Estimation of the eddy diffusivity coefficient in a warm monomictic tropical Lake

We used a two-year dataset (1998-1999) of monthly temperature profiles from Lake Alchichica, Mexico to estimate values of the vertical coefficient of eddy diffusivity. This lake is located in a tropical region at high altitude and shows considerable seasonal variations (i.e., rainy and dry seasons). It has an area of 2.3 km² and a mean depth of 40.9 m. Alchichica is a warm monomictic lake, which annually becomes isothermal near the end of December or early January at the onset of the dry season and remains stratified for the rest of the year (from late March or early April to early December) during the warm-rainy season. Mathematical models of the spatial and temporal variation of passive substances in lakes and oceans require a quantitative formulation of the vertical transport. Vertical mixing is generally a function of the density profile, which, in lakes, can be directly related to the temperature profile. A widely used method to estimate the vertical diffusion coefficients in lakes from temperature data is the flux-gradient method. In the present study, we applied a simple approach to calculate the eddy diffusivity coefficient (K_z) based on the solution of the vertical component of the modeled temperature equation. We characterized the eddy diffusivity coefficient (K_z) in Lake Alchichica as a dynamic coefficient that changes during the year, between years, and with depth, ranging from 10^-10 to 10^-6 m² s^-1, whereas typical values of K_z in thermally stratified lakes range from 10^-9 to 10^-2 m² s^-1. As expected, we found the lowest values in the deeper regions of the lake, and that the temporal variation of temperature with depth showed a quasi-bimodal shape from one year to the next. We also found a structure of alternating peaks and troughs in the vertical K_z, which indicates a response to oscillating vertical mixing. We concluded that the solution of the vertical component of the temperature equation could be a useful tool to estimate the eddy diffusivity in lakes. The major advantage of this method is its simplicity. We also conclude that the differences observed in the estimations of eddy diffusivity coefficients in other lakes are attributable to the differences in local characteristics of the thermal conditions in each lake.