In the subsequent sections we are going to predict values of a spatially distributed variable at locations where it was not observed based on a set of observations. In the first example we make inferences on the mean annual rainfall in Germany based on a set of observations at 586 DWD weather stations. In the second example we predict the spatial distribution of Zinc in Lake Rangsdorf based on 32 sediment samples taken during a field survey in 2017.

The general procedure is outlined below. First, if necessary, we prepare the data for subsequent analysis. Then we investigate the sample variogram and propose a variogram model that fits the observational data. Then we evaluate the different models using the root mean squared error (RMSE) as model assessment metric. Finally we use the `gstat`

package for spatial prediction.

- Data preparation

- Sample variogram

- Variogram modelling

- Model evaluation

- Spatial prediction

Before we continue recall **Tobler’s first law of geography**:

“everything is related to everything else, but near things are more related than distant things.”