Calibration

1
Calibration Sensitivity Analysis
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Targets in Model Calibration

• Head measured in an observation well is known
  as a target. Baseflow measurements or other
  fluxes (e.g., ET)
• are also used as targets during calibration.

• The simulated head at a node representing an
  observation well is compared with the measured
  head in the well. (Similarly for flux targets)
• Residual error observed - simulated

3
Calibration Targets
associated error
calibration value
???0.80 m
20.24 m
Target with smaller associated error.
Target with relatively large associated error.
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Examples of Sources of Error

• Surveying errors
• Errors in measuring water levels
• Interpolation error
• Transient effects
• Scaling effects
• Unmodeled heterogeneities

5
Leave this box unchecked so that gwv will compare
simulated heads at the node with the
target values.
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Targets in Model Calibration

• Head measured in an observation well is known
  as a target. Baseflow measurements or other
  fluxes are also used as targets during
  calibration.

• The simulated head at a node representing an
  observation well is compared with the measured
  head in the well. (Similarly for flux targets)
• Residual error observed - simulated

• During model calibration, parameter values
  (e.g., R and T) are adjusted until the simulated
  head matches the observed value within some
  acceptable range of error. Hence, model
  calibration solves the inverse problem.

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Basecase simulation for the 2006 Final Project
All heads are too low.
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Residual observed - simulated
9
2006 values
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Calibration parameters are parameters whose
values are uncertain. Values for these
parameters are adjusted during model calibration.
Typical calibration parameters include hydraulic
conductivity and recharge rate.
Parameter values can be adjusted manually by
trial and error. This requires the user to do
multiple runs of the model.
or parameter adjustment can be done with the
help of an inverse code. The inverse code will
automatically find a set of parameters that
matches the observed head values.
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Automated calibration using inverse modeling
Codes MODFLOWP used in MODFLOW2000 GV
Calibration PEST UCODE
Available in GWV for use with MODFLOW 88/96
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Island Recharge Problem- Forward Problem
L
y
2L
h 120.014
ocean
well
Parameters known with certainty R 0.003375
ft/d K 100 ft/day
Solve for head
x
ocean
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Island Recharge Problem Inverse Problem
y
ocean
Head in well 120.014 feet (target)
2 parameters and 2 targets Ideally should have
at least 1 more target.
well
Uncertain parameters Initial guesses R 0.001
ft/d K 50 ft/day
x
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Targets h 120.014 ft F -57120 ft3/day
We are trying to estimate R and K. Correct
answers K 100 ft/day R 0.003375 ft/day
2 parameters and 2 targets Ideally should have
at least 1 more target.
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• Sensitivity analysis is used
• During calibration
• (Sensitivity coefficients
• ?sum of squared residuals/?parameter value
• or ?h/?parameter value)
• As an uncertainty analysis after calibration

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The Problem of Zonation
Most inverse codes estimate parameters
in pre-determined, fixed zones.
Yet, the boundaries/existence of such zones is
usually uncertain.
Pilot points can be used instead. Parameters are
estimated at arbitrarily selected points known as
pilot points. Then parameter values are
interpolated between pilot points.