Optimization of Streamflow Forecasts in West-Central Florida using Multiple Climate Predictors

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Title:
Optimization of Streamflow Forecasts in West-Central Florida using Multiple Climate Predictors A Case Study of Tampa Bay Water
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1 online resource (145 p.)
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english
Creator:
Risko, Susan Lea
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University of Florida
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Thesis/Dissertation Information

Degree:
Master's ( M.E.)
Degree Grantor:
University of Florida
Degree Disciplines:
Agricultural and Biological Engineering
Committee Chair:
Martinez, Christopher J
Committee Members:
Kiker, Gregory
Waylen, Peter R
Kumaran, Muthusami

Subjects

Subjects / Keywords:
climatology -- el-nino -- enso -- exceedence -- exceedence-probability -- florida -- forecast -- multi-model -- non-parametric -- probability -- streamflow -- svd -- water-supplies -- weighting-techniques
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
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Agricultural and Biological Engineering thesis, M.E.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
Improvement of surface water supply forecasts may be obtained through the incorporation of climatic influences.  The El Niño Southern Oscillation (ENSO)phenomenon imparts a strong influence on the world’s climate and alternatively its water resources. Previous work has shown climate indices specific to ENSO are known to have significant correlations with stream flows, for example the Niño 3 and Niño 3.4 indices are associated with stream flows in the southeastern United States. These established relationships guided an analysis to find optimal climatic influences on stream flow within the Tampa Bay area.  A computer program was developed to account for multiple input datasets of twelve 3-month seasons and multiple lags. Climatic variables, including sea surface temperatures (SST) and established climate indices, served as inputs along with historical streamflows. The model incorporates a weighting scheme to identify the optimal combination of climatic data for forecasting.  Model output provides streamflow forecasts in the form of probability of exceedance plots and error scores that indicate model skill as well as the associated influence for each climatic predictor in the form of a weighting scheme.  Additionally, the general ENSO indices used provide input data that tends to be spatially static.  Therefore, through the use of singular value decomposition (SVD) methods it was speculated that an optimal spatial distribution of sea surface temperatures could be identified to replace thestatic indices for various seasons and lags. Results show that a combination of four climate indices, specifically Niño 1.2, Niño 3 and Niño 4 in combination with historical streamflows, as predictors provided similar results to the two predictors, historical flows and Niño 3.4, are used. In addition, a spatial distribution of sea surface temperatures found to be best correlated over time with historical streamflows were used in SVD analysis and were found to be a better predictor than the predictor combinations.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Susan Lea Risko.
Thesis:
Thesis (M.E.)--University of Florida, 2012.
Local:
Adviser: Martinez, Christopher J.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-02-28

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1 OPTIMIZATION OF STREAMFLOW FORECASTS IN WEST CENTRAL FLORIDA USING MULTIPLE CLIMATE PREDICTORS: A CASE STUDY OF TAMPA BAY WATER By SUSAN LEA RISKO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2012

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2 2012 Susan Lea Risko

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3 To my Mother and F ather

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4 ACKNOWLEDGMENTS To make it this far in my graduate studies, I have many people to thank for their contributions to this process. First of all I would not have even started graduate school if ujak and Tom Mirti I thank Ima for believing in me more than I believed in myself I would also like to thank Tom for spen ding countless hours with me while I attempted to determine my path in life The entire experience would not have even been possible w ithout my committee. I send thanks and appreciation to my committee Chris Martinez, Peter Waylen, Greg Kiker and Dr. K umaran, for their hours of dedication, professional support and guidance in this endeavor I would like to send a thank you to Ian Hanian for his time and patience teaching me Matlab. XD A special thank you goes out to Gareth Lagerwall and Julie Padowski for their encouragement through difficult times throughout the entire journey I thank Nate Johnson for his spiritual assurance in prepara tion of my defense Lastly, and most importantly, I would like to thank my sister, Paula, for when I thought all hope was lost she was there to pick up the pieces and help me move forward.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 14 2 CLIMATE DIAGNOSTICS ................................ ................................ ....................... 16 Climatic Indicators ................................ ................................ ................................ .. 16 Impact of Climate on Water Resources ................................ ................................ .. 18 Study Site ................................ ................................ ................................ ............... 20 Data ................................ ................................ ................................ ........................ 21 Hydrologic Variables ................................ ................................ ........................ 21 Climatic Variables ................................ ................................ ............................. 21 Methodology ................................ ................................ ................................ ........... 22 Results ................................ ................................ ................................ .................... 24 Sea Surface Temperatures ................................ ................................ .............. 24 Sea Level Pressure ................................ ................................ .......................... 25 Geopotenti al Heights ................................ ................................ ........................ 26 Conclusion ................................ ................................ ................................ .............. 26 3 FORECAST MODEL ................................ ................................ ............................... 40 Background ................................ ................................ ................................ ............. 40 Data ................................ ................................ ................................ ........................ 43 Hydrologic ................................ ................................ ................................ ........ 43 Climatic ................................ ................................ ................................ ............. 45 Methodology ................................ ................................ ................................ ........... 46 Model Overview ................................ ................................ ................................ 46 Model Statistics ................................ ................................ ................................ 47 Model Cross Validation ................................ ................................ .................... 49 Model Skill ................................ ................................ ................................ ........ 49 Single Predictor Runs ................................ ................................ ....................... 52 Combin ation Forecasts ................................ ................................ ..................... 52 Singular Value Decomposition Analysis ................................ ........................... 53

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6 Results ................................ ................................ ................................ .................... 55 LEPS Skill Scores ................................ ................................ ............................ 55 Predictor Weights ................................ ................................ ............................. 57 Conclusions ................................ ................................ ................................ ............ 58 4 TAMPA BAY CASE STUDY ................................ ................................ ................... 69 Background ................................ ................................ ................................ ............. 69 Study Site ................................ ................................ ................................ ............... 69 Establishment of Organization ................................ ................................ ................ 70 Applied Model ................................ ................................ ................................ ......... 70 Results ................................ ................................ ................................ .................... 71 Probability of Exceedance Plots ................................ ................................ ....... 74 Investigated Withdrawal Relationships ................................ ............................. 75 Conclusion ................................ ................................ ................................ .............. 76 5 CONCLUSIONS AND RECOMMENDATIONS ................................ ....................... 90 Summary ................................ ................................ ................................ ................ 90 Conclusions ................................ ................................ ................................ ............ 91 Recommendations for Future Work ................................ ................................ ........ 91 Investigation of Alternative Hydrologic Variables ................................ .............. 91 Investigate Local Methods for Nonparametric Modeling ................................ ... 92 Transformation of Streamflow Forecasts into Forecasted Withdraw Volumes 92 Application to Alternative Loc ations ................................ ................................ .. 92 ENSO Phases ................................ ................................ ................................ .. 93 APPENDIX A MODEL PSEUDOCODE ................................ ................................ ......................... 94 B MODEL CODE ................................ ................................ ................................ ........ 97 C STREAMFLOW PROBABILITY OF EXCEEDANCE PLOTS ................................ 121 LIST OF REFERENCES ................................ ................................ ............................. 139 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 145

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7 LIST OF TABLES Table page 2 1 Rainfall data used in this study. ................................ ................................ .......... 28 2 2 Streamflow data used in this study. ................................ ................................ .... 29 2 3 Demand data used for this study. ................................ ................................ ....... 29 3 1 Period of record for each United States Geological Sta tion within the Greater Tampa Bay Area used in this analysis. ................................ ............................... 61 4 1 Period of record for stations specific to Tampa Bay Water. ................................ 77

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8 LIST OF FIGURES Figure page 2 2 Pearson's correlation of standardized streamflow with concurrent and lagged sea surface temperatures. ................................ ................................ .................. 31 2 3 Nio Regions along the equatorial Pacific ................................ .......................... 32 2 4 Composite anomalies (C) of concurrent and lagged sea surface temperatures. ................................ ................................ ................................ ..... 33 2 5 Seasonal lagged correlation of the Nio 3.4 index with mean standardized rainfall, mean standardized streamflow, and total regional demand. .................. 34 2 6 Seasonal lagged correlation of the Nio 3 index with mean standardized rainfall, mean standardized streamflow, and total regional demand .................. 35 2 7 Pearson's correlation of standardized streamflow with concurrent and lagged sea level pressures. ................................ ................................ ............................ 36 2 8 Composite anomalies (mb) of concurrent and lagged sea level pressures between 1950 and 2008. ................................ ................................ .................... 37 2 9 Seasonal lagged correlation of the SOI index with mean standardized rainfall, mean standardized streamflow, and total regional demand. .............................. 38 2 10 Seasonal lagged correlation of the eqSOI index with mean standardized rainfall, mean standardized streamflow, and total regional demand. .................. 39 3 1 United States Geological Service stations within the Greater Tampa Bay area used in this analysis ................................ ................................ ........................... 62 3 2 Weights for individual predictors (predictor 1, predictor 2, etc) for all triads and lags. ................................ ................................ ................................ ............. 63 3 3 Averaged LEPS scores for all stations ................................ ............................... 65 3 4 Predictor weights averaged for all stations using 2 predictors ............................ 66 3 5 Predictor weights averaged for all stations using 4 predictors ............................ 67 3 6 Predictor weights averaged for all stations using SVD data ............................... 68 4 1 Tampa Bay Water service area (green) with Hillsborough and Alafia River catchment areas (pink) within the Southwest Florida Water Management District (SWFWMD) (tan). ................................ ................................ ................... 78 4 2 LEPS scores for Alafia at Bell Shoals using 2 predictorsand 4 predictors. ........ 79

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9 4 3 Predictor weights for Alafia at Bell Shoals using 2 predictors. ............................ 79 4 4 Predictor weights for Al afia at Bell Shoals using 4 predictors ............................. 80 4 5 LEPS scores for Hillsborough River at Morris Bridge. ................................ ........ 81 4 6 Predictor weights for Hillsborough River at Morris Bridge using 2 predictors. .... 81 4 7 Predictor weights for Hillsborough River at Morris Bridge using 4 predictors. .... 82 4 8 LEPS scores for S160 using 2 predictors and 4 predictors ................................ 83 4 9 Predicto r weights for S160 using 2 predictor s ................................ .................... 83 4 10 Predictor weights for S160 using 4 predictors ................................ .................... 84 4 11 Example plot showing streamflow probability of exceedance and climatology, including upper and lower envelops, for Alafia at Bell Shoals for 1974. ............. 85 4 12 Streamflow probability of exceedance ensemble of Alafia at Bell Shoals for years 1974 2008. ................................ ................................ ................................ 85 4 13 Example plot showing streamflow probability of exceedance and climatology, including upper and lower envelops, for Hillsborough River at Morris Bridge for 19 72. ................................ ................................ ................................ ............. 86 4 14 Streamflow probability of exceedance ensemble of Hillsborough River at Morris Bridge for years 1972 2008. ................................ ................................ .... 86 4 15 Example plot showing streamflow probability of exceedance and climatology, including upper and lower envelops, for S160_Adjusted for 1974. ..................... 87 4 16 Streamflow probability of exceedance ensemble of S160_Adjusted for years 1974 2002. ................................ ................................ ................................ ......... 87 4 17 Correlation of streamflows with withdrawals for the Alafia at Bell Shoals station. Monthly streamflows were summed from daily. ................................ .... 88 4 18 Relationship of natural log streamflows with withdrawals for the Alafia at Bell Shoals station. Monthly streamflows were summed from daily. Best fit lin e demonstrates an R squared of 0.911. ................................ ................................ 89

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10 LIST OF ABBREVIATION S AMJ April, May, June ASO August, September, October eqSOI equato rial Southern Oscillation Inde x ENSO El Nio Southern Oscillation ERSSTV2 E xtended reconstruction of sea surface temperatures version 2 DJF December, January, February FDEP Florida Department of Environmental Protection FMA February, March, April GPH G eopo tential heights HCDN Hydroclimatic Data Network ICOADS International Comprehen sive Ocean Atmosphere Data Set IRI International Research Institute for Climate and Society JAS July, August, September JFM January, February, March JJA June, July, August KNMI The Royal Netherlands Meteorological Institute K NN K nearest neighbor LEPS Li near Error in Probability Space MAM March, April, May MCA Maximum Covariance Analysis MEI Multivariate ENSO Index MGD Million gallons per day MJJ May, June, July MCA Maximum Covariance Analysis

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11 NCAR National C enter for Atmospheric Research NCDC National Climatic Data Center NCEP National Cente r for Environmental Prediction NOAA National Oceanic and Atmospheric Association NDJ November, December, January NSFM Non Parame tric Seasonal Forecast Model OND October, November, December PCA Principal component analysis PNA Pacific North American pattern SFWMD Southwest Flo rida Water Management District SOI Southern Oscillation Index SON September, October, November SLP S ea level pressure SST S ea surface temperatures SVD Singular Value Decomposition USGS United States Geological Service

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12 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering OPTIMIZATION OF STREAMFLOW FORECASTS IN WEST CENTRAL FLORIDA USING MULTIPLE CLIMATE PREDICTORS: A CASE STUDY OF TAMPA BAY WATER By Susan Lea Risko August 2012 Chair: Christopher J. Martinez Major: Agricultural and Biological Engineering Im provement of surface water supply forecasts may be obtained through the incorporation of climatic influences. The El Nio Southern Oscillation (ENSO) water resources. Previ ous work has shown climate indices specific to ENSO are known to have significant correlations with streamflows, for example the Nio 3 and Nio 3.4 indices are associated with streamflows in the southeastern United States. These established relationships guided an analysis to find optimal climatic influences on streamflow within the Tampa Bay area. A computer program was developed to account for multiple input da tasets of twelve triads comprised of 3 month means and multiple lags. Climatic variables, incl uding sea surface temperatures (SST) and established climate indices, served as inputs along with historical streamflows. The model incorporates a weighting scheme to identify the optimal combination of climatic data for forecasting. Model output provides streamflow forecasts in the form of probability of exceedance plots and error scores that indicate model skill as well as the associated influence for each climatic predictor in the form of a weighting scheme. Additionally, the

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13 general ENSO indices used provide input data that tends to be spatially static. Therefore, through the use of singular value decomposition (SVD) methods it was speculated that an optimal spatial distribution of sea surface temperatures could be identified to replace the static ind ices for various seasons and lags. Results show that a combination of four climate indices, specifically Nio 1.2, Nio 3 and Nio 4 in combination with historical streamflows, as predictors provided similar results to the two predictors, historical flows and Nio 3.4, are used. In addition, a spatial distribution of sea surface temperatures found to be best correlated over time with historical streamflows were used in SVD analysis and were found to be a better predictor than the predictor combinations.

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14 C HAPTER 1 INTRODUCTION 15 years placing increased pressure on available water resources (FDEP, 2010). This increased demand in conc ert with seasonal variability of the resource requires sophisticated techniques for supply management. Fortunately, there is a strong El Nio Southern Oscillation (ENSO) signal within this region (Yin, 1994) increasing the possibility for better streamflo w forecasts through the incorporation of climate indices as streamflow predictors. Water resource demands are increasing as a result of population growth and increased water use. According to the Florida Department of Environmental protection (2010), Flori conjunction with an increase in water use trends of 30 percent (FDEP, 2010). Historically, the two main contributors to water use demands can be attributed to the public water supply sect or and agricultural irrigation (FDEP, 2010). Total public supply withdrawals, alone, increased by 80 percent from 1980 to 2005 and is expected to increase another 49 percent from 2000 to 2025, accounting for the majority of the increase in statewide demand (FDEP, 2010). Demand increases such as these for public water supply indicate that resources need to be monitored and managed effectively to ensure future use. Monitoring resource availability in some cases incorporates the delicate balancing act of sourc e rotation when multiple water sources are available. This study has been conducted in support of Tampa Bay Water, a water wholesaler in west central Florida,

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15 system is de signed to handle various sources such as ground water, surface water and desalinized sea water, however, the scope of this study is focused solely on surface water, more specifically, supply forecasting of the Hillsborough and Alafia Rivers involving a tec hnique that incorporates large scale climatic data. Grantz et al. (2005) performed a study in the Truckee and Carson River basins in the Sierra Nevada Mountains using this idea to incorporate a gridded climate dataset into streamflow forecasts. Whil e the study performed by Grantz et al. (2005) focused on the western United States and recognized climatic patterns specific to those regions, it provided a basis for this analysis. Applying this example to southwest Florida, it was expected that large sca le climatic influences that have an effect on the seasonality of streamflows in the Tampa Bay region would be identified and offer insight into the behavior of water resources in this area.

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16 CHAPTER 2 CLIMATE DIAGNOSTICS Climatic Indicators Of all the major climate oscillations, the El Nio Southern Oscillation (ENSO) is the strongest and most predictable system that influences climate variability ( Rasmusson and Carpenter, 1982; Ropelewski and Halpert, 1986; Rosenzweig, 2008). The reason for this being that the phenomenon affects the sea surface temperatures of an area covering nearly one global annual temperature (Rosenzweig, 2008). Next to annual seasonality, ENSO is the second largest source of climate variation for tropical and subtropical climates and a moderate influence on the mid latitudes (Rosenzweig, 2008) and is the largest known predictable climatic signal at seasonal and interannual time scales (Gershunov and Barnett, 1998 ; Tren berth, 2001 ). Oscillating pressure systems within the South Pacific, give rise to the phenomenon known as the Southern Oscillation. Generally, the eastern South Pacific is exposed to a persistent high atmospheric pressure, while the western South Pacific e xperiences an equally persistent low pressure. This atmospheric pressure differential occurs as the southeast trade winds move westward from high to low pressure as a result of westward oceanic movement across the equatorial pacific, maintaining warmer sea surface temperatures in this location (Kahya and Dracup, 1993, Zorn and Waylen, 1997 ; Coley and Waylen, 2006 ). These normal conditions shift as a result of changes within the normalized height index between Darwin, Australia and Tahiti, Society Islands, t he continuous shifting the system experiences is known as the Southern Oscillation (Rasmusson and Carpenter, 1982).

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17 ENSO is a combined oceanic atmospheric process that can be characterized most notably by anomalous changes in sea surface temperatures of th e eastern tropical Pacific Ocean (Rosenzweig, 2008 ; Tren berth, 2001 ). The alternating phases of this oscillation, El Nio neutral and La Nia, exhibit different behaviors of sea surface temperatures. During normal conditions trade winds move the equatoria l Pacific Ocean Pacific causing a sea surface temperature gradient with warmer SSTs in the central Pacific and cooler SSTs along the eastern Pacific ( Clarke, 2008) During E l Nio, sea surface temperatures are higher than normal in the eastern Pacific while La Nia is characterized by lower than normal sea surface temper atures (Kadioglu et al., 1999). Periods that do not exhibit variations from the norm are recognized as the neutral phase. Most El Nio events begin in the boreal spring or summer and peak from November to January in sea surface temperatures (Tren berth, 1997). As a result of the extent to which ENSO impacts global climate and oceanic circulations, research has been largely focused on this phenomenon in hopes to further explain variations in the realm of water resources. While ENSO tends to be the most significant of all the climate oscillations as documented in the literature, there are others existing oscillati ons that may contribute to climate variability such as the PN A (Opitz Stapleton et al 2007) and the PDO (Tootle and P iechota, 2004 ; van Beynen et al., 2004 ) It was intended through this analysis to exploit relationships between climate oscillations identified as potentially having an impact on water resources in order to forecast streamflows.

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18 Impact of Climate on Water Resources Impacts that macro scale climate teleconnections have on water resources have been studied for various locations as well as for different types of climatic data (e.g. Kock 2000; McCabe and Dettinger, 2002; Grantz et al., 2005 ; Kennedy et al., 2009 ) As a result of the large extent to which ENSO impacts the globe this phenomenon has influence over water resources that is far stronger than other teleconnections. It has been well documented that precipitation and streamflows are influenced by the ENSO phenome non These influences can be observed at many geographic regions for example the west ern United States (Cayan, 1994 ; Kock, 2000 ), the entire southeastern United States (Yin, 1994 ; Gershunov and Barnett, 1998 ) and even more specifically in Florida ( Douglas and Englehart, 1981; Zorn and Waylen, 1997 ; Tootle and Piechota, 2004 2006 ; Grantz et al., 2005 ) The impact of ENSO varies base d on the phase of ENSO, El Nio, La Nia or neutral as well as by season. Particularly in Florida, El Nio events cause an in crease, while La Nia demonstrates a decrease, in precipitation (Schmidt, 2001). During boreal winters of an El Nio event Ropelewski and Halpert (1986) found that moisture is advected from the tropical Pacific by the sub tropical jet stream into the sout heastern United States. Summer rainfall and streamflow are mostly affected by convectional and tropical storms; however the ENSO phase determines the impact of such events (Gray, 1984). For example, during El Nio years, tropical storm development decrease s, while during La Nia years it increases (Bove et al., 1998). Schmidt (2001) believed c hanges in streamflow in the southeast during El Nio summers and falls are more likely due to the effects of convective storms, while during La Nia less likely.

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19 T he relationship between ENSO and streamflows, as indicated by the abovementioned patterns, were further utilized through this investigation to determine if such lar g e scale climatic indicators could be used to forecast streamflow Although ENSO has been ident ified as impacting the southeastern United States, this study was focused on a smaller scale in west central Florida, more specifically within the Hillsborough and Alafia watersheds. The relationship of specific m acro scale climatic indices to hydrologic variable s can be determined through various techniques, such as correlation and composite analysis or principal component analysis ( e.g. Bretherton et al., 1992; Oplitz Stapleton et al. 2007 ) Each climate index is defined by a single or multiple climatic variables, for example ENSO Is defined by anomalous sea surface temperatures ( Rasmusson and Carpenter, 1982; Ropelewski and Halpert, 1986; Gershunov and Barnett, 1998 ; Tootle and Piechota, 2006 ) while the Multivar iate ENSO Index (MEI) is defined by various oceanic and atmospheric indicators such as SLPs, zonal and meridional surface winds, SST, surface air temperature, and total cloudiness fraction of the sky into a single index (Wolter and Timlin, 1993; Wolter and Timlin, 1998). Changes in sea level pressures were also discovered to (Rasmusson and Carpenter, 1982 ; Bradley et al., 1987 ) reflect the influence of ENSO. Additionally, Grantz (2005) found a custom index of 50 0 mb geopotential heights as a more significan t predictor of streamflows in the Truckee Carson River system than ENSO Based upon previous studies of large scale climate oscillations and the associate d climatic indicators of such o sci l lations, the initial climate variables chosen for this analysis con sisted of sea surface temperatures, sea level pressures and geopotential

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20 heights. Through a preliminary study summarized here, these l arge scale climatic variables were used to determine the specific climate indices to impact hydrologic variables in the g reater Tampa Bay area Study Site On average Florida receives 127 152 cm (50 60 in) of rainfall annually with maximum precipitation and river flows occur during summer months as a result of convective storms and the occasional tropical storm. Southwest F lorida in particular receives between 136 and 144 cm (54 57 in) of mean annual rainfall per year, more than half that amount occurs during the typical wet season, June through September. Southwest Florida has a subtropical climate regime, with warm, wet summers and mild, dry winters. Average annual temperatures range between 21 and 24 degrees Celsius (70 75 degrees Fahrenheit) (Tomasko et al., 2005). The greater Tampa Bay area on the western coast of central F lorida was the location of focus for this research (Figure 2 1). The Tampa Bay drainage area covers 3550 Km 2 (1371 mi 2 ) Within this area lies a surficial aquifer, recharged through precipitation, in addition to deeper aquifers. Springs intermittently cove r the landscape along with the existing rivers categorized as gaining rivers (Schmidt, 2001). In order to determine the climate indices influencing water resources within the focus region, correlation and composite analyses were performed. Through this eff ort multiple macro scale climatic variables were considered in order to determine the most relevant climate data to the area. A summary of this work has been provided here, however, a complete report of the analysis, including results and figures, is avail able at h ttp://ufdc.ufl.edu/AA00012272/

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21 Data Hydrologic Variables Historical records of monthly/seasonal triads rainfall, streamflow, and demand were used in this analysis. Monthly gauge rainfall records were obtained from the National Climatic Data Cent er (Table 2 1), streamflow records were obtained from the United States Geological Survey National Water Information System and Tampa Bay Water (Table 2 2), and monthly demand was obtained from Tampa Bay Water (Table 2 3). For the rainfall and streamflow datasets the mean of standardized anomalies of all gauges/stations was calculated for analysis, c onverting each station into standardized anomalies where the mean equals zero and standard deviation equals one. The monthly data was converted into twelve tri ads per each year of data with each triad comprised of 3 month means. This magnitude towards its variability and equally weights each station. In doing so, it is assumed that that the basic hydrologic characteristics of e ach station are relatively similar. As a result of in terms of relief it is a reasonable assumption. Climatic Variables This work used sea surface temperatures, geopotential heights (GpHs) and sea level pressures (SLP s ) in this analysis. The sea surface temperature data was obtained from the National Climatic Data Center (NCDC) and was compiled by the National Oceanic and Atmospheric Association (NOAA, 2008 a ). It is an extended reconstruction of sea surface tempera tures version 2, known as ERSSTV2, which was reconstructed using the International Comprehensive Ocean Atmosphere Data Set (ICOADS) and improved statistical methods that allow stable reconstruction using sparse data. Sea

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22 surface temperatures cover a global grid 180 X 89 in 2 X 2 (NOAA, 2008a). The global area covered was 180 E to 0 W and 30 S to 75 N. This dataset begins in January 1854, however, it is heavily damped before 1880 due to sparse data. Monthly gridded data sets on a global grid of 2.5 x 2.5 consisting of SLPs (IRI, 20 12a) and 500 mb GpHs (IRI, 2012 ) from the National Center for Environmental Prediction (NCEP)/ National Center for Atmospheric Research (NCAR) reanalysis project with NOAA (2008b) by (Kalnay et al., 1996) were obtaine d from the data library of the International Research Institute for Climate and Society (IRI). Since reanalysis data were limited to 1949 present the resulting correlation and composite analyses were limited to this time period. More information on the r eanalysis project can be found at http://www.cdc.noaa.gov/cdc/reanalysis/reanalysis.shtml Gridded SSTs, SLPs, and GpHs were converted into 3 month seasonal anomalies for correlation a nd composite analysis. Three month averages were used to reduce noise in the analyses. Subsequent evaluation of indices based on the correlation and composite analyses are presented in both 3 month and monthly values. Methodology Linear correlation and co mposite analyses were used to identify relationships between seasonal gridded climate datasets and hydrologic variables. Correlation and composite analyses of gridded climate variables have been shown to be effective techniques in the selection of climate indices (e.g. Grantz et al., 2005; Oplitz Stapleton et al., 2007; Sveinsson et al., 2008). Correlations and composites were d etermined for concurrent triads (lag 0) and with climate datasets lagging hydrologic observations. Lagged correlations between 3 month averaged hydrologic observations and 3 month averaged climate variables were conducted in 3 month increments for a total of 12

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23 months (lags of 0, 3, 6, 9, and 12 months) for SSTs and SLPs and in 1 month increments for a total of 4 months for GpHs. The rationale for this difference in evaluated lags was based on the lagged response each variable was expected to have on climate in the southeast United States as well as our own initial analyses. For example, changes in SSTs in the tropical Pacific Oce an do not have a direct effect, but rather influence atmospheric pressure and atmospheric flow patterns over the Pacific which may in turn influence the southeast via the jetstream (Horel and Wallace, 1981). Correlations were used to identify linear relati onships between 3 month gridded climate datasets and hydrologic observations. Only spatially coherent (approximately stationary and persistent) and statistically significant correlation patterns were considered in climate index selection. Composite anal ysis, sometimes referred to as superposed epoch analysis (Bradley et al., 1987; Kadioglu et al., 1999 ; as summarized by Martinez et al., 2009 ) or just epoch analysis, was conducted to examine differences in climate states that coincide to extreme hydrologi c conditions. Composite analysis consists of sorting data into categories and examining differences in the means of different categories. The advantage of composite analysis is that it makes no assumption of symmetry and can be used to identify nonlinear relationships. The drawbacks to composite analysis are that it is based on a limited set of the original data and can be vulnerable to leveraging, resulting from the influence of a single large anomaly. For this study the 10 th and 90 th percentiles of ra infall and streamflow were chosen to identify extreme wet and dry years for each triad For total regional demand the 20 th and 80 th percentiles were used to increase the composite sample size. Composite maps of gridded climate variables

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24 during these extr emes were created to identify typical climate patterns that correspond to these extremes and are displayed as departures from climatological means. Climatological means were defined by the length of each hydrologic dataset (no single reference period was used). Composite maps are simply the mean conditions (mean anomalies) of climate variables during the wet and dry periods identified (Martinez et al., 2009). Based on the correlation and composite patterns found, climate indices were identified and the concurrent and lagged correlation of hydrologic variables with these moment correlation and climate index was selected for evaluation from each gridded climate dataset. Relationships between the selected indices and hydrologic variables are presented using both triad means and monthly values (Martinez et al., 2009). Results Results presented here exemplify the findings for streamflows only during the January, February and March season since streamflow correlations were stronger and contained less noise than results obtained from use of rainfall or demand. While only the highl ights of the results are presented here for simplicity, further details of the findings for this portion of the analysis are available in a project report developed for Tampa Bay Water, provided at Http://ufdc.ufl.edu/AA00012272/ Sea Surface Temperatures Correlations between SSTs and mean standardized streamflow demonstrate the influence of ENSO in the focus reg ion. Figure 2 2 exemplifies the Pearson's correlation of January March (left column), February April (center column), and March May (right

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25 column) standardized streamflow with concurrent and lagged sea surface temperatures. Lags are evaluated at 3 month intervals from lag 0 (bottom row) to lag 12 (top row). Pearson correlation of 0.195 is significant at p = 0.10. Also in Figure 2 2, the described p begin within the central Pacific and move eastward over time. The ENSO pattern (Figure 2 3 ) is also present in the generated composite maps (Figure 2 4) as a result of sea surf ace temperatures with a large departure from the mean. Composite anomalies (C) were illustrated in Figure 2 4 of concurrent and lagged sea surface temperatures during January March for years of the 10 percent lowest (left column) and the 10 percent highest streamflow (right column) between 1932 and 2008. Lags were evaluated at 3 month intervals from lag 0 (botto m row) to lag 12 (top row). When comparing the overall correlation patterns ove r multiple triad s and lags between Nio 3.4 and each of the hydrologic variables, rainfall, streamflow and demand (Figure 2 5 ), noticeable differences appear. Streamflows demons trated a longer seasonal response to both Nio 3 and Nio 3.4 as a result of its lagged response in comparison to rainfall even ts. Correlating Nio 3 with each of the hydrologic variables (Figure 2 6 ) provided slightly stronger corr elation results than Ni o 3.4. Correlations using the Multivariate ENSO Index ( MEI ) de monstrated correlation patterns similar to results from the use of ENSO indices, but slighter weaker in strength (Martinez et al., 2009). Sea Level Pressure Correlation patterns from the use of sea level pressure (Figure 2 7) indicated the influence of the Southern Oscillation. Figure 2 7 demonstrates results from Pearson's correlation of January March (left column), February April (center column), and March May (right column) standardized stream flow with concurrent and lagged sea level

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26 pressures. Lags were evaluated at 3 month intervals from lag 0 (bottom row) to lag 12 (top row). Pearson correlation of 0.231 i s significant at p = 0.10. These patterns were less linear than those found using sea surface temperatures. While a linear relationship may still exist, as demonstrated in the correlations maps, the Southern Oscillation is generally absent from the composite maps indicating the anomalies are either small in magnitude or noisy and thus not a prominent feature Figure 2 8 illustrate the c omposite anomalies (mb) of concurrent and lagged sea level pressures during January March for years of the 10 percent lowest (left column) and the 10 percent highest streamflow (right column) between 1950 and 2008. Lags were evaluated at 3 month intervals from lag 0 ( bottom row) to lag 12 (top row) (Martinez et al., 2009). The climate indices chosen from correlations using sea level pressure included the Southern Oscillation Index (SOI) and the equatorial Sou thern Oscillation Index (eqSOI). Results from correlations using these in dices are presented in Figures 2 9 and 2 10, respectively, for each hydrologic variable. Geopotential Heights The correlation and composite results through the use of geopotential hei ghts indicated a relationship with the tropics and the center of action of the Pacific North American (PNA) pattern. This index was then selected for further correlations of which the results did not demonstrate significant findings in comparison to SSTs a nd SLPs. R esults are not pres ented here, but are available at Http://ufdc.ufl.edu/AA00012272/ Conclusion Of the three predictors used, SSTs, GpHs and SLP s the SSTs demonstrated the strongest relationship with streamflows. The location within the equatori al Pacific Ocean where the highest correlation between streamflows and SSTs occurred indicated the

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27 relevance of specific climate indices such as Nio 1.2, Nio 3, Nio 3.4 and Nio 4. Of these, the most prevalent correlations were Nio 3 and Nio 3.4. It w as also noted that the Southern Oscillation Index (SOI) or the equatorial Southern Oscillation Index (eqSOI) offer additional f orecasting ability (Martinez et al 2009). The SOI offers greater reliability than ENSO indices during periods where SSTs have been reconstructed due to the fact that SOI is b ased on gauge data (Martinez et al 2009). The eqSOI may be the preferential predictor during the onset of the dry period as it demonstrates stronger correlations compared to the Nio 3 or Nio 3.4 indices d uring September through November (SON) and October thro ugh December (OND) (Martinez et al 2009). Results provided through this portion of the analysis supported the decision to use Nio 3 and Nio 3.4 as separate forecasting indices, since the defined l ocation for these two indices overlaps as was shown in Figure 2 3 It was also determined that the Nio 3 index could be complemented with additional indices to increase forecasting ability, such as Nio 1.2 and Nio 4 since they spatially and temporally c omplement each other (Tren berth 2001) These results also indicated that forecasting potential for streamflows was greater th an that of rainfall and demand Rainfall and demand results contained more noise than that of streamflow with sporadic correlatio ns. Noise for the demand data illustrated the complexity associated with this data, believed to be the result of anthropogenic influences. While rainfall offered less noise than demand, ultimately the streamflows provided the best results and therefore wer e chosen for further analysis as described in Chapter 2.

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28 Table 2 1 R ainfall data used in this study. COOP ID Station n ame County Latitude Longitude Data r ange a 80478 Bartow Polk 27.90 81.85 10/1900 8/2008 80645 Bradenton 5 ESE Manatee 27.45 82.50 4/1965 9/2008 81046 Brooksville Chin Hill Hernando 28.62 82.37 10/1900 9/2008 81163 Bushnell 2 E Sumter 28.67 82.08 11/1936 9/2008 81632 Clearwater Pinellas 27.97 82.77 9/1931 3/1977 83153 Fort Green 12 WSW Manatee 27.57 82.13 9/1955 9/2008 83986 Hillsborough River SP Hillsborough 28.15 82.23 9/1943 9/2008 86880 Parrish Manatee 27.62 82.35 1/1958 8/2008 87205 Plant City Hillsborough 28.02 82.15 2/1903 9/2008 87851 St. Leo Pasco 28.33 82.27 10/1900 9/2008 87886 St. Petersburg Pinellas 27.77 82.63 8/1914 9/2008 88788 Tampa Intl. Airport Hillsborough 27.97 82.53 2/1950 9/2008 88824 Tarpon Springs SWG Pinellas 28.15 82.75 3/1901 9/2008 89430 Weeki Wachee Hernando 28.52 82.58 10/1969 9/2008 a Some years missing or contain missing values

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29 Table 2 2 Streamflow data used in this study USGS ID Station n ame Latitude Longitude Data r ange a 2301000 North Prong at Keysville (Alafia) 27.88 82.10 10/1950 9/2008 2301300 South Prong near Lithia (Alafia) 27.80 82.12 10/1963 9/2008 2301500 Alafia River at Lithia 27.87 82.21 10/1932 9/2008 Alafia River at Bell Shoals b 10/1974 9/2008 2303000 Hillsborough River Near Zephyrhills 28.15 82.23 10/1939 9/2008 2303330 Hillsborough River at Morris Bridge 28.10 82.31 10/1972 9/2008 S160 Adjusted (Tampa Bypass Canal) c 10/1974 9/2002 a Some years missing or contain missing values b Calculated by Tampa Bay Water from Lithia Springs and Lithia Gauge (USGS ID 2301300 and 2301500) c Adjusted flow over S160 structure, withdrawals by City of Tampa removed Table 2 3 Demand data used for this study. Total and member government d emand Data r ange Total Regional Demand 10/1991 12/2008 City of Tampa WDPA a 10/1991 12/2008 New Port Richey WDPA 10/1991 12/2008 Northwest Hillsborough WDPA 10/1991 12/2008 Pasco County Delivered 10/1991 12/2008 Pasco County Self Supply 6/1998 12/2008 Pinellas WDPA 10/1991 12/2008 South Central Hillsborough WDPA 10/1991 12/2008 St. Petersburg WDPA 10/1991 12/2008 a WDPA = Water Demand Planning Area

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30 Figure 2 1 Rainfall and Streamflow stations used for the preliminary climate dia gnostics within the greater

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31 Figure 2 2 Pearson's correlation of standardized streamflow with concurrent and lagged sea surface temperatures.

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32 Figure 2 3 Nio Regions along the equatorial Pacific Reprinted with permission from Martinez.C.J., personal communication,June 5, 2012

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33 Figure 2 4 Composite anomalies (C) of concurrent and lagged sea surface temperatures

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34 Figure 2 5 Seasonal lagged correlation of the Nio 3.4 index with mean standardized rainfall (upper left), mean standardized streamflow (upper right), and total regional demand (bottom).

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35 Figure 2 6 Seasonal lagged correlation of the Nio 3 index with mean standardized rainfall (upper left), mean standardized streamflow (upper right), and total regional demand (bottom).

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36 Figure 2 7 Pearson's correlation of standardized streamflow with concu rrent and lagged sea level pressures.

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37 Figure 2 8 Composite anomalies (mb) of concurrent and lagged sea level pressures between 1950 and 2008.

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38 Figure 2 9 Seasonal lagged correlation of the SOI index with mean standardized rainfall (upper left), mean standardized streamflow (upper right), and total regional demand (bottom).

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39 Figure 2 10 Seasonal lagged correlation of the eqSOI index with mean standardized rainfall (upper left), mean standardized streamflow (upper right), and total regional demand (bottom).

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40 CHAPTER 3 FORECAST MODEL Forecasting hydrologic variables through the use of climate information requires sophisticated tools. Through this research a model was developed and tested that incorporates hydrologic and climatic inpu ts and provides outputs of probability of exceedance plots as well as skill scores. Results obtained from previous correlation and composite analyses were used as inputs for this portion of the study. The preliminary study, which involved correlation and composite analysis provided the necessary preliminary findings to determine the climate indices most relevant to the Tampa Bay area streamflows. These identified climate indices Nio 1.2, Nio 3, Nio 3.4 and Nio 4 were then chosen as inputs to a model developed for this study. Of these identified indices, those having the most significant impact on streamflows in the Tampa Bay area include Nio 3 and Nio 3.4 as determined through previous research (Martinez et al., 2009). Background Once spatial and t emporal correlation patterns for climatic variables identified relevant indices, the weighted impacts that each of these climate indices have on streamflow were evaluated. Based upon previous studies, various statistical methods for such e fforts can be em ployed, such as, parametric and non para metric regression (Rajagopalan et al., 2005), as well as, additional approaches that have been used more recently including semiparametric sampling and multimodel techniques ( Golembesky et al., 2009). Statistical models have been chosen due to the fact that they require less initial data and parameters and do not need to be calibrated like deterministic models do (Grantz et al. 2005).

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41 Parametric regression is a statistical method, which models through mathematical formulation, the relationship between dependent and independent variables. Through the use of this method, the dependent variable, for example streamflow, can be represented as a function of the various combinations of independent variables, sea surface temperature, geopotential height, and sea level pressure. Parametric regression, as opposed to a non parametric regression, requires the choice of a regression equation (Statistics Glossary, 2004 2009). Implementing such techniques has the additional be nefit that the procedures for parameter estimation and hypothesis testing of this method are well developed. However, the main drawbacks are an assumption of Gaussian distribution of data errors, an assumption of a linear relationship between the predicto rs and the dependent variables, higher order fits require large amounts of data for fitting, and lastly, the models are not portable across data sets (Rajagopalan et al. 2005). Other types of forecast methods include non parametric regression techniques, based, splines, K nearest neighbor (K NN) local polynomials, and locally weighted polynomials. The latter two, K nearest neighbor (K NN) local polynomials, and locally we ighted polynomials are very similar. Owosina (1992) performed an extensive comparison on a number of regression methods both parametric and nonparametric on a variety of synthetic datasets and found that the nonparametric methods out perform parametric al ternatives (Rajagopalan et al. 2005). Of the non parametric techniques discussed here, this study employs a kernel based approach.

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42 Since non parametric methods have been found to result in better approximations, this was considered the better choice metho d and therefore the basis for this portion of the study. Local polynomial methods estimate the value of the function by fitting a polynomial to a small set of neighbors whose distance is determined using either Euclidean or Mahalanobis calculations. Howe ver, there are also other means of determining this function, which include, weighting the predictors differently in the distance calculation by obtaining coefficients from a linear regression between the dependent variable and predictors (Rajagopalan et a l. 2005). Unlike the parametric techniques no prior assumptions are necessary regarding the functional form of the relationship (Rajagopalan et al. 2005). Golembesky et al. (2009) performed a study that compared parametric regression, semiparametric samp ling and multimodel techniques, which combines the two previously mentioned. Semiparametric sampling uses both parametric and non parametric components. Through this study it was determined that the semiparametric sampling method provided a less risk tha n using parametric regression, but that a multimodel technique produced more accurate results. This could be a result of combining the two previous techniques in such a way that they are alternated based on their characteristic strengths ( Golem besky et al 2009). Since the multimodel technique was found better in comparison to the parametric regression and semiparametric sampling, but non parametric out performs parametric regression, it was intended through this research that multimodel and non parametri c regression techniques were explored.

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43 A combination of the method s discussed in Chapter 2 for determining a spatial and temporal outline of climatic influences on streamflow, in conjunction with, a function that represents the significance each climatic factor has in influencing streamflows provided the framework towards building a streamflow forecast model. Appendix A attached, offers pseudo code for this model, while Appendix B provides the actual model code. Data Data for this study was obtained from multiple sources and is comprised of hydrologic and climatic variables, which are described in the following paragraphs. Hydrologic Streamflow data used for this study was obtained from the United States Geological Survey (USGS) (USGS, 2011). The USGS reco gnizes the importance for using unaltered streamflow data in order to identify the sole impact climate imparts on streamflow (Slack and Landwehr, 1994). Therefore, the USGS conducted a study to identify the streamflow gauges throughout the United States re latively unaffected by anthropogenic influences. Results from these efforts were compiled and are known as the Hydroclimatic Data Network or HCDN (USGS 2006). This network of stations was preferential and provided initial guidelines to identify stations for this analysis. HCDN stations were chosen when their characteristics satisfied established metrics. Streamflow data sets used in this analysis were selected based on criteria such as location and dataset length. Stations located within the Tampa Bay area w ere the central focus from which additional station locations broadened outward, but remained within the boundaries of the Southwest Florida Water Management District (SFWMD). The stations selected took precedence due to their existence on larger streams. In addition, as a result of their general flow direction towards the Gulf of Mexico it was

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44 assumed they were part of the drainage system surrounding the Tampa Bay area. The boundaries of the Florida Water Management Districts were determined based on the natural basin geography; therefore, assuming the stations chosen within SWFWMD were part of a single basin was reasonable. It is important to note, however, that as a res exists in locations where the limestone has eroded. Thirteen stations in total were averaged and used for this analysis with locations along t he Withlacoochee, Anclote, H illsborough, Alafia, Little Manatee, Manatee, Peace and Myakka Rivers as demonstrated by Figure 3 1. Stations used for this study were chosen based on their existence along the above mentioned dataset is disp layed in Table 3 1 which ranged from 43 to 80 years. The raw data sets had a monthly time step and various yearly ranges. In preparation for model runs each st grouped into 12 triads with each triad comprised of 3 month means. The beginnin g month, from one triad to the next, was a single monthly time step, establishing 12 periods from January, February, March (JFM) through December, January, February (DJF). During the Singular Value Decomposition (SVD) analysis (as described below) only nin e stations w ere used as indicated in Table 3 1 The same grouping occurred, but each predictor dataset was limited in years by the shortest dataset available providing a total of 70 years from October 1939 through September 2010.

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45 Climatic Correlation and composite analyses of gridded climate variables have been shown to be effective techniques in the selection of climate indices (e.g. Wallace and Gutzler, 1980; Grantz et al., 2005; Oplitz Stapleton et al., 2007; Sveinsson et al., 2008, as s ummarized by Martinez et al., 2009). Previous correlation and composite analysis performed for the Greater Tampa Bay area illustrated a strong relationship between streamflow and the SSTs located in the equatorial Pacific (Martinez et al., 2009). Results from the preliminary study identified climate indices, Nio 1.2, Nio 3, Nio 3.4 and Nio 4, as influential indices for the area of location and were chosen as inputs to a model developed for this study. Of these identified indices, those having the most significant impact on streamflows in the Tampa Bay area include Nio 3 and Nio 3.4 as determined through previous research (Martinez et al., 2009). ENSO indices are located along the equatorial Pacific from off the Coast of Ecuador towards the mid Pacific region; with certain regions of the equatorial Pacific differentiated as distinct ENSO i ndices as previously shown in Figure 2 3 These ENSO indices represent spatial regions where sea surface temperature anomalies occur during different time periods (Cla rke, 2008) These climate indices, Nio 1.2, Nio 3, Nio 3.4 and Nio 4, were obtained through the Royal Netherlands Meteorological reconstructed sea surface temperatures version 3b, which includes data from 1880 until now (Smith et al., 2008). Additional data inputs used during this portion of the analysis consisted of SSTs within the range of 120 E to 60 W and 30 N to 30 S determined to be best correlated over space and time through SVD analysis, discussed later. Grantz et al. (2005) used a

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46 similar technique. Since the slight movement of established indices over time would cause decreases in correlation, predictors other than standard indices were used (Grantz et al. 2005). Methodology Model Overview A model was developed that would provide a streamflow forecast with associated skill scores. These forecasts, expressed as exceedance probabilities, provide the probability that a given streamflow will be exceeded during a user d efined time period. Depicted as continuous probability distribution functions, outputs from the model provide probabilities of streamflow forecasts for which water resource managers can determine the particular level of risk they are willing to take. A 10 percent risk would correspond to a streamflow value that has a 90 percent probability of exceedance (Piechota et al., 2001). Model functionality was adapted from established methods and includes weighting techniques as developed by Piechota et al. (1998, 2001). An Australian model known as the Non Parametric Seasonal Forecast Model or NSFM (Chiew and Siriwardena, 2005), which previously used the techniques developed by Piechota et al. (1998,2001) provided verification of output for the model developed in this study. Whereas the NSFM uses a maximum of two predictors and a single triad and lag, the model developed in this study accounts for multiple predictors, currently accommodating for between two and four predictors, twelve triad s and nine lags with resu lts discussed later in this paper. The model operates using non parametric methods and therefore does not assume a normal distribution of data. Water resource data usually does not tend to follow a normal distribution due to various reasons, such as the no n existence of

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47 negative values and outliers that more frequently occur on the high side, all of which result in a positive skewness (Helsel and Hirsch, 2002). It is assumed, however, that the predictor input data is longer than the predictand, except for i n the case when the predictor is the predictand, such as when only historical flows are used. Model Statistics This model integrates the use of statistical methods to achieve probability of exceedance plots. Exceedance graphs were created by establishing p robability density functions for each predictor (historical streamflow and historical climatic data) which were then incorporated into use of Bayes Probability theorem to identify specific exceedance probabilities for a given streamflow. Plotting these pro babilities against streamflows produces probability of exceedance graphs that can be used as a forecast tool (Chiew and Siriwardena, 2005). Further details for this procedure follow. In order to formulate probability of exceedance plots, a set of exceedanc e and non exceedance probability distribution functions were created for each of the streamflow values within the dataset. The probability that a streamflow for a given year exceeds the remaining streamflows in the data set was then calculated. Performing this for each streamflow in the dataset created subsets of exceedance and non exceedance probabilities. Using these two subsets, two additional subsets were created for corresponding values of the predictor variables (Piechota et al., 2001) Probability distributions were then fitted for each of the four predictor subsets, and an estimate was made of the probability density f unction f ( x i ) for each subset using a kernel density estimator, details for which are discussed in the study of Piechota et al. (1998) The kernel density estimator used was of type normal as opposed to rectangular, Epanechnikov or triangular. Studies have shown the choice of the kernel

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48 density estimator is secondary to the bandwidth chosen ( Piechota et al., 1998) The bandwidth, h was determined by multiplying 0.9 times the minimum value between the standard deviation of the predictor values for flows that exceed a given flow or the 75 th less the 25 th percentile divided by 1.34 (Eq. 3 1). This value was then multiplied by the number of streamflow values that exceeded the given streamflow raised to the power of 0.2 ( Piechota et al., 1998) If h is chosen too small, spurious fine structure will show, if chosen too large, the bimodal nature of the distribution is obscured (Silverman, 1986). Apart from a rec tangular estimator, or histogram, the kernel density estimator is the most common (Silverman, 1986). (3 1) where, h = bandwidth, and y = vector of predictor values for flows that exceed given data Next, using Bayes probability theorem (Eq. 3 2 and 3 3 below), the posterior probability that a streamflow, Q i will be exceeded was calculated given the initial conditions of the predictors: the climate index ( x ) or historical streamflow ( y ). The prior probabilities of predictors were denoted by f 1 corresponding to streamflow greater than the given streamflow, Q i and f 2 corresponding to streamflow less than Q i while p 1 was the prior exceedance probability and p 2 the prior nonexceedance probability, both of which were based on climatology for stre amflow greater than/less than Q i respectively (Chiew and Siriwardena, 2005).

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49 For single predictor, climate index, (3 2) For single predictor, streamflow, (3 3) This procedure, to obtain exceedance probabilities based upon historical records, was repeated for each of the streamflow values of the triad or single month to be forecast, Q i in the time series (Piechota et al., 2001) Model Cross Validation This model uses a leave one out approach for cross validation. Cross validation is performed by removing one year of data and running the model for the missing year, giving an independent forecast for that particular year. The data for that year is then returned to the data set and the subsequent year is removed and forecasted for using the model. This is performed consecutively for each year in the data set (Piechota et al., 2001) Cross validation provides a more independent assessment of the forecast skil l and of the weights applied to each model (Elsner and Schmertmann, 19 94; Michaelsen, 1987) Model Skill forecasted streamflow over the entire probability distribution. This method of scoring can b e used on both continuous and categorical data. (Ward and Folland, 1991; Potts et al.,

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50 1996; Ruiz et al., 2006; Tootle and Piechota, 2004). Essentially, the LEPS score is an attempt to measure the error in a forecast according to the distance between the p osition of the forecast and the corresponding observation in units of their respective cumulative probability distributions (Potts et al., 1996). Other scoring systems are available for use such as root mean squared error (RMSE) and anomaly correlation, ho wever, the LEPS scoring system was developed by Ward and Folland (1991) in an attempt to reduce some of the problems associated with the other scoring methods. Standard correlation has the disadvantage that no account is taken of systemic differences betwe en the variance of the forecasts and that of the observations. Anomaly correlation is sensitive to small differences between the forecasts and the observations when both are near the observed climatological average. While the Sutcliffe score does penalize errors based on severity, it does not have the property that the expected score is the same for each observation. This means the Sutcliffe score can vary according to fluctuations in recent climate and give a false impression of skill (Potts et al., 1996). The method for calculating the LEPS score is intricate. While it is a measure of the probability space, the calculation itself uses the sum of this space. These values ran ge from 100 to 100, with higher scores indicating a better forecast.

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51 For each predictor value, the space between the observed probability and the forecasted probability was calculated using Equation 3 4. (3 4) where, Pf = the forecast probability, and Po = the observed probability Next the best space (Equation 3 5) and worst space (Equations 3 6 or 3 7) are calculated based on the sign convention for the sum of S for all years. (3 5) If the observed probability of observed streamflow is greater than 0.5 then Equation 6 is used, otherwise Equation 3 7 is implemented. (3 6) (3 7) S(j), Sworst and Sbest are calculated and summed for each forecasted probability value for each year and summed for all years. If the total space is greater than zero, then Sbest is used in the calculation of the LEPS score (Equation 3 8), otherwise, Sworst (Equation 3 9). (3 8)

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52 (3 9) A LEPS score of zero signifies that the forecast is based solely on climatology (historical streamflows), while scores greater than zero indicate an increased level of skill through the use of climatic data as a predictor (Chiew and Siriwardena, 2005) LEPS scores greater than zero indicate that the model, incorporating climatological data, produced better forecast skill than if only historical streamflows were used as a predictor (Chiew and Siriwardena, 2005). According to Tootle and Piechota (200 4 ), LEPS scores of 10 or highe r, demonstrate noteworthy skill, however for purposes of this study scores above zero were considered noteworthy. Single Predictor Runs The model performs these calculations for 12 triad s JFM through DJF and nine lags. The tr iads are defined using a 3 month average and a 1 month time step. Stepping the climatic data triad back by a monthly time step from 1 month to 9 months then summed to represe triad and time period for each individual station. Combination Forecasts Based on previous research performed by Casey (1995) and again by Piechota, et al. (1998), the concept of combination forecasts, involving mul tiple climate indices as predictors, was performed in this analysis. This essentially takes the results from the single predictor runs and combines them using a weighting scheme that reflects their individual skill.

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53 The final exceedance probability foreca st was found by combining the individual forecasts into one consensus forecast as described here. Weights ranging from 0 to 1 are applied to each predictor in increments of 0.1 so that they add up to 1. The number of combinations was dependent on the numbe r of predictors. For example, a 2 predictor combination result ed in 11 different weighting schemes, a 3 predictor combination 62 different weighting schemes and a 4 predictor combination 258 weighting schemes. Optimal weighting schemes were identified by e valuating the LEPS score for each weighting scheme for an individual predictor combination. The final consensus forecast is the weighted combination that produces the highest LEPS score. For this analysis two different predictor combinations were chosen to identify optimum forecast skill, comprised of a 2 and 4 predictor combination. The 2 predictor combination consisted of historical flows joined with Nio 3.4, while the 4 predictor combination included historical flows, Nio 1.2, Nio 3 and Nio 4. Overa ll, Nio 3 demonstrated the best results from correlation and composite analysis. Four predictors were used rather than just Nio 3 in order to improve results by taking into account the spatial relevance of these indices over time ( Trenberth, 2001; Clarke 2008) Results were determined for each individual station and summarized by averaging the LEPS scores for all stations during a single triad and lag. Averaging was repeated for each time sequence and applied to the individual predictor weights as well. Singular Value Decomposition Analysis The overall input datasets used in this analysis were unaltered as described above. However, in order to improve the results for this model, an additional dataset was created using a technique that would exploit the co variance between streamflows and SSTs. Valid use of this technique, known as Singular Value Decomposition (SVD)

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54 analysis ( Bretherton et al., 1992; Tootle et al., 2006) also known as Maximum Covariance Analysis (MCA), occurs when one has evidence of couplin g which can be obtained through methods such as principal component analysis (PCA) (Cherry, 1997) or correlation and composite analysis (Bretherton et al., 1992). The latter method, performed during the preliminary stages of this study, found the two datase ts, hydrologic and climatic, strongly correlated with geographical relevance, providing a fairly strong indication of coupling (Cherry, 1997). SVD can be used to find linear combinations of two sets of variables such that the linear combinations have the m aximum possible covariance (Cherry, 1997). Evidence of coupling prompted the use of SVD analysis which was performed using multiple time series of both sea surface temperatures (SSTs) and streamflows. Since the length of datasets used in SVD analysis were limited by the shortest dataset only nine streamflow stations were chosen for this portion of the analysis to achieve at least 70 years of data. SVD was used to reduce this multitude of time series into a single representative time series that encompasse d the best correlation between each of the two variables, SSTs and streamflows, over time. The results of SVD analysis are presented as multiple modes, where mode 1 is a single times series of SSTs reflective of the greatest covariance with streamflows, mo de 2 the second highest covariance between SSTs and streamflows and, lastly, mode 3 the third greatest covariance between SSTs and streamflows. Although more modes are produced by SVD methods, only the first three resulting modes were used for purposes of this study since they represent the three SST datasets best correlated with streamflow.

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55 Results LEPS Skill Scores LEPS scores greater than zero indicate that the model, incorporating climatological data, produced better forecast skill than if only historical streamflows were used as a predictor. While Tootle and Piechota (2004) considered skill scores of 10 or greater as good skill, this is an arbitrary threshold. Values greater than zero indicate skill; therefore for purposes of this study, the skill threshold was set at zero with the knowledge that higher LEPS scores indicate greater forecast skill. Of the 13 stations that were investigated for the 2 and 4 predictor combinations, general trends were exhibited by all stations. Therefore in order to summarize these overall trends, results discussed here represent the mean of all 13 stations. Comparing the three different combinations of predictors, the 2 predictor combination consisting of historical flows joined with Nio 3.4, t he 4 predictor combination that included historical flows, Nio 1.2, Nio 3 and Nio 4 and the SVD data set, which included modes 1, 2 and 3, it can be noted that each combination has a different seasonal strength. The 2 predictor combination produced high er skill than the 4 predictor during the fall and winter. While the 4 predictor combination had slightly lower scores than the 2 predictor combination in the fall and winter, it produced higher scores during the late spring and sum mer, as can be seen in Fi gure 3 2 (a,b). The SVD dataset produced higher LEPS scores than both the 2 and 4 predictor co mbinations as shown in Figure 3 2 (c). The 2 predictor combination (Figure 3 3(a)) historical flows joined with Nio 3.4, resulted in slightly higher forecast skill than the 4 predictor combination during the late winter, JFM, through early spring, March, April, May (MAM ) LEPS scores for the 2

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56 predictor combination indicate skill for all nine lags during these triad s from JFM until MAM. The 4 predictor combinat ion (Figure 3 3(b)) demonstrated good skill from late spring, April, May, June (AMJ), to early winter, DJF. LEPS scores were higher than the 2 predictor combination for these triad s during lags 1 9 (AMJ), lags 1 5 and lags 7 9 for May, June, July (MJJ), la gs 1 3 and 8 9 for June, July, August (JJA) and lags 1 3 f or July, August, September (JAS ). The skill increased during the fall and early winter months for the 4 predictor combination and continued to fare better compared to the 2 predictor combination for lags 1 8 for August, September, October (ASO) and SON. Skill observed for all nine lags for the 4 predictor combination were higher than the skill observed in the 2 predictor combination from OND until DJF. Use of the SVD dataset resulted in LEPS scores (Figure 3 3(c)) that were higher than scores obtained from the 2 predictor and 4 predictor combinations. This was the case for all triad s and lags. When examining the LEPS scores that resulted from use of the SVD data inputs, it can be seen that the skill level produced for all predictor combinations during the late fall, winter, and early spring were in most cases greater than zero. Summer forecasts demonstrate less skill, however the fact that there appears to be some skill during the summer is rather imp ortant. A study performed by Tootle and Piechota (2004) using climate and persistence, as well as the preliminary correlations for this study, indicated that a strong correlation is not present during summer months. However, using the probability technique s demonstrated through this analysis, some level of skill may be obtained. The negative LEPS scores that did appear during summer were slightly below

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57 zero and, for these cases, using persistence or historical streamflows as a predictor would be recommended Predictor Weights The resulting LEPS scores of each combination for each triad and lag represent the best possible score obtained by applying various weights to each predictor. Weighting the different predictors according to their forecasting ability res ulted in greater overall LEPS scores. Discussed here are the results for each separate weighting scheme to indicate the individual predictors of greatest influence for a single scheme. In the case of the 2 predictor scenario, historical flows joined with N io 3.4, the weight distribution resulted in inverses for the two predictors as shown in Figure 3 4 During the mid to late winter, JFM to MAM, Nio 3.4 received the majority of the weight for lags 2 9, while historical streamflows received the majority of weight during earlier lags, for example lag 1. Moving forward in time to the AMJ triad the historical flows predictor received the majority of weight, but only for a 1 to 2 month lag. During MJJ historical flow remains as the prominent predictor and the forecasting window increases with the optimal forecast period around two and five months prior. As time progresses into summer and fall from JJA to November, December, January (NDJ), the forecast window becomes narrow again and historical flow lends itsel f as a skillful predictor only during short term forecast periods such as one to two months. During early winter, Nio 3.4 provides better prediction skill and the forecast window expands to a six month range during lags 4 through 9. In the case of the 4 p redictor combination, which included historical flows, Nio 1.2, Nio 3, and Nio 4, the most influential predictors were historical flows and Nio 3 as demonstrated in Figure 3 5 The seasonal influence for each of these predictors

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58 varied similar to the p atterns observed for the 2 predictor combination except that the weights themselves were slightly less due to the distribution of weights among four predictors rather than only two. The pattern of heavier weights was similar between the historical flow pre dictors as well as between Nio 3.4 and Nio 3. The slight increase in skill level during the summer months for the 4 predictor combination, in comparison to the 2 predictor combination, is the resulting contribution supplementary predictors offer. Lastly, the weights for individual SVD data sets, which included modes 1, 2 and 3, place the majority of weight exclusively on the SVD data set mode 1 with a minor contribution from the dataset of historical flows as shown in Figure 3 6 The majority of weight pl aced on the SVD data set mode 1 occurred during mid winter (JFM) through early spring (MAM) for a period of two to nine months prior. During the months from AMJ through JJA, the SVD data set mode 1 received the heaviest weight and only during the five mont hs prior to the forecast period. Starting in JAS weight was placed for the most part again on the mode 1, however the range of influence increased up to nine months prior to the forecast period, including lags 1 to 9. This range of influence tapers off unt il the heaviest weight spans only a month, four months in advance of the forecast period. The range of influence for the heaviest weights of mode 1 expands during DJF to lead into the range discussed for the JFM triad Conclusions Since each predictor or c limate index has spatial and temporal characteristics that define it (Tren berth, 2001), it was speculated that combining predictors with overlapping influence would improve the overall skill of the forecast model. An increase in the number of predictors wo uld allow for complimentary predictors to be combined in such a

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59 way that encompasses a broader array of the spatial and temporal periods where climate strongly impacts the hydrologic resources. Results indicate that it is not the quantity of predictors tha t improves skill, but the period of influence the chosen predictors encompass. The 2 predictor combination demonstrated that Nio 3.4 provides increased forecast skill during the winter; however, Nio 1.2 and Nio 3 in the 4 predictor combination contribut e to the majority of increased skill during summer months. This is believed to be a direct result of the SST anomalies spatial locations. Warm sea surface temperatures tend to occur in the central equatorial Pacific, but as the trade winds weaken, decreasi ng the upwelling of the thermocline off the coast of Peru, the SSTs in the eastern Pacific become warmer than normal and the area is considered to experience an El Nio event ( Wang 1995; Clarke, 2008) El Nio events have been defined as beginning in the b oreal spring or summer and peak from November to January in sea surface temperatures (Tren berth, 1997). While the seasonal timing of El Nio event (May to January) occurs prior to the period of maximum correlations of SSTs with streamflows in the Tampa Bay region ( November to late Spring ) the seasonal lag that occurs between SSTs in the Pacific and streamflows in Tampa Bay may be a result of the delay caused by atmospheric circulation and rainfall runoff events. It is thought the warm SSTs anomalie s that occur in Spring/Summer result in strong correlations with streamflows in November and so on. It is important to note the actual difference in skill level between the 2 predictor and 4 predictor combinations. Although the difference is rather minut e, the fact that the skill scores for the 4 predictor combination are not only higher during the summer, but that they are positive (above zero skill) demonstrates that using such a combination of

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60 predictors results in better forecast skill than solely usi ng historical streamflows, or what is called climatology. Results obtained from the SVD dataset, in comparison to the 2 predictor and 4 predictor, provided the best results. This was believed to be due to the fact that each mode was a compilation of sea su rface temperatures determined most closely correlated over space and time with the streamflow data used. Mode 1, by definition of SVD analysis, was predicted to provide the best results followed by mode 2 and lastly mode 3, as was indeed the case. In fact, the distribution of weights indicted that mode 1 was the overall best predictor. In summary, although the skill provided here in some instances is only slightly higher than when persistence alone is used, it is in fact an improved forecast. Therefor e, the use of such a method does indeed provide additional information that can further assist water resource managers with making an informed decision in terms of water supply availability.

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61 Table 3 1 Period of record for each United States Geological St ation within the Greater Tampa Bay Area used in this analysis. No. USGS Id Station n ame Data r ange Predictor Combo I and II Year s pan Latitude Longitude Drainage a rea ( Km 2 ) 1 2301500 Alafia River At Lithia* 10/1932 9/2010 78 27.87 82.21 868 2 2301300 Alafia River Near Lithia (South Prong) 10/1963 9/2010 47 27.80 82.12 277 3 2310000 Anclote River Near Elfers* 10/1946 9/2010 64 28.21 82.67 188 4 2303000 Hillsborough River Near Zephyrhills* 10/1939 9/2010 71 28.15 82.23 570 5 2300100 Little Manatee River Near Ft. Lonesome 10/1963 9/2010 47 27.70 82.20 81 6 2300500 Little Manatee River Near Wimauma* 10/1939 9/2010 71 27.67 82.35 386 7 2299950 Manatee River Near Myakka Head 10/1966 9/2010 44 27.47 82.21 169 8 2298830 Myakka River Near Sarasota* 10/1936 9/2010 74 27.24 82.31 593 9 2296750 Peace River At Arcadia* 10/1931 9/2010 79 27.22 81.88 3541 10 2295637 Peace River At Zolfo Springs* 10/1933 9/2010 77 27.50 81.80 2139 11 2312000 Withlacoochee River At Trilby* 3/1930 9/2010 80 28.48 82.18 1476 12 2310947 Withlacoochee River Near Cumpressco 10/1967 9/2010 43 28.31 82.06 725 13 2313000 Withlacoochee River Near Holder* 9/1931 9/2010 79 28.99 82.35 4714 *used in SVD analysis, 70 years of data ranging from 10/1940 9/2010 (USGS, 2011)

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62 Figure 3 1 United States Geological Service stations within the Greater Tampa Bay area used in this analysis (USGS, 2011).

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63 Figure 3 2 Weights for individual predictors (predictor 1, predictor 2, etc) for all triad s and lags for the (a) 2 predictor combination, (b) 4 predictor combination and (c) SVD Modes. Shaded values represent triad s and lags when LEPS scores are above zero, an indica tion of improved skill compared to only using historical flow as a predictor a. b.

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64 Figure 3 2 continued c.

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65 (a) 2 predictors: historical flows and Nio 3.4 (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4 (c) SVD data: hi storical flows, SVD mode 1, SVD mode 2 and SVD mode 3 Figure 3 3 Averaged LEPS scores for all stations using (a) 2 predictors: historical flows and Nio 3.4, (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4 and (c) SVD data: historical flows, SVD mode 1, SVD mode 2 and SVD mode 3.

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66 (a) Historical flows (b) Nio 3.4 Figure 3 4 Predictor weights averaged for all stations using 2 predictors: (a) historical flows and (b) Nio 3.4.

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67 (a) Historical flows (b) Nio 1.2 (c) Nio 3 (d) Nio 4 Figure 3 5 Predictor weights averaged for all stations using 4 predictors: (a) historical flows, (b) Nio 1.2, (c) Nio 3 and (d) Nio 4.

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68 (a) Historical flows (b) SVD Mode 1 (c) SVD Mode 2 (d) SVD Mode 3 Figur e 3 6 Predictor weights averaged for all stations using SVD data: (a) historical flows, (b) SVD mode 1, (c) SVD mode 2 and (d) SVD mode 3.

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69 CHAPTER 4 TAMPA BAY CASE STUDY Background Historically, Tampa Bay Water relied heavily on groundwater sourc es, however with changing environmental conditions plans were made to increase surface water usage. Goals were set in place to ensure surface water accounted for nearly half (41.8 percent) of the water in the system at Tampa Bay by 2012 (Tampa Bay Water, 2 010). The transformation of resource reliance fr om groundwater to surface water reinforces the significance of findings for such a study. Study Site The main focus for this portion of the research project included the Alafia and Hill sborough River Basins (Figure 4 1 ). The Alafia River Basin covers the majority of Hillsborough County and a small portion of west central Polk County across an area of 1,061.9 Km 2 (410 mi 2 ). Originating as several small creeks in Polk County the system flows through Hillsborough County for 38.6 Km (24 mi ) until reaching Hillsborough Bay, the Northeastern segment of Tampa Bay. The North Prong originating in Polk County west of Plant City and south of Lakeland covers 16.1 Km ( 10 mi ), while th e South Prong, originating in Hookers Prairie of southeast Polk County, covers a distance of 40.2 Km (25 mi ). There are 17 lakes, a reservoir and two springs, Lithia and Buckhorn springs, located on this river. It should be noted the reservoir is a reclaim ed phosphate pit that covers an area of 3.1 Km 2 ( 1.2 mi 2 ) (FDEP, 2012). The Hillsborough River watershed is slightly larger than that Alafia covering 1,787.1 Km 2 (690 mi 2 ). It extends through Hillsborough, Polk and Pascoe Counties originating in east north east Zephyrhills of southeastern Pascoe and northwestern Polk

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70 Counties flowing 86.9 Km (54 mi ) into the Hillsborough Bay. It should be noted that Sixmile Creek, renamed Tampa Bypass Canal, was channeled to intersect the Hillsborough River at the union of T rout Creek and near the midpoint of the Tampa Reservoir. This reservoir supplies drinking water to the city of Tampa, while the canal itself assists to control flooding through two canals, the Harney Canal (C 136) and C 135. Lake Thonotosassa 8.5 Km 2 (3.3 mi 2 ) and two second magnitude springs, Crystal and Sulfur Springs, are located on the Hillsborough River with discharges of 6.46 to 64.6 million gallons per day. It should be noted this watershed also receives overflow from the Withlacoochee River (FDEP, 2 012). Establishment of Organization Tampa Bay Water, located in Clearwater, Florida is a unique water wholesaler created to develop, store, and supply water to the surrounding 6 government members located in the tri county area of Pinellas, Hillsborough, and Pascoe counties. Alternating the use of various water supplies, such as surface water, groundwater, and desalinated seawater, allows Tampa Bay Water to maximize availability potential of each source to address supply concerns, while taking into consideration environmental impacts and economic factors affiliated with each of these sour ces (Governance, 2006). Applied Model For this case study, the model was applied to three streamflow stations monitored by Tampa Bay Water for public water supply availability, Alafia River at Bell Shoals, Hillsborough River at Morris Bridge and S160, a ca nal whose recorded levels have been adjusted to account for a nthropogenic influences (Table 4 1 ). While the exact procedure performed by Tampa Bay Water to account for anthropogenic influences was not disclosed here, it generally involves accounting for st reamflow changes that result

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71 from the opening and closing of canal access points. Climate predictors for this portion of the analysis were comprised of Nio 1.2, Nio 3, Nio 3.4 and Nio 4 and grouped into predictor combinations with historical streamflow s, providing a 2 and 4 predictor combination, historical streamflows with Nio 3.4 and historical streamflows with Nio forecast skill between the two different predictor combinations. Results LEPS scores for Alafia at Bell Shoals appear slightly higher when using the 4 predictor combination rather than the 2 predictor comb ination (Figure 4 2 ). This holds true for nearly all triad s and lag times except during JFM around a 9 month lag, when the 2 predictor combination provides more skill. Closer inspection of the individual predictor weights reveals that the predictors most responsible for the higher LEPS scores in the 4 predictor combination are a result of historical flow s Nio 1.2 and Nio 3 (Figure 4 4 ). The temporal influence of historical flows as a predictor mainly occurs during shorter lags, up to two months prior to the triad of interest, during MAM through JAS as a result of persistence that streamflows exhibit du ring short time scales Nio 1.2 demonstrates its influence from JFM through AMJ and again from ASO through DJF. This is rather unexpected due to the fact that the location of SST anomalies oscillates only once within an annual cycle, rather than multiple times, therefore the anomalies occurring in the Nio 1.2 region during two different time periods was rather unpredictable It is not known what may have caused such re sults. In mid to late winter this influence occurs between 2 and 4 month lags then exte nds during early spring to include lags 6 to 9 months and 3 month lags and again between 5 and 8 month lags The impact of Nio 3 during FMA can be

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72 observed five to eight months prior. This index again re sults as the main predictor influencing JJA and can be observed between five and nine months prior. During the few triad s and lags that the 2 predictor combination faired better than the 4 predictor combination, it should be noted that Nio 3.4 carried the majority of weight rather than historical streamflows (Figure 4 3 ). The 2 predictor combination resulted in better skill than the 4 predicotor on two occasions, during JFM around a 9 month lag and during DJF between a 6 and 8 month lag. Results for the H illsborough River at Morris Bridge station for 2 predictor and 4 predictor combinations significantly resembled one another (Figure 4 5 ). LEPS scores for both predictor combinations exemplified similar patterns. Triad s from JFM until AMJ demonstrated LEPS scores greater than 10 for u p to 2 month lags. During this period, only MAM at a 3 month lag continued to show higher LEPS scores. This pattern continued through greater lags, but moved later in the period of influence until early MJJ up to a 7 month lag. The only other period for which noteworthy LEPS scores occurred was during OND through DJF for a single lag. During these triad s both predictor combinations did show LEPS scores above zero for greater lags however, the scores were highest during shorter lags. The periods for which higher LEPS scores were displayed corresponded to triads and lags when historical flows contributed the most weight. Nio 3 contributed to the increased LEPS scores during OND an d NDJ during lags of 2 to 3 months for the 4 pre dictor combination (Figure 4 7 ). Greater lags, such as lags of 7 or 8 months during OND may be slightly affected by other predictors such as Nio 3. 4 for the 2 predictor

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73 (Figure 4 6 ) or Nio 4 for the 4 pr edictor combination. Overall the majority of forecast skill for this particular station was a result of historical flows. Model results for the S160 station demonstrated higher LEPS skill scores than for Alafia at Bell Shoals or Hillsborough R iver at Morri s Bridge (Figure 4 8 ) however results for S160 may not be as reliable as the other stations due to the fact that S160 is a canal that has been adjusted to account for anthropogenic influences. When results for the 2 predictor and 4 predictor combination data sets were compared, it was observed that the 2 predictor combination (Figure 4 9 ) provided higher skill as a predictor than the 4 predictor combination (Figure 4 10 ) with slight differences. The 4 predictor combination scored higher LEPS skill scores during late fall, early winter, but only for 8 to 9 month lags and even then the difference is rather irrelevant since the skill level of the 2 predictor model during this time demonstrated skill scores near or above ten indicating good forecast skill. Th e higher LEPS scores generated by the 2 predictor combination are a result of the historical streamflows and Nio 3.4 as predictors. These two predictors alternate and demonstrate distinct periods and lags when they are responsible for the majority of the forecast skill. Accordi ng to results shown in Figure 4 9 (a), historical streamflows provide good forecast skill for early lags, from early winter (OND) through late spring (MJJ) when the overall forecast skill scores are best. During greater lag periods, t he influence of Nio 3.4 offers greater forecast skill. For example, from JAS through FMA the higher LEPS skill scores are a result of Nio 3.4. The influence of Nio 3.4 can be used as a predictor between 4 and 9 months in adva nce as demonstrated in Figu re 4 9 (b).

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74 Weights for individual predictors of the 4 predictor combination for station S160 demonstrated differences among influ ence as illustrated in Figure 4 10 Historical flows contributed the most while Nio 1.2 came in second, Nio 3 third and Nio 4 offered some skill. The range of influence offered by the predictor historical flows occurred up to 2 month lags during NDJ through JFM at which point the number of lags begins to increase until JJA when the range of influence increases to an 8 month lag During ASO and SON triad s there is no contribution from this predictor. Although the contribution in terms of weights for predictors Nio 3 and Nio 4 are much less than Nio 1.2, the skill level in terms of LEPS scores was greater for these two predicto rs and therefore their contribution more significant. The small area during JFM and FMA at 7 and 8 month lags from Nio 3, as well as, the small sliver of influence offered from Nio 4 during SON at a 7 month lag which then extends to NDJ at a 9 month lag offer s LEPS skills greater than 10. Probability of Exceedance Plots The model developed through this study has the capability to produce probability of exceedance plots for user defined variables, for example rainfall or streamflow. Given that the LEPS sc ores indicate forecast skill, probability of exceedance plots may be generated for all years of a specific period and lag during calibration. To further illustrate an example of model output useful to water resource managers the model was run using stream flow data from Alafia at Bell Shoals, Hillsborough at Morris Bridge and S160 Adjusted during the JFM triad for a single lag time incorporating historical streamflow and Ni o 3.4 as predictors. Figures 4 11, 4 13 and 4 15 demonstrate the resulting probabili ty of exceedance plots of these stations for the first year of each data set remaining years are included in Appendix C Included in

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75 these plots were the upper and lower envelopes that were averaged to calculate the probability of exceedance, as well as, the climatological probability exceedance, the probability of exceedance based solely on h istorical streamflows. Figure 4 12, 4 14 and 4 16 demonstrate ensembles of probability of exceedance plots for all years dur ing this defined period and lag for each station, Alafia at Bell Shoals, Hillsborough at Morris Bridge and S160 Adjusted, respectively. These plots provide an example of model outputs that would be useful for water resource manager s. Although these illustrations of a streamflow foreca st are for JFM during a 1 month lead time these are only examples for a single scenario. T he period and lag/lead time are user defined parameters that can accommodate any desired time period While the one month lag is represented here, water resource manage rs may be more interested in results for lags between three and six months for planning purposes. Investigated Withdrawal Relationships Tampa Bay Water utilizes a system of operating rules in order to determine the most appropriate streamflow withdrawal am ounts to refrain from causing adverse environmental impacts. For this portion of the investigation, monthly withdrawals for the Alafia River were calculated from recorded streamflows of the Bell Shoals station based on operating rules established by Tampa Bay Water. Streamflow records were then plotted against calculated withdrawal amounts and a relation ship was investigated (Figure 4 17 ). It was anticipated that through a method known as the ladder of power s (Helsel and Hirsch, 2002) a linear relationship could be determined between two variables by transforming the data. The streamflow and withdrawal datasets, plotted against each other as mentioned above, were each transformed using varying degrees of power. A

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76 best fit line was then used to represent thi s linear relationship, and could be used to transform streamflows into withdrawals. Varying degrees of power used for these transformations for each variable ranged through natural log, reciprocal root, reciprocal and reciprocal squared. The most linear b ehavior between streamflow s and withdrawal s occurred when the natural log of streamflows were plotted against withdrawal calculations. This relationship further improved when the streamflow dataset was reduced, as was guided and validated through the metho d of least squares, eventually obtaining an R 2 value of 0.911. In order to encourage a more distinct linear relationship with withdrawals, only streamflow data greater than 50 MGD was incor porated into the plot (Figure 4 18 ), otherwise non linear character istics were more prominent. Removal of this data was an arbitrary cut off that reduced the actual dataset by a minimal 7 percent, but provided more distinct linear relationship Conclusion Results from this study provide Tampa Bay Water with streamflow for ecasts in the form of probability of exceedance plots for short t erm source allocation decisions, a methodology and software tools that can assist water resource managers Additionally, these tools can be applied to any geographic region to identify climat ic influences on regional water resources and better forecast these hydrologic variables.

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77 Table 4 1 Period of record for stations specific to Tampa Bay Water. No. Station n ame Data r ange Predictor Combo I and II Year s pan 1 Alafia River At Bell Shoals 10/1974 9/2008 34 2 Hillsborough River Near Zephyrhills 10/1972 9/2008 36 3 S160_ Adjusted 10/1974 9/2002 28

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78 Figure 4 1 Tampa Bay Water service area (green) with Hillsborough and Alafia River catchment areas (pin k) within the Southwest Florida Water Management District (SWFWMD) (tan).

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79 (a) 2 predictors: historical flows and Nio 3.4 (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4 Figure 4 2 LEPS scores for Alafia at Bell Shoals using (a) 2 predictors: historical flows and Nio 3.4 and (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4. (a) Historical flows (b) Nio 3.4 Figure 4 3 Predictor weights for Alafia at Bell Shoals using 2 predictors: (a) historical flows and (b) Nio 3.4.

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80 (a) Historical flows (b) Nio 1.2 (c) Nio 3 (d) Nio 4 Figure 4 4 Predictor weights for Alafia at Bell Shoals using 4 predictors: (a) historical flows, (b) Nio 1.2, (c) Nio 3 and (d) Nio 4.

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81 (a) 2 predictors: historical flow s and Nio 3.4 (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4 Figure 4 5 LEPS scores for Hillsborough River at Morris Bridge using (a) 2 predictors: historical flows and Nio 3.4 and (b) 4 predictors: historical flows, Nio 1.2, Ni o 3, and Nio 4 (a) Historical flows (b) Nio 3.4 Figure 4 6 Predictor weights for Hillsborough River at Morris Bridge using 2 predictors: (a) historical flows and (b) Nio 3.4.

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82 (a) Historical flows (b) Nio 1.2 (c) Nio 3 (d) Nio 4 Figure 4 7 Predictor weights for Hillsborough River at Morris Bridge using 4 predictors: (a) historical flows, (b) Nio 1.2, (c) Nio 3 and (d) Nio 4.

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83 (a) 2 predictors: historical flows and Nio 3.4 (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4 Figure 4 8 LEPS scores for S160 using (a) 2 predictors: historical flows and Nio 3.4 and (b) 4 predictors: historical flows, Nio 1.2, Nio 3, and Nio 4. (a) Historical flows (b) Nio 3.4 Figure 4 9 Predictor weights for S160 using 2 predictors: (a) historical flows and (b) Nio 3.4.

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84 (a) Historical flows (b) Nio 1.2 (c) Nio 3 (d) Nio 4 Figure 4 10 Predictor weights for S160 using 4 predictors: (a) historical flows, (b) Nio 1.2, (c) Nio 3 and (d) Nio 4.

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85 Figure 4 11 Example plot showing streamflow probability of exceedance and climatology, including upper and lower envelops, for Alafia at Bell Shoals for 1974. Figure 4 12 Streamflow probability of exceedance ensemble of Alafia at Bell Shoals for years 1974 2008.

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86 Figure 4 13 Example plot showing streamflow probability of exceedance and climatology, including upper and lower envelops, for Hillsborough River at Morris Bridge for 1972. Figure 4 14 Streamflow probability of exceedance ensemble of Hillsborough River at Morris Bridge for years 1972 2008.

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87 Figure 4 15 Example plot showing streamflow probability of exceedance and climatology, including upper and lower envelops, for S160_Adjusted for 1974. Figure 4 16 Streamflow probability of exceedance ensemble of S160_Adjusted for years 1974 2002.

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88 Figure 4 17 Correlation of streamflows with withdrawals for the Alafia at Bell Shoals station. Monthly streamflows were summed from daily.

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89 Figure 4 18 Relationship of natural log streamflows with withdrawals for the Alafia at Bell Shoals station. Monthly streamflows were summed from daily. Best fit line demonstrates an R squared of 0.911.

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90 CHAPTER 5 CONCLUSIONS AND RECO MMENDATIONS Summary Nio 3 and streamflow correlation results illustrated positive correlation patterns that extended across more period s than that of correlations produced using Nio 3.4. However, Nio 3.4 offered positive correlations for a greater number of lags than that offered by Nio 3. LEPS scores illustrated that the model provides skill during most triad s and lags, especially winter. There was even skill offered through summer months, but only during shorter lags with higher sc ore s produced by the 4 predictor combination. For the 2 and 4 predictor combinations the model offers good skill across multiple triad s and lags in a pattern that mirrors results obtained through the correlation of SSTs with streamflows reaffirming the mo del skill as a result of the incorporated climatic predictors. The best forecast results were provided through the use of SVD data sets as was predicted since this is a conglomeration of the SSTs within the equatorial Pacific best correlated with streamf lows in the Tampa Bay area. Mode 1, resulting from the SVD analysis, is recommended as the input data for future streamflow forecasts in this area. Resulting forecasts of streamflow stations monitored by Tampa Bay Water, Alafia River at Bell Shoals, Hillsb orough River at Morris Bridge and S160_Adjusted, expressed strong similarities between the two different predictor combinations, historical flows with Nio 3.4 and historical flows with Nio 1.2, Nio 3 and Nio 4. Even though results from the two differen t predictor combinations were quite similar in comparison to each other for both the Alafia at Bell Shoals and Hillsborough River at Morris Bridge, there were enough differences between the two combinations that picking one over the other was

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91 rather subjec tive to the temporal periods of interest. This same subjectivity also applies to the individual predictors within each predictor combination, since for the most part there is relatively equal weighting among indices, with the exception of Nio 4, which har dly contributes. The model skill for S160_Adjusted rather favors the 2 predictor combination, yet weights are divided rather equally among the two predictors, historical streamflow and Nio 3.4. Conclusions Although the overall idea to incorporate climate data into streamflow forecast models has been in practice for areas in the western United States for quite some time, the southeastern region has been focused more towards these efforts in recent years. ast several decades has been fueled by its climate and abundant water resources. As a result, increases in population growth and urban development have significantly impacted water resources in the state. With the knowledge that climate represents one dir ect link to the availability of water supplies and can influence the demand for this resource, by studying the patterns associated with climatic influences, water resource managers could be better equipped with the tools necessary for more accurate water s upply projections. Recommendations for Future Work Investigation of Alternative Hydrologic Variables While it was chosen to only focus on streamflows as a result of the noise encountered from the use of rainfall and demand data, these hydrologic variable s may offer additional insight of this system and the over all climatic impact. Further in depth investigation of rainfall and demand influences could be an integral part of this work.

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92 Noise for the demand data illustrated the complexity associated with su ch data, believed to be the result of anthropogenic influences. Investigate Local Methods for Nonparametric Modeling The different methods for local polynomial estimation could be investigated further to determine if a better option exists compared to kern el density estimation. Transformation of Streamflow Forecasts into Forecasted Withdraw Volumes The relationship that exists between streamflows and withdrawals in conjunction with the streamflow exceedance probabilities could be further exploited to create withdrawal probability of exceedance plots for more applicability in Tampa Bay decision making process. Application to Alternative Locations It may be beneficial to apply the model to alternative locations to further cability. Performing a comparison between heavily managed systems in urban areas, such as that presented here for Tampa Bay, with an area of low impact might offer additional insight into the effect that managed systems have on the link between climate and water resources. As determined by Yin (1994) variations in moisture conditions for areas such as Tennessee and Alabama can be explained by teleconnection patterns, therefore applicability of the model in more rural environments within these locations woul d offer additional insight.

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93 ENSO Phases Ano t her interesting future aspect of this work could incorporate knowledge of the various phases of ENSO. Dividing the input data sets according to ENSO phase, El Nio La Nia and Neutral, it is speculated t hat model results could be improved by increased awareness of the ENSO phenomenon may offer improved results.

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94 APPENDIX A MODEL PSEUDOCODE maxVal = maximum number of rows in dataset DataLOO = data sortedDataLOO = DataLOO sorted smallest to largest maxDataLOO = maximum number of row in sortedDataLOO runModel.m Read in data. For i = 1:12 %Forecast season For j = 1:9 %Number of Lags trimData.m Trim predictor data sets according to length of predictand data. Results depend on the defined season and lags. Climatology.m Develops climatological forecast (forecast based on hydrology) Creates new dataset by interpolating values for 101 points forecast1 calls SinglePredictorCV.m SinglePredictorCV.m Performs calibration For i = 1: maxVal Leave one out method DataLOO= [] BayesForecast.m (creates exceedance probability) For i = 1:maxDataLoo Define bandwidth Determine probability of f1x using kernel density estimator Define bandwidth Determine probability of f2x using kernel density estimator p1 = probability of exceedance p2 = probability of nonexceedance End EnvelopesUpdated.m (uses climatologyE to extend exceedance p rob to 0 and 1) Create upper envelope Create lower envelope Extrapolate upper env to 0 Extrapolate lower env to 0 Extrapolate upper env to 1 Extrapolate lower env to 1 Interpolate upper and lower env to 100 points at 0.01 increments between 0 and 1 Find th e mean between these two envelopes Plot probability of exceedance End

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95 forecast2 calls SinglePredictorCV.m BayesForecast.m EnvelopesUpdated.m Plot probability of exceedance forecast3 calls SinglePredictorCV.m BayesForecast.m EnvelopesUpdated.m Plot probability of exceedance forecast4 calls SinglePredictorCV.m BayesForecast.m EnvelopesUpdated.m Plot probability of exceedance LEPS1 calls ensembleLEPS.m ensembleLEPS.m Create empirical cdfs of all observations and forecasts for this time step (month) f or i = 1:length(observations) Define this Obs Define iObs Define Po for j = 1:length(thesePred) Define Pf Calculate LEPS score using formula Calc Sbest Calc Sworst End sumS sumSbest sumSworst end totalS = sum(sumS) Use totalS and sumSbest or sumSworst to calc LEPSskillScore LEPS2 calls ensembleLEPS.m LEPS3 calls ensembleLEPS.m LEPS4 calls ensembleLEPS.m Depending on the number of predictors lagLEPS1(j,i) = LEPS1 lagLEPS2(j,i) = LEPS2 lagLEPS3(j,i) = LEPS3 lagLEPS4(j,i) = LEPS4

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96 weightedForecasts.m Ea ch generated forecast(1 4) is sent to this subroutine If forecast(2 4) are empty (only 1 predictor) skip weightedForecasts.m Switch numPred Case 2 = 2 predictors Performs 101 combinations thisWeightedForecast = a(forecasts1) + b(forecasts2) Case 3 = 3 predictors Performs 5027 combinations thisWeightedForecast = a(forecasts1) + b(forecasts2) + c(forecasts3) Case 4 = 4 predictors Performs 167002 combinations thisWeightedForecast = a(forecasts1) + b(forecasts2) + c(forecasts3) + d(forecasts4) For each case the maxWeightedLEPS is set by the initial weights and if the subsequent LEPS scores are greater than the maxWeightedLEPS is replaced with the LEPS score stored as the current LEPS a.k.a the variable weightedLEPS End (loop through lags) End (loop through seasons)

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97 APPENDIX B MODEL CODE There are 8 Matlab m files that comprise the model. The general sequence of these files, in order they are applied, are: runModel.m, trimData.m, Climatology.m, SinglePredictorCV.m, BayesForecast.m, EnvelopesUpdated.m, ensembleLEPS.m and weightedForecasts.m. The runModel.m file is the main file that calls each of the subroutines. This portion of code calculates the LEPS scores using a cross validation method of leave one out. From runModel.m the subr outine trimData.m is called where the data is cropped in such a way that the predictor dataset is longer than the predictand. Next the runModel.m file calls for the subroutine Climatology.m to create a forecast using only historical streamflows. RunModel.m calls SinglePredictorCV.m for each predictor used, which currently allows for up to four. SinglePredictorCV.m create the exceedance probability forecasts for each year by looping through all years of the dataset. SinglePredictorCV.m calls the subroutine B ayesForecast to run the model statistics for a single year data. The forecast is then sent to the subroutine EnvelopesUpdated.m where upper and lower envelopes for the dataset are created. An average of the two envelopes then produces the final exceedance probability forecast, which can be plotted from this subroutine. Once forecasts for all years have been provided. EnsembleLEPS then calculates LEPS scores for each year, which are then summed to produce a total LEPS score for a single predictor. This again is repeated for each predictor. If multiple predictors were used, then runModel.m calls weightedForecast.m. This subroutine steps through various combinations of weights for each of the predictors results of which are then passed to EnsembleLEPS to

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98 determined the LEPS score. Weights are then saved for the highest LEPS score generated. RunModelSVD.m is similar to runModel.m, with the exception that it accounts for differen t input data as produced from a separate SVD analysis. runModel.m clear tic % Read data % Predictors are always assumed to be have a longer history than the % predictand. One exception: When flow is a predictor. %% Predictand data cd( 'PredictandInput') [n,t]=xlsread('S160_Adjusted.xls'); %Predictand historical flow data predictandData = n(:,:); cd('..') %% Predictor data parts of this can be commented out for fewer predictors predictor1Data =[]; predictor2Data =[]; predictor3D ata =[]; predictor4Data =[]; cd('predictorInput') [p,t]=xlsread('Nino12.xls');%Predictor 1 predictor1Data = p(:,:); predictor2Data = predictandData; [p,t]=xlsread('Nino3.xls');%Predictor 3 predictor3Data = p(:,:); [p ,t]=xlsread('Nino4.xls');%Predictor 4 predictor4Data = p(:,:); cd('..') forecasts1=[]; forecasts2=[];

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99 forecasts3=[]; forecasts4=[]; lagLEPS1=[]; lagLEPS2=[]; lagLEPS3=[]; lagLEPS4=[]; lagWeightedLEPS=[]; lagWeightedForecast=nan(9,12,101,size(predicta ndData,1)); lagWeight1=[]; lagWeight2=[]; lagWeight3=[]; lagWeight4=[]; %% Forecast month/season and lags for i = 1:12 % Forecast season for j=1:9 % Lags [years, thisPredictandData, thisPredictor1Data, thisPredictor2Data,... thisPredictor3Data, thisPredictor4Data]= trimData(predictandData,... predictor1Data, predictor2Data, predictor3Data, predictor4Data, i, j); ClimatologyE = Climatology(thisPredictandData); forecasts1 = SinglePredictorCV(thisPredictandData, thisPredictor1Data, ClimatologyE, years); forecasts2 = SinglePredictorCV(thisPredictandData, thisPredictor2Data, ClimatologyE, years); forecasts3 = SinglePredictorCV(thisPredic tandData, thisPredictor3Data, ClimatologyE, years); forecasts4 = SinglePredictorCV(thisPredictandData, thisPredictor4Data, ClimatologyE, years); LEPS1 = ensembleLEPS(thisPredictandData, forecasts1); LEPS2 = ensembleLEPS(thi sPredictandData, forecasts2); LEPS3 = ensembleLEPS(thisPredictandData, forecasts3); LEPS4 = ensembleLEPS(thisPredictandData, forecasts4); lagLEPS1(j,i)=LEPS1; if isempty(LEPS2) else

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100 lagL EPS2(j,i)=LEPS2; end if isempty(LEPS3) else lagLEPS3(j,i)=LEPS3; end if isempty(LEPS4) else lagLEPS4(j,i)=LEPS4; end %% Weighted forecasts weightStep = 0.1; [weightedLEPS, weightedForecast, weight1 weight2 weight3 weight4] =... weightedForecasts(thisPredictandData, forecasts1, forecasts2,... forecasts3, forecasts4, weightStep); if isempty(weightedLEPS) % do nothing else lagWeightedLEPS(j,i) = weightedLEPS; lagWeightedForecast(j,i,:,1:size(weightedForecast,2)) = weightedForecast; lagWeight1(j,i) = weight1; end if isempty(weight2) % do nothing else lagWeight2(j,i) = weight2; end if isempty(weight3) % do nothing else lagWeight3(j,i) = weight3; end if isempty(weight4) % do nothing else lagWeight4(j,i) = weight4; end

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101 end % end loop thru lags end % end loop thru seasons cd('Results') save S160_Adjusted_12_3_4 toc runModelSVD.m clear tic matlabpool open % CJM 5/22/11 added for parfor added to SinglePredictorCV.m % Read data % Predictors are always assumed to be have a longer history than the % predictand. One exception: When flow is a predictor. %% Predictand data cd('predictandInput') [n,t]=xlsread('AlafiaRiveratLithia_02301500.xls'); %Predictand historical flow data predictandData = n(:,:); cd('..') %% Predictor data parts of this can be commented out for fewer predictors predictor1Data =[ ]; predictor2Data =[]; predictor3Data =[]; predictor4Data =[]; predictor1Data = predictandData; cd('predictorInput') mode1 = nc_varget('WY1940SVD.nc','mode1'); mode2 = nc_varget('WY1940SVD.nc','mode2'); mode3 = nc_varget('WY1940SVD.nc','mode3'); % th ese years are stored for each lag and refer to the streamflow to be % PREDICTED svdYears = nc_varget('WY1940SVD.nc','forecastYears'); cd('..') forecasts1=[]; forecasts2=[];

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102 forecasts3=[]; forecasts4=[]; lagLEPS1=[]; lagLEPS2=[]; lagLEPS3=[]; lagLEPS4=[]; lagWeightedLEPS=[]; lagWeightedForecast=nan(9,12,101,size(predictandData,1)); lagWeight1=[]; lagWeight2=[]; lagWeight3=[]; lagWeight4=[]; %% Forecast month/season and lags for i = 1:12 % Forecast season for j=1:9 % Lags [years, thisPredictandData, thisPredictor1Data, thisPredictor2Data,... thisPredictor3Data, thisPredictor4Data]= trimData(predictandData,... predictor1Data, predictor2Data, predictor3Data, predictor4Data, i, j); [years, thisPredictandData, thisPredictor1Data, thisMode1, thisMode2,... thisMode3]= trimDataSVD(years, thisPredictandData, thisPredictor1Data,... mode1, mode2, mode3, svdYears, i, j); ClimatologyE = Climatology(thisPredictandData); forecasts1 = SinglePredictorCV(thisPredictandData, thisPredictor1Data, ClimatologyE, years); forecasts2 = SinglePredictorCV(thisPredictandData, thisMode1, ClimatologyE, years) ; forecasts3 = SinglePredictorCV(thisPredictandData, thisMode2, ClimatologyE, years); forecasts4 = SinglePredictorCV(thisPredictandData, thisMode3, ClimatologyE, years); LEPS1 = ensembleLEPS(thisPredictandData, forecasts1); LEPS2 = ensembleLEPS(thisPredictandData, forecasts2); LEPS3 = ensembleLEPS(thisPredictandData, forecasts3); LEPS4 = ensembleLEPS(thisPredictandData, forecasts4);

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103 lagLEPS1(j,i)=LEPS1; if isempty(LEP S2) else lagLEPS2(j,i)=LEPS2; end if isempty(LEPS3) else lagLEPS3(j,i)=LEPS3; end if isempty(LEPS4) else lagLEPS4(j,i)=LEPS4; end %% Weighted forecasts weightStep = 0.1; [weightedLEPS, weightedForecast, weight1 weight2 weight3 weight4] =... weightedForecasts(thisPredictandData, forecasts1, forecasts2,... forecasts3, f orecasts4, weightStep); if isempty(weightedLEPS) % do nothing else lagWeightedLEPS(j,i) = weightedLEPS; lagWeightedForecast(j,i,:,1:size(weightedForecast,2)) = weightedForecast; lagWe ight1(j,i) = weight1; end if isempty(weight2) % do nothing else lagWeight2(j,i) = weight2; end if isempty(weight3) % do nothing else lagWeight 3(j,i) = weight3; end

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1 04 if isempty(weight4) % do nothing else lagWeight4(j,i) = weight4; end end % end loop thru lags end % end loop thru seasons matlabpool close toc trimData.m function [years y1 x1 x2 x3 x4] = trimData(predictandData, predictor1Data,... predictor2Data, predictor3Data, predictor4Data, forecastSeason, lag) % Trimming data is done in 4 steps: % 1. Find first and last year of the predictand entire d ataset, then account % for NaN at beginning or end of the season of interest. % 2. Define predictor season based on the forecast season and lag. % 3. Modify predictand and predictor years for the case where a lag is not % available (e.g. when flow i s one of the predictors) % 4. Modify predictand and predictor years to account for NaN at start or end % of predictor datasets %% Get first and last years of the predictand for this season firstPredictandYear = min(predictandData(:,1)); lastPredictandYear = max(predictandData(:,1)); thisPredictand = predictandData(:, forecastSeason+1); years = predictandData(:,1); % Check fist and last value to see if they are NaN. This assumes that the % record is complete (no missing values in the middle of the time series) if isnan(thisPredictand(1)) thisPredictand(1) =[]; firstPredictandYear = firstPredictandYear+1; end if isnan(thisPredictand(end)) thisPredictand(end) =[]; lastPredictandYear = lastPredictandYear 1; end

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105 %% Dete rmine correct years and season for the predictor based on the predictand predSeason = forecastSeason lag; if predSeason < 3 predSeason = predSeason +10; firstPredYear= firstPredictandYear 1; lastPredYear= lastPredictandYear 1; else pred Season = predSeason 2; firstPredYear= firstPredictandYear; lastPredYear= lastPredictandYear; end %% Modify years for predictors and predictand if years are not available in % the predictor. Should only happen when flow is the predictor minYear1 = min(predictor1Data(:,1)); if isempty(predictor2Data) minYear2=[]; else minYear2 = min(predictor2Data(:,1)); end if isempty(predictor3Data) minYear3=[]; else minYear3 = min(predictor3Data(:,1)); end if isempty(predictor4Data) mi nYear4=[]; else minYear4 = min(predictor4Data(:,1)); end minVals =[minYear1 minYear2 minYear3 minYear4]; minYear = max(minVals); if minYear>firstPredYear % Lag not available. minYear defines the first year predictor is % available. Need to cut first year of predictand, since there is no % predictor available. Also, need to drop last predictor year, since % there is nothing to be predicted................ firstPredYear = minYear; firstPredictandYear = firstPredictandYear+1 ; iFirstYear = find(predictandData(:,1) == firstPredictandYear);

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106 iLastYear = find(predictandData(:,1) == lastPredictandYear); thisPredictand = predictandData(iFirstYear:iLastYear, forecastSeason+1); years = predictandData(iFirstYear:iLastYe ar,1); end iFirstPredYear = find(predictor1Data(:,1)==firstPredYear); iLastPredYear = find(predictor1Data(:,1)==lastPredYear); thisPred1 = predictor1Data(iFirstPredYear:iLastPredYear, predSeason+1); if ~isempty(predictor2Data) iFirstPredYear = fi nd(predictor2Data(:,1)==firstPredYear); iLastPredYear = find(predictor2Data(:,1)==lastPredYear); thisPred2 = predictor2Data(iFirstPredYear:iLastPredYear, predSeason+1); end if ~isempty(predictor3Data) iFirstPredYear = find(predictor3Data(:,1) ==firstPredYear); iLastPredYear = find(predictor3Data(:,1)==lastPredYear); thisPred3 = predictor3Data(iFirstPredYear:iLastPredYear, predSeason+1); end if ~isempty(predictor4Data) iFirstPredYear = find(predictor4Data(:,1)==firstPredYear); iLastPredYear = find(predictor4Data(:,1)==lastPredYear); thisPred4 = predictor4Data(iFirstPredYear:iLastPredYear, predSeason+1); end %% Modify years for predictors and predictand if year at the beginning has % an NaN the predictor. Should only hap pen when flow is the predictor if isnan(thisPred1(1)) minYear1 = firstPredYear+1; end if exist('thisPred2','var') if isnan(thisPred2(1)) minYear2 = firstPredYear+1; end end if exist('thisPred3','var') if isnan(thisPred3(1)) minYear3 = firstPredYear+1; end end

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107 if exist('thisPred4','var') if isnan(thisPred4(1)) minYear4 = firstPredYear+1; end end minVals =[minYear1 minYear2 minYear3 minYear4]; minYear = max(minVals); if minYear>firstPredYear % Lag not available. minYear defines the first year predictor is % available. Need to cut first year of predictand, since there is no % predictor available. Also, need to drop last predictor year, since % there is nothing to be predicted ................ firstPredYear = minYear; firstPredictandYear = firstPredictandYear+1; iFirstYear = find(predictandData(:,1) == firstPredictandYear); iLastYear = find(predictandData(:,1) == lastPredictandYear); thisPredictand = pre dictandData(iFirstYear:iLastYear, forecastSeason+1); years = predictandData(iFirstYear:iLastYear,1); iFirstPredYear = find(predictor1Data(:,1)==firstPredYear); iLastPredYear = find(predictor1Data(:,1)==lastPredYear); thisPred1 = predic tor1Data(iFirstPredYear:iLastPredYear, predSeason+1); if ~isempty(predictor2Data) iFirstPredYear = find(predictor2Data(:,1)==firstPredYear); iLastPredYear = find(predictor2Data(:,1)==lastPredYear); thisPred2 = predictor2Dat a(iFirstPredYear:iLastPredYear, predSeason+1); end if ~isempty(predictor3Data) iFirstPredYear = find(predictor3Data(:,1)==firstPredYear); iLastPredYear = find(predictor3Data(:,1)==lastPredYear); thisPred3 = predictor3Data(iFirstPredYear:iLastPredYear, predSeason+1); end if ~isempty(predictor4Data) iFirstPredYear = find(predictor4Data(:,1)==firstPredYear); iLastPredYear = find(predictor4Data(:,1)==lastPredYear); thisPred 4 = predictor3Data(iFirstPredYear:iLastPredYear, predSeason+1); end

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108 end y1 = thisPredictand; x1 = thisPred1; if isempty(predictor2Data) x2=[]; else x2 = thisPred2; end if isempty(predictor3Data) x3=[]; else x3 = thisPred3; end if isempty(predictor4Data) x4=[]; else x4 = thisPred4; end trimdataSVD.m function [years, predictandData, predictor1Data, thisMode1, thisMode2, thisMode3]... = trimDataSVD(years, predictandData, predictor1Data, mode1, mode2, mode3,... svdYears, forecastSeason, lag) firstPredictandYear = min(years); lastPredictandYear = max(years); thisSVDyears = squeeze(svdYears(forecastSeason,lag,:)); iYears = find(thisSVDyears >= firstPredictandYear and ... thisSVDyears <= lastPredictan dYear); thisMode1 = squeeze(mode1(forecastSeason,lag,iYears)); thisMode2 = squeeze(mode2(forecastSeason,lag,iYears)); thisMode3 = squeeze(mode3(forecastSeason,lag,iYears)); firstSVDyear = min(thisSVDyears); if firstSVDyear > firstPredictandYear

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109 iYears= find(years < firstSVDyear); years(iYears)=[]; predictandData(iYears)=[]; predictor1Data(iYears)=[]; end Climatology.m function [ClimatologyE]= Climatology (data) %% Climatology % Prior probabilities (Climatology) % C JM 9/9/10 Removed calculation of ClimatologyNE data = sortrows(data, 1); ClimatologyE = []; for i = 1:length(data); rank = i; % CM 9/8/10 changed to calculate from highest to lowest more straight forward EProb = (rank)/(le ngth(data)+1); ClimatologyE = [ClimatologyE; EProb]; end ClimatologyE = [ClimatologyE data(:,1)]; %combines flow data with probabilties %Extrapolate to prob = 1 at flow = 0 ClimatologyE=[ClimatologyE 1,0]; %Extrapolate to prob = 0 ClimatologyE=[0,ClimatologyE(1,2) ClimatologyE]; % Interpolate to 101 evenly spaced points dx = 0:0.01:1; ClimatologyE = interp1(ClimatologyE(:,1),ClimatologyE(:,2),dx); dx=dx'; ClimatologyE=ClimatologyE'; ClimatologyE=[dx ClimatologyE]; Singl ePredictorCV.m function [forecasts] = SinglePredictorCV(yy, xx, ClimatologyE, n)

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110 forecasts=[]; % If the predictor does not exist, exit if isempty(xx) return end data = [yy, xx]; maxVal = length(data); for i=1:maxVal year = n(i); DataLOO = data; % Each row of data will be removed sequentially for cross validation predictor = data(i,2); % Save the predictor and the 'observed' value that will be left out observation = data(i,1); %Historical Streamflow (forecast p eriod) DataLOO(i,:)=[]; % Remove this row (Leave One Out, LOO) % Sorted from smallest to largest flow sortedDataLOO = sortrows(DataLOO,1); maxDataLOO = length(sortedDataLOO); % I removed DataLOO since it is not u sed in BayesForecast.m CJM 9/8/10 [forecastE] = BayesForecast(predictor, sortedDataLOO, maxDataLOO); % Removed ClimatologyNE since it is not used here can get it from ClimatologyE at the point it is needed [E_FORECAST] = EnvelopesUpdated (forecastE, ClimatologyE,year); forecasts = [forecasts, E_FORECAST(:,2)]; end BayesForcast.m function [forecastE]= BayesForecast (predictor, sortedDataLOO, maxDataLOO) % Changed preallocation from zeros to NaNs CJM 9/8/10 forecastE = NaN(maxDataLOO 7,2);% Preallocate k=1; for i=1:maxDataLOO; %% Predictor Exceedance Probabilies (Q >= Qi)

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111 flowGreater = sortedDataLOO(i:maxDataLOO,:); predictorGreater = flowGreater(:,2);%Predictor values in 2nd column % Define ba ndwidth pct25 = prctile(predictorGreater,25); pct75 = prctile(predictorGreater,75); A = min(std(predictorGreater), ((pct75 pct25)/1.34)); h = 0.9*A*length(predictorGreater)^( 0.2);%Bandwidth f1x = ksdensity(predictorGreater, 'width', h); %defines the density at 100 evenly spaced points (values not actually used) f1xAtPredictor = ksdensity(predictorGreater, predictor, 'width', h); %defines probability at the predictor value left out %% Predict or Non exceedance Probabilies (Q <= Qi) flowLess = sortedDataLOO(1:i,:); predictorLess = flowLess(:,2); % Define bandwidth pct25 = prctile(predictorLess,25); pct75 = prctile(predictorLess,75); A = min( std(predictorLess), ((pct75 pct25)/1.34)); h = 0.9*A*length(predictorLess)^( 0.2);%Bandwidth f2x = ksdensity(predictorLess,'width', h); %defines the density at 100 evenly spaced points (values not actually used) f2x AtPredictor = ksdensity(predictorLess, predictor, 'width', h); %defines probability at the predictor value left out %% p1 = length(predictorGreater)/(maxDataLOO+1); %probability of exceedence of Q >=Qi p2 = length(predictorLess)/(maxDataLO O+1); %probability of non exceedence Q<=Qi if 4<=i and i<=maxDataLOO 3; forecastE(k,1) = p1*f1xAtPredictor/(p1*f1xAtPredictor+p2*f2xAtPredictor); %forecast is a vector to hold (exceedance probability, sf) forecastE(k,2) = sorted DataLOO(i,1); % When one of the terms in the denominator in the above equation is % near zero, forecastE = 1, and the code later blows up when creating % the upper envelope in CMEnvelopes.m. if forecastE(k,1)==1 forecastE(k,1)= forecastE(k,1) (k*0.000000000001); end

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112 if forecastE(k,1)==0 forecastE(k,1)= forecastE(k,1)+(k*0.000000000001); end nan_locations = find(isnan(forecastE)); forec astE(nan_locations) = k*0.000000000001; k=k+1; end end EnvelopesUpdated.m function [E_FORECAST]= EnvelopesUpdated(forecastE, ClimatologyE,year) %% Upper Envelope DforecastE=sortrows(forecastE, 2);%sorts vector forecastE in descending order to comprise UPPER envelope, direction=( decending/+accending), column=2 r=1; %initializes row at 1 rr=1; upperenv = []; %creates a vector to contain plotting points of only the upperenv for r = 1:siz e(DforecastE); if r==1, %for the first row set the 2 vectors, upperenv and PPyDescend equal upperenv(rr,:) = DforecastE(r,:); prevVal = DforecastE(r,:); % Save this value as prevVal since just looking at r 1 will not always w ork rr=rr+1; else if DforecastE(r,1)> prevVal(1); %include the next lowest y data point if its x is greater upperenv (rr,:)= DforecastE(r,:); prevprob = upperenv(rr 1,1); if upperenv(rr,1)== prevprob; upperenv (rr,:)= [upperenv(rr,1)+ 0.000001, upperenv(rr,2)]; end prevQ = upperenv(rr 1,2); if upperenv(rr,2)== prevQ; upperenv (rr,:)= [upperenv(rr,1), upperenv(rr,2)+ 0.000001]; end prevVal = DforecastE(r,:); rr=rr+1; continue; end

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113 end end %% Lower Envelope AforecastE=sortrows(forecastE,2); %sorts vector forecastE in ascending order to comprise LOWER envelope, direction=( decending/+accending), column=2 r=1; %initializes row at 1 rr=1; lowerenv = []; %creates a vector to contain plotting points of only the lowerenv for r = 1:size(AforecastE, 1); if r==1, %for the first row set the 2 ve ctors, lowerenv and PPyAscend equal lowerenv(rr,:) = AforecastE(r,:); prevVal = AforecastE(r,:); rr=rr+1; else if AforecastE(r,1)< prevVal(1); %include the next highest y data point if its x is greater lowerenv (r r,:)= AforecastE(r,:); prevVal = AforecastE(r,:); rr=rr+1; continue; end end end %% Extrapolate upper envelope at low probability lowestUpper = upperenv(1,1); %Find climatological Q value at this point(lowestUpper) by interpolating % interp1(x values, y values, x value(s) to find from interpolation) climQ = interp1(ClimatologyE(:,1),ClimatologyE(:,2),lowestUpper); % If the Q with the lowest exceedance prob is less than climatology, extend % horizontally to excee dance of zero if upperenv(1,2) < climQ upperenv = [0,upperenv(1,2) upperenv]; % If lowest is greater than climatology, extend horizontally to the % climatology curve and then follow it else

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114 % The 'find' command returns the position (r ows) within ClimatologyE that match the argument iUpper = find(ClimatologyE(:,2) >= upperenv(1,2)); upperenv = [ClimatologyE(iUpper,:) upperenv]; end %% Extrapolate lower envelope at low probability (done the same as for upper envelope) lowerenv=sortrows(lowerenv, 2); lowestLower = lowerenv(1,1); %Find climatological Q value at this point climQ = interp1(ClimatologyE(:,1),ClimatologyE(:,2),lowestLower); % If the Q with the lowest exceedance prob is less than climatology, extend % horizontally to zero if lowerenv(1,2) < climQ lowerenv = [0,lowerenv(1,2) lowerenv]; % If lowest is greater than climatology, entend horizontally to the % climatology curve and then follows it else iUpper = find(ClimatologyE(:,2) >= l owerenv(1,2)); lowerenv = [ClimatologyE(iUpper,:) lowerenv]; end %% Extrapolate Upper Envelope at high probability % Extend to flow of zero at probability of 1 upperenv = [upperenv 1,0]; %% Extrapolate Lower Envelope at high probab ility % Extend vertically down to Q = 0 and same probability % NOTE! the addition of 0.000001 is done so the curve can later be % interpolated using interp1 (does not accept x values that are the same) lowerenv = [lowerenv 1,0]; %% Interpolate all dx = 0:0.01:1; upperenv = interp1(upperenv(:,1),upperenv(:,2),dx); lowerenv = interp1(lowerenv(:,1),lowerenv(:,2),dx); %ClimatologyE = interp1(ClimatologyE(:,1),ClimatologyE(:,2),dx); % CJM

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115 %12/15/10 This is now done in Climatology.m dx=dx'; upperenv=upperenv'; lowerenv=lowerenv'; %ClimatologyE=ClimatologyE';% CJM 12/15/10 This is now done in Climatology.m upperenv=[dx upperenv]; lowerenv=[dx lowerenv]; %ClimatologyE=[dx ClimatologyE]; % CJM 12/15/10 This is now done in Climatology.m %% Calculate exceedance forecast as the mean of the upper and lower envelopes E_FORECAST=(upperenv(:,2) + lowerenv(:,2))/2; E_FORECAST=[dx E_FORECAST]; % % Plots a single prob exeed. graph for every year in the time series % % Plot upper and lower envel opes, avg probability of exceedance, and climatology % figure('Name','Probabilities of Exceedance','NumberTitle','off'); % %Added forecastE points to the plot % plot(upperenv(:,1),upperenv(:,2),':',E_FORECAST(:,1),E_FORECAST(:,2),' ', lowerenv(:,1), ... % lowerenv(:,2),':',ClimatologyE(:,1), ClimatologyE(:,2),' -', forecastE(:,1), forecastE(:,2),'o'); % axis([0 1 0 (upperenv(1,2)+100)]); % xlabel('Probabilities, %'); % ylabel('Streamflows, MGD'); % title(int2str(year)); % legend('Upper Envelope','Exceedance Probability', 'Lower Envelope', 'Climatology'); ensembleLEPS.m function [LEPSskillScore] = ensembleLEPS(observations, predictions) LEPSskillScore=[]; % If there was not a forecast, exit if isempty(predictions) return end pr edictions=predictions'; % These are all of the forecasts for this time step (month) for all years % essentially, this is the 'climatology' of the forecasts temp=reshape(predictions, size(predictions,1)*size(predictions,2),1);

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116 % create empirical cdfs of all observations and forecasts for this % time step (month) [fobs,xobs] =ecdf(observations); [fpred,xpred] =ecdf(temp); for i=1:length(observations) % Loop thru years thisObs = observations(i); iObs = find(xobs==thisObs); Po = fobs(iObs); % We only need a single value of Po, but I have found occassions where % there were 2 of the same values in xobs. So I used the mean Po % value. if length(Po)>1 Po=mean(Po); end thesePred = predictions(i,:); fo r j = 1:length(thesePred) thisPred=thesePred(j); iPred = find(xpred==thisPred); Pf = fpred(iPred); if length(Pf)>1 Pf=mean(Pf); end % Calculate the LEPS score S(j)= 3*(1 abs(Pf Po)+Pf^2 Pf+Po^2 Po) 1; % Sbest and Sworst are for later calculating the skill score. Which is % used will depend on the sign of the sum of S for all years Sbest(j) = 3*(1 abs(Po Po)+Po^2 Po+Po^2 Po) 1; if Po >=0.5 Sworst(j) = 3*(1 abs(0 Po)+0^2 0+Po^2 Po) 1; else Sworst(j) = 3*(1 abs(1 Po)+1^2 1+Po^2 Po) 1; end end sumS(i)=sum(S); sumSbest(i)=sum(Sbest);

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117 sumSworst(i)=sum(Sworst); end totalS=sum(sumS); if totalS >0 LEPSskillScore = (totalS*100)/sum(sumSbest); else LEPSskillScore = ( 1*totalS*100)/sum(sumSworst); end weightedForecasts.m function [maxWeightedLEPS, maxWeightedForecast, maxWeight1 maxWeight2... maxWeight3 maxWeight4] = weightedForecasts(thisPredictandData,... forecasts1, forecasts2, forecasts3, forecasts4, step) if isempty(forecasts2) andand isempty(forecasts3) andand isempty(forecasts4) % No weighting can be done with a single predictor maxWeightedLEPS=[]; maxWeightedForecast=[]; maxWeight1=[]; maxWeight2=[]; maxWeight3=[]; maxWeight4=[]; return elseif isempty(forecasts3) andand isempty(forecasts4) numPred = 2; maxWeight3=[]; maxWeight4=[]; elseif isempty(forecasts4) numPred = 3; maxWeight4=[]; else numPred = 4; end switch numPred case 2 % Two predictors i=1;

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118 for a = 1: step:0 b = 1 a; thisWeightedForecast = a* forecasts1 + b* forecasts2; weightedLEPS=ensembleLEPS(thisPredictandData, thisWeightedForecast); if i ==1 maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeig htedForecast; maxWeight1 = a; maxWeight2 = b; else thisLEPS = weightedLEPS; if thisLEPS > maxWeightedLEPS maxWeightedLEPS = weightedLEPS; ma xWeightedForecast = thisWeightedForecast; maxWeight1 = a; maxWeight2 = b; end end i=i+1; end case 3 % Three predictors i=1 ; for a = 1: step:0 x = 1 a; for b = x: step:0 c = 1 a b; thisWeightedForecast = a* forecasts1 + b* forecasts2 + c* forecasts3; weightedLEPS=ensembleLEPS(thisPredictandData, thisWeightedForecast); if i ==1 maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeightedForecast; maxWeight 1 = a; maxWeight2 = b; maxWeight3 = c; else thisLEPS = weightedLEPS;

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119 if thisLEPS > maxWeightedLEPS maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeightedForecast; maxWeight1 = a; maxWeight2 = b; maxWeight3 = c; end end i=i+1; end end case 4 % Four predictors i=1; for a = 1: step:0 x = 1 a; for b = x: step:0 y = 1 a b; for c = y: step:0 d = 1 a b c; thisWeightedForecast = a* forecasts1 + b* forecasts2 + c* forecasts3 + d* forecasts4; weightedLEPS=ensembleLEPS(thisPredictandData, thisWeightedForecast); if i ==1 maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeightedForecast; maxWeight1 = a; maxWeight2 = b; maxWe ight3 = c; maxWeight4 = d; else thisLEPS = weightedLEPS; if thisLEPS > maxWeightedLEPS maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeightedForecast; maxWeight1 = a; maxWeight2 = b; maxWeight3 = c; maxWeight4 = d;

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120 end end i=i+1; end end end end % end switch

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121 APPENDIX C STREAMFLOW PROBABILI TY OF EXCEEDANCE PLO TS These streamflow probability of exceedance plots, including cl imatology and upper and lower envelops, for (a.) Alafia at Bell Shoals for each year from 1974 to 2007, (b.) Hillsborough River at Morris Bridge for each year from 1972 to 2007 and (c.) S160 Adjusted for each year from 1974 to 2001. (a.) Alafia at Bell Sho als for each year from 1974 to 2007

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127 (b.) Hillsborough River at Morris Bridge for each year from 1972 to 2007

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134 (c.) S160 Adjusted for each year from 1974 to 2001

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139 LIST OF REFERENCES Nino on U.S. landfalling hurricanes,revisited. Bulletin of the American Meteorological Society 79 2477 2482. Bradley, R. S., Diaz, H. F., Kiladis, G. N., & Eischeid, J. K. (1987). ENSO Signal in Continental Temperature and Precipitation Records. Nature 327 497 501. Brenner, I. S. (2004). The Relationship between Meteorological Parameters and Daily Summer Rainf all Amount and Coverage in West Central Florida. Weather and Forecasting 19 286 300. Bretherton, C. S., Smith, C., & Wallace, J.M. (1992). An Intercomparison of Methods for Finding Coupled Patterns in Climate Data. Journal of Climate 5 541 560. Casey, T. (1995). Optimal Linear Combination of Seasonal Forecasts. Australian Meteorological Magazine 44 219 224. Cayan, D. R., Redmond, K. T., & Laurence, G. R. (1999). ENSO and Hydrologic Extremes in the Western United States. Journal of Climate 12 2881 2893. Cherry, S. (1997). Some Comments on Singular Value Decomposition Analysis. Journal of Climate 10 1759 1761. doi:10.1175/1520 0442(1997)010<1759:SCOSVD>2.0.CO;2 Chiew, F., & Siriwardena, L. (2005). NSFM Non parametric Seasonal Forecast Model : User Guide. Retrieved from http://www.toolkit.net.au/Tools/NSFM Clarke, A. J. (2008). An Introduction to the Dynamics of El Nino and the Southern Oscillation London, UK: Elsevier. Retrieved from http://books.google.com/books?id=VeLCizqfzIoC&pg=PA19&lpg =PA19&dq=dese r+and+wallace+1990&source=bl&ots= vq_vjABXS&sig=Ujhucuj86I7ja5UM3XrjxhsyYoI&hl=en&sa=X&ei=YewKUO6IA8 O 2gWZmZgd&ved=0CGUQ6AEwBQ#v=onepage&q=deser%20and%20wallace%2 01990&f=false Climate Services and Monitoring Division. (n.d.). Nino Regions. NO AA/National Climatic Data Center Retrieved July 4, 2011, from http://www.ncdc.noaa.gov/teleconnections/enso/indicators/sst.php#nino regions Coley, D. M., & Waylen, P. (2006). Forecasting Dry Season Streamflow on the Peace River at Arcadia, Florida, USA. Journal of the American Water Resources Association 42 (4), 851 862.

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140 Douglas, A., & Englehart, P. (1981). On a Statistical Relationship between Autumn Rainfall in the Central Equatorial Pacific and Subsequent Winter Precipitation in Florida. Monthly Weather Review 109 2377 2382. doi:1520 0493(1981)109<2377:OASRBA>2.0.CO;2 Elsner, J., & Schmertmann, C. P. (1994). Assissing Forecast Skill through Cross Validation. Weather and Forecasting 9 (4), 619 624. Florida Department of Environmental Protection (FDEP). (2010). Annual Report on Regional Water Supply Planning: Sustaining Out Water Resources. Retrieved from http://www.dep.state.fl.us/water/waterpolicy/docs/sustaining our water resources.pdf Florida Department of Environmental Protection (FDEP). (2 to Protect. Retrieved June 4, 2012, from http://www.protectingourwater.org/watersheds/map/tampa_bay_tributaries/alafia/ Gershunov, A., & Barnett, T. P. (1998). ENSO Influence on Intraseasonal Extreme Rainfall and Temperature Fr equencies in the Contiguous United States: Observations and Model Results. Journal of Climate 11 1575 1586. Golembesky, K., Sankarasubramanian, A., & Devineni, N. (2009). Improved Drought Management of Fall Lake Reservoir: Role of Multimodel Streamflo w Forecasts in Setting Up Restrictions. Water Resources Planning and Management 135 (3), 188 197. doi:10.1061/(ASCE)0733 Governance. (2006). Tampa Bay Water Retrieved March 6, 2009, from http://www.tampabaywater.org/about/governance.aspx Grantz, K., Raj agopalan, B., Clark, M., & Zagona, E. (2005). A Technique for Incorporating Large Scale Climate Information in Basin Scale Ensemble Streamflow Forecasts. Water Resources Research 41 (W10410). doi:10.1029/2004WR003467 Gray, W. M. (1984). Atlantic Seasonal Hurricane Frequency Part Ii: Forecasting Its Variability. Monthly Weather Review 112 1669 1683. Helsel, D., & Hirsch, R. (2002). Statistical Methods in Water Resources In Techniques of Water Resources Investigations of the United States Geological Surve y: Book 4 Hydrologic Analysis and Interprestation (Chapter A3) Retrieved from http://water.usgs.gov/pubs/twri/twri4a3/ International Research Institute for Climate and Society (IRI). (2012). NOAA NCEP NCAR CDAS 1 Monthly Intrinsic MSL Pressure: Pressure Data. Retrieved from http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCEP NCAR/.CDAS 1/.MONTHLY/.Intrinsic/.MSL/.pressure/

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141 Kahya, E., & Dracup, J. A. (1993). U.S. Streamflow Patterns in Relation to the El Nino/Southern Oscillation. Water Resources Research 29 (8), 2491 2503. Kaplan, A., Cane, M., Kushnir, Y., Clement, A., Blumenthal, M., & Rajagopalan, B. (1998). Analyses of Global Sea Surface Temperature 1856 1991. Journal of Geophysical Research 103 (18), 567 589. Kardioglu, M., Tulunay, Y., & Borham, Y. (1999). Variability of Turkish Precipitation Compared to El Nino Events. Geophysical Research Letters 26 (11), 1597 1600. Kennedy, A. M., Garen, D. C., & Koch, R. W. (2009). The association between climate teleconnection indices and Upper Klamath seasonal streamflow: Trans Nino Index. Hydrological Processes 23 973 984. doi:10.1002/hyp.7200 Kock, R.W., & Fisher, A.R. (2000). Effects of Inter annual and Decadal scale Climate Variability on Winter and Spring Streamflow in western Oregon and Washington. Pro ceedings of the Western Snow Conference (pp. 1 11). Port Angeles, Washington. Martinez, C. J., Risko, S. L., Graham, W. D., & Jones, J. W. (2009). Analysis of Large Scale Climate Datasets and Hydrologic Variables in the Tampa Bay Region: Selection of Pred ictor Climate Indices (Report presented during the Tampa Bay Water project meeting held by Chris Martinez (University of Florida)). Department of Agricultural and Biologial Engineering, University of Florida. http://ufdc.ufl.edu/AA00012272/ McCabe, G. J., & Dettinger, M. D. (2002). Primary Modes and Predictability of Year to Year Snowpack Variations in the Western United States from Teleconnections with Pacific Ocean Climate. Journal of Hydrometeorology 3 13 25. Michaelsen, J. (1987). Cross Validation i n Statistical Climate Forecast Models. Journal of Climate and Applied Meteorology 26 (11), 1589 1600. National Oceanic and Atmospheric Association (NOAA). (2008a). Sea Surface Temperature Datasets. National Climatic Data Center Web site Retrieved Novembe r 20, 2008, from http://lwf.ncdc.noaa.gov/oa/climate/research/sst/sst.php National Oceanic and Atmospheric Association (NOAA). (2008b). NCEP/NCAR Reanalysis Monthly Means and Other Derived Variables. Earth System Research Laboratory Website Retrieved Nov ember 20, 2008, from http://www.cdc.noaa.gov/data/gridded/data.ncep.reanalysis.derived.html Opitz Stapleton, S., Gangopadhyay, S., & Rajagopalan, B. (2007). Generating Streamflow Forecasts for the Yakima River Basin Using Large Scale Climate Predictors. J ournal of Hydrology 341 131 143.

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142 Owosina, A. (1992). Methods for assessing the space and time variability of groundwater data. Utah State University, Logan, Utah. Piechota, T. C., Chiew, F. H. S., & Dracup, J. A. (1998). Seasonal streamflow forecasting in eastern Australia and the El Nino Southern Oscillation. Water Resources Research 34 (11), 3035 3044. Piechota, T. C., Chiew, F. H. S., Dracup, J. A., & McMahon, T. A. (2001). Development of Exceedance Probability Streamflow Forecast. Journal of Hydrolo gic Engineering 6 (1), 20 28. Climate Model Simulations and Long Range Forecasts. Journal of Climate 9 34 53. Rajagopalan, B., Grantz, K., Regonda, S., Clark, M., & Zagona, E. (2005). Ensemble Streamflow Forecasting: Methods and Applications in Aswathanarayana, U. (Ed.). Advances in Water Science Methodologies 97 113. Rasmusson, E. M., & Carpenter, T. H. (1982). Variations in Tropical Sea Surface Temperature and Su rface Wind Fields Associated with the Southern Oscillation/El Nino. Monthly Weather Review 110 354 384. Ropelewski, C., & Halpert, M. (1986). North American Precipitation and Temperature Patterns Associated with the El Nino Southern Oscillation (ENSO). Monthly Weather Review 114 2352 2362. doi:10.1175/1520 0493(1986)114<2352:NAPATP>2.0.CO;2 Rosenzweig, C. R. (2008). Climate Variability and the Global Harvest New York: Oxford University Press. Ruiz, J. E., Cordery, I., & Sharma, A. (2006). Impact of Mid Pacific Ocean Thermocline on the Prediction of Australian Rainfall. Journal of Hydrology 317 104 122. doi:10.1016/j.jhydrol.2005.05.012 Schmidt, N., Lipp, E. K., Rose, J. B., & Luther, M. E. (2001). ENSO Influences on Seasonal Rainfall and River Dis charge in Florida. Journal of Climate 14 615 628. Silverman, B. W. (1986). Density estimation for statistics and data analysis (Chapter 2) New York: Chapman and Hall/CRC. Retrieved from http://books.google.com/books?hl=en&lr=&id=e xsrjsL7WkC&oi=fnd&pg= PR9&dq=Silverman,B.+W.,++Density+Estimation+for+S tatistics+and+Data+Analysi+1986&ots=ivMtru3FVm&sig=4bS7d1nwUjUsu DUyzjvZccZizw#v=onepage&q=Silverman%2CB.%20W.%2C%20%20Density%2 0Estimation%20for%20Statistics%20and%20Data%20Analysi%201986&f=false

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143 Slack, J. R., Lumb, A. M., & Landwehr, J. M. (1994). Hydro Climatic Data Network (HCDN): A USGS Streamflow Data Set for the U.S. for the Study of Climate Fluctuations. Retrieved from http://pubs.usgs.gov/wri/wri934076/1st_page.html Smith, T. M., & Reynolds, R. W. ( 2004). Improved Extended Reconstruction of SST (1854 1997). Journal of Climate 17 2466 2477. Smith, T. M., Reynolds, R. W., Peterson, T. C., & Lawrimore, J. (2008). Improvements Ocean Surface Temperature Analysis (1880 2 006). Journal of Climate 21 2283 2296. Statistics Glossary: 2004 2009 (n.d.). Sveinsson, O. G. B., Lall, U., Gaudet, J., Kushnir, Y., Zebiak, S., & Fortin, V. (2008). Analysis of Climate States and Atmospheric Circulation Patterns that Influence Quebe c Spring Streamflows. Journal of Hydrologic Engineering 13 (6), 411 425. Tampa Bay Water. (2010). Supply Management. Retrieved from http://www.tampabaywater.org/supplies/ The Royal Netherlands Meteorological Institute (KNMI). (2009). Climate Indices. Climate Explorer Retrieved from http://climexp.knmi.nl/selectindex.cgi?someone@somewhere Tomasko, D. A., Corbett, C. A., Greening, H. S., & Raulerson, G. E. (2005). Spatial and Temporal Variation in Seagrass Coverage in Southwest Florida: Assessing the R elative Effects of Anthropogenic Nutrient Load Reductions and Rainfall in Four Contiguous Estuaries. Marine Pollution Bulletin 50 797 805. Tootle, G. A., & Piechota, T. C. (2006). Relationships between Pacific and Atlantic ocean sea surface temperatures and U.S. streamflow variability. Water Resources Research 42 (W07411). doi:10.1029/2005WR004184 Tootle, G., & Piechota, T. (2004). Suwannee River Long Rang Streamflow Forecasts Based on Seasonal Climate Predictors. Journal of the American Water Resources Association 40 (2), 523 532. Trenberth, K. E. (1997). The Definition of El Nino. Bulletin of the American Meteorological Society 78 (12), 2771 2777. Trendberth, K. E., & Stepaniak, D. P. (2001). Letters Indices of El Nino Evolution. Journal of Climate 14 1697 1701. United States Geological Survey (USGS). (2006). Hydro Climatic Data Network Retrieved from http://pubs.usgs.gov/of/1992/ofr92 129/

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144 United States Geological Survey (USGS). (2011). Water Data for the Nation. National Water Information Sys tem Retrieved August 20, 2008, from http://waterdata.usgs.gov/nwis van Beynen, P. E., Asmerom, Y., Polyak, V., & Soto, L. (2004). Variable intensity of teleconnections during the late Holocene in subtropical North America from an isotopic study of speleo them from Florida. Geophysical Research Letters 34 doi:10.1029/2007GL031046 Wallace, J. M., & Gutzler, D. S. (n.d.). Teleconnections in the Geopotential Height Field during the Northern Hemisphere Winter. Monthly Weather Review 109 784 812. Wang, B. (1995). Interdecadal Changes in El Nino Onset in the Last Four Decades. Journal of Climate 8 267 284. Ward, M., & Folland, C. (1991). Prediction of Seasonal Rainfall in the North Nordeste of Brazil using Eigenvectors of Sea surface Temperature. Internat ional Journal of Climatology 11 (7), 711 743. doi:10.1002/joc.3370110703 Wolter, K., & Timlin, M. S. (1993). Monitoring ENSO in COADS with a seasonally adjusted principal component index. Proceedings of the 17th Climate Diagnostics Workshop (pp. 52 57). P resented at the NOAA/NMC/CAC,NSSL Oklahoma Clim Survey, Norman, OK: CIMMS and the School of Meteorology, University of Oklahoma. Wolter, K., & Timlin, M. S. (1998). Measuring the strength of ENSO events how does 1997/98 rank? Weather 53 315 324. Yin, Z. (1994). Moisture Condition in the South Eastern USA and Teleconnection Patterns. International Journal of Climatology 14 (9), 947 967. doi:551.S13.7551.577.38(73):519.2 Zorn, M. R., & Waylen, P. R. (1997). Seasonal Response of Mean Monthly Streamflow to El Nino/Southern Oscillation in North Central Florida. The Professional Geographer 49 (1), 51 62. doi:10.1111/0033 0124.00055

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145 BIOGRAPHICAL SKETCH Susa n Lea Risko obtained a Bachelor of Science in environmental s cience from the School of Natural Resour ces and Environment at the University of Florida in 2004. After working for two years at the St Johns River Water Management District, one of five state run water management agencies, she enrolled in gra duate school and obtained a Master of Engineering from the Department of Agricultural and Biological Engineering at the Univers ity of Florida with a focus in land and water r esources. This endeavor was in pursuit to expand a technological knowledge base before entering entrepreneurial vent ures in the nonprofit sector. In addition to this skill set, she obtained a m inor in organizational leadership for nonprofits from the Department of Family, Youth and Community Sciences also at the University of Florida. Upon graduation, she will pursue a professional e ngineering license to complete her technical training. Lifelong goals involve transition ing from an extensive technical background in environmental systems and infrastructure design to learning about community developme nt, urban and regional planning and the nonprofit sector with the hope of infusing these to promote sustainable infrastructure development with a focus on local communities Upon graduation in August 2012, she intend s to commence plans for a U nited S tates based nonprofit to assi st informal settlement redevelop ment efforts in eastern South Africa.