Agriculture Reference
In-Depth Information
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and hence the areal coverage of drought is equal to n 1 or n 1 / m . For the
subsequent time interval, t , there are ( m
n 1 ) drought-prone subareas.
Assuming that the evolution of possible SMD and SMS spells along the time
axis is independent over mutually exclusive subareas, similar to the concept
in equation 4.16, it is possible to write for the second time interval (Tase,
1976; ¸ en, 1980b). The PDFs of areal agricultural droughts for this model
are shown in figure 4.5 with parameters m
=
10, p r =
0.3, p t =
0.2 and i
=
1, 2, 3, 4, and 5. The probability functions exhibit almost symmetrical
forms regardless of time intervals, although they have very small positive
skewness.
Another version of the multiseasonal model is interesting when the num-
ber of continuously SMD subareas appear along the whole observation
period. In such a case, the probability of drought area in the first time in-
terval can be calculated using equation 4.16. At the end of the second time
interval, the probability of j subareas with two successive SMDs given that
already n 1 subareas had SMD in the previous interval can be expressed as
[50],
n 1 ) n 1
j
p t q n 1 j
Line
——
1.3
——
Cust
* PgEn
P 2 t ( A d =
j
|
A d =
n 1 )
=
P t ( A d =
[4.17]
t
This expression computes the probability of having n 1 subareas to have
SMD, out of which j subareas are hit by two SMDs; in other words, there
are ( n 1
j ) subareas with one SMD. Hence, the marginal probability of
continuous SMD subarea numbers is
j k
p t q t
m
j
P t A d =
+
j
[50],
P 2 t ( A d =
j )
=
k
+
[4.18]
j
k
=
0
In general, for the i th time interval, it is possible to write
j k
p t q t
m
j
P ( i 1 ) t A d
+
j
P i t ( A d
=
j )
=
=
k
+
[4.19]
j
k
=
0
Th e numerical solutions of this expression are presented in figure 4.6 for
m
=
10, p r =
0.3, and p t =
0.5. The probability distribution function is
po sitively skewed.
Figure 4.5 Probability of drought area for multiseasonal model ( m = 10; p r = 0.3; p t = 0.2).
 
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