National Weather ServiceRiver Forecast System

Model Calibration

Fritz Fiedler

Hydromet 00-3

Tuesday, 23 May 2000

2290 East Prospect Road, Suite 1Fort Collins, Colorado 80525

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Calibration Calibration process

– Estimation of parameter values which will minimize differences between observed and simulated streamflows

Calibration problems

– Parameter interaction

– Non-unique solutions

– Time-consuming

– Inaccuracies

– Non-linearities

– Lack of understanding

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Calibration System

Parameter estimation/optimization and watershed simulation

Input

– Point or areal estimates of historical precipitation, temperature, and potential evaporation

– Initial hydrologic conditions

Output

– Basin areal averages for point value inputs

– Simulated hydrographs for historical analysis or use in ESP

– Parameter values for models in operational forecast and ESP systems

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Calibration System (continued)

Characteristics

– Performs computations for few forecast points for many time steps

– Uses operations table

– Compatible with operational system and ESP

– Produces graphical output for manual calibration

– Includes algorithms for automatic optimization

Applications

– Historical watershed simulation

– Model calibration

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Model Calibration Strategy

– Select river system

– Prepare data

MAP - Mean Areal Precipitation

MAT - Mean Areal Temperature

PE - Potential Evaporation

QME - Mean Daily Discharge

QIN - Instantaneous Discharge

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Model Calibration (continued)

– Calibrate least complicated headwater basins

Select calibration period

Estimate initial parameter - observed Qs

Trial and error using MCP

Statistics, observed versus simulated plots

Proper approach to parameter adjustment

Automatic parameter optimization - OPT

Fine tuning - MCP

– Calibrate other headwater areas

– Calibrate local areas

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Model Calibration (continued)

Important considerations

– Model structure, simulation processes

– Effects of parameter changes

– Use of the forecast information

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Data PreparationMAP Algorithms - Mean Areal Precipitation

Techniques for converting point precipitation measurements into areal measurements and distributing them properly in time

Daily and hourly data

Grid point algorithm• Estimating precipitation at a point (1/D2)• Estimate: >least, <greatest• 100-150 points within basin• Normalize at each grid point, then renormalize

Thiessen weights

Grid point versus Thiessen

Two-pass algorithm - distribute daily, then estimate missing

Consistency plots

MAT Algorithms - Mean Areal Temperature

Max - min data

Grid point algorithm (1/D)

Elevation weighting factor

Centroid (1/DP)

Conversion to mean temperatures

Consistency plots

MAPE - Mean Areal Potential EvaporationEvaporation pan data

MAPE vs. Mean seasonal curveQME

QIN

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Historical Data AnalysisGeneral Information Needed

• Station data on Calibration files

• Station history infro - obs times, changes, location, moves

• Topog map of basin

MAP Specific Information

Non- Mountainous Mountains

--basin boundary --isohyetal map

--station weights

MAT Specific Information--mean max/min temperatures

Non-Mountainous Mountains

--basin boundary --areal-elev curve

MAPE Specific Information--Evaporation maps

--mean monthly evap

--station weights

MAP3

• (re)check consistency

• generate time series of MAP

PXPP

• check consistency

• compute normals

MAT3• generate time series of MAT

MAT3• check consistency

TAPLOT3• get mean max/min for mean zone elevation

MAPE• check consistency

• generate daily time series of MAPE

Precipitation Temperature Evaporation

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Sacramento Soil Moisture Accounting Model

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Sacramento Model Structure

E T Demand

Impervious Area

E T

E T

E T

E T

Precipitation Input

Px

Pervious Area

E T

Impervious Area

Tension Water

UZTW Free Water

UZFW

PercolationZperc. Rexp

1-PFREE PFREE

Free WaterTension Water P S

LZTW LZFP LZFS

RSERV

Primary Baseflow

Direct Runoff

Surface Runoff

Interflow

Supplemental Base flow

Side Subsurface Discharge

LZSK

LZPK

Upper Zone

Lower Zone

EXCESS

UZK

RIVA

PCTIM

ADIMP

Total Channel Inflow

Distribution Function Streamflow

Total Baseflow

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Hydrograph Decomposition

Supplemental Baseflow

Primary Baseflow

Interflow

Surface RunoffImpervious and Direct Runoff

Dis

char

ge

Time

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Sacramento Soil Moisture Components

Impervious and Direct Runoff

Surface Runoff

Interflow

Supplemental Baseflow

Primary Baseflow

SAC-SMA Model

Evaporation

Precipitation

Upper

Zone

Lower

Zone

Pervious Impervious

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Initial Soil-moisture ParameterEstimates By Hydrograph Analysis

Parameters for which good estimates generally can be obtained

LZPK - minimum baseflow recession

recession rate Kr = t/1

1

2

QQ

LZPK = 1.0 - Kr

Things to consider

Ground melt in winter Riparian vegetation ET in summer Extended supplemental recessions Reservoirs - diversions Variable primary recession

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Initial Soil-moisture Parameter Estimates By Hydrograph Analysis (continued)

LZSK - Supplemental baseflow recession (always > LZPK)

Flow that typically persists anywhere from 15 days to 3 or 4 months

recession rate Kr = t/1

1

2

QQ

LZSK = 1.0 - Kr

Things to consider

Combination of supplemental and primary is not a straight line on semi-logplot

Better (but not necessary) to replot with primary subtracted

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Initial Soil Moisture Parameters Estimates by Hydrograph Analysis (continued)

PCTIM - minimum impervious areaOnly storm runoff that occurs when UZTWC not full

Use small rise in summer following a week or more of dry weather

PCTIM = Runoff Volume/(Rain + Melt)

Things to consider

Use a number of events, take average of ones with the smallest PCTIM Be aware of approximate magnitude of ET-demand Derive in conjunction with UZTWM

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Initial Soil Moisture Estimates by Hydrograph Analysis (continued)

Methods Extension of recession Examination of semi-log plot (Search through semi-log plot and try to approximate

the highest level of primary baseflow runoff that occurs. This is Qx.)

LZFPM = Qx/LZPK

Things to consider This is a minimal estimate because LZFPC probably never equals LZFPM. Fills to 60 to 90+

percent capacity. Lowest percentage usually associated with most permeable soils.

Further recharge normally occurs after Qx.

LZFPM - lower zone free water capacity

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Multiyear Statistical OutputMULTIYEAR STATISTICAL SUMMARY

STAT-QME AREA (SQ KM) = 2826.5 WATER YEARS 1965 TO 1972

Monthly Simulated mean (cmsd)

Observedmean (cmsd)

Percent bias

Monthly bias (SIM-OBS)(mm)

Maximum error(SIM-OBS) (cmsd)

Percent averageabsolute error

Percent daily rms error

Max monthly volume error(mm)

Percent avg abs monthly vol error

Percent monthly vol rms volRMS error

October 2.058 2.883 -28.61 -0.782 -86.957 44.09 238.04 -4.315 34.72 64.47November 1.521 1.853 -17.92 -0.305 -30.655 45.6 138.3 -1.564 19.33 34.1December 4.763 3.906 21.95 0.812 -122.272 69.81 254.32 7.349 49.21 80.93January 1.501 0.78 92.34 0.683 26.376 118.49 433.66 3.162 99.92 183.88February 5.416 3.672 47.51 1.493 85.814 75.87 271.45 4.519 48.36 76.41March 4.021 2.856 40.8 1.104 55.495 51.71 210.83 6.953 42.72 97.84April 0.485 0.57 -14.95 -0.078 2.349 28.32 59.54 -0.238 18.76 23.87May 0.411 0.445 -7.64 -0.032 1.431 31.11 44.53 -0.228 21.25 28.06June 1.184 0.804 47.27 0.349 -25.129 101.07 349.7 2.303 70.03 123.04July 11.926 10.463 13.98 1.386 88.298 69.64 128.66 7.116 29.62 39.7August 12.941 18.146 -28.68 -4.932 -59.106 48.29 73.02 -10.723 28.68 33.49September 5.769 5.371 7.41 0.365 -72.167 82.52 184.48 -6.814 59.86 79.77YEAR AVG 4.32 4.307 0.29 0.063 -122.272 60.97 184.85 -10.723 37.28 68.78

Daily rms error(cmsd)

Daily averageabs error (cmsd)

Average abs monthly vol error (mm)

Monthly volume rms error (mm)

Correlation Coefficient daily flows

Line of best fitObs = a + b*sim a b

7.962 2.626 1.494 2.757 0.7801 .5786 .8632

Flow interval

Number of cases

Simulated mean (cmsd)

Observed mean (cmsd)

Percent bias Bias(sim-obs) (mm)

Maximum error (cmsd)

Percentavg abs error

Percentrms error

.00 - 1.05 1769 0.715 0.541 32.23 0.0053 18.388 61.3 169.651.05 - 3.27 306 3.989 1.889 111.12 0.0642 48.455 152.89 356.343.27 - 10.47 281 7.971 5.953 33.91 0.0617 85.814 85.97 164.95

10.47 - 32.71 182 17.549 18.621 -5.76 -0.0328 88.298 58.77 80.9732.71 - 104.68 75 39.368 52.609 -25.17 -0.4048 -72.167 42.46 51.8

104.68 - 327.14 4 108.221 182.5 -40.7 -2.2705 -122.272 40.7 44.5327.14 and above No Cases

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Multiyear Statistical Output (continued)

25 Largest Daily Error Values in CMSD

Month Day Year Observed Simulated Error(sim-obs)

Percent error Percent totalsq deviation

Percentreduction ofdaily rms iferror equal

zeroDecember 16 1967 235 112.728 -122.272 -52.03 9.01 4.61July 9 1968 31.2 119.498 88.298 283.01 4.7 2.38October 29 1971 212 125.043 -86.957 -41.02 4.56 2.31February 13 1968 7.15 92.964 85.814 1200.2 4.44 2.24September 3 1965 89.4 17.233 -72.167 -80.72 3.14 1.58August 2 1968 100 40.894 -59.106 -59.11 2.11 1.06July 10 1968 36.9 94.346 57.446 155.68 1.99 1March 3 1968 48.5 103.995 55.495 114.42 1.86 0.93August 18 1966 75.2 23.887 -51.313 -68.24 1.59 0.8December 31 1965 2.4 50.855 48.455 2018.95 1.42 0.71July 29 1971 57.9 9.707 -48.193 -83.23 1.4 0.7September 12 1969 7.5 55.563 48.063 640.83 1.39 0.7July 28 1971 54.4 6.91 -47.49 -87.3 1.36 0.68February 11 1968 1.92 49.141 47.221 2459.42 1.34 0.67February 15 1968 148 101.437 -46.563 -31.46 1.31 0.66August 4 1967 13 57.378 44.378 341.37 1.19 0.6July 19 1968 58.6 14.454 -44.146 -75.33 1.17 0.59September 6 1970 8.65 51.856 43.206 499.49 1.13 0.56August 24 1967 45.7 2.933 -42.767 -93.58 1.1 0.55August 12 1966 43.2 85.601 42.401 98.15 1.08 0.54September 13 1969 10.2 51.597 41.397 405.85 1.03 0.52February 14 1968 135 93.678 -41.322 -30.61 1.03 0.52December 15 1967 21.9 62.726 40.826 186.42 1 0.5July 16 1968 50.7 10.025 -40.675 -80.23 1 0.5July 22 1971 58.8 19.387 -39.413 -67.03 0.94 0.47

12 Largest Monthly Volume Errors in mm

Month Year Observed Simulated Error(sim-obs)

Percent error Percent total sqdeviation

Percent reduction ofmonthly rms if error

equal zeroAugust 1966 33.065 22.342 -10.723 -32.43 17.6 9.23August 1971 19.947 12.537 -7.41 -37.15 8.4 4.29December 1965 6.42 13.769 7.349 114.48 8.27 4.22July 1969 2.814 9.93 7.116 252.9 7.75 3.95March 1968 16.044 22.997 6.953 43.34 7.4 3.77September 1965 10.579 3.764 -6.814 -64.42 7.11 3.62September 1970 5.504 11.959 6.455 117.29 6.38 3.24July 1971 10.31 4.882 -5.427 -52.64 4.51 2.28August 1970 14.02 8.596 -5.424 -38.69 4.5 2.28July 1967 10.182 15.148 4.966 48.78 3.78 1.91February 1968 15.468 19.987 4.519 29.21 3.13 1.57October 1971 13.153 8.838 -4.315 -32.81 2.85 1.44

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Automatic Optimization Program OPT3

– Uses operations table

– Compatible with MCP, OFS, ESP

– Objective functions

Daily RMS error

Monthly volume RMS error

| S - O |**Exp.

| log S - log O | **Exp.

Correlation coefficient

Maximum Likelihood Estimator

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Automatic Optimization (continued)

Program OPT3 (continued)

– Optimization schemes

Pattern search

Adaptive random search

Shuffled complex evolution

– Buffer

– Exclusion periods

– Low flows

– Convergence criteria

– Optimize SAC-SMA, SNOW-17, UG, API-SLC, XIN-SMA