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Automated ParameterEstimation
CE En 547
Brigham Young University
Inverse Modeling
Observed heads and fluxes are enteredusing standard calibration tools
A set of parameter zones are defined
PEST/UCODE modifies parameters andlaunches MODFLOW repeatedly untilresidual is minimized
Observed heads and fluxes are enteredusing standard calibration tools
A set of parameter zones are defined
PEST/UCODE modifies parameters andlaunches MODFLOW repeatedly untilresidual is minimized
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Acknowledgements John Doherty
Watermark Computing
PEST
Wrote bulk of external utilities for GMSPEST/UCODE interface
Eileen Poeter Colorado School of Mines
UCODE
John Doherty Watermark Computing
PEST
Wrote bulk of external utilities for GMSPEST/UCODE interface
Eileen Poeter Colorado School of Mines
UCODE
Basic Steps1. Build a working MODFLOW model
2. Enter field-observed data
3. Define parameter zones with key values
4. Create parameter list
5. Select the obs. coverage you wish to use
6. Edit PEST/UCODE options
7. Run the Check Simulation command8. Save MODFLOW simulation
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Step 2. Enter field-observed
data
Use standard calibration tools to enterobserved head and fluxes
Pay special attention to calibrationinterval/standard deviation
Weight assigned to each measurementin objective function = 1/std.dev.
Use standard calibration tools to enterobserved head and fluxes
Pay special attention to calibrationinterval/standard deviation
Weight assigned to each measurementin objective function = 1/std.dev.
Step 3. Define parameterzones
Identify set of input values you want theinverse model to optimize("parameterization")
Number of parameters must be lessthan the number of observations
Identify set of input values you want theinverse model to optimize("parameterization")
Number of parameters must be lessthan the number of observations
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Zonation
Arrays are split into zones
Zones best defined in conceptualmodel using polygons
Multiplication Arrays
Array is modified by multiplication factor
Use array multipliers in MODFLOW interface
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Legal Parameters Starting head
Kh
Kv
Specific storage
Specific yield
Layer anisotropy
Recharge rate
ET extinction depth
Max ET rate Well Q
River stage
River conductance
GHB head
GHB conductance
Drain conductance
Stream Q
Stream conductance
Stream width
Stream roughness HFB hyd. characteristic
CHB head
Key Values
Parameter zones are defined byentering "key values"
Use a value that would not be expectedin the input file (-900, -800, -700, etc.)
Can be entered via conceptual model orgrid model
Parameter zones are defined byentering "key values"
Use a value that would not be expectedin the input file (-900, -800, -700, etc.)
Can be entered via conceptual model orgrid model
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Step 4. Build parameter list Define a parameter for each key value
For each parameter
Starting value
Min value
Max value
Can be developed quickly using"Initialize from Model" feature
Define a parameter for each key value
For each parameter
Starting value
Min value
Max value
Can be developed quickly using"Initialize from Model" feature
Parameter List
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Step 5. Select Obs. Coverage If you have multiple obs. coverages,
select the coverages you want to use
Use the General Options property sheetin the Inverse Code Options dialog
More than one coverage may be used
If you have multiple obs. coverages,select the coverages you want to use
Use the General Options property sheetin the Inverse Code Options dialog
More than one coverage may be used
Step 6. Edit PEST/UCODEOptions
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Step 7. Run the Check
Simulation Command
Checks for obvious errors in input data
Check includes errors unique toPEST/UCODE data
Checks for obvious errors in input data
Check includes errors unique toPEST/UCODE data
Step 8. Save MODFLOWsimulation
Saves MODFLOW data with key values
Saves extra data to a set of files usedby PEST/UCODE
Observations (values and weights)
Parameters
Options
Saves MODFLOW data with key values
Saves extra data to a set of files usedby PEST/UCODE
Observations (values and weights)
Parameters
Options
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Step 9. Run
GMS2PEST/GMS2UCODE Must be run prior to launching
PEST/UCODE
Purpose
Replaces key values in input files withspecial markers
Sets up standard PEST/UCODE run files
Must be run prior to launchingPEST/UCODE
Purpose
Replaces key values in input files withspecial markers
Sets up standard PEST/UCODE run files
Step 10. Run PEST/UCODE
Runs in separate window
Takes several minutes to several hoursdepending on
Size of model
Number of parameters
Runs in separate window
Takes several minutes to several hoursdepending on
Size of model
Number of parameters
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Step 11. Import optimal
parameters MODFLOW simulation corresponding to
optimal run is NOT saved
Output from PEST is a list of optimalparameter values
Can be loaded into starting value field inparameter list using the "Import
Parameter File" button
MODFLOW simulation corresponding tooptimal run is NOT saved
Output from PEST is a list of optimalparameter values
Can be loaded into starting value field inparameter list using the "Import
Parameter File" button
Step 12. Load parameters tomodel
Model still contains key values
Need to load optimal parameters tomodel before running model
Use "Load to Model" button
Values are copied to: Grid cells only
Grid cells and conceptual model
Model still contains key values
Need to load optimal parameters tomodel before running model
Use "Load to Model" button
Values are copied to: Grid cells only
Grid cells and conceptual model
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Step 13. Save and run
MODFLOW Save simulation with optimal values
loaded
Run MODFLOW
Read solution
Plot results using calibration targets andplots
Save simulation with optimal valuesloaded
Run MODFLOW
Read solution
Plot results using calibration targets andplots
Inverse Model Stability
MODFLOW must converge in order forPEST/UCODE to run successfully
Cells going dry cause irregularities inobjective function, resulting in instabilityin optimization algorithm
MODFLOW must converge in order forPEST/UCODE to run successfully
Cells going dry cause irregularities inobjective function, resulting in instabilityin optimization algorithm
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Convergence Options
Even if calibration targets are satisfied,calibrated parameters may not be"correct"
A different set of parameters may alsosatisfy calibration targets
Model Non-uniqueness
Even if calibration targets are satisfied,calibrated parameters may not be"correct"
A different set of parameters may alsosatisfy calibration targets
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Example #1 Vary recharge and K
Calibrate to observation points
StreamSpec.Head
Bound.
Obs. Pts.
Recharge
K
Results (Side View)
Ground
Surface
FixedHead
Bound.
ComputedWater Table
Surface
Calib. Targets
Bedrock
Solution #1: High RechargeHigh K
Solution #2: Low RechargeLow K
Which is correct?
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Well-posed conceptual model
More observation data
Both well AND flux observations
Improving Uniqueness Well-posed conceptual model
More observation data
Both well AND flux observations
Example #2
Vary recharge and K
Calibrate to observation pointsAND flux in stream
StreamSpec.
HeadBound.
Obs. Pts.
Recharge
K
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Results
Unique Solution
Recharge is limitedby the stream fluxobservation
A degree offreedom isremoved
Solution is muchmore accurate