Vegetation-Erosion Dynamics - River Dynamics and Integrated River Management - page 82

2.3 Vegetation-Erosion Dynamics

Vegetation-erosion dynamics is a new interdisciplinary science, studying the laws of evolution of watershed
vegetation under the action of various ecological stresses (Wang et al., 2003a). Different from other
stresses, soil erosion not only impacts the vegetation but also is affected by the vegetation. Vegetation and
erosion are a pair of competing and mutually interacting aspects of a watershed. In nature, the development
of vegetation cover and variation of soil erosion affect each other, following a dynamic law. For a watershed,
vegetation and erosion may reach an equilibrium state if the circumstances remain unchanged for a long
period of time, as shown in Fig. 2.29. However, the equilibrium may not be stable. Ecological stresses,
especially human activities, may disturb the balance and initiate a new cycle of dynamic processes.

Fig. 2.29 Vegetation and erosion may reach an equilibrium state, if the circumstances remain unchanged for a long
period of time (See color figure at the end of this topic)

The vigor of trees is dynamic responding to the impact of various stresses and is an important indicator
if the instantaneous state of the vegetation is studied. For the functions of wind erosion control, habitat,
and primary production of vegetation, both the vegetation cover and vigor are important and must be
considered in any dynamic model. For rainfall and runoff erosion control, vigor is not important and only
the vegetation cover need be studied and modeled.

2.3.1 Differential Equations
The vegetation cover is a function of the mortality stresses, soil erosion, and human activities. Different
from other stresses, soil erosion not only impacts the vegetation but also is affected by the vegetation. In
sediment engineering, erosion usually is quantitatively represented by E , the rate of sediment eroded
from a unit area per year. In general, the existing vegetation favors vegetation development due to the
effects of canopy cover providing shadow and propagation of mature vegetation, but erosion destroys the
vegetation cover. Therefore, the rate of change of vegetation is proportional to the vegetation but inversely
proportional to the erosion rate. The dynamics of the vegetation under the action of ecological stresses is
described by the following differential equation:

d V

aV cE K G () t V (2.11)

inst 0 R

d t

Where V is the fraction of vegetation cover, and a and c are parameters, the third term on the right
hand side represents the mortality stresses which are usually instant stresses. The fourth term V R represents
the human stresses, which may be positive (reforestation) or negative (deforestation). In the equation, a is