1

Calibration of Watershed Models

• Why calibrate?– OFS: short term forecasts– ESP: no run time mods– Learn model and hydrology– Good training for forecasting

• Basic Methods– Manual/Expert – guided manual adjustment of parameters until

simulated response agrees with observed.– Mathematical Optimization

• Driven by evaluation of an objective function- searches error surface for minimum point

• Not a substitute for manual calibration• Purpose: to refine parameter estimates previously developed

manually

2

NWSRFS Components

Historical Data

Historical DataAnalysis

areal timeseries

ModelCalibration

parameters,information

Calibration System (CS)

Real-TimeObserved

andForecast

Data

Operational Forecast System (OFS)

Ensemble StreamflowPrediction (ESP) System

Hydrologicand

Hydraulic Models

HydrometAnalysis

observed andpredicted

values

Hydrologic/Hydraulic Models

short term forecasts

current states

StatisticalAnalysis

ProbabilisticPredictions

time

window

Interactive Forecast Program (IFP)

InteractiveAdjustments

3

NWSRFS Programs

• MCP – Manual Calibration Program– Based completely on the operations table– Executes a single segment for a long period

of time, usually years– Simulates a long period of record by

executing the operations table one month at a time.

• ICP – Interactive Calibration Program– GUI for MCP

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NWS Hydrologic Modeling

A

B

Operations TableSnow A

SAC-SMA A

UHG A

Stage Q 1

Display 1

Rout 1->2

Snow B

SAC-SMA B

UHG B

ADD/SUB 1+2

Stage-Q 2

Display 2

1

2

5

Period of Record

• Calibration– Use at least a 10 year period east of Mississippi R.– In dryer West, may need longer period to obtain more

events– Select period with low flow and high flow events– May be easier to identify some parameters in slightly

wetter periods– For ESP, entire area to be run must have the same

period of record• Verification

– Choose period with extreme lows and highs to check parameters.

6

Automatic Optimization

• Program: OPT3• Search Algorithms

– Pattern Search– Adaptive Random Search– Shuffled Complex Evolution

• Problems– One number to evaluate agreement at all flow ranges– Can lead to non-sensical values– Can lead to inconsistency across watersheds in a

basin• NEW Simplified Line Search

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Automatic Optimization, cont’d

• Problem Solutions– Mult-step Automatic Calibration Scheme

(MACS)– Use of a-priori SAC parameter estimates to

constrain the search space (Koren et al, 2002) and preserve natural variability

– Simplified Line Search w/ a-prior parms.

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Automatic Optimization, cont’d

• MACS Procedure1. Base flow:

1. Use LOG objective function2. Optimize all SAC parameters

2. Fast Response1. Fix base flow parameters from step 1.2. Use DRMS objective function3. Optimize fast response parameters

3. Base Flow1. Fine tune base flow parameters2. Use log objective function

4. Check Monthly Percent Bias1. Optional2. Manual, since OPT3 can’t optimize the ET-Demand curve

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20

30

40

50

60

70

0 2000 4000 6000 8000 10000

Number of function evaluations

Mu

lti-

scal

e O

F

Min (SCE)

0

1

2

0 2000 4000 6000 8000 10000

Number of function evaluations

Dis

tan

ce

SCE soil

SLS soil

37.5

38

38.5

39

39.5

0 1 2 3

Relative distance

MS

OF

SCE SLS

Simplified Line Search vs Shuffled Complex Evolution

1) SLS needs less function evaluations, but it leads to similar result;

2) SLS stops much faster and closer to the start point (a priori parameters);

3) On some basins, SCE misses the nearest ‘best’ solution.

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Comparison of multi-scale criteria from SCE and SLS for calibration and validation periods

BasinSCE SLS

1 2 3 4 5 1 2 3 4 5

Calibration

GBHT2 14.1 14.0 13.8 14.3 13.8 14.3 14.4 14.0 14.6 14.1

GETT2 18.3 18.6 18.9 12.6 18.3 18.8 18.9 19.5 12.9 18.8

HBMT2 31.9 33.5 32.9 33.3 32.1 33.4 35.4 34.8 35.0 33.0

HNTT2 36.8 38.8 28.3 34.2 36.5 36.9 38.8 28.6 34.5 36.7

JTBT2 11.7 12.6 7.21 15.7 13.2 12.6 12.2 7.15 15.6 13.8

KNLT2 15.0 18.7 18.0 18.7 10.9 17.3 20.1 19.8 19.7 11.2

LYNT2 12.7 12.8 12.3 12.2 8.54 12.7 13.0 12.4 12.3 8.69

MTPT2 38.0 41.7 41.3 40.0 38.0 37.9 41.5 41.3 40.1 37.9

Validation

GBHT2 13.0 14.6 15.4 10.3 15.0 14.8 14.3 15.7 11.4 15.4

GETT2 14.2 9.73 3.57 27.7 13.9 14.1 8.71 3.50 26.2 13.0

HBMT2 29.9 27.9 25.1 21.5 35.9 27.0 34.6 27.6 25.2 47.1

HNTT2 33.3 4.81 66.1 47.4 32.0 32.0 4.51 66.3 44.1 32.0

JTBT2 12.4 4.32 25.9 9.59 26.2 4.96 3.79 24.7 6.47 17.6

KNLT2 31.9 4.38 13.7 18.0 47.9 28.5 11.1 10.8 15.3 43.1

LYNT2 11.4 5.89 11.0 11.4 36.9 11.8 4.92 10.3 11.1 37.3

MTPT2 45.1 16.2 20.9 34.2 52.4 45.4 14.5 19.6 33.7 52.0

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