DMMF (version 0.5.2.0)

DMMF_Simple: Simplified Daily based Morgan--Morgan--Finney (DMMF) soil erosion model for one element during a day

Description

This is the simplified version of DMMF for simple one element (cell) during a day

Usage

DMMF_Simple( W, L = W/cos(S), S, 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, 
            Q_in = 0, IF_in = 0, SL_c_in = 0, SL_z_in = 0, SL_s_in = 0, R_type = 0)

Value

The output of the function DMMF_Simple is a data frame that contains following numeric elements:

• Q_out: Volume of surface runoff flowing from the element (unit: L)

• IF_out: Volume of subsurface water flowing from the element (unit: L)

• theta_r: Remaining soil water content of the element (unit: vol/vol)

• SL_c_out: Mass of clay outputs from the element (unit: kg)

• SL_z_out: Mass of silt outputs from the element (unit: kg)

• SL_s_out: Mass of sand outputs from the element (unit: kg)

• A: Surface area of the element (unit: \(\mathrm{m^2}\))

Arguments

W

Width of an element (cell) (unit: m)

L

Length of an element (cell) (unit: m). If L is not specified, the function assumes L as W/cos(S) (i.e., The function assumes a cell as a subset of DEM with slope angle of S).

S

Slope angle of an element (cell) (unit: rad)

R

Daily rainfall per unit area (unit: mm)

RI

Mean hourly rainfall intensity during a day (unit: mm/h)

ET

Evapotranspiration per unit area (unit: mm)

P_c

Proportion of clay particles in surface soil (0-1)

P_z

Proportion of silt particles in surface soil (0-1)

P_s

Proportion of sand particles in surface soil (0-1)

theta_init

Initial soil water content of entire soil profile per unit area (unit: vol/vol)

theta_sat

Saturated soil water content of entire soil profile per unit area (unit: vol/vol)

theta_fc

Soil water content at field capacity of entire soil profile per unit area (unit: vol/vol)

SD

Soil depth of entire soil profile (unit: m)

K

Saturated lateral hydraulic conductivity of entire soil profile (unit: m/d)

P_I

Proportion of permanent interception area of rainfall (0-1)

n_s

Manning's roughness coefficient of the soil surface (unit: \(\mathrm{s/m^{1/3}}\))

CC

Proportion of area with canopy cover (0-1)

GC

Proportion of area with pervious vegetated ground cover (0-1)

IMP

Proportion of area with impervious ground cover (0-1)

PH

Average height of vegetation or crop cover where leaf drainage start to fall (unit: m)

D

Average diameter of individual plant elements at the surface (unit: m)

NV

A number of individual plant elements per unit area (unit: \(\mathrm{number/m^2}\))

d_a

Typical flow depth of surface runoff (unit: m)

DK_c

Detachability of clay particles by rainfall (unit: g/J)

DK_z

Detachability of silt particles by rainfall (unit: g/J)

DK_s

Detachability of sand particles by rainfall (unit: g/J)

DR_c

Detachability of clay particles by surface runoff (unit: g/mm)

DR_z

Detachability of silt particles by surface runoff (unit: g/mm)

DR_s

Detachability of sand particles by surface runoff (unit: g/mm)

Q_in

The volume of surface runoff from outside of an element (cell) (unit: L)

IF_in

The volume of subsurface interflow from outside of an element (cell) (unit: L)

SL_c_in

The mass of clay particles from outside of an element (cell) (unit: kg)

SL_z_in

The mass of silt particles from outside of an element (cell) (unit: kg)

SL_s_in

The mass of sand particles from outside of an element (cell) (unit: kg)

R_type

Integer object of each rainfall type for estimating kinetic energy of direct throughfall (DT) (0-8) (see details)

Author

Kwanghun Choi and Bjoern Reineking

Details

Detailed information about options of R_type can be found in details of DMMF.
This function is suitable for projecting the DMMF model for a field represented in one element during a day.

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.

Arnhold, S., Ruidisch, M., Bartsch, S., Shope, C., Huwe, B. (2013). Simulation of runoff patterns and soil erosion on mountainous farmland with and without plastic-covered ridge-furrow cultivation in South Korea. Transactions of the ASABE, 56(2):667--679.

Morgan, R. P. C. (2005). Soil erosion and conservation. Blackwell Publishing, Malden, MA, 3rd ed. ISBN 1-4051-1781-8

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 for fields and catchments with more than one element.

Examples

if (FALSE) {
## Load example data for test running DMMF_Simple function
data(Potato.Convex)
attach(Potato.Convex)
## Make toy dataset using summary statistics of field datasets of "Potato.Convex" data.
## The width and slope of the field are set according to the slope length of the convex field 
## from Arnhold et al. (2013)
W = 25
L = 25 
## The slope of the field is set as the average slope angle of the field from Arnhold et al. (2013)
S <- pi/180 * 9
## The proportion of impervious areas are estimated as the mean value of the IMP map.
IMP <- cellStats(s.map$IMP, stat='mean', na.rm=TRUE)
## "n_s" estimated using the guide value of RFR using paraplough (10cm/m) 
## and conversion equation from RFR to Manning's n from Morgan and Duzant (2008).
n_s <- 0.171  
## Using the ridge height of the field from Arnhold et al. (2013) 
## as the hydrological radius (flow depth) of the field.
d_a <- 0.15
## We use dynamic variables of the 12th day that has enough rainfall to produce soil erosion.
d.var_12<- d.var[12,]

## Run DMMF_Simple function
Output <- DMMF_Simple( W = W, L = L, S = S, R = d.var_12$R, RI = d.var_12$RI, ET = d.var_12$ET, 
                      P_c = s.var$P_c, P_z = s.var$P_z, P_s = s.var$P_s, 
                      theta_init = s.var$theta_fc, theta_sat = s.var$theta_sat, 
                      theta_fc = s.var$theta_fc, SD = s.var$SD, K = s.var$K, P_I = s.var$P_I, 
                      n_s = n_s, CC = d.var_12$CC, GC = s.var$GC, IMP = IMP, PH = d.var_12$PH, 
                      D = s.var$D, NV = s.var$NV, d_a = d_a, 
                      DK_c = s.var$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, 
                      Q_in = 0, IF_in = 0, SL_c_in = 0, SL_z_in = 0, SL_s_in = 0, R_type = 0)

## Print outputs.
Output
## Calculate per unit surface area
## Runoff per surface area of the field
Output$Q_out / Output$A 
## Interflow per surface area of the field
Output$IF_out / Output$A 
## Soil loss per surface area of the field
(Output$SL_c_out + Output$SL_z_out + Output$SL_s_out) / Output$A 
}