A Geostatistical Methodology for the Optimal Design of Space-Time Hydraulic-Head Monitoring-Networks and Application to the Valle De Querétaro Aquifer

This paper presents a new methodology for the optimal design of space-time hydraulic-head (HH) monitoring-networks and its application to the Valle de Querétaro aquifer in México. In the design we consider spatial and temporal correlations between historical HH data measured in the aquifer. The choice of sampling positions and times is made using a Kalman filter (KF) combined with an optimization method. The KF requires as input the covariance matrix, which was derived from a space-time geostatistical analysis. A heuristic optimization method that selects one location at a time, that minimizes a function of the variance, was used. A redundant analysis for the 38 wells of an existing monitoring network (MN) was done. The database for the geostatistical spatiotemporal analysis consisted of 273 wells located within the aquifer for the period 1970-2007. A total of 1435 HH data were used to construct the experimental space-time semivariogram, a theoretical model was fitted to it, which in turn was used to derive the covariance matrix required by the KF. The objective function used was the estimation error variance over an equally-weighted space-time estimation grid (82 positions and 11 years) for the period 1997-2007. The 38 positions of the wells (MN) for 11 years were selected as possible space-time sampling-points. Each space-time sampling-point contributed in the variance reduction in present and future times. 350 space-time sampling-points were selected for the optimal monitoring network (OMN). The differences between the HH estimation with the OMN and the estimation using the MN (maximum possible level of information) are: mean difference of -0.26 m, minimum difference of -16.80 m, maximum difference of 8.61 m, and minimum squared difference (MSD) of 1.76 m². The MSD indicates that we have a difference of 1.33 m approximately in the HH estimation over the space-time estimation grid.