**3. Study Cases**

### *3.1. Synthetic Case for Algorithm's Validation*

A synthetic case is used to investigate the convergence of the automatic registration algorithm and to validate the morphing. The synthetic precipitation fields are generated on a regular *nx* × *ny* grid, with *nx* = *ny* = 65(= 26 + 1). The synthetic rainfall events are represented by ellipses and are added to a zero precipitation field (Figure 2). The fields *u* and *v* have two rainfall events each. However, they are at different positions. The distortion between the fields include both a rotation and a shear. The events also differ by their intensity and shape. The event in the lower right corner has the same shape in both fields *u* and *v*, but has a difference of intensity of 5 mm/h. The event in the upper-left corner has the same intensity in both *u* and *v*, but the ellipse has a different inclination.

**Figure 2.** Precipitation fields *u* and *v* for the synthetic case, shown respectively in (**a**) and (**b**).
