(a)Overland and channel routing (b) Calibration Lecture 4

Routing Outline Conceptual model Parameter estimation –Connectivity –Slopes –Channel hydraulic properties Local customization steps

Real HRAP Cell Hillslope model Cell-to-cell channel routing Routing Model

Separate Treatment of Fast and Slow Runoff

ABRFC ~33,000 cells MARFC ~14,000 cells OHD delivers baseline HRAP resolution connectivity, channel slope, and hillslope slope grids for each CONUS RFC HRAP cell-to-cell connectivity and slope grids are derived from higher resolution DEM data. HRAP Cell-to-cell Connectivity Examples

Representative Slopes Are Extracted from Higher Resolution DEMS (North Fork of the American River (850 km 2 )) Slopes from 30-m DEM Hillslope Slope (1/2 HRAP Resolution) Average = 0.15 Slopes of all DEM cells within the HRAP pixel are averaged. Main Channel Slope (1/2 HRAP Resolution) Average = 0.06 Channel slopes are assigned based on a representative channel with the closest drainage area. Local Channel Slope (1/2 HRAP Resolution) Average = 0.11 Slope (m/m)

A B Main Channel Slope vs. Local Channel Slope (1)Slopes of each stream segment are calculated from the DEM (2) Model cell slopes are assigned from representative segments that most closely match either the cell’s cumulative or local drainage area. In this case, the slope of segment A is taken as the ‘main’ channel slope and slope of segment B is taken as the ‘local’ channel slope. Segment Slopes (m/m)

Channel Routing Model Uses implicit finite difference solution technique Solution requires a unique, single-valued relationship between cross-sectional area (A) and flow (Q) in each grid cell (Q= q 0 A qm ) Distributed values for the parameters q0 and qm in this relationship are derived by using – USGS flow measurement data at selected points – Connectivity/slope data – Geomorphologic relationships Training on techniques to derive spatially distributed parameter grids is provided in this workshop

Kinematic Wave Equations Solved by HL-RDHM: Hillslope Flow Koren et al. (2004) q = discharge per unit area of hillslope h = average overland flow depth R s = fast runoff from water balance S h = hillslope slope n h = hillslope roughness D = drainage density L h = hillslope length (continuity)(momentum) Conceptual Hillslopes (higher D = more hillslopes and faster response)

Kinematic Wave Equations Solved by HL-RDHM: Channel Flow Koren et al. (2004) ‘Kinematic’ wave solution assumes slope dominates all other forces (e.g. inertial (rapid changes), pressure, wind, tides) (continuity)(momentum) Q = channel discharge A = channel cross-sectional area q Lh = overland flow rate at the hillslope outlet R g = slow runoff component from the water balance F c = grid cell area L c = channel length within a cell

Kinematic Wave vs. Unit Hydrograph If (qm != 1), channel velocity will vary with flow level (linear superposition does not apply). Typically qm > 1, resulting in faster flood propagation at high flows. If qm == 1, channel flow behavior would be similar to a unit hydrograph in the case of uniform runoff (overland flow velocity can still be flow dependent). Smaller flood delayed Larger flood accelerated Treating KW 25.4 like UG Same q0,qm

Two Simple Channel-Flood Plain Models are Available in HL-RDHM The ‘Rating Curve’ model estimates the parameters q0 and qm directly for each model cell using hydraulic measurements at an outlet gauging station, cell drainage areas, and geomorphologic relationships. The ‘Channel shape’ method assumes a simple parabolic channel geometry and uses outlet hydraulic measurements, cell drainage areas, slopes, the Chezy-Manning equation, and geomorphologic relationships to estimate q0 and qm for each cell. Both models have produced good results in our applications. q0 qm

‘Channel Shape’ Model Assume simple relationship between top width (B) and depth (H) Solve for  and  at a USGS gauge using streamflow measurement data Use geomorphologic relationships to derive spatially variable a values (see Koren, 2004 for details) Compute q0 and qm as a function of  and , channel slope (S c ) and channel roughness (n c )  = 1  < 1  > 1  = 0

‘Rating Curve’ Model Solve for q0 and qm at a USGS gauge using streamflow measurement data Use geomorphologic relationships to derive spatially variable a values (see Koren, 2004 for details)

WATTS (1645 km2) KNSO2 (285 km2) CAVESP (90 km2) SPRINGT (37 km2) Model predicted relationships (p) at points upstream from TALO2 (2484 km2) compared with local fits (l) Model Validation

Routing Parameter Grids Default grid values: rutpix_ALPHC: -1 (nodata) rutpix_BETAC: 1 rutpix_DS: 2.5 rutpix_Q0CHN: -1 (nodata) rutpix_QMCHN: rutpix_ROUGC: -1 (nodata) rutpix_ROUGH: 0.15 Rutpix7 = ‘channel shape’ Rutpix9 = ‘rating curve’

Routing Parameter Customization Procedures (User Manual Chapter 9) Determine best HRAP cell to represent basin outlet (XDMS) Add outlet to connectivity file header Adjust cell areas so the total drainage area matches USGS area (cellarea program) Download measurement data from USGS NWIS site (optional) Use preprocess.R to parse USGS flow measurement data for multiple stations into separate files Use outletmeas_manual.R to analyze station data Use genpar utility program to generate grids

2258 km km km 2 HRAP Cell Connectivity Model Resolution and Basin Size Considerations Percent errors in representing basins with 4 km resolution pixels. Open squares represent errors due to resolution only. Black diamonds represent errors due to resolution and connectivity. We correct for these errors by adjusting cell areas in the model so that the sum of the model cell areas matches the USGS reported area at the basin outlet.

1 2 3 User must choose which cell is the best outlet for this basin. Gauge Name Area (km 2 ) ID 4 km resolution does not allow accurate selection of an outlet for this subbasin because HRAP vs. ½ HRAP Implementation 2 km resolution allows more accurate delineation

Connectivity File Example Change this number when adding outlets User defined header lines

R Scripts Provided to Assist with Flow Measurement Analysis Outletmeas_manual.R automatically generates several plots and computes reqressions User can specify plotting and regression weight options Derived parameters are saved to a file for later use

Outletmeas_manual.R: Additional Plots Q vs. A for Two Methods

Outletmeas_manual.R User Options #---(1)--- input file name file.list<-"/fs/hsmb5/hydro/users/sreed/flow_measurements/dmip2/talo2meas3_29_07.d" #---(2)--- user specified weight exponent for regression Qwt.qa<-1 # for Q-A Qwt.ab<-1 # for A-B Qwt.n <-1 # for Manning's n #---(3)--- User specified relative weights for each of the USGS data quality flags ws<-c(1,1,1,1,1) # # Code Description # # E Excellent the data is within 2% (percent) of the actual flow # G Good the data is within 5% (percent) of the actual flow # F Fair the data is within 8% (percent) of the actual flow # P Poor the data are not within 8% (percent) of the actual flow # -1 Missing # The ws vector is ordered as above c(E,G,F,P,-1) #---(4)--- graph options plot_quality=T new_graphics=T #---(5)--- info for the channel shape method slope=0.002 #reread_data=TRUE #--- (6)--- output file names file.out<-"param.final.d"

Genpar Input Deck #genpar.card #enter the connectivity file name connectivity = /fs/hsmb5/hydro/users/zhangy/RDHM/Genpar/sequence/abrfc_var_adj.con #specify an input location for parameter grids input-path = /fs/hsmb5/hydro/rms/parameterslx/abrfc #specificy an output location output-path = /fs/hsmb5/hydro/users/zhangy/RDHM/Genpar/output #replace/update the existing grid or output the grid to the output-path, true or false # overwrite-existing-grid = false # #create a new grid instead of modify existing grid, the boundary in this # case is the boundary of all selected basins, true or false create-new-grid = true # #if the create-new-grid is true, the grid will be created in this window. #if this window is not consistent with the window from the connectivity, #the windows are combined into a big window that contains both subwindows. #window-in-hrap = # # Name of the parameter to be created, available names are: # slopc rougc betac alphc sloph ds rough Q0CHN QMCHM # They are case insensitive #genpar-id = slopc #genpar-id = rougc #genpar-id = alphc #the next line specifies the parameter for which values will be generated genpar-id = q0chn #genpar-id = qmchn #next line is an example input information for q0chn grid generation genpar-data = TALO Table 9.3 tells you what to put here

No.genpar-idArgumentsComments 1SLOPC Use defaults 2ROUGCn o The user should specify the first argument and use defaults for arguments 2 and 3. 3BETACBetac 4ALPHC-1 A o alphacEnter -1 for the first argument since it is no longer used. A o is a representative cross sectional area at the outlet. 5SLOPHconstantTypically, this option is not needed since reasonable values of SLOPH can be derived from the DEM. 6DSConstant 7ROUGHConstant 8Q0CHNq0chn qmchn 9QMCHNqmchn Required Arguments for Grid Generation Condensed Table 9.3

Calibration

Comparison Between Calibration Steps for Distributed and Lumped Modeling DistributedLumped DistributedLumped

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. We assume the spatial distribution of a-priori parameters is realistic. Parameters from 1 hour, lumped model calibrations can be a good starting point. Use of lumped model calibrated parameters has shown benefits, but may not be required to achieve useful results. Lumped model parameters can be used to derive initial scalar multipliers, i.e. multiplier for parameter A = [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

Manual Headwater Calibration Follow similar strategies to those used for lumped calibration except make changes to scalars, 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.

Automatic Calibration Stepwise Line Search (SLS) technique available Benefits of SLS: –Physically realistic posterior model parameter estimates –Algorithmic simplicity –Computational efficiency Multi-scale objective function available Possible strategy: (1) start with best a-priori or scaled lumped parameters, (2) run automatic calibration on SAC parameters, (3) make manual adjustments to routing parameters

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

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

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 =

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

Automatic Calibration: Example Input Deck time-period = T T23 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 = T T23 observed = /fs/hsmb5/hydro/dmip2/talo2/ws3/TALO2c_discharge.outlet_ts timescale-interval = 24 #timescale-interval = #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

Example Automatic Calibration Output (single parameter) func_opt: scale 1 = scale 2 = time of this step = 2 seconds function call at initial param par: 1 Iterration#= Parameter #=1 step = func_opt: scale 1 = scale 2 = time of this step = 2 seconds search direction/parameter/criteria/best criteria function call# func_opt: scale 1 = scale 2 = time of this step = 2 seconds search direction/parameter/criteria/best criteria function call# END PARAM#1 LOOP, ITER#1 Optimum Parameter at this step: Iterration#= Parameter #=1 step = func_opt: scale 1 = scale 2 = time of this step = 2 seconds search direction/parameter/criteria/best criteria function call# END PARAM#1 LOOP, ITER#8 Optimum Parameter at this step: Optimum found: icall= param: 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 optimimum parameters so you don’t have to restart from the beginning for the next calibration run.

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

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 User specifies scalars, and the R script plots velocities.

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)