An analytical model for remote sensing determination of the mixed layer depth

Abstract

An analytical mixed layer thermal inertia model based on remote sensing data is presented to estimate the diurnal mixed layer thickness and the thermal inertia of the mixed layer. The model depends on the concept that the diurnal sea surface temperature range (δSST) is primarily a function of the thermal inertia of the mixed layer, of local meteorological conditions, and physical characteristics of the sea surface. The value of δSST can be determined from satellite thermal infra-red imagery, albedo can be calculated from satellite broad-band visible and near infra-red imagery, wind speed can be estimated from satellite microwave radiometer imagery, and heat flux can be estimated using a standard method. Given these characteristics, the thermal inertia and diurnal mixed layer depth images are generated. The diurnal mixed layer depths predicted by the analytical remote sensing model agree well with observed data. Although it is limited by linearization of the upper boundary conditions and by some simplifying assumptions, the analytical method in the mixed layer thermal inertia model has a major advantage in its apparent simplicity in calculation. Special solutions are obtained in a closed analytical form, and the computation based on these solutions is made rapidly compared with the turbulence closure models. This advantage is most desirable for a remote sensing system, since the data base for image processing is orders of magnitude larger than the data base for any conventional observation. For further application of the model, the term scaled thermal inertia is defined and calibrated to generate surface wind images. We compare such images with microwave radiometer imagery and also discuss the limitations of the model.