PARAMETER OPTIMIZATION

1. PARAMETER OPTIMIZATION

2. ANALYSIS and SUPPORT TOOLS Currently Available Statistical and Graphical Analyses Rosenbrock Optimization Troutman Sensitivity Analysis Beta Testing Shuffle Complex Evolution Optimization Multi-Objective Generalized Sensitivity Analysis (MOGSA) Multi-Objective COMplex Evolution Algorithm (MOCOM) Generalized Likelihood Uncertainty Estimation (GLUE)

3. PARAMETER ESTIMATION (CALIBRATION) STRATEGY LEVELS • Estimate all parameters from digital databases (GIS Weasel) and other regional relations • Adjust ET parameter to match potential ET for area or region • Apply XYZ method for precipitation and temperature distribution • Calibrate parameters for hydrograph timing • Calibrate all sensitive parameters

4. Optimization:Distributed Parameter Fitting • Assume parameter values are spatially correct • assume relative magnitudes of parameter values are correct • Can fit all values of one parameter or subsets of a parameter • All values of set or subset are moved in the same direction at the same time • Values are moved either by the same fixed increment or as a percentage of their magnitude

5. MODEL CALIBRATION LIMITATIONS • Ungauged basins (streamflow, meteorological data) • Land-use change • Climate change • Over-parameterization • Parameter equifinality

6. å | Oi - Pi | i å ( Oi - Pi )2 i å | ln(Oi + 1)- ln( Pi+ 1) | i å ( ln(Oi + 1)- ln( Pi+ 1))2 i Objective Functions Rosenbrock Optimization

7. Multi-Objective COMplex Evolution Algorithm (MOCOM)

8. Pareto Solutions Pareto Optimality

9. Y1obs Y1(θ)  - - X1 F1(θ) + + M(θ) X2  F2(θ) X3 Y2(θ) Y2obs F1(θ) θ1 Pareto Solutions θ2 F2(θ) Multi-Criteria Optimization

10. Multi-Objective Uncertainty

11. Automatic Multicriteria Approach • Identify several characteristic features each representing unique behavior of the watershed. • Develop objective measures of the “closeness” of the model output to these features. • Simultaneously minimize all of these measures with an optimization routine (MOCOM-UA).

12. Identifying Characteristic Behavior

13. Developing Objective Measures peaks/timing quick recession baseflow

14. Testing of Automatic Multicriteria Approach with SAC-SMA model Leaf River Watershed (1950 km2) 11 years daily calibration data

15. MC: 500 Pareto Solutions

16. SAC-SMA Hydrograph Range

17. PARAMETER ESTIMATION and SENSITIVITY ANALYSIS

18. å | Oi - Pi | i å ( Oi - Pi )2 i å | ln(Oi + 1)- ln( Pi+ 1) | i å ( ln(Oi + 1)- ln( Pi+ 1))2 i Objective Functions (measures of performance)

19. PRMS Sensitivity Analysis • Sensitivity Matrix (relative sensitivity) • Information Matrix • Error Propagation Table • (5, 10, 20, 50% change in parameter value) • Joint & Individual Standard Errors in Parameters • (measure of confidence) • Correlation Matrix • Hat Matrix • (diagonal elements are measure of influence a day is having on optimization, range 0-1)

20. SR = (QPRED / PI)*(PI / QPRED) ¶ ¶ Relative Sensitivity

26. Generalized Likelihood Uncertainty Estimation -- GLUE a methodology based on Monte Carlo simulation for estimating the predictive uncertainty associated with models

27. DOTTY PLOTS

28. Solar Radiation Transmission Coefficient (rad_trncf) vs Cover Density

29. Rockies Sierras Cascades Parameter Equifinality (inches) Uncalibrated Estimate (deg F)

30. Weasel Value Parameter Sensitivity and Weasel Determined Value Animas River (Rockies) Objective Function rad_trncf soil_moist_max

31. Weasel Value Parameter Sensitivity and Weasel Determined Value EF Carson River (Sierras) Objective Function rad_trncf soil_moist_max

32. Weasel Value Parameter Sensitivity and Weasel Determined Value CleElum River (Cascades) Objective Function rad_trncf soil_moist_max

33. Multi-Objective Generalized Sensitivity Analysis (MOGSA)

34. Identifying Characteristic Behavior

35. Developing Objective Measures peaks/timing quick recession baseflow

36. MC: 500 Pareto Solutions

37. Parameter Sensitivity by Objective Function

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