Rearranging

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

ice-impacted discharges to occur only during or

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

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

(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

(8)

Sioux City. However, because of the very steady

1 *e*

nature of the flow at Yankton, the relatively close

11where *C*o 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 *V*a

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 *V*I is at a maxi-

are the date on which the maximum discharge deficit

mum when *C*o 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-

mum ice-caused discharge deficits on an annual,

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