*4.1. Synthetic Cases*

The coefficients *C*1, *C*<sup>2</sup> and *C*<sup>3</sup> in the cost function *J* are set empirically to *C*<sup>1</sup> = 1, *C*<sup>2</sup> = *C*<sup>3</sup> = 10. We will first look at the convergence of the minimization problem on each domain *Di* for *i* = 1, ..., *I*, with *I* = 5 (so that *mI* = 33 × 33 < *n* = *nx* × *ny* = 65 × 65, see Section 3). Then, we will look at the performance of the automatic registration and morphing procedure.

The coefficients *C*1, *C*<sup>2</sup> and *C*<sup>3</sup> influence the value of the cost function, and so the convergence. However, their impact on the mapped field is limited and mainly affect the area with no or low precipitation. For example, multiplying the coefficients by two will give similar results in terms of mean absolute error and root mean square error (see Appendix B).
