OHD/HLHydrologic Science and Modeling Branch

CalibrationDHM/HL-RDHM TrainingMARFC

Manual and Auto CalibrationAdjustment of parameter scalar multipliersUse manual and auto adjustment as a strategyAuto Calibration: Parameters optimized:Snow-17SAC-SMAHillslope and channel routingSearch algorithmsSLS: step-wise line searchObjective function: Multi-scale Use HL-RDHM and ICP

Multiply each grid value by the same scalarfactor. x 2 = Calibrate distributed model by uniformlyadjusting all grid valuesof each model parameter (i.e., multiply each parameter grid value by the same factor)1.Manual: manually adjust the scalarfactors to get desired hydrograph fit. 2.Auto: use auto-optimization techniques to adjust scalar factors. Example: Ithparameter out of N total model parametersCalibration ApproachPreserve Spatial Pattern of Parameters

HL-RDHM SAC-SMA, SAC-HTChannel routingSNOW -17P, T & ETsurface runoffrain + meltFlows and state variablesbase flowHillslope routingAutoCalibrationExecute these components in a loop to find the set of scalar multipliers thatminimize the objective function

(a) Fewer function evaluations than SCE with similar final objective function value(b) Final parameter set is closer to a priori with SLSStepwise Line Search (SLS) Automatic Calibration- Physically realistic posterior model parameter estimates- Algorithmic simplicity- Computational efficiency

Multi-Scale Objective Function (MSOF)Minimize errors over hourly, daily, weekly, monthly intervals (k=1,2,3,4nuser defined)q = flow averaged over time interval kn = number of flow intervals for averagingmk = number of ordinates for each intervalX = parameter set

Weight: -Assumes uncertainty in simulated streamflow is proportionalto the variability of the observed flow-Inversely proportional to the errors at the respective scales. Assume errors approximated by std. = Emulates multi-scale nature of manual calibration

For SCE, High frequency objectives do not start dramatically improving until lower frequency components reach some reasonable level.

For SLS in this example, low frequency objectives begin relatively close to optimal values based on a priori parameters

The weight assigned to each scale is basin-specific30 days10 days1 day1 hourMulti-scale Objective Component Behavior

Average monthly flowAverage weekly flowAverage daily flowHourly flowCalibration: MSOF Time ScalesMulti-scale objective function represents different frequencies of streamflow and its use partially imitates manual calibration strategy

Beforeautocalibrationof a prioriparametersAfter autocalibrationObservedExample of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Arithmetic ScaleAuto Calibration: Case 1

Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Semi-Log ScaleAuto Calibration: Case 1Beforeautocalibrationof a prioriparametersAfter autocalibrationObserved

Beforeautocalibrationof a prioriparametersAfter autocalibrationObservedAuto Calibration: Case 2Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Arithmetic Scale

Impacts of Scalar Multipliers to Routing Parameters on Discharge Hydrographs Rating relationship:Wave velocity:Flow velocity

R Scripts Provided to Assist with Routing Parameter Scaling TIP: It is best to consider the combined impacts rather than the individual impacts of parameter adjustments. In this example, the goal is to slow down high flows and at the same time, speed up low flows as allowed by the model equations. To do this, the q0 grids are scaled by 1.8 and qm grids are scaled by 0.92. User specifies scalars,and the R script plots velocities.

Routing scalar impacts on actual hydrographsTALO2TALO2KNSO2KNSO2TALO2Delayed high peakSpeed up low peakLess effect at upstream point.Pink: without scalarsYellow: with scalars (1.8q0, 0.92qm)

**In calibration we need to deal with scalar multipliers of each of the parameter grids. *Lets explore the concept of the scalar multipliers.Fairly common approachWe and many others think there is value in the underlying spatial pattern in the soils and parameters. *Distance is measured as the Euclidean norm of the vector connecting the apriori and optimized parameters. *Lets explore the MSOFEmulates multi-scale nature of manual calibrationHow??Uses multiple time scales instead of one. *IllustrationHourly flowDailyWeekly or 10 dayMonthly flow.