PARAMETER OPTIMIZATION

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)

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

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

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

Rosenbrock Optimization Objective Functions | O i - P i | i  ( O i - P i ) 2 i  | ln(O i + 1) - ln( P i + 1) | i  ( ln(O i + 1) - ln( P i + 1) ) 2 i 

Multi-Objective COMplex Evolution Algorithm (MOCOM)

Pareto Optimality Pareto Solutions

Multi-Criteria Optimization X1X1 X2X2 X3X3 M(θ) Y 1 (θ) Y 2 (θ) Y 2 obs Y 1 obs F 2 (θ) F 1 (θ)   F 2 (θ) θ1θ1 θ2θ2 Pareto Solutions

Multi-Objective Uncertainty

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

Identifying Characteristic Behavior

Developing Objective Measures peaks/timing baseflow quick recession

Testing of Automatic Multicriteria Approach with SAC-SMA model Leaf River Watershed (1950 km 2 ) 11 years daily calibration data

MC: 500 Pareto Solutions

SAC-SMA Hydrograph Range

PARAMETER ESTIMATION and SENSITIVITY ANALYSIS

Objective Functions (measures of performance) | O i - P i | i  ( O i - P i ) 2 i  | ln(O i + 1) - ln( P i + 1) | i  ( ln(O i + 1) - ln( P i + 1) ) 2 i 

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)

Relative Sensitivity S R = ( Q PRED / P I ) * (P I / Q PRED ) 

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

DOTTY PLOTS

Solar Radiation Transmission Coefficient (rad_trncf) vs Cover Density

Uncalibrated Estimate Parameter Equifinality (deg F) (inches) RockiesSierrasCascades

soil_moist_maxrad_trncf Objective Function Weasel Value Parameter Sensitivity and Weasel Determined Value Animas River (Rockies)

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

soil_moist_maxrad_trncf Parameter Sensitivity and Weasel Determined Value CleElum River (Cascades) Objective Function Weasel Value

Multi-Objective Generalized Sensitivity Analysis (MOGSA)

Identifying Characteristic Behavior

Developing Objective Measures peaks/timing baseflow quick recession

MC: 500 Pareto Solutions

Parameter Sensitivity by Objective Function

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