Long-Term Salinity Prediction with Uncertainty Analysis: Application for Colorado River Above Glenwood Springs, CO James Roger Prairie Dept.
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Long-Term Salinity Prediction with Uncertainty Analysis: Application for Colorado River Above Glenwood Springs, CO James Roger Prairie Dept. of Civil, Architectural, and Environmental Engineering Masters Defense Spring 2002 Motivation • Colorado River Basin – arid and semi-arid climates – irrigation demands for agriculture • “Law of the River” – Mexico Treaty Minute No. 242 – Colorado River Basin Salinity Control Act of 1974 Motivation • Salinity Control Forum – Federal Water Pollution Control Act Amendments of 1972 – Fixed numerical salinity criteria • 723 mg/L below Hoover Dam • 747 mg/L below Parker Dam • 879 mg/L at Imperial Dam • review standards on 3 year intervals – Develop basin wide plan for salinity control Salinity Damages and Control Efforts • Damages are presently, aprox. $330 million/year • As of 1998 salinity control projects has removed an estimated 634 Ktons of salt from the river – total expenditure through 1998 $426 million • Proposed projects will remove an additional 390 Ktons – projects additional expenditure $170 million • Additional 453 Ktons of salinity controls needed by 2015 Data taken from Quality of Water, Progress Report 19, 1999 & Progress Report 20,2001 Existing Colorado River Simulation System (CRSS) • Includes three interconnected models – salt regression model • USGS salt model – stochastic natural flow model • index sequential method – simulation model of entire Colorado River basin • implemented in RiverWare Existing Salt Model Over-Prediction Research Objectives • Investigate and improve generation of natural salt associated stochastic natural flow • Investigate and improve modeling natural hydrologic variability (stochastic natural flow) • Apply modifications to a case study in the Colorado River Basin Case Study Area • Historic flow from 1906 - 95 • Historic salt from 1941 - 95 USGS gauge 09072500 (Colorado River near Glenwood Springs, CO) Stochastic Simulation • Simulate from the conditional probability function f yt y , y ,..., y t 1 t 2 t p f ( yt , yt 1 , yt 2 ,..., yt p ) f (y , y t t 1 , yt 2 ,..., yt p ) dyt – joint over the marginal densities Index Sequential Method • Current stochastic hydrology model utilized by the USBR data wrapped from beginning 1906 1995 1st synthetic hydrology 1906 1931 90 extracted overlapping 25 year ISM sequences 2nd synthetic hydrology 1907 1932 89rd synthetic hydrology 1993 1929 90th synthetic hydrology 1994 Adapted from Ouarda, 1997 1930 Parametric PAR(1) • Periodic Auto Regressive model (PAR) – developed a lag(1) model y , 1, y , 1 1 , year season (month) – Stochastic Analysis, Modeling, and Simulation (SAMS) (Salas, 1992) • Data must fit a Gaussian distribution • Expected to preserve – mean, standard deviation, lag(1) correlation – skew dependant on transformation – Gaussian probability density function Traditional K-NN Model • K- Nearest Neighbor model (K-NN) (Lall and Sharma, 1996) • No prior assumption of data’s distribution – no transformations needed • Resamples the original data with replacement using locally weighted bootstrapping technique – only recreates values in the original data • Expected to preserve – all distributional properties • (mean, standard deviation, lag(1) correlation and skewness) – any arbitrary probability density function K-NN Algorithm k N 90 9 yt * yt-1 Modified Nonparametric K-NN Natural Flow Model • Improvement on traditional K-NN • keeps modeling simple yet creates values not seen in the historic record • perturbs the historic record within its representative neighborhood • allows extrapolation beyond sample Local Regression 4.5 Local Regression alpha = 0.3 or 27 neighbors Residual Resampling yt = yt* + et* yt * e t* yt-1 Model Evaluation • Natural flow 1906 to 1995 • Basic Statistics – mean,standard deviation, autocorrelation, skewness • Higher Order Statistics – probability density function – conditional probability • Minimum and Maximum Flows Conditional PDF Summary • Comparison of 3 stochastic hydrology models – ISM, PAR(1), modified K-NN • Modified K-NN addresses limitations of both the ISM and PAR(1) models – generates values and sequences not seen in the historic record – generates a greater variety of flows than the ISM Climate Links • Search for climate indicator in Northern Hemisphere related to flows in the Upper Colorado River basin – USGS gauge 09163500: Colorado River at Utah/Colorado stateline – represents flow in Upper Colorado River – climate indicators • sea surface temperature, sea level pressure, geopotential height 500mb, vector winds 1000mb, out going long wave radiation, velocity potential, and divergence • Correlations – search DJF months – only present in certain regions • Composites – identify climate patterns associated with chosen flow regimes • high, low, high minus low USGS gauge 09163500 (Colorado River at Utah/Colorado Stateline) climate and flow data available from 1951 to 1995 Low flow Composites High minus Low flow High flow USGS Salt Model • 12 monthly regressions – based on observed historic flow and salt mass from water year 1941 to 1983 – historic salt = f (historic flow, several development variables) – natural salt = f (natural flow, development variables set to zero) Statistical Nonparametric Model for Natural Salt Estimation • Based on calculated natural flow and natural salt mass from water year 1941-85 – calculated natural flow = observed historic flow + total depletions – calculated natural salt = observed historic salt - salt added from agriculture + salt removed with exports • Nonparametric regression (local regression) – natural salt = f (natural flow) • Residual resampling Nonparametric Salt Model and USGS Salt Model Comparison with Observed Historic Salt Natural Salt Mass from Nonparametric Salt Model and USGS Salt Model USGS Salt Model and New Salt Model with K-NN Resampling Comparison Summary • The new nonparametric salt model removed the over-prediction seen with the USGS salt model • Provides uncertainty estimates • Can capture any arbitrary relationship (linear or nonlinear) CRSS Simulation Model for Historic Validation calculated natural flow flow historic agriculture consumptive use estimated natural salt mass Natural salt 1941-95 salt irrigated lands agricultural salt loadings historic exports Natural flow 1906-95 salt removed with exports historic municipal and industrial Constant salinity pickup 137,000 tons/year Exports removed @ 100 mg/L historic effects of off-stream reservoir regulation USGS stream gauge 09072500 simulated historic flow simulated historic salt mass Compare results to observed historic for validation Model Validation Historic Flow • 1941-1995 natural flow • Subdued peak Model Validation Historic Salt Mass • 1941-1995 natural flow • 1941-1995 monthly and annual salt model 12 monthly regressions 1 annual regression Determining Salinity Concentration salt concentration (mg/L) salt mass (tons) 735.29 flow volume(acre- feet) Model Validation Historic Salt Concentration • 1941-1995 natural flow • 1941-1995 monthly and annual salt model 12 monthly regressions 1 annual regression Natural Flow vs. Total Depletion Annual Model With Resampling • Based on 1941-1995 natural flow • 1941-1995 annual salt model • Simulates 1941-1995 • Historic Flow and Concentration Modified and Existing CRSS Comparison Historic Flow • Based on 1906-1995 natural flows • Simulates 1941-1995 Modified and Existing CRSS Comparison Historic Salt Mass • Based on 1906-1995 natural flows • 1941-1995 monthly salt models • Simulates 1941-1995 Policy Analysis • Fictional Salinity Standards – Colorado River near Glenwood Springs, CO – Salinity standards • mass remains below 650,000 tons • salt concentration below 350 mg/L – Standards occur in tails of distribution Policy Analysis Historic Simulation > 650,000 tons salt > 350 mg/L salt concentration CRSS Simulation Model for Future Prediction synthetic natural flow flow associated synthetic natural salt mass • Natural flows based on 1906-1995 salt • Natural salt model based on 1941-1995 future agriculture consumptive use irrigated lands agricultural salt loadings salt removed with exports future exports future municipal and industrial • Constant Ag salt loading of 137,000 tons/year • Constant salt removal with exports of 100 mg/L/year USGS stream gauge 09072500 simulated future flow • Projected depletions 2002-2062 simulated future salt mass Stochastic Planning Runs Projected Future Flow and Salt Mass • Passing gauge 09072500 • Based on 1906-1995 natural flows • 1941-1995 monthly salt models • Simulating 2002 to 2062 Policy Analysis Future Projections > 750,000 tons salt > 600 mg/L salt concentration Conclusions • Developed a modified modeling system for the Colorado River Simulation System – stochastic natural flow model • modified nonparametric K-NN natural flow model – salt regression model • statistical nonparametric natural salt model – simulation model in the Colorado River basin • demonstrated on a case study for basin above USGS gauge 09072500 Conclusions – includes both flow and salt uncertainty • improved representation of flow variability • better representation of natural salt and flow relationship – discussed nonparametric techniques • flexible and easy to implement • can preserve any arbitrary distribution • conditioning with additional data – validation of observed historic record – demonstrated future projection Future Work • Extend the modified K-NN flow model to perform spacetime dissaggregation to simulate flow and salt over the entire basin • Move operational policy to an annual time step • Incorporate total depletions as a function of natural flow • Further research into the relationship between salt loading and land use • Continue work to incorporate climate information in streamflow generation Acknowledgements • Dr. Balaji Rajagopalan, Dr. Terry Fulp, Dr. Edith Zagona for advising and support • Upper Colorado Regional Office of the US Bureau of Reclamation, in particular Dave Trueman for funding and support • CADSWES personnel for use of their knowledge and computing facilities Extra Slides Follow Case Study • Colorado River above USGS gauge 09072500 (Colorado River near Glenwood Springs, CO) – flow data available from water year 1906-1995 – salt data available from water year 1941-1995 – model at a monthly timestep to accommodate the reservoirs operating policy in the simulation model Motivation • Generating synthetic natural flow – future variability • Index Sequential Method (ISM) – cannot produce values or traces that had not occurred in the past – limited variability among traces ENSO response in Colorado River Basin • Published by Cayan and Webb, 1992 • A weak response seen over Upper Colorado River Basin Correlation Sea Surface Temperature Sea Level Pressure Comparison with Calculated Natural Salt CRSS Simulation Model • Receives data from the; – Modified Nonparametric K-NN Natural Flow Model – Statistical Nonparametric Natural Salt Model • Simulates flow, salt mass, and salt concentration at USGS gauge 09072500 (Colorado River near Glenwood Springs, CO) Model Validation Natural Flow •1941-1995 natural flow •Utilizes subset of available record Model Validation Natural Flow •1906-1995 natural flow •Utilizes entire available record Model Validation Natural Salt Mass • 1941-1995 natural flow • Utilizes subset of available record • 1941-1995 monthly and annual salt model Model Validation Natural Salt Mass •1906-1995 natural flow •1941-1995 monthly salt models Annual model with no resampling •1906-1995 natural flow •1941-1995 annual salt model •Historic Flow and Concentration Modified and Existing CRSS Comparison Historic Salt Concentration • Based on 1906-1995 natural flows • 1941-1995 monthly salt models • Simulates 1941-1995 Policy Analysis Historic Simulation • > 350 mg/L salt concentration Incorporates total depletion as a function of natural flow Historic Salt Mass Future Salt Mass Modified Colorado River Simulation System (CRSS) • Includes three interconnected models – stochastic natural flow model • modified nonparametric K-NN natural flow model – salt regression model • statistical nonparametric natural salt model – simulation model of entire Colorado River basin • demonstrated on a case study for basin above USGS gauge 09072500