Practical notes on local data‐worth analysis

Abstract

These notes discuss the usefulness, limitations, and potential pitfalls of using sensitivity indices as a means to evaluate data worth and to guide the formulation and solution of inverse problems. A sensitivity analysis examines changes in model output variables with respect to changes in model input parameters. It appears straightforward to use this information to select influential parameters that should be subjected to estimation by inverse modeling and to identify the observations that contain information about these parameters and thus may be useful as calibration points. However, the results of such a sensitivity analysis do not account for parameter correlations and redundancies in observations and may not properly separate between calibration and prediction targets if used as criteria that guide inverse modeling; they may thus yield misleading recommendations about parameter identifiability and data worth. These issues (and some remedies) are discussed using an illustrative example, in which we examine the value of data sets potentially used for the calibration of a geothermal reservoir model. These notes highlight the importance of carefully formulating the objectives of a simulation study, which controls the setup of the inverse problem and related data needs.

An efficient numerical model for liquid water uptake in porous material and its parameter estimation

“…If the sensitivity coefficients are either small or correlated, the estimation problem is difficult and very sensitive to measurement errors. The sensitivity coefficient is defined as the first derivative of the (numerical) observations with respect to an unknown parameter [9,35]:…”

Three-dimensional fracture continuum characterization aided by surface time-domain electromagnetics and hydrogeophysical joint inversion—proof-of-concept

“…To assess a measure of significance for the shown inversion results, we calculate uncertainties for each estimated parameter. Parameter uncertainties correspond to variances, which are the diagonal elements of the covariance matrix C pp [10,19]:…”

Thermal Evolution near Heat-Generating Nuclear Waste Canisters Disposed in Horizontal Drillholes

“…A data-worth analysis identifies and ranks the relative contribution a data point makes when used in an inversion (e.g., for the estimation of thermal properties) and a subsequent predictive simulation (e.g., of maximum repository temperatures). The approach used in this study is described in Reference [47]. It is based on sensitivity coefficients, a linear estimation error analysis (to obtain the uncertainty in the estimated parameters given the available data and their uncertainties), and a linear uncertainty propagation analysis (to obtain the prediction uncertainty given uncertainty in the estimated parameters).…”