Methods to correct and compute confidence and prediction intervals of models neglecting sub-parameterization heterogeneity - From the ideal toward practice

•We derive methods to correct regression-based confidence and prediction intervals.•The corrections compensate for sub-parameterization heterogeneity.•The correction methods require from ideal to little geostatistical characterization.•Weighting can be estimated as part of the regression and the interval calculation.•Testing demonstrates the importance and accuracy of the interval corrections.

This paper derives and tests methods to correct regression-based confidence and prediction intervals for groundwater models that neglect sub-parameterization heterogeneity within the hydraulic property fields of the groundwater system. Several levels of knowledge and uncertainty about the system are considered. It is shown by a two-dimensional groundwater flow example that when reliable probabilistic models are available for the property fields, the corrected confidence and prediction intervals are nearly accurate; when the probabilistic models must be suggested from subjective judgment, the corrected confidence intervals are likely to be much more accurate than their uncorrected counterparts; when no probabilistic information is available then conservative bound values can be used to correct the intervals but they are likely to be very wide. The paper also shows how confidence and prediction intervals can be computed and corrected when the weights applied to the data are estimated as part of the regression. It is demonstrated that in this case it cannot be guaranteed that applying the conservative bound values will lead to conservative confidence and prediction intervals. Finally, it is demonstrated by the two-dimensional flow example that the accuracy of the corrected confidence and prediction intervals deteriorates for very large covariance of the log-transmissivity field, and particularly when the weight matrix differs from the inverse total error covariance matrix. It is argued that such deterioration is less likely to happen for three-dimensional groundwater flow systems.