2 Surface erosion models

Erosion models experienced a rapid evolution from the empirical USLE to event-oriented semi-deterministic models that work on a GIS-platform. However, recent models, such as KINEROS (Michaud and Sorooshian, 1994*) and EUROSEM (Morgan et al., 1994*) deliver realistic results of soil erosion and particle load for small watersheds, but are less efficient on even larger scales, because a great variety of erosion and transport processes and phenomena that require high spatial resolution are considered in these models. Table 1 provides an overview of some modern surface erosion models.

KINEROS is a single rainfall event model useful for the design of single-event storms and evaluating watershed management practices, especially structural measures. KINEROS is based on the SCS curve number method and divides the watershed into a cascade of elements of planes and channel segments, whereby flow and sediment are routed from one segment to another. The elements allow rainfall, infiltration, runoff and erosion to vary spatially. 1D Hortonian overland flow starts when rainfall exceeds infiltration capacity. The sediment transport is described by a mass balance equation and does not include any chemical and biological transformation. KINEROS provides reliable long-term simulations although it was developed to map single or repeated events (Kalin and Hantush, 2006).

EUROSEM is a single event process-based model with modular structure for predicting water erosion from fields and small catchments. Runoff is routed over the soil using the kinematic wave equation. Continuous exchange of particles between water flow and soil surface is balanced within the model. Soil loss is computed as sediment discharge by a dynamic mass balance equation. EUROSEM was tested for single catchments and showed good correlation between simulated and measured soil loss. However, EUROSEM significantly underestimates soil loss and runoff, because the model disregards the patchiness of vegetation (Mati et al., 2006).

Contrary to KINEROS and EUROSEM, LISEM (DeRoo et al., 1996) and EROSION-2D (Abel et al., 2000*) are raster-based models for single storm events. However, the latter two models describe the same processes as do EUROSEM and KINEROS, which account for rill and inter-rill erosion and transport. EROSION-2D was tested in a small German catchment and overestimated runoff at dump slope, but worked well at hill slope (Abel et al., 2000). LISEM revealed bad performance for low raster point densities, but worked better when the density was increased (Jetten et al., 2003*).

Contrary to the erosion models mentioned above, WEPP (Ascough II et al., 1997) was designed to calculate continuous simulations of particle-bound substances. The model is based on fundamentals of erosion theory, soil and plant science, channel flow hydraulics, and rainfall-runoff relationships, and contains hill slopes, channels, and impoundments as primary components. The hill slope and channel components can be further divided into hydrology and erosion components. WEPP partly incorporates equations from CREAMS (Rudra et al., 1985*) and includes gully erosion and channel transport. Small-scale morphological structures are additionally considered. In a Norwegian study, WEPP simulated fewer runoff events than measured, and improvements in winter hydrology calculations were recommended (Grønsten and Lundekvam, 2006).

In most erosion models, runoff and sediment load are only computed for one point in the catchment: the outlet. Therefore, validations can be only carried out for the outlet and just a few tests compared simulated erosion with observed erosion patterns. Most models predicted total runoff better than peak runoff, which again was better predicted than sediment load (Jetten et al., 2003). At any rate, calibration is desirable or necessary prior to any simulation runs. Correlations to measured runoff and loads were often good, but in most cases the models over- or underestimated empirical results especially for small erosion events.

In conclusion, modern erosion models combine high temporal resolution with the capability to simulate runoff on watershed scales. However, modelled results are often doubtful, because the spatial resolution of the models is insufficient to account for a small-scale heterogeneous environment. Furthermore, although erosion models may be capable to calculate the transport of soluble substances, these models do not consider any attenuation or partitioning during transport and therefore fail to predict loads of soluble pesticides to surface waters.