3.2.2. Data Pre-Processing

TAHMO measurements are given on an irregular grid, while the automatic registration algorithm assumes that all the data are defined on a regular grid. The TAHMO measurements were kriged on the same 0.1◦ lat/lon grid as IMERG estimates (Figure 5). We used ordinary kriging with a square root transform [40]. The ordinary kriging was done with *PyKrige*, a kriging toolkit for python (https: //pypi.org/project/PyKrige/). We choose an exponential variogram with a sill of 1.0 (mm2/h2), a range of 1.5◦ and a nugget of 0.01 (mm2/h2).

Contrary to the previous cases, this case uses real noisy data. Hence, some pre-processing (beside the kriging) is necessary before applying the automatic registration. First, light precipitation (<0.1 mm/h) is removed from both fields. Lighter precipitation is in general more difficult to detect, hence subject to large uncertainties. Second, we add a zero-precipitation padding area around the study domain. This area is added to avoid problems near the boundary due to the minimization constraints. The extended domain corresponds to a *nx* × *ny* pixel grid, with *nx* = *ny* = 65. Finally, we normalized

the two fields such that the maximum rainfall is equal to 50 mm/h for both. Figure 6a,b show the fields *u* (IMERG-Late) and *v* (TAHMO) after the three pre-processing steps described above. The study domain is delimited by the dotted line, while the extended domain including the zero-padding area is delimited by the solid line. The extended domain corresponds to a regular *nx* × *ny* grid, with *nx* = *ny* = 65. These modified precipitation fields will be used as inputs for the automatic registration procedure to find the mapping *T*. Once the mapping *T* is found, it will be applied to the original fields *u* (Figure 4) on the extended domain.

**Figure 5.** TAHMO measurements (circles) and TAHMO kriged (background) within the study domain (dotted line) for the selected event.

(**a**) (**b**) **Figure 6.** Fields *u* (IMERG-Late) and *v* (TAHMO) after pre-processing and used as inputs. The dotted line delimits the study domain and the solid line the extended one, with the zero-padding area in-between. (**a**) Field *u* (IMERG) after pre-processing. (**b**) Field *v* (TAHMO) after pre-processing.
