1000
Dec 1
J ec 15
800
Jan 1
Fan 15
Feb 1
600
eb 15
400
200
0
2
5
10 20
100
Figure 16. Yankton accumulated freez-
ing-degree-days (December 1 start
Return Interval (years)
date).
14 10 3
12
10
Envelope
8
6
4
2
0
100
200
300
400
500
600
700
800
900
1000
0
Figure 17. Maximum discharge deficit vs.
AFDD (Yankton).
AFDD
deficits occurring in each AFDD category are shown
In Figure 17 the maximum discharge deficits list-
in Figure 18. As with the previous statistical analysis,
ed in Table 5 are plotted against the AFDD that
the return interval for each AFDD category is found
occurred on the day that the maximum discharge
by assigning each maximum discharge deficit a
deficit occurred. It can be seen that in general there is
an "envelope" that describes the limit of the dis-
probability, P, defined by J/(N+1), where J is the rank
charge deficit and that the upper limit of this enve-
of the deficit and N is the total number of data points
lope decreases with increasing AFDD. This decrease
available. The return interval is then 1/(1P). We can
reflects the fact that as each winter progresses (and
see that, in large part, the data are normally distrib-
uted except for the category 100200 AFDD. This
the number of AFDD increases), the amount of ice in
category is somewhat comparable to the time period
the river is increased and the amount of open water
1631 December. As with that time period, the data
decreased. With the reach fully ice covered, dis-
for this category suggest a mixed population, and
charge deficits should not occur.
separate probability curves have been drawn to indi-
To complete this analysis, we can group the dis-
cate the two populations. At this time it is not pos-
charge deficits into AFDD categories as shown in
sible to explain the mixed population appearance of
Table 7. It can be seen that not every AFDD category
this data.
is reached every year and that ice-impacted periods
do not occur every year during each AFDD category
To further extend the statistical analyses, we
that is reached. The annual maximum discharge
must take note that discharge deficit cannot be ex-
15
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