Optimal Interpolation of the Multivariate Spatial Estimation for Groundwater Balance Data with Boundary Conditions

This research dealt with estimation of water balance between groundwater levels by spatial interpolation of multivariate using the cokriging technique in unknown locations and at border points. One of the objectives of this research is to arrive at a method for estimating the probability curves for the specific boundary effects of groundwater aquifers, as well as to obtain a smooth approach and method for spatial covariance models, as well as to obtain the spatial relationship between probability, slope, and universal cokriging method to estimate the directional derivatives of a regional spatial variable from scattered measurements of the variable and gradient measurements for groundwater levels. The data used in this research are real data for groundwater levels in the city of Mosul. Unbiased estimation and least variance estimation were used to obtain the estimated values ​​of the spatial observations and obtained good results that support the advantages of the cokriging method. Accuracy becomes clear to us through the smallest errors by applying the basic error criteria in forecasting. The resulting estimate describes spatial associations and illustrates multivariate covariance model analysis. The conclusion gives us the benefit of using the Mathron variation model with the ability to adjust the parameter for second-order fields to determine the groundwater balance, while the gradient is considered an approach to the specific difference between the groundwater levels studied. This paper discusses the use of the universal cokriging, which is a widely used multivariate linear estimator for geostatistics. In the context of spatial random processes, the paper covers the possibility of increasing the spatial resolution of the spatial variable (downscaling), estimating direction derivatives, and spatial interpolation with respect to boundary conditions. All spatial estimators are unbiased and reduce the variance of the estimation error. Multivariate is an effective method for improving the contour maps between the hydraulic head and the rest of the other data under study.