Ricrit is the critical Richrdson number (= 0.25), m0 = 1.5, γ = 0.42 is the fraction of the insolation that is not immediately absorbed at the surface but penetrates into the ocean, hB = 20m, is the e-folding length scale for the absorption of solar radiation, u* is the friction velocity, σθ is the potential density, Qs is the heart flux due to solar insolation, α and β are the analytically determined expansion coefficients. The minimum mixed layer depth is 5 m. As was suggested by Oberhuber [1990], the turbulent kinetic energy (TKE) dissipation is assumed to be dependent on the Ekman layer length scale, i.e.,
to keep mid-latitude mixed-layers from becoming too deep (in consequence of the geophysically fixed mixed-layer parameters), with κ = 0.4 and μ = 2 being determined by optimization experiments. The TKE input is taken from ECMWF observations prepared by Oberhuner of the mean wind and its standard deviation. Since monthly mean u* will be severely underestimated from monthly mean winds, the effective monthly mean u* is approximated by
The coupling of the mixed layer to the interior conserves momentum, mass, heat, and salt.
2.3. Atmospheric Forcing
The monthly surface fluxes used to force the ocean model are the fluxes of momentum, heat, fresh water, turbulent kinetic, energy, and buoyancy. Required datasets are surface air temperature, sea surface tempertaure, relative humidity, cloudiness, the time averaged absolute wind speed, and its standard deviation, wind stress vector, rainfall, and surface salinity. Except for anual-mean surface salinity, the data are monthly mean climatological values.
The surface heat flux, Q1, consists of short-wave, long wave, sensible heat, and latent heat fluxes. The sensible heat and latent heat fluxes are computed according to the bulk formulae,
