(Zheng and Bennett) Steps in Transport Modeling Calibration step (calibrate flow model & transport model) Adjust parameter values Traditional approach

Comparison of measured and simulated concentrations

Average calibration errors (residuals) are reported as: Mean Absolute Error (MAE) = 1/N   calculated i – observed i  Root Mean Squared Error (RMS) =  1/N  (calculated i – observed i ) 2  ½ Sum of squared residuals =  (calculated i – observed i ) 2 Minimize errors; Minimize the objective function 

(Zheng and Bennett) Steps in Transport Modeling Calibration step (calibrate flow model & transport model) Adjust parameter values Traditional approach

Input Parameters for Transport Simulation Flow Transport hydraulic conductivity (K x, K y K z ) storage coefficient (S s, S, S y ) porosity (  ) dispersivity (  L,  TH,  TV ) retardation factor or distribution coefficient 1 st order decay coefficient or half life recharge rate pumping rates source term (mass flux) All of these parameters potentially could be estimated during calibration. That is, they are potentially calibration parameters.

(Zheng and Bennett) Steps in Transport Modeling Calibration step (calibrate flow model & transport model) Adjust parameter values Traditional approach

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 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.

Dr. John Doherty Watermark Numerical Computing, Australia PEST Parameter ESTimation

New Book 2007 Mary C. Hill Claire R. Tiedeman USGS Modelers

Multi-model Analysis (MMA) From Hill and Tiedeman 2007 Predictions and sensitivity analysis are now inside the calibration loop

Model calibration conditions Input files PEST Input files Model predictive conditions Output files Maximise or minimise key prediction while keeping model calibrated

p1p1 p2p2 Estimated parameter values; nonlinear case:- Objective function minimum

p1p1 p2p2 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-peaked source concentration (best calibration) Simulated: smooth source 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 Metheny for the PhD under the direction of Prof. Scott Bair, Ohio State University Case Study: Woburn, Massachusetts TCE (Trichloroethene)

01000 feet TCE in 1985 W.R. Grace Beatrice Foods Woburn Site Municipal Wells G & H Aberjona River Geology: buried river valley of glacial outwash and ice contact deposits overlying fractured bedrock The trial took place in Did TCE reach the wells before May 1979? Wells G&H operated from October 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 May 1979 Simulation from Jan to Dec using 55 stress periods (to account for changes in pumping and 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 calibration parameter in the Woburn model Other possible calibration parameters include: K, recharge, boundary conditions dispersivities chemical 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 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. Woburn Model: Trial & Error Calibration 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.

Traditional approach Steps in Modeling New Paradigm Calibration step: calibrate flow model & transport model

“Automated” Calibration From Zheng and Bennett Codes: UCODE, PEST, MODFLOWP Case Study

From Zheng and Bennett source term Sum of squared residuals =  (calculated i – observed i ) 2 Transport data are useful in calibrating a flow model recharge

Comparison of observed vs. simulated concentrations at 3 wells for the 10 parameter simulation. From Zheng and Bennett