K and C factors in the USLE-M

Applying the USLE to an event gives

A_e = K_e C_e [EI₃₀] L S P_e....................................................................................................(1)

where A_e is event soil loss, K_e is event soil erodibility, C_e is the crop factor for the event, L and S are the slope length and gradient factors, and P_e is the soil conservation practice factor for the event. The USLE operates in such a manner that the values of C_e, L, S and P_e all have a value of 1.0 when the surface is in a bare fallow condition, the length of slope is 62.5 feet, the slope gradient is 9 % and cultivation takes place up and down the slope. Under these conditions, the soil loss for the unit plot (A_e.1) where C_e = L = S = P_e = 1 is given by

A_e.1 = K_e [EI₃₀]..................................................................................................................(2)

and

C_e = A_e.C / A_e.1...................................................................................................................(3)

where A_e.C is the soil loss from the cropped plot where L = S = P_e = 1. A similar equation applies to P_e:

P_e = A_e.P / A_e.1...................................................................................................................(4)

where A_e.P is the soil loss from a plot where P ¹ 1 but C= L = S = 1.

In the USLE-M, the erosivity index is the product of the runoff ratio (Q_R) and EI₃₀. Thus, for the USLE-M,

A_e = K_e.UM C_e.UM [Q_R EI₃₀] L S P_e.UM.............................................................................(5)

It follows that the soil loss for the unit plot is given by

A_e.1 = K_e.UM [Q_R.1 EI₃₀].....................................................................................................(6)

where Q_R.1 is the runoff ratio for the unit plot, and that

C_e.UM = A_e.C / A_e.1.............................................................................................................(7)

where, as stated above, A_e.C is the soil loss from the cropped plot. It follows from Eq. 4 and 7 that, under these circumstances, C_e.UM = C_e and P_e.UM = P_e. However, there are often events where no erosion may occur on a cropped area while erosion occurs on the unit plot while, in some circumstances, erosion may occur on a cropped plot when no erosion occurs on the unit plot. Since these non-erosion events are associated with no runoff, it is more appropriate to use an erosivity index that is associated with the runoff that occurs on the cropped plot than the unit plot. This approach is adopted in the USLE-M. As a result, the long term average annual values of K_UM and C_UM are given by

N
S (A_e.1)_n
n=1

K_UM = ^{___________________}...............................................................................................(8)

N
S (Q_R.1 EI₃₀)_n
n=1

and

N
S (A_e.C)_n
n=1

C_UM = ^{___________________________}.................................................................................(9)

N

K_UM S (Q_R.1 EI₃₀)_n
n=1

where L = S = P_UM = 1.0, N is the number of rainfall events that have produced soil loss, and the subscript C indicates that the data is associated with a cropped area. A similar expression is used to determine P_UM. Since, in most cases, the runoff ratio for a cropped area is less than for the bare fallow condition, C_UM values tend to be higher than the C values obtained for the USLE.

Examples of average annual C_UM values for crops at various USA locations

(from Kinnell and Risse, Soil Sci Soc Amer J 62 (1998) 1667-1672)

Location	Crop	CUM	CU	CUM/CU	CU/CUM
Bethany, Missouri	alfalfa	0.008	0.002	4.0	0.250
	corn	0.674	0.628	1.1	0.932
	corn/meadow/wheat	0.188	0.106	1.8	0.564
Clarinda, Iowa	corn	0.634	0.316	2.0	0.498
	corn/oats/meadow	0.424	0.168	2.5	0.396
Guthrie, Oklahoma	cotton	2.435	1.357	1.8	0.557
	Bermuda grass	0.064	0.002	32.3	0.031
	wheat/clover/cotton	0.913	0.344	2.7	0.377
LaCrosse, Wisconsin	corn	0.527	0.469	1.1	0.890
Madison, S.Dakota	corn(ploughed)	0.486	0.337	1.4	0.693
	corn(mulch till)	0.384	0.250	1.5	0.651
Morris, Minnesota	corn	0.520	0.434	1.2	0.835
	meadow/corn/oats	0.046	0.010	4.6	0.217
Presque Isle, Maine	potatoes	0.634	0.316	2.0	0.498

A value of 1.0 for the ratio of C_UM to C_U indicates that the crop has no impact on runoff. The higher the C_UM to C_U ratio, the greater the impact the crop has on runoff. Note that Corn tends to have little effect on this ratio while Bermuda Grass has a large effect because of its capacity to reduce runoff.

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Catchment Erosion: AGNPS-UM