forcing the lid: calibrating hec-hms for flood … · forcing the lid: calibrating hec-hms for...
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Forcing the lid: Calibrating HEC-HMS for flood management studies
California Water & Environmental Modeling Forum
May 28, 2008
David Ford David Ford Consulting Engineers, Inc.
A system is a big black boxOf which we can't unlock the locks,And all we can find out about Is what goes in and what comes out.
Perceiving input output pairs Related by parameters Permits us, sometimes, to relate An input, output, and a state.
If this relation's good and stable,Then to predict we may be able. But if this fails us - heaven forbid We'll be compelled to force the lid!
---K. Boulding
A system is a big black boxOf which we can't unlock the locks,And all we can find out about Is what goes in and what comes out.
Perceiving input output pairs Related by parameters Permits us, sometimes, to relate An input, output, and a state.
If this relation's good and stable,Then to predict we may be able. But if this fails us - heaven forbid We'll be compelled to force the lid!
---K. Boulding
HEC-HMS
Application steps
• Identify decisions
• Determine info required
• Define, discretize time + space
• Identify models; select one
• Fit and verify
• Develop BC + IC
• Apply
• Check
• Get info from results
Application steps
• Identify decisions
• Determine info required
• Define, discretize time + space
• Identify models; select one
• Fit and verify
• Develop BC + IC
• Apply
• Check
• Get info from results
Start
Finish
Yes
No
Collect rainfall & runoff data
Select starting
estimates of parameters
Simulate system behavior with
parameters
Improve parameter estimates
Compare computed hydrograph
with observed
Satisfied?
Gotta have...
•Model
• Initial estimates of parameters
• Performance index
• Systematic procedure for correcting
• “Input output pairs”
• Univariant gradient method (Newton’s method)
• Nelder and Mead method
Objective function
Parameter value
Iteration 1
Best estimate
Iteration 2
)*2/()( which in
*)()/1( Z minimize 2
1
avgavgii
ii
NQ
i
i
QOBSQOBSQOBSWT
WTQCOMPQOBSNQ
+=
−= ∑=
How we force the lid
• I-O pairs aren’t representative
• Kidnapped by cookbookery, mathematistry, naïve trust
• Results aren’t confirmed
from Dr. Dave Curtis
• 132 sq mi watershed in Colorado R. basin (Texas)
• Surface rain observation and gage-corrected radar available
• HEC-HMS model used for real-time forecasting
June 2007 storm data from Melinda Luna, LCRA
RaingageOptimization start
RadarOptimization start
Best-fit parametersParameter
(1)Initial value(2)
Rain gage value(3)
Radar value(4)
Initial baseflow (cfs/mi2) 0.1 0.103 0.163
Constant loss rate (in/hr) 0.15 0.138 0.164
Initial deficit (in) 0.83 0.784 1.505
Max deficit (in) 4.583 3.192 4.230
Recession constant
1 1 1
Snyder peaking coefficient 0.70 0.605 0.398
4.22 sq mi, urbanized
Pre
cip
(in
)
0.00
0.04
0.08
0.12
12:00 15:00 18:00 21:00 00:00 03:00 06:00 09:00 12:00
22Jan1997 23Jan1997
Flo
w (
cfs
)
0
100
200
300
400
500
600
SAME ZONE OBSERVED PRECIP-INC OUTLET OBSERVED FLOW BASIN COMPUTED FLOW
Parameter “Optimized” estimate
tp, hr 2.33
cp 0.39
initial loss, in 0.49
uniform rate, in/hr 0.11
Pre
cip
(in
)
0.00
0.04
0.08
0.12
12:00 15:00 18:00 21:00 00:00 03:00 06:00 09:00 12:00
22Jan1997 23Jan1997
Flo
w (
cfs
)
0
100
200
300
400
500
600
700
SAME ZONE OBSERVED PRECIP-INC BASIN COMPUTED FLOW CORABELL OBSERVED FLOW
Parameter “Optimized” estimate
tp, hr 4.69
cp 0.73
initial loss, in 0.11
uniform rate, in/hr 0.09
Calibration results from 5.51 sq mi watershed
ErrorIter. tP(hr)
CP Initialloss(in)
Uniformloss rate
(in/hr)Peak(%)
Volume(%)
Time ofpeak(hr)
Obj.function
0 1.06 0.48 0.48 0.13 . . . .
1 0.92 0.40 0.03 0.18 16.5 1.3 -0:20 72.1
2 0.81 0.33 0.02 0.18 12.1 -0.3 -0:20 67.5
3.
.
.
0.75.
.
.
0.30.
.
.
0.02.
.
.
0.18.
.
.
12.8.
.
.
0.8.
.
.
-0:20.
.
.
65.3.
.
.
Finaltrial
0.42 0.17 0.02 0.17 10.8 3.0 -0:40 51.2
Woo-hoo
Calibration results from 5.51 sq mi watershed
ErrorIter. tP(hr)
CP Initialloss(in)
Uniformloss rate
(in/hr)Peak(%)
Volume(%)
Time ofpeak(hr)
Obj.function
0 1.06 0.48 0.48 0.13 . . . .
1 0.92 0.40 0.03 0.18 16.5 1.3 -0:20 72.1
2 0.81 0.33 0.02 0.18 12.1 -0.3 -0:20 67.5
3.
.
.
0.75.
.
.
0.30.
.
.
0.02.
.
.
0.18.
.
.
12.8.
.
.
0.8.
.
.
-0:20.
.
.
65.3.
.
.
Finaltrial
0.42 0.17 0.02 0.17 10.8 3.0 -0:40 51.2
Oops
•Cookbookery. … to force all problems into … one or two routine techniques, insufficient thought being given to real objective … or to relevance of assumptions …
•Mathematistry. …development of theory for theory's sake, …tendency to redefine problem rather than solve it.
G.E.P. Box (1976) "Science and Statistics" J. Amer. Stat. Assoc. 71, 791-799.
Verify or validate?
• “…determination that model indeed reflects behavior of real world” (US Dept. of Energy)
• Verification and validation impossible (Oreskes, et. al, Science, 1994) because:
•Hydrologic systems not closed(p ⇔ q)
•Model results non-unique
Confirm
• Confirm partially by demonstration of agreement between observation and prediction
• Options
•Split record
• Independent estimate
USGS photo
USGS photo
CN
“Calibrated”HEC-HMSmodel
“Calibrated”HEC-HMSmodel
Annual exceedence probability
DischargeRainfall depth
Time
map from USGS, Open-File Report 2008-1084
12.5 sq mi + upstream watershed; no gage;
Good rainfall data for 1986 event; used as pattern for 3-day design event
100-yr 72-hr storm peaks
2296NT Drain
1973Spanish Springs outflow
Q100 with CN (cfs)
Location
Not consistent with Q/A for nearby gaged
watersheds
Green-Ampt model
Green-Ampt model parameters
Flood Control District of Maricopa County
100-yr 72-hr storm peaks
14022296NT Drain
8271973Spanish Springs outflow
Q100 with G-A (cfs)
Q100 with CN (cfs)
Location
DRAFT
Should we ever force the lid?
Time of forecast
“Look back” period Forecast
Time of forecast
“Look back” period Forecast
Time of forecast
“Look back” period Forecast
• Use I-O pairs that are representative
• Don’t be kidnapped by cookbookery, mathematistry, naïve trust
• Confirm results