Table 5. Measurements of water temperature entering breakup ice jams. The heat-transfer length is the
distance from the head of a jam to the point where the water has lost > 90% of its sensible heat.
Entering water
Heat-transfer
temp., ∆T
length
(F32)
Reference
River
(miles)
Comments
Calkins (1984)
Ottaquechee R.
1.3
0.8
Upstream of refrozen jam, time between
breakup and measurement unknown.
Prowse and Marsh (1989)
Liard R.
3.1
2
Measured during breakup event.
Beltaos et al. (1998)
Matapedia R.
4.5
0.2
Time between breakup and measurement
unknown.
This work
Cazenovia Cr.
1.8
unknown
Measured by USGS about 12 hours after
peak of 1985 ice-jam hydrograph.
water entering a jam is lost to melting ice, we relate the
We used the hydrographs from the 1972 and 1985
volumetric melt rate of ice, Vm, to discharge, Q, via:
ice-jam events (see Fig. 2) to estimate the rise time for
discharge after ice jam formation (i.e., from just after
Vm ≈ 0.008 ⋅ Q(cfs) ⋅ ∆T (F)
˙
(4)
the initial spike to the broad, ice-free peak). This yielded
400 cfs/hr and 500 cfs/hr for the 1972 and 1985 events,
where ∆T is the water temperature difference above
respectively. We will use a straight-line hydrograph that
32F. Thus, water entering a jam 1F above freezing
rises at 500 cfs/hr from a jam-formation discharge of
will cause a volumetric melt rate of about 1% of river
2000 cfs. Although a hydrograph rises more slowly
discharge. The data in Table 4 support a temperature
during the early portion of an event, use of the faster,
difference at least this high. The expected rise in ∆T as
near-peak rate produces a conservative estimate of the
the event proceeds should compensate for loss of sen-
ice volume lost to melting and washouts.
sible heat through the toe of the jam as it becomes short-
er. Therefore, we will use Vm (cfs) = 0.01 ⋅ Q(cfs) as our
˙
Ice-jam volume versus discharge
best estimate for the volumetric melt rate of the ice jam
We may combine the preceding terms to estimate
retained by the ICS.
the volume of ice in the jam retained by the ICS as a
function of discharge, Vj(Q). Transport losses of 30%
reduce the estimated 10 106 ft3 pre-breakup ice sup-
Ice washouts
ply to an initial jam volume of Vj (2000 cfs) = 7 106
During the model tests, we did not quantify the rate
ft3. Following a straight-line hydrograph that rises at
of ice loss attributable to major washouts or ultimate
releases through the ICS. However, observations dur-
500 cfs/hr, melting losses occur at a rate of 1% of dis-
ing washouts or releases at high discharge suggest
charge throughout the event. Above 8000 cfs, additional
approximately 1% ice concentrations downstream of
losses ascribable to washouts at the ICS occur at a rate
the ICS. Washouts of smaller ice floes through the ICS
of 1% of discharge.
and onto the floodplain also took place throughout the
Figure 16 shows the resulting ice-jam volume at the
tests without release of the larger floes arched at the
ICS as a function of river discharge. Because losses
ICS. For simplicity, however, we will assume that the
increase with increasing discharge, ice jam volume
˙
washout rate, Vw , is zero below 8000 cfs, and increases
decreases. Ice losses become particularly significant
to Vw (cfs) = 0.01 ⋅ Q(cfs) for discharge above 8000 cfs.
˙
above about 8000 cfs, as we would expect from the
By neglecting washouts at low discharge, this approach
model tests, and that just above 11,000 cfs we would
expect essentially all the ice to have melted or washed
is probably conservative in its effect on ice jam vol-
out through the ICS. This estimate of Vj(Q) should be
ume.
conservative, and we used it to constrain the ice-jam
length to predict upstream water levels.
Hydrograph rise time
To determine ice-jam volume lost up to a given dis-
Numerical icehydraulic model
charge, we must integrate the loss rates (expressed in
terms of river discharge) with respect to time. This
Model formulation
requires an expression for the rise time of a character-
We used HEC-RAS, the Corps' numerical hydrau-
istic hydrograph: the slower the rate of rise, the more
lic model (U.S. Army 1998a), to calculate water sur-
ice volume is lost to melting and washouts up to a par-
face profiles through the ICS reach for both open-water
ticular discharge.
and ice-jam cases. Briefly, HEC-RAS treats water flow
15
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