Geoscience Reference
In-Depth Information
F(x)
0.
0
1
0.1
0
.2
0.3
0
.4
0
.5
0
.
6
0.
7
0
.
8
0
.9
0.
9
9
400
9
300
x
(m
3
s
−
1
)
200
5
4
100
2
1
0
−
2.5
−
1. 5
−
0.5
0
0.5
1.5
2.5
y=(x
−μ
)/
σ
Fig. 13.8 Annual means of the rate of flow of the Susquehanna River near Waverly, NY (circles), and of the
Chemung River at Chemung, NY (triangles), plotted on normal probability paper. The theoretical
straight line for the Susquehanna is calculated with a sample mean
M
=
214
.
7m
3
s
−
1
and a sample
standard deviation
S
=
46
.
8m
3
s
−
1
, and for the Chemung with
M
=
72
.
8m
3
s
−
1
and
S
=
20
.
8m
3
s
−
1
. Both the
y
-scale and the
F
(
x
)-scale are shown. (See Example 13.5.)
average annual precipitation over this basin appears to be of the order of 1200 mm.
After sorting the streamflow data in ascending order, the non-exceedance probability
F
(
x
) of each data point shown in the figure was estimated in accordance with Equa-
tion (13.19) as
P
m
=
m
/
58. The sample mean and standard deviation of these data are
85 m
3
s
−
1
, and these were used to calculate
the theoretical distribution (13.35), which is also shown in Figure 13.8. The Chemung
River station is located at approximately 42
◦
00
08
N, 76
◦
38
06
W, and 237 m above
sea level; the contributing drainage area is 6491 km
2
; over this second basin the aver-
age annual precipitation is probably closer to 1100 mm. For this basin each of the data
points was assigned the non-exceedance probability
m
7m
3
s
−
1
and
S
respectively
M
=
214
.
=
46
.
/
91. The sample estimates of the
81 m
3
s
−
1
. The
Chemung River is a major tributary of the Susquehanna, and the two rivers merge a short
distance south of the two stations; thus while the two stations are located closely, the
drainage areas do not overlap. The main point is that most of the data appear to obey the
normal distribution fairly well, although it can also be seen that the wettest years plot
above the best-fit line. As an aside, note that the largest mean flow rates at both stations
were recorded for the year of Tropical Storm Agnes. This event took place in June of
1972; the total precipitation varied, with reported maxima of up to 450 mm, but over
these two areas it was of the order of 150-250 mm over three days (Bailey
et al
., 1975).
It caused the most severe flood ever experienced in the entire Susquehanna basin and
resulted in the loss of some 120 lives; at the time, this flood was the most destructive and
=
.
79 m
3
s
−
1
=
.
moments of the Chemung record are
M
72
and
S
20
