(Zheng and Bennett)

1
Steps in Transport Modeling
Traditional approach
Adjust parameter values
(Zheng and Bennett)
2
Comparison of measured and simulated concentration
s
3
Average calibration errors (residuals) are
reported as
Mean Absolute Error (MAE) 1/N ?
?calculatedi observedi?
Root Mean Squared Error (RMS) ?1/N ?
(calculatedi observedi)2?½
?
Sum of squared residuals ? (calculatedi
observedi)2
Minimize errors Minimize the objective function
4
Steps in Transport Modeling
Traditional approach
Adjust parameter values
(Zheng and Bennett)
5
Input Parameters for Transport Simulation
Flow
hydraulic conductivity (Kx, Ky Kz) storage
coefficient (Ss, S, Sy)
recharge rate pumping rates
All of these parameters potentially could be
estimated during calibration. That is, they are
potentially calibration parameters.
Transport
porosity (?) dispersivity (?L, ?TH,
?TV) retardation factor or distribution
coefficient 1st order decay coefficient or half
life
source term (mass flux)
6
Steps in Transport Modeling
Traditional approach
Adjust parameter values
(Zheng and Bennett)
7
In a traditional sensitivity analysis, sensitive
parameters are varied within some range of the
calibrated value. The model is run using these
extreme values of the sensitive parameter while
holding the other parameters constant at their
calibrated values. The effect of variation
(uncertainty) in the sensitive parameter on model
results Is evaluated. A sensitivity analysis is
meant to address uncertainty in parameter values.
Problems with this approach
The model goes out of calibration. The results
of the sensitivity runs represent unreasonable
scenarios.
8
Dr. John Doherty Watermark Numerical Computing,
Australia
PEST Parameter ESTimation
9
New Book 2007
Mary C. Hill Claire R. Tiedeman
USGS Modelers
10
Multi-model Analysis (MMA)
Predictions and sensitivity analysis are now
inside the calibration loop
From Hill and Tiedeman 2007
11
Input files
Input files
PEST
Model calibration conditions
Model predictive conditions
Output files
Output files
Maximise or minimise key prediction while keeping
model calibrated
12
Estimated parameter values nonlinear case-
p2
Objective function minimum
p1
13
Objective function contours nonlinear model
Likely parameter values
p2
p1
14

• Calibration of a flow model is relatively
  straightforward
• Match model results to an observed steady state
  flow field
• If possible, verify with a transient
  calibration
• Calibration to flow is non-unique.

• Calibration of a transport model is more
  difficult
• There are more potential calibration parameters
• There is greater potential for numerical error
  in the solution
• The measured concentration data needed for
  calibration
• may be sparse or non-existent
• Transport calibrations are non-unique.

15
Borden Plume
Calibration is non-unique. Two sets of parameter
values give equally good matches to the observed
plume.
ZB, Ch. 14
16
R1
R3
observed
Assumed source input function
R6
Trial and error method of calibration
17
Case Study Woburn, Massachusetts
Modeling done by Maura Metheny for the PhD under
the direction of Prof. Scott Bair, Ohio State
University
TCE (Trichloroethene)
18
Woburn Site
TCE in 1985
Geology buried river valley of glacial outwash
and ice contact deposits overlying fractured
bedrock
Aberjona River
W.R. Grace

Municipal Wells G H
Wells GH operated from October 1964- May 1979
Beatrice Foods
The trial took place in 1986.
Did TCE reach the wells before May 1979?
19
Woburn Model Design
MODFLOW, MT3D, and GWV
6 layers, 93 rows, 107 columns (30,111 active
cells)
Simulation from Jan. 1960 to Dec. 1985 using 55
stress periods (to account for changes in
pumping and recharge owing to changes in
precipitation and land use)
Wells operated from October 1964- May 1979
The transport model typically took two to three
days to run on a 1.8 gigahertz PC with 1024K MB
RAM.
20

• Calibration of a flow model is generally
  straightforward
• Match model results to an observed steady state
  flow field
• If possible, verify with a transient
  calibration
• Calibration to flow is non-unique.

Calibration Targets Heads and fluxes

• Calibration of a transport model is more
  difficult
• There are more potential calibration parameters
• There is greater potential for numerical error
  in the solution
• The measured concentration data needed for
  calibration
• may be sparse or non-existent
• Transport calibrations are non-unique.

Calibration Targets concentrations
21
Source term input function
Used as a calibration parameter in the
Woburn model
Other possible calibration parameters include K,
recharge, boundary conditions dispersivities chem
ical reaction terms
From Zheng and Bennett
22
Woburn Model Trial Error Calibration

• Flow model (included heterogeneity in K, S and ?)
• Water levels
• Streamflow measurements
• Groundwater velocities from helium/tritium
  groundwater ages

Transport Model (included retardation) The
animation represents one of several equally
plausible simulations of TCE transport based on
estimates of source locations, source concentratio
ns, release times, and retardation. The group of
plausible scenarios was developed because the
exact nature of the TCE sources is not precisely
known.
It cannot be determined which, if any, of the
plausible scenarios actually represents what
occurred in the groundwater flow system during
this period, even though each of the plausible
scenarios closely reproduced measured values of
TCE.
23
Steps in Modeling
Calibration step calibrate flow model
transport model
New Paradigm
Traditional approach
24
Automated Calibration
Case Study
Codes UCODE, PEST, MODFLOWP
From Zheng and Bennett
25
recharge
Sum of squared residuals ? (calculatedi
observedi)2
Transport data are useful in calibrating a flow
model
From Zheng and Bennett
26
Comparison of observed vs. simulated
concentrations at 3 wells for the 10
parameter simulation.
From Zheng and Bennett