#### 2.1. Study Area

The investigated Dano catchment in the Ioba province covers an area of 126 km

^{2} and is located in the Southwest of Burkina Faso (

Figure 1). The study area is in a focal watershed of the WASCAL program (West African Science Service Center on Climate Change and Adapted Land Use). The multidisciplinary program is designed to study the influence of climate and land use/land cover change on human and environmental systems and to enhance their resilience.

Agricultural land use is the most important land use category in the region (

Figure 1d). The agricultural area has expanded in recent decades due to a growing demographic pressure indicated by an annual population growth of 3%. It has gradually been intensified accompanied by reduced fallow periods and expansion to marginal land areas with adverse effects on soil fertility [

4,

46,

47,

48,

49]. Since 1990 each year on average 2% of the savanna in the study area was converted to agricultural land [

49]. The general appearance of the vegetation in the Sudano savannah is dominated by open forests and wide arborous and shrubby areas. The main staple food crops cultivated in the region are sorghum (Sorghum bicolor), millet (Pennisetum glaucum), maize (Zea mays), cowpeas (Vigna unguiculata), and groundnut (Arachidis hypogaea). Cotton (Gossypium hirsutum) is the most important cash crop. During the rainy season between 40% and 70% of the soil is covered by vegetation.

The catchment is dominated by a flat and slightly undulating landscape characterized by low slope gradients (average and maximum gradients are 3.1% and 38%, respectively,

Figure 1b) and an elevation ranging from 236 to 565 m above sea level (m a.s.l). The annual mean temperature is 28.6 °C and annual precipitation ranges from 800 to 1200 mm/a for the period 1951–2005 [

50]. The rainfall pattern is uni-modal and characterized by a distinct rainy season from May to October and a dry season from November to April. Eighty percent of the rain falls between July and September with high rainfall intensities. As an example from the Dano catchment, 60 mm/h were measured as maximum in 2014. The flow regime is ephemeral and the channel geometry is divers ranging from strongly incised (3–4 m) clearly defined channels to broader inland valleys. Information on the ranges of measured parameters is given in

Table 3.

Most of the soils (73%) are plinthosols according to the World Reference Base for soil resources (WRB) [

51] characterized by a high content of coarse particles and a plinthitic subsurface layer in the first meter of the profile. Other soils that were formed in the region are gleysols, cambisols, lixisols, leptosols, and stagnosols (

Figure 1e).

#### 2.3. Model Description

Modeling of hydrological and erosion processes was performed using the physically based, spatially distributed and raster-based model SHETRAN [

11,

12]. SHETRAN is based on SHE (Système Hydrologique Europeen) which was jointly developed by the British Institute of Hydrology, the Danish Hydraulic Institute and the French consulting company SOGREAH [

54]. During the last thirty years SHETRAN has been continuously improved and equipped with new components that include e.g., the sediment component [

12,

55] and a fully 3D subsurface water flow component [

56]. A summary of SHETRAN applications with various objectives and in different regions is given in

Table 2.

Detailed information about the model is given in Bathurst [

57]. A short overview of the most important hydrological process descriptions of the model is summarized in the following list:

Fully 3D subsurface flow simulation based on Richards’ equation.

Infiltration is calculated using Richards’ equation.

Overland and channel flow is calculated using the diffusive wave approximations of the full Saint-Venant equation.

Potential evapotranspiration (ETp): Potential plant transpiration, evaporation from intercepting surfaces and from bare soil as well as water bodies was calculated externally based on the Penman-Monteith equation [

58] and added as input into SHETRAN.

Actual evapotranspiration (ETa) is estimated based on the approach introduced by Feddes et al. [

59] where the ratio ETa/ETp is a function of soil moisture tension. The ratio ETa/ETp at field capacity is the input parameter and the reduction of ETa with decreasing soil moisture tension is calculated based on this parameter.

Interception is calculated based on the approach by Rutter et al. [

60,

61] who relates interception to the leaf area index, the vegetation cover, and the maximum depth of water on leaves.

The parameterization and calibration of land use and soil properties was done based on data obtained from literature and measurements (see

Table 4 and

Table 5). The parameters (θ

_{sat}, θ

_{res}, α, n) used to describe the soil water retention curve after van Genuchten [

62] were determined from soil texture and organic matter content following Rawls and Brakensiek [

63]. Measured saturated hydraulic conductivity (K

_{sat}) was used for the top soil horizon. For the remaining horizons K

_{sat} was calculated using soil texture and organic matter content following Brakensiek and Rawls [

64].

SHETRAN requires different types of input data. Spatially distributed data, including digital elevation model (DEM), the soil and land use map, were used in a raster format with a grid resolution of 200 m × 200 m. The applied resolution is relatively coarse compared with other applications of SHETRAN with resolutions typically below 100 m (

Table 2). Nevertheless, the topography of the study area is characterized by long straight slopes which are well represented in this resolution. Zhang [

33] applied a resolution of 2 km to a larger catchment (705 km

^{2}) and compared it with resolutions of 0.5 and 1 km. The performance measure using the Nash-Sutcliff-Efficiency (NSE) decreased by 3.7% with decreasing resolution (from 1 to 2 km) as a result of information loss as land use and soil type maps become coarser.

Precipitation and potential evapotranspiration (ETp) are given as time series over two years for each of the five stations considered in the modeled catchment. The area that is represented by each station is determined by Thiessen polygons. A pre-processing software uses the DEM to determine the river geometry and produce the input files [

65]. The temporal resolution of 1 hour used here is the standard timestep of SHETRAN and commonly used in other studies (see

Table 2). The precipitation input has an hourly timestep.

A short summary of erosion processes simulated by SHETRAN is given below.

Soil detachment is accounted for by three separate equations describing detachment by raindrop/leaf drip (Equation (1)) [

66], by overland flow (Equation (2)) [

67] and by channel flow (Equation (3)) [

68]:

where D

_{r} is the rate of soil detachment (kg/m

^{2}/s), F

_{w} (-) accounts for the protection against drop detachment by surface water, k

_{r} is the raindrop impact erodibility coefficient (J

^{−1}), C

_{g} is the proportion of ground covered by near ground vegetation (%), C

_{r} is the rock cover (-), M

_{r}/M

_{d} is the momentum squared of raindrops/leaf drips reaching the ground per unit time and area (kg

^{2}/s

^{3}),

where D

_{q} is the rate of soil detachment per unit area (kg/m

^{2}/s), k

_{f} is the overland flow erodibility coefficient (kg/m

^{2}/s), C

_{r} is the proportion of ground shielded by rock cover (-), τ is the shear stress exerted by overland flow (N/m

^{2}), τ

_{ec} is the critical shear stress for the initiation of motion (N/m

^{2}),

where E

_{b} is the detachment rate of bank material per unit area (kg/m

^{2}/s), BKB is the bank erodibility coefficient (kg/m

^{2}/s), τ

_{bc} is the critical shear stress for the initiation of motion of bank material (N/m

^{2}) and τ

_{b} is the shear stress acting on the bank (N/m

^{2}).

Sediment is transported based on the transport capacity of overland (Equation (4)) [

69] and channel flow (Equation (5)) [

70]:

where G

_{tot} is the transport capacity rate for overland flow (m

^{3}/s), τ is the shear stress (N/m

^{2}), p is the water density (kg/m

^{3}), l is the width of flow (m), Q is the water discharge (m

^{3}/s), D

_{50} is the median sediment diameter, δ and a are parameters,

where G

_{i} is the transport capacity rate of particle size in group i (m

^{3}/s), D

_{i} is the particle diameter in size group i (m), H is the water flow depth (m), U is the mean water flow velocity (m/s),

${\mathrm{u}}_{*}$ is the shear velocity (m/s), G

_{gr,i} is the dimensionless sediment transport rate for sediment size group i.

Further details are given in Morgan and Nearing [

71] and Wicks [

55].

#### 2.4. Model Sensitivity, Calibration, and Validation

Several parameters of SHETRAN need to be calibrated by comparing simulated and observed variables. Prior to the calibration of parameters to which the model output is most sensitive the corresponding initial values were identified based on previous studies that used SHETRAN and based on sensitivity analyses. The sensitivity analyses were done based on the “one factor at a time” (OFAT) method using Equation (6) [

72]:

where SI

_{90} is the sensitivity index, O

_{90} and O

_{-90} the model output resulting from a parameter value increased or decreased by 90%, and O

_{0} the model output from the base run.

A list of parameters to which the model output responds sensitively and the corresponding calibration ranges used in this study are given in

Table 5. The parameter range of k

_{f} is quite low compared with that indicated in literature. However, as this parameter is considered to be a calibration parameter [

55], we assume that the range is representative for the soil properties in the study area.

Latin Hypercube Sampling (LHS) [

73] was used to generate 300 parameter sets within the defined value ranges. This is considered as a reasonable compromise between the necessary model executions which are dependent on the number of parameters used and the run time. The hydrological component of SHETRAN was calibrated based on the observed hydrograph in 2014. The soil erosion component was calibrated based on the observed SSL in 2014. The model performance was statistically evaluated by the coefficient of determination (R

^{2}), the Nash-Sutcliff efficiency (NSE) [

74], and the Kling-Gupta efficiency (KGE) [

75,

76]. The model was validated using data from the year 2015.