1

Advancing Hydrologic Ensemble Forecasting using Distributed

Watershed Models

Thorsten Wagener, Chris Duffy, Patrick Reed, Yong Tang, Katie Goodwin and Maitreya Yadav

NWS Talk May 2006

http://www.engr.psu.edu/ce/Divisions/Hydro/hydro.html

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Overall Objective

To provide reliable forecasts of hydrologic variables for different water resources tasks, at gauged and ungauged locations, including estimates of uncertainty.

Understanding how to build and work with a new generation of more complex distributed hydrologic models.

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Outline

1. Background

2. Model Building

3. Calibration

4. Observations/Hydrologic Theory

5. Simulation

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DYNAMICRESPONSEBEHAVIOR

INPUTSTATE

OUTPUT

MODEL

CONCEPTUAL STRUCTUREFUNCTIONAL FORM

PARAMETER VALUES

DATA ASSIMILATION & MODEL CALIBRATION

WATERSHEDWATERSHED CHARACT.SYSTEM INVARIANTS

A PRIORI KNOWLEDGE

MODEL BUILDINGOBSERVATIONS & HYDROLOGIC THEORY

FORECASTING

STREAMFLOWINUNDATED AREAS

WATER QUALITY

SIMULATION

UNCERTAINTY

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WATERSHED

MODELDYNAMIC

RESPONSEBEHAVIOR

CONCEPTUAL STRUCTUREFUNCTIONAL FORM

PARAMETER VALUES

WATERSHED CHARACT.SYSTEM INVARIANTS

A PRIORI KNOWLEDGE

MODEL BUILDING

FORECASTING

UNCERTAINTY

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Model Building Questions

• How to build distributed watershed models?• What is the necessary degree of coupling of

processes?• What are appropriate levels of complexity for

different water resources tasks?• What are efficient ways of domain

decomposition?

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Duffy et al. Approach

To develop physically-based, multi-scale model for water, solute, sediment, and energy budgets in complex large-scale hydrologic systems

MOTIVATION:• to simplify complex, large-scale spatio-temporal models • to study or uncover new and emergent physical

phenomena in coupled hydrologic systems• to provide reliable water, solute and energy budgets• to estimate recharge, bank storage, ephemeral stream

losses, climate and landuse effects across river basins• to provide predictive tools for water resource forecasting

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Integrated Hydrologic Model (PIHM)

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Unstructured Grid - TINs

Flexibility in fitting a complex-shaped domain

– Ability to grade from small to large elements over a relatively short distance

– Decrease in number of nodes

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Nested Triangulation

Seamless assimilation of forcings and parameters at different resolutions

Combine large-scale simulations with nested mesoscale forecasts

Weber River Watershed

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General System

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Modular Modeling System (MMS)

• Background: In 1992, The USGS (George Leavesley) released a Unix-based Modular Modeling System (MMS) that incorporated their Performance and Results Measurement System (PRMS) surface runoff model.

• A more generic framework, (Leavesley et al., 1996) where different modules and model structures can be selectively combined to form an ‘optimal’ integrated model for environmental and water resources analysis.

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Major Components of MMS

• pre-process component– tools to build and analyzes the input data.

• model component– tools to apply the different models.

• post-process component– tools to analyze the output statistically and

graphically and pass the output to the decision support system or other software.

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Set-up

A schematic showing the different conceptual components of the Modular Modeling System (MMS) (Adapted from Leavesley et al. 1983)

Data Storage

GISWeasel

DataCollection

GUI

DMI DMI

Pre-Process

ModuleLibrary

Modular Model

GUI

DMI

Model

XmBuild

GUI

Visualization

Statistics

DSS

GIS Weasel

DMI

Post-Process

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Susquehanna River Basin GeoDataBase• Climate

– Temperate (controlled by polar front, prevailing westerlies & Atlantic)

– Orographic effects (P:35-45”, ET:15-50”)• Drainage

– 71,410 km2

– Main channel: 714 km– Headwaters: Finger lake uplift and

Appalachian mountain and plateau– Mouth: Chesapeake Bay, MD

• Physiography– Appalachian plateau– Ridge & Valley– Piedmont

• Hydrogeology– Flat/folded sandstone and shale– Some carbonate valleys– Some igneous dikes, sills, and fractures

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Conceptual Hydrologic Model: Susquehanna River

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Initial Results

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Weak or Strong Coupling?• Interception• Snowmelt• Evapotranspiration• Overland flow• Subsurface• Channel routing

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WATERSHED

MODELDYNAMIC

RESPONSEBEHAVIOR

INPUTSTATE

OUTPUT

CONCEPTUAL STRUCTUREFUNCTIONAL FORM

PARAMETER VALUES

DATA ASSIMILATION

& MODEL CALIBRATION

FORECASTING

UNCERTAINTY

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Background

QQ

timetime

: parameters: parameters

x : statex : state variablesvariables

z : output z : output u : input u : input

: uncertainty: uncertainty

zzttcompcomp

Model Model f f ( )( )

xxoo

uuttobsobs zztt

obsobs

Real WorldReal World

Court

esy

of

S. P

inker

uutttruetrue

zztttruetrue

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Model Calibration/D.A. Questions

• What are efficient optimization algorithms for highly complex models?

• How can parallel computing frameworks be used for efficient model calibration?

• What are appropriate calibration strategies for distributed watershed models?

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Comparison of 3 Multi-objective Population-based Search Algorithms

• Epsilon Nondominated Sorted Genetic Algorithm-II– Developed by Kollat and Reed (2005)– Extension of Deb et al. (2002)

• Multiobjective Shuffled Complex Evolution Metropolis – Developed by Vrugt et al. (2004)– Extension of Yapo et al. (1998)

• Strength Pareto Evolutionary Algorithm-II– Developed by Zitzler et al. (2001)– Extension of Zitzler & Thiele (1999)

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What are efficient optimization algorithms for highly complex models?

Testing of the efficiency and effectiveness of different multi-objective optimization algorithms resulted in improved understanding of how complex a problem can be solved in what time and with what reliability.

Test case: Sacramento model with Leaf River Data

RMSE(T): Box-Cox Transformed RMSERMSE(R): RMSE of raw data

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Reliability?

• Binary metric top ranking ratios– SPEA2 has the highest binary metric top ranking

ratio (i.e., it is the most reliable algorithm)

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Convergence?

• Dynamic unary metrics (best runs)– ε-NSGAII’s best trial run is superior to those of

SPEA2 and MOSCEM-UA

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How can parallel computing frameworks be used for efficient model

calibration?

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What are appropriate calibration strategies for distributed watershed models?

Main problem: The ‘open’ calibration of complex distributed hydrologic models is too complex. How can the calibration problem be simplified?

• For the Sacramento/HLRMS framework.

• For PIHM.

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Juniata River Basin

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Sacramento/HLRMS Model Scenarios

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Sensitivity Analysis

Which parameters dominate the model response?

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SensitivityAnalysis

Sacramento Model at Saxton

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Hierarchical Calibration

ANNUAL

HOURLY

COARSE

DETAILED

DATA MODEL

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WATERSHED

MODELDYNAMIC

RESPONSEBEHAVIOR

INPUTSTATE

OUTPUT

WATERSHED CHARACT.SYSTEM INVARIANTS

A PRIORI KNOWLEDGE

OBSERVATIONS & HYDROLOGIC

THEORY

FORECASTING

UNCERTAINTY

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Observations/Hydrol. Theory Questions

• How can our understanding about the link between watershed structure and watershed behavior be used to constrain hydrologic predictions?

• A new approach to the ungauged basins problem?

• How can we use our understanding about watershed function to decompose the model domain?

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Predictions in Ungauged Basins – October 1970

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0 100 200 300 40050Kilometers

0 100 200 300 40050Kilometers

0 100 200 300 40050Kilometers

0 100 200 300 40050Kilometers

J F M A M J J A S O N D0

0.5

1

1.5

2

Rai

n (m

m/d

)

Monthly Average Values (1980-1990)

J F M A M J J A S O N D0

0.5

1

1.5

Flo

w (

mm

/d)

J F M A M J J A S O N D0

0.2

0.4

0.6

Month

PE

(m

m/d

)

Flo

w (

mm

/d)

Percentage time flow is exceeded

Flow Duration Curve

0 20 40 60 80 10010

-2

10-1

100

101

102

0 2 40

0.5

1

P/PE

R/P

(a)

(b)

(c)

(d)(e)

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Regionalizing Watershed Behavior

BFIHOST

DLD

1 1.5 2 2.5 30

2

4

6

8

10

12

Prediction Limits

Confidance Interval

Line of Regression

R2 = 0.88195

y = -2.743.643 * x

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Ensemble Evaluation?

RELIABILITY: How much of the observations are contained by the ensemble?

SHARPNESS: How wide are the ensemble prediction ranges?

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Flo

w (

mm

/day

)

0 50 100 150 200 250 300 3500

10

20

30

Total Range Flow

Confidence Interval

Observed

Nor

mal

ized

Ran

ge

Time (days)0 50 100 150 200 250 300 350

0

0.2

0.4

0.6

0.8

1

(a)

(b)

Reliability and SharpnessF

low

(m

m/d

ay)

80 90 100 110 120 130 140 150

0

2

4

6

8

Nor

mal

ized

Ran

ge

Time (days)0 50 100 150 200 250 300 350

0

0.2

0.4

0.6

0.8

1

(a)

(b)

Coquet@Morwick

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10 20 30 40 50 60 70 80 90 100

F3 F2 R2

MA9MA8MA7MA6MA4MA3MA2

MA1ML1

MH8MH7MH6MH5MH4MH3MH2

Reliability for Confience intervals

Flow Percentiles

Res

pons

e C

hara

cter

istic

s

85 – 90%,80 – 85% 90 – 95% 95 – 100%

10 20 30 40 50 60 70 80 90 100

F3 F2 R2

MA9MA8MA7MA6MA4MA3MA2

MA1ML1

MH8MH7MH6MH5MH4MH3MH2

Sharpness for Confidence intervals

Flow Percentiles

Res

pons

e C

hara

cter

istic

s

18.5 – 26%11 – 18.5% 26 – 33.5% 33.5 – 41%

Reliability and Sharpness per Flow Percentile

Reliability Values Sharpness Values

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Time (days)

Flo

w (

mm

/day

)

0 100 200 300 400 500 600 7000

2

4

6

8

10

12

14

16

18

20

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Multiple Response Characteristics as Constraints

All 19 indices used as constraint on ensemble predictions

Dove@Kirkby Mills Reliability = 80%Sharpness = 75%Behavioral = 1%

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DPSBAR (Slope) – Median,Runoff ratio

J F M A M J J A S O N D0.5

1

1.5

2

Flo

w (

mm

/day

)

P/PE – Max Feb, Max Nov, Mean, Runoff ratio

J F M A M J J A S O N D0.5

1

1.5

2

Flo

w (

mm

/day

) Rainfall

Elevation

Hydrogeology

Tillingbourne@Shalford

BFIHOST – High flowDischarge, skewness and variability in flow,High pulse count

J F M A M J J A S O N D0.5

1

1.5

2

Flo

w (

mm

/day

)

Low Flows

Low Flows

Low and Mid Flows

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Next Step: Using U.S. MOPEX Data

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WATERSHED

MODELDYNAMIC

RESPONSEBEHAVIOR

FORECASTING

STREAMFLOWINUNDATED AREAS

WATER QUALITY

SIMULATION

UNCERTAINTY

CONCEPTUAL STRUCTUREFUNCTIONAL FORM

PARAMETER VALUES

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Simulation Questions

• How can we estimate the reliability of forecasts?

• How can we create ensemble (probabilistic) predictions of inundated areas?

• What is needed for long term simulations incl. climate change impacts (droughts & floods)?

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Probabilistic Inundation and Hazard Maps

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Partial support for this work was provided by SAHRA under NSF- STC grant EAR-9876800, and the National Weather Service Office of Hydrology under grant numbers NOAA/NA04NWS4620012,UCAR/NOAA/COMET/S0344674, NOAA/DG 133W-03-SE-0916. We thank The British Atmospheric Data Center for providing the temperature data (http://badc.nerc.ac.uk/home/index.html).

Acknowledgements

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References

Yang, T., Reed, P. and Wagener, T. 2006. How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration? Hydrology and Earth System Sciences. In Press.

Wagener, T. and Gupta, H.V. 2005. Model identification for hydrological forecasting under uncertainty. Stochastic Environmental Research and Risk Assessment. DOI 10.1007/s00477-005-0006-5.

Ajami, N.K., Gupta, H.V., Wagener, T. and Sorooshian, S. 2004. Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system. Journal of Hydrology, 298(1-4), 112-135.

Yang, T., Reed, P. and Kollat, J. 2006. … . Advances in Water Resources, in Review.Yadav, M., Wagener, T. and Gupta, H.V. 2006. Regionalization of constraints on hydrologic

watershed behavior . Advances in Water Resources, in Preparation. Wagener, T. and Kollat, J. Visual and numerical evaluation of hydrologic and environmental models

using the Monte Carlo Analysis Toolbox (MCAT). Environmental Modeling and Software, in Press pending minor Revisions.

Vrugt, J.A., Gupta, H.V., Dekker, S.C., Sorooshian, S., Wagener, T. and Bouten, W. 2006. Confronting parameter uncertainty in hydrologic modeling: Application of the SCEM-UA algorithm to the Sacramento Soil Moisture Accounting model. Journal of Hydrology, In Press.

Wagener, T. and Wheater, H.S. 2006. Parameter estimation and regionalization for continuous rainfall-runoff models including uncertainty. Journal of Hydrology, 320(1-2), 132-154.