1. Long-Term Salinity Prediction with Uncertainty Analysis: Application for Colorado River Above Glenwood Springs, CO James Prairie Water Resources Division, Civil, Architectural, and Environmental Engineering Department, and U.S. Bureau of Reclamation, University of Colorado, Boulder Balaji Rajagopalan Water Resources Division, Civil, Architectural, and Environmental Engineering Department, University of Colorado, Boulder Terry Fulp U.S. Bureau of Reclamation, University of Colorado, Boulder Edith Zagona Center for Advanced Decision Support for Water and Environmental Sysytems (CADSWES), University of Colorado, Boulder Hydrology Days 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. Existing Salt Model Over-Prediction

6. Stochastic Simulation Simulate from the conditional probability function –joint over the marginal densities

7. 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

8. 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

9. y t-1 y t * e t * Residual Resampling y t = y t * + e t *

14. Conditional PDF

16. 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

17. Comparison with Observed Historic Salt

18. Comparison With Calculated Natural Salt

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

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

22. Based on 1906-1995 natural flows 1941-1995 monthly salt models Simulates 1941-1995 Modified and Existing CRSS Comparison Historic Salt Mass

23. Policy Analysis Historic Simulation > 650,000 tons salt > 350 mg/L salt concentration

24. 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

25. Conclusion Developed a modeling framework for long- term salinity with uncertainty in the Colorado River –modified nonparametric K-NN natural flow model –statistical nonparametric natural salt model –validation of historic record –demonstrated future projection

26. Future Work Extend the modified K-NN flow model to perform space- time dissaggregation to simulate flow and salt over the entire basin Move operational policy to an annual time step Further research into the relationship between salt loading and land use Continue work to incorporate climate information in streamflow generation

27. Acknowledgements Balaji Rajagopalan, Terry Fulp, 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

28. Extra Slides Follow

29. Conclusions –developed and tested a new statistical nonparametric natural salt model –discussed nonparametric techniques flexible and easy to implement can preserve any arbitrary distribution conditioning with additional data –validation of historic record –preservation of historic salinity violations

30. 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

31. 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

32. ENSO response in Colorado River Basin Published by Cayan and Webb, 1992 A weak response seen over Upper Colorado River Basin

33. Sea Surface Temperature Sea Level Pressure Correlation

34. Alpha = 0.4 or k = 18 et*et* Residual Resampling y t-1 yt*yt* y t = y t * + e t *

35. Model Validation Natural Flow 1941-1995 natural flow Utilizes subset of available record

36. Model Validation Natural Flow 1906-1995 natural flow Utilizes entire available record

37. Model Validation Natural Salt Mass 1941-1995 natural flow Utilizes subset of available record 1941-1995 monthly and annual salt model

38. Model Validation Natural Salt Mass 1906-1995 natural flow 1941-1995 monthly salt models

39. Annual model with no resampling 1906-1995 natural flow 1941-1995 annual salt model Historic Flow and Concentration

40. Future Salt Mass

41. Motivation Salinity Control Forum –Federal Water Pollution Control Act Amendments of 1972 –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

42. 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

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

44. 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

45. 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)

46. Policy Analysis Historic Simulation Incorporates total depletion as a function of natural flow > 350 mg/L salt concentration

47. CRSS Simulation Model for Future Prediction Natural flows based on 1906-1995 Natural salt model based on 1941-1995 Projected depletions 2002-2062 Constant Ag salt loading of 137,000 tons/year Constant salt removal with exports of 100 mg/L/year

48. Policy Analysis Future Projections > 750,000 tons salt > 600 mg/L salt concentration