Formulating Lake Models which Preserve Spectral Statistics

The ability of numerical lake models to predict verifiable results is very poor. Difficulties with the popular point by point verification method are intractable when confronted with these turbulent flows which have only reproduceable statistics. A lake transport model is formulated which permits the calculation of not only mean field quantities but the known spectral details of turbulent flow. Higher order spatial averaging of the nonlinear terms by a low pass filter results in a sequence of third order differential terms. Additionally, the correlated terms resulting from the filtration are closed with the Smagorinsky subgrid scale viscosity representation. Finite difference representations were used with second order accurate schemes on the third order corrective differential terms and fourth order on all others. Mean flow field computations were verified by intercomparison with existing rigid lid circulation models. Differences between computations were negligible with only small increases in time and storage.