DOE OSTI2020
In cases of complex but only partially known geology and a lack of spatial control in observation well locations, water table elevation estimation is very challenging. In some cases, auxiliary information, such as observations of the movement of tracers, operation of injection and extraction wells, and calibration of groundwater models against the historical elevation data, can be combined with expert judgement to estimate flow directions in areas of sparse data and to aid in the production of more reliable contour maps (and associated rasters) than could be produced by relying on sparse well elevation data alone. Given a historical sequence of these raster maps, the question arises how to automate, to the extent possible, the process of producing new raster maps to reflect data from previous times, the current data and the operation of expert judgement. One solution is to adopt a Bayesian point of view and to regard the historical well elevation data, auxiliary information and historical raster maps as prior information. The well elevations for water table wells, as well as those for injection/extraction wells and the data associated with other relevant variables, can be viewed as predictors for the raster surface. From this prior information, we can, conditional on the values of these predictors for a new time period, compute an expected value map and a standard deviation map for the new raster. These then can be taken to specify a prior predictive distribution for the pixels in the new raster map. Then we condition the pixels, corresponding to water level observation wells within the raster, on the observed values in those wells (which in general will differ from the regression estimate) for the new time period. Given the smoothness of the water table surface, we then smooth the surface of deviations from the mean surface, based on the variograms of the historical rasters, and add this smoothed surface to the regression mean surface. The error structure of the produced raster map is defined by the regression error structure and the error due to smoothing based on the estimated variograms. This methodology has been developed and is being further refined for groundwater monitoring and remediation at LANL. It is a very flexible method that can also be applied with a variety of other predictors applied to model the water level wells in the area of interest over the historical record. The smoothness of the spatial process and its possible evolution over time can then be estimated from the residuals from this regression. This can be augmented by expert hydrogeological opinion based on site topography and hydrogeology. (authors)
54 ENVIRONMENTAL SCIENCES↗