Variational Computation of Sensible and Latent Heat Flux over Lake Superior

Sensible and latent heat fluxes over Lake Superior are computed using a variational approach with a Bowen ratio constraint and inputs of 7 years of half-hourly temporal resolution observations of hydrometeorological variables over the lake. In an advancement from previous work focusing on the sensible heat flux, in this work computations of the latent heat flux are required so that a new physical constraint of the Bowen ratio is introduced. Verifications are made possible for fluxes predicted by a Canadian operational coupled atmosphere-ocean model due to recent availabilities of observed and model-predicted fluxes over Lake Superior. The observed flux data with longer time periods and higher temporal resolution than those used in previous studies allows for the examination of detailed performances in computing these fluxes. Evaluations utilizing eddy-covariance measurements over Lake Superior show that the variational method yields higher correlations between computed and measured sensible and latent heat fluxes than a flux-gradient method. The variational method is more accurate than the flux-gradient method in computing these fluxes at annual, monthly, daily, and hourly time scales. Under both unstable and stable conditions, the variational method considerably reduces mean absolute errors produced by the flux-gradient approach in computing the fluxes. It is demonstrated with 2 months of data that the variational method obtains higher correlation coefficients between the observed and the computed sensible and latent heat fluxes than the coupled model predicted, and yields lower mean absolute errors than the coupled model. Furthermore, comparisons are made between the coupled-model-predicted fluxes and the fluxes computed based on three buoy observations over Lake Superior.