James Roger Prairie Dept. of Civil, Architectural, and Environmental Engineering Masters Defense

1. 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

2. 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

4. 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

5. 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

6. 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

7. Existing Salt Model Over-Prediction

8. 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

9. Case Study Area • Historic flow from 1906 - 95 • Historic salt from 1941 - 95 USGS gauge 09072500 (Colorado River near Glenwood Springs, CO)

11. Stochastic Simulation • Simulate from the conditional probability function • joint over the marginal densities

12. Index Sequential Method • Current stochastic hydrology model utilized by the USBR Adapted from Ouarda, 1997

13. Parametric PAR(1) • Periodic Auto Regressive model (PAR) • developed a lag(1) model • 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

14. 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

15. y * t y t-1 K-NN Algorithm

16. 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

17. Local Regression 4.5

18. Local Regression alpha = 0.3 or 27 neighbors

19. e * t y * t y t-1 Residual Resampling yt = yt* + et*

20. 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

27. Conditional PDF

28. 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

30. 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

31. USGS gauge 09163500 (Colorado River at Utah/Colorado Stateline) climate and flow data available from 1951 to 1995

32. Low flow Composites High minus Low flow High flow

34. 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)

35. 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

36. Nonparametric Salt Model and USGS Salt Model

37. Comparison with Observed Historic Salt

38. Natural Salt Mass from Nonparametric Salt Model and USGS Salt Model

39. USGS Salt Model and New Salt Model with K-NN Resampling Comparison

40. 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)

42. CRSS Simulation Model for Historic Validation Natural flow 1906-95 Natural salt 1941-95 Constant salinity pickup 137,000 tons/year Exports removed @ 100 mg/L Compare results to observed historic for validation

43. Model Validation Historic Flow • 1941-1995 natural flow • Subdued peak

44. Model Validation Historic Salt Mass • 1941-1995 natural flow • 1941-1995 monthly and annual salt model 12 monthly regressions 1 annual regression

45. Determining Salinity Concentration

46. Model ValidationHistoric Salt Concentration • 1941-1995 natural flow • 1941-1995 monthly and annual salt model 12 monthly regressions 1 annual regression

47. Natural Flow vs. Total Depletion

48. Annual Model With Resampling • Based on 1941-1995 natural flow • 1941-1995 annual salt model • Simulates 1941-1995 • Historic Flow and Concentration

49. Modified and Existing CRSS ComparisonHistoric Flow • Based on 1906-1995 natural flows • Simulates 1941-1995

50. Modified and Existing CRSS ComparisonHistoric Salt Mass • Based on 1906-1995 natural flows • 1941-1995 monthly salt models • Simulates 1941-1995