v









OLS Multiple Regression Models ............................................ ...............28
A N N M o d els .................................................................................................. 2 8
F ertilization ................................................................................................. ..... 29
Suggestions for Future Effort .................................... ................... ................29
C o n clu sio n s..................................................... ................ 3 2

3 REMOTE SENSING AND SIMULATION TO ESTIMATE FOREST
PRODUCTIVITY IN SOUTHERN PINE PLANTATIONS...................................34

Introduction ............... ......... ..... .................. ...............34
M eth o d s .............................................................................. 3 7
Study Area .............. ...... .. ............................................37
Integration of Remote Sensing and Ground Referenced Data .........................39
Processing Data with the GSP-LAI and SPM-2 Models.............................. 39
R e su lts ............. ................... .................................................... 3 9
D isc u ssio n ............. ................... ................................................. 4 0
C o n clu sio n s..................................................... ................ 4 4

4 SYNTHESIS ................ .......... ... ..............................46

R results and C conclusions .......... ....................................................... ............... 46
F further Study .................................................................. 47

APPENDIX

A VARIABLES USED IN MODELS................................................................. 48

B G SP -L A I C O D E .................. .................. ................................. ..... ..51

L IST O F R E FE R E N C E S ............................................................................. .............. 62

B IO G R A PH IC A L SK E TCH ...................................................................... ..................67
















LIST OF TABLES


Table p

2-1. Catalog of images used in study. .................................................... ..............13

2-2. Summary of linear models fitted to dataset. ............. ........ ........................................24

2-3. Summary of OLS multiple regression models fitted to dataset..............................25

2-4. Summary of ANN models fitted to dataset .............. ................. ....................26

2-5. ANOVA analysis of significant variables in OLS multiple regression....................30

2-6. Significance and ranking of variables used in ANN multiple regressions ...............31
















LIST OF FIGURES


Figure page

2-1. Map of the Intensive Management Practices Assessment Center, Alachua County,
Florida, U SA .................. ....... ... ................... ..................... 12

2-2. Characterization of north-central Florida climate during study period 1991-2001 ....15

2-3. Annual cycle of variation in leaf phenology illustrating two populations of
n e e d le s ........................................................................ 1 6

2-4. Comparison of the range of LAI values for slash and loblolly pine........................23

2-5. Differences in effect of fertilizer treatment on slash and loblolly pine ................. 23

3-1. Predicted LAI values for closed canopy slash and loblolly pine. Bradford FL..........41

3-2. Predicted NEE values for closed canopy slash and loblolly pine. Bradford FL ........41

3-3. Predicted LAI values for southern pine plantations in north-central Florida.............42

3-4. Predicted NEE values for southern pine plantations in north-central Florida............43

3-5. Effect of variable FERT on LAI prediction............... .............. ......... .......... 45















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

REMOTE SENSING AND SIMULATION TO ESTIMATE FOREST PRODUCTIVITY
IN SOUTHERN PINE PLANTATIONS

By

Douglas A. Shoemaker

August, 2005

Chair: Wendell P. Cropper, Jr.
Major Department: Forest Resources and Conservation

Pine plantations of the Southeastern United States constitute one-half of the world's

industrial forests. Managing these forests for maximum yield is a primary economic goal

of timber interests; the rate at which these forests remove and sequester atmospheric

carbon as woody biomass is of interest to climate change researchers who recognize

forests as the only significant human-managed sink of greenhouse gases.

To investigate a given pine plantation's productivity and corresponding ability to

store carbon two significant parameters were predicted: net ecosystem exchange (NEE)

and leaf area index (LAI). Measurement of LAI in situ is laborious and expensive;

extraction of LAI from satellite imagery would have the advantages of making

predictions spatially explicit, scalable, and would allow for sampling of inaccessible

areas. Consequently the study was conducted in three steps: 1) the development of an

LAI extraction model using satellite imagery as a primary data source, 2) application of

the model to a study extent, and 3) determination of NEE using derived LAI values and

Cropper's SPM-2 forest simulation model.








We derived several models for extracting LAI values using various prediction

techniques. Of these a best model was selected based on performance and potential for

operational application. The generalized southern pine LAI predictive model (GSP-LAI)

was developed using artificial neural network (ANN) multivariate regression and

incorporating important local information including phenological and climatic data. In

validation tests the model explained > 75% of variance (r2 = 0.77) with an RMSE < 0.50.

The GSP-LAI model was applied to Landsat ETM+ image recorded September 17,

2001, of the Bradford forest, north of Waldo, FL. Within the extent are substantial slash

(Pinus elliottii) and loblolly (P. taeda) pine plantations. Based on image and stand data

projected LAI values for 10,797 ha (26,669 acres) were estimated to range between 0 and

3.93 m2 m-2 with a mean of 1.53 m2 m-2. Input of slash pine LAI values into SPM-2

yielded estimates of NEE for the area ranging from -5.52 to 11.06 Mg ha-1 yr- with a

mean of 3.47 Mg ha-1 yr1. Total carbon sequestered for the area analyzed is 33,920

metric tons, or approximately 1.4 tons per acre.

Based on these results a map of the Bradford forest was drawn locating areas of

carbon loss and gain and LAI values for individual stands. Ownership and accounting of

carbon stores are prerequisites to anticipated carbon trading schemes. The availability of

stand-level LAI values has significance for forest managers seeking to quantify canopy

response to silvicultural treatments. Efficiencies may be realized in management

practices which optimize leaf growth based on site potential rather than focusing on

resource availability.














CHAPTER 1
BACKGROUND

The monitoring of forest biological processes has become increasingly important

as nations seek to control their outputs of carbon dioxide (CO2), the primary component

of climate-changing greenhouse gasses, in the face of global climate change. Forests in

general and trees specifically provide the essential service of removing CO2 from the

atmospheric reservoir of carbon through photosynthesis, where carbon is fixed as

energy-storing sugars. The metabolic processes of the tree respire carbon back to the

atmosphere but a portion is isolated from environment in the durable biomass of the

plant, namely wood. Carbon will re-enter the atmosphere when wood decomposes or

burns, however the period of carbon sequestration is on the terms of decades, perhaps

longer if that wood is built into a structure or buried as waste in a landfill.

Carbon sequestration via forestry is currently the only means by which mankind

can significantly remove carbon from the atmosphere; agricultural plantings are not

counted as the carbon returns to the environment too quickly to have an appreciable

effect (Tans & White 1998). The Kyoto Protocol of 1997, an international accord which

seeks to reduce the emissions of greenhouse gasses, calls for the cooperation of nations

in finding and maintaining sinks, or reservoirs, of greenhouse gases. This language lays

the foundation for the trade in carbon credits, whereby a nation exceeding its emissions

of CO2 could pay another nation to sequester carbon, e.g., let stand a forest scheduled

for harvest. The emissions trading scheme (ETS) identifies value (and a potential new

revenue source) from what was previously an un-valued, non-market services provided









by the forest. Carbon credits are not simply economic talk-on October 1, 2003, carbon

credits traded for the first time in an international market, the Chicago Climate

Exchange, for $.98 per metric ton (Doran, 2003).

Modeling and Leaf Area Index

Economists and ecologist want to better understand the flow of carbon in and out of

forests on a regional and global scale. Forest ecosystems are complex, and systems

ecologists use models to analyze the responses and productivity of forests, especially the

movements of carbon (Waring & Running 1998). Models such as SPM-2 aim to

characterize the flows of carbon between the atmosphere, the trees and the soil (Cropper

2000). This model, specific to coastal plain slash pine (Pinus elliottii) forests, uses dozens

of input parameters ranging from rainfall and humidity to wind speed; outputs include

carbon assimilation (g CO2 m-2 d-1 and Mg C ha-1 yr-) and annual stem growth (g m-2).

In forest system models the complexities of leaf area, including canopy structures

and geometry, may be simplified into a ratio of total leaf area to unit ground area known

as the leaf area index (Waring & Running 1998). This leaf area index (LAI) composes the

most basic input into current forest system models (Stenberg et al. 2003).

Unfortunately LAI is notoriously difficult to determine for a number of logistical

reasons to be illustrated and for many species it changes within the growing season. In

the subject species P. elliottii, LAI varies seasonally because trees bear two age classes of

leaves through most of the year. A maximum LAI occurs around mid-September when

last year's leaf class has not yet senesced and the new leaves have reached their

maximum elongation. Workers thus need to be aware of the time-of-year when the

sample is taken and account for this seasonal variation (Gholz et al. 1991). The climatic









conditions at time of sampling are also important, as drought or leaf loss due to storms

can depress the index.

LAI is measured in situ three distinct ways: the area-harvest method, the leaf litter

collection method, and the canopy transmittance method. A fourth indirect method

involves the use of satellite imagery to measure electromagnetic energy reflected from

the forest canopy at specific indicative wavelengths. Though laborious and limited in

spatial extent, in situ methods provide important ground truth estimates for validating and

training remote sensing techniques (Stenberg et al. 2003).

The area-harvest method involves randomly choosing a tree in a forest

community similar to that of the study, measuring the footprint of the tree, harvesting it,

and giving each leaf collected a specific leaf area (SLA), which is the ratio of fresh leaf

area to dry leaf mass. Age class of leaves should be accounted for as SLA can differ by a

factor of two between old and new foliage. The number of trees measured in this fashion

should reflect a sample size sufficient to represent the spatial heterogeneity of community

studied (Stenberg et al. 2003).

The leaf litter collection method involves a sample selection process similar to the

area-harvest method, however leaves are continuously collected in leaf traps and each

assessed as to area and age class. Extrapolation techniques then extend the information

along a timeline to determine LAI at a given time (Stenberg et al. 2003).

Field determinations of LAI may also be made without laborious collection using

the canopy transmittance method. Optical sensors that measure light not intercepted by

leaves, or canopy gap, are placed beneath the canopy. The amount of light recorded is

then compared with a model of canopy architecture, and from there an LAI is derived

(Stenberg et al. 2003). This method assumes the distribution of leaves in the canopy to be









random; thus it is invalid for open-canopy forests, such as coniferous forests (Gholz et al.

1991).

In situ LAI determinations are the standard of comparison for all new techniques,

and are currently the most reliable data available. Area-harvest methods and leaf litter

collection are assumed to be more accurate than canopy transmittance methods, however

Gower reports that all in situ methods are within 70% to 75% accurate for most canopies,

exceptions being non-random leaf distributions and LAI > 6 (Stenberg et al. 2003).

Use of Remote Sensing Data

Because of the arduous nature of determining LAI in situ there has been emphasis on

developing new methods which use remotely sensed data captured by sensors on airborne

or satellite platforms (Gholz et al. 1991; Sader et al. 2003). These methods take

advantage of the fact that photosynthetically active vegetation absorb specific

wavelengths of the incident electromagnetic (EM) spectrum and reflect others.

Specifically, blue (0.45-0.52 [m) and red (0.63-0.69km) are absorbed, green (0.53-

0.62[m) and near infrared (0.7-1.2 [im) are reflected (Jensen 2000). Reflectance of green

wavelengths creates the green appearance of foliage, while reflected NIR is invisible to

the human eye. Measurements of absorbance and reflectance comprise unique spectral

signatures that distinguish between vegetation and other ground features, or between

different genera of plants.

The reflectance of NIR bandwidths are of particular interest as they are indicative

of the amount of leaves within the canopy at the time of imaging. Reflected wavelengths

consist of EM energy the plant cannot use which leaves reflect or allow to pass through

(transmit). Transmitted radiation falls incident on a leaf below, which in turn reflects









50% and transmits 50%. This characteristic is called the leaf additive reflectance, and it is

indicative of amount of leaves within a canopy.

Several remote sensing indices have been created to classify and measure foliage

from space using the differential reflectance and absorption characteristics of red and

near infrared bandwidths. The most widely used algorithms (Trishchenko et al. 2002)

include Simple Ratio (Birth & Mcvey 1968) and Normalized Difference Vegetative

Index (Eklundh et al. 2003). The formula for Simple ratio (SR) is described as:

SR = NIR/red

Normalized Difference Vegetative Index (NDVI) is described as:

NDVI = (NIR red) / (NIR + red)

The ratios have the advantage of using two of the seven or more bands typically

collected, and requiring no other auxiliary data for calculation. However, they require

calibration from in situ reference locations in order to produce secondary data, such as

physical measurements of biomass (Wood et al. 2003). Additionally, variability is

introduced to the index by soil reflectance, atmospheric effects, and instrument

calibration (Holben et al. 1986; Huete 1988). Of these three soil reflectance is pervasive

and its contribution to vegetation indices is ideally subtracted using a two-stream solution

developed by Price (Soudani et al. 2002).

A Leaf area index is a secondary datum produced by linking in situ reference data

with a vegetation index, typically NDVI (Sader et al. 2003). The data are connected

through regression analysis resulting in a linear relationship (Ramsey & Jensen 1996).

Scale and Resolution

The use of satellite imagery has also brought the issue of scale to the forefront. The

spatial extent of forest systems modeled has typically been limited to a stand or woodlot









scale due to the restrictive nature of in situ LAI sampling. Estimates of LAI from satellite

imagery may be the only way to measure vegetative processes of forest at a regional or

larger scale (Sader et al. 2003). A fundamental question in choosing a data source is one

of resolution. In remotely sensed data, a pixel, or picture element, represents a spatial

extent on the ground that is the minimum area capable of resolution by a particular

sensor. For the Thematic Mapper (TM) carried by the satellite platform Landsat the pixel

size is a 30 meter by 30 meter square. Thus the resolution of Landsat TM is said to be 30

meters. Different sensors have different resolutions. The French SPOT satellite carrying

the High Resolution Radiometer (HRR) has a 10 meter resolution (Jensen 2000). In

working with vegetation, resolution should match the size of the feature-of-interest as

closely as possible.














CHAPTER 2
PREDICTION OF LEAF AREA INDEX FOR SOUTHERN PINE PLANTATIONS
FROM SATELLITE IMAGERY

Introduction

Pine plantations of the Southeastern United States constitute one-half of the world's

industrial forests. In Florida alone annual timber revenue exceeds $16 billion and is the

dominant agricultural sector (Hodges et al. 2005). Managing these forests for maximum

yield is a primary economic goal of timber interests; the rate at which these forests

remove and sequester atmospheric carbon as woody biomass is of interest to climate

change researchers who recognize forests as the only significant human-managed sink of

greenhouse gases.

Leaf area index (LAI) is a key parameter for estimation of a given pine plantation's

productivity or net ecosystem exchange of carbon (NEE). In this study we focus on the

estimation of LAI, a primary biophysical parameter used in forest productivity modeling,

carbon sequestration studies, and by forest managers seeking to quantify canopy

responses to silvicultural treatments (Cropper & Gholz 1993; Sampson et al. 1998;

Gower et al. 1999; Reich et al. 1999). LAI is the ratio of leaf surface area supported by a

plant to its corresponding horizontal projection on the ground, and it is difficult and

expensive to assess in situ resulting in sparse sample sets that are necessarily localized at

a stand scale and thus difficult to extrapolate to larger extents (Fassnacht et al. 1997).

Determination of LAI from remotely sensed data would have the advantage of

being spatially explicit, scaleable from stand to regional or larger extents, and could









sample remote or inaccessible areas (Running et al. 1986). An ideal empirical model

linking ground-referenced LAI to remote sensing data would make reliable predictions at

various extents and image dates and be general enough to incorporate important local

information such as climatological and phenological data.

As Gobron et al. (1997) point out the range of variation that exists in vegetative

biomes of interest worldwide preclude the likelihood of a single universal relationship

between LAI and remote sensing products; but regional prediction of LAI in important

subject systems such as the extensive and economically important holdings of industrial

pine plantations across the southeastern U. S. should have important applications.

There have been previous attempts to remotely estimate LAI for this specific forest

system. Industrial plantations in the south typically consist of dense plantings of loblolly

(Pinus taeda) and slash (Pinus elliottii) pine (Prestemon & Abt 2002). Gholz, Curran et

al (1991) studied a north-central Florida mature slash pine plantation where they

evaluated LAI determination techniques and related those to remote sensing data

collected by Landsat TM. Flores (2003) looked at loblolly pine in North Carolina and

related ground-based indirect LAI values to hyperspectral remote sensing data.

These studies used ordinary least squares (OLS) regression analysis to establish an

empirical relationship between vegetative indices (VI) and ground-referenced LAI. The

best understood VIs are the normalized difference vegetative index (NDVI) (Rouse et al.

1973) and the simple ratio (SR) (Birth & Mcvey 1968) both of which make use of

recorded values for red and near infrared wavelengths. In the case of Gholz et al (1991)

three predictive equations were produced using NDVI. Flores used SR in his predictor.

We evaluated these models using a new dataset assembled for this study and found none









exhibited significant predictive ability (see Table 2-2 in results). While linear regression

remains a popular approach, variations in surface and atmospheric conditions as well as

the structural considerations of satellite remote sensing have foiled attempts to establish a

universal relationship between LAI and VIs (Gobron et al. 1997; Fang & Liang 2003).

Perhaps this failure is due to under- or misspecification of the models. The

biochemical and structural component of the forest canopy is complex, varying in both

time and locale (Raffy et al. 2003). Cohen et al (2003) suggest that the incorporation of

other recorded spectra and the use of data from multiple dates as predictive variables as a

way to improve regression analysis in remote sensing. Multivariate regression techniques

allow for the incorporation of more types of data, including important locational

information such as climate or categorical stand data. When OLS regression is used

variable selection techniques permit the exploration of a wide range of data for

significance.

Despite these advantages many of the assumptions necessary for OLS regression

are violated by remote sensing data which characteristically exhibits non-normality and

tends to suffer multicollinearity and autocorrelation. For these reasons a nonparametric

technique, regression with artificial neural networks, was investigated as an alternative to

OLS regression.

Artificial neural networks (ANN) are loosely modeled on brain function: a series of

nodes representing inputs, outputs and internal variables are connected by synapses of

varying strength and connectivity (Jensen et al. 1999). The network architecture is

typically oriented as a perception which 'learns' by passing information from inputs to

outputs (forward propagation) and from output to inputs (back propagation) to optimize









the accuracy of prediction by adjusting weights. The ability to accommodate complexity

can be made by altering the construction of the network to include multiple layers of

internal nodes. These networks are attractively robust in that many of the assumptions

needed for OLS regression are relaxed, including requirements of normality and

independence.

In this study our objective was to develop a single 'general' empirical model

capable of producing reliable LAI predictions at various extents and image dates. We

hypothesized that such a solution would require multivariate statistics to incorporate

important local information such as climatological and phenological data. Three

regression techniques, linear OLS, multiple OLS and ANN, were applied to a large

dataset constructed from data acquired by Landsat sensors over a 10 year period and the

resultant models evaluated for performance using a validation process. Models were

developed in strata of increasing complexity to identify high performing yet simple

solutions.

Methods

Study Sites

Two plantations of southern pine were used in this study: the Intensive

Management Practices Assessment Center (IMPAC) operated by the Forest Biology

Research Cooperative (FBRC) and the Donaldson tract, part of the Bradford forest owned

by Rayonier, Inc. and site of a Florida Ameriflux eddy covariance monitoring station.

Both sites are planted with southern pine species loblolly (Pinus taeda L.) and slash

(Pinus elliottii var. elliottii) which have similar physiology and seasonal foliage dynamics

(Gholz et al. 1991).









The IMPAC site is located 10 km north of Gainesville, Florida USA (290 30' N,

820 20' W, Figure 2-1.) The site is flat with elevation varying < 2 m and experiences a

mean annual temperature of 21.70C and 1320 mm annual rainfall. Soils are characterized

as sandy, siliceous hyperthermic Ultic Alaquods (Swindle et al. 1988). The stand was

established in 1983 at a stocking rate of 1495 seedlings per hectare, a dense planting

typical of industrial pine plantations. The site was surveyed using a differentially

corrected global positioning system (DGPS) in February, 2004.

The site consists of 24 study plots, each 850 m2, exhibiting factorial combinations

of species (loblolly and slash pine), fertilization (annual or none) and control of

understory vegetation (sustained or none) in three replicates. Fertilization of respective

plots occurred annually for ages 1-11, was ceased for ages 12-15, and resumed at age 16.

The Donaldson tract is located 12 km east of the IMPAC site (290 48' N, 820 12'

W) the stand was established in 1989 and stocked at a rate of 1789 slash pine seedlings

per hectare. The site is flat and well drained. Within the stand are four 2,500 m2 plots

from which leaf litterfall was collected starting at age 10 (1999). Plots were surveyed

with GPS May, 2002. Estimates of LAI based on needlefall from 10 randomly located

traps were collected by Florida Ameriflux averaged into a single value for all four plots

beginning April, 1999.

Remote Sensing Data

The study acquired 18 cloudless images recorded of the study area between 1991

and 2001 by the Landsat 5 and 7 satellite platforms (Table 2-1.). This series of images

contain examples of each of the four phenological categories and is concurrent with

cycles of dry and wet periods for the region (Figure 2-2).







12






















37525=2: -:
375225


IMPAC Study 'te s
Monteocho Qluadrant
Alachua C',ounry Flonda
tIJTM 1 7 North











C C11



,.' a e, I thr Fe&

SI Fresive Mgettinn n

Co Nun Foest Landcver FaseCobrCosa s
IM PAC Study P lots R = aEds 1, 2, 3
O ate." January A 1999


375225 :


Figure 2-1. Map of the Intensive Management Practices Assessment Center, Alachua
County, Florida, USA.









Table 2-1. Catalog of images used in study.
Number Image Datet Sensor Phenological period PHDIJ
1 1/17/91 TM Declining LAI -1.75
2 3/22/91 TM Minimum LAI -0.63
3 10/16/91 TM Declining LAI 2.63
4 1/20/92 TM Declining LAI 1.59
5 8/31/92 TM Maximum LAI 1.22
6 3/27/93 TM Minimum LAI 1.85
7 8/18/93 TM Maximum LAI -2.76
8 1/25/94 TM Minimum LAI 2.78
9 9/6/94 TM Maximum LAI 1.3
10 6/7/96 TM Expanding LAI 0.83
11 9/30/97 TM Maximum LAI -0.86
12 6/29/98 TM Expanding LAI 0.59
13 1/7/99 TM Minimum LAI -1.9
14 9/4/99 TM Maximum LAI -2.38
15 1/2/00 ETM+ Declining LAI -2.29
16 4/7/00 ETM+ Minimum LAI -2.71
17 8/13/00 ETM+ Maximum LAI -4.02
18 1/4/01 ETM+ Declining LAI -3.05
t All images are Path 17N, row 39. Datum NAD83/GRS 80. Georectification error +0.5 pixels
I Palmer hydrological drought index: negative values indicate dry conditions, positives wet,
normal z 0. National Climatic Data Center.


Images were captured with the both the Thematic Mapper (TM) sensor aboard

Landsat 5 and the Enhanced Thematic Mapper Plus (ETM+) aboard Landsat 7. These

sensors are functionally identical for the bandwidths used in the study: visible spectra

blue (0.45 0.52 am, band 1), green (0.52 0.60 am, band 2) red (0.60 0.63 am, band

3) and infrared spectra: near (0.69 0.76 [am, band 4) mid (1.55 1.75 [am, band 5) and

reflected thermal (2.08 2.35 am, band 7). Spatial resolution for these bands is 30m.

Band 6, which detects emitted thermal radiance between 10.5 12.5am, has a resolution

of 120 m for TM and 60m for ETM+.

Brightness values (BV) were recovered from the data based on the center point of

each study plot. All images were individually rectified using a second order polynomial

equation with between 30 and 40 ground control points; while the images maintained the









accepted rectification accuracy of 0.5 pixels the overlay with study plots varied from

image to image.

Seasonal LAI Dynamics and Leaf Litterfall Data

P. taeda and elliottii are evergreen trees that maintain two age classes of leaves

throughout much of the year, needles from both the previous and current growing seasons

(Gholz et al. 1991; Curran et al. 1992; Teskey et al. 1994). In north Florida these classes

overlap between July and September, establishing a period of peak leaf area categorized

as maximum LAI. As such the phenological year is typically categorized into four

periods: minimum LAI, leaf expansion, maximum LAI and declining LAI (Figure 2-3).

This dynamic must be well understood to interpret LAI from remotely sensed data.

















5


x 4
WET
3

-2











DRY
-4
2
0

ca

o A










-5
3 CU3 U (U -R / F; li (CU CU (CU (U -CU (3 (3 -i (3 -i (3
I -) -) ) ) ) -) -)
QI -2
E
cc
03
DRY IV
-4

-5



Figure 2-2. Characterization of north-central Florida climate during study period 1991-2001 (National Climatic Data
Center 2005).











Mid-rotation Pinus elliottii
600

MAXIMUM LAI
500
DECLINE
MINIMUM EXPANSION DCI
400 MINIMUM
| 400 M. .

-0 -----, /
S300
-0
/ "**
/
200

/
100 /
"- OVERALL
S-NEW
0 -. .................... ------ .. ......OLD
JAN FEB MAR APR MAY JUN JULY AUG SEP OCT NOV DEC



Figure 2-3. Annual cycle of variation in leaf phenology illustrating two
populations of needles (Cropper and Gholz, 1993).

In situ estimates of LAI were calculated by leaf litterfall collection. Needlefall was


collected monthly from six 0.7m2 traps distributed randomly within each of the 24


IMPAC study plots from year 8 (1991) with the assumption of closed canopy through

2001. A similar method was used at the Donaldson site's four study plots, the results of

which were aggregated into a single value for the tract.

LAI from litterfall was estimated using foliage accretion models (Martin & Jokela

2004). LAI results were presented as hemi-surface leaf area and converted to projected


leaf area for integration with remote sensing data.

Integration of Ground Referenced LAI and Remote Sensing Data

LAI data based on monthly leaf litterfall collection from all 24 study plots was


ground referenced to plot centroids based on GPS survey. Data from IMPAC ranged in

date from January 1991 with the assumption of canopy closure at age 8 to February 2001,









the latest calculations available. Data from the Donaldson Tract ranged from April, 1999

with a similar assumption of canopy closure, to February 2001.

Landsat images were overlaid with plot locations within a geographic information

system (GIS). Surface reflectance data and ground referenced LAI were related by a point

method which joined LAI values to pixels based on the presence of a plot centroid. LAI

data, aggregated monthly, were matched with image date based on proximity.

The integration resulted in a dataset based on the point method of 453 samples

which linked 28 locations with their respective surface reflectance values at specific

times over a period of 11 years. All rows were randomized within the table and 51 cases

were extracted and withheld for external validation.

The data were densified with vegetative indices including normalized difference

vegetative index (Birth, 1968), simple ratio (Rouse et al. 1973; Crist & Cicone 1984) and

tasseled cap analysis components (Crist and Cicone 1984). Ancillary data were

incorporated into the set including climate indexes and categorical plot data representing

species type, plot treatment and phenological period. The complete list of variables used

in modeling is included in Appendix A.

Climate variables

Local climatic conditions were represented by the Palmer Hydrological Drought

Index (PHDI), a monthly index of the severity of dry and wet spells used to access long-

term moisture supply (Karl & Knight 1985). The variety of indexes developed by Palmer

and others standardize climatic indicators to allow for comparisons of drought and

wetness at different times and locations. The PHDI was used instead of the better known

rainfall-based Palmer Drought Severity Index (PDSI) because it accounts for site water

balance, outflows and storage of water based on short-term trends.









The time scales at which climate influences leaf area are unknown. Therefore

several variables were developed to explore specific lags: a simple annual lag, a

summation of PHDI values during the leaf expansion period, that summation with an

annual lag and finally a summation for PHDI during leaf expansion for current and

previous growing years. This last variable is an attempt to capture the cumulative effect

of climate when represented by two age classes of needles present during the maximum

LAI period. Correct chronological sequence between phenology and climate indicators

was maintained by interacting lagged variables with appropriate phenological periods.

Statistical analysis

Statistical analysis was performed on the integrated data set including descriptive,

principle component and autocorrelation analysis using NCSS statistical software (Hintze

2001). The likelihood of spatial autocorrelation was explored using GEODA 0.9.5

geostatistical software (Anselin 2003).

Regression Techniques

Three types of regression processes were evaluated; two based on ordinary least

squares (OLS), the third artificial neural networks (ANN).

Linear regression

Linear regression represents the simple form of OLS regression where a single

independent variable, often a vegetative index, was regressed against the dependent

variable LAI. Linear regression has been the typical approach in previous studies

including Gholz and Curran (1991) using NDVI and Flores (2003) using SR.

Multivariate regression

In the multiple form of OLS regression, many independent variables, including

surface reflectance data, vegetative indices, climate data and categorical data were









regressed against the dependent LAI. Stepwise variable selection was used to identify

variables significant at p-value < 0.05.

Artificial neural network

Construction and processing of ANNs was accomplished with the neural network

module of Statistica statistical software (StatSoft 2004). Architectures were limited to

Multilayer Perceptron with a maximum of four hidden layers as suggested by Jensen et al

(1999). A back-propagation training algorithm was used to train the network with a

sigmoidal transfer function activating nodes. Sample sets were bootstrapped based on

available cases. One hundred architectures were evaluated per model, with the top 5

retained based on the lowest ratio of standard deviation between residuals and

observation data. From these five a 'best' model was selected based on the relationship

between predicted and observed values from the training and validation set (r2, RMSE).

Use of ancillary data to specify model sets

An advantage of multiple regressions (including ANN) over linear regression is the

ability to include important locational information that is available but outside of the

primary data source through the use of additional continuous or categorical variables. In

particular the incorporation of categorical variables specifying phenological periods,

species and treatments allow the relationship between LAI and its predictors to be

generalized to a single model.

Three classes of multiple regression models are evaluated in this work: (1) simple

models whose constituent variables are generated solely from remote sensing data and

corresponding vegetation indices only; (2) intermediate models that additionally

incorporate image date (and therefore phenological information) and climate data: (3) the

most complex models that add stand level data such as species and treatment. Following









precedent set by Gholz and others the simple and intermediate models sets were

developed for single species and single phenological periods.

Results

LAI values from leaf litterfall collection vary from just under 0.5 to 4.5 with a

mean of 2.38 m2 m-2.There is considerable overlap in LAI for slash and loblolly (Figure

2-4.). There is a disproportionate effect of fertilization on species, with loblolly

exhibiting an increase of 1.0 in mean LAI as compared to 0.56 for slash (Figure 2-5.).

One of the limitations of relating LAI to remote sensing data is spatial

autocorrelation. Band 6, which detects emitted thermal radiation, exhibited significant

spatial autocorrelation (Moran's I = 0.53) likely due to its coarse resolution of 120m

(Landsat TM), an extent which overlays several plots at once. Spatial autocorrelation was

not indicated for the reflectance values of the other 5 bands and LAI (Moran's I =0.03

and -0.02 respectively).

When two or more of the independent variables of a multiple regression are

correlated, the data is said to exhibit multicollinearity. Multicollinearity may result in

wide confidence intervals on regression coefficients. Principle component analysis of

spectral variables used revealed eigenvalues near 0.0 for 5 of the 9 resultant components,

indicating multiple collinearity. There was, however, little correlation between regional

climate conditions, as indicated by the Palmer hydrological drought index and LAI for

both species.

In general, the simplest possible predictive model is desirable. Simpler models are

easier to apply to new cases because of the reduced requirements for input data. Complex

environmental systems with multiple interacting biological and physical components are









however not likely to be adequately modeled by the simplest models. In this study we

have examined a range of models from simple linear models through non-linear ANN

multiple regression models. Our goal was to find a model that was a good predictor for

separate validation data. The latter requirement was necessary as a guard against

"overtraining" (Mehrotra et al. 2000).

Linear Models

For comparison purposes previously published models are listed above new models

(Table 2-2). Of the 20 models tested 16 failed to reject the null hypothesis 31= 0. No

model exceeded an r2 >0.12. These simple models were not adequate predictors of LAI

for the training data. Even the published models with a history of useful predictors of

southern pine LAI failed for this dataset.

Multiple Regression Models

All models tested statistically significant for slope representing improvement over

linear models. r2 values ranged from 0.31 to 0.70. In validation testing, increasingly

complex models accounted for greater variation in LAI for training data, but performance

with testing data was mixed. (Table 2-3). ANOVA analysis of significant variables

appear in Table 2-5. Significant variables include presence or absence of fertilization

treatments and phenological periods.

ANN Multiple Regression Models

The ANN predictions improved on OLS multiple regressions at each class strata. r2

values ranged from 0.4 to 0.85 in training validation, and from 0.02 to 0.77 in testing

(Table 2-4).









The generalized southern pine LAI predictive model (GSP-LAI) was selected as the

top performing model (Figure 2-6). In validation tests the model explained > 75% of

variance (r2 = 0.77) with an RMSE < 0.50.

Discussion

In this study we created GSP-LAI, a model which effectively predicted LAI for a

managed southern pine forests system of two species, multiple management treatments

and climate variability on annual and seasonal scales. The model's development was

guided by three major factors: 1) a focus on a relatively simple and well understood

forest system for which there was ample data, 2) a desire to create an operational solution

with wide applicability, and 3) the willingness to employ sophisticated regression

techniques.

The intensively managed pine plantation is a simple system compared to natural

regrowth forests or mixed coniferous/deciduous forests in terms of the presence of even-

aged stands and the reduction of canopy layers (Gholz et al. 1991). Although seemingly

an ideal system for LAI prediction, previously published southern pine LAI predictors

applied to new remote sensing data lead to results so inaccurate as to be unusable as

inputs for forest productivity modeling. New simple linear regression models constructed

using single vegetative indices and trained on the study's large database offered no

improvement.





























3.0 [


2.6


2.4 [


1.8 F


ABSENCE (0) OR PRESENCE (1) OF FERTILIZATION TREATMENT


0 1

SLASH


0 1

LOB


SLASH LOBLOLLY




Figure 2-4. Comparison of the range of LAI values for slash Figure 2-5. Differences in effect of fertilizer
and loblolly pine for all sites, 1991-2001. treatment on slash and loblolly pine.












Table 2-2. Summary of linear models fitted to dataset. First two models are previously published.


Spp.


Phenological
category
END
MAX


MIN


Flores
(2003) L EXP/END 139
LAI= a+
b(SR)


MIN
EXP
MAX
END
MIN
EXP
MAX
END


a
Intercept
-14.31
-20.02


b
Slope
32.25
43.62


r2
0.03
<0.01


36 -10.80 26.29 <0.01


-0.83


1.65
3.76
2.54
0.85
1.61
3.54
2.95
-0.60


RMSE
1.50
6.66


3.59


0.56 0.01 1.75


-0.15
-3.70
-0.12
1.95
0.82
-1.57
0.49
6.05


<0.01
0.03
<0.01
0.02
0.02
<0.01
<0.01
0.12


0.43
0.46
0.59
0.54
0.75
0.97
1.02
0.80


T
Value
20.80
37.7


Prob.
Level
<0.001
<0.001


Rej ect
HO
yes
yes


-0.21 0.8344 no


0.25 0.2487 no


-0.2
-0.72
-0.21
1.40
0.68
-0.15
0.46
3.20


0.9821 no
0.4762 no
0.8356 no
0.1652 no
0.5018 no
0.8805 no
0.6468 no
0.0020 yes


MIN 36 1.67 -0.01 <0.01 0.43 -0.08 0.9353 no
EXP 20 4.03 -0.75 0.03 0.46 -0.79 0.4308 no
MAX 73 2.55 -0.3 <0.01 0.59 -0.21 0.8320 no
LAI= a+ END 79 1.15 0.22 0.02 0.54 1.18 0.2397 no
b(SR) MIN 31 1.53 0.17 0.02 0.75 0.69 0.4928 no
EXP 21 3.58 -0.29 <0.01 0.97 -0.16 0.8779 no
L
MAX 68 2.83 0.13 <0.01 1.02 0.62 0.5375 no
END 74 -0.19 0.87 0.12 0.80 3.12 0.0025 yes
tBased on surface reflectance values j Based on exoatmospheric reflectance values


Model
Gholz
(1991)
LAI= a+
b(NDVI)


LAI= a +
b(NDVI)


--


..... .....


...... .....


--


.... ... .... ...


.... .... .... ...












Table 2-3. Summary of OLS multiple regression models fitted to dataset


Validation


Class


Remote
sensing
data only


Include
Categorical
and
Climate
Variables


Label

PASEND


Model f
LAI = -0.54+ 5.70E-02(B 1)-
5.27E-02(B5)+ 8.08E-
02(TCA-2)


LAI = -2.48 + 1.23(SR)+
PALEND
A0.11(TCA-3)


LAI = 2.35- 0.79(EXP)-
PBSTOT 0.045(LAG-PHDI) -
0.63(MAX) 0.40(MIN)-
6.32(NDVI) + 0.06(PHDI) +
1.20(SR) + 0.06(TCA-3)

LAI = 2.04 -1.03(EXP) -
0.74(MAX) -0.68(MIN) -
14.78(NDVI) + 3.02(SR)+
0.09(TCA-3)


Phenolo
gical
Spp. category


Training

n r2 RMSE


S END 79 0.31 0.459


L END 74 0.33 0.707




S ALL 208 0.42 0.497





L ALL 194 0.43 0.794


Testing

n r2 RMSE

13 0.51 0.37


8 0.05 1.05


27 0.02 1.40


20 0.17 0.92


LAI = 4.48-1.038(EXP)-
.902(FERT)-.508(HERB)-
.835(MAX)-.515(SPP)+
0.0308(TCA-3)


ALL ALL 402 0.70


0.49


47 0.63 1.97


General
Model


PCTOT


fB1= Band 1; B5= Band 5; TCA-2, 3= Tassel cap analysis component 2, 3; SR= Simple ratio vegetative index; MIN, EXP, MAX= phenological period: minimum LAI,
expanding LAI, maximum LAI; PHDI= Palmer hydrological drought index; LAG-PHDI= PHDI one year previous; NDVI= Normalized difference vegetative index;
FERT= Fertilization; HERB= Herbicide application; SPP= Species of tree. Details about variables are contained in Appendix A.












Table 2-4. Summary of ANN models fitted to dataset


Validation


Label

ASEND5


ALEND9


Inpi

6


Network architects

Hidden Nc
uts Layers

2


Include
Cate BSCLIM10 14 2
Categoric
al and
Climate BLCLIM5 15 2
Variables

General
General GSP-LAI 18 2
Model

f Number of cases available for bootstrap samplin;


Training


ure:

odes per


Testing


Phenolo
gical


Layer Spp. category nt r2

16, 12 S END 79 0.40


4 L END 74 0.40


16,6 S ALL 213 0.42


16,7 L ALL 190 0.49


16, 7 ALL ALL 402 0.85


RMSE n r2 RMSE

0.422 26 0.02 1.10


0.650 18 0.26 1.30


0.490 27 0.39 0.52


0.784 24 0.12 0.94


0.347 51 0.77 0.40


Class


Remote
Sensing
data only


.... .... .... ...













GSP-LAI = 0.3675+0.8406*x


5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0
0.0


0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
OBSERVED LAI


Figure 2-6. Plot of LAI values predicted by GSP-LAI for training data.

It is unclear if the previously published models were ever intended for use outside

of the image from which they were created; they were developed with relatively few

samples and with few sample dates. Climate history and leaf phenology would

necessarily differ from remote sensing data used for model calibration. These

shortcomings lead to a criterion that LAI estimation should not be limited to a single

image, location, phenological period or satellite sensor. The poor performance of linear

regression techniques applied to a robust dataset lead us to the conclusion that even this

simple system was too complex to be predicted by a single variable.









In addition to the remote sensing data there are many variables that might be useful

predictors of the system, including climate variables, management treatments such as

fertilization, the presence and/or contribution of understory, phenological period, and

others. To incorporate these variables multivariate regression techniques were necessary.

The availability of ANN regression functions in modern statistical software allowed for

the quick explorations of predictive networks to compare to OLS regressions.

In both OLS and ANN regression the highest performing models were the most

general, capable of incorporating both continuous and categorical variables into a single

solution. The assignment of categorical variables is a useful and underexploited technique

permitting the development of models with wide domains of application.

OLS Multiple Regression Models

OLS regression revealed some of the probable drivers of this system, namely

phenological period and management treatment. Tassel cap component 3 was the only

consistent remote sensing variable used between models (Table 2-5). This component,

also known as "wetness", is typically associated with evapotranspiration (ET) which is

expected to increase with increased LAI. Tassel cap components are the product of

coefficients for all 6 bands of reflected radiation that TM and ETM+ record and as such

exploit more spectra than the commonly used NDVI and SR (Cohen et al. 2003).

ANN Models

The best general model was the product of ANN regression. This non-parametric

technique was able to incorporate climate data as represented by PHDI and its lagged

derivatives. Climate, while assumed to be important, is typically absent in the

development of these sorts of empirical models. It is a difficult problem: eligible satellite

images are all captured on sunny days, and the various temporal scales on which local









climate influences vegetation is mostly unknown and likely to be species and site

specific. Typical data used in multitemporal analyses exhibit serial autocorrelation,

necessitating transformations in order to become valid OLS inputs. The improved

performance conveyed by the ANN regression suggests that 1) climatic variables are

significant and 2) OLS regression was unable to use the variables as employed.

The GSP-LAI model is deterministic and easily implemented. Code for the model

is detailed in Appendix B.

Fertilization

In the OLS and ANN generalized models fertilization represents a significant

variable (Tables 2-5, 2-6). This result supports observations (Figure 2-5) and also Martin

and Jokela's (2004) analysis of IMPAC leaf litterfall data. Fertilization is a focal

treatment in intensive management practices, and indications of canopy response in the

form of LAI assessment could direct the location and frequency of application. The

availability of reliable LAI data could lead to a paradigm change in management

practices were the goal becomes optimization of leaf growth based on site potential.

Suggestions for Future Effort

The improved performance of increasingly complex models provides insight into

variables which drive or improve the predictability of LAI. Of these climate variables are

particularly interesting in that they are widely assumed to play a role in canopy

appearance and yet are rarely incorporated in empirical analysis. Difficulties exist in how

to characterize climate, i.e. in terms of rainfall or temperature, and on what temporal

scales it operates. Climate data necessarily suffers serial autocorrelation, a violation of

assumptions required for OLS regression.













Table 2-5. ANOVA analysis of highly significant variables in OLS multiple regression. Other, less significant variables not shown.


Df r2 Sum of Square Mean Square F-ratio Prob. level Power (5%)


Model Variable

FERT

PCTOT MAX

EXP

MAX
PBSTOT
TCA-3

TCA-3
PBLTOT
MAX

PASEND TCA-2

SR

PALEND TCA-3

Bl


69.48608

50.91658

33.25625

12.7119

7.697152

32.37256

16.85336

4.925346

11.53746

10.87232

3.284696


69.48608

50.91658

33.25625

12.7119

7.697152

32.37256

16.85336

4.925346

11.53746

10.87232

3.284696


286.143

209.674

136.949

51.476

31.169

51.311

26.713

23.39

23.087

21.756

15.599


<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

0.0002


1

1

1

1

0.9998

1

0.9993

0.9976

0.9973

0.9959

0.9737


0.22

0.1612

0.1053

0.149

0.0902

0.1572

0.0818

0.2165

0.2191

0.2065

0.1444









Sensitivity analysis of the GSP-LAI model indicates that a non-parametric, non-

linear technique can make use of that data at various lags, a tantalizing clue which should

inspire additional research (Table 2-6).

Table 2-6. Sensitivity analysis of variables used in ANN multiple regressions.
Model Label
Rank ASEND ALEND BSCLIM BLCLIM GSP-LAI
1 TCA-1 B2 BI END END
2 B5 TCA-3 B4 MAX FERT
3 B4 TCA-1 EXP-PHDI B7 B2
4 B2 SR TCA-3 LAG1-PHDI B5
5 TCA-2 TCA-2 SUM-EXP-PHDI B1 SPP
6 BI B4 B5 NDVI HERB
7 BI MIN MIN PHDI
8 EXP B3 TCA-1
9 LAG-PHDI SR MIN
10 TCA-2 PHDI B3
11 SR EXP-PHDI EXP
12 B7 TCA-3 EXP-PHDI
13 PHDI B2 SUM-EXP-PHDI
14 B2 TCA-2 LAG1-PHDI
15 B4 B7
16 LAG-PHDI
17 TCA-2
18 TCA-3
Variable codes appear in Appendix A.


The effectiveness of LAI predictions would be enhanced with a reduction of time

between the acquisition of remote sensing data and its analysis. The use of ground

referenced LAI from litterfall necessitates an 18 month lag in processing from collection

to value. Using optical methods to indirectly measure LAI in situ would likely reduce this

lag provided corrections as suggested by Gower et al (1999) were incorporated to

maintain accuracy.

With minor modification the GSP-LAI model can be adapted to new remote sensor

that share 'legacy' characteristics with TM and ETM+. Due to mechanical malfunctions









the ETM+ sensor has become an unreliable source of remote sensing data. Data captured

by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is

particularly interesting for this application. Aboard the TERRA platform, ASTER flies

the same orbit as Landsat and shares similar spectral, radiometric and temporal resolution

as ETM+ with recording at additional bandwidths. Integrating ASTER data into GSP-

LAI would allow for continuous analysis into the reasonable future.

The substantial LAI data collected by the researchers at IMPAC and other sites

should be maintained and expanded if possible. These sites should be oriented to Landsat

legacy coordinates, and a minimum size is recommended at 1.5 times the 30 m pixel

resolution, which would allow for the 0.5 pixel georectification error. Designed in this

fashion sites could serve to train and 'calibrate' existing and future LAI predicting

models.

Conclusions

The development of empirical models relating ground-referenced parameters to

remote sensing data may be greatly facilitated using multivariate regression techniques.

The specification of ancillary variables are an effective way to include the unique biology

of a given system, in this study represented by seasonal leaf dynamics, variation in local

climate and influential management practices. The use of these local variables was

essential for developing a model which met the objectives of multitemporal and spatial

applicability.

The evaluation of increasingly complex regression models was designed to expose

simple solutions to the problem of LAI prediction if they existed. In this study none were

found, and instead advanced non-linear techniques were required to incorporate






33


important data with non-normal distributions and multicollinearity such as serially

correlated climate data.














CHAPTER 3
REMOTE SENSING AND SIMULATION TO ESTIMATE FOREST PRODUCTIVITY
IN SOUTHERN PINE PLANTATIONS

Introduction

Pine plantations of the Southeastern United States constitute one-half of the world's

industrial forests and account for 60% of the timber products used in the United States

(Prestemon & Abt 2002). In Florida alone industrial timber is the leading agricultural

sector, generating $16.6 billion in revenues in 2003 (Hodges et al. 2005). Almost half the

State's land area is in forests concentrated in northern and central counties where this

study is centered.

Managing these forests for maximum yield is a primary economic goal of timber

interests; the rate at which these forests remove and sequester atmospheric carbon as

woody biomass is of interest to climate change researchers who recognize forests as the

only significant human-influenced sink of greenhouse gases (Tans & White 1998).

Sequestered carbon is likely to become another revenue source as the global community

endeavors to limit CO2 emissions through cap-and-trade carbon exchange schemes such

as those outlined by the Kyoto Protocol of 1997.

The net ecosystem exchange of carbon (NEE) in a landscape may be estimated

through simulation given the system is somewhat homogenous, well understood and

important biophysical parameters are known (Turner et al. 2004b). The SPM-2 model

(Cropper & Gholz 1993; Cropper 2000) estimates NEE for slash pine (Pinus elliottii)

plantations, a dominant plantation type in Florida and the subject of several studies









(Gholz et al. 1991; Teskey et al. 1994; Clark et al. 2001; Martin & Jokela 2004). SPM-2

simulates hourly fluxes of C02 and water, and accounts for the contributions of typical

understory components including saw palmetto (Serenoa repens), gallberry (Ilex galabra)

and wax myrtle (Myrica cerifera). Annual estimates of net ecosystem carbon exchange

simulated by SPM-2 matched measured values from an eddy covariance flux tower site

(Clark et al. 2001).

Although SPM-2 was originally designed to simulate individual stand dynamics it

may be scaled to broad biogeographical extents with inputs of spatially referenced leaf

area index (LAI) and stand age. LAI is the ratio of leaf surface supported by a plant to its

corresponding horizontal projection on the ground; as such LAI has direct

correspondence with the ability of the canopy to absorb light to conduct photosynthesis

(Asner & Wessman 1997).

LAI's contribution as a primary biophysical parameter in NEE simulation also

makes it an important indicator of productivity for land managers. Current silvicultural

practices focus on improving the availability of resources, through fertilization and

herbicidal control of understory, to increase stem growth. Sampson et al (1998) suggest

management for increased leaf growth could introduce efficiencies related to site growth

potential that would otherwise be missed.

LAI is difficult and expensive to assess in situ resulting in sparse sample sets that

are necessarily localized at a stand scale and thus difficult to extrapolate to larger extents

(Fassnacht et al. 1997). A model which determined LAI from remotely sensed data

would have the advantage of being spatially explicit, scaleable from stand to regional or

larger extents, and would sample remote or inaccessible areas (Running et al. 1986). An









ideal empirical model linking ground-referenced LAI to remote sensing data would be

make reliable predictions at various extents and image dates and be general enough to

incorporate important local information such as climatological and phenological data.

The generalized southern pine LAI predictive model (GSP-LAI) described in

Chapter 2 satisfies many of these criteria in that it uses Landsat Thematic Mapper (TM)

and Enhanced Thematic Mapper Plus (ETM+) imagery to make high resolution (30 m)

estimates of LAI for slash and loblolly plantations captured within the image's 185 km

wide swath. Climate variables are incorporated in the form of Palmer's Hydrological

Drought Index (Karl & Knight 1985) at image date and in various lags; categorical

variables representing phenological period and stand data such as age and silvicultural

treatments are also included.

With the input of spatially explicit LAI values NEE may also be simulated for the

same extent and resolution. Previous studies have estimated components of NEE with

coupled remote sensing and simulation model approaches for diverse forest stands with

multiple dominant species (Lucas et al. 2000; Smith et al. 2002; Turner et al. 2004a). The

GSP-LAI model was developed for loblolly and slash pine plantations and the SPM-2

models is limited to closed-canopy slash pine forests (age 8 or older). Slash pine

plantations are an important forest type in northern Florida, and the simple forest

ecosystem provides the potential for greater precision and for outputs relevant to

commercial forestry.

Objectives. In this study we apply the GSP-LAI model to a Landsat ETM+ image

of an extensive pine plantation holding in North-Central Florida and estimate 1) Leaf

Area Index and 2) NEE based on integration with the SPM-2 model.









Methods

Spatially explicit LAI values were estimated for the plantation pine within the

study extent using the GSP-LAI model and brightness values recorded by the Landsat 7

Enhanced Thematic Mapper Plus sensor on September 17, 2001. LAI values and stand

age were used to generate estimates of NEE using the slash pine specific forest

productivity model SPM-2.

Study Area

The study extent is comprised of a 178,655 ha (441,467 acre) landscape centered at

290 51.5' N, 820 10.7'W near Waldo, Florida USA (Figure 3-1). This extent contains

many classes of land cover/ land use including open water, urban and agricultural. Of

specific interest are 11,142 ha (27,520 acres) of intensively managed slash and loblolly

plantation forests which as of image date were closed canopy (8 years old or older). Of

this 83% was planted in slash and 17% loblolly pine. Other classes of forest were

excluded from analysis including natural regrowth areas, recently cut or planted stands,

and stands which contained other species of pine, such as longleaf pine (Pinuspalustris),

or hardwoods.

Stand data was provided by Rayonier, Inc. and indicated date of establishment,

planting density and silvicultural treatments, including date of fertilization or herbicide

application.

































































402214


Figure 3-1. Map of the Bradford Forest, Florida, USA. Yellow indicates forest extent;
background is a false color mosaic from Landsat ETM+.









Integration of Remote Sensing and Ground Referenced Data

The study extent was imaged by Landsat 7 Enhanced Thematic Mapper Plus

(ETM+) on September 17, 2001 at approximately 11:00 am on a cloudless day. The

image was geographically rectified using a second order polynomial equation with

between 30 and 40 ground control points. Rectification error reported as < 0.5 pixels.

Vector-based stand data was converted to raster format and matched to remote

sensing data in an overlay procedure within image processing software (Leica

Geosystems GIS and Mapping 2003). Ancillary information such as climatic and

phenological data was incorporated in the same manner. The resultant layer stack was

reported as a text file with over 150,000 rows of pixel information including coordinates

and imported into a Statistica spreadsheet (StatSoft 2004) where it was densified with

tassel cap components 1-3 (Huang et al. 2002).

Processing Data with the GSP-LAI and SPM-2 Models

The GSP-LAI model was employed within the Statistica neural network interface.

Resultant LAI values were reported in spreadsheet format and made ready for SPM-2 by

1) masking of non-forest pixel anomalies comprised of negative LAI values, and 2)

extraction of slash-only values.

Processing of LAI values and stand age resulted in an estimate of NEE in Mg ha-1

yr1 for each pixel defined by coordinates. Both NEE and LAI results were imported into

a geographic information system (ESRI 2003) and projected as a map.

Results

The GSP-LAI model estimated LAI for 10,797 ha (26,700 acres) of slash and

loblolly pine plantations. Values ranged from 0 to 3.93 with a mean of 1.06 (Figure 3-1).









Approximately 1% of the area analyzed exhibited very low LAI values (< 0.1) which

were associated with forest edges.

The SPM-2 model estimated NEE for plantation slash pine totaling 9,770 ha

(24,131 acres). Values ranged from -5.52 to 11.06 Mg ha-1 yr1 with a mean of 3.47 Mg

ha-1 yr1 (Figure 3-2). As with the LAI values very low NEE was exhibited at forest

edges. Approximately 1.6% of the area analyzed exhibited NEE values greater than 8.0

Mg ha-1 yr1, a maximum value reported by Starr et al (2003) from a Florida Ameriflux

study of slash pine in north-central Florida. Total carbon balance for the area analyzed is

33,920 metric tons representing 87,243 tons of CO2 or about 9 tons per acre.

By means of associated map coordinates these values were categorized and

displayed on a map along with the Landsat image used as the primary data source (Figure

3-3, 3-4).

Discussion

The feasibility of estimating forest productivity in terms of NEE was demonstrated

using empirical and simulation models based on remotely sensed data. Despite our

inability to ground-truth the resultant values for LAI and NEE are plausible and in the

realm of expected values. The utility of these estimates is enhanced by their landscape

scale and that carbon gain and loss are attributed to specific stands and ownership. These

results offer proof of concept and further work is encouraged.

Based on the May 27, 2005 price of $1.30 per 100 T C02 the estimated value of

carbon sequestered in this analysis is $102,891.10 or $4.26 per acre (Chicago Climate

Exchange 2005).





















35000


30000


25000


m 20000
0
0
S15000


10000


5000


0


26000

24000

22000

20000

18000

16000

14000

12000

10000

8000

6000

4000

2000

0


I



-4 -2 0 1 2 3 4
NEE


5 6 7 8 9 10


Figure 3-1. Predicted LAI values for closed canopy slash and

loblolly pine. Bradford FL


Figure 3-2. Predicted NEE values for closed canopy slash and

loblolly pine. Bradford FL


00 05 10 15 20 25 30 35 40




















397214


377214


382214 387214 392214 397214
Landsat ETM+ Imagery UTM 17N Resolutin 30m, RGB=4,3,2 Scale Units Meters
Leaf Area Index


= 00-05 1 106- 1 11 -15 1 16-2 21


402214 -'



25 26-3


Figure 3-3. Predicted LAI values for southern pine plantations in north-central Florida

for September 17, 2001


372214


372214


377214


382214


387214


392214


402214

















379093---' 380593- 382093 .. 383593 '' 385093---' 386593


379093 380593 382093 383593 385093 386593.. 388093
Landsat ETM+ Imagery UTM 17NResoluton 30m RGB=4,3,2 Scab Units Meters


Net Ecosystem Exchange


389593 391093

8


=-30 i -1 0 to-3 0 -1 0 to 1 0 10to30 30oto50 50to 80
Negative values
indicate
loss to atmosphere





Figure 3-4. Predicted NEE values for southern pine plantations in north-central
Florida for September 17, 2001.


388093 .. 389593-'-, 391n93-









Visual analysis of the map (Figure 3-4.) reveals low LAI and NEE values along

logging roads and for other mixed pixels representing partial contributions of forest.

These values were not masked as they represent valid data and offer some confidence that

the models are selective and appropriate.

The bimodal distribution of LAI values in Figure 3-1 can be traced to the effect of

the variable fertilizer on the model (Figure 3-3). Fertilization is known to increase LAI in

slash and loblolly (Martin & Jokela 2004); however ground truthing is needed to assess

how close model predictions are to observations. Fertilization is a focal treatment in

intensive management practices, and indications of canopy response could lead to

efficiencies in the location and frequency of application. The availability of reliable LAI

data could lead to a paradigm change in management practices were the goal becomes

optimization of leaf growth based on site potential.

The conceptual framework presented here represents one way by which carbon

sequestration may be monitored and inventoried, providing necessary underpinning for

carbon trading schemes. Landscape-scale valuations of carbon sinks could lead to a

revaluation of ecosystem services as nations acknowledge the benefits of removing

greenhouse gases from the atmosphere.

Conclusions

This work provides a conceptual model whereby forest productivity may be

estimated for a forest system using an empirically derived LAI prediction model and a

process simulation model. Spatially explicit results of LAI and NEE values relate

important forest attributes to specific ownership creating new opportunities for improved

management.





































0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


Absence of Fertilization


50000

45000

40000

35000

30000

25000

20000

15000

10000

5000

0


Presence of Fertilization


Figure 3-5. Effect of variable FERT on LAI prediction.


0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0














CHAPTER 4
SYNTHESIS

Results and Conclusions

In this study we developed an LAI prediction model which was novel in many

respects: it used an advance regression technique to establish a non-linear relationship

between the dependent and independent variables; the independent variables included

important local information, an example being climate data, which is a widely recognized

yet seldom employed driver of all things vegetative; models underwent a validation

process. The GSP-LAI model represents an improvement over previous efforts in our

study system.

The requirement of stand data by GSP-LAI may be criticized researchers desirous

of LAI determination without apriori knowledge. The stratified model methodology

illustrated that only tenuous relationships were established with remote sensing data only;

furthermore significant explanatory improvements (r2> 0.1) are realized simply through

the incorporation of basic phenology as indicated by image date.

The visualization of net ecosystem exchange of carbon via a map represents an

advance in our management of slash pine carbon sequestration. It is noteworthy that these

carbon totals are linked to specific ownership. It is foreseeable that industry rather than

academia will advance carbon sequestration research once the perceived values of forest

properties adjust to these new appraisals.

Pragmatically the availability of timely LAI data might influence a paradigm shift

among forest managers away from current goals emphasizing resource availability









through fertilization and herbicide application, to an integrated approach that considers

canopy response to treatments in the context of site potential and biological potential.

Management approaches of this type are likely to improve yield while decreasing

expense and impact on the environment.

Further Study

The substantial LAI data collected by the IMPAC and other sites should be

maintained and expanded if possible. These sites should be oriented to Landsat legacy

coordinates, and a minimum size is recommended at 1.5 times the 30 m pixel resolution,

which would allow for the 0.5 pixel georectification error. Designed in this fashion sites

could serve to train and 'calibrate' existing and future LAI predicting models.

As technology advances higher quality remote sensing data is becoming available.

Data from the Advanced Spaceborne Thermal Emission and Reflection Radiometer

(ASTER) sensor integrates well with Landsat legacy operations yet offers an additional 7

bandwidths for analysis. Physical tree structure below the canopy is being recorded with

light detecting and ranging (LIDAR) sensors. Many of the techniques presented in this

study are able to integrate data from disparate sources.















APPENDIX A
VARIABLES USED IN MODELS













Variable
Band 1
Band 2
Band 3
Band 4
Band 5
Band 6
Band 7
Normalized
Difference
Vegetative
Index
Simple Ratio
Tasseled Cap
Analysis
Component 1
Tasseled Cap
Analysis
Component 2
Tasseled Cap
Analysis
Component 3
Species

Fertilizer


Tag
Bl
B2
B3
B4
B5
B6
B7


NDVI


SR

TCA-1


TCA-2


TCA-3


SPP

FERT


Herbicide HERB


Type
Continuous
Continuous
Continuous
Continuous
Continuous
Continuous
Continuous


Continuous


Continuous

Continuous


Continuous


Continuous


Categorical

Categorical

Categorical


Equation/ Bandwidth
0.45 0.524m Blue
0.52 0.60tm Green
0.60 0.63tm Red
0.69 0.76tm Near infrared
1.55 1.75pm Mid infrared
10.5 12.5am Emitted thermal
2.08 2.35am Mid infrared


(B4 B3)/(B4 + B3)


B4/B3
0.2043(B1) + 0.4158(B2) +
0.5524(B3) + 0.5741(B4) +
0.3124(B5) + 0.2303(B7)
(-0.1603(B1)) + (-0.2819(B2))
+ (-0.4934(B3)) + 0.7940(B4)
+ 0.0002(B5) + (-0.1446(B7))
0.0315(B1) + 0.2021(B2) +
0.3102(B3) + 0.1594(B4) + (-
0.6806(B5)) + (-0.6109(B7))
Loblolly = 1
Slash = 0
Fertilized = 1
Not Fertilized = 0
Treated = 1
Untreated = 0


Range
0 -255
0 -255
0 -255
0 -255
0 -255


Notes
Surface reflectance, 8-byte
rr rr


Variable not used due to severe
0 255
spatial autocorrelation
0 255 Surface reflectance, 8-byte


-1.0-
1.0

0 -255











N/A

N/A


N/A


Vegetation index


Vegetation index
n-space vegetation index:
"Brightness"

n-space vegetation index:
"Greenness"

n-space vegetation index:
"Wetness"

Type of tree

Based on previous season

Maintained understory control













Minimum
LAI
period
Expanding
LAI period
Maximum
LAI period

Declining
LAI period

Palmer
Hydrological
Drought
Index
One year lag
PHDI
Expansion
period PHDI
Previous
season
expansion
period PHDI
Two
consecutive
years
expansion
period PHDI


MIN


EXP

MAX


END


PHDI


LAG PHDI


EXP PHDI


LAG1 PHD
I



SUM PHDI


Categorical


Categorical

Categorical


Categorical


Continuous


Continuous


Continuous
Interactive


Continuous
Interactive



Continuous
Interactive


Within Minimum = 1
Other periods = 0
Within Expansion = 1
Other periods = 0
Within Maximum = 1
Other periods = 0

Within needlefall = 1
Other periods = 0


Values generated by NOAA


Monthly PHDI- 1 year

Average PHDI for March,
April, May


Lagged Average PHDI for
March, April, May



Sum Lagged Average PHDI
for March, April, May


S Minimum leaf biomass; spans
N/A
March through April in region

N/A Increasing leafbiomass; spans
May through June in region
A Maximum leaf biomass; spans
July through September
Minimum leafbiomass; spans
SOctober through February in
study area. Implicit in multiple
regressions
Monthly: indicates severity of
-7.0 dry and wet spells; dry negative
7.0 values, wet positive values,
norms z zero


-7.0-
7.0
-21.0-
21.0


-21.0-
21.0



-42.0-
42.0


Previous year's PHDI
PHDI during leaf expansion;
interacts with phenological
period.
PHDI during leaf expansion;
interacts with phenological
period.


PHDI during leaf expansion;
interacts with phenological
period.














APPENDIX B
GSP-LAI CODE

Note: this code written in python.


from Numeric import *
import math


class Predict LAI:

"' prediction of LAI by Artifical Neural Network model
GSP-LAI model is 18:16:7:1 18 inputs, 2 hidden layers and 1 output
Doug Shoemaker and Wendell Cropper June, 2005"'


def init (self):



self.pattern = [25.0, 24.0, 48.0, 14.0, 101.1557, 9.9365,
4.0215, -0.63, -1.25, -4.94, -4.94,
-4.94, 0, 1, 1, 1, 0, 0]

self.in labels = ['B2 ','B3 ','B5 ','B7 ','TCA1 ','TCA2 ','TCA3 ','PHDI ','LAGPHDI',
'EXP PHDI','LAG1 PHDI','SUM EXP PHDI','SPP','FERT','HERB','MIN LAI',
EXPLAIN' 'END ']


self.N_hidden = [16, 7] #number of nodes in each hidden layer; in order
# e.g., [4, 6, 9] for three layers
self.Ninput = 18

self.Nlayers = 2 # number of hidden layers

self.afunc = [self.activ, self.activ] # each layer may have a separate activation
function
# [self.activ, self.activ, self.a2] for example


self.W = zeros((self.Ninput + 1, self.Nhidden[0]), Float32)









self.W2 = zeros((self.N hidden[0] + 1, self.N hidden[l]), Float32)
self.WO = zeros((self.N hidden[l] + 1), Float32)

#weights from input to hidden


self.W[0][0] =
self.W[2][0] =
self.W[4][0] =
self.W[6][0] =
self.W[8][0] =
self.W[10][0]
self.W[12][0]
self.W[14][0]
self.W[16][0]
self.W[18][0]


-0.68070867581967331; self.W[1][0] = -0.47077273479909026
-0.85230477952479411; self.W[3][0] = 0.33897992017428513
0.27701895076167499; self.W[5][0]= -1.0572088503393293
0.36528134122444544; self.W[7][0] = -0.99617510476443649
-0.50428492164536609; self.W[9][0] = -0.18280550315894767
= -0.94167697838932418; self.W[11][0] = 0.98202982430634478
= 0.61440222032592962; self.W[13][0]= 1.1844340063249028
= -0.25002768723088353; self.W[15][0] = 0.63030042820138565
= 0.51299032922949417; self.W[17][0] = 0.44325306956489968
= 0.2248803488147274 #bias weight input should be 1.0


# NOTE: the bias (Threshold weight signs have been reversed (* -1)
# from the Statistica program c code to match the algorithm in SNNCode.cc


self.W[0][1] =
self.W[2][1] =
self.W[4][1] =
self.W[6][1] =
self.W[8][1] =
self.W[10][1]
self.W[12][1]
self.W[14[1]
self.W[16][1]
self.W[18][1]

self.W[0][2] =
self.W[2]1[2]=
self.W[4][2] =
self.W[6][2] =
self.W[8][2] =
self.W[10][2]
self.W[12][2]
self.W[14][2]
self.W[16][2]
self.W[18][2]

self.W[0][3] =
self.W[2][3] =
self.W[4][3] =
self.W[6][3] =
self.W[8][3] =


0.51346930771036581; self.W[1][1]= -0.82554800347023094
0.90426603023396934; self.W[3][1] = 0.58889085506156402
-0.95958368729266708; self.W[5][1] =-0.90469199829822045
-0.14307625257737089; self.W[7][1]= -0.20554967720687164
-0.21554929367886586; self.W[9][1] =-0.34579555496400843
= 0.83046571076512765; self.W[11][1] =0.32340290066403304
= -0.18118559428067804; self.W[13][1] = -0.75238704258583811
= -0.37747431711820228; self.W[15][1] = 0.85923511162687338
= 0.39065411751788415; self.W[17][1] = -0.20355515889674639
= 1.0246810022363515 #bias weight input should be 1.0

-0.35311763505484994; self.W[1][2] = -0.4386456022349271
-0.87637948900026352; self.W[3][2] = -0.72428696217924937
-0.31671942062831882; self.W[5][2] = 0.05527068372351699
0.56535409825860228; self.W[7][2] = 0.51021420192585065
0.016770303367016015; self.W[9][2] = 0.34584426212393066
= -0.2487170315158326; self.W[11][2]= -0.10550485203992196
= -0.48798944879736178; self.W[13][2] = -0.6190887070661879
= -0.22993121833505939; self.W[15][2] = 0.50627708251063963
= -1.0785292527624635; self.W[17][2] = 0.033937996367607123
= 0.65202105499593555 #bias weight input should be 1.0


-1.0409218053604059; self.W[1][3]
0.33260785739356169; self.W[3][3]
-0.64306159332498813; selfW[5][3]
-0.78619166931548001; self.W[7][3]
-0.30551820237080174; self.W[9][3]


-1.0248054352063849
:-0.26650614694911684
= -0.59743303482074173
=0.45658535946357542
=0.99383562833852823









self.W[10][3]
self.W[12][3]
self.W[14][3]
self.W[16][3]
self.W[18][3]

self.W[][4] =
self.W[2][4]=
self.W[4][4]=
self.W[6][4] =
self.W[8][4] =
self.W[10][4]
self.W[12][4]
self.W[14][4]
self.W[16][4]
self.W[18][4]

self.W[0][5] =
self.W[2][5]=
self.W[4][5]=
self.W[6][5] =
self.W[8][5]=
self.W[10][5]
self.W[12][5]
self.W[14][5]
self.W[16][5]
self.W[18][5]

self.W[0][6] =
self.W[2][6]=
self.W[4][6] =
self.W[6][6] =
self.W[8][6] =
self.W[10][6]
self.W[12][6]
self.W[14][6]
self.W[16][6]
self.W[18][6]

self.W[O][7] =
self.W[2][7] =
self.W[4][7] =
self.W[6][7] =
self.W[8][7] =
self.W[10][7]
self.W[12][7]


= 0.58314990180960924; self.W[11][3] = 0.37535417400887111
=-0.28530757703577508; self.W[13][3] -0.090269033578186067
= 0.064328952896598818; self.W[15][3] = 0.97787174712308034
= 0.19248517688726832; self.W[17][3] = 0.33429026289740676
= -0.035729304447247368 #bias weight input should be 1.0

-0.69171961247455427; self.W[1][4] = -0.19318811287043236
-0.24535334151780164; self.W[3][4] = 0.83124440482653728
-0.25125881212500051; self.W[5][4] = 0.67654822161911254
1.1935093304341891; self.W[7][4]= -0.1061578514825464
0.97769969375119914; self.W[9][4] = -0.62531219673983507
= 0.44887478855493629; self.W[11][4] = 0.25089122271948444
= 0.39739937692561506; self.W[13][4] = -0.11329258567683172
=-0.58529954873398038; self.W[15][4] = 1.0085035066605659
= 0.16742174428496126; self.W[17][4] = 0.58995422198121061
= 0.3348083808274705 #bias weight input should be 1.0

-0.77429576139488687; self.W[1][5]= -0.15475931985401509
0.73579372223419681; self.W[3][5] = 0.1381863709121455
0.6873206129011652; self.W[5][5] = 0.46745295715611929
0.41009374571990187; self.W[7][5] = -0.87188230719585069
-0.72335484095791835; self.W[9][5] = -0.91529433041239316
= -0.58370952581324753; self.W[11][5]= -0.67397946658272845
= -0.34210837715877956; self.W[13][5] = -0.41773337644458219
= 0.47038952274991436; self.W[15][5] = 0.093448267923307141
= 0.26835793839884453; self.W[17][5] = 0.22325046302604781
= -1.0210341534849725 #bias weight input should be 1.0

0.080858496314387546; self.W[1][6] = 0.0084803147734866177
-0.45972948915316991; self.W[3][6]= -1.0221823283337763
-0.011916970527570785; self.W[5][6] = 0.2898749572896876
-0.70301410605914416; self.W[7][6] =-0.96795643773447171
0.19725907114720687; self.W[9][6] = 0.20975438358448029
= 0.36924810928999657; self.W[11][6] = -0.10139479969175098
= -0.060662670497412904; self.W[13][6] = -0.34857292408604584
= -0.58353859501523964; self.W[15][6] = -0.41258775067250342
= 0.91182517839270993; self.W[17][6] = -0.56916166564089354
=-1.0285604223454949 #bias weight input should be 1.0

-0.32865925594153583; self.W[1][7] = 0.04942365443898445
0.94576664098391583; self.W[3][7]= -0.52058188611049716
0.34173019628887918; self.W[5][7] = 0.23316279649833077
0.93354218924489529; self.W[7][7] = -0.3672399273616016
0.24492040865298623; self.W[9][7] = 0.62309764743750939
= -0.31738646556078642; self.W[11][7] = 0.49240143356911215
= -0.63613804743008662; self.W[13][7] = 0.27255090370977308









self.W[14][7] = -0.077490270085429441; self.W[15][7] = 0.03996644688196864
self.W[16][7]= -0.42607929700787811; self.W[17][7]= 0.070260106536832997
self.W[18][7] = 0.68278617148868181 #bias weight input should be 1.0

self.W[O][8] = -0.5203133183715809; self.W[1][8] = 0.76526828167302097
self.W[2][8] =0.11362124877625604; self.W[3][8] = 0.93936007101853969
self.W[4][8]= -0.32325776716962157; self.W[5][8]= -0.50373426830327472
self.W[6][8]= -0.61124578984982036; self.W[7][8]= -0.55151966342108183
self.W[8][8] =-0.50104432378214458; self.W[9][8] =-0.30459007736977906
self.W[10][8]= -0.3159522940418959; self.W[11][8]= -0.065342188976498211
self.W[12][8] = 0.39061159628437425; self.W[13][8] = 0.59170422967153369
self.W[14][8] = -0.16956740248484886; self.W[15][8] = 0.18794488956438776
self.W[16][8] = -0.34436713394629842; self.W[17][8] = 0.63513932853507671
self.W[18][8] = 0.30307186938747249 #bias weight input should be 1.0

self.W[0][9] = -0.8275124467384023; self.W[1][9] = -0.11677639936330871
self.W[2][9] = -0.1251652096057006; self.W[3][9] = -0.34447644211000494
self.W[4][9] = 0.44231016923933497; self.W[5][9] = -0.67835978699981769
self.W[6][9] = 0.10671669828894725; self.W[7][9] = 0.052493351739184235
self.W[8][9] = -0.13220081875069595; self.W[9][9] = -0.37290173453154851
self.W[10][9]= 0.037026514129265595; self.W[11][9] = -0.38829556664334314
self.W[12][9]= -0.41969064484146179; self.W[13][9]= 1.0370135682327706
self.W[14][9] = 0.72233117331089669; self.W[15][9] = -0.26787152887521748
self.W[16][9]= -0.032418233516579437; self.W[17][9] = -0.47082294426757276
self.W[18][9] = 0.58984303347455413 #bias weight input should be 1.0

self.W[O][10] = 0.99545420020183517; self.W[1][10] = 0.40670899831678181
self.W[2][10] = 0.11853073510231668; self.W[3][10] = 0.58812453777427598
self.W[4][10] = -0.79645600422265672; self.W[5][10] = 0.25972144416010789
self.W[6][10]= -0.74823811652818473; self.W[7][10]= 0.60024217417752057
self.W[8][10] = -0.0073119157875114237; self.W[9][10] = 0.84124958610319833
self.W[10][10] = -0.2617949002805095; self.W[11][10] = 0.64006977894777428
self.W[12][10] = 0.9477926706115315; self.W[13][10] = -0.29951602470691668
self.W[14][10] = 0.30016030289901718; self.W[15][10] = -0.83346922323500006
self.W[16][10] = 0.17169493427772073; self.W[17][10] = 0.40107106183219271
self.W[18][10] = 0.70903533284002751 #bias weight input should be 1.0

self.W[O][11] = -1.142759022542396; self.W[1][11] =0.44985414251574563
self.W[2][11]= 0.3895513876502969; self.W[3][1 1] =-1.226383084875748
self.W[4] [ 1] =-0.92868023640950426; self.W[5][ 1] = -0.49184381233707225
self.W[6][11] = 0.17925844190885934; self.W[7][11] = -0.20505890929724421
self.W[8][11] = 0.64675932461962349; self.W[9][11] = 0.14682528315075502
self.W[10][11] = 0.035955907391130484; self.W[11][11] = -0.24746822575992516
self.W[12][1 1] = -0.50773043572067322; self.W[13][ 1] =0.24967556622437737
self.W[14][11]= 0.80942581518738244; self.W[15][11]= 0.69574565324455129
self.W[16][11]= 0.23778917275425218; self.W[17][11]= 0.89204034325895742









self.W[18][11] = 0.2218448568058044 #bias weight input should be 1.0


self.W[0][12] =
self.W[2][12]=
self.W[4][12] =
self.W[6][12] =
self.W[8][12] =
self.W[10][12]
self.W[12][12]
self.W[14][12]
self.W[16][12]
self.W[18][12]

self.W[0][13]
self.W[2][13]
self.W[4][13]
self.W[6][13] =
self.W[8][13] =
self.W[10][13]
self.W[12][13]
self.W[14][13]
self.W[16][13]
self.W[18][13]

self.W[O][14]=
self.W[2][14] =
self.W[4][14] =
self.W[6][14] =
self.W[8][14] =
self.W[10][14]
self.W[12][14]
self.W[14][14]
self.W[16][14]
self.W[18][14]

self.W[O][15]=
self.W[2][15]=
self.W[4][15]=
self.W[6][15]=
self.W[8][15]=
self.W[10][15]
self.W[12][15]
self.W[14][15]
self.W[16][15]
self.W[18][15]


-0.35511846140043241; self.W[1][12] = 0.70733180758484104
-0.83165126184425742; self.W[3][12] = -0.83504960919917026
-0.13755256747487241; self.W[5][12] = -0.52966103620956229
0.25071078472815855; self.W[7][12] = -0.35216098305186072
0.088542557230076688; self.W[9][12] =-1.1040221735380804
= 0.79594009769706098; self.W[11][12] = -0.73714848198026295
= -0.18180847746449641; self.W[13][12] = 0.41331841770555355
= 0.41428659784606314; self.W[15][12] = -0.4290960896492258
= -0.98897305155024584; self.W[17][12] = 0.78215239795834623
= -0.44364199938191162 #bias weight input should be 1.0

0.79858959493477089; self.W[1][13] = 0.10650095639849158
0.41879177374855703; self.W[3][13] = 1.0263932028577394
0.189570080155397; self.W[5][13] =-0.44376619219939994
-0.60203148870373557; self.W[7][13] = 0.74519204084468549
0.20937947312546459; self.W[9][13] = -0.73403570501855497
= 0.030778866771470657; self.W[11][13] = 0.28322753361566022
= 0.92880385369204232; self.W[13][13] = 0.1644240293137085
= -0.21608287824017328; self.W[15][13]= -0.2904478515294443
=-0.41154041855238949; self.W[17][13]= 0.90293535522249624
= 0.97015377694600791 #bias weight input should be 1.0

-1.0325407768158865; self.W[1][14]= -0.84527794204417972
-0.25248895386672582; self.W[3][14] = 0.47151219855652071
-0.94815743730612323; self.W[5][14] = 0.067206226767283619
0.54728649621049807; self.W[7][14] = -0.87468384013164791
-0.0083579697762564686; self.W[9][14] = 0.74901199144024511
= -0.63222006168505462; self.W[11][14] = -0.87475753047840932
= 0.9016299328644094; self.W[13][14] = -0.11257067471748695
= -0.27838527717268613; self.W[15][14] = 0.95224921487717162
=0.50084256089794099; self.W[17][14] =-0.71743881771230811
= -0.02701900591046871 #bias weight input should be 1.0

1.0437741273389674; self.W[1][15] =-0.45408494721878151
0.96511020810437909; self.W[3][15] =-0.30063151326050935
-0.071082781756073923; self.W[5][15] = 0.2447287444213701
-0.24195063780165757; self.W[7][15] = 0.98824904641780897
0.74073183617769423; self.W[9][15] = 0.43863706340778019
=-1.0108726386238427; self.W[11][15] = -0.79646911633394357
= -0.36001428038607081; self.W[13][15] = 0.17255191773894921
= -0.16546627399110897; self.W[15][15]= -0.3996833211136836
= -1.2185776823559316; self.W[17][15] = -0.1455316758747702
= 1.1403808043303105 #bias weight input should be 1.0









self.W2[0][0] =
self.W2[2][0]=
self.W2[4][0]=
self.W2[6][0]=
self.W2[8] [0]=
self.W2[10][0]
self.W2[12][0]
self.W2[14][0]
self.W2[16][0]

self.W2[0][1]=
self.W2[2][1] =
self.W2[4][1] =
self.W2[6][1] =
self.W2[8][1] =
self.W2[10][1]
self.W2[12][1]
self.W2[14][1]
self.W2[16][1]

self.W2[0][2] =
self.W2[2]1[2]=
self.W2[4]1[2]=
self.W2[6]1[2]=
self.W2[8][2]=
self.W2[10][2]
self.W2[12][2]
self.W2[14][2]
self.W2[16][2]

self.W2[0][3] =
self.W2[2][3]
self.W2[4][3] =
self.W2[6][3] =
self.W2[8][3]=
self.W2[10][3]
self.W2[12][3]
self.W2[14][3]
self.W2[16][3]

self.W2[][4] =
self.W2[2][4] =
self.W2[4] [4]=
self.W2[6][4] =
self.W2[8][4] =
self.W2[10][4]


-0.84028171889997116; self.W2[1][0] = -0.43346076499958708
-0.43557589480677411; self.W2[3][0] = -0.42513219690958287
0.54188493979188723; self.W2[5][0]= -0.046737792182397153
-0.80478664818881229; self.W2[7][0]= -0.678851216176377
0.71149222702874249; self.W2[9][0] = 0.68341599319600177
= 1.0328752945835469; self.W2[11][0] = 0.24740667798727475
= -0.2469023592420069; self.W2[13][0] = 0.508095168051796
=-0.69387411534727783; self.W2[15][0] = 0.19338083305716081
=0.18211612650330075 #bias weight input should be 1.0

0.2859958155039441; self.W2[1][1] = 0.24091476574654414
0.91115699781689941; self.W2[3][1] = 0.48388496460003888
-0.68637080910887738; self.W2[5][1] =0.61678116159010321
0.071795625009126882; self.W2[7][1] -0.73207375760099258
0.6556064256037778; self.W2[9][1]= -0.44088680852652473
= -0.20501788340358035; self.W2[11][1]= -0.4010598542444288
=-0.45119284181746144; self.W2[13][1] = 0.52587578563884863
= -0.22088901355724097; self.W2[15][1] = 0.2495482636642444
=-0.60347877573598951 #bias weight input should be 1.0

0.42336720355483193; self.W2[1][2] = 0.50245942687953626
0.21654723337885157; self.W2[3][2] = 0.70531360649670838
0.093535694516742818; self.W2[5][2] = -0.21420036356255232
-0.012639507473030611; self.W2[7][2] = 0.31554596948648805
-0.0040929337148137854; self.W2[9][2]= -0.17044839540087706
= 0.46951908908293116; self.W2[11][2] = -0.66754027180472342
= 0.82473208826382194; self.W2[13][2] = -0.1571156431250397
= -0.42213152740242382; self.W2[15][2] = 0.79329857749148425
= 0.80557575135338377 #bias weight input should be 1.0

-0.13255563062284348; self.W2[1][3] = 0.37810476302366636
0.21070959566965541; self.W2[3][3] = -0.89366749130281953
1.0078487477830862; self.W2[5][3] = 0.42900826466769421
0.39769863416066875; self.W2[7][3] = -0.49379617511626256
0.26323002509449323; self.W2[9][3] =-0.37429078671305493
= 0.86815937993400716; self.W2[11][3] = -0.59414843110057125
= 0.51956225729714856; self.W2[13][3] = -0.34767642086198647
= -1.0664791956925401; self.W2[15][3] = 0.81194836042924168
= 0.38600602910012766 #bias weight input should be 1.0

-0.7852457933457988; self.W2[1][4] = 0.67182369199536496
0.11976172539016033; self.W2[3][4] = -0.35345828007455571
-0.75884001297513415; self.W2[5][4]= -0.68270928953850274
0.039984026585529499; self.W2[7][4] = 0.1324556886239189
-0.42219247413963362; self.W2[9][4] = 0.76451311676056533
= 0.67287618465966093; self.W2[11][4] = 0.17620257431174735









self.W2[12][4]
self.W2[14][4]
self.W2[16][4]

self.W2[0][5]=
self.W2[2][5]=
self.W2[4][5]=
self.W2[6][5] =
self.W2[8][5] =
self.W2[10][5]
self.W2[12][5]
self.W2[14][5]
self.W2[16][5]

self.W2[0][6] =
self.W2[2][6] =
self.W2[4] [6]=
self.W2[6][6] =
self.W2[8][6] =
self.W2[10][6]
self.W2[12][6]
self.W2[14][6]
self.W2[16][6]


= -0.37423290298627587; self.W2[13][4] = 0.15449217725083536
= 0.15546713985527782; self.W2[15][4] = 0.94462533981671326
= 0.52053670319683165 #bias weight input should be 1.0

-0.11383317674524207; self.W2[1][5] = 1.093880403742064
0.48574982685208123; self.W2[3][5]= -0.36562169083116408
0.8476825029450753; self.W2[5][5] = -0.2273487774476374
-0.84103370298577607; self.W2[7][5] = -0.47561685116962277
0.76334113447610374; self.W2[9][5] = 0.5048639068148526
= -0.53656874325571335; self.W2[11][5] = -0.33513742916677347
= -0.28172906506309481; self.W2[13][5] = -0.76272398129498198
= -0.66025788802885732; self.W2[15][5] = 0.95701289266244449
= -0.3592191351002838 #bias weight input should be 1.0

-0.21764607397928706; self.W2[1][6] = 0.75056281843678718
-0.55413003683237416; self.W2[3][6]= -0.13285829175998887
0.58529457481651215; self.W2[5][6]= -0.7624180695963737
0.31736963218013603; self.W2[7][6] = -0.9402512575105112
-0.67112980522916854; self.W2[9][6] = -0.7235067875934823
= -0.26022571343166184; self.W2[11][6] = -0.43886863821482747
= 0.3063464033973422; self.W2[13][6] = -0.58939225217425462
= 0.45724366645921521; self.W2[15][6] = 0.5685444957630944
= -0.88450826792892168 #bias weight input should be 1.0


self.wts = [self.W, self.W2] #list of weight arrays for each layer; in order
# [W, W2, W3] for three hidden layers


#weights from hidden to output


self.WO[0]
self.WO[1]
self.WO[2]
self.WO[3]
self.WO[4]
self.WO[5]
self.WO[6]
self.WO[7]


-0.26706611706223854
-0.42003016388263759
0.72028255111376516
0.28335883323926864
-0.89717920199668166
-0.49025758877601794
-0.38930986874947926
0.30361700984309659 #bias sign change !to subtract threshold


def scaler(self):

'" linear scaling of input values; -9999 is missing value '"


missing = [0.27413464591933939, 0.30335820895522386, 0.31809701492537301,









0.26026119402985076, 0.37654065907577805, 0.65600816582363053,
0.65964013022874357, 0.50367098331870064, 0.37765094021418316,
0.4680048264547062, 0.50156899600184768, 0.58077275397528705 ]

# slope and intercept for scaling inputs

lineareq= {0:(0.021276595744680851, -0.34042553191489361), 1:(0.025, -0.3),
2:(0.020833333333333332, -0.4375), 3:(0.03125, -0.125),
4:(0.011224516139170531,-0.67367525454396482),
5:(0.027361802376646153, 0.50862854437947536),
6:(0.028418294561306793, 0.30574390569673132),
7:(0.14705882352941174, 0.5911764705882353),
8:(0.14124293785310735, 0.43926553672316382),
9:(0.053361792956243326, 0.50266808964781207),
10:(0.053361792956243326, 0.50266808964781207),
11:(0.033355570380253496, 0.59239492995330223) }

categ_eq = {0:0.45149253731343286, 1:0.39925373134328357,
2:0.48134328358208955, 3:0.15298507462686567,
4:0.089552238805970144, 5:0.55970149253731338}

lines = len(missing)

for i in range(lineqs):

if self.pattern[i] == -9999:
self.pattern[i] = missing[i]
else:
self.patter[i] = self.pattern[i] lineareq[i][0] + linear eq[i][1]


for i in range(len(categ_eq)):

if self.pattern[i + lines] == 0:

self.patter[i + lines] = categ_eq[i]

elif self.pattern[i + lines] == 1:

self.pattern[i + lines] = 0

else:


self.pattern[i + lines]









#print self.pattern


def activ(self, x):

"' sigmoidal activation: inputs to hidden '"

ifx > 100.0: x = 1.0
ifx < -100.0: x = -1.0

el = math.exp(x)
e2 = math.exp(-x)

#print x, el, e2

return (el e2) / (el + e2)


deflayerX(self, nh, invalues, W, activ): #number hidden nodes in layer,
# of inputs, Wt matrix, activation func

'" from inputs to hidden layer '"


hidden = matrixmultiply(invalues, W)

#print hidden

for i in range(len(hidden)):

hidden[i] = activ(hidden[i])

#print hidden[i]

hidden = zeros((nh + 1), Float32)

hidden2[nh] = 1.0 #bias or threshold input

for i in range(nh):

hidden2[i] = hidden[i]

return hidden


def layer out(self):











self.pattern.append(1.0) #bias or threshold input

inputs = self.pattern

for i in range(self.Nlayers):


inputs = self.layerX(self.Nhidden[i], inputs, self.wts[i], self.afunc[i])


return matrixmultiply(inputs, self.WO)



def outscale(self, x):

'" inverse scaling to get LAI output '"

self. prediction = (x + 0.099788683247846094)/ 0.23868893546020067


def predict(self):

self. scaler) # scale input pattern
x = self.layerout( #apply weights and activation function
self.outscale(x) # predict LAI (self.prediction)




if name ==' main ':

test = PredictLAI()
test.predicto
print "LAI for test pattern should be 1.41547"
print "This program calculates: "
print test.prediction
print '
test.pattern = []
for i in range(18):
x = rawinput(test.inlabels[i])
x = float(x)
test. pattern. append(x)
print '






61


test.predicto
print 'LAI= ',test.prediction
zzz = raw input('DONE')















LIST OF REFERENCES


Anselin L. (2003) GEODA 0.9 User's Guide. University of Illinois, Urbana-Champaign,
IL

Asner G.P. & Wessman C.A. (1997) Scaling PAR Absorption from the Leaf to
Landscape Level in Spatially Heterogeneous Ecosystems. Ecological Modelling,
103, 81-97

Birth G.S. & Mcvey G.R. (1968) Measuring Color of Growing Turf with a Reflectance
Spectrophotometer. Agronomy Journal, 60, 640-649

Chicago Climate Exchange (2005) Carbon Financial Instrument Market Data
http://www.chicagoclimatex.com/trading/stats/daily/index.html: May 30, 2005

Clark K.L., Cropper W.P. & Gholz H.L. (2001) Evaluation of Modeled Carbon Fluxes
for a Slash Pine Ecosystem: SPM2 Simulations Compared to Eddy Flux
Measurements. Forest Science, 47, 52-59

Cohen W.B., Maiersperger T.K., Gower S.T. & Turner D.P. (2003) An Improved
Strategy for Regression of Biophysical Variables and Landsat ETM+ Data. Remote
Sensing ofEnvironment, 84, 561-571

Crist E.P. & Cicone R.C. (1984) A Physically-Based Transformation of Thematic
Mapper Data the Tm Tasseled Cap. IEEE Transactions on Geoscience and
Remote Sensing, 22, 256-263

Cropper W.P. (2000) SPM2: A Simulation Model for Slash Pine (Pinus elliottii) Forests.
Forest Ecology and Management, 126, 201-212

Cropper W.P. & Gholz H.L. (1993) Simulation of the Carbon Dynamics of a Florida
Slash Pine Plantation. Ecological Modelling, 66, 231-249

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BIOGRAPHICAL SKETCH

Douglas Allen Shoemaker was born in Washington, DC, on August 26, 1962, first

of three sons to Wayne B. and Joanne Shoemaker. Raised in the nearby suburbs of

Maryland, Douglas cultivated a love for the outdoors on frequent hunting, hiking and

fishing trips with his father and brothers. On his entry to the University of Maryland in

1980, he brought with him college credits earned through advanced placement English

and biology testing while still in high school. Originally a zoology major, his interests

changed and after two years he left UM to drift through a series of jobs including

elephant keeper, construction worker and semiprofessional bicycle racer. Douglas was

nearly killed in a 1988 boating accident off of St. Croix, U.S.V.I., an experience that

dramatically changed his life. Returning to the U.S.A. he promptly undertook a career in

retail sales, an occupation he maintained for the next 12 years. During this period

Douglas married Kathryn Jean Goody of Andover NH and had the first of two daughters,

Brook Hanna. In 2001 Douglas left his position and returned to finish his education,

entering the University of Massachusetts majoring in biology and geographic information

science. Graduating with a Bachelor of Science degree summa cum laude, Douglas

arrived at the University of Florida's School of Forest Resources and Conservation in

2003 to work with Dr. Wendell Cropper, Jr. modeling forest processes using remote

sensing