Vertical Diffusivities

Turbulent diffusivities and surface exchange coefficients for one dimensional lacustrine transport are not only a function of the site but also whether the governing equation is areally averaged or not. Given the same initial conditions, nonaveraged equations require much higher values than areally averaged versions in order to predict the same temperatures or concentrations. To account for the effects of area averaging research was performed to determine a quantitative relationship between the diffusivities and surface exchange coefficients in the two systems. It was found that ratio of these values between the two systmes is approximately equal to the ratio of average area of the heated surface water to the surface area. An exact solution for clinolimnion diffusivities also indicates the area independence. This empirical analysis was verified by comparing 1968 Cayuga Lake temperature predictions from the two different governing forms.