Calibration

Mike Smith, Victor Koren, Zhengtao Cui, Seann Reed, Fekadu Moreda

DOH Science ConferenceJuly 17, 2008

HL-RDHM

SAC-SMA, SAC-HT

Channel routing

SNOW -17

P, T & ET

surface runoff

rain + melt

Flows and state variables

base flowHillslope routing

SAC-SMA

Channel routing

P& ET

surface runoff

rain

Flows and state variables

base flowHillslope routing

AWIPS DHM

Mods

AutoCalibration

DHM-TF

ForecastingCalibration

(Forecast)

ICP

Current Status

Manual and Auto Calibration• Adjustment of parameter scalar multipliers• Use manual and auto adjustment as a strategy• Start with hourly lumped calibration• Model parameters optimized in auto calb:

– SAC-SMA– Hillslope and channel routing– Snow-17

• Search algorithms– Simple local search

• Objective function: Multi-scale • Limited to headwater basins

48

5632 62

4230 44

40

4442

32

36 42

40

24

2816 31

2115 22

20

2221

16

18 21

20

Multiply each grid value by the same scalarfactor.

x 2 =

Calibrate distributed model by uniformly adjusting all grid valuesof each model parameter (i.e., multiply each parameter grid value by the same factor)

1. Manual: manually adjust the scalar factors to get desired hydrograph fit. 2. Auto: use auto-optimization techniques to adjust scalar factors.

Example: Ith parameter out of N total model parameters

Calibration Approach

Preserve Spatial Pattern of Parameters

HL-RDHM

SAC-SMA, SAC-HT

Channel routing

SNOW -17

P, T & ET

surface runoff

rain + melt

Flows and state variables

base flowHillslope routing

AutoCalibration

Execute these components in a loop to find the set of scalar multipliers thatminimize the objective function

km

iiksiko

k k

XqqJ1

2

,,,,1

2

1n

Multi-Scale Objective Function (MSOF)

• Minimize errors over hourly, daily, weekly, monthly intervals (k=1,2,3,4…n…user defined)

• q = flow averaged over time interval k• n = number of flow intervals for averaging q

• mk = number of ordinates for each interval

• X = parameter set

k1

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- time scale nature of manual calibration

Average monthly flow

Average weekly flow

Average daily flow

Hourly flow

Calibration: MSOF Time Scales

Multi-scale objective function represents different frequencies of streamflow and its use partially imitates manual calibration strategy

Beforeautocalibrationof a prioriparameters

After autocalibration

Observed

Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Arithmetic Scale

Auto Calibration: Case 1

Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Semi-Log Scale

Auto Calibration: Case 1

Beforeautocalibrationof a prioriparameters

After autocalibration

Observed

Beforeautocalibrationof a prioriparameters

After autocalibration

Observed

Auto Calibration: Case 2Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2

Arithmetic Scale

HL-RDHM and ICP

• Display time series

• ICP modifications

– Run MCP3 or HL-RDHM

– Copy optimized parameters to HL-RDHM input file

– Re-run HL-RDHM