**1. Introduction**

Soil erosion, as a process of the detachment, transport and accumulation of soil materials from any part of the Earth's surface, plays an important role in research since it assumes the most significant position among the individual degradation processes [1,2]. The importance of soil erosion research lies in the protection of soil as a fundamental resource for human food supplies; therefore, the understanding of soil erosion processes has important practical implications over large areas of the Earth [3,4].

Research on soil erosion and sediment transport has rapidly increased, thanks to technical developments and the increasing use of computer applications. Predictions of sediment yields can be carried out by taking advantage of an erosion model and a mathematical operator that expresses the efficiency of the sediment transport of a hill slope and channel network [5–9]. Mathematical simulation models have been developed, starting with empirical models such as the Universal Soil Loss Equation (USLE) by [10]. Empirical models are observation-based with a primary focus on the prediction of average soil loss, while conceptual models are based on the representation of catchments [11]. However, the USLE only generates annual mean soil losses but ignores the highly non-continuous character of erosion processes.

Nowadays, the development of models is based on the concept of equations for the conservation of mass, momentum, and energy [12], the use of equations describing streamflow or overland flows, and the equation for the conservation of mass for sediments. These models belong to the group

of physically-based models and represent mathematical relationships derived from physical laws and the mechanisms controlling erosion, which means that the parameters used are measurable [13], i.e., they allow for the sufficient representation and quantitative estimation of the detachment, transport of soil, and deposition processes [14]. In comparison with empirical models, the main advantages of physically-based models are distinguished by their more appropriate representation of erosion, deposition processes and extrapolation to different land uses in a more satisfactory style, as well as a more precise estimation of erosion, deposition and sediment yields from an event-based rainfall or application to complex varying soil conditions and surface characteristics [15].

Despite the large number of soil erosion and sediment transport models, choosing a suitable model is still a very complex and complicated task. There are many models that suffer from a range of problems, such as overestimation due to the uncertainty of the models and the unsuitability of the assumptions and parameters in conformity with the local conditions [16]. It needs to be stated that the modelling of a natural system is always limited by many variations in terms of spatial and temporal scales, spatial heterogeneity, the transport media, and the lack of available data [17]. Different types of factors affecting water erosion, such as the climate, topography, soil structure, vegetation and anthropogenic activities, tillage systems and soil or conservation measures [18], can result in different values of sediment generation and deposition as well. Among the factors mentioned above, rainfall intensity and the runoff rate are the major triggers of splash and sheet erosion [19], together with the human activities in rivers, causing changes in the magnitude and nature of material inputs to estuaries, which can trigger erosion with consequences for populations and ecosystems [20].

The amount of sediment in a catchment is heterogeneous in space and over time, depending on the land use, vegetation cover, climate, and landscape characteristics, i.e., the soil type, topography, any slopes, and the drainage conditions [21,22]. The quantification of eroded material can be made by a variety of methods, and the selection of the method depends on the financial support, objectives, the size of the study area and the characteristics of the research group [23]. The bathymetric measurement of sediment deposited in a reservoir is a suitable method for assessing the volume of eroded material in a study area. Boyle et al. [24] noted that calculating the lake sediment is useful for quantifying the historical impact of agriculture on soil erosion and sediment yield, as well as a good approach for calibrating and testing the erosion models compared to the actual bathymetry measurements.

This paper presents a suitable approach as to how to validate an erosion model through the sedimentation in a small reservoir. The aims of the paper are as follows:


#### **2. Materials and Methods**

#### *2.1. EROSION-3D Model*

The EROSION-3D model is a physically-based computer tool predominantly developed for simulating runoff and deposition processes on arable land. The model can be applied for predicting the amount of soil loss on agricultural land, sediments, depositions, the volume and concentration of eroded sediments, and the amount of surface runoff produced by intensive rainstorms [25,26]. The EROSION-2D model was initially developed by [25]. Based on that concept, the EROSION-3D model has been developed since 1995 by Michael von Werner at the Department of Geography at the Free University of Berlin [27]. The difference between EROSION-3D and EROSION-2D is that EROSION-2D simulates soil erosion on a slope profile and EROSION-3D model is raster-based and uses digital elevation model which determines connectivity processes between raster cells uses. Testing of the model was done during comprehensive rainfall simulation studies that were carried out on agricultural land in Saxony, Germany, from 1992 to 1996 [27].

The structure of the EROSION-3D model consists of two main submodels, i.e., the infiltration and the erosion models (Figure 1). The calculations of the soil erosion are conducted by the erosion submodel, which considers the processes such as rainfall infiltration, generation of surface runoff, detachment of soil particles through the kinetic energy of raindrops and surface runoff or long-term modifications of the land surface relief due to soil erosion [27]. Because the EROSION-3D model is raster based, it requires a grid cell representation of a catchment.

**Figure 1.** The EROSION-3D model structure [24].

The erosion submodel represents soil erosion processes in three steps, i.e., the detachment of soil particles from the impact of raindrops as well as their transport and deposition. The mathematical expression of the erosion submodule is based on the momentum flux approach [25], which involves an overland flow and is defined by the Equation:

$$
\varphi\_{\eta \mathcal{D}} = \frac{q \times \rho\_{\eta} \times \upsilon\_{\eta}}{\Delta x},
\tag{1}
$$

where <sup>ϕ</sup>*qD* is the momentum of the flux exerted by overland flow (N); *<sup>q</sup>* is the flow (m3/(m·s)); <sup>ρ</sup>*<sup>q</sup>* is the fluid density (kg/m3); *vq* is the mean velocity of the flow according to Manning (m/s); and Δ*x* is the length of a specified slope segment (m). Because the infiltration process is complicated, the mathematical description of the infiltration process is divided into the gravitational component *i1* and the matrix component *i2* as described below.

The gravitational component (*i1*) is defined by the gravitational potential as follows:

$$i\_1 = k\_\ $ \times \frac{\Delta \psi\_\mathcal{S}}{x\_{f1}} = k\_\$  \times \mathcal{g},\tag{2}$$

where *i1* is the infiltration rate of the gravitational component (kg/(m2·s)); *ks* is the hydraulic conductivity of the transport zone ((kg·s)/m3); <sup>Δ</sup>ψ*<sup>g</sup>* is the gravitational potential ((N·m)/kg); *xf1* is the depth of the wetting front of the gravitational component (m); and *g* is the gravitational constant (m/s2).

The dynamic component of the matrix *i2* is described by a function of the matrix potential Δψ*m*:

$$i\_2 = k\_s \times \frac{\Delta \psi\_m}{x\_{f2}(t)},\tag{3}$$

where *i2* is the infiltration rate of the matrix component (kg/(m2·s)); *ks* is the hydraulic conductivity of the transport zone ((kg·s)/m3); <sup>Δ</sup>ψ*<sup>m</sup>* is the matrix potential ((N·m)/kg); and *xf2(t)* is the depth of the wetting front of the gravitational component (m) in time *t*.

The saturated hydraulic conductivity depends on the soil structure, soil texture, and the occurrence of macropores. For determining the saturated hydraulic conductivity, an empirical equation according to [28] is used:

$$k\_s = 4 \times 10^{-3} \left( 1.3 \times 10^{-3} / \rho\_b \right)^{1/3b} \exp\left( -0.069T - 0.037UI \right), \tag{4}$$

$$b = (10 - 3 \, D) - 0.5 + 0.2 \, \delta p\_\prime \tag{5}$$

where *ks* is the saturated hydraulic conductivity (kg·s/m3); <sup>ρ</sup>*<sup>b</sup>* is the bulk density (kg/m3); *<sup>T</sup>* is the clay content (kg/kg); *U* is the silt content (kg/kg); *D* is the average particle size (m); δ*p* is the standard deviation (-); and *b* is the local parameter (−).
