Rearranging
Selection of initial reach
for study
QOUT = QIN B ∆ d ∆X
The ice-impacted discharge periods can be iden-
(6)
tified by comparing the discharges recorded at the
∆t
upstream and downstream end of a specific reach. If
we see that the flow out of the reach will be less than
the upstream discharges are relatively constant and
the flow in as long as the water level is rising. As the
unaffected by ice, this increases the ease with which
water level rises in response to the presence of the
the comparisons can be made. The most appropriate
stationary ice cover, the discharge downstream of
reach then is the most upstream reach in the study
the location where the ice cover initially arches must
area, from Yankton to Sioux City, because the flow at
be reduced. This reduction will occur as long as the
Yankton reflects the discharge released at the Gavins
ice cover is progressing upstream and the water level
Point Dam, approximately 5.3 miles upstream. The
under the cover is increasing in elevation.
releases at Gavins Point Dam are not affected by ice
The impacted discharges can be expected
in the Missouri River.
whenever a stationary ice cover in the Missouri
River is progressing upstream. We would expect
Determining the ice-impacted
ice-impacted discharges to occur only during or
discharge periods
immediately following cold periods when ice was
Generally, the flow at Yankton follows a consis-
generated in the open water areas of the river.
tent pattern during the winter months. During No-
Once a stationary ice cover has formed, further
vember and the earliest part of December the flow at
growth in thickness of the ice has a minimal impact
Yankton is declining until a stable level is reached
on the water level. The magnitude of discharge
and maintained for the remainder of December,
deficit can be estimated in the following manner.
January, and February. There can be some small
We rewrite eq 6 so that
fluctuations in the flow at Yankton during this time,
but historically the flow is maintained at a fairly
QDIFF = QIN QOUT = B DI Do VI
(7)
constant level. The ice-impacted discharge periods
are determined by comparing the discharge at
where VI is the progression rate of the ice cover,
Yankton and Sioux City. Ideally, the flow at Yankton
which can be estimated as
should be numerically "routed" to Sioux City and
this routed flow compared to the flow measured at
VI = Co Va
(8)
Sioux City. However, because of the very steady
1 e
nature of the flow at Yankton, the relatively close
11where Co is the volumetric concentration of the ice
spacing of both stations (70 miles), and the fact that
arriving at the leading edge of the stationary ice
only daily average discharges were available, flow
cover, e is the porosity of the stationary cover, and Va
routing was found not to be necessary. The ice-
is the mean arrival velocity. Unfortunately, the value
impacted discharge periods were determined by
of these parameters can only be roughly estimated at
subtracting the discharge at Sioux City from that at
this time. We can see that the ice cover progression
Yankton each day. Those days when the results were
rate is strongly proportional to the concentration of
positive were then selected as the ice-impacted dis-
the arriving ice. The ice concentration in turn is a
charges. This was done for all winters from 197071
strong function of the heat transfer rate from the
through 198788. The resulting data, listed in Table 5,
water surface. We would expect that VI is at a maxi-
are the date on which the maximum discharge deficit
mum when Co is at its maximum, and we would
occurred (that is, the largest difference between the
expect that the maximum impact on the discharge
Sioux City gage and the Yankton gage), the magni-
would occur during the intense cold periods, when
tude of the discharge deficit, the length of the im-
the maximum heat transfer rates occur.
pacted discharge period in days, and the accumu-
lated freezing-degree-days (C) from 1 December at
In the remainder of this section we will select a
reach in which the ice-impacted discharge periods
the time of the maximum discharge deficit. There are
are easily identified, then we will determine all of the
65 recorded periods of discharge deficits.
impacted discharge periods over a suitable length of
record. Next we will statistically analyze the maxi-
Statistical analysis of ice-impacted
mum ice-caused discharge deficits on an annual,
discharges by time period
half-month, and accumulated freezing-degree-day
A histogram of discharge deficit maximums that
(AFDD) basis.
occurred during the ice-impacted periods is shown
11
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