Impact of measurement errors in stochastic inverse conditional modelling by the self-calibrating approach

A synthetic study is presented analyzing the impact of measurement errors on transmissivity and/or hydraulic head in the stochastic inverse modeling of groundwater flow, using the sequential self calibrated method. The scenarios studied can be divided into two different groups: (1) The modeler assumes the data are error-free when they are not; the attempt to reproduce these erroneous data yields biases and artifacts in the final conditional models. (2) The modeler recognizes that the data have measurement errors, makes an estimation of their magnitude, and accounts for them in the simulation; there are no biases or artifacts in this case, just an increase in the uncertainty about the final conditional models. The impact of the errors is analyzed in terms of the ensemble means and variances of the conditional realizations of transmissivity and the ensemble means and variances of the resulting hydraulic head fields after solution of the flow equation in the conditional transmissivity realizations. For the cases analyzed here, both transmissivity and head errors yield a worse characterization of the flow situation and transmissivity errors are less important than errors on hydraulic head for estimating the hydraulic head field. The characterization of the hydraulic head and transmissivity reference fields is better when the modeler estimates correctly the measurement error variance and takes into account the measurement errors in the modeling as outlined in the paper. In case the erroneous transmissivity data are treated as error-free, the ensemble standard deviation of transmissivity becomes unrealistic low. The synthetic study does not clearly reveal the existence of an interaction between hydraulic head measurement errors and transmissivity measurement errors; the effect of the errors seems to be additive.