Geoscience Reference
In-Depth Information
The
ʸ I function is determined from the expression:
2
h i ¼ a i exp b b i c i s B
c i ¼ 1
; ...;
4 Þ
where the a i
ʸ i , c i
coef
cient is equal to a maximum of
is the biological time of a
flux to the ith organ, the b i
maximum of assimilates
' fl
coef
cient determines the
ʸ i function.
steepness of the
˄ B into the ith organ of the plant is
The
fl
flux of assimilates at a time moment
equal to m5θi 5 ʸ i (
˄ B ).
Assume that respiration connected with the growth of the ith organ of a tree is
proportional to the rate of its increment and equal to r i dm i /dt, and the respiration for
maintenance of leaves and sucking roots is proportional to their mass and equal to
p i m i (i = 1, 2, 4). The pi i coef
cient depends on temperature:
p i ¼ a i exp k i
T T p
½
ð
Þ
where a i is the respiration for maintenance at a temperature T p .
The respiration for maintenance of the trunk and thick roots is in proportion to
the trunk area s 3 and is equal to s 3 p 3
b s p , where
ʲ st is the share of the trunk mass in
m 3 . The dying-off of the organs is considered to be in proportion to their masses
with the coef
, 4).
The water cycle in a tree is described by a system of equations that parameterize
the water motion over the territory, in soil, in a tree and its elements. The water is
one of the limiting factors of the tree
cients di i (i =1,
s growth through a value of the stomatal
resistance that affects the photosynthetic activity of plants. The water cycle on the
forest territory is the sum of two basic parts
'
abiotic and biotic, which describe the
processes of water motion in soil and its absorption by the root system, its motion in
the plant, and transpiration. There are a lot of models of these processes. The
difference between them is determined by different suppositions about the character
of the soil structure and the location of the root system. Kirilenko (1990) proposed
to describe the water motion in the soil with an equation that generalizes the Darsi
classical model when the soil is considered a homogeneous porous layer:
@x
@
t ¼ q
K P B
U P B @
@x
@
f ð z
t Þ
U P B
;
n
n
z lx
z þ x
þ
;
q S
@
@x
@
n
m
V ð z ; t Þ ¼K P B
lx
z þ x
with the boundary conditions:
¼ 1
U z g ; t
;
V 0
; ðÞ ¼W ðÞ L ðÞ
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