The effects of thermal pollution on river ice conditions

An attempt is made to calculate the length of the ice‐free reach that develops during the winter below a thermal pollution site on a river. A differential equation for the steady‐state heat balance of a volume element of a river is developed, which leads to the expression x=Cx∫TwoTwxdTw/Q* where x is distance downstream from the pollution site to the cross section where the water temperature equals Twx, Two is water temperature at x equals zero, Q* is rate of heat loss from the water surface, and Cx is a constant that includes flow velocity and depth. The value of x at Twx equals 0°C is taken as the length of the ice‐free reach. Q* is the sum of heat losses due to evaporation, convection, long‐ and short‐wave radiation, and other processes, each of which is evaluated by an empirical or theoretical expression. The two principal limitations in accurately calculating downstream temperature changes are related to difficulties in evaluating the degree of lateral mixing in natural rivers and the convective and evaporative heat losses under unstable atmospheric conditions. Observations of lengths of ice‐free reaches on the Mississippi River are in good agreement with the calculated values. Significant portions of the St, Lawrence Seaway can be kept ice‐free by the installation of nuclear reactors at appropriate locations.