Optimal design of measurement networks for groundwater flow predictions

This paper presents a methodology to optimise measurement networks for the prediction of groundwater flow. Two different strategies are followed: the design of a measurement network that aims at minimizing the log-transmissivity variance (averaged over the domain of interest) or a design that minimises the hydraulic head variance (averaged over the domain of interest). The methodology consists of three steps. In the first step the prior log-transmissivity and hydraulic head variances are estimated. This step is completely general in the sense that the prior variances maybe unconditional, or maybe conditioned to log-transmissivity and/or hydraulic head measurements. In case hydraulic head measurements are available in the first step, the inverse groundwater flow problem is solved by the sequential self-calibrated method. In the second step, the full covariance matrices of hydraulic head and log-transmissivity are calculated numerically on the basis of a sufficiently big number of Monte Carlo realisations. On the basis of the estimated covariances, the impact of an additional measurement in terms of variance reduction is calculated. The measurement that yields the maximum domain averaged variance reduction is selected. Additional measurement locations are selected according to the same procedure. The procedure has been tested for a series of synthetic reference cases. Different sampling designs are tested for each of these cases, and the proposed strategies are compared with other sampling strategies. Although the proposed strategies indeed reach their objective and yield in most cases the lowest posterior log-transmissivity variance or hydraulic head variance, the differences as compared to alternative sampling strategies are frequently small. For the cases considered here, a sampling design that covers more or less regularly the aquifer performs well. The paper also illustrates that for the optimal estimation of a well catchment a heuristic criterion (spreading measurement points as regularly as possible over the zone where there is some uncertainty regarding the capture probability) yields better results than a sampling design that minimises the posterior log-transmissivity variance or posterior hydraulic head variance.