## 5 Results and Discussion  
### Annual Precipitation  
To explore the quality of GPM precipitation data, a comparison between the estimates from rain gauges and GPM was carried out based on data collected from 2015 to 2017. Figures 7 and 8 show the scatterplots of GPM IMERG satellite precipitation versus rain gauge data at annual scales over Mexico from 2015 to 2017. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistical Metrics** & **Unit** & **Perfect Value** \\ \hline Correlation Coefficient (CC) & N/A & 1 \\ Root Mean Square Error (RMSE) & mm & 0 \\ Mean Absolute Error (MAE) & mm & 0 \\ Relative Bias (BIAS) & N/A & 1 \\ Probability of Detection (POD) & N/A & 1 \\ False Alarm Ration (FAR) & N/A & 0 \\ Critical Success Index (CSI) & N/A & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The range and perfect values of statistical performance measures. Figure 7: Comparison of the precipitation between GPM satellite and rain gauges in (**a**) 2015; (**b**) 2016; and (**c**) 2017 at annual scale. Figure 8: _Cont._  
As can be observed, the conventional evaluation metrics are also indicated in these figures, and all the evaluation results are presented in Table 4. As mentioned before, the scale of the GPM data was projected into 5 km by 5 km since the STEPS model can process the data in the range from 5 km by 5 km to 1 km by 1 km. In theory, each graph should have 2829 points (one point for each station). As expected, GPM showed a relatively high degree of agreement with rain gauges at annual scales, because the values of CC are close to 1 (0.91, 0.88 and 0.90), which meets the finds by [PERSON] et al. (2017) Similar study obtained the close CC results. However, there are significant gaps in the data points of 2017, as shown in Figure 7c, because the precipitation data for rain gauges in 2017 were missing for some gauge stations (perhaps due to maintenance). The RMSE for 2017 is therefore significantly lower than for the previous two years. The values of RMSE are 416.29 mm and 406.79 mm in 2015 and 2016, respectively. Furthermore, the GPM shows a slight underestimation of precipitation according to the BIAS value, which means that GPM generated negative errors (bias \(<\) 0); the greater the BIAS value is from 1, the more biased the data is. Thus, the BIAS is shown to have decreased from \(-\)4.01% to \(-\)8.63% between 2015 and 2017, which indicates the data for 2017 is more biased, and GPM is underestimating more. This may because the GPM is not sensitive to light precipitation. In addition, the values of MAE fluctuated from 0.29 to 0.33 for the three years, with the lowest value in 2016 and the highest in 2017. In terms of probabilistic statistical evaluation metrics, the POD (0.73 to 0.86), FAR (0.19 to 0.25) and CSI (0.55 to 0.73) are very satisfying, indicating that GPM IMERG can  
Figure 8: Comparisons of the daily precipitation for a single gauge between GPM and single gauge (**a**) gauge 1084 (**b**) gauge 7038 (**c**) gauge 25074 in 2015 (**a**–**c**); (**d**) gauge 1084 (**e**) gauge 7038 (**f**) gauge 25074 in 2016 (**d**–**f**); and (**g**) gauge 1084 (**h**) gauge 7038 (**i**) gauge 25074 in 2017 (**g**–**i**), respectively. capture most precipitation events over Mexico. Due to the missing data for rain gauges in 2017, the POD, FAR and CSI are relatively bad. Overall, the results are acceptable and the GPM IMERG product is able to reproduce a mostly consistent distribution of precipitation at the annual scale. In order to evaluate the performance of the GPM versus rain gauges at the national scale, Figure 9 presents the mean annual precipitation for the three-year period from 2015 to 2017, and the results of the evaluation metrics for GPM for the period 2015-2017 are shown in Table 4. From both, it can be seen that GPM present an underestimation of mean annual precipitation over Mexico, especially for the southern low altitude regions where observations of GPM can improve.