## 2 Materials and Methods
### Soil and Water Assessment Tool (SWAT)  
The Soil and Water Assessment Tool (SWAT) is a semi-distributed physically-based basin-scale model developed in [41]. Based on daily/sub-daily precipitation data, temperature, relative humidity, and wind speed data, the SWAT model uses the soil conservation services (SCS) method and simulates hydrological processes, such as surface runoff, snowmelt runoff, lateral flow, and infiltration in a river basin, as well as water balance and streamflow [42; 43; 44]. In the SWAT model, vegetation and soil characteristics are categorized by their hydrologic response unit (HRU). Run-off is calculated separately from the HRUs, and the total run-off of the entire catchment is calculated using the hydrological model [34]. The SWAT hydrological model is based on the basic water balance equation:  
\[SW_{t}=SW_{0}+\sum_{t=1}^{t}(R_{day}-Q_{surf}-E_{a}-W_{sep}-Q_{gw}), \tag{1}\]  
where \(SW_{t}\) (mm H\({}_{2}\)O) is the final soil water content, \(SW_{0}\) (mm H\({}_{2}\)O) is the initial soil water, \(t\) is the time (in days), \(R_{day}\) is the daily precipitation amount, \(Q_{surf}\) is the surface run-off, \(E_{a}\) is the actual evapotranspiration, \(W_{sep}\) is the amount of water that percolates to the vadose zone on day \(t\), and \(Q_{gw}\) is the return flow on day \(t\).  
Water yield is one of the critical parameters for analyzing sustainable water resource management. The water yield is the cumulative amount of water leaving the HRU and entering the main tributary during a given time step [41; 45]. Water yield within a basin is evaluated by the model based on the following equation:  
\[W_{yield}=Q_{s}+Q_{gw}+Q_{lat}-T_{loss}, \tag{2}\]  
where \(W_{yield}\) is the measure of water yield (mm), \(Q_{s}\) is the surface runoff (mm), \(Q_{gw}\) is the groundwater flow (mm), \(Q_{lat}\) is the lateral flow contribution to the streamflow (mm), and \(T_{loss}\) is the total losses (mm) from the tributary in the hydrologic response unit (HRU) by means of transmission through the bed. The water yield is one of the main components of water balance. The water balance is the (Precipitation = Water Yield + Evapotranspiration - Transmission Losses). Evapotranspiration is considered as the major loss. Water yield is the sum of surface runoff, groundwater flow, and lateral flow, subtracting transmission losses and pond abstractions. Total water yield (WYLD) is the amount of streamflow leaving the watershed outlet amid the time step. Surface runoff can be estimated using the Soil Conservation Service (SCS) curve number system by the United States Department of Agriculture (USDA), given by:  
\[Q_{s}=\frac{\left(P_{daily}-0.2S\right)2}{\left(P_{daily}+0.8S\right)}, \tag{3}\]  
\[S=25.4\left(\frac{100}{CN}-1\right), \tag{4}\]  
where \(P_{daily}\) is the daily precipitation (mm), \(S\) (Equation (4)) is the retention parameter (mm), and \(CN\) is the curve number. The prediction of lateral flow by the SWAT model is defined as:  
\[Q_{lat}=0.024\left(\frac{2S*SC\sin\alpha}{\theta_{d}L}\right), \tag{5}\]  
where \(Q_{lat}\) is the lateral flow (mm/day), \(S\) is the trainable volume of soil water per unit area of saturated thickness (mm/day), \(SC\) is the saturated hydraulic conductivity (mm/hr), \(L\) is the flow length, \(\sin\alpha\) is the land slope, and \(\theta_{d}\) is the trainable porosity. The groundwater flow, \(Q_{gw}\), contributes to the main channel, which can be calculated as:  
\[Q_{gw}=Q_{gw-1}\times e^{-\omega\Delta t}+W_{aqu}\left(1-e^{-\omega\Delta t }\right), \tag{6}\]  
where \(Q_{gw}\) is the groundwater flow (mm), \(\omega\) is the baseflow recession constant, \(\Delta t\) is the time step, and \(W_{aqu}\) is the water recharge entering the aquifer (mm/day).