RSM Training HESM Instructional Materials for Training Purposes Only
Module 13: PEST - Introduction
Hydrologic and Environmental Systems Modeling Page 13.1
Lecture 13: PEST – Introduction. Parameter ESTimation Software
ThislectureintroducestheParameterEstimation(PEST)Software.
Formoredetailedinformation,refertothePESTUserManual,PEST:Model‐IndependentParameter
Estimation.UserManual5thEdition.Doherty,John.WatermarkNumericalComputing.July,2004.
PES
T
-Introduction
PES
T
-Introduction
Parameter ESTimation Software
Parameter ESTimation Software
John Doherty
RSM Training HESM Instructional Materials for Training Purposes Only
Module 13: PEST - Introduction
Page 13.2 Hydrologic and Environmental Systems Modeling
NOTE:
A copy of the PEST User Manual can be found in the labs/lab13 directory.
RSM Training HESM Instructional Materials for Training Purposes Only
Module 13: PEST - Introduction
Hydrologic and Environmental Systems Modeling Page 13.3
TheParameterEstimation(PEST)methodis
thebasisofthecalibrationapproachused
fortheRegionalSimulationModel(RSM).
ThePESTsoftwareisfreewaredesignedto
runonLinuxandWindows.Sincethe
methodismodelindependent,theRSM
doesnothavetobemodifiedtoworkwith
PEST.
PESThas
advancedtoolstoimprove
calibration.And,itprovidesseveral
methodsforadjustingparametervaluesto
minimizeauser‐definedobjectivefunction.
KeyfeaturesofthePESTmethodarelisted
here.Foramorein‐depthreviewofeach
feature,thereaderisencouragedtoreferto
thePESTUserManual.
2
PES
T
- Introduction
PES
T
- Introduction
Paramete
r
EST imation – (Freeware developed by John Doherty*)
Optimization of parameters using model output
Model independent
Highly flexible
• Prediction
• Regularization
• Single value decomposition
(
SVD)
* Many of the slides in this lecture are borrowed with permissionfrom
Doherty.
www.pest.com o
r
www.sspa.com/pes
t
Paramete
r
EST imation – (Freeware developed by John Doherty*)
Optimization of parameters using model output
Model independent
Highly flexible
•
Prediction
•
Regularization
•
Single value decomposition
(
SVD)
* Many of the slides in this lecture are borrowed with permissionfrom
Doherty.
www.pest.com o
r
www.sspa.com/pes
t
3
PES
T
–
Optimization Overview
PES
T
– Optimization Overview
Optimization function based on least squares
Uses Gauss-Marguardt-Levenberg algorithm fo
r
parameter estimation
One-step optimization for linear models, iterative for non-
linear models
A
djusts parameter values based on the derivatives of the
observations with respect to the parameters (i.e.,
sensitivity or Jacobian matrix)
Provides several methods for adjusting and constraining
the parameter values
Optimization function based on least squares
Uses Gauss -Marguardt-Levenberg algorithm fo
r
parameter estimation
One-step optimization for linear models, iterative for non-
linear models
A
djusts parameter values based on the derivatives of the
observations with respect to the parameters (i.e.,
sensitivity or Jacobian matrix)
Provides several methods for adjusting and constraining
the parameter values
RSM Training HESM Instructional Materials for Training Purposes Only
Module 13: PEST - Introduction
Page 13.4 Hydrologic and Environmental Systems Modeling
Inatypicalmodelrun,somesetofinputexcitations(X),suchasrainfall,potentialevapotranspiration
andinflowacrosstheboundaries,andmodelparameters(b),areusedtoproduceasetofresults(c).
Conceptually,theinputsreactwitheachparametertoproducetheresults.
4
Typical Simulation Model
Typical Simulation Model
X b = c
where:
x
p
1
b
1
+ x
p
2
b
2
+ …+ x
p
n
b
n
= c
p
Parameters
Results
Inputs
RSM Training HESM Instructional Materials for Training Purposes Only
Module 13: PEST - Introduction
Hydrologic and Environmental Systems Modeling Page 13.5
Theobjectivefunctionisbasedonthebestsetoflinearcombinationsoftheparameters(b),asaffected
bythemodelinputs(X),comparedtotheobservations(c),
where (m) is the number of observations
and (n) is the number of parameters
Thevarianceandcovariancecanbecalculatedfromtheobjectivefunction.
5
Objective Function
Objective Function
Best linear unbiased estimator of the parameters
()()
t
cXbcXb
1
()
t
t
bXXXc
2 /() mn
21
()()
t
C
bXX
where
and
5
Objective Function
Best linear unbiased estimator of the parameters
()()
t
cXbcXb
1
()
tt
bXXXc
2
/( )mn
21
() ( )
t
C
bXX
where
and
