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 2 nd Federal Interagency Hydrologic Modeling Conf.

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 –Salinity Control Forum

Existing Salt Model Over-Prediction

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

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

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

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

Conditional PDF June May

Statistical Nonparametric Model for Natural Salt Estimation Based on calculated natural flow and natural salt mass from water year –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

Comparison with Observed Historic Salt

Comparison With Calculated Natural Salt

CRSS Simulation Model for Historic Validation Constant salinity pickup 137,000 tons/year Exports 100 mg/L Compare results to observed historic for validation Natural flow Natural salt

Annual Model With Resampling Based on natural flow annual salt model Simulates Historic Flow and Concentration

Based on natural flows monthly salt models Simulates Modified and Existing CRSS Comparison Historic Salt Mass

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

Stochastic Planning Runs Projected Future Flow and Salt Mass Passing gauge Based on natural flows monthly salt models Simulating 2002 to 2062

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

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