Spatial modeling

Variogram

Experimental variogram

We begin the analysis with variogram analysis.

Plus on s’éloigne du point plus la semi variance est importante. Il y a donc de forte disparité géographique.

Variogram at 0 °, 45 °, 90 ° and 135 °

The variogram at 0 ° is little variant and resembles a nugget effect, compared to the other angles which have a greater tendency to increase the variance over the distant distances.

Using a variogram model

To use kriging linear modeling, we need a variogram model representative of our data. We use a spherical model to represent our variograms. The model used is quite close to the four angles and seems a good compromise, strongly attenuating some angles and increasing others.

Kriging on a spatial grid

The result of kriging is as follows: As seen in the exploratory analysis, we have a vertical axis that breaks down into two distinct parts. The lowest values ​​in this axis and the larger values ​​on the left and right sides. The representation on a grid, shows us clearly the distribution of the variable Y which has two weakly polluted zones in the middle of other very polluted zones.

Prediction error

It can be seen that prediction errors are very important to the right and to the left of a vertical axis. The errors are due to the compromise made with our variogram model. On the left and right are strong values ​​close to low values. The linear model, smoothing the values, releases these errors.