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Koray K. Yilmaz Maitreya YadavHoshin Gupta Thorsten Wagener
[email protected], [email protected], [email protected], [email protected]
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
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
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