## 2 Materials and Methods
### Methods of Analysis
#### 2.2.2 Statistical Indicators  
To analyze the capability of IMERG to estimate precipitation, the following three parameters were considered: annual precipitation total, annual precipitation frequency, and precipitation intensity. Annual precipitation total is the sum of all hourly precipitation amounts throughout the year and is measured in mm/y; annual precipitation frequency is the number of records greater than 0.1 mm/h divided by the total number of hours throughout the year and is expressed as a percentage; and finally, precipitation intensity is the annual precipitation total divided by the number of hours with records greater than 0.1 mm/h throughout the year. The spatial differences in the multi-year averages of these parameters between station-derived observations and IMERG data were analyzed and compared.  
The ability of IMERG to estimate precipitation at the hourly time scale was evaluated by comparing its estimates with observations derived from meteorological stations using conventional statistical indicators [57; 58], including the Pearson correlation coefficient (CC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Relative Bias (RB). CC reveals the linear relationship between satellite-derived precipitation data and station observations; the closer the CC value is to 1, the stronger the correlation. Additionally, the one-sample \(t\)-test at 0.05 level is used to detect whether the generated correlation coefficient is significant. MAE represents the average of the absolute differences between the two types of data. RMSE measures the degree of dispersion between the two datasets; the closer the RMSE value is to 0, the smaller the degree of dispersion. RB indicates the percentage of the difference between satellite-derived precipitation data and station observations relative to the latter; the smaller the bias is, the closer the error is to 0.  
The diurnal variation of the gauge-derived and IMERG data can be illustrated by the changes of hourly total precipitation, frequency, and intensity throughout the day (24 h). Several qualitative indicators are commonly used to measure the capabilities of satellite precipitation products. Similar to previous studies, the data obtained from IMERG at different hours of the day were evaluated using the following metrics [10; 21; 47; 59]: Probability of Detection (POD), False Alarm Ratio (FAR), and Critical Success Index (CSI). Specifically, POD represents the fraction of precipitation hours that IMERG detects among the total actual precipitation hours, and FAR represents the fraction of unreal precipitation hours among all the hours recorded by IMERG [60]. The CSI can actually be expressed as a function of POD and FAR combining the characteristics of false alarms and missed precipitation hours [61]. These metrics comprehensively assess the performance of satellite precipitation products, clearly determining their advantages and disadvantages [15; 18]. The methods used to calculate these parameters and their optimal values are shown in Table 1.  
Figure 1: Spatial distribution of meteorological stations used in this study over land areas of the northern hemisphere. The four rectangles represent the regions with a relatively large number of stations: North America (25\({}^{\circ}\)–59\({}^{\circ}\)N, 125\({}^{\circ}\)–50\({}^{\circ}\)W), Europe (40\({}^{\circ}\)–59\({}^{\circ}\)N, 15\({}^{\circ}\)W–50\({}^{\circ}\)E), North Asia (30\({}^{\circ}\)–59\({}^{\circ}\)N, 50\({}^{\circ}\)–150\({}^{\circ}\)E), and South Asia (10\({}^{\circ}\)–30\({}^{\circ}\)N, 60\({}^{\circ}\)–150\({}^{\circ}\)E).