Understanding Water Temperature Regulating of Lakes Through the Energy Balance Approach: Direct Observations (Agamon Hula, Israel) and Analytical Solutions

Air-water interactions regulate lake-water temperature by balancing the rate of change of water temperature (stored heat) with the incoming and outgoing heat fluxes, which are functions of water temperature and external forcing. Yet, there is a large knowledge gap in quantifying the thermoregulation of a lake, and especially managed lakes, which is hypothesized to be related to both external environmental forcing and management decisions on the lake depth and water discharge. Here we explore the thermoregulation of a restored and managed Mediterranean lake (Agamon Hula, Israel), by direct measurements of all major heat fluxes and interpret the results with a rigorous analysis of the energy balance equation. We provide general solutions of (i) the steady-state water temperature under given constant external conditions and show that it is unrelated to water depth, (ii) the time response of the lake’s temperature to reach a steady-state following an abrupt change in various environmental conditions and show its relation to water depth and thermal properties of water, and (iii) the response of the lake’s temperature to a pre-defined oscillations of the environmental forcing (diurnal, seasonal or other cycles). The amplitude of water temperature fluctuations, and the time delay from steady-state are functions of the environmental conditions oscillations and the ratio of the forcing’s time period over the thermal response time of the lake. The summertime measured CO₂ fluxes of Agamon Hula revealed the lake acts as a CO₂ source to the atmosphere, overpassing similar water bodies from different climates.