*2.2. The SWAT Model: Basins and Impoundments*

SWAT is one of the few hydrological models that have an input for ponds [47], which makes it an ideal tool for this study. SWAT is a semi-physical deterministic distributed and continuous hydrologic model that functions at a daily time step with options for sub-hourly routing, as well [55]. It is a quite complex model with significant input data demands. However, the basic components can be readily obtained and are relatively simple [56]. Essential inputs consist of weather data, digital elevation model (DEM), soil, and land occupation maps [57]. Based on these inputs, SWAT divides the basin into sub-basins, which further divides into smaller hydrological response units (HRUs) [58]. HRUs are defined as units with homogeneous land occupation, topography, and pedological properties [59]. These are generated in order to lump somewhat similar areas scattered through the basin into a single unit, simplifying the model's run by avoiding unpractical simulations while accounting for the diversity of different factors in the basin [60]. Within SWAT, ponds are defined as waterbodies,

being an integral part of a sub-basin's hydrological network; they are capable of intercepting surface runoff [60], thereby modifying the hydro-sedimentary behavior of the basin. Since this work targets the erosion/sedimentary behavior of the SWAT model, only their related equations will be presented. Further details can be found in Neitsch et al. (2011) [47].

**Figure 1.** Study area.

Soil erosion is calculated based on the Modified Universal Soil Loss Equation (MUSLE) using the following formula [55]:

$$\text{seed} = 11.8 \times (Q\_{\text{surf}} \cdot q\_{\text{pank}} \cdot area\_{\text{hru}})^{0.56} \times K\_{\text{USLE}} \times C\_{\text{USLE}} \times P\_{\text{USLE}} \times LS\_{\text{USLE} \times \text{CFRG}} \tag{1}$$

where *sed* is the HRU sediment yield (t); *Qsurf* is the surface runoff volume (mm); *qpeak* is the peak runoff rate (m3/s); *areahru* is the area of the HRU (ha); *KUSLE* is the Universal Soil Loss Equation (USLE) soil erodibility factor; *CUSLE* is the USLE cover and management factor; *PUSLE* is the USLE support practice factor; *LSUSLE* is the USLE topographic factor; and C*FRG* is the coarse fragment factor.

It should be noted that MUSLE virtually calculates the sediment yields due to soil erosion that reach the main streams of the sub-basins in a unit of time. This is the reason why sediment delivery ratios are not required, contrarily to USLE and RUSLE [61].

The mass balance equation of sediment in ponds is described by the following formula [47]:

$$scd\_{wb} = scd\_{wbi} + scd\_{flawin} - scd\_{stl} - scd\_{flawout} \tag{2}$$

where *sedwb* is the amount of sediment at the end of the day; *sedwbi* is the amount of sediment at the day's beginning; *sedflowin* is the amount of sediment provided from inflows; *sedstl* is the amount of settled sediments; and *sedflowout* is the amount of sediment transported as outflow. All components are expressed in metric tons.

#### *2.3. The CORINE Erosion Model*

The CORINE erosion model is a simplification of the USLE model. In the CORINE model, erosion risks are classified on a scale of 0–3, with 0 corresponding to the no-erosion class, 1 to low erosion risks, 2 to moderate erosion risks, and 3 to high-erosion risks [62]. For the estimation of erosion using the

CORINE model, parameters such as soil erodibility, climate erosivity, topography (slope), and LU/LC (vegetation cover) are required [61]. Each parameter, in turn, consists of several sub-factors, and is classified according to the CORINE model into respective indices (Figure 2). Once established, the soil erodibility index is combined with climate erosivity and slope, to yield the potential soil erosion risk map. Subsequently, the potential soil erosion risk map indices (0–3) are crossed with those of the vegetation cover to yield the actual soil erosion map.

**Figure 2.** CORINE model framework, MFI: Modified Fournier Index [63]; Pi is the total precipitation in month i and *P* is the mean annual total precipitation; BGI: Bagnouls–Gaussen Index [64]; ti the mean temperature for the month i; Pi the total precipitation in month i and ki the proportion of the month i in which 2ti − Pi > 0 [62].

*2.4. Input Data and Adaptation to the SWAT and CORINE Models*

The input data used in this study, along with a short description, are summarized in Table 1.


#### **Table 1.** CORINE erosion model and SWAT input data.

† The correspondence of the Claise basin to a natural park renders any human induced modifications on soils minor. Further, the Claise's land occupation pattern is relatively stable. Therefore, climate is the only variable factor in the study area. Hence, the temporal difference of the utilized datasets does not cause temporal induced biases.

ArcSWAT version 2012.10\_3.19 was applied in an ArcGIS 10.3 (Environmental Systems Research Institute, Inc. (Esri), 380 New York Street, Redlands, California, USA) environment to perform simulations at a daily time step for the period 1970–2018. The first seven years of the simulation, from 1970 to 1976, were used for the model's warm up. The calibration and validation phases of the model were carried out by means of comparison between simulated discharges and measured discharge data from the station L6202040–La Claise au Grand–Pressigny (Pont de Fer), obtained from Eau France Banque HYDRO–Ministère de l'Ecologie, de l'Energie, du Développement Durable et de l'Aménagement du Territoire (MEEDDAT)/Direction Générale de la Prévention des Risques (DGPR)/Service des Risques Naturels et Hydrauliques (SRNH). Due to the unavailability of sediment records for this study, only a hydrologic calibration was performed. However, surface runoff and stream flow—regardless of the approach used to model the sedimentary cycle—are the driving forces of runoff and streambed erosion, as well as of overland and stream sediment transport [65]. Hence, one might say that the calibration of the sediment part of the study might be implicit, but nonetheless robust. According to Hallouz et al. (2018) [66], a calibrated hydrologic model gives a certain degree of reliability to the sedimentary output. However, the availability of sediment data is often a constraint in relative studies, as measurements, either in the form of gross or net erosion or in the form of total sediment discharge, in streams, are often nonexistent. Even in cases where such data is available, it is in the form of sparse discrete measurements and rarely in the form of continuous sediment graphs, where they could be used for a robust calibration. In the case of the Claise, this would be a very challenging task, given the large number of ponds. For this reason, SWAT was calibrated according to the calibration scheme of Jalowska and Yuan (2019) [38], where a complete representation of an impoundment effect (here, ponds) is ensured. Nonetheless, the absence of sediment records poses some short of limitation that needs to be considered by the decision-makers of the basin.
