Vegetation-Erosion Dynamics - River Dynamics and Integrated River Management - page 83

a parameter representing the effect of shadow and propagation with dimensions [time -1 ] and units (yr -1 ).
The value of a depends on the precipitation, soil, and species composition of the vegetation and must
be determined using field data. The parameter c represents the damage to vegetation by erosion, with
dimensions [area/mass] and units (km 2 /t). The value of c depends on soil texture and the species
composition of the vegetation. If the soil is thin and erosion may seriously impair the vegetation, the
value of c is large.
It must be noted that the erosion rate in the equation is a moving average value over a certain period of
time because the erosion rate fluctuates following rainfall and runoff, but the vegetation is affected by the
long-term action of erosion, which is represented by an average rate of erosion. For instance, the
averaging period may be 10 years, then the moving average value of the erosion rate is attributed to the
year in the center of the averaged range of years. For example, the average from the 1st to 10th year is
plotted at the 6th year, the value for the 7th year is the average from the 2nd to 11th year, and so on. E in
the equations is not a fluctuating parameter but a rather smooth function of time, as shown in Fig. 2.30.
The Anjiagou Gully located in Dingxi County of Gansu Province is in the watershed of the Donghe
River, which is a tributary of the Zuli River on the Loess Plateau of China. The annual runoff, the rate of
erosion, and the moving average rate of erosion over a 10-year period for the Anjiagou Gully are shown
in Fig. 2.30. The rate of erosion fluctuates with variation in runoff but the moving average of erosion
reflects only the trend of variation. The rate of erosion in Eq. (2.11) is the moving average value of
erosion but is still called the rate of erosion for convenience.

Fig. 2.30 Variation of the annual runoff, the annual rate of erosion, and the moving average rate of erosion of the
Anjiagou Gully in Gansu Province, China

K t G , E , and V R are known as functions of time and the parameters a and c are determined, the
vegetation development under the action of the stresses can be determined. Nevertheless, the rate of erosion
E is usually not given because it depends, in turn, on the vegetation, therefore, one more equation is needed
to solve for V and E . Thornes (1985) proposed coupled differential equations for the vegetation-erosion
processes. The equation for erosion is applied and revised here by introducing the impact of human
activities on erosion:

If

() i

d
d

E

(2.12)

bE fV E

R

t

in which b and f are parameters to be determined with field data, E R represents the impact of human
activities on erosion, including the increase of erosion due to mining, road construction, land-use change,
and agriculture; and the reduction of erosion by the application of soil conservation measures, such as
terrace field replacing slope tillage, structures controlling slope erosion, and sediment-trapping dams. The