National Weather Service River Forecast System Model Calibration

1. National Weather ServiceRiver Forecast SystemModel Calibration Fritz FiedlerHydromet 00-3Tuesday, 23 May 2000 2290 East Prospect Road, Suite 1 Fort Collins, Colorado 80525

2. 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

3. 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

4. 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

5. 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

6. 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

7. Model Calibration (continued) • Important considerations • Model structure, simulation processes • Effects of parameter changes • Use of the forecast information

8. 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/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 Evaporation Evaporation pan data MAPE vs. Mean seasonal curve QME QIN

9. 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 • PXPP • check consistency • compute normals • MAT3 • check consistency • MAPE • check consistency • generate daily time • series of MAPE • TAPLOT3 • get mean max/min for • mean zone elevation • MAP3 • (re)check consistency • generate time series • of MAP • MAT3 • generate time • series of MAT Temperature Evaporation Precipitation

10. Sacramento Soil Moisture Accounting Model

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

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

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

14. Initial Soil-moisture ParameterEstimates By Hydrograph Analysis

15. 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

16. Initial Soil Moisture Parameters Estimates by Hydrograph Analysis (continued)

17. Initial Soil Moisture Estimates by Hydrograph Analysis (continued)

18. Multiyear Statistical Output

19. Multiyear Statistical Output (continued)

44. 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

45. 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