252++ln1+1−16ς0.52−2arctan(1−16ς0.25)+π4, equation(5o) ψh=2ln1+1−16ς0.52. The conservation equation for heat reads: equation(6) ∂ρcpT∂t+W∂ρcpT∂z=∂∂zμeffρσeffT∂ρcpT∂z+Γsum+Γh, where T and cp are the temperature of sea water and the heat capacity (4200 J Kg− 1 K− 1), respectively, σeffT the turbulent Prandtl number www.selleckchem.com/products/PLX-4720.html (set equal to one in the present version of the model), and Γsum and Γh the respective source terms associated with solar radiation in- and outflows. The source terms Γsum and Γh are given by equation(7a) Γsum=Fsw1−η1e−βD−z, equation(7b) Γh=ρcpQinTinΔVin−QoutToutΔVout, where Fws is the short-wave radiation through

the water surface, η1(= 0.4) the infrared fraction of short-wave radiation trapped in the surface

layer, β the bulk absorption coefficient of the water (0.3 m− 1), D the total depth, Tin and Tout the respective temperatures of the in- and outflowing water, and ΔVin and ΔVout the respective volumes of the grid cells at the in- and outflow levels. The selleck inhibitor boundary condition at the surface for heat reads: equation(8a) Fnet=μeffρσeffT∂ρCpT∂z, equation(8b) Fnet=Fh+Fe+Fl+δFsw, where Fh is the sensible heat flux, Fe the latent heat flux, Fl the net longwave radiation and δFWs the short-wave radiation part absorbed in the surface layer. The conservation equation for salinity reads: equation(9a) ∂S∂t+W∂S∂z=∂∂zμeffρσeffS∂S∂z+ΓS, equation(9b) ΓS=QinSinΔVin−QoutSoutΔVout−QfSsurΔVsur, where ΓS is the source term associated with in- and outflows, σeffS the turbulent Schmidt number (equal to one), Qf the river discharge to the basin, Sin and Sout the salinity of the in- and outflowing water respectively, Ssur f the sea surface salinity, and ΔVsur the volume of the upper surface grid

cell. The boundary conditions at the surface for salinity (S) read: equation(10a) μeffρσeffS∂S∂z=Fsalt, equation(10 b) Fsalt=Ss(P−E),Fsalt=SsP−E, next where Fsalt is the salt flux associated with net precipitation, Ss the surface salinity and P the precipitation rate (calculated from given values). Evaporation (E) is calculated by the model as equation(10c) E=FeLeρo, where Fe is the latent heat flux, Le the latent heat of evaporation, and ρo the reference density of sea water (i.e. 103 kg m− 3). It should be noted that equation (10a) connects the water and heat balances. The vertical turbulent transports in the surface boundary layer are calculated using the well-known k-ε model (e.g. Burchard & Petersen 1999), a two-equation model of turbulence in which transport equations for the turbulent kinetic energy k and its dissipation rate ε are calculated. The transport equations for k and ε read: equation(11) ∂k∂t+W∂k∂z=∂∂zμeffρσk∂k∂z+Ps+Pb−ε, equation(12) ∂ε∂t+W∂ε∂z=∂∂zμeffρσε∂ε∂z+εkcε1Ps+cε3Pb−cε2ε, where Ps and Pb are the production/destruction due to shear and stratification respectively, σk (= 1) the Schmidt number for k, and σε (= 1.11) the Schmidt number for ε.