BRIDGING THE LANDSAT DATA GAP: EVAL UATING ASTER AS AN ALTERNATIVE By FORREST R. STEVENS 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 2009 1
2009 Forrest R. Stevens 2
To my father, Bob and with many lovi ng memories of my mother, Stephenie 3
ACKNOWLEDGMENTS My sincerest gratitude must be given to my peers, colleagues, friends and family. Their support and guidance, thoughts and questions, and help through many problems untold are reflected in every word you read here. To name only a few I would like to thank first my wife, Gabriela Stocks, for her proddi ng and understanding, and an unc ompromising intellect that leaves no claim unchallenged. I would like to acknowledge the quality and constant motivation provided by my peers in the University of Flor ida Geography Department. Thanks also to the researchers collaborating in the MAP region of S outh America. Without the help of Dr. Michael Binford, Dr. Matt Marsik, Karla Rocha, Natlia H oyos, Amy Duchelle and Andrea Chavez, much of this studys data and legwork required for its use would be incomplete. This research was partially funded under a Na tional Science Foundation Human and Social Dynamics grant entitled, AOC: Infrastructu re Change, Human Agency, and Resilience in Social-Ecological Systems. I would like to tha nk Dr. Stephen J. Perz for his generous support for travel and fieldwork related to this studys data collection. My sincerest gratitude must also go out to my adviser, Dr. Jane Southworth. Her enthusiasm for research, the methods develope d and presented here, a nd the rigor that she espouses and upholds for her students and their work is critical to our success. In addition, I would like to sincerely thank my other comm ittee members, Dr. Timothy Fik and Dr. Greg Kiker, for their patience, guida nce and help in crafting my study and bringing it along from thought to data and paper. 4
TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................7LIST OF FIGURES .........................................................................................................................8LIST OF OBJECTS .......................................................................................................................10ABSTRACT ...................................................................................................................... .............11CHAPTER 1 INTRODUCTION ................................................................................................................ ..122 METHODS ..................................................................................................................... ........20Study Region ..........................................................................................................................20Data Preparation .............................................................................................................. .......21Data Analysis ..........................................................................................................................273 RESULTS ..................................................................................................................... ..........37Untransformed Comparisons ..................................................................................................37Theil-Sen Bisector Regressions ..............................................................................................39Transforming ASTER Data and its Outcomes .......................................................................40Transforming ASTER and its Effects on Calculated Vegetation Indices ...............................424 DISCUSSION AND CONCLUSION ....................................................................................65Study Implications ............................................................................................................ ......65Conclusion .................................................................................................................... ..........69APPENDIX A ORIGINAL SOURCE CODE FOR DISCUSSED ANALYSES ...........................................70ASTER Top-of-Atmosphere Reflectance C onversion from At-Sensor Radiance .................70Theil-Sen and H-M-S Intercept Regression ...........................................................................73ASTER Tasseled Cap Calculations and Conversion ..............................................................75License for Appended Source Code .......................................................................................77B SAMPLE ENVI CONFIGURATION TEMPLATES FOR ATMOSPHERIC CORRECTION .................................................................................................................... ...78Notes on Atmospheric Correction in ENVITM ........................................................................78 5
ASTER FLAASH/MODTRAN Configuration File for ENVI ...............................................78Landsat FLAASH/MODT RAN Configuration File for ENVI ...............................................79LIST OF REFERENCES ...............................................................................................................81BIOGRAPHICAL SKETCH .........................................................................................................85 6
LIST OF TABLES Table page 1-1 Key sensor and platform characteristic s for the ASTER and Landsat ETM+ systems. .........182-1 Data acquired and subset for ASTER and ETM+ comparisons. ............................................343-1 Transformation coefficients as calcluated for the specified year and band combinations. ....463-2 Transformation results of original data after applying the derive d coefficients from Table 2-1. ...........................................................................................................................473-3 Transformation results of data after applying the indepe ndently derived coefficients from Table 2-1 to MY01 data. ...........................................................................................483-4 Comparison of derived vegetation indi ces from post-transformation MY01 ASTER and original ETM+ data. ...........................................................................................................49 7
LIST OF FIGURES Figure page 1-1 System response curve comparison for the EOS ASTER and Landsat ETM+ sensors. ........192-1 Study region map showing the areas subset from the various data sources used. ...................352-2 Outline of the workflow for each data file type, grouped by year and subset. ......................363-1 Comparison by band of estimated Theil-Se n bisector slopes for ETM+ vs. ASTER L1A and L1B FLAASH surface reflectances derived for the MS01 subset. .............................503-2 The K-M-S bisector intercept estimat es for ETM+ vs. ASTER L1A and L1B FLAASH surface reflectances for each band combination, corresponding to the slope estimates from Figure 3-1. .............................................................................................................. ...503-3 Illustrating the effects of ETM+ B7 MY01 being regressed on ASTER MY01. ..................513-4 Comparison of estimated, post-transformati on Theil-Sen bisector slopes for ETM+ vs. ASTER L1A FLAASH MS01 surf ace reflectances that were spectrally resampled to match ETM+ B7. ...............................................................................................................523-5 Comparison of estimated, post-transformati on K-M-S bisector intercepts matching the slopes from Figure 3-3. ......................................................................................................5 23-6 Visual representation of transformation effects on estimated regression coefficients for the ETM+ MS01 regressed on ASTER MS01 preand post-transformation. ..................533-7 Transformation effects are shown as measur ed by metrics of spread and centrality for preand post-transformation of ASTER MS01 by its own MS01 regression coefficients. .......................................................................................................................543-8 Each of the five matching ETM+ MY01 ba nds and their diagnostic regressions are plotted against the corresponding tr ansformed ASTER MY01 data. ..............................553-9 Transformation effect as measured by the preand post-transformation regression coefficients for ETM+ MY01 regressed on ASTER MY01 bands after transforming with MS01 estimated coefficients. .....................................................................................563-10 Post-transformation effects on MY01 (tra nsformed by MS01) as measured by metrics of spread and centrality. .....................................................................................................563-11 Scatterplots and their diagnostic Theil-Sen bisector regressi ons of ETM+ derived NDVI and EVI2 vegetation indices, ag ainst the MY01 (transformed by MS01) derived indices. .............................................................................................................. ....57 8
3-12 The spatial distribution of EVI2 valu es calculated for th e MY01 subset after transformation using estimated Theil-Sen bisector coefficients from the MS01 sample. ....................................................................................................................... ........583-13 This map shows the artifacts created by mapping the difference of visible red bands, calculated by subtracting the ETM+ band from the MY01, untransformed data. ...........593-14 The visible artifacts, though still present are clea rly located near the center of the error distribution as the differencing of the transformed ASTER MY01 visible red and ETM+ band shows. ..........................................................................................................603-15 Scatter plot of ETM+ visible red data against the transfor med ASTER MY01band. .........613-16 Calculated EVI2 layer with cha nged pixels based on the transformed MY01 (transformed by the estimated coefficients of MS01) overlayed. .....................................623-17 Image difference map of MY01 (tra nsformed by MS01 coefficients) minus ETM+ EVI2 data. .................................................................................................................... ......633-18 Illustration of pixel locati ons of visible red difference shif ts within scatterplots of the calculated vegetation indices in post-transformation data. ...............................................64 9
LIST OF OBJECTS Object page A-1 GNU General Public License Version 3 (.txt file 35 KB) .....................................................77 10
11 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Master of Science BRIDGING THE LANDSAT DATA GAP: EVALUA TING ASTER AS AN ALTERNATIVE By Forrest R. Stevens May 2009 Chair: Jane Southworth Major: Geography Longitudinal studies of land use and land c over change (LULCC) increasingly utilize remotely sensed data from multiple sensors. Comparing multiple-sensor data presents challenging, technical problems that are often poorly documented and th at, without solutions, severely limit many analytical tools for multi-da te change detection. This study compares sameday data collected by the Landsat 7 ETM+ and ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) sensors from the South American tri-national border of Brazil, Peru, and Bolivia. Same-day imagery minimizes environmental variability between collected data and allows for an accurate asse ssment of sensor-specific differences in data products. A non-parametric, Theil-Sen bisector regression approa ch is introduced as both a comparison and transformation method, allowing fo r more robust cross-sensor comparisons in the presence of common sources of error in remo tely-sensed data. Aspects of multi-sensor data comparisons including techniques for calibration, image registration, resampling techniques, and noise are addressed. The use of the new EVI2 ve getation index is also explored across both ASTER and Landsat data. The results of these co mparisons and their relevance to land change science are used to develop gui delines for furt her research.
CHAPTER 1 INTRODUCTION Earth-observing satellites are re lied on for their ability to co llect longitudinal land change data, allowing researchers to study land use and la nd cover change over time. The motivation for such study varies widely across diverse scientific fields, but as noted by researchers spanning the human and natural sciences, the me thods and applications for mon itoring land change have given rise to a new land change science (Gutman et al. 2004). Though approaches vary nearly as much as the diverse fields of its research community, one critical component for studying human-environment interactions and land change sc ience is agreed upon: the ability to observe and monitor changes of the Earths surface (e.g., Ri ndfuss et al. 2004). Existing at the nexus of a variety of land change monitoring requirements, the jointly developed platforms and sensors of the National Aeronautics and Space Administrati on (NASA) and the United States Geological Survey (USGS) Landsat program are heavily cite d as the most important land change monitoring tools over the last 35 years (e.g., Cohen and Goward 2004; Woodcock et al. 2001). Among those citations are many reasons for the Landsat programs success, but most call on the Landsat platforms and their sensor characteristics, the spatial, radiometric, temporal, and spectral resolutions, coupled with the scales at which th ey operate, and how they match a broad spectrum of land monitoring appl ications (Jensen 2005). Much of the NASA Landsat programs success is founded on uninterrupted access to remotely-sensed, multi-spectral land imaging data since 1972. With the failure of the scan line corrector (SLC) of the ETM+ sensor on Landsat 7 in 2003 (Markham et al. 2004) and subsequent solar array drive problems on the aging La ndsat 5 platform in 2005-2006 (United States Geological Survey (USGS) 2006), ongoing longitudinal research u tilizing Landsat data seems increasingly threatened. The threat is highly ag gravated by the fact that the replacement for both 12
aging Landsat platforms, slated to be launched with the Lands at Data Continuity Mission (LDCM), is estimated to begin collecting data at the earliest in 2012 (U nited States Geological Survey (USGS) 2007). Even with efforts to eke utility from Landsat 7 SLC-off data (e.g., Trigg et al. 2006) and prolong the life of Landsat 5 by correcting its sp ectral and radiom etric drift as well as maintain data download coverages, a hi gh likelihood exists of a multi-year data gap (United States Geological Survey (USGS) 2008). In addressing the likelihood and consequences of this data gap, Wulder et al. (2008b) highlighted not only Landsats many applications operating considerations and successes, but also discussed several Landsat alternatives currently available among active, Earth-observing satellites. Among these altern atives is the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), a sensor that or bits on the Terra platform. The Terra satellite was launched as part of NASAs Earth Observing System (EOS) in 1999 and is a joint effort by the Japanese Ministry of Economy, Trade and Indu stry and Japans Earth Remote Sensing Data Analysis Center (ERSDAC). The ASTER sensor and its platform share many similarities with Landsat. These similarities extend across its spectral and radiometric ranges, temporal availability, and nearly identical orbital characteristics (Table 1-1), that in general make both good tools for land change scientists. However, de spite these similarities, important differences do exist. These differences include data access a nd availability limitations, spatial resolution and geometry configurations, and perhaps most importa ntly, differences in radiometric and spectral range characteristics. Data access and availability is a vital characteri stic of the Landsat program and its utility for longitudinal studies of land change. The La ndsat data archive and its importance for being able to extend land change study back through ti me has been well explored (e.g., Markham et al. 13
2004; Vicente-Serrano et al. 2008 ; Woodcock et al. 2001; Wulder et al. 2008a). Landsats success in this area lies primarily in its relativ ely uninterrupted timeline of data that has been collected, downloaded and archived for the past 35 years. For us to consider any gap-filling alternative, its ability to continue that timeline must be closely examined, and few sensor/platform combinations ar e adequate (United States Geol ogical Survey (USGS) 2007). ASTER is perhaps one of the leas t appropriate with regards to te mporal continuity because of a limited ability to collect and download data. The ASTER sensor is considered on-demand, meaning that scene collection must be tasked by researchers for any observations consid ered local, (including urgent and emergent events). Non-local data collection tasks may fa ll into the longer-term mission goals of regional monitoring (glacial change, volca noes, and Long-Term Ecological Research (LTER) field sites) or the one-time coverage, global mapping proj ect (Abrams et al. 2002). But across these priorities, due to memory and download limitations the ASTER system can only acquire about 650 scenes per day (approximately 2.34 million km2), compared to Landsat 7s estimated 300 scenes per day (approximately 9.44 million km2) (National Aeronautics and Space Administration (NASA) 2008). Of those 650, about 150 of ASTER s scenes are typically processed to the more user-friendly, Level 1B and other derived products. Though not temporally or spatially contiguous to an extent matching Landsat, ASTER data may still be considered a useful tool for ongoing, long-term studies of land change. Two other considerations must be made: 1) the scale of the research question is limited by the logistics of a smaller footprint and spatial sc ale; and 2) the spectral differences between Landsat and ASTER data should be understood. The first issue of sc ale is first considered by the nature of the question being asked of the data and the charact eristics of the study region. If ASTER is 14
applicable to the region and quest ion given the data availability issues already discussed, then many areas of active research may be drawn on to inform the logistics of utilizing remotely sensed data across multiple spa tial and temporal scales via techniques such as resampling, upscaling and image fusion (Hay et al. 1997; Southworth et al. 2006; Wang et al. 2004; Wu 2004; Zhukov et al. 1999). This study is focused primarily on the second of these issues, how comparable are Landsat and ASTER data across their overl apping spectral bands? And where systematic departures exist is it possible to empirically transform ASTER data to better match the Landsat data? These issues are most commonly side-stepped if the research question employs only discrete land-cover classifications, utilizing signatures derived from data within individual scenes and within the time series or for each sensor. This approach is common in research dealing with land cover conversion, where describing transitions from one th eoretically distinct class to another is the primary goal, even when utilizing multi-scala r or multi-sensor data (e.g., Asner et al. 2005; Capolsini et al. 2003). The issu e can also be avoided if land change is being modeled or described using data reduction methods such as multi-date principal components analysis, decision-tree classification or logistic regression. The issue of spectral comparability beco mes paramount, however, when moving beyond simple classification approaches or when conversi on from one discrete class to another is less important than degradation, for example. Often land cover classifications are convenient fictions used to simplify a more complex, continuously varying landscape with the hope that it will facilitate our understanding of the processes affecting its change. More often now, these simplistic representations of the landscape are bei ng passed over in favor of measuring change in non-discrete measures of land c over characteristics. These st udies may employ multi-spectral 15
indices, such as the ubiqu itous Normalized Difference Vegetation Index (NDVI) or more complex manipulations of multi-spectral data. To compare these continuous measures between time-steps, researchers must rely on careful ca libration of data at each time step, otherwise systematic bias is introduced. Calibrati on, most often occurring through radiometric normalization or by atmospheric correction, is of ten difficult even among time series involving a single sensor, let alone those invol ving sensors with different spec tral characteristics (VicenteSerrano et al. 2008). Though the ASTER visual and near-infrared (VNIR) and shortwave-infrared (SWIR) sensors were designed to be compatible with the Landsat sensors it followed, especially in terms of applied science, bandpass modifications were applied (Figure 1-1). These modifications included changes to the bandpass widths of th e VNIR and SWIR1 bands and the separation and shift of the ETM+ B7 band into five separate ba nds in the ASTER SWIR sensor. These sensor differences leave researchers with distinct spectral incompatibilities between ASTER and Landsat data, differences that preclude direct comparison of measured reflectances due to differing average spectral responses within the overlapping regions. This study introduces an empirical approach with the goals of describing and correcting systematic differences in spectral measurements between ASTER and Landsat 7 ETM+ data. Though similar to other comparison and cross-vali dation approaches utilizing multiple sensors and modeled reflectance values (Teillet et al. 2007), this study uses multiple same-day dataset pairs, radiometrically calibrated and atmospherically corrected to give accurate estimates of surface reflectance. Similar approaches were developed to describe differences between ASTER and MODIS data (Gao and Masek 2008; Miur a et al. 2008) and for comparing ASTER and Landsat thermal infrared (TIR) measurements (Chen and Zhou 2004). However, comparisons of 16
ASTER and Landsat ETM+ VNIR/SWIR data usi ng robust statistical techniques have not yet been described in the literature. Th is study attempts to fill that gap. The matched, overlapping surface reflectance data sets are statistically compared using a combination of bisector nonparametric, TheilSen and Hettmansperger-McKean-Sheather (H-MS) regression. Within the remote sensing litera ture this is a novel a pproach, robust to issues common in studies utilizing remotely sensed data. Through their description and use here the methodology will hopefully be acknowledged for its ut ility in these types of applications. The regressions are used to describe the association between bands and to transform the ASTER data to more closely match Landsat ETM+ surface re flectances. Vegetation indices, including the newly formulated Enhanced Vegetation Index 2 (E VI2) (Jiang et al. 2008 ), are calculated from the transformed ASTER datasets and compared with those calculated from the same-day ETM+ data in order to assess whether combining ASTER and ETM+ datasets in non-classificationbased, longitudinal studies of land change is viable. Specifically, the research questions to be addressed by this study are 1. How highly associated are ASTER and Landsat data under ideal, same-day conditions? 2. By using coefficients estimated from bisect or, nonparametric regression can ASTER data be transformed to more closely match Landsat data? 3. Do derived, continuous datasets from pos t-transformation ASTER data, such as vegetation indices like NDVI and EVI2, more closely match Landsat-derived indices? 4. What are the implications for using ASTER data, with or without transformations applied, to extend longitudinal studies in conjunction with Landsat data? 17
Table 1-1. Key sensor and plat form characteristics for the ASTER and Landsat ETM+ systems. ASTER (Terra platform)a Landsat 7 ETM+b Swath and Pointing VNIR and SWIR: 60 km, push-broom TIR: 60km, cross-track scanning cross-track pointing, VNIR .54 cross-track pointing, SWIR & TIR 185 km, cross-track scanning Orbit 705 km altitude Sun-synchronous Re-visit: 5 days (see off-nadir, cross-track pointing ability) Cross equator: ~10:15-10:30 AM Identical orbit, Terra orbits ~15-16 minutes behind Landsat 7 Re-visit: 16 days (nadir only) Cross equator: ~10:00-10:15 AM Footprint (samples x lines) ~60 km (across-track) x 60 km 4200 x 4100 (L1A VNIR) 2100 x 2048 (L1A SWIR) 700 x 700 (L1A TIR) 4200 x 4980 (L1B VNIR) 2100 x 2490 (L1B SWIR) 700 x 830 (L1B TIR) ~185 km (across-track) by 170 km 6600 x 6000 (VNSWIR) 3300 x 3000 (TIR) 13200 x 12000 (Pan) Spatial Resolution 15 m (VNIR, bands 1-3N) 30 m (SWIR: bands 4-9) 60 m (TIR: bands 10-14) 30m (VNSWIR: bands 1-5, 7) 60 m (TIR: band 6) 15 m (Pan.: band 8) Radiometric Resolution 8-bits (VNSWIR) 12-bits (TIR) Uncertainty: < 4% (for VNIR, terrain, gain dependent) 8-bits Uncertainty: < 5% Geolocation Accuracy < 0.2 pixels intra-telescope < 15 m relative m absolute < 0.17 pixels inter-band < 8 m relative m absolute a(Abrams et al. 2002), b(National Aeronautics and Space Administration (NASA) 2008) 18
19 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 450 500 550 600 650 700 750 800 850 900 950Relative Spectral ResponseWavelength (nanometers)ASTER VNIR B1 B2 B3N ETM+ (B2) Vis.Green Vis.Red (B3) NIR (B4) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 15001600170018001900200021002200230024002500Relative Spectral ResponseWavelength (nanometers)ASTER SWIR1SWIR2ETM+ MIR(B5) MIR(B7)SWIR3 SWIR4 SWIR5 SWIR6 Figure 1-1. System response curv e comparison for the EOS ASTER and Landsat ETM+ sensors. Subtle shifts in bandpasses were designed into the ASTER sensor to provide better contrast along the red edge. This is visualized by the differences in ASTER B2 and B3N compared to the ETM+ Vis. Red and NIR bands. The width of the overlapping the ASTER SWIR1 bandpass was also great ly reduced. The largest deviation is displayed by the separation of the ETM + B7 bandpass into the ASTER SWIR2-6 bands.
CHAPTER 2 METHODS Study Region The study region represents an area where l ong-term measurement of land change is critical. The area is located in the southwestern Amazon, near the shared borders of the Peruvian state Madre de Dios, Acre in Brazil, and the Bolivian department of Pando (MAP). The MAP tri-national frontier is still largely forested and ha s been designated a global biodiversity hotspot (Myers et al. 2000). Though the larger scope of work covers eight La ndsat scenes and is concerned primarily with transitions measured by discrete classifications, several smaller subsets are under study for more subtle shifts in forest structure and vegetation d ynamics. One of these areas is to the west of the Interoceanic Highway in Madre de Dios that connects the towns of Assis, Brazil in the north, Iapari, and Tauhaman Peru in the south. (Figure 2-1). The northern river in the study area is the Rio Acre, and the southern is the Tauhaman. Development on the northern border with Brazil, observable in pink in Figure 2-1, are the sister towns of Assis, Brazil and Inapari, Peru. The Peruvian town of Tauhaman is visible in the SE corner. The MAP region exhibits mostly humid, warm tropical climatic conditions. Long run averages indicate 1600-2750 mm of rain per year, and mean temp eratures of 24-32 degrees C. The dry season ranges from 3-5 months, with the warmest part of the summers occurring between October and November, while the coldest occurs in July (Ministrio do Meio-Ambiente Cooperao Brasil-Alemanha 2000). Rivers have historically played a very impor tant role in the transportation of goods and people throughout the MAP region. They provide resources and fish for food, though recently due to long-term drought conditions many rivers in the area have been severely depleted of fish and other traditionally harvested aquatic resour ces. But the large Acre and Madre de Dios 20
watersheds, including the Tauhaman River visibl e in the study region subset (Figure 2-1), are still regionally important for transportation and some resource uses. The geology and soils in the MAP region are a result of the pre-cambric formation, and then tertiary and quaternary se dimentation from the Andes. Th e soils within the region, like many in the Amazon, are fairly poor in nutrients They are also poor draining material and exhibit high flood risks. Furthermore, soil nutrien ts are typically vegetation structure dependent, and rely on dynamics at or near the surface fo r nutrient cycling. So agriculture is limited primarily to swidden-type systems, although alluvial plain soils of the majo r rivers are typically more fertile (Ministrio do Meio-Amb iente Cooperao Brasil-Alemanha 2000). For this study a representative area that include d tropical forest, water, and developed areas was needed. The area covered by the overla pping ASTER and ETM+ datasets was chosen because it provided a representative mixture of land cover types and representative reflectance common to the tropical, forested regions of Western Amazonia. This includes both rivers and ongoing development. By ensuring typical land cove rs are represented, the data samples provide enough dynamic range and variability to sub-samp les extracted from the subsets so that statistical tests are not biased. Data Preparation ASTER and ETM+ image pairs from the region with multiple year overlaps were selected that met this studys requirements. Between 2000 and 2007, 130 ASTER scenes were identified within 20 km of the MAP regions Interoceanic Hi ghway having less than 10% cloud cover. Of those, six were located that ha d significant overlap with a single, same-day Landsat footprint. Four of these were chosen as suitable and of these, three were selected for further processing based on scene conditions, overlap and the need to capture representative land cover for the region. For the three scenes both ASTER L1A and L1B (version 003) data were ordered and 21
downloaded through the USGS Globa l Visualization Viewer (GLOVI S) web interface (Table 21). For these three ASTER scenes, the correspond ing same-day ETM+ scene was acquired for the two years included in this study (Table 2-1) The relatively large ov erlap area between years (see MY00 and MY01 in Figure 2-1) is an area with relatively undisturbed tropical forest. The overlap areas of the 2001 scenes included both forest and developed areas (MS01). In order to make valid comparisons between datasets, all data were pre-processed, corrected for sensor calibration and geometry effects, converted to common units and coregistered as accurately as possible. Without doing so, direct pixel-to-pixel comparisons are invalid and any empirical relationships between ETM+ and ASTER data would be inapplicable across other datasets. The general outline of the workflow for each data set is presented (Figure 2-2). ETM+ data were pre-pro cessed to the same units and derivations by using the ENVI 4.3 softwares calibration features to convert the raw di gital numbers to at-sensor radiance and topof-atmosphere reflectance (ITT Visual Inform ation Solutions 2007). There are a lack of resources that describe ASTER data preparation in detail, th erefore, the methodology for ASTER processing is more well-documented here in the hope that this study is more useful to the research community. The ASTER HDF files were downloaded with th eir metadata and opened directly in ENVI. By processing the HDF file in ENVI, the individu al bands are extracted from the single HDF file into logical groups (visual/near-infrared (VNI R B1-3N), backward-looking near-infrared (B3N), short-wave infrared (SWIR1-6), and thermal-in frared (TIR B1-5). After extraction, the ENVI software automatically converts each ASTER band to at-sensor radiance (ASRAD, measured in 22
Watts(m-2sr-1m-1)) by reading the gain and bias coefficient for each bands wavelength and version from the HDF metada ta file (if available). ASTER L1A data are downloaded as the raw DN that were measured and captured by the sensor. The metadata included with each HDF file contain the calibra tion coefficients and georeferencing grid that are requi red to convert these DN into at -sensor radiance and orient the scene. ENVI applies the radiometric conversion automatically upon loading, however, georeferencing must be complete d on the VNIR, SWIR and TIR bands separately. The ENVI ASTER georeferencing tool was run with the VNIR and SWIR bands using triangulation and 1500 gridded warp points. These settings prov ided the best corresponde nce with the ERSDAC processed L1B data. During georeferencing no re sampling occurs because each pixel location is given exact geographic coordinates which are saved in separate layers of the same dimension as the raw data. The georeferenced L1A data were then layerstacked, during which the 30 m pixels of the SWIR bands were subsampled to match the 15 m pixels of the VNIR data. During the layerstacking process, th e data is resampled, gridded and tran sformed to match the georeferenced coordinates. Resampling during this stage was completed once us ing the nearest-neighbor (NN) and separately using the cubic convolution (CC) method. The two separate methods were used in order to explore both resa mpling techniques and their effect s on the empirical relationships with ETM+ data. The ASTER L1B data, having been already georeferenced to specifications and accuracies provided by ERSDAC (Abrams et al. 2002), were then layerstacked, combining the VNIR and SWIR bands (B1-3N, SWIR1-6) into a single file During layerstacking the bands are resampled using the nearest neighbor (NN) process, as the approximately ne gative eight degree, along-path scene rotation is converted to north-up, and the 30 m SWIR pixels are subsampled to match the 23
15 m VNIR pixels. It sh ould be noted that L1B data are by-default already resampled during processing at ERSDAC using CC, but a specia l request may be made during ordering to resample the data using NN. For this studys purposes the NN processing was not requested, since the L1A data should provide a NN comparison for empirical testing, and the L1B default settings are likely to be the most common in data used by the broader research community. The ASTER L1A and L1B data, after georefer encing and layerstacking, ideally overlay with almost perfect accuracy (confirmed by la yerstacking bands from each and flickering or compositing them). Minor differences and pixe l shifts occur due to resampling technique, particularly with NN resampling, but since pixel sizes are identical and the geometric grid from which the data were georeferenced are the same, the layerstacks from the two different processing levels should need no further registra tion. Along-track scenes from each year were mosaicked using a simple cutline across overlapping areas. Level 1A and 1B ASTER datas georeferencing information is not orthorectified and has a 50 m absolute geolocation accuracy (Abrams et al. 2002). Since ETM+ L1G data has less accurate absolute positional accuracy (Table 1-1) and a coarser resolution across the VNIR bands, image-to-image registration was perfor med using the ASTER L1 A data as a base, reference image. The ASTER L1A, L1B and ET M+ data were roughly subset to the areas represented by the MY00 and MS01 boundaries in Fi gure 2-1. These subsets were imported to ERDAS Imagine 9.1 (ERDAS 2006) and its AutoSync automatic tie-point generating tool. By using the ASTER L1A data as a reference more than 200 tie points were automatically generated for each subset paired with its correspondi ng ETM+ data. However, automated image registration is far from error free, as large numbe rs of automatically generated tie points with an accumulation of small errors can still generate ve ry low root mean square error (RMSE) values, 24
and yield questionable image registrations. Care ful documentation and experimentation with tie point generation was conducted, yielding pixel-to-pixel RMSE values of less than 0.2 pixels and upon visual verification extremel y good overlay accuracies. Also during the registration output stage, the ETM+ data were resampled using NN to 15 m pixel sizes to match the ASTER layerstacks. The correctly georeferenced and registered da ta were then imported into ENVI for all subsequent processing and analys es. The ASTER at-sensor radi ance (ASRAD) was converted to top-of-atmosphere reflectance (TOAR, also known as at-sensor reflectance, apparent reflectance, etc.) using a custom IDL script (Appendix A). This script implements the algorithm and coefficients for spectral solar irradiance as es timated by the World Radi ation Center (Yarbrough et al. 2005) and outputs the top-of-atmosphere reflectance (TOAR), a un itless ratio measure. Accounting for the effects of the atmosphere and solar irradiance differences on the solar radiation transmission is critic al when looking at multi-date im agery (Jensen 2005). Since we are using same-date imagery to derive empirical relationships between ETM+ and ASTER data it is tempting to forego atmospheric correction. But since the goal is to employ these empiricallyderived transformations across multiple dates empirical relationships must be based on reflectance measurements that are free from bias. By using same-date imagery such bias is minimized, however the slight difference in acquisition time (14-30 minutes), sun angle and sensor geometry (ASTER pointing angles) may still introduce error. Simple methods of correct ing for atmospheric effects, such as dark/lightobject subtraction and scaling may be acceptabl e for image-to-image comparison across dates (Chavez 1996), however to derive functional relationships betw een datasets for application 25
across multiple dates these subtle differences should be corrected for. Therefore, more accurate estimates of at-surface reflectance are ideal. Many cross-calibration and efforts are aimed at deriving such estimates using firstprinciples radiometric derivations and modeled sensor characterist ics (Liu et al. 2004; Teillet et al. 2007). Though these approaches are vital for ch aracterizing theoretical sensor responses and radiometric drift over time, they often focus on ideal surfaces a nd estimated spectral response curves for simulation purposes rather than on ap plications for real-wor ld data. To create accurate estimates of surface reflectance the at -sensor-radiance subsets for ASTER L1A, L1B and ETM+ were corrected using the ENVI Fast Li ne-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) module. It uses the MO DTRAN4 radiative transfer code and is a sophisticated model derived from radiometric firs t principles (Berk et al. 1999; Cooley et al. 2002). The details for its use and settings are supplied in Appendix B. During the comparison of each ASTER VNIR and SWIR band, it was apparent that no one band in the ASTER SWIR was equi valent to the ETM+ B7. From a remote sensing perspective this is highly troublesome as ma ny optical indices rely on B7, especially those correcting for the reflectance of soil, fire scars, et c. As an alternative to choosi ng a single SWIR band to use as a proxy for B7, the ASTER SWIR2-6 bands were sp ectrally resampled using ENVI to match the B7 bandpass. The process, very common when pr ocessing hyperspectral da ta, assumes critical sampling and uses a Gaussian model to combine multiple bands into one estimate. The software calculates contributions to the resampled band ou tput from the multiple inputs based on the full width at half maximum (FWHM) wavelength characteristics for each band. The resulting output file for each ASTER input was a six band dataset, with null values for the visible blue band (B1), 26
data identical to ASTER inputs for B2-5, and the resampled SWIR2-6 bands combined as the equivalent to B7. Data Analysis The layerstacks for each of the overlayi ng datasets, both ASTER and ETM+, were compared using a variety of st atistical methods and sampling techniques. For each subset, MS01, MY00 and MY01, the ASTER L1A resampled with both NN and CC, were compared with ASTER L1B and ETM+ data. Bivariate comparisons were conducted by taking a random sample of 10,000 pixel locations from each subs et and extracting the data from each pixel location across all of the layers of both TOAR and FLAASH reflectance data. These samples represented a small fraction of the total number of pixels in each subset (2434 x 1995 = 4,855,830 for MS01, 2000 x 2967 = 5,934,000 for MY00 and MY01), however it was a large enough sample to capture most of the variability from each scene and minimize the effects of spatial autocorrelation. Spatial autocorrelation in regression errors and an alyses is a concern because of the scalar mismatch between ASTER and Landsat VNIR bands, as well as the bias present, however minimal, by remaining registration errors. The primary diagnostic and transformation test used to describe the relationship between ASTER and ETM+ data was the estimated slope a nd intercept coefficients from statistical regressions. Though it is common to see ordinary least squares (OLS ) regression used in remote sensing literature for describing associations between remotely-s ensed data, derived products and the biophysical characteristics relating to them, OLS use for this type of data regularly violates several assumptions required for the unbiased estimates of regression coefficients. As summarized by Fernandes and Leblanc (200 5) the most common violation occurs when there are measurement errors in both the indepe ndent and dependent data. They suggest that parametric estimators used in remote sensing ar e often biased because of inherently non-normal 27
and heteroscedastic data, censoring (occurs comm only in remote sensing applications where detectors are saturated beyond measurement cap ability), as well as common occurrence of outliers. Though many of these i ssues can be corrected for by truncation, scaling and subsampling, a more systematic approach is preferab le. To counteract these biases when functional and structural regression situa tions apply they, like others ha ve successfully employed the nonparametric Theil-Sen (T-S) estimator for the sl ope (Akritas et al. 1995 ; Fernandes and Leblanc 2005; Olthof et al. 2005). Theil-Sen regression is a nonparame tric regression methodology th at uses the median of all slopes of unique, pair-wise observations taken fro m the dependent and independent datasets as the best estimate for the population slope, After the median slope is estimated, the intercept is estimated for each pair of dependent and indepe ndent observations by calculating the remainder a from the standard linear relationship, y = x + a The median of all calculated a s is the Hettmansperger-McKean-Sheather (H-M-S) best-e stimate for the regression intercept, or (Hollander and Wolfe 1999). T-S regression is highly robust to up to ~29% outliers, nonlinearities, and heteroscedasti city (Fernandes and Leblanc 2005) The assumptions for this non-parametric estimator state: A1. At each of n fixed values, x1,xn ,of the independent (predictor) variable x we observe the value of the response random variable Y The values of x are assumed to be distinct straight line model is: and x1, < x2 < < xn The (2-1) Furthermore the x s are known constants and (intercept) and (slope) are unknown parameters. A2. The random variables e1, en are a random sample from a continuous population that has median 0. 28
Therefore, the assumptions placed on OLS are mos tly relaxed with the only restriction placed on the distribution of the errors being th at they have a median of zero. Concerns regarding OLS applicability and ot her parametric regression estimators apply to this study because it explores the functional relationship between tw o data sources where both have measurement error with heteroscedasticity and outliers. The issu e of measurement error needs to be considered separately. The depende nt or truth that is be ing measured by each set of data is in reality the true surface reflectance at each pixel s location on the ground. This is being measured, with various types of bias and error by both the ASTER and ETM+ data. It is not that we are predicting ETM+ data, but instea d we are trying to match the error distribution across the range of ETM+ values present. Th is yields the expectation, which makes sense intuitively as well as statistically, that there be a 1:1 correspondence w ith errors distributed symmetrically (and not strictly homoscedastically). Therefore, though a transformation for one data source is sought, ne ither data source is considered independent. Errors in measurem ent for both ASTER and ETM+ data are present due to radiometric and sensor inefficiencies, calibration and registra tion errors, resampling technique employed, among others. Much resear ch has relied on OLS or a simple Theil-Sen regression in the past with at l east partial success but for this study it is not clear whether we should be minimizing errors in the dependent variable ( y axis) for each value along the independent ( x axis) or the other way around. So using a regression approach that treats the da ta symmetrically is preferred. Research in other fields, including astronomic (Feigelson and Babu 1992; Isobe et al. 1990) and ecological literature (Warton et al. 2006), suggests that the OLS methodology of minimizing RMSE or errors in the dependent variable ( y axis) for each value along the independent ( x axis) is flawed if 29
both have measurement error or the relati onship between dependent (predicted) and independent (predictor) is unclear In these instances OLS bisect or regression, as described and calculated by Isobe et al. (1990) shows the highest degree of robus tness and is stable under more conditions than other symmetric techniques. Thes e techniques include reduced major axis and orthogonal regression, however both suffer from limitations when data has characteristics matching that of remotely-sensed reflectances. Therefore, Isobe et al and others, recommend the OLS bisector estimated slope coefficient. It is essentially the angular average of the two 1 = OLS(Y|X) and 2 = OLS(X|Y) slopes: (2-2) With te bisectot estimed as the following: hr intercepat ) (2-3) However, because it relies on OLS regression, all of the problems experienced with regards to violated assumptions inherent to the nature of remotely-sense d data still apply. This is particularly true with regards to the estimates of variance associated with the estimator. For this reason this study has used an approach unused in the remote sensing literature by combining Theil-Sen slope estimation with the OLS bisector approach. By replacing the estimates of OLS(Y|X) and OLS(X|Y) with Theil-Sen slope estimates, and estimating the K-M-S bisector intercept using the Theil-Sen bisector slope a nd using the median instead of means for the calculation of the intercept. Processing time is a consideration when cal culating Theil-Sen slopes and sub-sampling or resampling is necessary for large datasets. Since all pair-wise combinations of observations from both independent and dependent datasets must be calculated for the 10,000 pairs of observations 4,995,000 unique slopes must be calculated. Due to memory allocation limitations, it was 30
necessary to estimate slopes, intercepts and th e standard errors associated with each by implementing a computer-intensive resampling te chnique. A sub-sample of 200 pixel locations were extracted without replacement from each origin al subset and Theil-Se n bisector regressions were run for each. This sub-sample was performed 10,000 times. The resampled sampling distribution of Theil-Sen and K-M-S coeffe icients was normally distributed (KolmogorovSmirnov tests were employed for normality testing). The means of each sampling distribution converged on the large-sample estimated coeffici ents, and the calculated st andard deviations are presented as estimates of each coefficients variability. For each 10,000 pixel band comparison, the median of the absolute differences, bias, and Wilcoxon signed rank statistic were calculated. The median of absolute differences (MAD) provides a relative measure of how wide the sp read is around the 1:1 line for each comparison. A smaller MAD indicates less bivariate erro r and a tighter corre spondence to the 1:1 relationship. Bias was calculated betw een two samples by taking the differences ( Yi (dependent) xi independent) for each pair of observations within the 10,000 pixel sa mple and determining what percentage of those differe nces fell below zero, and subtra cting that from 50%. Negative bias values indicate more than 50% of the di fferences were below zero. This corresponds to relationships where more observations fall below th e 1:1 line than above it. The closer the bias is to 0% the more evenly distributed ar ound the 1:1 line the bivariate relationship is. The Wilcoxon signed rank test was used as a st atistical measure of location and hence is related indirectly to the bias, where standardi zed values (approximately normally distributed, ~N(=0, =1) are calculated and correspond to th e departure from the large sample approximation of the estimated number of posi tively signed ranks (Hol lander and Wolfe 1999). This is a non-parametric test for a shift in location (difference in median) between two 31
populations, with the assumption that the calculat ed differences are distributed symmetrically around a common median. After estimating transformation coefficients, th e MS01 subset data were used to calculate two vegetation indices, the normalized difference vegetation index (NDVI) and Enhanced Vegetation Index 2 (EVI2) (Jia ng et al. 2008). NDVI is an ex tremely common vegetation index that has a highly associated w ith net primary productivity, leaf area index (LAI), absorbed photosynthetically active radiation and is in general used to eval uate the relative condition of vegetation across a wide spectrum of land cove r types (Jensen 2005). The formula for NDVI utilizevible red (R) and near-infrared (NIR) measures of estimated surface reflectance. s the is (2-4) NDVI, however, has been shown to saturate at even moderate levels of vegetation (Huete et al. 1997) and therefore loses utility for detecting subtle changes in vegetated areas such as the tropical forests in this studys region. Theref ore the Enhanced Vegetation Index (EVI) was proposed as an alternative (Liu and Huete 1995). It is calculated by incl uding a gain correction and adjusts NDVI with the visible blue band, th ereby saturating at a much higher level of vegetation productivity. However, because ASTER does not include a band in the visible blue part of the spectrum, the normal EVI cannot be calculated. A two-band alternative has been suggested and calibrated with optimal parameters that uses only the red and NIR bands, but maintains a very high degree of correl ation with EVI (Jiang et al. 2008). (2-5) It is critical to note that calibrated indices su ch as EVI2 must be cal culated using estimated surface reflectance values ranging from 0.0 to 1.0. If scaled data are used then the calibration 32
coefficients no longer correctly account for the re lative ranges in the red and NIR bands and will yield outputs outside the range of -1.0 to 1.0. ASTER data transformed by estimated coeffici ents from an independent subsample were used to calculate NDVI and EVI2. The same was done for ETM+ data from the corresponding subset and these vegetation indices were co mpared preand post-transformation. The differences between the post-transformed were then used to examine the spatial variability of the performance of the empirical transformation on the ASTER data. 33
34 Table 2-1. Data acquired and subs et for ASTER and ETM+ comparisons. Subset ASTER Landsat 7 ETM+ MS01 Granules AST_L1A_00307292001151125 AST_L1B_00307292001151125 (Processed, ver. 03, 2007-09-11) L71003068_06820010729_HDF.L1G Path 003, Row 068 Acq. Date/Time 2001-07-29 15: 11:25 2001-07-29 14:59:00 Sun Elevation 52.641 45.649 Sun Azimuth 38.642 47.462 Point Angle 2.878 0.000 (Nadir) Resampled NN (L1A), CC (L1A and L1B) CC MS01, MY01 Granules AST_L1A_00307292001151134 AST_L1B_00307292001151134 Date/Time 2001-07-29 15:11:34 Sun Elevation 52.109 Sun Azimuth 38.286 Point Angle 2.878 Resampled NN (L1A), CC (L1A and L1B) MY00 Granules AST_L1A_00307262000151816 AST_L1B_00307262000151816 (Processed, ver. 03, 2007-09-11) p003r068_7t20000726_z19 Path 003, Row 068 Acq. Date/Time 2000-07-26 15: 18:16 2000-07-26 14:37:20 Sun Elevation 52.597 45.598 Sun Azimuth 38.823 46.316 Point Angle 0.022 0.000 (Nadir) Resampled NN (L1A), CC (L1A and L1B) NN
360000 360000 400000 400000 440000 440000 8720000 8720000 8760000 8760000 8800000 8800000 A S T E R 2 0 0 0 A S T E R 2 0 0 0 A S T E R 2 0 0 1 A S T E R 2 0 0 1 E T M + 2 0 0 0 2 0 0 1Multi-Year Data (MY00) (MY01) Multi-Scene Data (MS01) 010203040 5 Kilometers Landsat ETM+ Path 3 ,Row 68 5-4-3 RGB Composite Acquired: July 26th, 2000 July 29th, 2001 (shown) ASTER VNSWIR Scene Outlines: Descending path, Same-day Datum: WGS-84 Proj.: UTM Zone 19S 35Figure 2-1. Study region map showing the areas subset from the various data sources us ed. Overlapping regions from two years w ere acquired and subset into three pairs of ASTER L1A and L1B data: Multi-S cene 2001 (MS01), Multi-Year 2000 (MY00) and Multi-Year 2001 (MY01). There were three correspond ing subsets of the ETM+ data, two for the 2001 scene, corresponding to the subsets for MS01 and MY01, a nd one for 2000, corresponding to the MY00 subset.
36Figure 2-2. Outline of the workflow for each data file type, grouped by year and subset. All initial data ex traction, calibra tion to atsensor radiance (ASRAD) and top-of-atmosphere reflectance (TOAR) were performed using ENVI. Geo-registration was completed using ERDAS Imagine 9.1 and its AutoSync tool in order to maximize registra tion accuracy. Finally, all georegistered data were atmospherica lly corrected using the ENVI FLAASH module yielding estimates for surface reflectance. Subset to: MY00 MY01 MS01 Process for all acquired files from: 2000 2001 (Table 2-1)ASTERL1A Extractandconvert VNIR,SWIRtoatsensorradiance Wm-2sr-1m-1Georef.VNIR1-3N andSWIR1-6 separately Stack,Resample NearestNeighbor (NN) Top-of-atmosphere reflectance (L1ATOARNN) FLAASH atmospheric correction (L1AFLAASHNN) Stack,Resample CubicConvolved (CC) L1ATOARCC L1AFLAASHCC ASTERL1B Productcomes georeferenced, converttoat-sensor radiance Georegisterto ASTERL1A (CCbydefaultfrom provder) L1BTOARNN L1BFLAASHNN LandsatETM+L1G Convertbands1-5,7 toat-sensor radiance Georegisterto ASTERL1A (NN) ETM+TOARNN ETM+FLAASHNN (noaerosol extraction)
CHAPTER 3 RESULTS Untransformed Comparisons The results from initial comparisons using Theil-Sen bisector regression across the three subsets (MS01, MY00, MY01) were focused on narrowing down the number of subset and band combinations to use in subsequent analyses. Initial comparisons of top-of-atmosphere reflectance data were highly variable and the bi as introduced between ye ars and scenes due to sensor geometry and differential atmospheric effects for varying bandpasses was considered unacceptable and therefore further analyses with TOAR data were ruled out. All subsequent analyses were completed using the FLAASH, at mospherically corrected surface reflectance estimates. For each of the three subsets there were th ree sets of ASTER surface reflectance data generated: Level 1A (L1A) n earest-neighbor (NN) resampled data, L1A cubic convolved (CC) resampled data, and Level 1B (by default resampled using CC). For ETM+ there was one set of FLAASH surface reflectance data sampled for each subset from the appropriate year. The L1A CC data were compared with the L1B data with results showing virtuall y no difference across all of the metrics compared. This confirms that properly aligned and calibrated, L1A CC data are equivalent to L1B, as we should expect, and so L1A CC comparisons ar e not presented here. Across all overlapping bandpasses, Theil-Sen bisector and K-M-S bi sector slopes were calculated to compare L1A NN, L1B and ETM+ data The results for the MS01 subset, which is representative of the other two, are displayed in Figures 3-1 a nd 3-2. As expected for data generated from the same sensor L1A NN has extremely high agreement with L1B data, with slope estimates centered on and conf idence intervals bracketing 1.0. Intercept estimates for all of the ASTER band combinations are statistically not different from 0.0. Comparing both ASTER 37
datasets to ETM+ shows higher agreement am ong the VNIR bands (slo pes closer to one, intercepts closer to zero) than among the comparisons with the SWIR bands. Recall that the ASTER SWIR1 band overlaps with ETM+ B5, wh ile the remaining SW IR2-6 overlap with ETM+ B7, and the comparisons in Figures 3-1 an d 3-2 reflect that. Th e regression estimates show that no one band in the SWIR2-6 range is clearly better associated with ETM+ than any other, so spectrally resampled data we re used in all subsequent comparisons. Also visible in Figures 3-1 and 3-2 is the slightly bette r agreement between L1B and ETM+ data than for L1A NN data. This slight difference can be attributed to the smoothing effect that cubic convolution resampling has on the ASTER data. However, further analyses were conducted using L1A NN resampled data in order to encompass the greater amount of variability in the original, unsmoothed L1A NN data. To illustrate the regression estimates as both transformation tool and diagnostic method, a scatter plot presenting ETM+ B7 plotted agai nst the resampled SWIR2-6 surface reflectance estimates from the MY01 subset are displayed in Figure 3-3. The top plot shows the pretransformation relationship betw een SWIR2-6 and ETM+ B7. The estimated regression line is plotted as a solid line for the data as shown in each part of the plot In the first pane untransformed data represents a slope of 2.06 and an intercept of -0.079. As displayed, the pretransformed ASTER reflectance estimates are scaled at low reflectance to be much higher than the ETM+ estimates (falling below the 1:1 line). After the linear transformation by multiplying the ASTER resampled data by the estimated slope and adding the estimated intercept the plotted relationship falls neatly along the 1:1 line. Error in both of the measured variables produces a symmetric, representative oval shape to the scat ter plot. Since the regression was estimated by the Theil-Sen bisector method the regression line is calculated to bisect that oval (as opposed to 38
non-bisecting regressions that minimize the vertical distance to the regression line in the estimated errors). Theil-Sen Bisector Regressions The transformation represented in Figure 3-3 is the result of using the Theil-Sen bisector estimate for the slope and K-M-S bisector estimate for the intercept. These coefficient estimates, calculated for each subset are presented in Table 3-1 and henceforth when transformations are named they are referring to those regression co efficients. The coefficient estimates for each band differ significantly between subsets. This may be the result of differences in land cover between the two subset footprints as well as the change from y ear-to-year. However, the range is large enough, especially between slopes in the NIR and B5 vs. SWIR1 comparisons that a common transformation across a ll datasets may be difficult to estimate in this study. The effects of each transformation, applied to the ASTER data from which it was derived is presented in Table 3-2. The results are larg ely expected, as all dia gnostic Theil-Sen bisector slopes are not statistically different from 1.0 except for the SWIR2-6 coefficient in the MY00 subset. Similarly, all estimated K-M-S intercepts are not statistically significantly different from 0.0 except for the SWIR2-6 for the MY00 relati onship. An important result is the extreme reduction in bias in the post-tra nsformation data across all bands relative to the untransformed bias presented in Table 3-1. This represents th e shift of a large percen tage of the ASTER data across the 1:1 line, just as illustrated in Fi gure 3-3, which is exactly what the bi-sector transformation should accomplish. Furthermore, the relatively small standardiz ed Wilcoxon signed rank scores indicate nonsignificant differences in the median between th e original ETM+ data and transformed ASTER bands. Exceptions to these generally positive tran sformation results occur in all three subsets band combinations, indicating that despite large decreases in bias and median differences there 39
are still slight, unexplained differe nces in the association. It is important to consider, however, the sample size of 10,000 from which these metric s are calculated is large and even slight deviations in median are detected as signi ficant in rank sum calculations and coefficient estimates. To determine which transformation to carry fo rward as a possible candidate for subsequent analyses, each subset was tran sformed with the coefficients derived from the other subsets (transformations are named in Table 3-1). Figur es 3-4 and 3-5 show the comparison of estimated bisector regression coefficients of the MS01 da ta. The MS01 data were left untransformed, transformed by its derived MS01 coefficients, and also transformed by the independently-derived MY00 transformation. The MY00 transformation is predicted the most likely to be unsatisfactory across multiple datasets, since MY00 land cover is relatively uniform and there is the possibility that bias is intr oduced between years desp ite efforts to minimize this. The results show that transforming by its own coefficients provides the most correction. However, the independent transformation by MY00 coefficients doe s result in significant shift toward a 1:1 relationship, even for coefficients derived from such disparate data. Transforming ASTER Data and its Outcomes By examining the MS01 transformation coeffi cients (Table 3-1) the estimated effects across all bands trend smaller (le ss scaling and shifting) than in the other two transformations. This is likely due to the generally greater vari ability in land cover present in the MS01 subset and the larger range of values to estimate. Si nce this study is in search of a more general functional transformation to allo w direct comparison of ASTER a nd ETM+ in a wide variety of land cover situations, the MS01 co efficients were chosen to co nduct further tests with. The transformation effect on the ASTER data was meas ured using the Theil-Sen bisector regression coefficients, bias, absolute median of differen ces, and standardized Wilcoxon signed rank scores. 40
To better visualize the effects of transformation on bands critical to vegetation monitoring (visible red, NIR, MIR (B7)), rada r plots were constructed with each of these metrics. Figures 36 and 3-7 display the metrics in combination with absolute bias as the marker size (maximum absolute bias of 50% is represented in each as the size of the circ le). The visualized transformation effect of MS01on its own data is the observed cha nge between Tables 3-1 and 3-2 for MS01, preand post-transformation. Movement to ward the origin in this case represents a better approximation of the 1:1 ideal. The MY01 data was chosen as an independent test for the MS01 and MY00 transformation coefficients. These two sets of coefficients repr esent the two ends of th e spectrum, with regards to the amount of linear scaling applied during transformation. MS01, with the exception of the visual green band, has slopes closer to 1.0 a nd intercepts closer to 0.0 than the MY00 transformation. This again, is likely due to the more varied land cover and the increased variability in surface reflectances represented. MY00 on the other hand shows larger amounts of linear scaling and is likely more suited for transf orming data representing large tracts of forest, like in the data the coefficients were derived from. The MY01 data were transformed using both MS01 and MY00 coefficients and the results are presented in Table 3-3. The results show th at the MY00 transformation tends to over-correct the data. MY00 decreases bias overall but causes it to be larger in the positive direction than the results from the MS01 transformation. Because of this, MY00 is considered to be an overly aggressive transformation, likely to decrease bias relative to untransfor med data, but less likely than MS01 to increase the agreement between ETM+ and ASTER comparisons. To visualize the preferred effects of the MS01 transformation and its ability to reduce errors along the 1:1 relationship, scatterplots were constructed for each MY01 band combination (Figure 3-8). The 41
1:1 lines represent the ideal relationship and the grey soli d line represents the linear transformation applied to the underlying data. To visualize the transfor mation effect of the MS01 on the MY01, radar plots were again constructed (Figures 3-9 and 3-10). Transforming ASTER and its Effects on Calculated Vegetation Indices The MY01 preand post-transformed surface reflectances were used to generate NDVI and EVI2 estimates. These were compared to estimates derived from ETM+. The bivariate comparisons of these vegetation indices are presented in Table 3-4. The results show that the estimated slopes and intercepts for NDVI are not significantly differe nt from one and zero respectively, in the untransforme d or transformed data. This is likely due to the non-linearity introduced by saturation of ETM+-derived NDVI va lues. ASTER NDVI saturates less quickly due to a refinement in the visible red and NIR ba nds that better separates the red edge (Miura et al. 2008). But the effects of transformation show an overall trend toward the 1:1 relationship in both sets of post-transformation derived data But as we observe in Table 3-3, the MS01 transformation performed much better when comparing the derive d vegetation indices and their metrics of association. This extends to a Wilc oxon signed-rank result th at did not significantly differ from zero for the EVI2 comparison, indica ting that the transforma tion of the visible red and NIR ASTER bands can translate to very clos ely matching median results over a large sample size. Scatter plots of the vegetati on indices derived from the tr ansformed MY01 (by MS01) are presented in Figure 3-11. The sa turated NDVI values are clearly di splayed, showing that for this region transformation is unlikely to increase the utility of NDVI measurement in distinguishing vegetation conditions, given the clustering at the extreme high-end of NDVI values. However, the preand post-transformation plots for EVI2 s how that transformations applied to the visible 42
red and NIR ASTER bands can effectively increase the correspondence and measured association between derived indices of ASTER and ETM+. To this point departures from the expected 1: 1 association have been described statistically and numerically. However in any remote sensing application error is not likely to be spatially independent. To explore how the errors from the underlying data are translated onto the landscape, post-transformation ASTER EVI2 and ETM+ EVI2 results were compared in a small subset of the MY01 dataset. The transformed AS TER EVI2 data are presented in Figure 3-12. The EVI2 data displayed shows good dynamic range across a small region with high vegetative production, in both forested, wetland and riparian areas. The two bands used to calculate EVI2 are the visible red and NIR (see Equation 2-5). By looking at the transformation app lied by the MS01 coefficients (T able 3-1 and Figure 3-8), we see that the effect should be rath er subtle. Recall that the unde rlying data are estimated surface reflectances and are scaled, unitle ss values representing the percen t of solar radiation reflected from the Earths surface and take values between 0.0 and 1.0. The effect on the visible red band for the MS01 transformation is summarized by: ASTERTransformed Red = -0.00133 + 1.01077(ASTERUntransformed Red) (3-1) Because reflectances are very low in the visible red part of the spectrum for this study area (as there is an abundance of highly photosyntheti cally active vegetation), the negative intercept coefficient shifts the reflectance values towards th e origin by over one-tenth of one percent. This transformation is visualized in difference images of the visible red band (F igures 3-13 and 3-14). What is immediately apparent in the differen ce image of the untransformed data are visual artifacts across the scene. By looking at the raw, unprocessed original ETM+ visible red band the artifacts can be clear ly identified. These types of artifacts in ETM+ imagery (banding, 43
striping, noise, etc.) are common, es pecially in tropical imagery where very low dynamic ranges and significant haze is present. The fact that these artifacts are visi ble across a color-ramped range of 0.01 reflectance units indi cates that they may be very im portant in analyses, especially given the bulk of the data in the visible red region is located between reflectances 0.00 and 0.05 (Figure 3-8). The same difference, calculated using the transformed ASTER data, indicates a trend pulling the differences between the highs a nd lows of the artifacted region towards zero (Figure 3-14). The artifacts in the ETM+ regi on clearly occur across the variation contained in its data. By transforming the ASTER visible re d distribution towards th e median of the ETM+ data the difference image reflects a shift where the highs and lows across the artifacted regions are centered more towards zero than they were in the untransformed data (Figure 3-13). To observe the effect of the transformation on individual pixels a scatterplot of the ETM+ visible red data vs. transformed ASTER data for the region highlighted in Figures 3-13 and 3-14 was constructed (Figure 3-15). The pixels that changed signs from being positive in the pretransformed difference image to negative in the post-transformed are highlighted in the scatterplot in magenta. If it were plotted, thes e pixels would be locate d on the right of the 1:1 line in the corresponding untransform ed scatterplot, but after transf ormation they shift to the left of the 1:1 line. By identifying these pixels individually, we can plot where on the image these shifts in sign occurred (Figure 3-16). By comparing the location of the change pixels with the location of the color shift in the difference images it is apparent that the effects of transformation are not spatially independent. However, by look ing at the difference image of post-transformed ASTER EVI2 image minus the ETM + EVI2 estimates (Figure 3-17) we can see in general relatively low variability across the image, w ith most errors in the .05 EVI2 scale. 44
45 Last, we can identify where these pixels resi de relative to the 1:1 line in both of the transformed EVI2 and NDVI scatterplots. We can observe directly how though the shifted pixels are spatially autocorrelated in the differenc e image, they are represented without bias in the EVI2 estimates. Similarl y, the changed pixels show sli ghtly below the 1:1 line for the transformed NDVI results. These visual representa tions of course do not ta ke into consideration the relative density of these pi xels, however because the visible red band showed very close to a 1:1 association before transformation, the shifted slice of pixels near th e 1:1 line represents a large portion of pixels in the visible red band.
Table 3-1. Transformation coefficients as calcluat ed for the specified year and band combinations. Transformation Name ETM+ FLAASH ASTER L1A, NN FLAASH K-M-S Bisector Intercept ( ) SD ( ) Theil-Sen Bisector Slope ( ) SD ( ) Untransformed Bias MS01* MS01: MS01: Vis. Green B1 -0.00388 0.00033 0.89736 0.01204 -37.95% Vis. Red B2 -0.00133 0.00030 1.01077 0.01828 -7.13% NIR B3N 0.01586 0.00182 0.95870 0.00650 5.55% MIR (B5) SWIR1 -0.07755 0.00171 1.38874 0.01137 -41.17% MIR (B7) SWIR2-6 Resampled -0.05692 0.00188 1.67401 0.02808 -40.23% MY00* MY00: MY00: Vis. Green B1 -0.00717 0.00056 0.99106 0.02496 -39.91% Vis. Red B2 -0.00483 0.00042 1.12833 0.03052 -20.44% NIR B3N -0.01212 0.00228 1.04309 0.00805 -0.63% MIR (B5) SWIR1 -0.12961 0.00283 1.71166 0.01875 -45.88% MIR (B7) SWIR2-6 Resampled -0.09823 0.00331 2.23753 0.04998 -48.45% MY01* MY01: MY01: Vis. Green B1 -0.00538 0.00058 0.88481 0.02174 -44.38% Vis. Red B2 -0.00219 0.00042 1.00838 0.02714 -14.70% NIR B3N 0.02991 0.00186 0.90067 0.00679 4.27% MIR (B5) SWIR1 -0.09326 0.00242 1.50478 0.01645 -44.93% MIR (B7) SWIR2-6 Resampled -0.07878 0.00377 2.06198 0.05963 -44.32% 46 The MS01 subset contains far more development and more water and wetland pixels relative to the MY datasets (Figure 2-1). Thi s may account for relative differences in estimated coefficients.
Table 3-2. Transformation results of original data after appl ying the derived coefficients from Table 2-1. Transformation Performed ETM+ FLAASH ASTER FLAASH K-M-S Bisector Intercept ( ) SD ( ) TheilSen Bisector Slope ( ) SD ( ) PostTransf. Bias Median of Absolute Diff. Std. Wilcoxon Signed Rank Score (Z) SR p-value MS01 MS01: MS01: V. Green B1 0.00002 0.00028 0.996 0.0134 0.04% 0.00323 -1.2 0.120 Vis. Red B2 0.00003 0.00028 1.005 0.0181 0.44% 0.00289 -1.8 0.040 NIR B3N 0.00022 0.00192 1.000 0.0068 -0.89% 0.01681 -1.4 0.088 MIR (B5) SWIR1 -0.00140 0.00108 1.009 0.0082 -2.96% 0.00769 -4.6 0.000* MIR (B7) SWIR2-6 -0.00137 0.00093 1.027 0.0169 -4.23% 0.00466 -3.8 0.000* MY00 MY00: MY00: V. Green B1 -0.00007 0.00038 1.000 0.0252 -0.39% 0.00341 -1.2 0.110 Vis. Red B2 -0.00014 0.00029 1.027 0.0271 -0.18% 0.00315 -0.6 0.259 NIR B3N -0.00002 0.00219 0.999 0.0077 -0.51% 0.01764 -1.1 0.125 MIR (B5) SWIR1 -0.00225 0.00138 1.019 0.0107 -0.20% 0.00825 -0.1 0.479 MIR (B7) SWIR2-6 -0.00240 0.00105 1.048 0.0211 -0.66% 0.00496 -0.5 0.292 MY01 MY01: MY01: V. Green B1 0.00045 0.00045 0.977 0.0245 0.03% 0.00298 0.0 0.484 Vis. Red B2 0.00013 0.00036 0.995 0.0269 0.46% 0.00287 -2.4 0.008* NIR B3N 0.00163 0.00208 0.994 0.0075 -0.30% 0.01593 -1.0 0.155 MIR (B5) SWIR1 -0.00159 0.00136 1.012 0.0107 -0.44% 0.00703 -0.8 0.203 MIR (B7) SWIR2-6 -0.00146 0.00149 1.029 0.0290 -0.43% 0.00411 -0.6 0.277 47 Indicates a p-value for the standardized Wilcoxon signed-rank score below 0.01. Indicates that the estimated K-M-S intercept ( ) confidence interval cal culated as (1.96)(SD) does not contain the expected value of 0.0. Indicates that the estimated Theil-Sen Slope ( ) confidence interval calculated as (1.96)(SD) does not contain the ex pected slope of 1.0.
Table 3-3. Transformation results of data after applying the independently derived coefficients from Table 2-1 to MY01 data. Transformation Performed ETM+ FLAASH ASTER FLAASH K-M-S Bisector Intercept ( ) SD ( ) TheilSen Bisector Slope ( ) SD ( ) Bias Median of Absolute Diff. Std. Wilcoxon Signed Rank Score (Z) SR p-value None MY01: MY01: V. Green B1 -0.00538 0.00058 0.885 0.0217 -44.38% 0.00840 -84.8 0.000* Vis. Red B2 -0.00219 0.00042 1.008 0.0271 -14.70% 0.00300 -41.9 0.000* NIR B3N 0.02991 0.00186 0.901 0.0068 4.27% 0.01720 -10.6 0.000* MIR (B5) SWIR1 -0.09326 0.00242 1.505 0.0164 -44.93% 0.01900 -84.7 0.000* MIR (B7) SWIR2-6 -0.07878 0.00377 2.062 0.0596 -44.32% 0.01154 -85.4 0.000* MS01 MY01: MY01: V. Green B1 -0.00112 0.00048 0.966 0.0242 -14.35% 0.00333 -37.7 0.000* Vis. Red B2 -0.00074 0.00038 0.994 0.0269 -6.24% 0.00296 -17.9 0.000* NIR B3N 0.01521 0.00197 0.938 0.0071 -2.81% 0.01644 -7.4 0.000* MIR (B5) SWIR1 -0.01070 0.00147 1.095 0.0116 4.29% 0.00694 -11.9 0.000* MIR (B7) SWIR2-6 -0.00959 0.00173 1.251 0.0354 16.00% 0.00435 -42.8 0.000* MY00 MY01: MY01: V. Green B1 0.00101 0.00042 0.894 0.0219 8.27% 0.00325 -21.3 0.000* Vis. Red B2 0.00196 0.00030 0.914 0.0241 5.16% 0.00314 -18.6 0.000* NIR B3N 0.03936 0.00178 0.867 0.0065 4.82% 0.01767 -12.0 0.000* MIR (B5) SWIR1 0.01890 0.00114 0.893 0.0093 16.86% 0.00896 -43.7 0.000* MIR (B7) SWIR2-6 0.01042 0.00116 0.951 0.0268 36.91% 0.00855 -78.7 0.000* 48 Indicates a p-value for the standardized Wilcoxon signed-rank score below 0.01. Indicates that the estimated K-M-S intercept ( ) confidence interval cal culated as (1.96)(SD) does not contain the expected value of 0.0. Indicates that the estimated Theil-Sen Slope ( ) confidence interval calculated as (1.96)(SD) does not contain the ex pected slope of 1.0.
49Table 3-4. Comparison of derived vege tation indices from post-transformati on MY01 ASTER and original ETM+ data. Transformation Performed ASTER MY01 Index K-M-S Bisector Intercept ( ) SD ( ) TheilSen Bisector Slope ( ) SD ( ) Bias Median of Absolute Diff. Std. Wilcoxon Signed Rank Score (Z) SR p-value None NDVI 0.04848 0.02807 0.962 0.0314 15.23% 0.02104 -44.9 0.000* EVI2 0.06271 0.00583 0.891 0.0118 9.66% 0.02722 -24.4 0.000* MS01 NDVI 0.03289 0.02904 0.968 0.0322 5.13% 0.01892 -15.7 0.000* EVI2 0.03453 0.00610 0.928 0.0121 -0.30% 0.02536 -1.2 0.113 MY00 NDVI 0.10536 0.02598 0.878 0.0285 -4.38% 0.02084 -15.8 0.000* EVI2 0.07537 0.00552 0.852 0.0110 3.00% 0.02705 -7.0 0.000* Indicates a p-value for the standardized Wilcoxon signed-rank score below 0.01. Indicates that the estimated K-M-S intercept ( ) confidence interval cal culated as (1.96)(SD) does not contain the expected value of 0.0. Indicates that the estimated Theil-Sen Slope ( ) confidence interval calculated as (1.96)(SD) does not contain the ex pected slope of 1.0.
0.0000 0.5000 1.0000 1.5000 2.0000 Theil-Sen bi-sector MS01 ASTER Surface Reflectance: Slope ETM vs. L1A NN ETM vs. L1B L1B vs. L1A NN Figure 3-1. Comparison by band of estimated Theil-Sen bisector slopes for ETM+ vs. ASTER L1A and L1B FLAASH surface reflecta nces derived for the MS01 subset. -0.0800 -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 K-M-S bi-sector ( )MS01 ASTER Surface Reflectance: Intercept ETM vs. L1A NN ETM vs. L1B L1B vs. L1A NN Figure 3-2. The K-M-S bisector intercept estimates for ETM+ vs. ASTER L1A and L1B FLAASH surface reflectances for each ba nd combination, corresponding to the slope estimates from Figure 3-1. 50
B) Pre-transformed Relationship A) Post-transformed Relationship Figure 3-3. A) Illustrating th e effects of ETM+ B7 MY01 being regressed on ASTER MY01. Data are presented without transformation bu t with plotted estimated regression line (solid) compared to the 1:1 line (dashed). B) The post-transformation results for the same data are observed to fall almost comple tely on the 1:1 line a nd as expected split the data cloud symmetrically along the medial axes. 51
0.0000 0.5000 1.0000 1.5000 2.0000 Vis. GreenVis. RedNear-IRETM B5 v. SWIR1 ETM B7 v. SWIR 2-6 Res.Theil-Sen bi-sector MS01ASTER Transformed Surface Reflectance: Slope ETM vs. L1A Resampled ETM vs. L1A Transformed ETM vs. L1A Transf. (MY00) Figure 3-4. Comparison of estimated, post-transformation TheilSen bisector slopes for ETM+ vs. ASTER L1A FLAASH MS01 surface reflectan ces that were spectrally resampled to match ETM+ B7. The data shown compare the effects of the data transformed with its own estimates (MS01) to the effect of transforming by the MY01 estimated coefficients, and with both relative to the untransformed data. -0.0800 -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400 Vis. GreenVis. RedNear-IRETM B5 v. SWIR1 ETM B7 v. SWIR 2-6 Res.K-M-S bi-sector ( )MS01ASTER Transformed Surface Reflectance: Intercept ETM vs. L1A Resampled ETM vs. L1A Transformed ETM vs. L1A Transf. (MY00) Figure 3-5. Comparison of estimated, post-transformation K-M-S bi sector intercepts matching the slopes from Figure 3-3. 52
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -1-0.8-0.6-0.4-0.200.20.40.6K-M-S Intercept ( )Deviation From 1:1 (Theil-Sen Bi-sector Slope -1.0)ETM+ Regression on MS01, Before and After MS01 Transformation Vis. Red NIR MIR (B7) Vis. Red (Scaled) NIR (Scaled) MIR (B7) (Scaled) Reference: T-S Bi-sector Slope = 1.0 K-M-S Intercept = 0.05 Abs. Maximum Bias = 50% Figure 3-6. Visual representation of transformation effects on estimated regression coefficients for the ETM+ MS01 regressed on ASTER MS01 preand post-transformation. Note the transformation effect highlighted by the arrow on the pre-transformation coefficients for ETM+ B7 (red circles) as the slope changes to very close to 1.0 and intercept very close to 0.0 with a much smaller absolute bias (transformed, blue circles). 53
-140 -120 -100 -80 -60 -40 -20 0 20 40 60 00.020.040.060.080.10.120.140.160.180.2Standardized Wilcoxon Signed Rank ScoreMedian of Absolute Differences (ASTER -ETM+) ( )ETM+ Compared to MS01 (Transformation: MS01) Vis. Red NIR MIR (B7) Vis. Red (Scaled) NIR (Scaled) MIR (B7) (Scaled) Reference: Abs. Diff. Median = 0.5 Std. Rank Score = 3 Abs. Maximum Bias = 50% Figure 3-7. Transformation effects are shown as m easured by metrics of spread and centrality for preand post-transformation of AS TER MS01 by its own MS01 regression coefficients. Standardized Wilcoxon signed rank scores may be interepreted as a general measure of symmetry around the media n, or in the case of Theil-Sen bisector transformed data around the 1:1 line. 54
Figure 3-8. Each of the five matching ETM+ MY 01 bands and their diag nostic regressions are plotted against the corresponding transf ormed ASTER MY01 data. The MY01 ASTER data were transformed by estimated coefficients from the MS01 data. 55
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -1.5 -1 -0.5 0 0.5K-M-S Intercept ( )Deviation From 1:1 (Theil-Sen Bi-sector Slope -1.0)ETM+ Regression on MY01, Before and After MS01 Transformation Vis. Red NIR MIR (B7) Vis. Red (Scaled) NIR (Scaled) MIR (B7) (Scaled) Reference: T-S Bi-sector Slope = 1.0 K-M-S Intercept = 0.05 Abs. Maximum Bias = 50% Figure 3-9. Transformation effect as measured by the preand post-transformation regression coefficients for ETM+ MY01 regressed on ASTER MY01 bands after transforming with MS01 estimated coefficients. -140 -120 -100 -80 -60 -40 -20 0 20 40 60 0 0.005 0.01 0.015 0.02 0.025 0.03Standardized Wilcoxon Signed Rank ScoreMedian of Absolute Differences (ASTER -ETM+) ( )ETM+ Compared to MY01 (Transformation: MS01) Vis. Red NIR MIR (B7) Vis. Red (Scaled) NIR (Scaled) MIR (B7) (Scaled) Reference: Abs. Diff. Median = 0.5 Std. Rank Score = 3 Abs. Maximum Bias = 50% Figure 3-10. Post-transformation effects on MY 01 (transformed by MS01) as measured by metrics of spread and centrality. 56
Figure 3-11. Scatterplots and their diagnostic Theil-Sen bise ctor regressions of ETM+ derived NDVI and EVI2 vegetation indices, ag ainst the MY01 (transformed by MS01) derived indices. 57
01234 0.5 Kilometers Datum: WGS-84 Proj.: UTM Zone 19SEVI2 (MY01 transformed by MS01) MY00, MY01 MS01 > 0.8 < 0.11:100,000 Figure 3-12. The spatial distribution of EVI2 values calcula ted for the MY01 subset after transformation using estimated Theil-Sen bisector coefficients from the MS01 sample. Notice the lack of saturation and no visible artifacts in the resulting data. 58
00.751.52.253 0.375 Kilometers Datum: WGS-84 Proj.: UTM Zone 19SVis. Red Difference (Untransformed) (MY01 B2) (ETM+ 2001 Vis. Red) MY00, MY01 MS01 > 0.005 ( ) < -0.005 ( )1:50,000 Figure 3-13. This map shows the artifacts created by mapping the difference of visible red bands, calculated by subtracting the ETM+ band from the MY01, untransformed data. Notice the regular banding in roughly a N-NE direction. This is unlikely due to registration errors or other data mis-hand ling, as the artifacts may be observed in the original, uncalibrated ETM+ B3. This di fference image can be represented by the Vis. Red band scatterplots in in Figures 3-8 and 3-15. 59
00.751.52.253 0.375 Kilometers Datum: WGS-84 Proj.: UTM Zone 19SVis. Red Difference (Transformed) (MY01 B2 by MS01) (ETM+ 2001 Vis. Red) MY00, MY01 MS01 > 0.005 ( ) < -0.005 ( )1:50,000 Figure 3-14. The visible artifacts, though still pres ent are clearly located near the center of the error distribution as the differencing of the transformed ASTER MY01 visible red and ETM+ band shows. The overall distributi on has shifted markedly toward the red, indicating a greater degree of symmetry around the 1:1 line in the scatterplots of 3-8 and 3-15. 60
-0.007 0.070 0.070 ASTER MY01 B2 (transformed MS01) ( )ETM+ 2001Vis. Red ( ) Figure 3-15. Scatter plot of ETM+ visible red data against the transformed ASTER MY01band. The highlighted area in magenta represent pixels within the region that prior to transformation fell to the right, of the 1: 1 line in the figure, and hence prior to transformation representing pixels with positive differences in Figure 3-13 and negative differences in Figure 3-14. 61
00.751.52.253 0.375 Kilometers Datum: WGS-84 Proj.: UTM Zone 19SEVI2 Overlayed by Vis. Red Diff. Switched Signs MY01 (by MS01) ETM+ 2001 MY00, MY01 MS01 ETM > ASTER in both ETM < ASTER in transf. > 0.8 < 0.11:50,000 Figure 3-16. Overlaying the calculated EVI2 layer based on the transformed MY01 (transformed by the estimated coefficients of MS01) are the pixels from Figure 3-15 identified as having changed signs (i.e. moved from the right to left of the 1:1 line or changed from more purple to more yellow in Figures 3-13 and 3-14). 62
00.751.52.253 0.375 Kilometers Datum: WGS-84 Proj.: UTM Zone 19SEVI2 Difference (MY01 transformed by MS01) (ETM+ 2001) MY00, MY01 MS01 > 0.1 < -0.11:50,000 Figure 3-17. This image difference map of MY01 (transformed by MS01 coefficients) minus ETM+ EVI2 data shows that despite the spatial clustering of positive to negative differences in the visible red band, as disp layed in Figure 3-16, EVI2 seems relatively robust to this segregation. EVI2 generally are observed to fall within the range of .05, except for regions inundated with water. 63
64 0.00 0.80 0.80 ASTER MY01 (transformed MS01) EVI2ETM+ 2001 EVI2 0.70 1.00 1.00 ASTER MY01 (transformed MS01) NDVIETM+ 2001 NDVI Figure 3-18. Illustration of pixel locations of visible red difference shifts within scatterplots of the calculated vegetation indices in post-tra nsformation data. Note how EVI2 is quite symmetric about the 1:1 line relative to NDVI, and that th e shifted difference pixels are symmetrically distributed as well. This indicates that EVI2 is more robust to the effects of changes in the visible red band as well as departures from a strict 1:1 relationship.
CHAPTER 4 DISCUSSION AND CONCLUSION Study Implications This study finds that functional associati ons between same-day ASTER and ETM+ data are predictable for a representative tropical fo rested region in the Western Amazon. Results show the utility of Theil-Sen bisector regressi on in not only describing but also in transforming the linear relationships in these remote sensi ng data. Since both ASTER and ETM+ data contain various types of measurement error, the appli cability of a true independent and dependent relationship is questionable and bisector regression is necessa ry to fit the expected 1:1 relationship in these data. Recent studies in the remote sensing literature have recognized the use for bisector regression (Ji et al. 2008), just as some have al so incorporated the use of Theil-Sen estimators (Olthof et al. 2005). However, using Theil-Sen re gression to minimize the impact of outliers and heteroscedasticity is rarely em ployed in tandem with the bisect or approach. This study shows the Theil-Sen bisector applicability may be extrem ely useful when describi ng relationships in the presence of both bivariate error and when data do not meet the assumptions of OLS regression. This situation is extremely common in remote se nsing and land change science, where we are comparing two or more calculated metrics or measures that, both being estimates of some ground truth, have error and outliers, multi-moda lity and/or non-normality. For example this is often the case when comparing vegetation indi ces or estimated reflectance where there is an implicit expectation of a 1:1 re lationship between independent measurements (e.g., Ji et al. 2008). Theil-Sen bisector regression s hould be free from these biases while offering most of the power of an OLS approach, for both small and large sample sizes, without being affected by 65
heteroscedasticity, outliers and pa rametric considerations (Isobe et al. 1990; Wilcox 1998). To date, T-S bisector regression us e appears limited to astronomy and astrophysics (Bauer et al. 2002) but a full exploration of its use and implications are not in the literature. One reason for this is that estimating coefficients, standard e rrors and confidence interv als requires significant computing resources and custom software. Fu rthermore, sampled analyses likely must be bootstrapped or resampled, which adds extra burden on the researcher. This study suggests that future research should focus on describing limitations of the TheilSen bisector approach. This s hould include a comparison with OL S bisector and other bisector regression techniques for both descri ption and transformation of remo tely sensed data since they may be easier to employ given they are more we ll understood and standard error estimates for coefficients can be arithmetically derived (Isobe et al. 1990). Though the results showed very good results in same-day transformations leading to low bias and relatively high agreement between same-day ASTER and ETM+ data across all bands, a representative functional relati onship was not explicitly arrived at. This study showed that significant variability in transformation coefficien ts may occur across each of the subsets used. The best transformation with th e least aggressive, linear scalin g and highest cross-date and subset applicability was the MS01 transformation (Table 3-1). Its use in transforming the MY01 dataset significantly lowered bi as, absolute median of differe nces and standardized Wilcoxon rank scores, and in general increas ed the agreement greatly with ETM+ data. Further refinement of the transformations presented here may be po ssible and should be pursued in future research. To facilitate such research a semi-automat ed system for ASTER and ETM+ comparison and transformation is available upon request. As a by-product of the custom software developed to conduct the research presented, an ENVI 4.3 and IDL 6.3 (ITT Visual Information Solutions 66
2007) solution for spectrally resampling ASTER data, generating Theil-Sen bisector transformation coefficients, creati ng scatterplot diagnostics, and pr oviding general statistics may be a vital tool for other researcher s. As a more user-friendly tool it can be modified in the future to allow for the definition of regions-of-interest that represent unchanged overlap between time-steps in prior ETM+ data coupled with ne wer ASTER data. These overlapping areas may be compared and cross-calibration based on Theil-Sen bisector transformations may be automatically applied. The software generates bivariate and statistically compares the transformation outcomes. This approach may ev en be extended to non Landsat data, presenting an opportunity for a more general tool for cross-da te or cross-scene calibra tion of any two sets of data where bivariate measurement error in creases the difficulty in finding functional relationships and where Theil-Sen bisector regression may be useful. The various sources of such error were minimi zed to the greatest extent possible in this study. The use of same-date imagery was ideal fo r minimizing the effects of solar irradiation and atmospheric attenuation. The use of a s ophisticated atmospheric correction technique (FLAASH) also minimized error that is introduced by varying atmospheric conditions coupled with sensor response. Registration errors were also minimized to the greatest extent possible, however, after the inherent sensor differences between ASTER and ETM+, registration error may be the largest source of bivariate error in this study. The effects of misregistration on long-term cha nge detection in classified studies can be extreme. Research shows that errors of only one fifth of a pixel may lead to change detection errors of 10% or more (Dai and Khorram 1998) When looking at reflectances or derived continuous indices the effects of registration error are far more s ubtle, since differences between images are from a continuous distribution rath er than a categorical misclassification. The 67
impacts of resampling, either by smoothing in the case of bilinear and CC resampling, or data censoring and duplication in the NN case, also need to be better understood. This study showed higher levels of agreements with ETM+ for CC ASTER data than NN ASTER data. This is not surprising given that slight misreg istration and the scalar mismatch in pixel size likely account for a large degree of the observed variability around the 1:1 lines. Therefore, this study may be expanded to include comparisons of various types and levels of smoothed ASTER data with ETM+ data. Spectral fidelity was maximized he re, yet for finding a more general functional relationship this may not be the best approac h. Smoothing may ultimately help in increasing inter-subset agreement on transformation coefficients. The argument for a general set of transforma tion coefficients for ASTER data to match ETM+ can not be found from this studys results However, same-day results show great promise for increasing the level of agreemen t between ASTER and ETM+ surface reflectance values across all bands. This may also be an argument for the previously mentioned use of invariant regions-of-interest between dates, and their use to de velop study-specific transformations. Also of particular note were the results for agreements of resampled SWIR2-6 ASTER bands and ETM+ B7. The observed associ ations in transformed data are very encouraging, as the lack of comparable bands in this region was a significant limitation for using ASTER with ETM+ in longitudinal studies. Finally the, successful comp arison of ASTER and ETM+ derived EVI2 is extremely encouraging for the study of vegetation dynamics in tropical areas. The saturation limits of NDVI and lack of a blue band in the ASTER da ta make vegetation studies using continuous indices much more difficult. But high levels of agreement preand moreso post-transformation show that EVI2 is an extremely viable solution to the vegetation index problem faced in similar 68
69 study areas. Ongoing research should compar e ASTER-derived EVI2 with Landsat-derived EVI, just as in recent work with MODIS and AVHRR (Ji et al. 2008). Al so research using the techniques presented here should extend comparisons of ASTERand Landsat-derived products beyond vegetation indices to those su ch as tasseled cap, and vari ous other analyses. By first transforming ASTER data, tasseled cap results usi ng Landsat coefficients may be compared to those principal components coefficients presented for ASTER (Yarbrough, Easson and Kuszmaul (2005) (Appendix A). Conclusion Though the long-term viability of the Landsat program will no doubt continue, the nearterm likelihood of data gaps exists. It should be noted that the Landsat data gap is not just a concern for individual scientists or for U.S.-based research initiatives alone. Wulder et al. (2008) identify at least six global land monitoring prog rams that rely on Landsat data for their ongoing research efforts. Though ASTER could not be c onsidered a drop-in repl acement for any of these larger-scale monitoring programs, researchers working at a spatial and temporal scale appropriate to ASTER, and who intend to use th e hugely useful data derived from such longterm studies may utilize techniques presented here. The Theil-Sen bisector regression approach eases comparison and transformation of data and ma y be more widely app licable across remotesensing applications. And by minimizing the im pacts of spectral diffe rences between ASTER and ETM+ the techniques presented here may allo w for ASTER data to be used not just in classification-based studies of la nd change, but also in more direct comparisons. Doing so gives us one more potential bridge past data gaps by using ASTER in areas where the appropriate spatial and temporal scales allow.
APPENDIX A ORIGINAL SOURCE CODE FOR DISCUSSED ANALYSES ASTER Top-of-Atmosphere Reflectance Conversion from At-Sensor Radiance 1 ; ENVI and IDL Utilities for ASTER/Landsat Processing 2 ; Copyright (C) 2008 Forrest R. Stevens 3 ; 4 ; This program is free software: you can redistribute it and/or modify 5 ; it under the terms of the GNU General Public License as published by 6 ; the Free Software Foundation, either version 3 of the License, or 7 ; (at your option) any later version. 8 ; 9 ; This program is distributed in the hope that it will be useful, 10 ; but WITHOUT ANY WARRANTY; without even the implied warranty of 11 ; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 ; GNU General Public License for more details. 13 ; 14 ; You should have received a copy of the GNU General Public License 15 ; along with this program. If not, see < http://www.gnu.org/licenses/ >. 16 17 18 PRO ASTER_FILE_TOA_REFLECTANCE, hdf_file = hdf_file append_name= append_name 19 ; The only argument here should be the hdf_filename. The at-sensor-radiance 20 ; file that is fed into the top-of-atmosphere calculation is assumed to have 21 ; '_asrad.dat' at the end of the root name (without the processing date/time). 22 ; For example, the parameter above should be the first of the following list, 23 ; but the rest of the files are assumed to follow the naming convention as 24 ; displayed: 25 ; AST_L1B_00307292001151134_20070319101905_28000.hdf (parameter above) 26 ; AST_L1B_00307292001151134_20070319101905_28000.hdf.met (metadata file from 27 ; which solar elevation 28 ; is read) 29 ; AST_L1B_00307292001151134_asrad.dat (at-sensor radiance file) 30 ; AST_L1B_00307292001151134_toar.dat (output) 31 32 if N_params () GT 3 then begin 33 MESSAGE 'Syntax ASTER_FILE_TOA_REFLECTANCE, hdf_filename="data_filename_root", $ 34 append_name="appended name"' 35 endif 36 37 ; 38 ; Open the HDF file: 39 ; 40 infile = '' 41 if KEYWORD_SET ( hdf_file ) then begin 42 hdf_filename = hdf_file 43 endif else begin 44 ; Use the ENVI_SELECT function if you want to select a file on the fly rather than 45 ; use a filename passed on the command line... 46 hdf_filename = envi_pickfile( title= 'Input HDF Filename:' ) 47 endelse 48 49 ; Set the input file root name from the HDF file name: 50 data_fileroot = strmid ( hdf_filename 0 (strlen ( hdf_filename ) 24)) 51 52 ; 53 ; Extract solar elevation angle from the metadata file: 54 ; 55 nlines = file_lines( hdf_filename + '.met' ) 56 sarr = strarr (nlines) 57 openr, unit, hdf_filename + '.met' /get_lun 58 readf, unit, sarr 59 free_lun unit 60 61 if strpos ( hdf_filename 'L1B') ne 1 then begin 62 ; Solar elevation line for L1B is hopefully always line 776: 63 text_line = sarr[ 775] 64 solar_elevation = strmid (text_line, 34, 9 ) 70
65 endif else begin 66 ; Solar elevation line for L1A is hopefully always line 758: 67 ; Apparently not always, it's different for the 2000 data, found on line 817: 68 if strpos ( hdf_filename '2000' ) ne 1 then begin 69 text_line = sarr[ 816] 70 endif else begin 71 text_line = sarr[ 757] 72 endelse 73 74 solar_elevation = strmid (text_line, 30, 18) 75 endelse 76 77 78 ; 79 ; Open the input file 80 ; 81 append_name_text = '' 82 if KEYWORD_SET (append_name) then begin 83 infile = data_fileroot + 'asrad' + append_name + '.dat' 84 append_name_text = '_toar' + append_name 85 endif else begin 86 infile = envi_pickfile( title= 'Input ASRAD Filename:' ) 87 append_name_text = '_toar' 88 endelse 89 90 envi_open_file, infile, r_fid= fid 91 if (fid eq 1 ) then begin 92 MESSAGE 'Input file + infile + not found!' 93 endif 94 95 if (fid eq 1 ) then return 96 envi_file_query, fid, dims=dims, ns=ns, nl=nl, nb=nb, interleave= interleave, $ 97 data_type= data_type, xstart= xstart, ystart= ystart, $ 98 bnames= bnames, fname= fname, fwhm=fwhm, wl=wl 99 pos = indgen (nb) 100 101 ; 102 ; Create outfile string: 103 ; 104 outfile = '' 105 if KEYWORD_SET (outfile_name) then begin 106 outfile = outfile_name 107 endif else begin 108 ; Assumes the filename of the input has the first part of the AST_ specification 109 ; of the form: "AST_L1A_00307292001151134" 110 filestart = strpos (fname, "AST_" /REVERSE_SEARCH ) 111 outfile = strmid (fname, 0 filestart + 25) + append_name_text + $ 112 strmid (fname, 3 /REVERSE_OFFSET ) 113 endelse 114 115 ; Pull the map information for the current file to save with the final output... 116 map_info = envi_get_map_info( fid=fid) 117 118 119 ; NOTE: This is SPATIAL tiling, not spectral, like as seen in the ASTER TCA calculations. 120 ; Therefore we set the interleave to BSQ (this is regardless of whether the band order 121 ; is BSQ, BIL, or BIP in the original data... 122 openw, unit, outfile, /get_lun 123 tile_id = envi_init_tile(fid, pos, num_tiles= num_tiles, $ 124 interleave= 0 xs=dims[1 ], xe=dims[2 ], $ 125 ys=dims[3 ], ye=dims[4 ]) 126 127 ; Setup the progress bar, the ENVI_REPORT_STAT procedure below updates the bar 128 ; as we loop through the tiles... 129 ENVI_REPORT_INIT, [ 'Reading and writing data for:' outfile], $ 130 title= 'ASTER TOAR Conversion:' base=base 131 ENVI_REPORT_INC, base, num_tiles 132 133 for tile= 0L, num_tiles1 do begin 134 image_data = envi_get_tile(tile_id, tile, band_index= band_index) 135 71
136 image_toa = aster_toa_reflectance( TEMPORARY (image_data), hdf_filename $ 137 FLOAT(solar_elevation), bands= [band_index]) 138 139 writeu unit, image_toa 140 ;print, i 141 142 ENVI_REPORT_STAT, base, tile+ 1 num_tiles 143 endfor 144 145 ;envi_file_mng, id=fid, /remove 146 147 ENVI_REPORT_INIT, base=base, /finish 148 149 free_lun unit 150 151 envi_setup_head, fname= outfile, ns=ns, nl=nl, nb=nb, $ 152 data_type= 4 offset= 0 interleave= 0 $ 153 xstart= xstart+dims[ 1 ], ystart= ystart+dims[ 3 ], $ 154 bnames= 'TOAR + bnames, map_info= map_info, $ 155 descrip= 'ASTER TOAR conversion from: + fname, fwhm=fwhm, wl=wl, $ 156 /write /open 157 envi_tile_done, tile_id 158 END 159 160 161 FUNCTION ASTER_TOA_REFLECTANCE, image, hdf_filename solar_elevation, bands= bands 162 163 if N_params () LT 3 then begin 164 print, 'Syntax Result = ASTER_TOA_REFLECTANCE( image, hdf_filename,' $ 165 'solar_zenith, /bands=[bands] )' 166 return -1 167 endif 168 169 if NOT KEYWORD_SET (bands) then begin 170 ; This assumes that if bands weren't specified that the bands being fed would 171 ; follow the order below, specified as 1-9 in the bands array: 172 ; VNIR: 1, 2, 3N 173 ; SWIR: 4, 5, 6, 7, 8, 9 174 175 dimensions = size(image, /dimensions ) 176 if (n_elements (dimensions) eq 2 ) then bands = indgen ( 1 ) $ 177 else bands = indgen (dimensions[ 2 ]) 178 bands = bands + 1 179 endif 180 181 julian_date = JULDAY ( $ 182 LONG( STRMID ( hdf_filename (strlen ( hdf_filename ) 39), 2 )), $ 183 LONG( STRMID ( hdf_filename (strlen ( hdf_filename ) 37), 2 )), $ 184 LONG( STRMID ( hdf_filename (strlen ( hdf_filename ) 35), 4 )), $ 185 LONG( STRMID ( hdf_filename (strlen ( hdf_filename ) 31), 2 )), $ 186 LONG( STRMID ( hdf_filename (strlen ( hdf_filename ) 29), 2 )), $ 187 LONG( STRMID ( hdf_filename (strlen ( hdf_filename ) 27), 2 )) $ 188 ) 189 190 ; Debug code to test Julian date extraction from file name: 191 ;caldat, julian_date, Month1, Day1, Year1 192 ;print, Month1, Day1, Year1 193 194 ; These represent the mean solar exoatmospheric irradiance of each band of ASTER data 195 ; from the visual, near and shortwave IR bands: 196 ; VNIR: 1, 2, 3N 197 ; SWIR: 4, 5, 6, 7, 8, 9 198 esun = [ 1844.6 1556.5 1083.8 232.74 79.854 74.752 68.898 60.002 57.652 ] 199 200 pi = 3.14159 201 202 distance_to_sun = ( 1.0 (0.01672 COS( 0.9856 (julian_date 4.)))) 203 204 solar_zenith_rad = ( 90. solar_elevation) pi / 180. 205 206 if (n_elements (bands) gt 1 ) then begin 72
207 for band = 0 (n_elements (bands) 1 ) do begin 208 image[*,*,band] = float((pi image[*,*,band] $ 209 (distance_to_sun)^ 2 ) / (esun[bands[band] 1 ] $ 210 COS(solar_zenith_rad))) 211 endfor 212 endif else begin 213 image = float((pi image (distance_to_sun)^ 2.) / (esun[bands[ 0 ] 1.] $ 214 COS(solar_zenith_rad))) 215 endelse 216 217 return image 218 END Theil-Sen and H-M-S Intercept Regression 1 ; ENVI and IDL Utilities for Nonparametric Statistics 2 ; Copyright (C) 2008 Forrest R. Stevens 3 ; 4 ; This program is free software: you can redistribute it and/or modify 5 ; it under the terms of the GNU General Public License as published by 6 ; the Free Software Foundation, either version 3 of the License, or 7 ; (at your option) any later version. 8 ; 9 ; This program is distributed in the hope that it will be useful, 10 ; but WITHOUT ANY WARRANTY; without even the implied warranty of 11 ; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 ; GNU General Public License for more details. 13 ; 14 ; You should have received a copy of the GNU General Public License 15 ; along with this program. If not, see < http://www.gnu.org/licenses/ >. 16 17 18 PRO KENDALL, Xs, Ys, pointN= pointN, seed=seed 19 ; For problems 8.1 and 8.22, Hollander and Wolfe, 1990 20 21 ;X = [28.9, 32.8, 12, 9.9, 15, 38, 12.5, 36.5, 8.6, 26.8] 22 ;Y = [1, 7.7, 7.3, 7.9, 1.1, 3.5, 18.9, 33.9, 28.6, 25] 23 24 ;C: 3 4 4 3 4 2 4 8 1 5 25 ;D: 6 5 5 6 5 7 5 1 8 4 26 ;T: 0 0 0 0 0 0 0 0 0 0 27 ;C-D: -3 -1 -1 -3 -1 -5 -1 7 -7 1 28 ;Total: -14.0000 29 ;K: -7.00000 30 ;t: -0.155556 31 32 if KEYWORD_SET (pointN) then begin 33 if NOT KEYWORD_SET (seed) then begin 34 newseed = SYSTIME ( /seconds ) 35 endif else begin 36 newseed = seed 37 endelse 38 39 ; See the SIZE function for an explanation of the "type" keyword values, we're 40 ; generating a list of random indices for the two-dimensional band arrays 41 ; to set as our scatter plot points. 42 43 random_index = fix( N_ELEMENTS (Xs) RANDOMU (newseed, pointN), type=13) 44 X = Xs[random_index] 45 Y = Ys[random_index] 46 endif else begin 47 X = Xs 48 Y = Ys 49 endelse 50 51 52 N = n_elements (X) 53 C = indgen (N) 54 D = indgen (N) 73
55 T = indgen (N) 56 57 X = float(X) 58 Y = float(Y) 59 60 for i = 0 (N 1 ) do begin 61 pairsC = 0 62 pairsD = 0 63 pairsT = 0 64 for j = 0 (N 1 ) do begin 65 if i ne j then begin 66 concordance = (X[i] X[j])*(Y[i] Y[j]) 67 if concordance gt 0 then pairsC = pairsC + 1 68 if concordance lt 0 then pairsD = pairsD + 1 69 if concordance eq 0 then pairsT = pairsT + 1 70 endif 71 endfor 72 C[i] = pairsC 73 D[i] = pairsD 74 T[i] = pairsT 75 endfor 76 ;print, "C:", C 77 ;print, "D:", D 78 ;print, "T:", T 79 ;print, "C-D:", C D 80 print, "Total:" total(C-D) 81 print, "K:", total(C-D)/ 2. 82 print, "t:", 2 *(total(C-D)/2.) / (N*(N 1 )) 83 END 84 85 PRO THEIL, Xs, Ys, pointN= pointN, seed=seed 86 ; For problem 9.7, Hollander and Wolfe, 1990 87 88 ;X = [0, 5000, 10000, 15000, 20000, 25000, 30000, 100000] 89 ;Y = [0.924, 0.988, 0.992, 1.118, 1.133, 1.145, 1.157, 1.357] 90 91 ;Bhat: 5.54500e-006 92 93 if KEYWORD_SET (pointN) then begin 94 if NOT KEYWORD_SET (seed) then begin 95 newseed = SYSTIME ( /seconds ) 96 endif else begin 97 newseed = seed 98 endelse 99 100 ; See the SIZE function for an explanation of the "type" keyword values, we're 101 ; generating a list of random indices for the two-dimensional band arrays 102 ; to set as our scatter plot points. 103 104 random_index = fix( N_ELEMENTS (Xs) RANDOMU (newseed, pointN), type=13) 105 X = Xs[random_index] 106 Y = Ys[random_index] 107 endif else begin 108 X = Xs 109 Y = Ys 110 endelse 111 112 113 N = n_elements (X) 114 S = findgen (N*(N 1 )/2 ) 115 index = 0L 116 117 X = float(X) 118 Y = float(Y) 119 120 for i = 0 (N 2 ) do begin 121 for j = i + 1 (N 1 ) do begin 122 S[index] = (Y[j] Y[i]) / (X[j] X[i]) 123 index = index + 1 124 endfor 125 endfor 74
126 Bhat = median (S, /EVEN) 127 ;print, "S:", S 128 print, "Theil Bhat:" Bhat 129 print, "H-M-S Int.:" median ((Y X*Bhat), /EVEN) 130 END ASTER Tasseled Cap Calculations and Conversion 1 ; ENVI and IDL Utilities for ASTER/Landsat Processing 2 ; Copyright (C) 2008 Forrest R. Stevens 3 ; 4 ; This program is free software: you can redistribute it and/or modify 5 ; it under the terms of the GNU General Public License as published by 6 ; the Free Software Foundation, either version 3 of the License, or 7 ; (at your option) any later version. 8 ; 9 ; This program is distributed in the hope that it will be useful, 10 ; but WITHOUT ANY WARRANTY; without even the implied warranty of 11 ; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 ; GNU General Public License for more details. 13 ; 14 ; You should have received a copy of the GNU General Public License 15 ; along with this program. If not, see < http://www.gnu.org/licenses/ >. 16 17 18 19 PRO ASTER_TCA, infile_name= infile_name, outfile_name= outfile_name, append_name= append_name 20 ; I wrote this to implement the ASTER tasseled cap linear recombination as 21 ; outlined in Yarbrough, Easson and Kuszmaul (2005), Using at-sensor radiance... FRS, 2008 22 23 ; aster_tca, infile_name='AST_L1A_00307262000151816_asrad_nn.dat', $ 24 ; outfile_name='AST_L1A_00307262000151816_tca_nn.dat' 25 26 27 if N_params () GT 3 then begin 28 MESSAGE 'Syntax ASTER_TASSELED_CAP, infile_name="input file", + $ 29 'outfile_name="output file", append_name="text to append to output name"' 30 endif 31 32 append_name_text = '' 33 if KEYWORD_SET (append_name) then begin 34 append_name_text = append_name 35 endif else begin 36 if NOT KEYWORD_SET (outfile_name) then begin 37 append_name_text = '_tca' 38 endif 39 endelse 40 41 ; 42 ; Open the input file 43 ; 44 infile = '' 45 if KEYWORD_SET (infile_name) then begin 46 infile = infile_name 47 48 envi_open_file, infile, r_fid= fid 49 if (fid eq 1 ) then begin 50 MESSAGE 'Input file + envi_filename + not found!' 51 endif 52 endif else begin 53 ; Use the ENVI_SELECT function if you want to select a file on the fly rather than 54 ; use a filename passed on the command line... 55 envi_select, title= 'Input Filename' fid=fid, $ 56 pos=pos, dims=dims 57 endelse 58 59 if (fid eq 1 ) then return 60 envi_file_query, fid, dims=dims, ns=ns, nl=nl, nb=nb, interleave= interleave, $ 61 data_type= data_type, xstart= xstart, ystart= ystart, $ 75
62 bnames= bnames, fname= fname, fwhm=fwhm, wl=wl 63 pos = indgen (nb) 64 65 ; 66 ; Create outfile string: 67 ; 68 outfile = '' 69 if KEYWORD_SET (outfile_name) then begin 70 outfile = outfile_name 71 endif else begin 72 ; Assumes the filename of the input has the first part of the AST_ specification 73 ; of the form: "AST_L1A_00307292001151134" 74 filestart = strpos (fname, "AST_" /REVERSE_SEARCH ) 75 outfile = strmid (fname, 0 filestart + 25) + append_name_text + $ 76 strmid (fname, 3 /REVERSE_OFFSET ) 77 endelse 78 79 ; Pull the map information for the current file to save with the final output... 80 map_info = envi_get_map_info( fid=fid) 81 82 transform_matrix = [ $ 83 [ 0.63400000 0.62500000 0.44600000 0.09300000 ,-0.01500000 $ 84 0.00600000 0.00000000 ,-0.00100000 ,-0.00100000 ], $ 85 [ 0.04700000 ,-0.57600000 0.63200000 0.51100000 ,-0.06500000 $ 86 0.00800000 0.00300000 ,-0.00400000 ,-0.00300000 ], $ 87 [ 0.76800000 ,-0.49800000 ,-0.35100000 ,-0.19800000 ,-0.00700000 $ 88 0.00200000 ,-0.00200000 ,-0.00100000 0.00300000 ], $ 89 [0.08300000 ,-0.14100000 0.46400000 ,-0.77400000 ,-0.39200000 $ 90 0.02700000 ,-0.01600000 ,-0.06200000 0.03800000 ], $ 91 [0.01000000 ,-0.05200000 0.13200000 ,-0.17500000 0.48200000 $ 92 0.53400000 0.55100000 ,-0.26700000 ,-0.23600000 ], $ 93 [0.00900000 ,-0.05270000 0.14300000 ,-0.17600000 0.40600000 $ 94 0.30900000 0.12400000 0.78200000 ,-0.24200000 ], $ 95 [0.00900000 ,-0.04800000 0.12400000 ,-0.14400000 0.48300000 $ 96 0.36200000 ,-0.63000000 0.07000000 0.44200000 ], $ 97 [0.00300000 ,-0.03200000 0.08300000 ,-0.08800000 0.36600000 $ 98 0.48800000 ,-0.35100000 ,-0.51200000 ,-0.47600000 ], $ 99 [ 0.00000000 ,-0.01900000 0.05400000 ,-0.04500000 0.27700000 $ 100 0.50000000 0.40000000 ,-0.21500000 0.68000000 ] $ 101 ] 102 103 openw, unit, outfile, /get_lun 104 tile_id = envi_init_tile(fid, pos, num_tiles= num_tiles, $ 105 interleave= (interleave > 1 ), xs=dims[1 ], xe=dims[2 ], $ 106 ys=dims[3 ], ye=dims[4 ]) 107 108 ; Setup the progress bar, the ENVI_REPORT_STAT procedure below updates the bar 109 ; as we loop through the tiles... 110 ENVI_REPORT_INIT, [ 'Reading and writing data for:' outfile], $ 111 title= 'ASTER Tasseled Cap Transform:' base=base 112 ENVI_REPORT_INC, base, num_tiles 113 114 for tile= 0L, num_tiles1 do begin 115 image_data = envi_get_tile(tile_id, tile) 116 ; We read in the spectral slice (an array of NS x NB) and take a median 117 ; slice of it. The DIMENSION variable tells the median function to return 118 ; an array of one dimension smaller than the original with the median operating 119 ; over the specified dimension number, in this case, the NB dimension. So we 120 ; get an array of NS long as our output data... 121 size_vec = size(image_data) 122 n_cols = size_vec[ 1 ] 123 n_data = size_vec[ 2 ] 124 125 ; The number of linear combinations is equal to the number of rows in 126 ; the transformation matrix, but the transform needs a column for every 127 ; band in the original image data (i.e. to generate combinations for only 128 ; the first three TCA channels you could remove rows 4-9). 129 n_combines = ( size(transform_matrix))[ 2 ] 130 image_tca = fltarr (n_cols, n_combines) 131 for i=0 nb-1 do begin 132 for j=0 n_data1 do begin 76
77 133 image_tca[*, i] = image_tca[*, i] + transform_matrix[j, i] (image_data)[*, j] 134 endfor 135 endfor 136 137 writeu unit, image_tca 138 ;print, i 139 140 ENVI_REPORT_STAT, base, tile+ 1 num_tiles 141 endfor 142 143 ;envi_file_mng, id=fid, /remove 144 145 ENVI_REPORT_INIT, base=base, /finish 146 147 free_lun unit 148 149 envi_setup_head, fname= outfile, ns=ns, nl=nl, nb=nb, $ 150 data_type= data_type, offset= 0 interleave= (interleave > 1 ),$ 151 xstart= xstart+dims[ 1 ], ystart= ystart+dims[ 3 ], bnames= bnames, map_info= map_info, $ 152 descrip= 'ASTER Tasseled Cap Transformation for: + fname, fwhm=fwhm, wl=wl, $ 153 /write /open 154 envi_tile_done, tile_id 155 END 156 157 158 FUNCTION TEST_TRANSFORM, data, matrix 159 image_data = data 160 transform_matrix = matrix 161 162 size_vec = size(image_data) 163 n_cols = size_vec[ 1 ] 164 n_rows = size_vec[ 2 ] 165 n_data = size_vec[ 3 ] 166 167 ; The number of linear combinations is equal to the number of columns in 168 ; the transformation matrix: 169 n_combines = ( size(transform_matrix))[ 2 ] 170 image_tca = fltarr (n_cols, n_rows, n_combines) 171 for i=0 n_combines1 do begin 172 for j=0 n_data1 do begin 173 image_tca[*, *, i] = image_tca[*, *, i] + transform_matrix[j, i] (image_data)[*,*,j] 174 endfor 175 endfor 176 177 return image_tca 178 179 END License for Appended Source Code All original and appended source code is licensed and distributed under the GNU General Public License Version 3, C opyright 2007 Free Software F oundation, Inc. A copy of the license is available upon request from the author and appended as an attached object. Object A-1. GNU General Public Li cense Version 3 (.txt file 35 KB) .
APPENDIX B SAMPLE ENVI CONFIGURATION TEMPLA TES FOR ATMOSPHERIC CORRECTION Notes on Atmospheric Correction in ENVITM Both radiometric and atmospheric corrections are critical when comparing data across dates, sensors or space. An advanced atmos pheric correction add-on module is available in ENVITM, a remote sensing and general image analysis software package av ailable from ITT/VIS (ITT Visual Information Solutions 2007). The module, named Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) uses the MODTRAN4 radiative transfer code and is a sophisticated model derived from radiometric fi rst principles (Berk et al. 1999; Cooley et al. 2002). Results in this study derived from FLAA SH surface reflectance estimates were found to be much more reliable than t hose derived from simpler cros s-image atmospheric correction techniques such as dark/light-object subtraction (Chavez 1996) Since the documentation of FLAASH/MODTRAN4 implementations is scarce sample configuration files for the FLAASH module are appended here for rese archers looking for a model or for those looking to duplicate atmospheric correction results for data observed under similar conditions. ASTER FLAASH/MODTRAN Configuration File for ENVI ; ;ENVI FLAASH PARAMETERS TEMPLATE (4.3) ;Written Wed Jul 11 23:54:18 2007 ; ; Project Parameters enviacc.prj.radiance_file = D:\Documents\Graduate School\Research\ASTER\Data\ASTER\AST_L1A_00307292001151134_20070914104929_16374\AST_L1A_003072920 01151134_asrad_nn.dat enviacc.prj.reflect_file = D:\Documents\Graduate School\Research\ASTER\Data\ASTER\AST_L1A_00307292001151134_20070914104929_16374\AST_L1A_003072920 01151134_flaash_nn.dat enviacc.prj.filter_func_file = C:\Program Files\ITT\IDL64\products\envi44\filt_func\aster.sli enviacc.prj.filter_func_file_index = 0 enviacc.prj.water_band_choice = 1.13 enviacc.prj.red_channel = 2 enviacc.prj.green_channel = 1 enviacc.prj.blue_channel = 0 enviacc.prj.water_abs_channel = 0 enviacc.prj.water_ref_channel = 0 enviacc.prj.kt_upper_channel = 0 enviacc.prj.kt_lower_channel = 2 enviacc.prj.kt_cutoff = 0.1000 enviacc.prj.kt_ratio = 0.4500 enviacc.prj.cirrus_channel = 0 78
enviacc.prj.water_retrieval = 0 enviacc.prj.user_stem_name = flaash_ enviacc.prj.modtran_directory = D:\Documents\Graduate School\Research\ASTER\Data\ASTER\AST_L1A_00307292001151134_20070914104929_16374\FLAASH\ ; ; MODTRAN Parameters enviacc.modtran.visvalue = 40.0000 enviacc.modtran.f_resolution = 15.0000 enviacc.modtran.day = 29 enviacc.modtran.month = 7 enviacc.modtran.year = 2001 enviacc.modtran.gmt = 15.1925 enviacc.modtran.latitude = -11.2621 enviacc.modtran.longitude = -69.8538 enviacc.modtran.sensor_altitude = 705.0000 enviacc.modtran.ground_elevation = 0.2750 enviacc.modtran.view_zenith_angle = 177.1220 enviacc.modtran.view_azimuth = -90.0000 enviacc.modtran.atmosphere_model = 1 enviacc.modtran.aerosol_model = 1 enviacc.modtran.multiscatter_model = 2 enviacc.modtran.disort_streams = 8 enviacc.modtran.co2mix = 390.0000 enviacc.modtran.water_column_multiplier = 1.0000 ; ; Image Parameters enviacc.img.nspatial = 4999 enviacc.img.nlines = 4712 enviacc.img.data_type = 4 enviacc.img.margin1 = 0 enviacc.img.margin2 = 0 enviacc.img.nskip = 0 enviacc.img.pixel_size = 15.0000 enviacc.img.sensor_name = ASTER ; ; Analysis Parameters enviacc.ana.aerosol_scaleht = 2.0000 enviacc.ana.use_adjacency = 1 enviacc.ana.output_scale = 10000.0000 enviacc.ana.polishing_res = 0 enviacc.ana.aerosol_retrieval = 0 enviacc.ana.calc_wl_correction = 0 enviacc.ana.reuse_modtran_calcs = 0 enviacc.ana.use_square_slit_function = 0 enviacc.ana.convolution_method = fft enviacc.ana.use_tiling = 1 enviacc.ana.tile_size = 250.0000 ; ; Spectral Parameters enviacc.spc.wavelength_units = micron enviacc.spc.lambda = [ 0.5560, 0.6610, 0.8070, 1.6560, 2.1670, 2.2090, 2.2620, 2.3360, 2.4000] enviacc.spc.fwhm = [ -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000] enviacc.img.p_input_scale = [ 10.0000, 10.0000, 10.0000, 10.0000, 10.0000, 10.0000, 10.0000, 10.0000, 10.0000] Landsat FLAASH/MODTRAN Config uration File for ENVI ; ;ENVI FLAASH PARAMETERS TEMPLATE (4.3) ;Written Tue Jul 17 19:49:58 2007 ; ; Project Parameters enviacc.prj.radiance_file = D:\Documents\Graduate School\Research\ASTER\Data\Landsat\etm_3_68_2001_07_29\etm_3_68_2001_07_29_asrad.dat 79
80 enviacc.prj.reflect_file = D:\Documents\Graduate School\Research\ASTER\Data\Landsat\etm_3_68_2001_07_29\etm_3_68_2001_07_29_flaash_noaerosol.dat enviacc.prj.filter_func_file = C:\RSI\IDL63\products\envi43\filt_func\tm.sli enviacc.prj.filter_func_file_index = 12 enviacc.prj.water_band_choice = 1.13 enviacc.prj.red_channel = 3 enviacc.prj.green_channel = 2 enviacc.prj.blue_channel = 1 enviacc.prj.water_abs_channel = 0 enviacc.prj.water_ref_channel = 0 enviacc.prj.kt_upper_channel = 6 enviacc.prj.kt_lower_channel = 3 enviacc.prj.kt_cutoff = 0.1000 enviacc.prj.kt_ratio = 0.4500 enviacc.prj.cirrus_channel = 0 enviacc.prj.water_retrieval = 0 enviacc.prj.user_stem_name = flaash_no_aerosol_ enviacc.prj.modtran_directory = D:\Documents\Graduate School\Research\ASTER\Data\Landsat\etm_3_68_2001_07_29\FLAASH_No_Aerosol\ ; ; MODTRAN Parameters enviacc.modtran.visvalue = 40.0000 enviacc.modtran.f_resolution = 15.0000 enviacc.modtran.day = 29 enviacc.modtran.month = 7 enviacc.modtran.year = 2001 enviacc.modtran.gmt = 14.5900 enviacc.modtran.latitude = -11.5708 enviacc.modtran.longitude = -70.2069 enviacc.modtran.sensor_altitude = 705.0000 enviacc.modtran.ground_elevation = 0.2750 enviacc.modtran.view_zenith_angle = 180.0000 enviacc.modtran.view_azimuth = 0.0000 enviacc.modtran.atmosphere_model = 1 enviacc.modtran.aerosol_model = 1 enviacc.modtran.multiscatter_model = 2 enviacc.modtran.disort_streams = 8 enviacc.modtran.co2mix = 390.0000 enviacc.modtran.water_column_multiplier = 1.0000 ; ; Image Parameters enviacc.img.nspatial = 7891 enviacc.img.nlines = 6971 enviacc.img.data_type = 4 enviacc.img.margin1 = 0 enviacc.img.margin2 = 0 enviacc.img.nskip = 0 enviacc.img.pixel_size = 30.0000 enviacc.img.sensor_name = Landsat TM7 ; ; Analysis Parameters enviacc.ana.aerosol_scaleht = 2.0000 enviacc.ana.use_adjacency = 1 enviacc.ana.output_scale = 10000.0000 enviacc.ana.polishing_res = 0 enviacc.ana.aerosol_retrieval = 0 enviacc.ana.calc_wl_correction = 0 enviacc.ana.reuse_modtran_calcs = 0 enviacc.ana.use_square_slit_function = 0 enviacc.ana.convolution_method = fft enviacc.ana.use_tiling = 1 enviacc.ana.tile_size = 250.0000 ; ; Spectral Parameters enviacc.spc.wavelength_units = micron enviacc.spc.lambda = [ 0.4787, 0.5610, 0.6614, 0.8346, 1.6500, 2.2080] enviacc.spc.fwhm = [ -1.000000, -1.000000, -1.000000, -1.000000, -1.000000, -1.000000] enviacc.img.p_input_scale = [ 10.0000, 10.0000, 10.0000, 10.0000, 10.0000, 10.0000]
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BIOGRAPHICAL SKETCH Forrest Robert Stevens was born in 1976 in Pocatello, Idaho. He grew up among the dryland wheat farms, cattle ranches and rolling footh ills in Arbon Valley, and attended its two-room schoolhouse. After turning eight years old, his fam ily moved back into to wn, living in Pocatello, where he completed the rest of his elementary, junior and senior high school education. In 1994, he became the third generation of his family on his mothers side, Stephenie Kahm Stevens, to attend and graduate from Pocatello High School. He completed his Bachelor of Arts degree at the University of Chicago in 1998, finishing with high honors and majoring in biology, while specializing in ecology and evolution. In 2004, he started his graduate studies at the University of Florida, where he chose to pursue degrees in Geography and pl ans to earn a Ph.D. He then received his M.S. from the University of Florida in the Spring of 2009. 85