10/12/2017Mid-Atlantic Water Resources Conference

National Conservation Training Center, W.Va | Oct 12-13, 2017

ENSEMBLE FLOOD INUNDATION FORECASTING: A CASE STUDY IN THE TIDAL DELAWARE RIVERMichael Gomez & Al fonso Mej ia

Civi l and Environmental Engineering

Pennsylvania State Universi ty

Floods are among the deadliest natural disasters but alert systems are ineffective

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Sources: http://www.nws.noaa.gov/ohd/hurricane/inland_flooding.htmlhttps://www.weather.gov/okx/HurricaneSandy

Operational flood forecasting does not show spatial distribution of floods

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Numerical Weather

Prediction model

Precipitation and temperature forecast

Hydrological model

Source: http://water.weather.gov/ahps2/hydrograph.php?wfo=phi&gage=tren4

Two types of flood inundation forecasting: Inland and coastal

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Source: http://water.weather.gov/ahps2/inundation/index.php?gage=tren4 Source: https://tidesandcurrents.noaa.gov/ofs/ofs_animation.shtml?ofsregion=db

There is a gap between inland and coastal operational flood forecasts

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My objective with this research is

Improve flood inundation forecasting by using ensemble hydrometeorological forecasts and statistical postprocessing with a coupled hydrologic/hydraulic model

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These are some questions that I address with this research

1. How skillful are medium-range flood forecast maps?

2. Are weather ensembles able to enhance, over deterministic weather predictions, the mapping of flood inundation forecasts?

3. Can statistical postprocessing improve flood inundation forecast maps?

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RHEPS is coupled to a 1-D hydraulic model to produce flood inundation maps

Precipitation and temperature

medium-range forecasts

(GEFSRv2)

Hydrological model (HL-

RDHM)

Probabilistic (11-members)

Deterministic (control member)

Observed streamflow

and tide data

Hydraulic model

(HEC-RAS)

Reference

Deterministicforecast

Raw ensemble forecast

Quantile Regression (QR) Postprocessor

Verification strategy

Postprocessed forecast maps

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Hydrometeorologicalforecasts

Flood Inundation maps

The Delaware River near Philadelphia is the study reach

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Streamflow gages Tidal gages

A comprehensive verification of the inundation maps is done for a 6-yr period (2008-2013)

Reference Deterministic

Verification strategy• Multiyear• Multiple metrics• Conditional on flow

conditions• Applied at each cross

section

Raw ensemble Postprocessed

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Flood inundation maps

forecast forecast forecast

HL-RDHM was calibrated and the performance is satisfactory

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The calibration of the HEC-RAS model is also satisfactory

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Deterministic flood inundation forecast is skillful at day 7 but highly biased

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Raw ensemble flood inundation forecast skill improves over deterministic but still highly biased

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Postprocessing flood inundation forecasts improves error, bias and skill

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Ensemble and postprocessed flood maps show improvement (day 7 lead time)

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We conclude that…

• Flood inundation maps produced with GEFSRv2 weather ensemble forecasts show atendency to underforecast high stage events.

• Hydrometeorological forecast uncertainties can introduce high errors to the floodinundation forecasts during high flow conditions in the riverine-estuarine transition zone,especially at the later lead times.

• Flood inundation maps generated with the raw ensemble hydrometeorological forecastsshow more skill and less error than the deterministic flood inundation forecasts.

• Statistical postprocessing can improve the skill and reduce error and bias on floodinundation forecasts.

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Contact informationMichael Gomez: mvg5545@psu.eduAlfonso Mejia: amejia@engr.psu.edu

Verification metricsMean Absolute Error (MAE)

The MAE quantifies the absolute average error between the simulated values and their corresponding observations. The MAE is expressed as follows:

where Xi and Yi denote the simulated and observed flow, respectively, at time i.

Root mean square error

The RMSE quantifies the absolute average error between the simulated values and their corresponding observations. Given that the error is squared before averaging the metric is sensitive to larger errors. The RMSE is given by

where Xi and Yi denote the simulated and observed flow, respectively, at time i.

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1

1MAE

n

i i

i

X Yn

2

1

( )

RMSE

N

i i

i

X Y

n

Verification metrics

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Percent Bias (PB)

PB measures the average tendency of the simulated values to be larger or smaller than the observed. The PB is given by

where Si and Yi denote the simulated and observed flow, respectively, at time i.

Nash-Sutcliffe Efficiency (NSE)

The NSE is defined as the ratio of the residual variance to the initial variance. It is widely used to measure the accuracy of the simulated flows in comparison to the observed mean. The range of NSE can vary between negative infinity to 1. Any positive value close to 1 indicates a good match between the simulated and observed variable while a negative value indicates that the observed mean is better than the simulated. The NSE is defined as:

where Si, Yi, and are the simulated, observed, and mean observed flow, respectively, at time i.

1

1

( )

PB 100,

N

i i

i

N

i

i

Y S

Y

2

1

2

1

( )

NSE 1

( )

N

i i

i

N

i i

i

S Y

Y Y

Verification metrics

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Wilmott Skill (WS)

The WS is a widely used metric for measuring the performance of hydrodynamic models, especially in tidal rivers and estuaries. The range of the WS can vary between 0 and 1. A WS value of 1 means a perfect agreement between predictions and observations, and a value of 0 represents no skill. The WS can be expressed as:

where Xi, Yi and denote the simulate, observed and mean observed stage heights, respectively, at time i.

2

1

2

1

WS 1

N

i i

i

N

i i i i

i

Y X

Y X X X

Verification metrics

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Mean Continuous Ranked Probability Skill Score (CRPSS)

Continuous Ranked Probability Score (CRPS), which is less sensitive to sampling uncertainty, is used to measure the integrated square difference between the cumulative distribution function (cdf) of a forecast, , and the corresponding cdf of the observation, . The CRPS is given by

To evaluate the skill of the main forecast system relative to the reference forecast system, the associated skill score, the mean Continuous Ranked Probability Skill Score (CRPSS), is defined as:

where the CRPS is averaged across n pairs of forecasts and observations to calculate the mean CRPS of the main forecast system ( ) and reference forecast system ( ). The CRPSS ranges from -ꝏ to 1, with negative scores indicating that the system to be evaluated has worse CRPS than the reference forecast system, while positive scores indicate a higher skill for the main forecast system relative to the reference forecast system, with 1 indicating perfect skill.

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CRPS ( ) ( ) .x yF q F q dq

main

reference

CRPSCRPSS 1 ,

CRPS

( )xF q ( )yF q

mainCRPS referenceCRPS

Statistical postprocessor (QR)

QR is a statistical method for estimating the quantiles of a conditional distribution [7, 8].

Using the training dataset a set of quantile error models are derived for individual lead times:

Where and are regression constants that are determined by minimizing the sum of the residual from the training data set:

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, , , ,ˆ Qn n n na b

1

, , ,min ,ˆ ,QN

i

n n i n i ii

Statistical postprocessor (QR)

is the weighting function for the τth quantile defined as:

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Where is the residual, defined as the difference between the observed error and the quantile regression estimated error for a given lead time and quantile . Lastly, to obtain the calibrated forecast, , the following equation is used:

, ,

, ,

, ,

1 0.n i n i

n n i

n i n i

if

if

, ,

ˆ . n nnf Q

*

n

,n i

,nf