Environmental Engineering Reference
In-Depth Information
water demand is proportional to the soil water received from precipitation, which equals the long-term
average precipitation minus the average runoff depth. If the precipitation is more than the vegetation
water demand, the stress is positive and vegetation growth and vigor will be promoted. If drought occurs,
the stress is negative and the vegetation will suffer.
Instant stresses —For the instant ecological stress, a step function
G
()
t
' t
()
and an impulse function
are applied and given as follows
0if
tt
d
-
' ®
0
()
t
(2.4)
0
1 f
tt
!
¯
0
and
0f r
tt
z
d()
'
t
-
0
G
()
t
0
®
(2.5)
0
d
t
1f r
tt
¯
0
The instant ecological stresses can be mathematically expressed with the G -function.
(2.6)
in which K inst is a coefficient representing the reduction of vegetation due to the instant stress occurring at
time t 0 . For instance, the eruption of the Mount St. Helens volcano in the U.S in 1980 exerted an
extremely high but instant stress on the forest vegetation of more than ten thousand square kilometers of
the neighboring area. The forest vegetation cover was totally destroyed and the area was changed into
bare mountains and hills. Figure 2.27 shows the bare hills 13 years after the eruption of the volcano. The
vegetation had not recovered yet after a long period of time. This process can be then, without consideration
of other stresses, simply be described by the equation:
f
Kt
G
()
W
inst
d
V
K
G
(1980)
(2.7)
inst
d
t
in which V is the vegetation cover; t is time, K inst = 0.8 yr -1 because the vegetation was about 0.8 before
the eruption and it was totally destroyed by the eruption of the volcano. After integration the vegetation
process is obtained
Vt -
0.8
before
1980
¯
The stress resulting from logging can also be expressed by an impulse function. For instance, the
vegetation cover of the Xiaojiang watershed on the Yunnan-Guizhou Plateau of China was reduced by
5% due to logging in 1958. People cut the trees and burned the wood for iron and copper production. The
stress on the vegetation is then
()
0.0
after
1980
(2.8)
in which K inst = 0.05 yr -1 . The ecological stress by catastrophic wind can be expresses in the same way.
Reforestation has become the artificial ecological stress with the most positive influence. Usually it is
a continuous effort and is expressed with a continuous function. Assume the rate of the reforestation is
maintained at V R ( t ), the stress is then
f
K
G
(1958)
W
inst
W (2.9)
Of course, the recently planted trees do not behave immediately like mature trees. But as long as the
reforestation is continuously maintained, and the trees planted in the past years grow up, the expression
by Eq. (2.9) of the stress resulting from reforestation is correct.
Mortality and vigor stresses —Ecological stresses are classified into mortality stresses and vigor stresses
for modeling of the dynamic process. The watershed vegetation has the following ecological functions:
F
Vt
()
R
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