(a) Overland and channel routing(b) Calibration

Lecture 4

Routing Outline• Conceptual model

• Parameter estimation– Connectivity– Slopes– Channel hydraulic properties

• Local customization steps

Overland flow routed independently for each

hillslope

(adapted from Chow et al., 1988)

HRAP Cell (~ 4 km x 4 km) Uniform, conceptual hillslopes within a modeling unit are assumed

• Drainage density illustrated is ~1.1 km/km2• Number of hillslopes depends on drainage density

Conceptual channel provides cell-

to-cell link

Overland flow routed independently for each

hillslope

(adapted from Chow et al., 1988)

HRAP Cell (~ 4 km x 4 km) Uniform, conceptual hillslopes within a modeling unit are assumed

• Drainage density illustrated is ~1.1 km/km2• Number of hillslopes depends on drainage density

Conceptual channel provides cell-

to-cell link

Real HRAP Cell

Hillslope model

Cell-to-cell channel routing

Routing Model

Fast runoff components• Surface• Direct• Impervious

Slow runoff components• Interflow• Supplemental baseflow• Primary baseflow

Hillslope routing

Channel routing

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 km2))

Slopes from 30-m DEM

Hillslope Slope (1/2 HRAP Resolution)Average = 0.15Slopes of all DEM cells within the HRAP pixel are averaged.

Main Channel Slope (1/2 HRAP Resolution)Average = 0.06Channel 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=q0Aqm)

• 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 FlowKoren et al. (2004)

sh Rx

qL

t

h

3

53

52hqh

n

SDq s

h

h hLx 0

q = discharge per unit area of hillslopeh = average overland flow depthRs = fast runoff from water balanceSh = hillslope slopenh = hillslope roughnessD = drainage densityLh = hillslope length

(continuity) (momentum)

Conceptual Hillslopes (higher D = more hillslopes and faster response)

DLh 2

1

Kinematic Wave Equations Solved by HL-RDHM:Channel FlowKoren et al. (2004)

‘Kinematic’ wave solution assumes slope dominates all other forces (e.g. inertial (rapid changes), pressure, wind, tides)

c

cgL L

fRq

x

Q

t

Ah

cLx 0 mqAqQ 0

(continuity) (momentum)

Q = channel dischargeA = channel cross-sectional areaqLh = overland flow rate at the hillslope outletRg = slow runoff component from the water balanceFc = grid cell areaLc = 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).

0

200

400

600

800

1000

1200

1400

0 20 40 60 80

Time (hours)

Flo

w (

cms)

KW 12.7

KW 25.4

KW 50.8mm

2 x KW 25.4 mm

0.5 * KW 25.4

UG Peak Time

Smaller flood delayed

Larger flood accelerated

Treating KW 25.4 like UG

qmAQ q0

Same q0,qm

Two Simple Channel-Flood Plain Models areAvailable 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

qmAQ q0

‘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 (Sc) and channel roughness (nc)

B H

= 1

< 1

> 1

)1(32

0 )1(

c

c

n

Sq

13

5

mq

= 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)

qmAQ q0

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)

ModelValidation

Routing Parameter Grids

Default grid values:rutpix_ALPHC: -1 (nodata)rutpix_BETAC: 1rutpix_DS: 2.5rutpix_Q0CHN: -1 (nodata)rutpix_QMCHN: 1.333rutpix_ROUGC: -1 (nodata)rutpix_ROUGH: 0.15

Rutpix7 = ‘channel shape’Rutpix9 = ‘rating curve’

No. Grid Name Description Required for 1 rutpix_SLOPC channel slope (Sc) Rutpix7 2 rutpix_ROUGC channel roughness

(Manning’s n, nc) Rutpix7

3 rutpix_BETAC channel shape parameter ( in B = H)

Rutpix7

4 rutpix_ALPHC channel width parameter ( in B = H)

Rutpix7

5 rutpix_SLOPH hillslope slope (Sh) Rutpix7, rutpix9 6 rutpix_DS drainage density (D) Rutpix7, rutpix9 7 rutpix_ROUGH hillslope roughness (nh) Rutpix7, rutpix9 8 rutpix_Q0CHN q0 in Q = q0A

qm Rutpix9 9 rutpix_QMCHN qm in Q = q0A

qm Rutpix9

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 km2

285 km2

795 km2

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 TIFM7 Elk River near Tiff City Mo 22582 POWEL Big Sugar Creek near Powell MO 3653 LANAG Indian Creek near Lanagan MO 619

12

3

User must choose which cell is the best outlet for this basin.

Gauge Name Area (km2)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 namefile.list<-"/fs/hsmb5/hydro/users/sreed/flow_measurements/dmip2/talo2meas3_29_07.d"

#---(2)--- user specified weight exponent for regressionQwt.qa<-1 # for Q-AQwt.ab<-1 # for A-BQwt.n <-1 # for Manning's n

#---(3)--- User specified relative weights for each of the USGS data quality flagsws<-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 optionsplot_quality=Tnew_graphics=T

#---(5)--- info for the channel shape methodslope=0.002

#reread_data=TRUE

#--- (6)--- output file namesfile.out<-"param.final.d"

Genpar Input Deck

#genpar.card#enter the connectivity file nameconnectivity = /fs/hsmb5/hydro/users/zhangy/RDHM/Genpar/sequence/abrfc_var_adj.con#specify an input location for parameter gridsinput-path = /fs/hsmb5/hydro/rms/parameterslx/abrfc#specificy an output locationoutput-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 falsecreate-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 = 480 505 298 306 ## 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 generatedgenpar-id = q0chn#genpar-id = qmchn#next line is an example input information for q0chn grid generationgenpar-data = TALO2 0.31 1.2 Table 9.3 tells you what to

put here

No. genpar-id Arguments Comments

1 SLOPC 0.178 1.23 Use defaults

2 ROUGC no 0.272 -0.00011 The user should specify the first argument and use defaults for arguments 2 and 3.

3 BETAC

Betac

4 ALPHC

-1 Ao alphac Enter -1 for the first argument since it is no longer used. Ao is a representative

cross sectional area at the outlet.

5 SLOPH

constant Typically, this option is not needed since reasonable values of SLOPH can be derived from the DEM.

6 DS

Constant

7 ROUGH

Constant

8 Q0CHN q0chn qmchn

9 QMCHN qmchn

Required Arguments for Grid Generation

Condensed Table 9.3

Calibration

1 Get observed streamflow data

Same

2 Get outlet lat-lon, HRAP coordinates, lat-lon, drainage area

Get drainage area and lat-lon boundaries (or line segment definition, for MAPX)

3 Estimate channel routing parameters at outlet and generate parameter grids

Estimate unit graph (manually from hydrograph or using empirical method, e.g. IHABBs)

4 Add outlet to connectivity file

Not required

5 Adjust pixel areas to match USGS areas

Not required

6 Prepare HL-RDHM input deck

Prepare MCP3 input deck

7 Not required Run CAP to get mean a-priori parameter estimates (SAC and PE); enter values into MCP3 deck

8 Not required Run MAPX

9 Run HL-RDHM Run MCP3

10 Iteratively adjust scale factors for selected parameters option to meet calibration objectives (manual or automatic).

Iteratively adjust parameter values to meet calibration objectives (manual or automatic)

11 Plot mean precipitation, simulated, and observed flow and runoff time series to assist with parameter adjustments (e.g. using ICP).

Same.

12 No equivalent. Can output and plot time series of mean states or states at selected points but this information does not necessarily provide clear guidance on parameter changes. An R script is provided to assist with routing parameter adjustment.

Using ICP, examine the time variation of model states, percolation curve, and unit graph values to help with parameter adjustments.

13 Examine simulation statistics using STAT-QME and/or STAT_Q.

Same

14 Visually examine the spatial patterns of inputs, parameters, and model results (XDMS or GIS software).

No equivalent.

Comparison Between Calibration Steps for Distributed and Lumped Modeling

Distributed Lumped Distributed Lumped

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 flowHillslope routing

AutoCalibration

Execute these components in a loop to find the set of scalar multipliers thatminimize 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

km

iiksiko

k k

XqqJ1

2

,,,,1

2

1n

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

• mk = number of ordinates for each interval

• X = parameter set

k1

-Assumes uncertainty in simulated streamflow is proportionalto 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

k1

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 = 20040401T00 20040430T23ignore-1d-xmrg = falsetime-step = 1connectivity = /fs/hsmb5/hydro/rms/sequence/abrfc_var_adj2.conoutput-path = /fs/hsmb5/hydro/dmip2/talo2/ws3input-path = /fs/hsmb5/hydro/rms/parameterslx input-path = /fs/hsmb5/hydro/Hydro_Data/ABRFC/PRECIPITATION/RADAR/STAGE3/dmip2input-path = /fs/hsmb5/hydro/dmip2/talo2/ws3# calibration algorithmcalibration = slscalib-time-period = 20040401T00 20040430T23observed = /fs/hsmb5/hydro/dmip2/talo2/ws3/TALO2c_discharge.outlet_tstimescale-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, funcOptoperations = calsac calrutpix9 funcOpt

Example Automatic Calibration Output(single parameter)

func_opt: scale 1 = 16.2944 scale 2 = 15.6969time of this step = 2 secondsfunction call at initial param 22.9353 par: 1 Iterration#=1 1.000000 Parameter #=1 step = 0.025000

func_opt: scale 1 = 18.2721 scale 2 = 17.5934time of this step = 2 seconds search direction/parameter/criteria/best criteriafunction call# 2 1 1.025 25.7127 22.9353

func_opt: scale 1 = 14.2935 scale 2 = 13.7814time of this step = 2 seconds search direction/parameter/criteria/best criteriafunction call# 3 1 0.975 20.1276 22.9353 END PARAM#1 LOOP, ITER#1 Optimum Parameter at this step: 0.975000 Iterration#=2 1.000000 Parameter #=1 step = 0.025000

func_opt: scale 1 = 4.69664 scale 2 = 4.58429time of this step = 2 seconds search direction/parameter/criteria/best criteriafunction call# 11 -1 0.85 6.65424 5.5294 END PARAM#1 LOOP, ITER#8 Optimum Parameter at this step: 0.825000 Optimum found: icall=11 5.529395 5.529395 param: 0.825000

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

qm

qm

q

Qqqm

dQ

dQv

1

00

Rating relationship:

Wave velocity:

Flow velocity

qm

qm

q

Qq

A

Qv

1

00

qmAQ q0

qmq AQ 0

qmAQ q0

Q(2.5q0,qm)

Q(q0,qm)

Q(q0,0.5qm)

R Scripts Provided to Assist with Routing Parameter Scaling

qmAQ q0• 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.

qm

qm

q

Qq

A

Qv

1

00

qm

qm

q

Qqqm

dQ

dQv

1

00

User specifies scalars,and the R script plots velocities.

Routing scalar impacts on actual hydrographs

TALO2TALO2

KNSO2

KNSO2

TALO2

Delayed high peak

Speed up low peak

Less effect at upstream point.

Pink: without scalarsYellow: with scalars (1.8q0, 0.92qm)