National Weather Service River Forecast System Model Calibration Fritz Fiedler Hydromet 00-3 Tuesday, 23 May East Prospect Road, Suite 1 Fort Collins, Colorado 80525

C8 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

C8 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

C8 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

C8 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

C8 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

C8 Model Calibration (continued)  Important considerations –Model structure, simulation processes –Effects of parameter changes –Use of the forecast information

C8 Data Preparation MAP 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/D 2 ) Estimate: >least, <greatest 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/D P ) Conversion to mean temperatures Consistency plots MAPE - Mean Areal Potential Evaporation Evaporation pan data MAPE vs. Mean seasonal curve QME QIN

C8 Historical Data Analysis General 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 TemperatureEvaporation

C8 Sacramento Soil Moisture Accounting Model

C8 Sacramento Model Structure E T Demand Impervious Area E T Precipitation Input Px Pervious Area E T Impervious Area Tension Water UZTW Free Water UZFW Percolation Zperc. Rexp 1-PFREE PFREE Free Water Tension Water P S LZTW LZFP LZFS RSERV Primary Baseflow Direct Runoff Surface Runoff Interflow Supplemental Base flow SideSubsurface Discharge LZSK LZPK Upper Zone Lower Zone EXCESS UZK RIVA PCTIM ADIMP Total Channel Inflow Distribution Function Streamflow Total Baseflow

C8 Hydrograph Decomposition Supplemental Baseflow Primary Baseflow Interflow Surface Runoff Impervious and Direct Runoff Discharge Time

C8 Sacramento Soil Moisture Components Impervious and Direct Runoff Surface Runoff Interflow Supplemental Baseflow Primary Baseflow SAC-SMA Model Evaporation Precipitation Upper Zone Lower Zone PerviousImpervious

C8 Initial Soil-moisture Parameter Estimates By Hydrograph Analysis

C8 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

C8 Initial Soil Moisture Parameters Estimates by Hydrograph Analysis (continued)

C8 Initial Soil Moisture Estimates by Hydrograph Analysis (continued)

C8 Multiyear Statistical Output

C8 Multiyear Statistical Output (continued)

C8 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

C8 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