Overland and channel routing (b) Calibration

1
Overland and channel routing(b) Calibration

• Lecture 4

2
Routing Outline

• Conceptual model
• Parameter estimation
• Connectivity
• Slopes
• Channel hydraulic properties
• Local customization steps

3
Routing Model
Real HRAP Cell
Hillslope model
Cell-to-cell channel routing
4
Separate Treatment of Fast and Slow Runoff
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HRAP Cell-to-cell Connectivity Examples
ABRFC 33,000 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.

MARFC 14,000 cells
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Representative Slopes Are Extracted from Higher
Resolution DEMS (North Fork of the American River
(850 km2))
Slope (m/m)
Main Channel Slope (1/2 HRAP Resolution) Average
0.06 Channel slopes are assigned based on a
representative channel with the closest drainage
area.
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.
Local Channel Slope (1/2 HRAP Resolution) Average
0.11
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Main Channel Slope vs. Local Channel Slope
Segment Slopes (m/m)

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 cells 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.
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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 (Qq0Aqm)
• 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

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Kinematic Wave Equations Solved by
HL-RDHM Hillslope Flow Koren et al. (2004)
(continuity)
(momentum)
q discharge per unit area of hillslope h
average overland flow depth Rs fast runoff from
water balance Sh hillslope slope nh hillslope
roughness D drainage density Lh hillslope
length
Conceptual Hillslopes (higher D more
hillslopes and faster response)
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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 qLh overland flow rate at the hillslope
outlet Rg slow runoff component from the water
balance Fc grid cell area Lc channel length
within a cell
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Kinematic Wave vs. Unit Hydrograph
Larger flood accelerated
Same q0,qm
Treating KW 25.4 like UG
Smaller flood delayed

• If (qm ! 1), channel velocity will vary with
  flow level (linear superposition does not apply).
• Typically qm gt 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).

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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
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Channel Shape Model

• Assume simple relationship between top width (B)
  and depth (H)
• Solve for a and b 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 a and b,
  channel slope (Sc) and channel roughness (nc)

b 1
b lt 1
b gt 1
b 0
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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)

15
KNSO2 (285 km2)
WATTS (1645 km2)
Model Validation
CAVESP (90 km2)
SPRINGT (37 km2)
Model predicted relationships (p) at points
upstream from TALO2 (2484 km2) compared with
local fits (l)
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Routing Parameter Grids
Default grid values rutpix_ALPHC -1
(nodata) rutpix_BETAC 1 rutpix_DS
2.5 rutpix_Q0CHN -1 (nodata) rutpix_QMCHN
1.333 rutpix_ROUGC -1 (nodata) rutpix_ROUGH
0.15
Rutpix7 channel shape Rutpix9 rating curve
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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

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Model Resolution and Basin Size Considerations
HRAP Cell Connectivity

• 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.

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HRAP vs. ½ HRAP Implementation
Area (km2)
ID
Gauge Name
2
1
3
4 km resolution does not allow accurate selection
of an outlet for this subbasin because
User must choose which cell is the best outlet
for this basin.
2 km resolution allows more accurate delineation
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Connectivity File Example
Change this number when adding outlets
User defined header lines
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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

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Outletmeas_manual.R Additional Plots
Q vs. A for Two Methods
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Outletmeas_manual.R User Options
---(1)--- input file name file.listlt-"/fs/hsmb5/h
ydro/users/sreed/flow_measurements/dmip2/talo2meas
3_29_07.d" ---(2)--- user specified weight
exponent for regression Qwt.qalt-1 for
Q-A Qwt.ablt-1 for A-B Qwt.n lt-1 for
Manning's n ---(3)--- User specified relative
weights for each of the USGS data quality
flags wslt-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_qualityT new_graphicsT ---(5)---
info for the channel shape method slope0.002 re
read_dataTRUE --- (6)--- output file
names file.outlt-"param.final.d"
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Genpar Input Deck
genpar.card enter the connectivity file
name connectivity /fs/hsmb5/hydro/users/zhangy/R
DHM/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 r
eplace/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 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
generated genpar-id q0chn genpar-id
qmchn next line is an example input information
for q0chn grid generation genpar-data TALO2
0.31 1.2
Table 9.3 tells you what to put here
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Required Arguments for Grid Generation
Condensed Table 9.3
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
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Calibration
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Comparison Between Calibration Steps for
Distributed and Lumped Modeling
Distributed
Lumped
Distributed
Lumped
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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

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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.
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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

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HL-RDHM
P, T ET
SNOW -17
rain melt
Auto Calibration
SAC-SMA, SAC-HT
surface runoff
Execute these components in a loop to find the
set of scalar multipliers that minimize the
objective function
base flow
Hillslope routing
Channel routing
Flows and state variables
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(a) Fewer function evaluations than SCE with
similar final objective function value
(b) Final parameter set is closer to apriori with
SLS
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Multi-Scale Objective Function (MSOF)
Emulates multi-scale nature of manual calibration

• Minimize errors over hourly, daily, weekly,
  monthly intervals (k1,2,3,4n)
• q flow averaged over time interval k
• n number of flow intervals for averaging
• mk 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.
Weight
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Multi-scale Objective Component Behavior

• 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

1 hour
1 day
10 days
30 days
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Automatic Calibration Example Input Deck
time-period
20040401T00 20040430T23 ignore-1d-xmrg
false time-step
1 connectivity /fs/hsmb5/hydro/rms/sequence/abrf
c_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/PRECIP
ITATION/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.o
utlet_ts timescale-interval 24
timescale-interval 24 240 720 List any
number of parameters to be calibrated calib-param
eters sac_UZTWM0.50,1.5 calib-parameters
sac_UZFWM0.5,1.5 calib-parameters
sac_UZK0.75,1.75 calib-parameters
sac_ZPERC4.0,6.0 calib-parameters
sac_REXP0.25,2.0 calib-parameters
sac_LZTWM0.25,0.8 calib-parameters
sac_LZFSM0.5,1.0 calib-parameters
sac_LZFPM0.75,1.4 calib-parameters
sac_LZSK0.5,1.0 calib-parameters
sac_LZPK0.25,1.0 calib-parameters
sac_PFREE0.5,1.0 calib-parameters
rutpix_Q0CHN0.25,2.0 select
operations available snow17, sac, frz, api,
rutpix7, rutpix9, funcOpt operations calsac
calrutpix9 funcOpt
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Example Automatic Calibration Output(single
parameter)
func_opt scale 1 16.2944 scale 2
15.6969 time of this step 2 seconds function
call at initial param 22.9353 par 1
Iterration1 1.000000 Parameter 1 step
0.025000 func_opt scale 1 18.2721 scale 2
17.5934 time of this step 2 seconds
search direction/parameter/criteria/best
criteria function call 2 1 1.025 25.7127
22.9353 func_opt scale 1 14.2935 scale 2
13.7814 time of this step 2 seconds
search direction/parameter/criteria/best
criteria function call 3 1 0.975 20.1276
22.9353 END PARAM1 LOOP, ITER1 Optimum
Parameter at this step 0.975000 Iterration2
1.000000 Parameter 1 step 0.025000
func_opt scale 1 4.69664 scale 2
4.58429 time of this step 2 seconds
search direction/parameter/criteria/best
criteria function call 11 -1 0.85 6.65424
5.5294 END PARAM1 LOOP, ITER8 Optimum
Parameter at this step 0.825000 Optimum
found icall11 5.529395 5.529395 param
0.825000
RMS for 1 hour scale
RMS for 24 hour scale
Current and previous multi-scale objective values
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 dont have to restart from the
beginning for the next calibration run.
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Impacts of Scalar Multipliers to Routing
Parameters on Discharge Hydrographs
Rating relationship
Wave velocity
Flow velocity
38
R Scripts Provided to Assist with Routing
Parameter Scaling
User specifies scalars, and the R script plots
velocities.

• 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.

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