# An Equilibrium Model for the coupled ocean-atmosphere Boundary Layer in the tropics.

A coupled model is used to study the equilibrium state of the ocean-atmosphere boundary layer in the tropics. The atmospheric model is a one-dimensional thermodynamic model for a partially mixed, partly cloudy convective boundary layer (CBL), including the effects of cloud-top subsidence, surface momentum and heat (latent and sensible) fluxes, and realistic radiative transfer for both shortwave and longwave (Betts and Ridgway, 1988; 1989). The oceanic model is a thermodynamic model for a well-mixed layer, with a closure constraint based on a one-dimensional turbulent kinetic energy (TKE) equation following Kraus and Turner (1967). Results of several sets of experiments are reported in this paper. In the first two sets of experiments, with sea surface temperature (SST) specified, we solve the equilibrium state of the coupled system as a function of SST for a given surface wind (case 1) and as a function of surface wind for a given SST (case 2). In both cases the depth of the CBL and the ocean mixed layer (OML) increases and the upwelling below the OML decreases, corresponding to either increasing SST or increasing surface wind. The deepening of the equilibrium CBL is primarily linked to the increase of CBL moisture with increasing SST and surface wind.

The increase of OML depth and decrease of upwelling are due to a decrease of net downward heat flux with increasing SST and the generation of TKE by increasing wind. In another two sets of experiments, we solve for the coupled ocean-atmosphere model iteratively as a function of surface wind for a fixed upwelling (case 3) and a fixed OML depth (case 4). SST falls with increasing wind in both cases, but the fall is steeper in case 4, because the OML depth is fixed, whereas in case 3 the depth is allowed to deepen and the cooling is spread over a larger mass of water. The decrease of evaporation with increasing wind in case 4 leads to a very dry and shallow CBL. Results of further experiments with surface wind and SST (upwelling) prescribed as a function of longitude similar to the observed values across the Pacific show that the model gives realistic gradients of mixed-layer depth and upwelling (SST). This work suggests that the equilibrium state of the coupled system is very sensitive to the coupling of the boundary layers. Special efforts are needed to incorporate physical processes in the CBL and OML in coupled models.

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## Full Citation

**Sui, C-H., K-M. Lau and A. K. Betts, 1991**: An Equilibrium Model for the coupled ocean-atmosphere Boundary Layer in the tropics. J. Geophys. Res., 96, 3151-3163.