1 Introduction

The development of numerical pesticide models started when negative consequences of agricultural pesticide applications for humans had been recognized in the 1960s and 1970s. The driving forces of continual improvements of pesticide models over 40 years have been the intention to describe the dispersal of pesticides in terrestrial and aquatic systems and to assess the risk of pesticide applications. For the same reason in the 1970s, the registration and partly the prohibition of pesticides were initiated in industrialized countries in the northern hemisphere. Since 1992, the requirement of sustainable use of natural resources, prone to agricultural practices, provided further motivation to increase the performance of pesticide models.

Since the 1970s, numerous models of pesticide transport in the agricultural environment have been developed. Early conceptual and deterministic approaches to model the fate of pesticides on soil surface and in above-soil canopy were limited to certain pesticides and environments and described the transport of the soluble phase as one-dimensional (1D) flow without using geo-referenced data (Goodman et al., 1983; Vithayathil et al., 1979). However, from the very beginning of pesticide modelling, sorption and degradation of pesticides were explicitly incorporated as attenuation and retention factors. Figure 1* provides an influence diagram of processes affecting pesticides loads via runoff.

In a next phase, the focus was on leaching of pesticides to groundwater and a variety of 1D leaching models for agricultural soils was generated, which predict pesticide concentrations in various soil depths in the vadose and phreatic zones (Bonazountas, 1987; Matthies and Behrendt, 1991*; Crowe and Mutch, 1992; Persicani, 1996*; Wauchope et al., 2003). Few of these models include the transport mechanism runoff as loss term of pesticides and none distinguishes between surface and subsurface runoff.

As partly described in leaching models, preferential flow through soil macropores can significantly increase the risk of pollution of surface water bodies by pesticides. While many field studies have shown the importance of preferential flow on a field scale, few have included detailed numerical modelling of the processes involved (Gärdenäs et al., 2006*).

Contemporarily, modellers improved the universal soil loss equation (USLE) leading to a revised equation (RUSLE), and 1D or two-dimensional (2D) models of surface erosion and soil particle transport were created. Previous studies had recognized that surface erosion is a function of rainfall intensity rather than of total annual rainfall and therefore, event-oriented 1D and 2D approaches of surface erosion and particle transport were developed that are physically based or of hybrid nature with both, empirical and deterministic elements (Jetten et al., 2003*; Morgan et al., 1998). These models neglect subsurface flow and are hardly applicable for the transport of the soluble pesticide phase.

Dynamic hydrological models deal with these deficits and are able to predict transport and fate of soluble pesticides for small watersheds with moderate temporal and spatial resolution (Borah and Bera, 2004*; Tarboton et al., 2002). As a prerequisite of such simulations, Geographical Information Systems (GIS) were developed, so that hydrological models could be implemented on a GIS-platform that in turn allows for using and producing geo-referenced data. Hydrological and leaching models partly originate from the same roots, as it is exemplified by the leaching model GLEAMS (Sabbagh et al., 1993*), which is based on the hydrological model CREAMS (Rudra et al., 1985*).

Recognizing the need for models that enable the prediction of soluble pesticide losses via surface and subsurface runoff recently, leaching models and transport or erosion models were combined to calculate pesticide transport to the aquatic environment with high temporal and moderate spatial resolutions. The combination of both, elaborate descriptions of horizontal and vertical transport, and retention and detention mechanism within or above soil, resulted in reliable simulations of pesticide transport and fate on a watershed or even river basin scale (Röpke et al., 2004*; Jackson et al., 2005; Ramanarayanan et al., 2005*). Combinations of hydrological models with leaching models, which include the description of preferential flow, might augment the accuracy of predictions of pesticide concentrations in runoff even more.

All models mentioned above are capable to calculate realistic worst case scenarios, but are barely adequate tools for probabilistic approaches on a watershed scale. 2D and 3D erosion and hydrological models are supposed to be suitable tools for simulations at large scales, but these models demand extremely high computational effort for Monte Carlo simulations. In turn, leaching models scarcely incorporate horizontal flow and hence, they need to be combined with hydrological models if the aim is to simulate horizontal runoff. Therefore, another development of modelling pesticide transport via runoff started in the 1990s, which relies on simple empirical or hybrid approaches in order to make robust predictions of pesticide exposure by conducting Monte Carlo simulations (Franke and Teutsch, 1994*; Kapo and Burton Jr, 2006).

In summary, models of pesticide transport became more elaborate as time went by, including mathematical and numerical complexity, as well as spatial resolution and extent. However, the progresses made in model development have been confined by the state of scientific knowledge of pesticide behaviour in and above soil. For example, there are still deficits in describing preferential flow in soils and the sorption behaviour of pesticides, owing to the fact that every soil patch seems to have a different partitioning coefficient K_D. The discrepancy between small-scale patchiness of soils and vegetation and the purpose to provide reliable predictions of pesticide transport and fate at large scales remains unsolved. However, various types of models and model combinations experienced an evolution that enables the prediction of geo-referenced pesticide exposure from small to large scales. In the following, we will provide an overview of existing runoff models eligible for pesticides. We will discuss their advantages and disadvantages and give a perspective for future developments.