Fitting negative spatial covariances to geothermal field temperatures in Nea Kessani (Greece)

In this paper, we investigate the problem of negative empirical covariances for temperature data in a three-dimensional geothermal field. We make use of permissibility criteria that allow a linear combination of covariance functions to be positive definite even if some of the weights of the linear combination are set to be negative. We thus propose a generalized sum of spatial covariance structures to model negative spatial covariances. We evaluate the performance of the proposed model, together with that of other celebrated, and widely used covariance functions. Comparison is done in terms of cross-validation, which allows to evaluate the relative bias, accuracy of estimation, and goodness-of-fit.