I am currently using the Fields package from R to interpolate spatial data to a finer resolution using observations and elevations point data. I am using the SpatialProcess function with an elevation covariate and from what I understand, it's the same concept as kriging with a z covariate. However, when I look at the form of the spatial model given in the Fields package documentation ( https://cran.r-project.org/web/packages/fields/fields.pdf) they give the present form: Y.k= P(x.k) + Z(x.k)%*%beta2 + g(x.k) + e.k at the position x.k with P being a low degree polynomial, g is a mean zero, Gaussian stochastic process and e.k the measurement error I don't understand how it relates with kriging. I understand that the 2nd term is the one that takes elevation into account but I don't understand why a polynomial of x.k is used and I don't see which part of this model is linked with the observations as there's supposed to be in kriging. Would someone be able to explain what I am missing please?
I tried to use the SpatialProcess function with the default parameters but I got a result that was not taking enough the observations into account. I would like to know if it's possible to modify the weights on the observations and on the elevation covariate and how to do it.