Transport losses

For ice jams on smaller rivers, typical values of Lj/Lr ~

The river length from the ICS site to East Aurora is

0.1, Bj/Br ~ 2, hj/ti ~ 4 result in Ct ~ 0.5.

about 11 miles. Along this reach, the average cover

Nearly all of the available estimates of Ct, including

width should be about 100 ft. A good estimate of the

ones based on jams in Cazenovia Creek, equal or exceed

maximum average ice thickness immediately prior to

breakup is 1.5 ft. This yields an ice volume of 9 106

0.3. The exception is for an ice jam on the Winooski

ft3, which we may increase to 10 106 ft3 to allow for

River (which flooded Montpelier, Vermont, in March

1992), whose contributing reach was very short and had

minor ice supply from the east and west branches (U.S.

few overbank areas to strand ice. Therefore, although

Army 1986b). This becomes our best estimate for the

an average value of 0.5 could be justified, we will use

pre-breakup ice supply, Vr.

Ct = 0.3 as a conservative estimate for transport losses.

Transport losses

Ice melting

Field measurements have shown that the ice volume

Ice breakup normally occurs as a result of rapid

in a breakup jam can be substantially less than the vol-

snowmelt or rainfall during periods of above-freezing

ume of the pre-breakup ice cover on the contributing

air temperatures. Upstream of an ice jam, airwater

river reach. The formation of shear walls and the strand-

convection, solar radiation, groundwater inflow, fluid

ing of ice floes on small floodplains are the main trans-

friction, and geothermal flux will all add heat to the

port losses occurring during an ice run. The transport

river. Under the assumption that little ice remains

loss coefficient, Ct, is defined as the ratio of ice vol-

upstream or that it has been stranded above the water

ume lost during a breakup run to the volume of the pre-

level during the breakup surge, this heat flux will raise

breakup ice cover. It is thought to increase with the

the temperature of water entering the head of the jam.

length of contributing reach (U.S. Army 1982).

The resulting melting (and weakening) of ice floes within

Table 4 lists values of the Ct available in the litera-

a jam can be significant during long-duration, high-

ture and those calculated here for the 1972 and 1985

discharge events. Although loss of jam volume may not

ice jams on Cazenovia Creek. We derived the latter

be visibly obvious, these effects probably couple with

values using reported jam locations and lengths (U.S.

rising hydrodynamic forces to release natural ice jams.

Army 1972, Predmore 1985). The transport loss coef-

Table 5 presents measurements of water tempera-

ficient is related to the ice-supply and ice-jam parame-

ture entering breakup ice jams. Because of the high flow

ters as follows:

velocities and ice-jam roughness, nearly all the avail-

Lj Bj hj

⋅ (1 - p)

Ct = 1 -

⋅

able heat is transferred to ice melting within about

(3)

Lr Br ti

1 mile. If the jam is longer than this, ice melting at the

upstream end will predominate. As the jam shortens,

where L

= length of the jam

some warm water will persist to the toe and melt or

= width of the jam

weaken ice preferentially along main flow paths. In the

= thickness of the jam

case of a jam at an ICS, this process contributes to its

= porosity of the jam, assumed to be 0.4

ultimate release or washout.

(Prowse 1990)

The sensible heat of water is 1 Btu/lbm F or about

Lr = length of the contributing ice cover

62 Btu/ft3 F. The latent heat of fusion for ice is 144

Br = width of the contributing ice cover

Btu/lbm or about 8200 Btu/ft3 for solid ice (specific

ti = average ice thickness of the contributing

gravity 0.92). Assuming 100% of the sensible heat of the

ice cover.

Table 4. Transport loss coefficients for breakup ice jams.

Contributing

Transport

reach, Lr

loss coefficient

Reference

River

(mi.)

Comments

Calkins (1978)

Ottaquechee R.

0.9

Assumed jam porosity of 0.4

0.9

(Prowse 1986).

Prowse (1986)

Liard R.

300

0.8

Entire event.

0.4

Last 24 hours of movement.

Cumming-Cockburn (1986)

Credit R.

0.5

3 years of field surveys.

Tuthill et al. (1996)

Winooski R.

Short reach, few overbank areas.

This work

Cazenovia Cr.

0.30.5

1972 ice jam.

0.30.5

1985 ice jam.

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