Evaluation of prediction intervals for expressing uncertainties in groundwater flow model predictions

We tested the accuracy of 95% individual prediction intervals for hydraulic heads, streamflow gains, and effective transmissivities computed by groundwater models of two Danish aquifers. To compute the intervals, we assumed that each predicted value can be written as the sum of a computed dependent variable and a random error. Testing was accomplished by using a cross-validation method and by using new field measurements of hydraulic heads and transmissivities that were not used to develop or calibrate the models. The tested null hypotheses are that the coverage probability of the prediction intervals is not significantly smaller than the assumed probability (95%) and that each tail probability is not significantly different from the assumed probability (2.5%). In all cases tested, these hypotheses were accepted at the 5% level of significance. We therefore conclude that for the groundwater models of two real aquifers the individual prediction intervals appear to be accurate.