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<br />MODELING DYNAMIC ICE FORMATION IN THE GREEN RIVER ' <br /> <br />The formation and trans ort of river ice and the formation of stationary river ice covers can be <br />P <br />simulated through the use of numerical models (see for example Lal and Shen, 1993; Shen et. al., <br />1991; Beltaos, 1995). Such a numerical ice model (Daly, in prep.) was applied to the study reach <br />' <br />of the Green River. This model is composed of aone-dimensional unsteady flow sub-model, a <br />transport sub-model, and an ice cover progression sub-model. <br />The one-dimensional unsteady flow sub-model is the UNET model described above. The <br />UNET model simulates unsteady flow in a river channel by solving the complete one- <br />dimensional continuity and momentum equations. The equations are solved using the four-point, <br />implicit, finite difference scheme and the model used the actual surveyed and estimated river <br />cross sections, as described above, to represent the river channel. In this case, the UNET model <br />has been modified to incorporate the dynamic formation of river ice covers as determined by the <br />ice cover progression sub-model. The ice cover progression sub-model calculates the sections of <br />the channel in which a stationary floating ice cover will form. The presence of a stationary ice <br />cover in a reach changes the hydraulic properties of the reach. These changes include reducing <br />the cross-sectional area of the channel available for flow, reducing the hydraulic radius of the <br />channel cross section, and modifying the effective channel roughness. These changes in the ' <br />hydraulic properties in turn influence the discharge and stage calculated by the unsteady flow <br />model. <br /> <br />The transport sub-model calculates the advection of water temperature, surface ice, and <br />suspended frazil ice. Frazil ice production is assumed to begin through the introduction of seed <br />crystals at the water surface. The concentration of the frazil ice is calculated by balancing the <br />heat loss from the water surface and latent heat released from the growing frazil. The frazil ice is <br />assumed to rise to the water surface with a known velocity. At the water surface, the frazil ice <br />forms into floes which are advected by the flaw velocity. The heat loss from the water surface is <br />, <br />calculated as a linear function of the difference between the water temperature and the air <br />temperature. The transport sub-model uses the Preissman-Holly advection scheme (Gunge, <br />Holly, and Verwey 1980). This scheme has been shown to minimize numerical diffusion. <br />The ice cover progression sub-model determines the rate at which stationary ice covers <br />form. A stationary ice cover is assumed to initially form at apre-selected bridging location when <br />the concentration of surface ice has reached apre-selected value. The ice cover then progresses <br />upstream at a rate determined by the rate of arrival of the surface ice and the thickness of the ice <br />cover. The ice cover can thicken through heat transfer to the atmosphere from the ice surface and <br />through the deposition of frazil ice underneath the ice cover. The ice cover can melt out through <br />heat transfer from the water flowing beneath it. When the ice cover has lost a certain percentage <br />of its thickness, it is assumed to collapse and be transported in the downstream direction. <br />The ice model was applied to the Green River study reach for the winter of 1989-90 <br />through the winter of 1995-96. These are the winters for which water temperature and discharge <br />data were available at the Jensen Gage. The daily average discharge, air temperature, and water <br />temperature were used as inputs to the model. The river cross sections and channel roughnesses ' <br />18 <br />