1 Flash-flood forecast uncertainty for distributed models using radar data By Soni Yatheendradas...

Flash-flood forecast uncertainty for distributed models using radar data

Soni YatheendradasHoshin Gupta

Thorsten WagenerCarl Unkrich

David GoodrichMike SchaffnerAnne Stewart

Motivation: Flash flood importance

• What: Basin reaction time < 6 hours (as low as 15 minutes!)

• Where: Usually water-scarce arid/semi-arid regions:

1/3rd of land mass, 1/4th of mainland US, > ½ of Western US

• Loss of life: Significant in US: Highest among natural disasters (80%)

• Flood Fatalities: ~ 146/year for 1972-1991 (NWS, 1992)

• Property/economic loss: Millions of dollars in damages

• RFC’s: Continuous, lumped rainfall-runoff models (6 to 1-hourly)

• WFO’s (site-specific hydrologic guidance):

– Local model application (0.5 to 1-hourly )

– Directly from rain using Flash Flood Monitoring and

Prediction (FFMP) for small basins

• Accumulated rain

– Upstream, or @ forecast-pt

– Compared to Flash-Flood

Guidance (FFG) values

• Judgment & experience

• Accuracy improvement potential

in hydrograph timing, magnitude

Current NWS Flood-Forecasting procedures

• Missing FFMP components:

– dynamically varying soil moisture,

– highly non-linear rainfall-runoff transformation

• Semi-arid hydrology (infiltration excess,

ephemeral channels etc.) different from humid hydrology

• Rain Input: scale, resolution

• Distributed model resolution:

– Interaction scale: storm & basin geometry (Osborn,1964)

– Temporal & spatial variability

Operational flash-flood forecasting difficulty

Summertime storms: convective, high-intensity,

extremely localized, short-duration

Model!

Semi-arid physics!

Distributed input &

structure

Satellite Gage Radar

Project hypothesis: “A site-specific model for the Western Region (Western slopes of the Rocky Mountains down to the Pacific Ocean) providing specific hydrologic flash-flood forecasts would greatly improve services of the NWS and reduce potential loss of life and property”

COMET project

+ +University of Arizona Tucson NWS WFO USDA-ARS-SWRC

KINEROS2 model (used with AGWA preprocessor)

( http://www.tucson.ars.ag.gov/kineros/ &http://www.tucson.ars.ag.gov/agwa/)

WSR-88D DHR product (Maddox et al, 2002)

1 km by 1 degree,5-min data from summer 2003

Resources available (model and input)

6Flash-flood forecasting system in action (2006 monsoon)

Sabino Creek - KINEROS Site Specific Forecast Model

3 PM 4 PM 5 PM

09.06.2006

10,000

20,000

0.91 in

3.88 ft (2,298 cfs)

09.06.2006 3:28 PM

Bank FullFlood

Moderate Flood

Major Flood

Problems encountered:

• Frequent parameter set

recalibration

• Especially over severe storms

(e.g. July 31, 2006) (Magirl et al., 2007)

Operational forecast Uncertainty!

“Given operational uncertainties in the radar rain estimates,

model parameters and initial conditions, the predictive

uncertainties in the semi-arid flash-flood

forecasting model would be within desirable bounds

that are low enough to significantly improve the timely

issuance and cancellation of flood warnings and alarms.”

Hypothesis

• Errors in rainfall estimates dominate modeled uncertainty in semi-

arid runoff uncertainty (Goodrich et al, 1994)

– Inaccurate spatio-temporal representation (e.g. Michaud and Sorooshian, 1994)

– Variability in volume bias of estimates (Faures et al, 1995)

• Radar estimate power law: Z=aRb

• Summertime convective: standard NWS Z-R (a = 300, b = 1.4)

• Bias: NWS Z-R too high (Morin et al, 2005 got a = 655)

• Bias variability: a, b vary across storms

Significant depth bias range of 0.58-1.8 with a = 655

– Hail contamination (truncation @ top intensities)

• Hence:

“What is the influence of errors in rainfall estimates on

model response?”

Research question # 1

• Strong non-linear dependence of runoff on initial soil moisture in semi-arid

regions (Nicolau et al, 1996)

• Hence: “What is the influence of initial soil moisture on model

response, and how complex an inter-storm component is required?”

Research questions # 2 & # 3

• Model parameters need adjustment :• Hence: “Which model parameters

strongly influence the model

response?” homog.

(xeff,eff)

output

outputiden

heterog.

measurement

Real world

Research question # 4

Rain estimate uncertainty

Initial soil moisture uncertainty

Model parameter uncertainty

Hence: “How reliable is such a flash-flood

forecasting model in presence of

compounding effect of these uncertainties?”

Legend

Hillslope

elements

Channels

Watershed

Outlet

Rain Gages

Stock pond

outlet

Radar Pixels

Small test basin setup: Walnut Gulch Flume 11 (WG11)

• 6.5 km2 area• Almost spatially homogenous AGWA-based a priori parameters

12Methodology and Analytical tools

• Gage/radar rainfall merging• A priori parameter evaluation runs• Monte-Carlo simulations

– Spatial modifiers on 24 factors– 2 sets of runs

• Generalized Likelihood Uncertainty Estimation (GLUE) framework

• Variance-based Global sensitivity analysis• Multi-objective information in hydrograph

Rain + Initial condition + parameters

Initial condition + parameters

13Results obtained: Rainfall intercomparison

Event 6 Gage Rain Input

UTC time on Jul. 29, 2006

Simulations

Observed

6Event 6 Depth Bias-adjusted Radar Rain Input

6Event 6 Merged Rain Input

Uncertainty in spatial distribution

Merged • More behavioral factor set consistency across peaks• Better replication of peaks

Functional inconsistency

Structural inconsistency

Results obtained: Sensitivity Analysis (SA)Rain influence on response

Peak m

Peak t

15Results obtained: Sensitivity Analysis (SA)Relative rain influence on response (1st set of runs)

NSE Multi-objective Behavioral

16Results obtained: Sensitivity Analysis (SA)

Answer to research question # 1:

“While merging of high spatial resolution gage and radar

estimates might potentially provide better simulations

than either one by itself, the influence of rain

depth/volume bias uncertainty clearly almost completely

dominates the model response.”

17Results obtained: Sensitivity Analysis (SA)Model parameters’ influence on response (2nd set of runs)

ial co

Answer to research question # 2:“In general, uncertainties in the hillslope model parameters

impact predictions more than those in the channel

parameters for small basins. The most influential hillslope

parameter uncertainties stem from the soil saturated

hydraulic conductivity, the soil volumetric rock fraction, and

the soil surface roughness, while those for the channel are

from the soil surface roughness and the Woolhiser coefficient.

19Results obtained: Sensitivity Analysis (SA)Initial condition influence on response (2nd set of runs)

e init

“Initial hillslope soil moisture can have a dominant effect

on the predicted response. Hence, sophisticated inter-

storm model components are required to track it with a

high degree of accuracy.”

21Results obtained: Model predictive uncertainty

Uncertainty from prior events on E6P1: 90% confidence

0 UTC time on Jul. 29, 2006

Confidence Limits

Observed

Uncertainty from all events on E6P1: 90% confidence

Confidence Limits

Observed

(a)(b)

22Results obtained: Model predictive uncertainty

“Given current uncertainties in the radar rain estimates,

model parameters and initial conditions, the predictive

uncertainties in flash-flood forecasting can be much higher

than desired. Using a model is still a valuable tool for

forecasters, giving a reliable quantitative risk-based tool

for timely issuance and cancellation of flood warnings and

alarms.”

23Unresolved issues

• Behavioral factor set inconsistency

• No reduction in factor ranges

• Causes: Model structural error? Distributed model nonlinearity? Inadequate factor space sampling? Data errors?

– Synthetic study required!!

Sensitivity comparison with real data case: 23 factors

• Factor influences similar to those in real data study

• Behavioral factor set inconsistency due to inadequate

factor space sampling

• No reduction in factor set ranges due to high

distributed model non-linearity and parameter

interactions

Synthetic study conclusions

26Overall Study Results

• Methodology for operational flash-flood forecasting

with uncertainty• Applicable even when behavioral factor set

inconsistency exists• Uncertainty in bias of rain estimates from radar

recognized as biggest source of uncertainty• Influential yet poorly defined model parameters • Sophisticated inter-storm model component required

for continuous operational forecasting mode• Possibly similar results if strict behavioral constraints

set on humid hydrology models also: towards reducing

predictive uncertainty

“This is what we mean by science. That both question and answer are tied up with uncertainty, and that they are painful. But that there is no way around them. And that you hide nothing; instead, everything is brought out in the open.” -- Peter Høeg (1995), Borderliners

Acknowledgements:• COMET program• SAHRA NSF-STC• Soren Scott, University of Nebraska-Lincoln• Paul Jendrowski, NOAA-NWS• Stefano Tarantola, Joint Research Center, Italy

Conceptualization

Mathematical Representation (Equations)

System Invariants (Parameters)

U(t) f

Model(Prognostic Variables)

Output(Diagnostic Variables)

Forcing(Input Variables)

State(Prognostic Variables)

KINEROS2 Deterministic Simulation

[Rain]

[Initial Soil Moisture]

[Outflow]

[Soil moisture]

[Kinematic surface flow, Parlange 3-parameter infiltration etc.]

From HWR642

Results obtainedResults obtained

Results obtained: Behavioral ranges & correlations in Factors Factor correlation structures

pKsM vs. RainM (0.6-0.7)

• RainM in infiltrability equation

• Scaling: r*=(r - Ksmodel) / Ks

pKsM vs. pRocM (0.45-0.62)

• In model constraining equations

• Gr = ( (1- Ø) * (1- Vr) ) / (1- Ø * (1- Vr) )

• Ksrock = Ks

text * Gr

• Ksmodel = Ks

rock * (e0.0105*CI)

• Ksmodel=Ks

text *((1- Ø)*(1-Vr))/(1-Ø*(1- Vr))(e0.0105*CI)

+ve: quotient or difference

Difference: +ve corr.

Quotient: +ve corr.

No strong directional components in PCA

Results obtained: Sensitivity Analysis (SA)Rain influence on response

Peak m

Peak t

Answer to research question # 2:“In general, uncertainties in the hillslope model parameters

impact predictions more than those in the channel

parameters for small basins. The most influential hillslope

parameter uncertainties stem from the soil saturated

hydraulic conductivity, the soil volumetric rock fraction, and

the soil surface roughness, while those for the channel are

from the soil surface roughness and the Woolhiser coefficient.

• Note: factor identifiability factor sensitivity

• Already identified factors: hillslope soil saturated hydraulic

conductivity, hillslope soil surface roughness, channel soil surface

roughness, channel Woolhiser coefficient

33Research Motivation: Future importance of flash floods

• Future climate: Increasingly drier, more variable

• More arid regions: Due to global warming?

• Extreme precipitation: Increased global incidence (e.g., IPCC, 2001),

changing hydrological cycle (Oki & Kanae, 2006)

Task 1: Model Recoding and Task 1: Model Recoding and operational model performance operational model performance

Recoding of KINEROS2

• Outer space, inner time (Space-time) loop

• Procedural paradigm-based Fortran 77 code

• Well-defined, but dependent components of a

monolithic code

Earlier version

• Outer time, inner space (Time-space) loop for forecasting

• Object-oriented library of self-contained modules

• Easy future extensibility

• Code improved (applicable now to large basins)

New version

• Real-time forecasting requirement

• Current advances in computing

resources

• Object-oriented paradigm in Fortran

Changes

A PRIORI ESTIMATION VIEW:

IF a watershed model is theory-based & structurally consistent with reality & available distributed data

THEN all parameters specifiable directly from data & no calibration required.

CALIBRATION VIEW:

Watershed models are perceptual & conceptual simplifications of reality, so

certain model invariants will not correspond directly to observable

properties

THEN some “calibration” necessary.

Reality generally somewhere in between

Do apriori estimation where possible and calibrate the

remaining parameters

AGWA a priori estimates not working well

Manual calibration by

USDA-ARS-SWRC

From HWR642

A priori estimation vs. calibration

Task 2: Investigating operational Task 2: Investigating operational flash-flood forecasting flash-flood forecasting

uncertaintyuncertainty

• NWS: Reliable model-based flash-flood forecasts with acceptable

uncertainty levels

• Scientific: – Refining uncertainty in parameter estimates (Philosophy of

progressive uncertainty reduction)

• Consequent narrower forecast uncertainty

• Future regionalization efforts: ungaged basins

– Sensitivity/uncertainty analysis

• Uncertainties in Dominant but poorly identified/known

parameters needing reduction (field investigations)

• Redundant parameters fixable to reduce calibration burden

• Modifications needed in parameter-corresponding model

processes

Objectives

• Radar hail threshold– NWS: 103.8 mm/hr

– Can be 75-150 mm/hr (Fulton et al, 1998)

– Five-min max.:

• Gage data : ~ 250 mm/hr (Mendez et al,, 2003)

• Radar data max. : > 103.8 mm/hr (Morin et al, 2006)

– Flash-flood forecasting: • high-intensity, short return period (~10 yrs)

• Merging gage & radar– Gage data depth “more reliable” (0.01” accuracy)

Methodology and Analytical tools: Gage-radar merging

146.3 mm/hr (Mendez et al,, 2003)

Areal gage data

‘Point’ gage data

Thiessen weighting

Bulk adjustment

Gage-radar time lag

adjustment

Areal radar data

Adjusted radar data

Averaging Merged

45Methodology and Analytical Tools: Multi-objective informationFormulating objective functions (OFs): Minimization problem

obssim

magnitudePeak

magnitudePeakmagnitudePeakFQPge

)()(.,.

Normalized:

46Methodology and Analytical Tools: Multi-objective informationFormulating likelihood functions (LFs): Maximization problem

LFtemp = (OF)max-

LFtemp

LFtemp2

• 0 is non-behavioral

LF = LFtemp2 / sum

( LFtemp2 )• Summation to 1

Hence, e.g.:

Shape descriptor: Peak magnitude

OF: FQP

LF: LFQP

47Methodology and Analytical Tools: Multi-objective information

Initial Feasible factor

Uncertainty space

Overall behavioral factor

Uncertainty space

“Original” shape-based LFs

Overall behavioral LFB information

“Enhanced” shape-based LFs: combinedInformation

Overall behavioral: Monte Carlo Set-Membership Methodology (MCSM)(Van Straten & Keesman, 1991)

• Upper and lower behavioral constraint around observations• On a combination of basic shape descriptors here: LFB likelihood function

Uncertainty BoundsUncertainty BoundsQ

QNon-behavioral factor sets

Behavioral factor setsNon-behavioral factor sets

Behavioral factor sets

Illustrations by Koray Yilmaz

49Results obtained: Rainfall intercomparison

Gage vs. radar

50Results obtained: Behavioral ranges in Factors

Behavioral classification:

• Resultant uncertainty reduction : None !

• % of behavioral simulations: (<1%) !

• Only some restructuring tendency of some

distributions away from uniform (identifiability):

• PKsM (hillslope hydraulic conductivity)

• PnM (hillslope roughness)

• CnM (channel roughness)

• CWCoM (channel Woolhiser coefficient:

wetting)

• RainM (rain depth)

0.5 1 1.5 2

ParPostDis:WG11_23Par: BehLeast

0.5 1 1.5

x 10-5

0.8 1 1.2 1.4

x 10-5

0.8 0.9 1 1.1 1.20.5

2.5x 10

0.8 0.9 1 1.1 1.20.60.8

11.21.41.6

x 10-5

0.8 0.9 1 1.1 1.2

0.8 0.9 1 1.1 1.20.60.8

11.21.41.61.8

x 10-5

0.02 0.04 0.06

0.05 0.1 0.15 0.2 0.25

x 10-5

0.8 0.9 1 1.1 1.20.5

x 10-5

0.85 0.9 0.95 1 1.050.5

x 10-5

0.5 1 1.5 2

2.5x 10

0.5 1 1.50.5

x 10-5

0.5 1 1.5 2

0.02 0.04 0.06 0.08

x 10-5

0.8 1 1.2 1.40.60.8

11.21.41.61.8

x 10-5

0.9 0.95 1 1.05 1.10.5

x 10-5

0.5 1 1.5 2 2.5

0.4 0.5 0.60.5

x 10-5

0.960.98 1 1.021.041.061.08

0.3 0.4 0.5

x 10-5

0.3 0.4 0.5

0.5 1 1.5 2

ParPostDis:WG11_23Par: BehLeast

0.5 1 1.5

x 10-5

0.8 1 1.2 1.4

x 10-5

0.8 0.9 1 1.1 1.20.5

2.5x 10

0.8 0.9 1 1.1 1.20.60.8

11.21.41.6

x 10-5

)0.8 0.9 1 1.1 1.2

0.8 0.9 1 1.1 1.20.60.8

11.21.41.61.8

x 10-5

0.02 0.04 0.06

0.05 0.1 0.15 0.2 0.25

x 10-5

0.8 0.9 1 1.1 1.20.5

x 10-5

0.85 0.9 0.95 1 1.050.5

x 10-5

0.5 1 1.5 2

2.5x 10

0.5 1 1.50.5

x 10-5

0.5 1 1.5 2

)0.02 0.04 0.06 0.08

x 10-5

0.8 1 1.2 1.40.60.8

11.21.41.61.8

x 10-5

0.9 0.95 1 1.05 1.10.5

x 10-5

0.5 1 1.5 2 2.5

0.4 0.5 0.60.5

x 10-5

0.960.98 1 1.021.041.061.08

0.3 0.4 0.5

x 10-5

0.3 0.4 0.5

Entire Range

Restructuring

No restructuring

51Results obtained: A priori run evaluation on Walnut Gulch

Results obtained: Correlations in LFs

• Correlations in 5 original basic LFs :

• LFQP vs. LFVU (peak magnitude vs. volume)

• Hence:

• No correlations in 5 basic enhanced LFsU

Peak magnitude

Peak timing

End timing

Entire factor space

LFTSStart timing

• Enhanced LF SA indices similar to LFB indices

(behavioral)

– Low Power : Low % of behavioral simulations

– From here, only LFM (Multi-objective) & LFB

(behavioral) used.

Results obtained: Sensitivity Analysis (SA)

Task 3: Synthetic study of Task 3: Synthetic study of uncertainty in flash-flood model uncertainty in flash-flood model

predictions predictions

1 J ul. 29 '03 21:27 1 3.70 65822 Aug. 25 '03 19:35 1 2.68 64863 Aug. 28 '03 0:26 1 8.28 175734* Aug. 09 '05 23:09 1 1.271 2357

5 J ul. 29 '06 6:29 2

4.99 245336* J ul. 30 '06 14:24 1 2.46 55347* J ul. 31 '06 11:51 1 2.27 4433

* Rain modifier 1.3

volume

(cu. m.)

# Date (UTC)

Events used

57Reduced factor range behavioral consistency

21 22 23

Behavioral factor set consistency over reduced factor

ranges -> Sampling density inadequate over original range

Sensitivity comparison with reduced number of factors

59Results obtained: Predictive uncertainty comparison

(m3 /s

Uncertainty from prior events for 23 factors: 90% confidence

Confidence Limits

Observed

(m3 /s

Uncertainty from prior events for 8 factors: 90% confidence

Confidence Limits

Observed

23 factors 8 factors

60Spatial factor sensitivity

Hillslope soil saturated hydraulic conductivity: 10% perturbation

Digital Elevation model (DEM)

Watershed Discretization

Parameters: Grid to elemental

Land Cover

Model elemental parameter

AMBER GISRadar grid shapefile

AMBER code or DHR decoder

Pixel weights in

model elements

Pixel reflectivities from DHR

Pixel rains

KINEROS2 rain preprocessor module

KINEROS2 code execution

Model elemental rains

KINEROS2

Results

Single model run setup

Event hydrograph

Methodology and Analytical Tools: Multi-objective information

Peak magnitude

Peak timing

Volume

Start timing

End timing

Basic shape descriptorsInflection point

1 Flash-flood forecast uncertainty for distributed models using radar data By Soni Yatheendradas...

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