(zheng and bennett) steps in transport modeling calibration step (calibrate flow model &...

(Zheng and Bennett)

Steps in Transport Modeling

Calibration step(calibrate flow model& transport model)

Adjust parameter values

Traditional approach

Comparison ofmeasured andsimulatedconcentrations

Average calibration errors (residuals) are reported as:

Mean Absolute Error (MAE) = 1/N calculatedi – observedi

Root Mean Squared Error (RMS) = 1/N (calculatedi – observedi)2½

Sum of squared residuals = (calculatedi – observedi)2

Minimize errors; Minimize the objective function

(Zheng and Bennett)





Input Parameters for Transport Simulation

Flow

Transport

hydraulic conductivity (Kx, Ky Kz)storage coefficient (Ss, S, Sy)

porosity ()dispersivity (L, TH, TV)retardation factor or distribution coefficient1st order decay coefficient or half life

recharge ratepumping rates

source term (mass flux)

All of these parameterspotentially could be estimatedduring calibration. That is,they are potentially calibrationparameters.

(Zheng and Bennett)





Problems with this approach:

The model goes out of calibration.

The results of the sensitivity runs represent unreasonable scenarios.

In a traditional sensitivity analysis, sensitive parameters are varied withinsome range of the calibrated value.

The model is run using these extreme values of the sensitive parameterwhile holding the other parameters constant at their calibrated values.

The effect of variation (uncertainty) in the sensitive parameter on model resultsIs evaluated.

A sensitivity analysis is meant to address uncertainty in parameter values.

Dr. John DohertyWatermark NumericalComputing, Australia

PESTParameter ESTimation

New Book2007

Mary C. HillClaire R. Tiedeman USGS Modelers

Multi-modelAnalysis (MMA)

From Hill and Tiedeman 2007

Predictions and sensitivityanalysis are now insidethe calibration loop

Modelcalibration conditions

Input files

PEST

Input files

Modelpredictive conditions

Output files Output files

Maximise or minimise key prediction while keeping model calibrated

p1

p2

Estimated parameter values; nonlinear case:-

Objective function minimum

p1

p2

Likely parameter values

Objective function contours – nonlinear model

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.

Borden Plume

Simulated: double-peakedsource concentration(best calibration)

Simulated: smoothsource concentration(best calibration)

Z&B, Ch. 14

Calibration is non-unique.Two sets of parameter values give equally good matches to the observed plume.

“Trial and error”method of calibration

Assumed source input function

R=1 R=3

R=6 observed

Modeling done by Maura Methenyfor the PhD under the direction ofProf. Scott Bair, Ohio State University

Case Study: Woburn, Massachusetts

TCE (Trichloroethene)

1 0 1 0 0 1 0 0 0

C o n c e n t r a t i o n o f T C E i n m i c r o g r a m s p e r l i t e r

0 1000 feet

TCE in 1985

W.R.Grace

•

BeatriceFoods

Woburn Site

MunicipalWells G & H

Aberjona River

Geology:buried river valleyof glacial outwash andice contact depositsoverlyingfractured bedrock

The trial took place in 1986.

Did TCE reach the wells before May 1979?

Wells G&H operated from October 1964- May 1979

MODFLOW, MT3D, and GWV

6 layers, 93 rows, 107 columns (30,111 active cells)

Woburn Model: Design

The transport model typically took two to three days to run on a 1.8 gigahertz PC with 1024K MB RAM.

Wells operated from October 1964- May 1979

Simulation from Jan. 1960 to Dec. 1985using 55 stress periods (to account for changes in pumpingand recharge owing to changes in precipitation and land use)

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)

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 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

Calibration Targets:Heads and fluxes

Source term input function

From Zheng and Bennett

Used as a calibrationparameter in the Woburnmodel

Other possible calibrationparameters include:K, recharge, boundary conditions

dispersivitieschemical reaction terms

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

It cannot be determined which, if any, of the plausible scenariosactually represents what occurred in the groundwater flow system during this period, even though each of the plausible scenarios

closely reproduced measured values of TCE.

Woburn Model: Trial & Error Calibration

Transport Model (included retardation)The animation represents one of several equally plausible simulationsof TCE transport based on estimates of source locations, sourceconcentrations, release times, and retardation. The group of plausible scenarios was developed because the exact

nature of the TCE sources is not precisely known.


Steps in Modeling

New Paradigm

Calibration step:calibrate flow model& transport model

“Automated” Calibration


Codes: UCODE, PEST,MODFLOWP

Case Study


source term

Sum of squared residuals = (calculatedi – observedi)2

Transport data are useful incalibrating a flow model

recharge

Comparison of observed vs.simulated concentrations at3 wells for the 10 parametersimulation.


(zheng and bennett) steps in transport modeling calibration step (calibrate flow model &...

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