Model description, lake types, and climate scenarios
The quantification of OAB and TDM requires knowledge of the timing of ice off, the seasonal development of the underwater light climate in the mixed surface layer, and the temperature in the top 5 m of the water column. We derived this information from numerical simulations of the seasonal development of ice cover and underwater light and temperature profiles with the model LAKEoneD. This model combines a one-dimensional hydrodynamic model with an ice model (Jöhnk & Umlauf 2001; Hutter & Jöhnk 2004; Yao et al. 2014; Gronchi et al. 2021) (Supplement S2 Hydrodynamic model) and requires meteorological data, lake depth and water clarity as input variables.
In the reference scenario, LAKEoneD was driven with meteorological data from the global atmospheric reanalysis dataset ERA-Interim (Dee et al. 2011) produced by the European Centre of Medium-Range Weather Forecasts (ECMWF). We extracted from this dataset 3-hourly data on wind speed, air temperature, incident solar radiation, relative cloud cover, and relative humidity for a total of 1907 terrestrial locations covering Europe from 35° to 70° North and ‑10° to 20° East at a 0.5° resolution. All meteorological variables covered the period from 1979-2009 and were linearly interpolated to hourly values.
In addition to the reference scenario, we explored a warming scenario that used the same 31 years of meteorological data as the reference scenario except for assuming an increase in air temperature by +4°C at all locations and times. Similar simplified warming scenarios have been employed in earlier lake studies (Peeters et al. 2007; Trolle et al. 2011; Kupisch et al. 2012; Wahl & Peeters 2014; Straile et al. 2015), and warming by 4°C is within the range of pessimistic projections (Rajendra K. 2014).
At each location, we considered 16 different lake types defined by the factorial combination of four maximum lake depths (zmax = 5, 10, 30, and 100 m) with four light attenuation coefficients (Kd = 0.3, 0.6, 1.2, and 2.4 m-1). These values of zmaxand Kd cover the ranges encountered in a majority of lakes >1 ha (Pérez-Fuentetaja et al. 1999; Cael et al. 2017; Seekell et al. 2018). For certain statistical analyses (see below), we characterized the underwater light climate in each of the 16 lake types by its optical depth (OD) defined as
\(OD=K_d\cdot z_{\max}\) (4)
For each lake type and at each geographic location, we simulated 31 years of vertical temperature profiles for both climate scenarios, yielding a total of 1,891,744 simulated lake years. All simulations were performed by first simulating a spin-up period of 5 years using meteorology from 1979 to 1984. Vertical temperature profiles from the final day of the pre-run period were used as initial conditions for the main simulations, which were restarted on the 1st of January 1979 and run through 2009. In the warming scenario, the +4°C temperature increase was applied to both the pre-run and the main simulation periods. Based on these simulations and local incident radiation from the meteorological data, we generated for each lake type, geographic location, and climate scenario a 31-year time series of OAB, TDM, and PLD, respectively. We expressed the impact of climate warming on the individual phenologies by their respective time differences (warming minus reference scenario) OABdiff, TDMdiff, and PLDdiff.