normalized stage would be an indicator of a
2.0
severe or damaging ice event. For example, the
most damaging ice event at North Bend occurred
in March 1978. This event had a normalized stage
of more than 1.9, almost double the listed flood
stage of 8 ft. Using the regression approach, we
1.6
examined the relationships between a variety of
meteorological and hydrological parameters, in-
cluding air temperature and discharge on the day
of the ice event, AFDD, ATDD, accumulated pre-
cipitation and accumulated snowfall. Because we
1.2
thought that the rate of increase in discharge (and
hence stage) might be important in ice-cover
breakup and jam formation, we also looked at the
difference between the average daily discharge
on the day of the event and one, two, three, four
0.8
and five days before the event.
An examination of the data showed that accu-
mulated precipitation, accumulated snowfall and
air temperature on the day of the event were weak-
ly correlated with the normalized stage of ice
events at North Bend. We also found little rela-
0.4
0.8
1.2
1.6
2.0
tionship between stage and the difference between
Observed Normalized Stage
the discharge on the day of the ice event and one,
Figure 12. Relationship between the observed
two, three, four and five days previously. ATDD
and predicted values of normalized stage at
was slightly better correlated with the normal-
North Bend.
ized stage. A stepwise linear regression selected
Julian date, AFDD and the discharge on the date
of the ice event (Q) as significant parameters. The
resulting model is:
might be developed in the future with the inclu-
sion of additional ice-event data. If so, this could
NS = 1.60799 5.832 103 JD
provide a useful prediction of the stages that might
+ 2.59 104 AFDD + 1.1 105 Q
be expected for an ice event at North Bend.
Although the regression does not result in a
where NS is the normalized stage. The r2 for the
conservative prediction of the occurrence or se-
model is 0.5419. Most of the variation is due to the
verity of ice jams, it does identify the important
model rather than random error.
parameters (date, AFDD and discharge) that
By definition a regression equation will over-
should be considered in developing a prediction
predict and underpredict some values. Figure 12
model. It also provides a mean value of expected
is a graph of the normalized stages at North Bend
stage, which, if the uncertainty is recognized, can
predicted for ice-event years by the regression
be used to provide warning that damage is likely
relationship vs. observed normalized stages. As
or very likely.
can be seen in the figure, the regression tends to
The AFDD, discharge and Julian date of the ice
overpredict stage, but in eight cases it underpre-
jam were considered in a threshold analysis, which
dicts stages. The most serious shortcoming is
confirmed the conclusion reached during the eval-
uation of historic data for the study area--that
illustrated by the two cases in which the regres-
AFDD must reach at least 400 before an ice event
sion predicts a stage less than flood stage, but stages
will occur. Similarly discharges must exceed at
greater than flood stage occurred (1980 and 1955).
least 6000 cfs for an ice event to occur. Also, ice
The normalized stage was underpredicted by 19%
events occurred between Julian Day 131 and Julian
and 32%, respectively, in these cases. In the remain-
ing six cases the predicted normalized stage was
Day 182. From an examination of average daily
discharges at the time of maximum ice stages, a
above flood stage but was between 7% (1983) and
relationship between ice-event discharge and
23% (1978) lower than the observed normalized
Julian date was developed:
stage. It is possible that an improved regression
26
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