Vertical diffusion in small stratified lake: Data and error analysis

Water temperature profiles were measured at 2-min intervals in a stratified temperate lake with a surface area of 0.06 Km² and a maximum depth of 10 m from May 7 to August 9, 1989. The data were used to calculate the vertical eddy diffusion coefficient K_z in the hypolimnion. The depth is representative of a large number of lakes in the north central United States. K_z was calculated over time intervals of 1 to 15 days and varied from 10⁻³  to 10⁻¹ cm²s⁻¹. A  numerical model was developed for heat conduction in the sediments, and heat flux between water and sediments was incorporated into the relationship from which eddy diffusivity was estimated. Heat flux between water and lake sediments, a term commonly neglected, was found to be important in the K_z values were related to stratification stability as measured by the Brunt-Vaisala frequency N using Welander's expression of the form K_z  = α(N²)^b.Values of a were on the order of 10⁻⁴ and b varied from −0.36 to −0.45 when K_z was given in cm²s⁻¹ and N is in s⁻¹. An error analysis was conducted and the effects of different choices of sampling intervals in time and depth on the eddy diffusivity estimates were evaluated. The longest time interval (15 days) and the smallest depth increment (1 m) used in this study were found to give the best K_z  estimation.