## 2 Materials and Methods
### Methodologies for the Assessment of Precipitation Products  
The accuracy of each precipitation product was assessed at daily, monthly, seasonal, and annual time scales by comparing precipitation estimates with observations at the 342 rain gauges. Based on the availability of the different products with CMORPH only available from December 2002 and APHRODITE to December 2007, the comparison was performed from January 2003 to December 2007. Point-to-pixel assessment was used to avoid additional errors when interpolating between the gauges [44]. All precipitation values are pooled together for the period 2003-2007 to find the overall performance of precipitation products [45]. In addition, NEM (November-February) and SWM (May-August) seasonal evaluations were conducted by using monthly precipitation (_i.e._, four months for five years = 20 months, 6840 precipitation values for 342 stations). A Student's _t_-test was applied to evaluate the level of significance of the differences between observations and estimations at the selected time steps. A typical significance level of 0.05 was used. For assessing the spatial variations in estimation error, the 38 MMD principal rain gauges with better quality were attributed to seven sub-regions in Malaysia, with each showing different precipitation patterns (Figure 1 and Table 1): (1) the northern PM (zone A); (2) the eastern PM (zone B); (3) the middle PM (zone C); (4) the western PM (zone D); (5) the southern PM (zone E); (6) the southern EM (zone F); and (7) the northern EM (zone G). Most of the regions received higher precipitation in December and January due to the Northeast monsoon, except for the northern and western regions of PM, which are sheltered by the Titiwangsa Range. By contrast, the middle PM described complex topography but included only two rain gauges (ID 48631 and 48631), located at altitudes of about 1500 m.a.s.l. We used various statistical measures to evaluate the performance of the various SPPs against the data from the rain gauges. The coefficient of determination (R\({}^{2}\)) is widely used as a means to quantify the correlation between two data sets (in this case one of the SPPs and the rain gauge data); the value of R\({}^{2}\) ranges between 0 (no correlation) and 1 (perfect correlation). The root mean square error (RMSE) and the mean absolute error (MAE) are different measures of the magnitude of the difference between two datasets, while the mean error (ME) allows us to study the bias between the two datasets. Finally, the relative bias (RB) estimates the systematic bias of satellite precipitation in percentage (%). A well performing product should have low ME, RMSE, and MAE values and a low value of the absolute \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No** & **Name** & **Spatial/Temporal Resolution** & **Coverage** & **Period** & **Data Reference** \\ \hline
1 & 3B42 RT & 0.25\({}^{\circ}\)/daily & global (50\({}^{\circ}\)N–S) & 2002–present & [37] \\
2 & 3B42V7 & 0.25\({}^{\circ}\)/daily & global (50\({}^{\circ}\)N–S) & 1998–present & [37] \\
3 & GPCP-1 DD & 1\({}^{\circ}\)/daily & global (50\({}^{\circ}\)N–S) & 1996–present & [39] \\
4 & PERSIANN-CDR & 0.25\({}^{\circ}\)/daily & global (60\({}^{\circ}\)N–S) & 1983–present & [41] \\
5 & CMORPH & 0.25\({}^{\circ}\)/3-hourly & global (50\({}^{\circ}\)N–S) & 2002–2013 & [43] \\
6 & APHRODITE & 0.25\({}^{\circ}\)/daily & Eurasia (84\({}^{\circ}\)N–15\({}^{\circ}\)S) & 1950–2007 & [28] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information on SPPs used in this study. magnitude of the RB. The equations for evaluating all these statistical indicators are given, for instance, by [PERSON] _et al._[14]. A probability distribution function (PDF) was computed to evaluate the frequency of different rainfall intensities. Such information is important because the same amount of rainfall occurring over two different durations will lead to different flood patterns [44].