Including precipitation observations from dynamic sensors and citizen observatories using geostatistical models, requires the revision of some of the most common assumptions. This chapter describes and revises three of these assumptions, namely homogeneity in measurement uncertainty, average temporal distribution of the precipitation within the observation interval, and spatial stationarity. One of the uncertainty sources in the measurement using dynamic sensors comes from the fact that there is partial information about the total amount of precipitation that is recorded in a time step. The proposed methodology is based on using a generalised covariance function. The objective of the Kriging interpolation is to simulate a precipitation field, which is optimal under assumptions of stationarity, linearity and Gaussianity. If the outcome of the stationarity evaluation is that the field is stationary in all its aspects, the current method will reduce to the conventional Kriging approximation, and therefore, it should be preferred due to parsimony.