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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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© 2012 Susan Lea Risko
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To my Mother and Father
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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
it weren’t for the tremendous encouragement I received from Ima Bujak and Tom Mirti I
thank Ima for believing in me more than I believed in myself. I would also like to thank
Tom for spending countless hours with me while I attempted to determine my path in
life. The entire experience would not have even been possible without my committee. I
send thanks and appreciation to my committee, Chris Martinez, Peter Waylen, Greg
Kiker and Dr. Kumaran, 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 preparation 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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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 Geopotential 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
Combination Forecasts..................................................................................... 52 Singular Value Decomposition Analysis ........................................................... 53
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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 Locations .................................................................. 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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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 Station 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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LIST OF FIGURES
Figure page 2-2 Pearson's correlation of standardized streamflow with concurrent and lagged
sea surface temperatures. .................................................................................. 31
2-3 Niño 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 Niño 3.4 index with mean standardized rainfall, mean standardized streamflow, and total regional demand. .................. 34
2-6 Seasonal lagged correlation of the Niño 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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4-3 Predictor weights for Alafia at Bell Shoals using 2-predictors. ............................ 79
4-4 Predictor weights for Alafia 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 Predictor weights for S160 using 2-predictors .................................................... 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 1972. ............................................................................................................. 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 line demonstrates an R-squared of 0.911. ................................................................ 89
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LIST OF ABBREVIATIONS
AMJ April, May, June
ASO August, September, October
eqSOI equatorial Southern Oscillation Index
ENSO El Niño Southern Oscillation
ERSSTV2 Extended reconstruction of sea surface temperatures version 2
DJF December, January, February
FDEP Florida Department of Environmental Protection
FMA February, March, April
GPH Geopotential heights
HCDN Hydroclimatic DataNetwork
ICOADS International Comprehensive 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 Linear 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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NCAR National Center for Atmospheric Research
NCDC National Climatic Data Center
NCEP National Center for Environmental Prediction
NOAA National Oceanic and Atmospheric Association
NDJ November, December, January
NSFM Non Parametric Seasonal Forecast Model
OND October, November, December
PCA Principal component analysis
PNA Pacific North American pattern
SFWMD Southwest Florida Water Management District
SOI Southern Oscillation Index
SON September, October, November
SLP Sea level pressure
SST Sea surface temperatures
SVD Singular Value Decomposition
USGS United States Geological Service
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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
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 streamflows, for example the Niño 3 and Niño 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 datasets of twelve triads comprised of 3-month means 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
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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 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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CHAPTER 1 INTRODUCTION
Florida’s population and water use trends are projected to increase over the next
15 years placing increased pressure on available water resources (FDEP, 2010). This
increased demand in concert with seasonal variability of the resource requires
sophisticated techniques for supply management. Fortunately, there is a strong El Niño
Southern Oscillation (ENSO) signal within this region (Yin, 1994), increasing the
possibility for better streamflow 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), Florida’s population is expected to increase by 57 percent before 2025 in
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 sector 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 source 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,
to improve water source rotation that enhances system reliability. Tampa Bay Water’s
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system is designed 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 technique 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. While 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-scale 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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CHAPTER 2 CLIMATE DIAGNOSTICS
Climatic Indicators
Of all the major climate oscillations, the El Niño 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-quarter of the earth’s surface and adds 0.1 degree Celsius to the
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; Trenberth, 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 experiences 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, the
continuous shifting the system experiences is known as the Southern Oscillation
(Rasmusson and Carpenter, 1982).
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ENSO is a combined oceanic-atmospheric process that can be characterized most
notably by anomalous changes in sea-surface temperatures of the eastern tropical
Pacific Ocean (Rosenzweig, 2008; Trenberth, 2001). The alternating phases of this
oscillation, El Niño, neutral and La Niña, exhibit different behaviors of sea surface
temperatures. During normal conditions trade winds move the equatorial Pacific Ocean
currents westerly, upwelling the ocean’s thermocline to the surface in the eastern
Pacific causing a sea surface temperature gradient with warmer SSTs in the central
Pacific and cooler SSTs along the eastern Pacific (Clarke, 2008). During El Niño, sea
surface temperatures are higher than normal in the eastern Pacific, while La Niña is
characterized by lower than normal sea surface temperatures (Kadioglu et al., 1999).
Periods that do not exhibit variations from the norm are recognized as the neutral
phase. Most El Niño events begin in the boreal spring or summer and peak from
November to January in sea surface temperatures (Trenberth, 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 oscillations that may contribute to
climate variability such as the PNA (Opitz-Stapleton et al., 2007) and the PDO (Tootle
and Piechota, 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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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
phenomenon. These influences can be observed at many geographic regions for
example the western 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 based on the phase of ENSO, El Niño, La Niña or
neutral, as well as by season. Particularly in Florida, El Niño events cause an increase,
while La Niña demonstrates a decrease, in precipitation (Schmidt, 2001). During boreal
winters of an El Niño event, Ropelewski and Halpert (1986) found that moisture is
advected from the tropical Pacific by the sub tropical jet stream into the southeastern
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 Niño years, tropical storm development decreases, while
during La Niña years it increases (Bove et al., 1998). Schmidt (2001) believed changes
in streamflow in the southeast during El Niño summers and falls are more likely due to
the effects of convective storms, while during La Niña less likely.
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The relationship between ENSO and streamflows, as indicated by the
abovementioned patterns, were further utilized through this investigation to determine if
such large scale climatic indicators could be used to forecast streamflow. Although
ENSO has been identified 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 macro-scale climatic indices to hydrologic variables
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 Multivariate 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 500 mb
geopotential heights as a more significant predictor of streamflows in the Truckee-
Carson River system than ENSO.
Based upon previous studies of large-scale climate oscillations and the associated
climatic indicators of such oscillations, the initial climate variables chosen for this
analysis consisted of sea surface temperatures, sea level pressures and geopotential
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heights. Through a preliminary study, summarized here, these large-scale climatic
variables were used to determine the specific climate indices to impact hydrologic
variables in the greater 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 Florida 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 Florida was the
location of focus for this research (Figure 2-1). The Tampa Bay drainage area covers
3550 Km2 (1371 mi2). Within this area lies a surficial aquifer, recharged through
precipitation, in addition to deeper aquifers. Springs intermittently cover 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 effort
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 available at
http://ufdc.ufl.edu/AA00012272/.
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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 Center (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, converting each station into standardized
anomalies where the mean equals zero and standard deviation equals one. The
monthly data was converted into twelve triads per each year of data with each triad
comprised of 3-month means. This shifts the focus from a station’s magnitude towards
its variability and equally weights each station. In doing so, it is assumed that that the
basic hydrologic characteristics of each station are relatively similar. As a result of
Florida’s homogenous geographic landscape in terms of relief, it is a reasonable
assumption.
Climatic Variables
This work used sea surface temperatures, geopotential heights (GpHs) and sea
level pressures (SLPs) 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, 2008a). It is an extended reconstruction
of sea surface temperatures 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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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 2.5º x 2.5º consisting of SLPs (IRI,
2012a) 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 obtained 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 reanalysis 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 and 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 composite 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 determined 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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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 Ocean 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 relationships 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 analysis, 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 hydrologic 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 10th and 90th
percentiles of rainfall and streamflow were chosen to identify extreme wet and dry years
for each triad. For total regional demand the 20th and 80th percentiles were used to
increase the composite sample size. Composite maps of gridded climate variables
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during these extremes 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
indices were presented using plots of lagged Pearson’s product-moment correlation and
Spearman’s rank correlation. Where multiple spatial patterns existed more than one
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 highlights 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 region. 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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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
pattern of ENSO’s movement can be observed. During earlier lags the correlations
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 surface 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 (bottom row) to lag-12 (top row). When
comparing the overall correlation patterns over multiple triads and lags between Niño
3.4 and each of the hydrologic variables, rainfall, streamflow and demand (Figure 2-5),
noticeable differences appear. Streamflows demonstrated a longer seasonal response
to both Niño 3 and Niño 3.4 as a result of its lagged response in comparison to rainfall
events. Correlating Niño 3 with each of the hydrologic variables (Figure 2-6) provided
slightly stronger correlation results than Niño 3.4. Correlations using the Multivariate
ENSO Index (MEI) demonstrated 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 streamflow with concurrent and lagged sea level
26
pressures. Lags were evaluated at 3-month intervals from lag-0 (bottom row) to lag-12
(top row). Pearson correlation of 0.231 is 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 composite
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 Southern Oscillation Index (eqSOI). Results from correlations using these
indices 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 heights
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 and SLPs.
Results are not presented here, but are available at Http://ufdc.ufl.edu/AA00012272/.
Conclusion
Of the three predictors used, SSTs, GpHs and SLPs, the SSTs demonstrated the
strongest relationship with streamflows. The location within the equatorial Pacific Ocean
where the highest correlation between streamflows and SSTs occurred indicated the
27
relevance of specific climate indices such as Niño 1.2, Niño 3, Niño 3.4 and Niño 4. Of
these, the most prevalent correlations were Niño 3 and Niño 3.4. It was also noted that
the Southern Oscillation Index (SOI) or the equatorial Southern Oscillation Index
(eqSOI) offer additional forecasting 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 based 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 Niño 3 or Niño 3.4 indices during September through
November (SON) and October through December (OND) (Martinez et al., 2009).
Results provided through this portion of the analysis supported the decision to use
Niño 3 and Niño 3.4 as separate forecasting indices, since the defined location for these
two indices overlaps as was shown in Figure 2-3. It was also determined that the Niño 3
index could be complemented with additional indices to increase forecasting ability,
such as Niño 1.2 and Niño 4 since they spatially and temporally complement each other
(Trenberth, 2001).
These results also indicated that forecasting potential for streamflows was greater
than that of rainfall and demand. Rainfall and demand results contained more noise
than that of streamflow with sporadic correlations. 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 were chosen for further analysis as described in
Chapter 2.
28
Table 2-1. Rainfall data used in this study.
COOP ID Station name County Latitude Longitude Data rangea
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
29
Table 2-2. Streamflow data used in this study.
USGS ID Station name Latitude Longitude Data rangea
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 Shoalsb 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 demand Data range
Total Regional Demand 10/1991 – 12/2008 City of Tampa WDPAa 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
30
Figure 2-1. Rainfall and Streamflow stations used for the preliminary climate diagnostics within the greater
31
Figure 2-2. Pearson's correlation of standardized streamflow with concurrent and lagged sea surface temperatures.
32
Figure 2-3. Niño Regions along the equatorial Pacific. Reprinted with permission from Martinez.C.J., personal communication,June 5, 2012.
33
Figure 2-4. Composite anomalies (°C) of concurrent and lagged sea surface temperatures.
34
Figure 2-5. Seasonal lagged correlation of the Niño 3.4 index with mean standardized rainfall (upper left), mean standardized streamflow (upper right), and total regional demand (bottom).
35
Figure 2-6. Seasonal lagged correlation of the Niño 3 index with mean standardized rainfall (upper left), mean standardized streamflow (upper right), and total regional demand (bottom).
36
Figure 2-7. Pearson's correlation of standardized streamflow with concurrent and lagged sea level pressures.
37
Figure 2-8. Composite anomalies (mb) of concurrent and lagged sea level pressures between 1950 and 2008.
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).
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).
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 inputs 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, Niño 1.2,
Niño 3, Niño 3.4 and Niño 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 Niño 3 and Niño 3.4 as determined through
previous research (Martinez et al., 2009).
Background
Once spatial and temporal 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 efforts can be employed, such as, parametric and non-parametric 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).
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 benefit 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 predictors 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,
which estimate the function “locally.” Some examples of these approaches are kernel-
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
weighted 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 alternatives (Rajagopalan et al., 2005). Of the non-parametric techniques
discussed here, this study employs a kernel-based approach.
42
Since non-parametric methods have been found to result in better approximations,
this was considered the better choice method 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. However, 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 al., 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 sampling 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 than 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 (Golembesky 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-parametric regression techniques were
explored.
43
A combination of the methods 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 recognizes 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 relatively unaffected by
anthropogenic influences. Results from these efforts were compiled and are known as
the Hydroclimatic DataNetwork 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 were 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
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
result of Florida’s karst limestone geology, the possibility for watershed basins to mix
exists in locations where the limestone has eroded. Thirteen stations in total were
averaged and used for this analysis with locations along the Withlacoochee, Anclote,
Hillsborough, 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 rivers The period of record for each station’s dataset is displayed 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 station’s data was
grouped into 12 triads with each triad comprised of 3-month means. The beginning
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 nine stations were 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.
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
summarized 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, Niño 1.2, Niño 3, Niño 3.4
and Niño 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 Niño 3 and Niño 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 indices as previously shown in Figure 2-3. These ENSO
indices represent spatial regions where sea surface temperature anomalies occur
during different time periods (Clarke, 2008). These climate indices, Niño 1.2, Niño 3,
Niño 3.4 and Niño 4, were obtained through the Royal Netherlands Meteorological
Institute’s Climate Explorer’s website (KNMI, 2009) and consist of extended
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
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 defined 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 triads and nine lags with results 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 non-existence of
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 in 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 probability 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 probabilities 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 exceedance 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 function f (xi) 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
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 75th
less the 25th 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 rectangular 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, Qi, 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 f1 corresponding to streamflow greater than
the given streamflow, Qi , and f2 corresponding to streamflow less than Qi , while p1 was
the prior exceedance probability and p2 the prior nonexceedance probability, both of
which were based on climatology for streamflow greater than/less than Qi, respectively
(Chiew and Siriwardena, 2005).
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, Qi, 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 skill
and of the weights applied to each model (Elsner and Schmertmann, 1994; Michaelsen,
1987).
Model Skill
The Linear Error in Probability Space (LEPS) score is a measure of the model’s
skill and is based upon a comparison between the recorded streamflow and the model’s
forecasted streamflow over the entire probability distribution. This method of scoring can
be used on both continuous and categorical data. (Ward and Folland, 1991; Potts et al.,
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
position 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, however, 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 between 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
error between the recorded streamflow and the model’s forecasted streamflow within
probability space, the calculation itself uses the sum of this space. These values range
from -100 to 100, with higher scores indicating a better forecast.
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)
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 (2004),
LEPS scores of 10 or higher, 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 triads, JFM through DJF and nine
lags. The triads 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
produces lags. LEPS scores are recorded for each year’s probability of exceedance
then summed to represent the model’s skill for that particular 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 multiple 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.
53
The final exceedance probability forecast 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 number of predictors. For example, a 2-predictor
combination resulted 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 evaluating 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 Niño 3.4, while the 4-predictor
combination included historical flows, Niño 1.2, Niño 3 and Niño 4. Overall, Niño 3
demonstrated the best results from correlation and composite analysis. Four predictors
were used rather than just Niño 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 covariance between streamflows
and SSTs. Valid use of this technique, known as Singular Value Decomposition (SVD)
54
analysis (Bretherton et al., 1992; Tootle et al., 2006) also known as Maximum
Covariance Analysis (MCA), occurs when one has evidence of coupling 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 datasets,
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 maximum 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 encompassed 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, mode 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.
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 Niño 3.4, the 4-predictor
combination that included historical flows, Niño 1.2, Niño 3 and Niño 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 higher 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 summer, as can be seen in Figure 3-2(a,b). The SVD
dataset produced higher LEPS scores than both the 2- and 4-predictor combinations as
shown in Figure 3-2(c).
The 2-predictor combination (Figure 3-3(a)), historical flows joined with Niño 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-
56
predictor combination indicate skill for all nine lags during these triads from JFM until
MAM.
The 4-predictor combination (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 triads during lags 1-9 (AMJ), lags 1-5 and lags 7-9 for
May, June, July (MJJ), lags 1-3 and 8-9 for June, July, August (JJA) and lags 1-3 for
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 triads 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 important. 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 techniques demonstrated through this analysis, some level of skill may be
obtained. The negative LEPS scores that did appear during summer were slightly below
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 resulted 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 Niño 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, Niño 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 itself as a skillful predictor only
during short-term forecast periods such as one to two months. During early winter, Niño
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-predictor combination, which included historical flows, Niño
1.2, Niño 3, and Niño 4, the most influential predictors were historical flows and Niño 3
as demonstrated in Figure 3-5. The seasonal influence for each of these predictors
58
varied similar to the patterns 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 predictors as well as between Niño 3.4 and Niño 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 placed 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 months 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 until 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 climate index has spatial and temporal characteristics that
define it (Trenberth, 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 would allow for complimentary predictors to be combined in such a
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 that improves skill, but the
period of influence the chosen predictors encompass. The 2-predictor combination
demonstrated that Niño 3.4 provides increased forecast skill during the winter; however,
Niño 1.2 and Niño 3 in the 4-predictor combination contribute 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, decreasing 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 Niño event (Wang 1995; Clarke,
2008). El Niño events have been defined as beginning in the boreal spring or summer
and peak from November to January in sea surface temperatures (Trenberth, 1997).
While the seasonal timing of El Niño 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 anomalies 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 minute, 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
60
predictors results in better forecast skill than solely using 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 surface 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.
Therefore, 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.
61
Table 3-1. Period of record for each United States Geological Station within the Greater Tampa Bay Area used in this analysis.
No. USGS Id Station name Data range
Predictor Combo I and II Year span Latitude Longitude
Drainage area (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)
62
Figure 3-1. United States Geological Service stations within the Greater Tampa Bay area used in this analysis (USGS, 2011).
63
Figure 3-2. Weights for individual predictors (predictor 1, predictor 2, etc) for all triads and lags for the (a) 2-predictor combination, (b) 4-predictor combination and (c) SVD Modes. Shaded values represent triads and lags when LEPS scores are above zero, an indication of improved skill compared to only using historical flow as a predictor.
a.
b.
64
Figure 3-2. continued
c.
65
(a) 2-predictors: historical flows and Niño 3.4 (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4
(c) SVD data: historical 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 Niño 3.4, (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4 and (c) SVD data: historical flows, SVD mode 1, SVD mode 2 and SVD mode 3.
66
(a) Historical flows (b) Niño 3.4
Figure 3-4. Predictor weights averaged for all stations using 2-predictors: (a) historical flows and (b) Niño 3.4.
67
(a) Historical flows (b) Niño 1.2
(c) Niño 3 (d) Niño 4
Figure 3-5. Predictor weights averaged for all stations using 4-predictors: (a) historical flows, (b) Niño 1.2, (c) Niño 3 and (d) Niño 4.
68
(a) Historical flows (b) SVD Mode 1
(c) SVD Mode 2 (d) SVD Mode 3
Figure 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.
69
CHAPTER 4 TAMPA BAY CASE STUDY
Background
Historically, Tampa Bay Water relied heavily on groundwater sources, 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, 2010).
The transformation of resource reliance from 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
Hillsborough 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 Km2 (410 mi2). 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 the 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 reclaimed phosphate
pit that covers an area of 3.1 Km2 (1.2 mi2) (FDEP, 2012).
The Hillsborough River watershed is slightly larger than that Alafia covering
1,787.1 Km2 (690 mi2). It extends through Hillsborough, Polk and Pascoe Counties
originating in east-northeast Zephyrhills of southeastern Pascoe and northwestern Polk
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 Trout 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 Km2 (3.3 mi2) 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, 2012).
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 sources (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 canal whose recorded levels have
been adjusted to account for anthropogenic 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 streamflow changes that result
71
from the opening and closing of canal access points. Climate predictors for this portion
of the analysis were comprised of Niño 1.2, Niño 3, Niño 3.4 and Niño 4 and grouped
into predictor combinations with historical streamflows, providing a 2- and 4-predictor
combination, historical streamflows with Niño 3.4 and historical streamflows with Niño
1.2, Niño 3 and Niño 4, respectively. Results show minute differences in the model’s
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 combination (Figure 4-2). This holds
true for nearly all triads 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 flows, Niño 1.2 and Niño 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 during short time scales. Niño
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 Niño 1.2 region during two different time periods was rather
unpredictable. It is not known what may have caused such results. In mid to late winter
this influence occurs between 2- and 4-month lags then extends during early spring to
include lags 6- to 9-months. Niño 1.2’s influence reappears in fall during 2- and 3-month
lags and again between 5- and 8-month lags. The impact of Niño 3 during FMA can be
72
observed five to eight months prior. This index again results as the main predictor
influencing JJA and can be observed between five and nine months prior.
During the few triads and lags that the 2-predictor combination faired better than
the 4-predictor combination, it should be noted that Niño 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 Hillsborough 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. Triads from JFM until AMJ
demonstrated LEPS scores greater than 10 for up 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 triads 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. Niño 3 contributed to the
increased LEPS scores during OND and NDJ during lags of 2- to 3-months for the 4-
predictor 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 Niño 3.4 for the 2-predictor
73
(Figure 4-6) or Niño 4 for the 4-predictor 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 River at Morris 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.
The higher LEPS scores generated by the 2-predictor combination are a result of
the historical streamflows and Niño 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. According 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, the
influence of Niño 3.4 offers greater forecast skill. For example, from JAS through FMA
the higher LEPS skill scores are a result of Niño 3.4. The influence of Niño 3.4 can be
used as a predictor between 4- and 9-months in advance as demonstrated in Figure 4-
9(b).
74
Weights for individual predictors of the 4-predictor combination for station S160
demonstrated differences among influence as illustrated in Figure 4-10. Historical flows
contributed the most while Niño 1.2 came in second, Niño 3 third and Niño 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 triads there is no contribution from this predictor. Although the contribution in
terms of weights for predictors Niño 3 and Niño 4 are much less than Niño 1.2, the skill
level in terms of LEPS scores was greater for these two predictors and therefore their
contribution more significant. The small area during JFM and FMA at 7- and 8-month
lags from Niño 3, as well as, the small sliver of influence offered from Niño 4 during
SON at a 7-month lag which then extends to NDJ at a 9-month lag offers 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 scores 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 streamflow 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 Niño 3.4 as predictors. Figures 4-11, 4-13
and 4-15 demonstrate the resulting probability of exceedance plots of these stations for
the first year of each data set, remaining years are included in Appendix C. Included in
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 historical streamflows. Figure 4-12, 4-14 and
4-16 demonstrate ensembles of probability of exceedance plots for all years during 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 managers. Although these illustrations
of a streamflow forecast are for JFM during a 1-month lead time these are only
examples for a single scenario. The 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 managers 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 amounts 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 relationship was investigated
(Figure 4-17).
It was anticipated that through a method known as the ladder of powers (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
76
best-fit line was then used to represent this 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
behavior between streamflows and withdrawals 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 method of least squares, eventually obtaining an R2 value of 0.911. In order
to encourage a more distinct linear relationship with withdrawals, only streamflow data
greater than 50 MGD was incorporated into the plot (Figure 4-18), otherwise non-linear
characteristics 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 forecasts in the
form of probability of exceedance plots for short-term 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 climatic influences on
regional water resources and better forecast these hydrologic variables.
77
Table 4-1. Period of record for stations specific to Tampa Bay Water.
No. Station name Data range Predictor Combo I and II
Year span
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
78
Figure 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).
79
(a) 2-predictors: historical flows and Niño 3.4 (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4
Figure 4-2. LEPS scores for Alafia at Bell Shoals using (a) 2-predictors: historical flows and Niño 3.4 and (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4.
(a) Historical flows (b) Niño 3.4
Figure 4-3. Predictor weights for Alafia at Bell Shoals using 2-predictors: (a) historical flows and (b) Niño 3.4.
80
(a) Historical flows (b) Niño 1.2
(c) Niño 3 (d) Niño 4
Figure 4-4. Predictor weights for Alafia at Bell Shoals using 4-predictors: (a) historical flows, (b) Niño 1.2, (c) Niño 3 and (d) Niño 4.
81
(a) 2-predictors: historical flows and Niño 3.4 (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4
Figure 4-5. LEPS scores for Hillsborough River at Morris Bridge using (a) 2-predictors: historical flows and Niño 3.4 and (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4.
(a) Historical flows (b) Niño 3.4
Figure 4-6. Predictor weights for Hillsborough River at Morris Bridge using 2-predictors: (a) historical flows and (b) Niño 3.4.
82
(a) Historical flows (b) Niño 1.2
(c) Niño 3 (d) Niño 4
Figure 4-7. Predictor weights for Hillsborough River at Morris Bridge using 4-predictors: (a) historical flows, (b) Niño 1.2, (c) Niño 3 and (d) Niño 4.
83
(a) 2-predictors: historical flows and Niño 3.4 (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4
Figure 4-8. LEPS scores for S160 using (a) 2-predictors: historical flows and Niño 3.4 and (b) 4-predictors: historical flows, Niño 1.2, Niño 3, and Niño 4.
(a) Historical flows (b) Niño 3.4
Figure 4-9. Predictor weights for S160 using 2-predictors: (a) historical flows and (b) Niño 3.4.
84
(a) Historical flows (b) Niño 1.2
(c) Niño 3 (d) Niño 4
Figure 4-10. Predictor weights for S160 using 4-predictors: (a) historical flows, (b) Niño 1.2, (c) Niño 3 and (d) Niño 4.
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.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1974
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for Alafia River at Bell Shoals using Niño 3.4 for years 1974-2008
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.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1972
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for Hillsborough River at Morris Bridge
using Niño 3.4 for years 1972-2008
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.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
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Probability, %
Str
eam
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, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1974
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
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Probability, %
Str
eam
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, M
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Probability of Exceedance for S160 Adjusted
using Niño 3.4 for years 1974-2002
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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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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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CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS
Summary
Niño 3 and streamflow correlation results illustrated positive correlation patterns
that extended across more periods than that of correlations produced using Niño 3.4.
However, Niño 3.4 offered positive correlations for a greater number of lags than that
offered by Niño 3.
LEPS scores illustrated that the model provides skill during most triads and lags,
especially winter. There was even skill offered through summer months, but only during
shorter lags with higher scores produced by the 4-predictor combination. For the 2- and
4-predictor combinations the model offers good skill across multiple triads and lags in a
pattern that mirrors results obtained through the correlation of SSTs with streamflows
reaffirming the model 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 streamflows 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, Hillsborough River at Morris Bridge and S160_Adjusted, expressed
strong similarities between the two different predictor combinations, historical flows with
Niño 3.4 and historical flows with Niño 1.2, Niño 3 and Niño 4. Even though results from
the two different 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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rather subjective 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 Niño 4, which
hardly 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 Niño 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.
Florida’s economic and social development over the past 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 direct 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 supply 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 variables may
offer additional insight of this system and the overall climatic impact. Further in-depth
investigation of rainfall and demand influences could be an integral part of this work.
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Noise for the demand data illustrated the complexity associated with such 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 kernel 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 Water’s
decision-making process.
Application to Alternative Locations
It may be beneficial to apply the model to alternative locations to further
investigate the model’s applicability. 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 would offer additional insight.
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ENSO Phases
Another 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
Niño, La Niña and Neutral, it is speculated that model results could be improved by
removing the variability associated with each of these phases. Therefore, a user’s
increased awareness of the ENSO phenomenon may offer improved results.
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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 Use baye’s probabilty theorem
End EnvelopesUpdated.m (uses climatologyE to extend exceedance prob
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 the mean between these two envelopes Plot probability of exceedance
End
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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) for 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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weightedForecasts.m
Each 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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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 subroutine 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 BayesForecast 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
generated, runModel.m runs SinglePredictor.m for additional predictors, given they’re
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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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 different 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 =[]; predictor3Data =[]; 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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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); ClimatologyE = Climatology(thisPredictandData); forecasts1 = SinglePredictorCV(thisPredictandData, thisPredictor1Data, ClimatologyE, years); forecasts2 = SinglePredictorCV(thisPredictandData, thisPredictor2Data, ClimatologyE, years); forecasts3 = SinglePredictorCV(thisPredictandData, thisPredictor3Data, ClimatologyE, years); forecasts4 = SinglePredictorCV(thisPredictandData, thisPredictor4Data, ClimatologyE, years); LEPS1 = ensembleLEPS(thisPredictandData, forecasts1); LEPS2 = ensembleLEPS(thisPredictandData, forecasts2); LEPS3 = ensembleLEPS(thisPredictandData, forecasts3); LEPS4 = ensembleLEPS(thisPredictandData, forecasts4); lagLEPS1(j,i)=LEPS1; if isempty(LEPS2) else
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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, 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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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'); % these 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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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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lagLEPS1(j,i)=LEPS1; if isempty(LEPS2) 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, 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
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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 dataset, 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 is 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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%% Determine 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 predSeason = 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) minYear4=[]; 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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iLastYear = find(predictandData(:,1) == lastPredictandYear); thisPredictand = predictandData(iFirstYear:iLastYear, forecastSeason+1); years = predictandData(iFirstYear:iLastYear,1); end iFirstPredYear = find(predictor1Data(:,1)==firstPredYear); iLastPredYear = find(predictor1Data(:,1)==lastPredYear); thisPred1 = predictor1Data(iFirstPredYear:iLastPredYear, predSeason+1); if ~isempty(predictor2Data) iFirstPredYear = find(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 happen 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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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 = predictandData(iFirstYear:iLastYear, forecastSeason+1); years = predictandData(iFirstYear:iLastYear,1); iFirstPredYear = find(predictor1Data(:,1)==firstPredYear); iLastPredYear = find(predictor1Data(:,1)==lastPredYear); thisPred1 = predictor1Data(iFirstPredYear:iLastPredYear, predSeason+1); if ~isempty(predictor2Data) iFirstPredYear = find(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 = predictor3Data(iFirstPredYear:iLastPredYear, predSeason+1); end
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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 <= lastPredictandYear);
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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iYears= find(years < firstSVDyear);
years(iYears)=[];
predictandData(iYears)=[];
predictor1Data(iYears)=[];
end
Climatology.m function [ClimatologyE]= Climatology (data) %% Climatology % Prior probabilities (Climatology) % CJM 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)/(length(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];
SinglePredictorCV.m function [forecasts] = SinglePredictorCV(yy, xx, ClimatologyE, n)
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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 period) 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 used 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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flowGreater = sortedDataLOO(i:maxDataLOO,:); predictorGreater = flowGreater(:,2);%Predictor values in 2nd column % Define bandwidth 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 %% Predictor 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) f2xAtPredictor = 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)/(maxDataLOO+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) = sortedDataLOO(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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if forecastE(k,1)==0 forecastE(k,1)= forecastE(k,1)+(k*0.000000000001); end nan_locations = find(isnan(forecastE)); forecastE(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:size(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 work 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
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 vectors, 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 (rr,:)= 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 exceedance 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
114
% The 'find' command returns the position (rows) 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) >= lowerenv(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 probability % 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
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 envelopes, 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 predictions=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);
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,:); for 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);
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;
118
for a = 1:-step:0 b = 1-a; thisWeightedForecast = a* forecasts1 + b* forecasts2; weightedLEPS=ensembleLEPS(thisPredictandData, thisWeightedForecast); if i ==1 maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeightedForecast; maxWeight1 = a; maxWeight2 = b; else thisLEPS = weightedLEPS; if thisLEPS > maxWeightedLEPS maxWeightedLEPS = weightedLEPS; maxWeightedForecast = 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; maxWeight1 = a; maxWeight2 = b; maxWeight3 = c; else thisLEPS = weightedLEPS;
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; maxWeight3 = c; maxWeight4 = d; else thisLEPS = weightedLEPS; if thisLEPS > maxWeightedLEPS maxWeightedLEPS = weightedLEPS; maxWeightedForecast = thisWeightedForecast; maxWeight1 = a; maxWeight2 = b; maxWeight3 = c; maxWeight4 = d;
120
end end i=i+1; end end end end % end switch
121
APPENDIX C STREAMFLOW PROBABILITY OF EXCEEDANCE PLOTS
These streamflow probability of exceedance plots, including climatology 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 Shoals for each year from 1974 to 2007
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1974
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1975
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1976
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1977
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
122
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1978
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1979
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1980
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1981
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
1200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1982
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1983
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
123
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1984
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1985
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1986
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
1200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1987
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1988
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1989
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
124
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1990
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
1200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1991
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1992
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1993
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
1200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1994
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1995
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
125
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1996
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
1200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1997
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1998
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 1999
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2000
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2001
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
126
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2002
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2003
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2004
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2005
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2006
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forAlafia River at Bell Shoals using Niño 3.4 for 2007
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
127
(b.) Hillsborough River at Morris Bridge for each year from 1972 to 2007
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1972
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1973
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1974
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1975
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
128
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1976
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1977
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1978
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1979
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
129
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1980
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1981
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1982
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1983
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1984
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1985
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
130
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1986
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1987
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1988
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1989
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1990
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1991
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
131
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1992
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1993
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1994
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1995
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1996
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1997
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
132
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1998
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 1999
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2000
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2001
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2002
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2003
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
133
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2004
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2005
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2006
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance forHillsborough River at Morris Bridge using Niño 3.4 for 2007
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
134
(c.) S160 Adjusted for each year from 1974 to 2001
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1974
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1975
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1976
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1977
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1978
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1979
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
135
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1980
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1981
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1982
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1983
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1984
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1985
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
136
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1986
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1987
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1988
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1989
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1990
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1991
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
137
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1992
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1993
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1994
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1995
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1996
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1997
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
138
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1998
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 1999
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 2000
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
200
Probability, %
Str
eam
flow
, M
GD
Probability of Exceedance for S160 Adjusted using Niño 3.4 for 2001
Upper Envelope
Exceedance Probability
Lower Envelope
Climatology
139
LIST OF REFERENCES
Bove, M. C., Elsner, J. B., Landsea, C. W., Niu, X., & O’Brien, J. J. (1998). Effects of El 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
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BIOGRAPHICAL SKETCH
Susan Lea Risko obtained a Bachelor of Science in environmental science from
the School of Natural Resources 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 graduate school and
obtained a Master of Engineering from the Department of Agricultural and Biological
Engineering at the University of Florida with a focus in land and water resources. This
endeavor was in pursuit to expand a technological knowledge base before entering
entrepreneurial ventures in the nonprofit sector. In addition to this skill set, she obtained
a minor 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 engineering license to complete her technical training. Lifelong
goals involve transitioning from an extensive technical background in environmental
systems and infrastructure design to learning about community development, 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 intends to commence plans for a United States-based
nonprofit to assist informal settlement redevelopment efforts in eastern South Africa.
