## 3 Methodology
### Hydrological Models  
Hydrological models are utilized for various applications. Previous studies comparing lumped and distributed models in outlet streamflow simulation have found minimal differences in performance between the two model types [48; 49]. Given the scope of this study and the prevalent use of lumped models for hydrological simulation and forecasting, lumped models were selected. Distributed models were excluded due to their complexity and data demands. Two lumped hydrological models were used in this study: the Xiannjiang model (XAJ) [50] and the mod'ele du G'enie Rural 'a 4 param'etres (GR4J) [51]. These two models are widely used for streamflow simulation and have proven effective in various hydrological contexts [52; 53; 54]. The XAJ proposed by [50] is a lumped hydrological model designed for humid and semi-humid regions. This model conceptualizes the catchment as a soil box, consisting of upper, lower, and deep soil layers. The XAJ model's computational process consists of four modules (Figure 2): (1) Calculation of catchment evapotranspiration and soil moisture, using a three-layer evapotranspiration model--rainfall first replenishes the upper layer, then the lower and deep layers; evapotranspiration initially depletes the upper layer's soil moisture, followed sequentially by the lower and deep layers. (2) Runoff generation, which utilizes a saturation excess runoff model where a storage capacity curve controls the distribution of precipitation throughout the catchment to calculate total runoff. (3) Water source partitioning, using a free water storage capacity curve to separate the total runoff into surface runoff, subsurface flow, and underground runoff. (4) Catchment routing, where surface runoff typically uses the unit hydrograph method, while interflow and groundwater flow use the linear reservoir method. The XAJ model is characterized by 15 parameters: 4 related to evaporation, 2 for runoff generation, and 9 for runoff routing. These parameters (Table 2) require calibration using observed streamflow to accurately reflect the hydrological characteristics of a specific watershed. Further details can be found in the study by [PERSON] [50]. Figure 2: Structure of the XAJ model ([PERSON], 1992 [50]). Developed in 2003 by French scholar [PERSON] et al., based on the GR3J model [55], the GR4J model has a simple structure with only four free parameters (Table 2) and uses two nonlinear reservoirs for production and routing calculations (Figure 3): (1) The production reservoir first determines effective precipitation \(Pn\) and residual evaporation capacity \(En\) based on catchment precipitation \(P\) and evaporation capacity \(E\), then calculates the precipitation \(Ps\) and replenishes the production reservoir and the evapotranspiration \(Es\). (2) The routing reservoir employs time segment unit hydrographs for routing calculations. Different runoff components have different routing times; thus, rainfall is split into two parts: 90% of the rainfall is routed using unit hydrograph UH1, needing adjustment through the routing reservoir, and the remaining 10% flows directly to the catchment outlet section, routed using unit hydrograph UH2. More details are available from [PERSON], [PERSON] [51].