Forcing the lid: Calibrating HEC-HMS for flood … · Forcing the lid: Calibrating HEC-HMS for...

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