Geoscience Reference
In-Depth Information
1
2
3
4
3
4
5
6
7
8
d
3,17
9
10
11
12
13
d
4,17
14
15
16
18
19
d
2,17
d
1,17
2
17
1
20
23
24
21
22
25
Fig. 3.12 Sketch illustrating the application of the inverse distance method. For example, the precipitation over
subarea 17 is determined as
i
=
1
d
−
2
i
,
17
P
i
/
i
=
1
d
−
2
i
,
17
. The average precipitation over the entire
catchment is then obtained as the weighted average of all subarea values, as shown in Equation (3.2).
The locations of the stations are indicated by the numbered circles.
where
n
is the number of rain gage stations in the area, and
A
is the surface area of the
catchment, that is the sum of the subareas, or
A
=
i
=
1
A
i
.
The
inverse distance
method is equally simple in principle, but it is easier to imple-
ment. It is based on the assumption that the precipitation at any given point is influenced
by all stations in the area, each weighted by the inverse of a power of its distance from
the point. Note, as an aside, that the principle can also be used to calculate missing
data. To obtain the areal average, the method is applied by subdividing the area into
m
rectangular subareas, each with an assumed uniform precipitation as calculated for the
point at its center; the resulting mean precipitation is then
n
−
1
m
n
1
A
d
−
b
ij
d
−
b
P
=
A
j
ij
P
i
(3.2)
j
=
1
i
=
1
i
=
1
in which
A
j
is the surface area of the
j
th subarea,
A
is the total surface area of the
catchment, and
n
the total number of precipitation stations;
d
ij
is the distance of the center
of the
j
th subarea from the
i
th rain gage in the catchment and
b
is a constant, which
in most applications has been taken as 2. It can be seen that, for
b
=
0, Equation (3.2)
produces the arithmetic mean. Dean and Snyder (1977) found that
b
2 yielded the
best results in the Piedmont region of the southeastern United States, whereas Simanton
and Osborn (1980) concluded from measurements in Arizona that
b
can range between
1 and 3 without significantly affecting the results. Figure 3.12 illustrates the application
of this method.
=
