## 3 Materials and Methods
### Process-Based or Conceptual Models  
Process-based models employ diagrams and interlinks among parallel processing and flowcharts of mass transfer in between different zones (entities) to facilitate complex physical and biochemical interactions of soil, crops and water bodies [18]. Soil particle redox potential, electrical conductivity, etc., are ion transfer diffusion phenomena and leaching controllers [17]. Organic chemical screening is performed using leaching models, which account for the mobility of the chemicals in the soil. Despite not being able to forecast concentrations, they are still straightforward and only need information that can be found in reports from soil surveys and scientific publications. They can also be readily coupled with GIS to produce an effective evaluation tool for the control of non-point sources in agricultural watersheds [23; 24]. Simple models with semi-empirical process descriptions of the lumped conceptual type which utilize time series of averaged accumulated water, e.g., on catchment level within predefined blocks [25], are presented next, such as ANSWERS [26], for watersheds where sub-catchments are divided into hydraulically interconnected elements (grids), a model structure approach known as 'fully distributed' that demands heaps of data and requires high computational burden, CREAMS [27; 28], a field-scale model for chemical runoff and soil erosion, GLEAMS [29; 30], developed to assess agricultural chemicals' effects on water quality, SWRRB [31], a modified CREAMS, AGNPS [32] and AquiMod [33]. In such models, there has been a flux between segregated water body blocks following physical principles, i.e., surface flow, groundwater recharge, infiltration, percolation, subsurface flow, water table recharge, etc. [25]. Conceptually, leaching encompasses both the top layer of soil and the area beneath a plant's roots depicting the soil-groundwater system. It could be considered that a soluble part of pesticide mass is instantly mobilized at the surface causing surface water infiltration into the rhizosphere. In pastures, soil type contributes to 12% when referring to (N) leaching and a smaller contribution to (N\({}_{2}\)) fixation. Still, soil profile and type remain the most significant factors involved in % (N) loss [34]. The agro-ecosystem model, EcoMod, with subsequent versions, was developed as a biophysical, pastoral simulation model [35]. Plants' growth rate and carbon flux on the soil were simulated. Model modules regarding water and nutrient presence incorporate calculations for water and solute circulation, nutrients' fate, leaching, adsorption, ammonium nitrification, gaseous (N\({}_{2}\)) losses, and other geochemical phenomena, i.e., gradual immobilization, mineralization, etc. Fertilization and irrigation practices are included as well. Climate conditions were based upon data selected by means of stochastically created 99-year series climate documents by employing a modified version [36] of a daily climate model and incorporating data derived from the 'Stochastic Climate Library'. By utilizing EcoMod, better regional management is applied via the feeding animal type for the pasture to be selected, i.e., cattle or sheep, and the adequate use of nitrogen-based fertilizers to be applied, for optimal results over sustaining the adequate pasture without all the negative leaching effects caused by nitrate pollution over the catchment of the zone of experimental interest (New Zealand). Nitrogen leaching appeared to be more intense during the winter. Furthermore, the application of nitrogen-based fertilizers, though increasing quantities of monthly nitrogen leaching and fate, still did not alter the pattern of % nitrogen loss, i.e., the cyclic pattern of nitrogen fixation [34]. A biogeochemical model based on denitrification-decomposition processing (DNDC) was developed by [37; 38] for simulating dynamics of both carbon and nitrogen forms in soils for agro-ecosystems. DNDC simulates crop yield, carbon sequestration in soil, and nitrogen leaching when irrigated.