*3.3. Evaluation of ST-CORAbico*

The evaluation was done by comparing the bias-corrected results with two widely used probabilistic bias correction methods— the Distribution Transformation (DT) method and the Gamma Quantile Mapping (GQM). The DT method was originally developed for the statistical downscaling of climate model data [68]. The method corrects the mean and difference in variation of the SPP by matching the satellite and the observed distribution based on Equation (11):

$$DT = (SAT(t) - \mu\_{sat})DT\_{\text{\tiny{\pi}}} + \pi\_{sat} \times DT\_{\mu} \tag{11}$$

where, *μ* and *τ* are the mean and standard deviation of the observed and satellite, respectively. *DTμ* and *DTτ* are the mean and standard deviation ratio between the observed and satellite data at time *t*.

The Gamma Quantile Mapping method uses the same methodology as the Empirical Quantile mapping method (10), based on the assumption that both observed *OBS* and satellite *SAT* intensity follows a gamma distribution [69]. DT and GQM are implemented for each time-step in order to correct the storm event. The bias correction performance is evaluated based on three widely used error metrics: the Root Mean Square Error (Equation (12)) for evaluating the magnitude error, the bias level (Equation (13)) to evaluate the systematic bias, and the correlation coefficient (Equation (14)) in order to analyse the linear correlation between the observed and the bias-corrected storm event.

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} (OBS\_i - SAT\_i)^2} \tag{12}$$

$$Bias = \frac{\sum\_{i=1}^{N} (SAT\_i - OBS\_i)}{\sum\_{i=1}^{N} (OBS\_i)} \tag{13}$$

$$r = \frac{\sum\_{i=1}^{N} (SAT\_i - \overline{SAT})(OBS\_i - \overline{OBS})}{\sqrt{\sum\_{i=1}^{N} (SAT\_i - \overline{SAT})^2} \sqrt{\sum\_{i=1}^{N} (OBS\_i - \overline{OBS})^2}} \tag{14}$$

where, *OBS* represents the rainfall values of the reference rain gauge data and *SAT* are the satellite and the bias-corrected storm obtained with each method.
