# Evaluation of Grid-Based Rainfall Products and Water Balances over the Mekong River Basin
## 3 Methods
### Modeling Method for Hydrological Evaluation of Daily Rainfall Series
#### 3.2.2 Model Calibration  
The parameters and the default range recommended by previous studies [27; 43; 44; 45] were first selected for sensitivity analysis and calibration in the current study. Then, one-at-a-time (OAT) in SWAT Calibration and Uncertainty Procedures (SWAT-CUP), each parameter was held constant, changing only one parameter at a time, to identify its effect on the model output or objective function. The results were used to fill out more sensitive parameters among the initial selection. The SWAT-CUP software package with the SUFI-2 algorithm was used for calibration, validation, and sensitivity analysis [45], because it is recognized as a robust tool for model calibration and validation [16; 42; 46]. The values of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistical Metric** & **Unit** & **Equation** & **Optimal Value** \\ \hline Correlation coefficient (CC) & - & CC = \(\frac{\sum_{i=1}^{n}(\text{O}_{i}-\overline{\text{O}})(\text{P}_{i}-\overline{ \text{P}})}{\sqrt{\sum_{i=1}^{n}(\text{O}_{i}-\overline{\text{O}})}^{2}}\) & 1 \\ Standard error (SE) & & SE = \(\frac{\overline{\text{S}}}{\sqrt{\overline{\text{S}}}}\) & \\ Root-mean-squared deviation (RMSD) & mm & RMSD = \(\sqrt{\frac{1}{\text{N}}\sum\limits_{i=1}^{n}(\text{O}_{i}-\text{P}_{i})^{2}}\) & 0 \\ Mean absolute error (MAE) & mm & MAE = \(\frac{1}{\text{N}}\sum\limits_{i=1}^{n}\text{O}_{i}-\text{P}_{i}\) & 0 \\ Percent bias (PBIAS) & \% & PBIAs = \(\frac{\sum_{i=1}^{n}(\text{O}_{i}-\text{O}_{i})}{\sum_{i=1}^{n}(\text{O}_{i}- \overline{\text{O}})}\times 100\) & 0 \\ Nash–Sutcliffe efficiency & - & NSE = \(1-\frac{\sum_{i=1}^{n}(\text{O}_{i}-\overline{\text{O}})^{2}}{\sum_{i=1}^{n}( \text{O}_{i}-\overline{\text{O}})^{2}}\) & 1 \\ Probability of detection (POD) & - & POD = \(\frac{1}{\text{T}_{i}^{2}\text{M}}\) & 1 \\ False alarm ratio (FAR) & - & FAR = \(\frac{\overline{\text{T}}_{i}^{2}\text{F}}{\text{T}_{i}^{2}\text{F}}\) & 0 \\ Critical success index (CSI) & - & CSI = \(\frac{\overline{\text{T}}_{i}^{2}\text{M}+\overline{\text{T}}}{\text{T}+ \overline{\text{T}}}\) & 0 \\ \hline \hline \end{tabular} Note: n, number of samples; O, observed precipitation (or observed streamflow); P, the precipitation estimates from the evaluated products (or simulated streamflow); T, the total number of the rainy days that the gridded precipitation products (GPPs) successfully detect rain; M, the number of days that the GPPs fail to detect the observed rain; F, the number of days that the GPPs fail to detect no-rain cases (unsuccessful no-rain detection); \(\sigma\), standard deviation.  
\end{table}
Table 3: The statistical metrics and their corresponding equations used for evaluating the overall performance of satellite precipitation products.  
the parameters were calibrated with four iterations, using 1500 model runs for each iteration, by the SUFI-2 method.  
To evaluate model performance, the NSE [47] and the coefficient of determination (R2) were used. Uncertainties were quantified by two measures: P-factor and R-factor. P-factor is the percentage of observation points bracketed by 95% prediction uncertainty (95 PPU) to measure the degree of uncertainty, and R-factor is the average width of the 95 PPU band divided by the standard deviation of the observed values to reflect the strength of the uncertainty analysis, for which a P-factor above 0.70 and an R-factor of around 1 are considered satisfactory simulations [45].