## 3 Methodology and Study Area  
To evaluate the GPM IMERG, several steps were carried out, which are presented in Figure 1 below. The process started with the preparation of the rain gauge precipitation measurement data and the GPM data processing and preparation. The following step consisted of data comparison, which involved four major steps carried out by MATLAB processing [39], the last step of which was precipitation nowcasting of the observed GPM data by using the STEPS model. The STEPS nowcasting model is an available advanced Quantitative Precipitation Forecast (QPF) system, which was developed in the cooperation of the Australian Bureau of Meteorology and the UK MetOffice. A detailed mathematical description of the STEPS model can be found in [40; 41]. The model generates ensembles of rainfall nowcasts by employing both the extrapolation of radar images and the downscaled rainfall output of Numerical Weather Prediction (NWP) models. The basis behind STEPS is to represent the uncertainty caused by the unpredictable rainfall growth and decay processes by adding stochastic perturbations to the deterministic extrapolation of radar images. The stochastic perturbations are designed to account for the unpredictable rainfall growth and decay processes and to reproduce the dynamic scaling of rainfall fields. Some studies have proved this model is reliable in several applications, such as prediction of flows in the sewer system [42] and hydrological forecasting in catchment [43]. The study area of this project is the whole of mainland Mexico, which is located at 23.626\({}^{\circ}\) N and 102.538\({}^{\circ}\) W in the southern portion of North America and covers a land surface area of 1964 million square kilometers [44]. The climate in Mexico is determined by different factors, such as latitude, elevation and ocean currents. As a result of its geographical location, the northern part of the country is located in a temperate area, while the southern part is in the inter-tropical area of the globe. Nearly two-thirds of the territory is considered semi-arid or arid, with annual precipitation lower than 500 mm, whereas one third is regarded as humid (the southeast), with precipitation of over 2000 mm per year [44]. Figure 2 shows the precipitation distribution in Mexico from 2010 to 2015 observed by ground weather radar, with more precipitation in the south of Mexico and less in the north during this period. The west coast of Mexico has a relatively low intense rainfall, while the east coast of Mexico has a relatively high intense rainfall, the details can be referred from [45]. This graph was used in this study as a reference for the GPM rainfall observations comparison. In most parts of Mexico, precipitation is more intense in the summertime when there is often torrential rain. Figure 3 presents the monthly average rainfall and temperature in the period of 1943 to 2018 over Mexico. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Satellite** & **Spatial** & **Temporal** & **Coverage** & **Minimum** & **Period** & **Algorithm** \\
**Mission** & **Resolution** & **Resolution** & **Accuracy** & **Accuracy** & **Accuracy** & **Accuracy** \\ \hline GPM ‘Early’ & & & & 4 h & & \\ \hline GPM ‘Late’ & 0.1\({}^{\circ}\) & 0.5 h & 65\({}^{\circ}\) S–65\({}^{\circ}\) N & 12 h & 2015-present & IMERG \\ \hline GPM ‘Final’ & & & & 2.5 months & & \\ \hline TRMM & 0.25\({}^{\circ}\) & 3 h & 50\({}^{\circ}\) S–50\({}^{\circ}\) N & 9 h & 1997–2015 &
\begin{tabular}{c} Probability \\ Matching \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 1: The key characteristics of GPM and TRMM. Figure 1: Flowchart of the evaluation process of the project. Figure 2: Maps showing the distribution of mean annual precipitation (mm) (2010–2015) (source: National Water Commission (CONAGUA)). Rain gauge data was applied to provide a ground-based precipitation reference for GPM satellite data in this study.