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Calibration step (calibrate flow model & transport model). Steps in Transport Modeling. Traditional approach. Adjust parameter values. (Zheng and Bennett). Comparison of measured and simulated concentrations. Average calibration errors (residuals) are reported as:.

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Presentation Transcript
slide1

Calibration step

(calibrate flow model

& transport model)

Steps in Transport Modeling

Traditional approach

Adjust parameter values

(Zheng and Bennett)

slide2

Comparison of

measured and

simulated

concentrations

slide3

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

slide4

Calibration step

(calibrate flow model

& transport model)

Steps in Transport Modeling

Traditional approach

Adjust parameter values

(Zheng and Bennett)

slide5

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)

slide6

Calibration step

(calibrate flow model

& transport model)

Steps in Transport Modeling

Traditional approach

Adjust parameter values

(Zheng and Bennett)

slide7

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.

slide8

Dr. John Doherty

Watermark Numerical

Computing, Australia

PEST

Parameter

ESTimation

slide9

New Book

2007

Mary C. Hill

Claire R. Tiedeman

USGS Modelers

slide10

Multi-model

Analysis (MMA)

Predictions and sensitivity

analysis are now inside

the calibration loop

From Hill and Tiedeman 2007

slide11

Input files

Input files

PEST

Model

calibration conditions

Model

predictive conditions

Output files

Output files

Maximise or minimise key prediction while keeping model calibrated

slide12

Estimated parameter values; nonlinear case:-

p2

Objective function minimum

p1

slide14

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.
slide15

Simulated: smooth

source concentration

(best calibration)

Simulated: double-peaked

source concentration

(best calibration)

Borden Plume

Calibration is non-unique.

Two sets of parameter values give equally good matches to the observed plume.

Z&B, Ch. 14

slide16

R=1

R=3

observed

R=6

Assumed source input function

“Trial and error”

method of calibration

slide17

Case Study: Woburn, Massachusetts

Modeling done by Maura Metheny

for the PhD under the direction of

Prof. Scott Bair, Ohio State University

TCE (Trichloroethene)

slide18

0

1000 feet

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 G&H operated from

October 1964- May 1979

Beatrice

Foods

The trial took place in 1986.

Did TCE reach the wells before May 1979?

slide19

Five sources of TCE were included in the model:

  • New England Plastics
  • Wildwood Conservation Trust (Riley Tannery/Beatrice Foods)
  • Olympia Nominee Trust (Hemingway Trucking)
  • UniFirst
  • W.R. Grace (Cryovac)

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.

slide20

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

slide21

Source term input function

Used as a calibration

parameter in the Woburn

model

Other possible calibration

parameters include:

K, recharge, boundary conditions

dispersivities

chemical reaction terms

From Zheng and Bennett

slide22

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

concentrations, 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 reproducedmeasured values of TCE.

slide23

Steps in Modeling

Calibration step:

calibrate flow model

& transport model

New Paradigm

Traditional approach

slide24

“Automated” Calibration

Case Study

Codes: UCODE, PEST,

MODFLOWP

From Zheng and Bennett

slide25

source term

recharge

Sum of squared residuals

=  (calculatedi – observedi)2

Transport data are useful in

calibrating a flow model

From Zheng and Bennett

slide26

Comparison of observed vs.

simulated concentrations at

3 wells for the 10 parameter

simulation.

From Zheng and Bennett