Methods and Guidelines for Effective Model Calibration

Abstract

The methods and guidelines described in this report are designed to promote accuracy when simulating complex systems with mathematical models that need to be calibrated, and in which the calibration is accomplished using inverse modeling. This report focuses on the implementation of the described methods in the computer codes UCODE (Poeter and Hill, 1998) and MODFLOWP (Hill, 1992), which perform inverse modeling using nonlinear regression, but the methods have been implemented in other codes. The guidelines as presented depend on statistics described in this work, but other statistics could be used. Many aspects of the approach are applicable to any model calibration effort, even those conducted without inverse modeling. The methods and guidelines presented have been tested in a variety of groundwater modeling applications, many of which are cited in this report, and are described in the context of groundwater modeling concepts. They are, however, applicable to a much wider range of problems.

Inverse modeling of BTEX dissolution and biodegradation at the Bemidji, MN crude-oil spill site

“…The criteria generally used to evaluate inverse model results are: the estimated parameter values must be reasonable; the model should give a reasonable fit to the data; the residuals should be randomly distributed in space and time; and, the correlation between parameter values must be low (Hill, 1998). These criteria were satisfied only when: coupled transport and degradation processes were incorporated into the model; a single dissolution rate coefficient was used for all BTEX components; biodegradation reactions were simplified to first-order processes; the longitudinal dispersivity was fixed; and, a fast aerobic biodegradation rate was assumed.…”

“…As model and hydrologic system complexity increase, trial-and-error calibration becomes very difficult and highly uncertain. Formal inverse modeling facilitates objective determination of model parameters that produce the best possible fit to available observations, quantification of the quality of fit, and quantification of the reliability of parameter estimates (Hill, 1998). Inverse modeling can also be used to diagnose inadequate data, identify parameters that cannot be estimated with the given data set, evaluate the conceptual model representation, and quantify the uncertainty of model simulated values.…”

A soil‐water‐balance approach to quantify groundwater recharge from irrigated cropland in the North China Plain

“…However, because all parameters are completely correlated, only their ratios can be estimated. Therefore, flow data-preferably stream baseflow-are essential for achieving a unique solution (Hill, 1998). Because groundwater no longer discharges to streams in the North China Plain, inverse modelling cannot yield reliable recharge estimates.…”

Simulation of groundwater and surface-water resources and evaluation of water-management alternatives for the Chamokane Creek basin, Stevens County, Washington

“…Sensitivity analysis is used to assess the effects of different conceptual models (different model designs and parameter values) on the simulated heads and flows, and to develop useful nonlinear regressions (Hill, 1998;Hill and Tiedeman, 2003). The ability to estimate a parameter value using nonlinear regression is a function of the sensitivity of simulated values such as groundwater levels and streamflow to changes in the parameter value.…”

“…Observations and, therefore, residuals are weighted to allow a meaningful comparison of measurements with different units (weighted residuals are dimensionless) and to reduce the influence of measurements with large errors or uncertainty. The initial observation weight was defined using methods suggested by Hill (1998) and Hill and Tiedeman (2007). Errors in groundwater-level measurements were limited by the accuracy at wells whose locations were not measured using a GPS and by the accuracy of the DEM used to estimate the altitude.…”