Overview of formulas and units in WaTEM/SEDEM
The aim of this page is to present an overview of the formulas and the units used in WaTEM/SEDEM. The motivation for this page is to clarify the differences between the units used in the model description, model inputs, model states and model outputs. This overview can help interpret the outputs of WaTEM/SEDEM.
As explained in the model description of WaTEM/SEDEM, the amount of erosion and deposition in each pixel, as well as the amount of sediment leaving a pixel downstream (\(S_o\)) is determined by comparing the mean annual soil erosion \(E\) and incoming sediment \(S_i\) with the transport capacity \(TC\) at the pixel level. In the model code this is done by comparing volumes (\(m^3\)):
with the units for \(E\) and \(TC\):
These units are converted to \(\frac{m^3}{year}\) (\(E_v\) and \(TC_v\)) by making use of the pixel area (\(A_c, unit: m^2\)), the soil bulk density (\(\rho, unit: \frac{kg}{m^3}\)) and the slope correction factor for the grid cell dimension (\(x\), resolution multiplied by \(|sin (\alpha)|+|cos (\alpha)|\)).
The values for the outgoing sediment per pixel are in the code thus defined as state variables in \(\frac{m^3}{year}\). Consequently, the values for the incoming sediment (\(S_i\)) for every (river) pixel is also expressed in the model as volumes. These computations are all defined in the procedure Water in the file lateralredistribution.pas.
The model inputs for WaTEM/SEDEM in the .inifile that are used to compute \(E\) and \(TC\) are the \(R\)-value, the \(C\)-raster, the \(K\)-raster, the \(P\)-raster and the digital height model raster (\(LS\), slope). \(LS\) and \(\tan(\text{slope})^{0.8}\) are dimensionless, and are considered as model outputs as they are computed in WaTEM/SEDEM. The \(C\)- and \(P\)-rasters have no units.
The units of the \(R\)-value and \(K\)-raster are equal to:
\(R = \frac{\text{MJ.mm}}{\text{ha}.\text{h.year}}\). The unit of the R-value is converted (in WaTEM/SEDEM) to \(\frac{\text{MJ.mm}}{\text{m}^2.\text{h.year}}\).
\(K = \frac{\text{kg.h}}{\text{MJ.mm}}\).
The model outputs incoming sediment \(S_i\) (SediIn), outgoing sediment \(S_o\) (SediOut), sediment export \(S_e\) (SediExport) and transport capacity \(TC\) (Capacity) all have unit kg (converted by using \(\rho\)). The model output RUSLE \(E\) value (RUSLE) is expressed in \(\frac{\text{kg}}{\text{m}^2}\)!
Note that \(S_e\) is equal to \(S_o\), yet masked respectively for river and land pixels.
WaTEM/SEDEM outputs include an erosion map that expresses \(E\) in kg/m²/year, equivalent to area-specific erosion rates reported in most other studies. Values can be multiplied with 10 to obtain typical erosion rates in ton/ha/year. A transport capacity map is also provided as an output, whereby the amount of sediment that can be transported through a pixel in downstream direction is shown in kg/pixel/year.
In the table below the units of import input and output values/rasters are listed.
Variable |
Symbol |
Model input |
Model output |
Unit |
Type |
|---|---|---|---|---|---|
Potential soil loss |
E |
x |
kg/[m^2.year] |
raster |
|
Transport capacity |
TC |
x |
kg/[pixel.year] |
raster |
|
R-factor |
R |
x |
[MJ.mm]/[ha.h.year] |
value |
|
K-factor |
K |
x |
[kg.h]/[MJ.mm] |
raster |
|
C-factor |
C |
x |
raster |
||
P-factor |
P |
x |
raster |
||
DTM |
DTM |
x |
x |
m |
raster |
LS |
LS |
x |
raster |
||
Slope |
slope |
x |
radians |
raster |
|
Sediment input |
Si |
x |
kg/year |
raster |
|
Sediment output |
So |
x |
kg/year |
raster |
|
Sediment export |
Se |
x |
kg/year |
raster |