function of the area within the given basin that is represented by that particular
station. To put it another way, if a station adjacent to the basin is so close to the basin
that the perpendicular bisector of a line between a station immediately outside of the
basin and its closest station inside the basin falls within the basin, then the area closer
to the outside station, but within the basin, is considered representative of the results
of the station located outside the basin. In order to depict this, a stylized drainage
basin is chosen as shown in Fig. 6.5. The points indicate the location of precipitation
measuring stations within and adjacent to the basin. In order to determine the portion
of the total area represented by each station, construction lines (shown as dotted lines
in the figure) are drawn between each adjacent station. Then perpendicular bisectors
of each of these dotted lines are drawn. The perpendicular bisectors are extended
until they meet a similar perpendicular bisector of an adjacent line. With careful
construction all lines should meet in points and it can be determined whether or not
an area inside the basin is closer to a measuring station outside the basin. The
perpendicular bisectors are drawn as solid lines on the figure. Then by means of a
planimeter the area represented by each station may be measured. The total precipitation in the basin is then derived from the sum of all of the individual values of
precipitation at the representative measuring stations multiplied by the fractions of
the area of influence within the basin from that measuring station. A typical example
of the calculations involved is shown in Table 6.1.
A third method for measuring precipitation in a large basin is the isohyetal
method. Here the values of precipitation for each station are indicated on a map
showing the location of each station. Smooth lines are drawn through areas of equal
precipitation, as shown in Fig. 6.6. Now the area between each contour line is
measured with a planimeter and the average precipitation between the two lines is
multiplied by the ratio of that area to the total basin area, the sum of the individual
Table 6.1 Calculations for Thiessen method
(1)
(2)
(3)
(4)
(5)
or (5a) omit (4)
Location
Ppt’n
cm
Area
km
À2
Fraction (or %) of
total area
a
Weighted ppt’n, cm
(2) Â (4)
Ppt’n  Area
(2) Â (3)
A
1.65
7
0.01
0.0165
11.55
B
3.71
120
0.90
0.7049
445.20
C
4.88
109
0.18
0.8784
531.92
D
3.91
20
0.03
0.1173
78.20
E
6.83
120
0.19
1.2977
819.60
F
7.16
0
–
–
–
G
7.57
92
0.15
1.1355
696.44
H
11.43 76
0.12
1.3716
868.88
I
12.70 82
0.13
1.6510
1041.40
J
4.44
0
–
–
–
K
4.95
0
–
–
–
Σ
626
1.00
7.17
4492.90/
626 ¼ 7.18
a (4) ¼ A/ΣA ¼ (3)/Σ(3) (Â100 if using %)
6 Basic Hydrology, Water Resources, and DAF Boat Plant for Lake Restoration
243
station. To put it another way, if a station adjacent to the basin is so close to the basin
that the perpendicular bisector of a line between a station immediately outside of the
basin and its closest station inside the basin falls within the basin, then the area closer
to the outside station, but within the basin, is considered representative of the results
of the station located outside the basin. In order to depict this, a stylized drainage
basin is chosen as shown in Fig. 6.5. The points indicate the location of precipitation
measuring stations within and adjacent to the basin. In order to determine the portion
of the total area represented by each station, construction lines (shown as dotted lines
in the figure) are drawn between each adjacent station. Then perpendicular bisectors
of each of these dotted lines are drawn. The perpendicular bisectors are extended
until they meet a similar perpendicular bisector of an adjacent line. With careful
construction all lines should meet in points and it can be determined whether or not
an area inside the basin is closer to a measuring station outside the basin. The
perpendicular bisectors are drawn as solid lines on the figure. Then by means of a
planimeter the area represented by each station may be measured. The total precipitation in the basin is then derived from the sum of all of the individual values of
precipitation at the representative measuring stations multiplied by the fractions of
the area of influence within the basin from that measuring station. A typical example
of the calculations involved is shown in Table 6.1.
A third method for measuring precipitation in a large basin is the isohyetal
method. Here the values of precipitation for each station are indicated on a map
showing the location of each station. Smooth lines are drawn through areas of equal
precipitation, as shown in Fig. 6.6. Now the area between each contour line is
measured with a planimeter and the average precipitation between the two lines is
multiplied by the ratio of that area to the total basin area, the sum of the individual
Table 6.1 Calculations for Thiessen method
(1)
(2)
(3)
(4)
(5)
or (5a) omit (4)
Location
Ppt’n
cm
Area
km
À2
Fraction (or %) of
total area
a
Weighted ppt’n, cm
(2) Â (4)
Ppt’n  Area
(2) Â (3)
A
1.65
7
0.01
0.0165
11.55
B
3.71
120
0.90
0.7049
445.20
C
4.88
109
0.18
0.8784
531.92
D
3.91
20
0.03
0.1173
78.20
E
6.83
120
0.19
1.2977
819.60
F
7.16
0
–
–
–
G
7.57
92
0.15
1.1355
696.44
H
11.43 76
0.12
1.3716
868.88
I
12.70 82
0.13
1.6510
1041.40
J
4.44
0
–
–
–
K
4.95
0
–
–
–
Σ
626
1.00
7.17
4492.90/
626 ¼ 7.18
a (4) ¼ A/ΣA ¼ (3)/Σ(3) (Â100 if using %)
6 Basic Hydrology, Water Resources, and DAF Boat Plant for Lake Restoration
243