Three‐dimensional analytical model for the mixed layer depth

Abstract

We have recently developed a three‐dimensional semi‐analytical mixed layer remote sensing model which includes the horizontal advection and diffusion processes in our previous one dimensional model (Yan et al., 1991a). The three‐dimensional (3‐D) model can be used as a supplement to the one‐dimensional (1‐D) model in the area where advection is important and for a finer resolution grid prediction. The 3‐D thermal inertia model is based on the 3‐D thermal energy conservation equation. Using sine transformation and inverse sine transformation methods, we obtained the solution for mixed layer thermal inertia which, in turn, can be used to calculate mixed layer depth using a similar method to that of Yan et al. (1991a). In the solution, the thermal inertia (which is proportional to the mixed layer depth) is expressed as functions of sea surface temperature changes (δSST), heat flux (Q) and surface layer velocity (u, v, and w). The vertical entrainment and wind effects are accounted for in the model by eddy diffusivity while changes of δSST result from entrainment, e.g., if vertical entrainment is larger, δSST will be smaller and vice versa. The advantages of this model are that it can be easily forced by remotely sensed data and that it is much simpler to compute than numerical 3‐D mixed layer turbulence closure models. The model was tested using the data from the advanced very high resolution radiometer/multichannel sea surface temperature data set and the Cooperative Ocean Atmosphere Data Set for the North Pacific Ocean. The model‐predicted mixed layer depths compared favorably with the mixed layer depths calculated from 14 years of Volunteer Observing Ship/expendable bathythermograph observation data. The model/data comparison also exhibited a number of mesoscale features of seasonal changes and anomalies of the mixed layer depth.