DMMF {DMMF}  R Documentation 
Daily based Morgan–Morgan–Finney (DMMF) soil erosion model
Description
Estimating surface runoff and sediment budget using the Daily based Morgan–Morgan–Finney soil erosion model using the algorithm from Choi et al. (2017)
Usage
DMMF(DEM, R, RI, ET, P_c, P_z, P_s, theta_init, theta_sat, theta_fc,
SD, K, P_I, n_s, CC, GC, IMP, PH, D, NV, d_a = 0.005,
DK_c = 0.1, DK_z = 0.5, DK_s = 0.3,
DR_c = 1.0, DR_z = 1.6, DR_s = 1.5,
Breaking, Init_point, Sinks, R_Type = 0, slpMode = 2, ALL = TRUE)
Arguments
DEM 
RasterLayer object of digital elevation model (DEM) 
R 
Numeric vector or RasterBrick object of daily rainfall per unit area (unit: mm) 
RI 
Numeric vector or RasterBrick object of mean hourly rainfall intensity during a day (unit: mm/h) 
ET 
Numeric vector or RasterBrick object of evapotranspiration per unit area (unit: mm) 
P_c 
Numeric vector or RasterLayer object of proportion of clay particles in surface soil (01) 
P_z 
Numeric vector or RasterLayer object of proportion of silt particles in surface soil (01) 
P_s 
Numeric vector or RasterLayer object of proportion of sand particles in surface soil (01) 
theta_init 
Numeric vector or RasterBrick object of initial soil water content of entire soil profile per unit area (unit: vol/vol) 
theta_sat 
Numeric vector or RasterLayer object of saturated soil water content of entire soil profile per unit area (unit: vol/vol) 
theta_fc 
Numeric vector or RasterLayer object of soil water content at field capacity of entire soil profile per unit area (unit: vol/vol) 
SD 
Numeric vector or RasterLayer object of soil depth of entire soil profile (unit: m) 
K 
Numeric vector or RasterLayer object of saturated lateral hydraulic conductivity of entire soil profile (unit: m/d) 
P_I 
Numeric vector or Raster* object of proportion of permanent interception area of rainfall (01) 
n_s 
Numeric vector or Raster* object of Manning's roughness coefficient of the soil surface (unit: 
CC 
Numeric vector or Raster* object of proportion of area with canopy cover (01) 
GC 
Numeric vector or Raster* object of proportion of area with pervious vegetated ground cover (01) 
IMP 
Numeric vector or Raster* object of proportion of area with impervious ground cover (01) 
PH 
Numeric vector or Raster* object of average height of vegetation or crop cover where leaf drainage start to fall (unit: m) 
D 
Numeric vector or Raster* object of average diameter of individual plant elements at the surface (unit: m) 
NV 
Numeric vector or Raster* object of number of individual plant elements per unit area (unit: 
d_a 
Numeric vector or Raster* object of typical flow depth of surface runoff (unit: m) 
DK_c 
Numeric vector or RasterLayer object of detachability of clay particles by rainfall (unit: g/J) 
DK_z 
Numeric vector or RasterLayer object of detachability of silt particles by rainfall (unit: g/J) 
DK_s 
Numeric vector or RasterLayer object of detachability of sand particles by rainfall (unit: g/J) 
DR_c 
Numeric vector or RasterLayer object of detachability of clay particles by surface runoff (unit: g/mm) 
DR_z 
Numeric vector or RasterLayer object of detachability of silt particles by surface runoff (unit: g/mm) 
DR_s 
Numeric vector or RasterLayer object of detachability of sand particles by surface runoff (unit: g/mm) 
Breaking 
Numeric vector of starting points of each simulation period (0: during the period points, 1: breaking points), If 
Init_point 
Numeric vector of starting points of each rainfall event (0: during the period points, 1: breaking points), If 
Sinks 
RasterLayer object of sinks (e.g., streams, reservoirs, and lakes) of sediments and surface runoff (optional). 
R_Type 
Integer object of each rainfall type for estimating kinetic energy of direct throughfall (DT) (08) (see details) 
slpMode 
Integer object of slope calculation algorithm (2: second order, 3: third order) 
ALL 
Logical object of selection for the entire output results 
Details
R_Type
can be chosen among options appropriate for each regions according to Morgan (2001) and Morgan (2005). Default option adopts recent universal relationships between kinetic energy density and mean hourly rainfall intensity (RI
) from Shin et al. (2016). Default option is recommended when users have measured RI
. Detailed descriptions are described below.
Option  Region  Kinetic energy density of throughfall [\mathrm{J/m^{2}/mm} ] 
0  Universal (Default)  10.3 \cdot \mathrm{RI}^{2/9} 
1  North America  11.87 + 8.73 \cdot \log_{10}(\mathrm{RI}) 
2  Northwest Europe  8.95 + 8.44 \cdot \log_{10}(\mathrm{RI}) 
3  Mediterranean  9.81 + 11.25 \cdot \log_{10}(\mathrm{RI}) 
4  West Mediterranean  35.9 \cdot (1.0  0.56 \cdot \exp(0.034 \cdot \mathrm{RI})) 
5  Tropics  29.8  ( 127.5 / \mathrm{RI} ) 
6  East Asia  9.81 + 10.60 \cdot \log_{10}( \mathrm{RI} ) 
7  Temperate Southern hemisphere  29.0 \cdot ( 1.0  0.6 \cdot \exp( 0.04 \cdot \mathrm{RI} ) ) 
8  Universal  28.3 \cdot ( 1.0  0.52 \cdot \exp( 0.042 \cdot \mathrm{RI} ) )

Multiflow direction algorithm (MD\infty
) from Seibert and McGlynn (2007) is built in the DMMF
model.
Value
The output of the function DMMF
is a list of RasterLayer or RasterBrick objects containing the following elements:

A
: Surface area size of each element considering slope (unit:\mathrm{m^2}
) 
Rf
: The amount of effective rainfall reaching each element (unit:\mathrm{mm}
) 
SW_c
: Surface water infiltration capacity of each element (unit:\mathrm{mm}

theta_r
: Remaining soil water content of each element (unit: vol/vol) 
TC
: Transport capacity of the runoff of each element (unit:\mathrm{kg/m^2}
) 
Q_in
: Volume of surface runoff flowing into each element (unit: L) 
Q_out
: Volume of surface runoff flowing from each element (unit: L) 
IF_in
: Volume of subsurface water flowing into each element (unit: L) 
IF_out
: Volume of subsurface water flowing from each element (unit: L) 
SS_c
: Area density of clay delivered to surface runoff in unit area of each element (unit:\mathrm{kg/m^2}
) 
SS_z
: Area density of silt delivered to surface runoff in unit area of each element (unit:\mathrm{kg/m^2}
) 
SS_s
: Area density of sand delivered to surface runoff of each element (unit:\mathrm{kg/m^2}
) 
G_c
: Area density of available clay for transport by surface runoff of each element (unit:\mathrm{kg/m^2}
) 
G_z
: Area density of available silt for transport by surface runoff of each element (unit:\mathrm{kg/m^2}
) 
G_s
: Area density of available sand for transport by surface runoff of each element (unit:\mathrm{kg/m^2}
) 
SL_c_in
: Mass of clay inputs into each element (unit: kg) 
SL_z_in
: Mass of silt inputs into each element (unit: kg) 
SL_s_in
: Mass of sand inputs into each element (unit: kg) 
SL_in
: Mass of sum of total sediments inputs into each element (unit: kg) 
SL_c_out
: Mass of clay outputs from each element (unit: kg) 
SL_z_out
: Mass of silt outputs from each element (unit: kg) 
SL_s_out
: Mass of sand outputs from each element (unit: kg) 
SL_out
: Mass of sum of total sediments outputs from each element (unit: kg)
Author(s)
Kwanghun Choi and Bjoern Reineking
References
Choi, K., Arnhold, S., Huwe, B., Reineking, B. (2017). Daily based Morgan–Morgan–Finney (DMMF) model: A spatially distributed conceptual soil erosion model to simulate complex soil surface configurations. Water, 9(4), 278.
Shin, S. S., Park, S. D., and Choi, B. K. (2016). Universal power law for relationship between rainfall kinetic energy and rainfall intensity. Advances in Meteorology, Article ID 2494681, 11 pages.
Seibert, J., McGlynn, B. L. (2007). A new triangular multiple flow direction algorithm for computing upslope areas from gridded digital elevation models. Water Resources Research, 43(4):W04501.
Morgan, R. P. C. (2005). Soil erosion and conservation. Blackwell Publishing, Malden, MA, 3rd ed. ISBN 1405117818
Morgan, R. P. C. (2001) A simple approach to soil loss prediction: a revised Morgan–Morgan–Finney model. Catena, 44(4):305–322.
See Also
DMMF_Simple
for one element during a day.
Potato.Convex
for the description of the data.
Examples
## Not run:
## Load example data for test running DMMF model
data(Potato.Convex)
attach(Potato.Convex)
## Run DMMF function using Potato.Convex data
Result < DMMF(DEM = s.map$DEM, R = d.var$R, RI = d.var$RI, ET = d.var$ET,
P_c = s.var$P_c, P_z = s.var$P_z, P_s = s.var$P_s,
theta_init = d.map$theta_init, theta_sat = s.var$theta_sat,
theta_fc = s.var$theta_fc,
SD = s.var$SD, K = s.var$K, P_I = s.var$P_I, n_s = s.map$n_s,
CC = d.var$CC, GC = s.var$GC, IMP = s.map$IMP, PH = d.var$PH,
D = s.var$D, NV = s.var$NV, d_a = s.var$d_a,
DK_c = s.var$DK_c, DK_z = s.var$DK_z, DK_s = s.var$DK_s,
DR_c = s.var$DR_c, DR_z = s.var$DR_z, DR_s = s.var$DR_s,
Breaking = d.var$Breaking, Init_point = d.var$Init_point,
R_Type = 0, slpMode = 2, ALL = TRUE)
## Check results
## 1a. Total volume of runoff generated from each element
plot(Result$Q_out)
## 1b. Total volume of runoff per unit surface area generated from each element
plot(Result$Q_out/Result$A)
## 2a. Total mass of eroded soil from each element
plot(Result$SL_out)
## 2a. Total mass of eroded soil per unit surface area from each element
plot(Result$SL_out/Result$A)
## End(Not run)