Displacement Correction

Displacement correction corresponds to removing the shifting effect of the estimated storm. In this step, the Principal Component Analysis method (PCA, Johnson and Hebert [66]) is used in order to obtain the weighted centroid and orthogonal variables (eigenvectors, eigenspace) of the SPP storm and reference data (Figure 4a). Once the geometric properties of the objects are obtained, the weighted centroid is matched and the object is rotated accordingly to fit the eigenvectors of the reference storm data.

**Figure 4.** ST-CORAbico systematic error subtraction. (**a**) In error correction, storm centroid and eigenvectors derived from principal component of GPM-IMERG are fitted to the observed event; and, (**b**) magnitude subtraction using both satellite and observed empirical distribution functions, with respect to intensity.

#### Volume Correction

Volume correction corresponds to the subtraction of the magnitude source of error of the SPP. Using the statistical Empirical Quantile Method (EQM) [67], magnitude error is subtracted by adjusting all moments of the empirical cumulative distribution functions (*ecdf s*) of the SPP in terms of intensity, with respect to the reference data (Figure 4b). EQM builds the *ecdf* for the observed (*ecdfobs*) and the satellite (*ecdfsat*) while using the intensity storm distribution *Is*, as:

$$EQM = ecdf\_{obs}^{-1}(ecdf\_{sat}(l\_s))\tag{10}$$
