Estimation of the Thermally Reactive Layer in Lakes Based on Surface Water Temperature

How fast does lake surface water temperature (LSWT) react to climate warming or cooling? The thermal response of lakes varies with the season and, typically, day-to-day fluctuations are larger in summer. The reason is that lakes are stratified systems where the thermally reactive volume is smaller in summer and, hence, its heat capacity (thermal inertia) is reduced. We define the dimensionless parameter delta as the ratio between the surface volume reacting to the net heat flux through the air-water interface and the volume of the whole lake. By referring to a fully controlled case study obtained by means of a one-dimensional physically based model (Simstrat), we investigate the variability of delta throughout the year and its dependence on LSWT. Then, we compare the results with the parameterization adopted in the hybrid data-driven model air2water. Our analysis confirms that delta follows an exponential decay with increasing LSWT (i.e., a thinner surface layer in summer), and shows that this functional dependence varies between the warming and the cooling periods. These findings contribute to the understanding of the effect of a warming climate on water bodies and ecosystems by providing a simple tool to estimate the rate of change in lakes' water temperature.