## 2 Materials and Methods
### Hydrologic Model  
HEC-HMS (Hydroologic Engineering Center's Hydrologic Modeling System) is a widely used hydrological model developed by the US Army Corps of Engineers (USACE) for applications such as flood analysis and simulation [51]. It is primarily classified as a lumped hydrologic model as it predominantly utilizes relatively simple methods such as the SCS Curve Number, unit hydrograph, and Muskingum routing for estimating effective rainfall, watershed transformation, and river routing calculations, respectively. Although it mainly employs point-based data (i.e., rain gauge observation), it is possible to construct a model that incorporates gridded radar-based rainfall data by utilizing the tools of HEC-GeoHMS (Geospatial Hydrologic Modeling Extension) [52] and the ModClark (modified Clark) method [1; 53; 54]. Figure 5 depicts the schematic diagram of the ModClark watershed transformation method, which is a modification of [PERSON]'s unit hydrograph method [55] to enable the simulation of spatially distributed grid-based rainfall data.  
In this approach, individual unit hydrographs are computed for each grid cell, taking into account the transitions between cells. The determination of the unit hydrograph for each grid cell involves the consideration of the time of concentration, which relates to the travel time of water through the watershed, as described in Equation (1). These unit hydrographs undergo storage attenuation processes across the entire watershed, as indicated with  
Figure 5: ModClark conceptual model, taken from [54].  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**IMERG Specifications**} \\ \hline File Name: 3B-HHR\(\_\)MS\(\_\)MRG\(\_\)3 IMERG\(\_\)SYYY\(\_\)SMM\(\_\)SDD-S\(\_\)HH\$MM\$NNN- \\ ESHH\$MM\$NNN\$MMM.V06B.HDF5.nc4 \\ \hline Resolution & Description \\ \hline Temporal & 30 min (final run, 3.5 months latency) \\ Spatial & about 10 km (from 90\({}^{\circ}\) N-90\({}^{\circ}\) S) \\ \multicolumn{2}{c}{60\({}^{\circ}\) N-60\({}^{\circ}\) S full} \\ \hline Data structure & Description \\ \hline Map system & WGS84 \\ \hline \hline \end{tabular}
\end{table}
Table 3: IMERG data (version 06) specifications.  
Equation (2), resulting in the generation of individual cell hydrographs at the watershed outlet. The storage attenuation can be attributed to the overall retention characteristics of the watershed. By convolving these individual cell hydrographs with excess rainfall for each grid cell, the direct rainfall-runoff hydrograph for the entire watershed can be obtained.  
\[\left[\text{travel time}\right]_{\text{cell}}=\text{T}_{\text{c}}\frac{\left[ \text{travel length}\right]_{\text{cell}}}{\left[\text{travel length}\right]_{\text{max}}} \tag{1}\]  
\[\text{O}_{\text{i}}=\left[\frac{\Delta\text{t}}{\text{R}+0.5\times\Delta \text{t}}\right]\text{I}_{\text{avg}}+\left[1-\frac{\Delta\text{t}}{\text{R}+0. 5\times\Delta\text{t}}\right]\text{O}_{\text{i}-1} \tag{2}\]  
where \(\text{T}_{\text{c}}\) refers to the time of concentration for the entire watershed [T], \(\text{O}_{\text{i}}\) represents the unit discharge at time i [L\({}^{3}\)T\({}^{-1}\)], R denotes the storage coefficient [T], \(\text{I}_{\text{avg}}\) represents the average inflow between time i \(-\) 1 and i [L\({}^{3}\)T\({}^{-1}\)], and \(\Delta\)T signifies the time interval [T].