Dimensionless numbers for classifying the thermodynamics regimes that determine water temperature in shallow lakes and wetlands

Abstract

The influence of sediments in the heat budget of water bodies has been reported to be determinant in shallow lakes and wetlands, whereas it is usually neglected in larger water bodies. In this article, we address the question of whether or not sediments should be considered in the computation of water temperature, by defining two dimensionless numbers that describe the thermodynamics regimes of shallow lakes and wetlands. These dimensionless numbers rise from the analysis of the role of periodic heat exchanges at the sediment–water interface (SWI) on the water temperature of shallow lakes and wetlands. The analysis was based on the derivation of an analytic solution that adopts the solution for the second Stokes problem for computing the sediment temperature, when the system is forced by periodic (diurnal, seasonal, decadal) heat exchanges with the atmosphere. The first dimensionless number is the ratio between the thermal inertia of the active sediments and the thermal inertia of the water column, and quantifies the role of sediments on the heat budget. The second dimensionless number, on the other hand, is defined as the ratio between the timescale of changes in the external forcing and the timescale required to reach the heat equilibrium at the SWI, and characterizes the influence of turbulence on the water column on heat exchanges across the SWI. We complemented the analysis with field observations conducted in shallow lakes of 5–15 cm depth, whose thermodynamics is controlled by heat exchanges between the water column and the sediments. As the dimensionless numbers defined here are frequency dependent, we show that one particular process can be neglected for one specific frequency, while it cannot be neglected for other frequencies. In the case of lakes and deep wetlands, sediments could be neglected in a diurnal time-scale, while they should be included for seasonal or decadal time-scales. The relevance of this frequency-dependence is that it suggests that sediments should always be considered in long-term climatic simulations.