Over the land, soil erosion, also called soil loss, is closely linked to the water cycle. The main processes governing sediment generation are splash erosion from rain droplets, and sheet and rill erosion from the shear stress caused by overland flow. The intensity of soil erosion by rain or flow depends on the land and soil characteristics such as slope, land use or soil type. Once soil is eroded, the detached particles can be transported downslope by overland flow. Along the transport pathways, soil particles can also be deposited due to a low flow velocity, a change of topography in depressions, footslopes or valley bottoms, and/or can be filtered and stopped by a change in vegetation such as field boundaries.

The inland part of the sediment gathers these different processes, separated in a vertical structure for the soil loss and lateral structure for the transport in overland flow.

Overview of the different processes for a land cell in wflow_sediment.


Soil Erosion

The first process to consider in sediment dynamics is the generation of sediments by land erosion. The main processes behind soil loss are rainfall erosion and overland flow erosion. In order to model such processes at a fine time and space scale, physics-based models such as ANSWERS and EUROSEM were chosen here.

The choice of rainfall erosion method is set up in the model section of the TOML:

rainerosmethod = "answers" # Rainfall erosion equation: ["answers", "eurosem"]

Rainfall erosion

In wflow_sediment, rainfall erosion can both be modelled using EUROSEM or ANSWERS equation. The main difference between the models is that EUROSEM uses a more physics-based approach based on the kinetic energy of the rain drops impacting the soil (Morgan et al, 1998), while ANSWERS is more empirical and uses parameters from the USLE model (Beasley et al, 1991).

In EUROSEM, rainfall erosion is modelled according to rainfall intensity and its kinetic energy when it reaches the soil according to equations developed by Brandt (1990). As the intensity of the rain kinetic energy depends on the length of the fall, rainfall intercepted by vegetation will then be reduced compared to direct throughfall. The kinetic energy of direct throughfall is estimated by (Morgan et al, 1998):

\[ KE_{direct} = 8.95 + 8.44\,log_{10}\,R_{i}\]

where $KE_{direct}$ is the kinetic energy of direct throughfall (J m$^{-2}$ mm$^{-1}$) and $R_{i}$ is rainfall intensity (mm h$^{-1}$). If the rainfall is intercepted by vegetation and falls as leaf drainage, its kinetic energy is then reduced according to (Brandt, 1990):

\[ KE_{leaf} = 15.8\,H_{p}^{0.5} - 5.87\]

where $KE_{leaf}$ is kinetic energy of leaf drainage (J m$^{-2}$ mm$^{-1}$) and $H_{p}$ is the effective canopy height (half of plant height in m). Canopy height can be derived from the global map from Simard & al. (2011) or by user input depending on the land use.

Kinetic energies from both direct throughfall and leaf drainage are then multiplied by the respective depths of direct throughfall and leaf drainage (mm) and added to get the total rainfall kinetic energy $KE$. The soil detached by rainfall $D_{R}$ (g m$^{-2}$) is then:

\[ D_{R} = k\,KE\,e^{-\varphi h}\]

where $k$ is an index of the detachability of the soil (g $J^{-1}$), $KE$ is the total rainfall kinetic energy (J m$^{-2}$), $h$ is the surface runoff depth on the soil (m) and $\varphi$ is an exponent varying between 0.9 and 3.1 used to reduce rainfall impact if the soil is already covered by water. As a simplification, Torri (1987) has shown that a value of 2.0 for $\varphi$ is representative enough for a wide range of soil conditions. The detachability of the soil $k$ depends on the soil texture (proportion of clay, silt and sand content) and corresponding values are defined in EUROSEM user guide (Morgan et al, 1998). As a simplification, in wflow_sediment, the mean value of the detachability shown in the table below are used. Soil texture can for example be derived from the topsoil clay and silt content from SoilGrids (Hengl et al, 2017).

Table: Mean detachability of soil depending on its texture (Morgan et al, 1998).

Texture (USDA system)Mean detachability $k$ (g/J)
Clay Loam1.7
Silt Loam1.5
Sandy Loam2.6
Loamy Sand3.0
Fine Sand3.5

Rainfall erosion is handled differently in ANSWERS. There, the impacts of vegetation and soil properties are handled through the USLE coefficients in the equation (Beasley et al, 1991):

\[ D_{R} = 0.108 \, C_{USLE} \, K_{USLE} \, A_{i} \, R_{i}^{2}\]

where $D_{R}$ is the soil detachment by rainfall (here in kg min$^{-1}$), $C_{USLE}$ is the soil cover-management factor from the USLE equation, $K_{USLE}$ is the soil erodibility factor from the USLE equation, $A_{i}$ is the area of the cell (m$^{2}$) and $R_{i}$ is the rainfall intensity (here in mm min$^{-1}$). There are several methods available to estimate the $C$ and $K$ factors from the USLE. They can come from user input maps, for example maps resulting from Panagos & al.'s recent studies for Europe (Panagos et al, 2015) (Ballabio et al, 2016). To get an estimate of the $C$ factor globally, the other method is to estimate $C$ values for the different land use type in from global land cover maps (e.g. GlobCover). An example is given for the global land cover map GlobCover, summed up in the table below, the values come from a literature study including Panagos et al.'s review (2015), Gericke & al. (2015), Mansoor & al. (2013), Chadli et al. (2016), de Vente et al. (2009), Borrelli et al. (2014), Yang et al. (2003) and Bosco et al. (2015).

The other methods to estimate the USLE $K$ factor are to use either topsoil composition or topsoil geometric mean diameter. $K$ estimation from topsoil composition is estimated with the equation developed in the EPIC model (Williams et al, 1983):

\[ K_{USLE} = \left\{ 0.2 + 0.3exp\left[-0.0256SAN\frac{(1-SIL)}{100}\right] \right\} \left(\frac{SIL}{CLA+SIL}\right)^{0.3} \\~\\ \left(1-\frac{0.25OC}{OC+e^{(3.72-2.95OC)}}\right)\left(1-\frac{0.75SN}{SN+e^{(-5.51+22.9SN)}}\right)\]

where $CLA$, $SIL$, $SAN$ are respectively the clay, silt and sand fractions of the topsoil (%), $OC$ is the topsoil organic carbon content (%) and $SN$ is $1-SAN/100$. These soil parameters can be derived for example from the SoilGrids dataset. The $K$ factor can also be estimated from the soil mean geometric diameter using the formulation from the RUSLE guide by Renard & al. (1997):

\[ K_{USLE} = 0.0034 + 0.0405e^{\left(-\dfrac{1}{2}\left(\dfrac{log_{10}(D_{g})+1.659}{0.7101}\right)^{2}\right)}\]

where $D_{g}$ is the soil geometric mean diameter (mm) estimated from topsoil clay, silt, sand fraction.

Table: Estimation of USLE C factor per Globcover land use type

GlobCover ValueGlobcover label$C_{USLE}$
11Post-flooding or irrigated croplands (or aquatic)0.2
14Rainfed croplands0.35
20Mosaic cropland (50-70%) vegetation (grassland/shrubland/forest) (20-50%)0.27
30Mosaic vegetation (grassland/shrubland/forest) (50-70%) / cropland (20-50%)0.25
40Closed to open (>15%) broadleaved evergreen or semi-deciduous forest (>5m)0.0065
50Closed (>40%) broadleaved deciduous forest (>5m)0.001
60Open (15-40%) broadleaved deciduous forest/woodland (>5m)0.01
70Closed (>40%) needleleaved evergreen forest (>5m)0.001
90Open (15-40%) needleleaved deciduous or evergreen forest (>5m)0.01
100Closed to open (>15%) mixed broadleaved and needleleaved forest (>5m)0.02
110Mosaic forest or shrubland (50-70%) / grassland (20-50%)0.015
120Mosaic grassland (50-70%) / forest or shrubland (20-50%)0.03
130Closed to open (>15%) (broadleaved or needleleaved, evergreen or deciduous) shrubland (<5m)0.035
140Closed to open (>15%) herbaceous vegetation (grassland, savannas or lichens/mosses)0.05
150Sparse (<15%) vegetation0.35
160Closed to open (>15%) broadleaved forest regularly flooded (semi-permanently or temporarily) - Fresh or brackish water0.001
170Closed (>40%) broadleaved forest or shrubland permanently flooded - Saline or brackish water0.0005
180Closed to open (>15%) grassland or woody vegetation on regularly flooded or waterlogged soil - Fresh, brackish or saline water0.04
190Artificial surfaces and associated areas (Urban areas >50%)0.0
200Bare areas0.0
210Water bodies0.0
220Permanent snow and ice0.0
230No data (burnt areas, clouds,…)0.0

Overland flow erosion

Overland flow (or surface runoff) erosion is induced by the strength of the shear stress of the surface water on the soil. As in rainfall erosion, the effect of the flow shear stress can be reduced by the soil vegetation or by the soil properties. In wflow_sediment, soil detachment by overland flow is modelled as in ANSWERS with (Beasley et al, 1991):

\[ D_{F} = 0.90 \, C_{USLE} \, K_{USLE} \, A_{i} \, S \, q\]

where $D_{F}$ is soil detachment by flow (kg min$^{-1}$), $C_{USLE}$ and $K_{USLE}$ are the USLE cover and soil erodibility factors, $A_{i}$ is the cell area (m$^{2}$), $S$ is the slope gradient and $q$ is the overland flow rate per unit width (m$^{2}$ min$^{-1}$). The USLE $C$ and $K$ factors can be estimated with the same methods as for rainfall erosion and here the slope gradient is obtained from the sinus rather than the tangent of the slope angle.

Delivery to the river system

Once soil is detached, it can be transported by overland flow and reach the river system. This process is described in Sediment Flux in overland flow.


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