A Statistical-Distributed Hydrologic Model for Flash Flood Forecasting

International Workshop on Flash Flood ForecastingMarch 13, 2006

Seann Reed1, John Schaake1, Ziya Zhang1,3

1Hydrology Laboratory, Office of Hydrologic DevelopmentNOAA National Weather Service, Silver Spring, Maryland

2Consultant to Office of Hydrologic Development, Annapolis, MD 

3University Corporation for Atmospheric Research

Flash Flood Forecasting Goals and Strategies

• Goals– Improve accuracy– Improve lead times

• Hydrologic Modeling Strategies – Investigate a statistical-distributed hydrologic model

• Understand model errors at flash flood scales• Compare distributed model results to FFG results• Validate inherent bias correction of the statistical-distributed

model

– Investigate the use of high resolution, short-term QPF grids to force the statistical-distributed model

• Force the model with grids from the Multisensor Precipitation Nowcaster (MPN)

NWS Flash Flood Guidance (FFG)

TR

FFGWRainfall Depth

Run

off

Dep

th

FFGD

Wet

Dry1650 km2

800 km2

285 km2

(1) River Forecast Center (RFC)

Maintains 6 hr Lumped Model

Forecast points

(2) RFC Runs Flash Flood Guidance System

1 hr Gridded FFG

(3) RFC transmits FFG to Weather Forecast Offices

(WFO)(4) Forecaster compares mean areal basin rainfall (ABR) to FFG in in small, flashy basins (5 - 260 km2).

TR = Threshold runoff

Scale mismatch!

0

20

40

60

80

10 100 1000 10000

Area (km2)

Ave

rag

e %

A

bs.

Pe

ak

Flo

w E

rro

rs

0.0

0.3

0.6

0.9

1.2

Rq

High Resolution Modeling Brings Potential Benefits but Also Increased Uncertainty

• FFG system uses lumped (260 – 4000 km2) soil moisture states.

• A distributed hydrologic model can make computations at spatial and temporal scales consistent with flash flooding.

• Model errors tend to increase at smaller modeling scales.

• Will increased model errors in small basins mask the benefits of making calculations at the appropriate scales?

Flash floods

260

Distributed model (uncalibrated). Each point is an average peak flow error from approximately 25 events over an eight year study period.

Scaling relationship for an uncertainty index (Rq) from Carpenter and Georgakakos (2004) (secondary axis)

Log-linear regression for distributed model data

Forecastfrequencies

A Statistical-Distributed Model for Flash Flood Forecasting at Ungauged Locations

HistoricalReal-time

simulated historical

peaks (Qsp)

Simulated peaks distribution (Qsp) (unique for each

cell)

Archived

QPE

Initial hydro model states

StatisticalPost-processor

Distributed hydrologic

model

Distributed hydrologic

model

Real-time

QPE/QPF

Max forecastpeaks

• The statistical-distributed model produces gridded flood frequency forecasts.

• We express flood frequencies in terms of the Average Recurrence Interval (ARI) associated with the annual maximum flood.

Local/regional knowledge

Frequencythresholds

Compare

Why a frequency-based approach?

• Frequency grids provide a well-understood historical context for characterizing flood severity; values relate to engineering design criteria for culverts, detention ponds, etc.

• Computation of frequencies using model-based statistical distributions can inherently correct for model biases.

– This hypothesis is validated through probability matching at gauged locations (results in slide 10)

Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM)

• This implementation of HL-RDHM uses:– 2 km grid cell resolution

– 8 years of hourly, 4 km QPE and QPF grids are resampled to 2 km (nearest neighbor resampling)

– Gridded SAC-SMA

– Hillslope routing within each model cell

– Cell-to-cell channel routing

– Uncalibrated, a-priori parameters for Sacramento (SAC-SMA) and channel routing models (Koren et al., 2004)

• Similar HL-RDHM implementations showed good performance in the Distributed Model Inter-comparison Project (DMIP) (Smith et al., 2004; Reed et al., 2004)

• An operational prototype version of HL-RDHM is running at two NWS River Forecast Centers (slated for official delivery in Fall 2006)

Study Basins

OK

AR

INX Radar

SRX Radar

N

No Short Station Name Area Period of record Time toName (km2) (hourly flow) peak (hrs)

1 SPRINGT Flint Ck at Springtown AR 36.8 6/1993-9/2004 3

2 SSILOAM Sager Ck nr W. Siloam Springs OK 48.9 9/1996-9/2004 3

3 CHRISTI Peacheater Ck at Christie OK 64.7 5/1993 - 9/2003 6

4 CAVESP Osage Ck near Cave Springs AR 89.9 4/2000-9/2004 4

5 DUTCH Baron Fork at Dutch Mills AR 105.1 10/1992-9/2004 2

6 KNSO2 Flint Ck near Kansas OK 284.9 6/1993- 9/2004 6

7 ELMSP Osage Ck near Elm Springs AR 336.7 10/1995-9/2004 7

8 ELDO2 Baron Fork at Eldon OK 795.1 10/1992 - 9/2004 13

9 ISILOAM Illinois R. South of Siloam Springs AR 1489.2 7/1995 - 9/2004 17

10 TALO2 Illinois R. near Tahlequah OK 2483.7 6/1993-9/2004 37

Interior,Flash floodbasins

Basins are well covered by either the INX or SRX radar

0102030405060708090

SPRINGT

SSILO

AM

CHRISTI

CAVESP

DUTCHA

vera

ge

Pe

rce

nt A

bso

lute

P

ea

k F

low

Err

or

Lumped States (FFG-Like) Distributed (Uncalib.)

• Peak flow errors are averages from approximately 25 events over an eight year study period. Peak flow errors are computed regardless of time.

• Correlation coefficients are based on the same events.

Distributed Model Simulations Compared to FFG-Like Simulationsfor the 5 Smallest Basins

(for events from Oct. 1996 – Sept. 2004)

Correlation coefficientsAverage absolute percent peak

flow errors

(37 km2) (49 km2) (65 km2) (105 km2)(90 km2)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

SPRING

T

SSILO

AM

CHRISTI

CAVESP

DUTCH

Cor

rela

tion

Coe

ffic

ient

for

Pea

ks

Inherent Bias Adjustment

• We suggest that the comparing model-calculated frequencies to frequency-based thresholds can produce an inherent bias correction.

• To validate this concept, we compute inherent adjustments at validation points using probability matching. This adjustment is only done for validation as we do not have the techniques and data to make explicit adjustments at ungauged locations.

DUTCH

0

0.2

0.4

0.6

0.8

1

1 10 100 1000

Flow (cms)

Pro

b. o

f Occ

urre

nce

Simulated161 cms

Adjusted271 cms

Simulated

Observed

DUTCH

0

0.2

0.4

0.6

0.8

1

1 10 100 1000

Flow (cms)

Pro

b. o

f Occ

urre

nce

Simulated161 cms

Adjusted271 cms

Simulated

Observed

Simulated

Observed

0

10

20

30

40

50

60

70

SPRINGT

SSILOAM

CHRISTI

CAVESP

DUTCH

Ave

rage

Per

cent

Abs

olut

e P

eak

Err

or

Distributed, Uncalibrated

Distributed, Uncalibrated w/ Adjustment

SPRINGT

0

50

100

150

0 50 100 150

Obs Qpeak (cms)

Sim

Qpe

ak (

cms)

Worst basin: inherent adjustment degrades peak results by 1% on average

Best basin: inherent adjustment improves peak results by 14% on average

Gain from Inherent Bias Adjustment

One inconsistently simulated event has a big impact

DUTCH

0

200

400

600

0 200 400 600

Obs Qpeak (cms)

Sim

Qpe

ak (

cms)

Distributed, Uncalibrated w/ Adjustment

Distributed, Uncalibrated

2 year flood flow

14 UTC 15 UTC

16 UTC 17 UTC

Maximum Forecast Frequencies at 4 Times on 1/4/1998 (Generated in hindcast mode using QPE up to the forecast time and 1 hr

nowcast QPF beyond)

In these examples, frequencies are derived from routed flows, demonstrating the capability to forecast floods in locations downstream of where the rainfall occurred.

Conclusions

• At scales down to 40 km2, results show gains from the distributed model over the current FFG method even from an uncalibrated distributed model

• Inherent bias adjustment in the statistical-distributed model further improves results

• Even further gains are possible with distributed model calibration (not shown here)

• In forecast mode, gridded QPF data from MPN can be used to force the model and gain lead time

– We have begun evaluating forecast case studies using both QPE and QPF (not shown here)