SUPPLEMENTARY MATERIAL

Lake ice model description The lake model used is MyLake (Multi-year simulation model for Lake thermo- and phytoplankton dynamics) which is a one dimensional process-based model. It simulates at a daily time step the vertical distribution of lake-water temperature, evolution of seasonal lake-ice and snow cover thickness and phosphorus-phytoplankton dynamics (Saloranta and Andersen, 2007; Saloranta et al., 2009). The most important physical, chemical, and biological processes are included in a relatively simple and transparent model structure which is coded in Matlab. MyLake was designed to be an investigative tool with a short runtime, allowing the simulation of a large number of lakes and over long periods. The model includes computational methods for simulating heat transfer at the air-water interface, advective heat transfer of inflow and outflow, and the internal vertical diffusion of thermal energy. The vertical profile of the lake is conceptualized as horizontal layers of equal height (ΔZ), each of them having a defined area and hence volume. The one-dimensional heat conservation equation for the temperature distribution in a horizontally homogeneous, vertically stratified lake is solved in each layer. The equation can be written as (Saloranta and Andersen, 2007)