Linear‐Circular Statistical Modeling of Lake Ice‐Out Dates

Abstract

AbstractOver the past few decades, lake ice phenology in northern temperate lakes has exhibited increased interannual variability. The resulting increase in the incidence of unusually early spring lake ice‐out dates has the potential to affect stability, health, and function of the lake ecosystems. Characterizing the dependency of spring lake ice‐out date to winter and/or spring climate variables offers foreknowledge on the annual lake ice cover season, as the spring ice‐out date is an integrated response to prevailing weather/climate conditions during winter and spring. Here a circular regression framework is presented where ice‐out date regression models, conditioned on a suite of predictor winter and/or spring climate variables (i.e., degree days and snowfall), are developed for 12 Maine lakes to determine the relative import of winter and spring meteorological conditions on year‐to‐year variability of ice‐out dates in Maine lakes. In the circular regression models, ice‐out dates are expressed as points on a unit circle instead of real line, as it preserves the periodicity and order of time‐of‐day variables independent of the choice of reference point. Results show that (a) the magnitude and variance of seasonal spring temperatures explain more than half of the total variability in spring ice‐out date for Maine lakes, (b) the modulating efficacy of spring snowfall on the timing of spring ice‐out dates is the strongest in northern interior Maine lakes, (c) the role of winter degree days in determining the ice‐out dates in Maine lakes is significant across all climate regions, and (d) the effect of winter snowfall on ice‐out dates is significant in coastal Maine lakes. Diagnostics suggest that there are other climatic and nonclimatic variables that produce shifts in the lake ice‐out dates.