the ice-affected water levels with the input configuration of the cover and also

determines if the cover is stable according to the stability parameter proposed by

Pariset et al. To generate an equilibrium thickness profile, many iterations are nec-

essary with modifications made to the ice thickness and roughness values.

DWOPER, an unsteady flow forecasting model developed by the U.S. National

Weather Service, was also adapted to investigate the effects of ice covers on water

levels. Daly and Ashton (1983) modified the St. Venant equations describing the

unsteady water flow to include the frictional resistance of the ice to the water flow.

They concentrated on running steady water discharges with a stationary ice cover

and then instantaneously removing the cover, simulating a complete cover failure

and passage downstream. The ensuing transients increased with increasing bed

slopes as would be expected. Their work did not include nonuniform covers or

jams and they pointed out the necessity of including ice motion in developing a

truly unsteady ice jam model.

Flato and Gerard (1986) and Flato (1987) applied their model, ICEJAM, to pro-

duce ice jam profiles for a range of steady-flow discharges. As it uses a form of the

differential equation describing the balance of forces on the ice cover, similar to

that of eq 19, it can be used to describe the complete thickness profile even if there

is not an equilibrium section. The input data necessary to run ICEJAM include

water discharge, ice jam characteristics (bulk specific gravity, angle of internal

resistance, and porosity), channel data, roughness of the bed and ice, and initial

estimates of water depth and jam thickness. The model first calculates the normal

depth (under ice) profile based on the initial estimates of ice thickness. It then solves

the ice force balance equation in a forward-difference mode, stepping downstream

from the upstream end of the jam. The hydraulic conditions are then modified for

these new ice thicknesses by means of the standard step-backwater calculation tech-

nique moving in an upstream direction. Iterations of the ice and water calculations

continue until an acceptable tolerance is met. Adjustments are made in the ice thick-

ness at the toe of the jam in relation to a prescribed ice erosion velocity. The model

produced reasonable and stable results when a damping factor of 1/3 was applied

to the calculated corrections for ice thickness.

RIVJAM is a model developed by Beltaos (1993). It is based on a similar model

proposed by Beltaos and Wong (1986). Both models use a steady water discharge

and include the seepage flow through the jam in an attempt to better define ice

thickness near the toe of the jam, which may be grounded. RIVJAM solves first-

order differential equations for the water depth beneath the cover and the ice thick-

ness. It does so by means of a predictorcorrector scheme, and the solution proce-

dure may progress in an upstream or downstream direction. Beltaos (1993) showed

that RIVJAM was able to reproduce ice thickness profiles for a variety of

nonequilibrium and potentially grounded jams quite well, with appropriate choices

of several model parameters. The most tenuous of these appears to be the seepage

coefficient, which is similar in concept to hydraulic conductivity (with units of

length/time) for high Reynold's number flows. The model, however, does not

include the unsteady movement of the ice cover and thus cannot include the effects

of ice momentum, which would be important in cases of grounded jams.

A utility program was developed by Wuebben et al. (1995) for use with HEC-2 to

simplify calculation of ice-affected water levels. The program, dubbed ICETHK,

uses standard output variables from a HEC-2 simulation and calculates ice thick-

ness based on an equation similar to eq 25. There are several calculation options,

such as width smoothing, ice thickness smoothing, and overbank ice and rough-

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