1. 1 Calibration of HL-RDHM Lecture 4b

2. 2 Calibration of SAC Parameters with Scalar Multipliers Use of scalar multipliers (assumed to be uniform over a basin) greatly reduces the number of parameters to be calibrated. This assumes the spatial distribution of a-priori parameters is realistic. Parameters from 1-hour, lumped model calibrations can be a good starting point. Lumped model parameters, if derived at the 1 hour time scale, can be used to derive initial scalar multipliers, i.e. multiplier = [lumped model parameter]/[basin average of gridded a-priori parameter values] Scalar multipliers are adjusted using similar strategies and objectives to those for lumped calibration Both manual and a combination of automatic and manual calibration on scalar multipliers have proven effective

3. 3 Comparison Between Calibration Steps for Distributed and Lumped Modeling DistributedLumpedDistributedLumped

4. 4 Manual Headwater Calibration Follow similar strategies to those used for lumped calibration except make changes to multipliers, e.g. from Anderson (2002): –“Remove large errors –Obtain reasonable simulation of baseflow –Adjust major snow model parameters, if snow is included\ –Adjust tension water capacities –Adjust parameters that primarily affect storm runoff –Make final parameter adjustments” Can still use PLOT-TS and STAT-QME Stat-Q event statistics summarize how well you do on bias, peaks, timing, and RMSE, etc over any # of selected events. R scripts assist with routing parameter adjustment. See HL-RDHM User Manual for a detailed example.

5. 5 HL-RDHM SAC-SMA, SAC-HT Channel routing SNOW -17 P, T & ET surface runoff rain + melt Flows and state variables base flow Hillslope routing Auto Calibration Execute these components in a loop to find the set of scalar multipliers that minimize the objective function

6. 6 Automatic Calibration Stepwise Line Search (SLS) technique available –Simple local search Benefits of SLS: –Physically realistic posterior model parameter estimates (start from apriori) –Algorithmic simplicity –Computational efficiency Multi-scale objective function

7. 7 (a) Fewer function evaluations than SCE with similar final objective function value (b) Final parameter set is closer to apriori with SLS SLS Benefits Relative to SCE

8. 8 Multi-Scale Objective Function (MSOF) Minimize errors over hourly, daily, weekly, monthly intervals (k=1,2,3,4…n) q = flow averaged over time interval k n = number of flow intervals for averaging m k = number of ordinates for each interval X = parameter set -Assumes uncertainty in simulated streamflow is proportional to the variability of the observed flow -Inversely proportional to the errors at the respective scales. Assume errors approximated by std. Emulates multi-scale nature of manual calibration Weight =

9. 9 For SCE, High frequency objectives do not start dramatically improving until lower frequency components reach some reasonable level. For SLS in this example, low frequency objectives begin relatively close to optimal values based on apriori parameters The weight assigned to each scale is basin-specific 30 days 10 days 1 day 1 hour Multi-scale Objective Component Behavior

10. 10 Before autocalibration of a priori parameters After autocalibration Observed Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Arithmetic Scale Auto Calibration: Case 1

11. 11 Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Semi-Log Scale Auto Calibration: Case 1 Before autocalibration of a priori parameters After autocalibration Observed

12. 12 Before autocalibration of a priori parameters After autocalibration Observed Auto Calibration: Case 2 Example of HL-RDHM Auto Calibration: ELDO2 for DMIP 2 Arithmetic Scale

13. 13 Possible Strategy Start with best a-priori or scaled lumped parameters Run automatic calibration Make manual adjustments (particularly for routing parameters) to get the preferred storm event shapes

14. 14 Automatic Calibration: Example Input Deck time-period = 20040401T00 20040430T23 ignore-1d-xmrg = false time-step = 1 connectivity = /fs/hsmb5/hydro/rms/sequence/abrfc_var_adj2.con output-path = /fs/hsmb5/hydro/dmip2/talo2/ws3 input-path = /fs/hsmb5/hydro/rms/parameterslx input-path = /fs/hsmb5/hydro/Hydro_Data/ABRFC/PRECIPITATION/RADAR/STAGE3/dmip2 input-path = /fs/hsmb5/hydro/dmip2/talo2/ws3 # calibration algorithm calibration = sls calib-time-period = 20040401T00 20040430T23 observed = /fs/hsmb5/hydro/dmip2/talo2/ws3/TALO2c_discharge.outlet_ts timescale-interval = 24 #timescale-interval = 24 240 720 #List any number of parameters to be calibrated #calib-parameters = sac_UZTWM=0.50,1.5 calib-parameters = sac_UZFWM=0.5,1.5 #calib-parameters = sac_UZK=0.75,1.75 #calib-parameters = sac_ZPERC=4.0,6.0 #calib-parameters = sac_REXP=0.25,2.0 #calib-parameters = sac_LZTWM=0.25,0.8 #calib-parameters = sac_LZFSM=0.5,1.0 #calib-parameters = sac_LZFPM=0.75,1.4 #calib-parameters = sac_LZSK=0.5,1.0 #calib-parameters = sac_LZPK=0.25,1.0 #calib-parameters = sac_PFREE=0.5,1.0 #calib-parameters = rutpix_Q0CHN=0.25,2.0 # #select operations #available snow17, sac, frz, api, rutpix7, rutpix9, funcOpt operations = calsac calrutpix9 funcOpt

15. 15 function call# 9 -1 0.825 3.01386 6.01109 END PARAM#1 LOOP, ITER#7 Optimum Parameter at this step: 0.825000 Iterration#=8 1.000000 Parameter #=1 step = 0.025000 entering calsacInCalLoop leaving CalsacInCalLoop func_opt: scale 1 = 4.7284e-05 scale 2 = 3.96251e-05 time of this step = 1 seconds search direction/parameter/criteria/best criteria function call# 10 -1 0.8 6.24174e-05 3.01386 END PARAM#1 LOOP, ITER#8 Optimum Parameter at this step: 0.800000 Iterration#=9 1.000000 Parameter #=1 step = 0.025000 entering calsacInCalLoop leaving CalsacInCalLoop func_opt: scale 1 = 2.16184 scale 2 = 2.08796 time of this step = 1 seconds search direction/parameter/criteria/best criteria function call# 11 -1 0.775 3.04681 6.24174e-05 entering calsacInCalLoop leaving CalsacInCalLoop func_opt: scale 1 = 2.13726 scale 2 = 2.06656 time of this step = 1 seconds search direction/parameter/criteria/best criteria function call# 12 -1 0.825 3.01386 6.24174e-05 END PARAM#1 LOOP, ITER#9 Optimum Parameter at this step: 0.800000 Optimum found: icall=12 0.000062 0.000062 param: 0.800000 Example Automatic Calibration Output (single parameter) Current and previous multi-scale objective values RMS for 1 hour scale RMS for 24 hour scale If calibration does not complete in first run for some reason (e.g. hardware/network glitches), you can go back and pick up the last set of optimum parameters so you don’t have to restart from the beginning for the next calibration run.

16. 16 Rating relationship: Wave velocity: Flow velocity Q(2.5q0,qm) Q(q0,qm) Q(q0,0.5qm) Impacts of Scalar Multipliers to Routing Parameters (q0 and qm) on Discharge Hydrographs

17. 17 R Scripts Provided to Assist with Routing Parameter Scaling TIP: It is best to consider the combined impacts rather than the individual impacts of parameter adjustments. In this example, the goal is to slow down high flows and at the same time, speed up low flows as allowed by the model equations. To do this, the q0 grids are scaled by 1.8 and qm grids are scaled by 0.92. User specifies scalars, and the R script plots velocities.

18. 18 Routing scalar impacts on actual hydrographs TALO2 KNSO2 TALO2 Delayed high peak Speed up low peak Less effect at upstream point. Pink: without scalars Yellow: with scalars (1.8q0, 0.92qm)