Definition of OAB and its controlling processes
As winter and early spring mixing typically replenish nutrients in the photic zone of most European lakes, the onset of the algal bloom (OAB) is primarily determined by light availability in the water column (Sommer et al. 2012; Peeters et al. 2013). We define the timing of the OAB as the first day of the year when the intensity of the average photosynthetically active radiation in the mixed surface layer,Imix , exceeds a critical light intensity,Icrit , above which net phytoplankton growth is positive. We used the empirically determined value (Siegel et al. 2002; Sommer & Lengfellner 2008; Mignot et al. 2014)Icrit = 1.3 mol photons⋅m‑2⋅d-1.Imix was calculated as
\(I_{\text{mix}}=I_{\text{ws}}\cdot\frac{(1-e^{-K_{d}\cdot z_{\text{mix}}})}{(K_{d}\cdot z_{\text{mix}})}\)(eq. 1)
where Iws [mol photons⋅m-2⋅d-1] is the incident radiation penetrating the water surface, Kd[m-1] the light attenuation coefficient, andzmix [m] the depth of the mixed surface layer. zmix was defined as the shallowest depth at which the water density exceeds the surface water density by 0.04 kg⋅m-3. This threshold is in the range of values used in numerous studies on stratified water bodies (de Boyer Montégut et al. 2004; Read et al. 2011; Giling et al. 2017). Iwswas calculated from incident solar radiation, taking into account reflection from the lake surface as in (Peeters et al. 2007). We furthermore assumed that Imix <Icrit whenever a lake is ice-covered. While phytoplankton can develop under clear ice conditions (Kalinowska & Grabowska 2016; Hampton et al. 2017), clear ice is uncommon at the end of the ice season when snow cover and/or low ice transparency often cause light limitation of phytoplankton growth (Weyhenmeyer et al. 1999; Adrian et al. 2006).
Underwater light levels required for the calculation of the OAB timing were derived from numerical simulations (see below). We distinguished three processes controlling this timing. For each of the 1.9 million simulated lake years, the simulated OAB (OABs) was compared with a hypothetical timing (OAB), which was determined analogous to OABs but assuming fully mixed conditions and no ice cover. OABh, therefore, provides a phenological ‘null model’ where the seasonal change in incident radiation is the sole factor controlling OAB. The process controlling OAB was then identified as: (I) the timing of ice-off if OABs occurs after OABh, i.e. if OABs > OABh + 2 days, (II) the onset of thermal stratification if OABs occurs before OABh, i.e. if OABs < OABh + 2 days, and (III) the seasonal increase in incident radiation if OABs occurs within two days of OABh, i.e. if |OABs–OABh| ≤ 2 days. The ±2-day time window made the categorization robust against minor inaccuracies in the meteorological data. Similar results were obtained with different time windows between ±1 and ±5 days. In years whenImix exceeded Icritalready on the first day of the year (suggesting that light was not limiting) the OAB was set to day 1. Lakes where this occurred in ≥16 of the simulated 31 years were categorized as not light-limited and were excluded from further statistical analyses.