Thermobaric circulation induced by cabbeling in a deep freshwater lake: a conceptual 1D model

Abstract. Numerical lake models are a powerful tool to optimize water management and mitigate changes due to climate change. Hence, detailed implementation of lake specific processes is crucial to ensure optimal results. However, common numerical lake models have so far omitted the effect of thermobaricity despite its significant influence on deep water circulation in deep lakes. The thermobaric effect is based on the temperature dependence of the compressibility of water. As a consequence, deep water can be significantly colder than 4 °C and deep water renewal becomes complex. For a proper investigation, numerical models can be appropriate tools to display and understand such processes better. Inspired by Lake Shikotsu, which is an excellent example for the influence of thermobaricity, we developed a simplified 1D model for thermobaric effects. Here, we used in situ density to replace potential density for stability considerations such as the Brunt-Väisälä frequency. To prevent any competing influences and isolate thermobaric effects, we excluded any external forcing except for the surface temperature input. Accordingly, we excluded salinity, chose a cylindrical bathymetry without shallow areas, and omitted any inflows. Therefore, the model reproduced deep water circulation solely based on thermal forcing at the surface. We were able to identify key features of the deep water circulation: (1) cabbeling occurs at the intersection of the temperature profile with the Tmd (temperature of maximum density) line due to diffusion and induces thermobaricity driven deep water circulation, (2) this deep water circulation cell is detached from the surface, but can extend over hundreds of meters to the lake bed, (3) the deep water stays isothermal, (4) and after the winter stratification the temperature profile aligns with the Tmd line. Additionally, we investigated the influence of previous deep water renewal events and the current surface temperature on the deep water circulation. Our results emphasize the feasibility and necessity of the implementation of thermobaricity in numerical lake models by basing stability (Brunt-Väisälä frequency) on in situ density.