## 2 Materials and Methods
### Methods
#### 2.2.2 Nutrient Loads Estimation
Surface runoff transports nutrients to the top 10 mm above the soil. Equation (13) was used to calculate the amount of nitrate in runoff. \[\text{NO3}_{\text{surf}}=\beta_{\text{NO3}}\cdot\text{Conc}_{\text{NO3,mobile }}\cdot\text{Q}_{\text{surf}}, \tag{13}\]  
Figure 3: Nitrogen transformation process in the soil taken into account by the SWAT model [33]. NO3 surf is the quantity of nitrate retained during surface runoff (kg ha\({}^{-1}\)), \(\beta_{\text{NO3}}\) represents the nitrate percolation coefficient, \(\text{Conc}_{\text{NO3},\text{mobile}}\) expresses the concentration of nitrate in the runoff water for the top 10 mm of soil (kg mm\({}^{-1}\)), \(\text{Q}_{\text{surf}}\) is the runoff height of the given day (mm). Surface runoff allows organic nitrogen, mostly attached to sediments, to transfer to the main channel in the watershed. The amount of organic nitrogen transported with the sediments to the watercourse is calculated using Equation (14) [63, 64]:  
\[\text{orgN}_{\text{surf}}=0.001\cdot\text{ConC}_{\text{orgN}}\cdot\frac{\text {sed}}{\text{area}_{\text{nru}}}\cdot\varepsilon_{\text{Nsed}} \tag{14}\]  
where \(\text{orgN}_{\text{surf}}\) is the amount of organic nitrogen contained in surface runoff transported in kg ha\({}^{-1}\), \(\text{ConC}_{\text{orgN}}\) is the concentration in g t\({}^{-1}\) of soil organic nitrogen in the first 10 mm above soil (g t\({}^{-1}\)), sed is the amount of sediment produced on the given day (metric tons), the area is the HRU area (ha), and \(\varepsilon_{\text{Nsed}}\) is the nitrogen enrichment rate. The nitrogen enrichment rate is estimated according to Menzel [65]. Thus, Equation (15) was used to calculate the nitrogen enrichment rate:  
\[\varepsilon_{\text{Nsed}}=0.78\cdot\left(\text{ConC}_{\text{sed,surq}}\right) \tag{15}\]  
where \(\text{ConC}_{\text{sed,surq}}\) is the in-runoff sediment concentration (t m\({}^{-3}\)). The concentration of sediment in surface runoff is calculated according to Equation (16):  
\[\text{ConC}_{\text{sed,surq}}=\frac{\text{sed}}{10.\text{area}_{\text{nru}} \cdot\text{Q}_{\text{surf}}} \tag{16}\]  
where sed is the amount of sediment on a given day (metric tons), \(\text{area}_{\text{nru}}\) is the HRU area (ha), and \(\text{Q}_{\text{surf}}\) is the amount of runoff on a given day (mm). Like nitrogen, SWAT also divides the phosphorus terrestrial cycle into six different interconnected pools [33]. These six pools are grouped according to their characteristics into two forms. Three phosphorus pools are inorganic form, and the other three are organic form. \"Fresh\" organic phosphorus is associated with crop residues and microbial biomass, and mineral phosphorus is associated with soil humus. The mineralization of organic phosphorus only takes place from the active pool containing the humic substances and from the residues' pool. The mineral forms of phosphorus are further subdivided into three \"pools\": solution, active and stable. The equilibrium between the pool in solution and the active pool is established quickly, from a few days to a few weeks, whereas the dynamic between the active and stable pool evolves much more slowly (Figure 4). \[\text{P}(\text{kg})=\text{\%P}\times\text{1 kg}(\text{of the fertilizer})/100 \tag{9}\]0 Phosphorus transformation process in the soil is taken into account by the SWAT model [33]. The movement of soluble phosphorus in the soil is by diffusion. Due to its low mobility, transfer by surface runoff only concerns soluble phosphorus stored in the top 10 mm of soil [64].