Multiple Linear Regression for Lake Ice and Lake Temperature Characteristics

Abstract

Lake ice and lake temperatures depend on climate and lake morphometry. Simulated lake ice and lake temperature characteristics of 10 large lakes in Minnesota were therefore related to climate parameters, geographic location, lake surface area, and depth by multiple linear regressions. The regression equations were developed because they are much easier to use than a deterministic, unsteady simulation model that requires time series of weather data as input and produces very detailed information as output. Some of the regression equations were then employed to hindcast the ice-in dates, ice-out dates, ice cover duration, and maximum ice thicknesses for several freshwater lakes in the United States and one in Canada. The hindcast results were compared with field data from the same lakes. The standard errors between observed and predicted ice-in dates, ice-out dates, ice cover duration, and maximum ice thicknesses for the lakes tested are 4 days, 6–7 days, 4–7 days, and 0.05–0.06 m, respectively, depending on the equations used. Ice-in date is slightly better predicted than ice-out date and ice cover duration. Because the 10 lakes used to develop the multiple linear regressions are all in Minnesota, and the lakes used to verify the regression equations are in Wisconsin, Maine, and Ontario, the regression equations are considered validated and applicable at least to lakes in the north-central United States and in southern Ontario.