IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND WATER-QUALITY CALIBRATION HSPF – CBWM
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Transcript of IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND WATER-QUALITY CALIBRATION HSPF – CBWM
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IMPLEMENTATION OF PEST TO IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND THE PHASE 5 SEDIMENT AND
WATER-QUALITY WATER-QUALITY CALIBRATIONCALIBRATIONHSPF – CBWM HSPF – CBWM
Modeling SubcommitteeModeling Subcommittee
Quarterly ReviewQuarterly Review
January 25, 2006January 25, 2006
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o = M (x,p,i)
What a model does:-
MInputs
iOutputs
o
Parameters p
x describes system configuration
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MInputs
iMeasurements
q
Parameters p
x describes system configuration
p= M-1 (x,i,q)
The inverse problem:-
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PESTPEST Parameter estimation: iterative Parameter estimation: iterative
processprocess Pest minimizes the weighted sum of Pest minimizes the weighted sum of
squared differences between model squared differences between model predictions and measured data.predictions and measured data.
Gauss-Marquardt-Lavenberg Gauss-Marquardt-Lavenberg algorithmalgorithm
Singular Value DecompositionSingular Value Decomposition
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qi
oi
ri
m
1i
2ii )rw(
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Hea
ds (
m)
Con
c (m
g/l *
10-3
)
very different units
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The weight pertaining to each observation should be proportional to the inverse of the standard deviation associated with each observation.
Theoretically:-
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Nonlinear parameter estimation …..
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Initial parameter estimate:-
o0 = M( p0 )
Initial estimates
Model outcomes Nonlinear model
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Using Taylor’s theorem
o=o0 + J(p - p0 )
Parameter vector
Model outcomes Jacobian matrix
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Jacobian matrix:-
o1 / p1 o1 / p2 o1 / p3 o1 / p4
o2 / p1 o2 / p2 o2 / p3 o2 / p4
o3 / p1 o3 / p2 o3 / p3 o3 / p4
o4 / p1 o4 / p2 o4 / p3 o4 / p4
o5 / p1 o5 / p2 o5 / p3 o5 / p4
o6 / p1 o6 / p2 o6 / p3 o6 / p4
o7 / p1 o7 / p2 o7 / p3 o7 / p4
o8 / p1 o8 / p2 o8 / p3 o8 / p4
etc
One model run (at least) per adjustable parameter to calculate derivatives using finite differences.
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p1
p2
Iterative solution improvement:-
At least n+1 model runs per optimization iteration (n = no. of adjustable parameters)
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Regularization and SimultaneousCalibration…..
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Simultaneous calibrationL
ZS
N
Watershed #1 #2 #3 #4 #5
ad
jus
tab
le
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Simultaneous calibration with regularisationL
ZS
N
Watershed #1 #2 #3 #4 #5
ad
jus
tab
le
minimum deviation from estimated average
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TSPROC
Input files
Output files
PEST
writes model input files
reads model output files
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Modelcalibration conditions
Input files Input files
Output files Output files
PEST Defaultcondition
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pi36 1.0 * log(irc1) - 1.0 * log(irc12) = 0.0 1.00 regulirpi37 1.0 * log(irc12) - 1.0 * log(irc23) = 0.0 1.00 regulirpi38 1.0 * log(irc23) - 1.0 * log(irc34) = 0.0 1.00 regulirpi39 1.0 * log(irc34) - 1.0 * log(irc45) = 0.0 1.00 regulirpi40 1.0 * log(irc45) - 1.0 * log(irc1) = 0.0 1.00 regulir
For the IRC parameter
pi26 1.0 * log(uzsn1) - 1.0 * log(uzsn12) = 0.0 1.00 reguluzpi27 1.0 * log(uzsn12) - 1.0 * log(uzsn23) = 0.0 1.00 reguluzpi28 1.0 * log(uzsn23) - 1.0 * log(uzsn34) = 0.0 1.00 reguluzpi29 1.0 * log(uzsn34) - 1.0 * log(uzsn45) = 0.0 1.00 reguluzpi30 1.0 * log(uzsn45) - 1.0 * log(uzsn1) = 0.0 1.00 reguluz
For the UZSN parameter
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pi55 1.0 * log(lzsn1) = 0.90308998699 1.00 regullz2pi56 1.0 * log(lzsn12) = 0.90308998699 1.00 regullz2pi57 1.0 * log(lzsn23) = 0.90308998699 1.00 regullz2pi58 1.0 * log(lzsn34) = 0.90308998699 1.00 regullz2pi59 1.0 * log(lzsn45) = 0.90308998699 1.00 regullz2
We may also have…
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Application to the Monocacy……
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Future Work……
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Evaluate the accuracy of the model Evaluate the accuracy of the model predictions with regularizationpredictions with regularization
Determine an optimum period of Determine an optimum period of calibration/verificationcalibration/verification
Try additional criteria for the Objective Try additional criteria for the Objective function (i.e., rating curve for sediment function (i.e., rating curve for sediment calibration)calibration)
Evaluate/Eliminate insensitive Evaluate/Eliminate insensitive parametersparameters
Extend application to entire watershedExtend application to entire watershed