1 koray k. yilmazmaitreya yadav hoshin guptathorsten wagener...

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Koray K. Yilmaz Maitreya YadavHoshin Gupta Thorsten Wagener

koray@hwr.arizona.edu, hoshin.gupta@hwr.arizona.edu, thorsten@engr.psu.edu, muy125@psu.edu

NWS OFFICE OF HYDROLOGIC DEVELOPMENTAnnual Meeting, 01/20/2006

Parameterization and Parameter Estimation of Distributed Models For Flash Flood and River Prediction

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• Parameterization of semi-distributed and distributed hydrologic models within Hydrology Laboratory-Research Modeling System (HL-RMS) framework

• Distributed parameter estimation - automated and/or semi-automated (e.g. regularization)

• A priori methods for parameter estimation in un-gauged basins using direct inference from watershed properties and statistical regression analysis

Objectives

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Work Completed Until Previous Annual Presentation (01/17/05)

• Hydrology Laboratory-Research Modeling System (HL-RMS) was implemented at the University of Arizona and tested

• Literature review of the frameworks developed for incorporating watershed physical properties (i.e. geology, soil properties, remote sensing)to model structure identification and parameter estimation

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SYSTEMINVARIANTS

MODELDYNAMIC

RESPONSEBEHAVIOR

INPUTSTATE

OUTPUT

CONCEPTUAL STRUCTUREFUNCTIONAL FORM

PARAMETER VALUES

DATA

ASSIMILATION

TOP-DOWN BOTTOM-UP

WATERSHEDA PRIORI KNOWLEDGE

DYNAMIC TO STATIC

STATIC TO DYNAMIC

Integrated Strategy (Presentation 1/17/05)

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Work Completed During Current Project Year (01/17/05–01/20/06)

• Hydrology Laboratory-Research Modeling System (HL-RMS) was linked to a automated optimization algorithm called “MOSCEM” (Multi Objective Shuffled Complex Evolution – Metropolis) – enables optimization of a priori parameter multipliers

• A model diagnostic interface was developed using MATLAB® environment

• A study was undertaken to :

• Analyze the consistency between the a-priori parameter information and the information contained in the input-output data, using multi-objective optimization

• Analyze the relationship between the uncertainty in the soil hydraulic

parameters and the uncertainty in the hydrologic model parameters

• Create an uncertainty framework to constrain ensemble predictions in

ungauged watersheds utilizing watershed indices

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HillSlopeWater

Depth (m)

Flow Area(m2)

Free &TensionWater Cont.

Surface

Flow

(mm/hr)

SubsurfaceFlow

(mm/hr)

Lower Zone

Water Cont.

Percolation

(mm/hr)

Flow & Precip.Timeseries

A snapshot from the model diagnostic interface (03/16/1998 7:00 UTZ)

F T

Upper Zone

Precipitation(mm/hr)

Model Diagnostics

SandySandy

ClayeyClayey

Blue RiverBlue River

SOIL TEXTURESOIL TEXTURE

• HL-RMS with a priori (Koren et al. 2000) model parameters

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Constraining Parameters of HL-RMS (Distributed Model)

Reduce the high dimensionality of the optimization problem

a priori information Optimization using MOSCEM

Allow MULTIPLIERS to vary within a range, so that model parameters are

physically meaningful

Assume spatial pattern of model parameters are well-defined by

a priori framework of Koren et al. (2000)

Optimize the a-priori parameter grid MULTIPLIERS using Input-Output

response information

Blue RiverBlue River

Grid Min : 11 Grid Max : 54

UZFWM

Feasible Limits : 5 – 150

MULTIPLIER Limits : 0.45 – 2.77

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Multi-Objective Optimization Setup

2

1

)(1

Nt

tt MO

N

Driven Flow Non-driven Flow

O observed flow

M model simulated flow

θ Model parameter multiplier

2

)(

Piapriorii

aprioriiiFPAR

PENALTY FUNCTION

2

1

)(1)(

Dt

tt MO

DFDATA

dWtd t

n

)()1()( FPARGFDATAGFTOTAL pd

Gd Scaling function for FDATA

Gp Scaling function for FPAR

σd error deviation of flow measurement (driven)

σn error deviation of flow measurement (non-driven)

Wd Scaling function for driven flow

P Number of optimized parameter multipliersD Driven flow time steps

N Non-Driven flow time steps Weighting parameter

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Error Variance of Streamflow Measurements• Wavelet filtering/denoisingWavelet filtering/denoising

Mother WaveletMother Wavelet•Symlet8

Denoising MethodDenoising Method•Level thresholding

Est. Err @ tEst. Err @ t

St. Dev (St. Dev (eet-3t-3: : eet+3t+3)) et+3et+2et+1etet-1et-2et-3

Moving Window

Time Step (hours)

e

FLOW TIME SERIESFLOW TIME SERIES

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Error Variance of Streamflow Measurements

BARON FORK BASIN

Lo

g(

Est

imat

ed E

rr.

Dev

iati

on

) (C

MS

)

Lo

g(

Est

imat

ed E

rr.

Dev

iati

on

) (C

MS

)

• Wavelet filtering/denoisingWavelet filtering/denoising

Mother WaveletMother Wavelet•Symlet8

Denoising MethodDenoising Method•Level thresholding

BARON FORK BASIN

FLOW TIME SERIESFLOW TIME SERIES

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Multi-Objective Optimization

)()1()( FPARGFDATAGFTOTAL pd

Baron Fork RiverBaron Fork River

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MODEL PARAMETER GRID MULTIPLIER SENSITIVITY TO DATAMODEL PARAMETER GRID MULTIPLIER SENSITIVITY TO DATA

Par

amet

er G

rid

Mu

ltip

lier

Par

amet

er G

rid

Mu

ltip

lier

BARON FORK RIVERBARON FORK RIVER

ParameterParameter

Multi-Objective Optimization

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Feasible SpaceFeasible Space

Objective FunctionObjective Function

LowHigh

MODEL PARAMETER GRID MULTIPLIER SENSITIVITY TO DATAMODEL PARAMETER GRID MULTIPLIER SENSITIVITY TO DATABARON FORK RIVERBARON FORK RIVER

Multi-Objective Optimization

ParametersParameters

DataData

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Baron Fork River – Calibration PeriodBaron Fork River – Calibration Period

Multi-Objective Optimization• Comparison of observed and simulated flowsComparison of observed and simulated flows

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Baron Fork River – Verification PeriodBaron Fork River – Verification Period

Multi-Objective Optimization• Comparison of observed and simulated flowsComparison of observed and simulated flows

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Multi-Objective Optimization

Until Now…Until Now…

Sacramento ModelConceptual Parameters

DATASoil Hydraulic Parameters

Soil Texture

Pedotransfer Pedotransfer FunctionsFunctions

Koren Koren EquationsEquations

CalibrationCalibration

Next…Next…Incorporate Uncertainty

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USDA Soil Texture Triangle

Analysis of Uncertainty in Soil Hydraulic Parameters

LEVEL “0”LEVEL “0”

INFOINFO

SOIL HYDRAULIC SOIL HYDRAULIC

PARAMETERSPARAMETERS

MODEL MODEL PARAMSPARAMS

% SAND θsat θfld UZTWM

%CLAY Ψsat θwlt UZFWM

CN Ψfld µ UZK

Ds Ψwlt ZPERC

b REXP

Ks PFREE

LZTWM

LZFPM

LZFSM

LZPK

LZSK

PEDOTRANSFERPEDOTRANSFERFUNCTIONSFUNCTIONS

PEDOTRANSFERPEDOTRANSFERFUNCTIONSFUNCTIONS

KORENKOREN EQUATIONSEQUATIONS

CN : Curve NumberDs : Stream Channel Densityθ : Soil moisture contentΨ : Matric potentialKs : Hydraulic conductivity @ saturationµ : Specific Yield

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USDA Soil Texture Triangle

Analysis of Uncertainty in Soil Hydraulic Parameters

LEVEL “0”LEVEL “0”

INFOINFO

SOIL HYDRAULIC SOIL HYDRAULIC

PARAMETERSPARAMETERS

MODEL MODEL PARAMSPARAMS

% SAND θsat θfld UZTWM

%CLAY Ψsat θwlt UZFWM

CN Ψfld µ UZK

Ds Ψwlt ZPERC

b REXP

Ks PFREE

LZTWM

LZFPM

LZFSM

LZPK

LZSK

PEDOTRANSFERPEDOTRANSFERFUNCTIONSFUNCTIONS

PEDOTRANSFERPEDOTRANSFERFUNCTIONSFUNCTIONS

KOREN KOREN EQUATIONSEQUATIONS

CN : Curve NumberDs : Stream Channel Densityθ : Soil moisture contentΨ : Matric potentialKs : Hydraulic conductivity @ saturationµ : Specific Yield

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Analysis of Uncertainty in Soil Hydraulic Parameters Propagation of Uncertainty through Pedotransfer Functions

θsat

Ψsat

b

θfld

θwlt

µ

Soil Texture Class

Soil Texture Class

Soil Texture Class Soil Texture Class

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SandySandy

ClayeyClayey

Only “Silty Loam”

“Silty Clay” dominated

Feasible Parameter RangesFeasible Parameter RangesUpperUpper 300 150 0.75 350 5 0.8 500 1000 400 0.05 0.35LowerLower 10 5 0.10 5 1 0 10 10 5 0.001 0.01

Sil

ty C

lay

Sil

ty L

oam

Analysis of Uncertainty in Soil Hydraulic Parameters Propagation of Uncertainty through Model Parameters

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Open Question?

The presented approach is so far based on the use of small scaledata to parameterize the model. The approach is thuslimited by the type of information contained in this data, e.g. problem with recession.

How can we include watershed scale behavior to constrain the model at ungauged sites?

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Constrain Ensemble Predictions

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

)

0 20 40 60 80 10010

-2

10-1

100

101

102

Percentage time flow is exceeded

Flo

w (

mm

/d)

Flow Duration Curve (Mean Normalized Flow)

(a)

(b)

(c)

(d)

The regionalization of model parameters is limited by model structuralproblems, problems of formulating the calibration task, data error etc.

A different approach is the regionalization of watershed behavior!

Pilot study using 30 UK watersheds.

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20 40 60 80 100 120 140 1600

0.2

0.4

0.6

0.8

1

DPSBAR

Run

off

Rat

io

Prediction Limits

Confidence Interval

Line of Regression

0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.01

0.02

0.03

0.04

0.05

BFIHOST

FD

C S

lope

R2 = 0.69

R2 = 0.58

(b)

(a)

y = 0.045 - 0.031*xy = 0.215 + 0.003*x

Initial test regionalizing two characteristics:

[1] The Runoff Ratio (Runoff/Precipitation)

[2] Mean slope of the flow duration curve (FDC Slope)

Watershed characteristics used are DPSBAR (topographic slope)and BFIHOST, a baseflow index derived from physical characteristics.

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SOIL MOISTURE ACCOUNTING ROUTING

VERTICAL PROCESSES HORIZONTAL PROCESSES

HUZ

XHUZ XCUZ

b

OV1

OV2

PPET

SLOW FLOW

QUICK FLOW

Xq1 Xq2 Xq3

Xs

Kq Kq Kq

Ks

QQ

F0 1

SOIL MOISTURE ACCOUNTING ROUTING

VERTICAL PROCESSES HORIZONTAL PROCESSES

HUZ

XHUZ XCUZ

b

OV1

OV2

PPET

SLOW FLOW

QUICK FLOW

Xq1 Xq2 Xq3

Xs

Kq Kq Kq

Ks

QQ

F0 1

Using a simple 5-parameter hydrologic model as test case:

(Remember that the approach is generally model independent!)

We ran a Uniform Random Sampling selecting 10,000Parameter sets from the a priori feasible space.

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We can constrain the feasible parameter and therefore the output spaceusing the regionalized dynamic behavior at the ungauged site:

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We can combine different constraints to achieve even ‘sharper’ predictions:

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Conclusions

1) Investigated a structured & logical Multi-Criteria Approach to assimilating Information into a distributed hydrologic model:

• A-priori Watershed Properties information (local information)• Watershed Input-Output Response information (global information)

2) Includes a way to handle estimates of uncertainty:

• Watershed Soil Property uncertainty• Streamflow Data uncertainty

3) Towards ensemble predictions in gauged and ungauged watersheds utilizing information derived at different scales

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• Faster Computing Time (parallel computing, use of computer clusters)

• Improved Handling of Multipliers

- Currently highly effected by the outliers in the a priori parameter grids

- Will look into clustering, non-linear transformation techniques

• Procedures for Diagnosing & Fixing Model Deficiencies

• Constraining hydrologic model behavior in ungauged basins within an uncertainty framework using regionalized watershed behavior

• More Complete Treatment of Uncertainty

- Uncertainty arising from the pedotransfer functions

- other aspects such as input, model structure uncertainty

Future Work

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• Yilmaz, K., Hogue, T.S., Hsu, K.-L., Sorooshian, S., Gupta, H.V. and Wagener, T. 2005. Evaluation of rain gauge, radar and satellite-based precipitation estimates with emphasis on hydrologic forecasting. Journal of Hydrometeorology. 6(4), 497–517.

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

• Yadav, M., Wagener, T. and Gupta, H.V. Regionalization of dynamic watershed behavior. In Andréassian, V., Chahinian, N., Hall, A., Perrin, C. and Schaake, J. (eds.) Large sample basin experiments for hydrological model parameterization Results of the MOdel Parameter Estimation

Experiment (MOPEX) Paris (2004) and Foz de Iguaçu (2005) workshops. IAHS Redbook. In Press.

• McIntyre, N., Lee, H., Wheater, H.S., Young, A. and Wagener, T. 2005. Ensemble prediction of runoff in ungauged watersheds. Water Resources Research, 41, W12434, doi: 10.1029/2005WR004289.

•Wagener, T. and Wheater, H.S. 2006. Parameter estimation and regionalization for continuous rainfall-runoff models including uncertainty. Journal of Hydrology. In Press. (Available online 2 September 2005)

• Hogue, T.S., Yilmaz, K., Wagener, T. and Gupta, H.V. Modeling ungauged basins with the Sacramento model. In Andréassian, V., Chahinian, N., Hall, A., Perrin, C. and Schaake, J. (eds.) Large sample basin experiments for hydrological model parameterization Results of the MOdel Parameter

Experiment (MOPEX) Paris (2004) and Foz de Iguaçu (2005) workshops. IAHS Redbook. In Press.

Recent References for more Information