# The Hydroological Balance in Micro-Watersheds Is Affected by Climate Change and Land Use Changes
## 2 Materials and Methods
### Hydrological Simulation  
We chose to use WEAP because it can be used to analyze a wide range of issues that water planners face using a scenario-based approach. In addition, WEAP uses monthly data instead of daily data, which represents an advantage over models that use daily data since such robust databases are not available in the study area. WEAP has five methods to calculate the hydrological simulation, although, in this study, the soil moisture method was applied as it is the most robust of the five. The method divides the soil into two layers: root zone and deep zone, to estimate through specific functions the processes of surface runoff, evapotranspiration, interflow, base flow, and soil moisture [31; 37] (Figure 2). According to [PERSON] et al. [37], Equations (1) and (2) are used to calculate the water balance in the root zone and in the deep zone, depending on the type of coverage.  
\[SW_{j}\frac{dz_{i,j}}{dt}=P_{e}(t)-PET(t)K_{ej}(t)\left(\frac{5z_{1,j}-2z_{1,j}^ {2}}{3}\right)-P_{e}(t)z_{1,j}^{LAl_{j}}-f_{j}k_{s}z_{1,j}^{2}-\left(1-f_{j} \right)k_{j}z_{1,j}^{2} \tag{1}\]  
\[Dw_{j}\frac{dz_{2,j}}{dt}=\left(1-f_{j}\right)k_{j}z_{1,j}^{2}-k_{2}z_{2,j}^{2} \tag{2}\]  
where: \(Sw_{j}\): is the water storage capacity in the root zone (mm), \(z_{1,j}\): initial moisture in the root zone (1, 0), \(P_{e}(t)\): effective precipitation over time (mm), \(PET\) (\(t\)): potential evapotranspiration of the reference crop (mm time\({}^{-1}\)), \(k_{c,j}(t)\): crop coefficient over time (dimensionless), \(LAI_{j}\): leaf area index (m\({}^{2}\) m\({}^{-2}\)), \(f_{j}\): preferential flow direction (1 = 100% horizontal, 0 = 100% vertical), \(k_{j}\): storage conductivity (mm time\({}^{-1}\)), \(Dw_{j}\): water storage capacity in the deep zone (mm) and \(z_{2,j}\): initial humidity in the deep zone (1, 0).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Land Use** & **Total Surface** & **\%** & **Chapingo River** & **\%** & **Texacco River** & **\%** & **Senardino River** \\ \hline Agriculture (rainfed) & 2294.8 & 29.6 & 420.4 & 21.6 & 1042.8 & 26.7 & 831.6 & 44.2 \\ Temperate forest & 2201.4 & 26.1 & 472.1 & 24.2 & 1448.5 & 37.1 & 100.8 & 5.4 \\ Reforestation & 1145.6 & 14.8 & 395.4 & 20.3 & 199.9 & 5.1 & 550.3 & 29.2 \\ Urban & 949.9 & 12.3 & 300.0 & 15.4 & 545.9 & 14.0 & 104.0 & 5.5 \\ Agriculture (irrigated) & 540.3 & 7.0 & 89.1 & 4.6 & 354.6 & 9.1 & 96.7 & 5.1 \\ Secondary vegetation & 438.7 & 5.7 & 160.9 & 8.3 & 166.3 & 4.3 & 111.5 & 5.9 \\ Mine & 212.2 & 2.7 & 87.0 & 4.5 & 39.4 & 1.0 & 85.9 & 4.6 \\ Agriculture (protected) & 80.8 & 1.0 & 18.7 & 1.0 & 60.2 & 1.5 & 1.9 & 0.1 \\ Pasture & 52.2 & 0.7 & 3.6 & 0.2 & 48.6 & 1.2 & 0.1 & 0.0 \\ Water & 4.6 & 0.1 & 1.3 & 0.1 & 3.3 & 0.1 & 0.0 & 0.0 \\ \hline Total & 7740.6 & 100.0 & 1948.5 & 100.0 & 309.4 & 100.0 & 1882.6 & 100.0 \\ \hline \hline \end{tabular} Source: Own elaboration based on [PERSON], 2022, [27].  
\end{table}
Table 1: Land use and occupied surface (hectares) in the studied micro-watersheds (based on [PERSON], 2022, [27]).  
Figure 2: Soil moisture distribution (adapted from [PERSON], 2005, [37]).