7 Diverse mathematical models at various scales

We presented an overview of models that predict pesticide loads via runoff in significantly different ways. Empirical models are opposed to mechanistic approaches, but some elements of the former are often incorporated into the latter. In general, leaching models are mainly of deterministic or hybrid nature and describe processes, such as microbial degradation, percolation, and plant uptake. Leaching models are mostly one-dimensional and therefore, the computational effort to calculate downward fluxes of pesticides is moderate, although the processes affecting pesticide concentrations in soils are described elaborately. The results of leaching models may feed into horizontal transport models, but the applicability of leaching models is confined to a field scale.

Mechanistic or hybrid erosion and hydrological models use the SCS curve number approach to describe the horizontal transport of pesticides. In some models, the retention of pesticides during runoff is only considered by applying a simple attenuation factor. These linear approaches seem to be poor compared to the complex nature of 2D- or 3D-hydrological and erosion models, but still progressive compared to the edge-to-field approach, which disregards any retention between application areas and surface waters. Therefore, complex hydrological and erosion models, such as MIKE SHE and EUROSEM, still have problems to predict pesticide loads during rainfall events on catchment scales. Furthermore, their spatial resolution is mostly insufficient to account for small-scale retention structures, and thus, these models often overestimate actual pesticide loads.

Above, we demonstrated a deficit of erosion model validation, which in the past was mainly performed for the outlets of catchments. Validation of hydrological models have the same problem, because contrary to leaching models, they are created to work at scales larger than field scale. However, validation procedures which regard locations within the simulation areas are confined by the great logistic demand of pesticide monitoring. For the same reason, the validation based on long-term monitoring has seldom been performed (but see: Herbst et al., 2005b).

Empirical models such as USLE and MONERIS use very simple equations often derived by simple linear regression analyses and provide relatively low spatial and temporal resolutions. Therefore, these empirical models are suitable tools to deliver robust predictions of long-term developments in pesticide loadings to surface waters on river basin scales, but fail to calculate short-term pulses of pesticide loads on field and catchment scales.

Recent developments of probabilistic approaches consider vegetation patches and small geomorphological structures as retention sites for pesticides during horizontal transport (Röpke et al., 2004; Bach et al., 2001*). The major advantage of the mathematical simplicity of these approaches is their small computational effort, which permits to conduct Monte Carlo-simulations for large river basins. Despite reliable results on a catchment scale, Bach et al. (2001) state that the results should be addressed mainly to comparative interpretations with the focus on the proportions between different active ingredients, soil regions, climates and application periods. In addition, the empirical equations implemented are in contrast to the high spatial resolution of these probabilistic approaches, and they still need to be validated on river basin scales.

Qualitative progress in modelling fate and transport of pesticides is also necessary concerning substance classes. Leaching models have been used for a variety of pesticides different in chemical properties and behaviour (Tiktak et al., 2002), but hydrological models working at regional scales were mainly used for one or two substances in one study. Therefore, there is still a lack of a comparative study in which the dispersal of the most important pesticide classes is simulated at river basin scale.

Future developments in computer hardware will enable to use probabilistic approaches on a GIS-platform to predict pesticide loads via runoff for river basins, applying reliable deterministic models and model combinations. In addition, it is desirable to increase spatial resolutions of hydrological models, so that small-scale geomorphological and canopy structures can be considered as potential retention sites of pesticides. In contrary, the commonly used edge-to-field approach leads to large overestimations of pesticide loads to surface waters and therefore should be avoided. Overall, the evolution of pesticide transport models probably will go into two major directions, which not necessarily are contradictive to each other: increase in spatial resolution and extension to large scales, both of which will be performed on GIS-platforms.