95 IV-2. SELFE 3-D CIRCULATION MODEL The 3-D circulation hydrostatic model SELFE [IV-1, IV-2] solves Reynolds-stress averaged Navier–Stokes (RANS) equations using a finite element approach and unstructured grids. The governing equations are conservation of mass, momentum, salt and heat with hydrostatic and Boussinesq approximations: ? ? ??? + ?? ?? = 0 (IV-1) ?? ?? + ? ? ? ??? ????? = 0 (IV-2) ???? ?? = ????? × ??? + ???? ? ? ?? ??? ? ? ?? ? ?? ?? + ? ? (?????? ) ? ?? ? ??? + ? ?? (?? ???? ?? ) (IV-3) ?? ?? = ? ?? (??? ?? ?? ) + ?? (IV-4) ?? ?? = ? ?? (??? ?? ?? ) + ? ???? + ?? (IV-5) Here (x, y) are horizontal Cartesian coordinates, in [m]; z is the vertical coordinate, positive upwards, in [m]; t is time [s]; ? is the free-surface elevation, in [m]; h is bathymetric depth, in [m]; D = h + ? is the water column total depth [m]; ??? is the horizontal velocity, with Cartesian components (u, v), in [m/s]; w is the vertical velocity, in [m/s]; f is the Coriolis parameter, in [s?1]; g is acceleration of gravity, in [m/s2]; ? is the Earth tidal potential, in [m]; ? is the e?ective Earth elasticity factor; ? is water density; its reference value is ?o = 1025 kg/m3; pa is atmospheric; pressure at the free surface, in [Pa]; S, T are salinity and temperature of the water [practical salinity units (psu), °C]; ?t is vertical eddy viscosity, in [m2/s]; KM is horizontal eddy viscosity, in [m2/s]; ??? is vertical eddy di?usivity for salt and heat, in [m2/s]; Fs and Ft are horizontal di?usion operators for transport equations. SELFE uses the Generic Length Scale (GLS) turbulence closure [IV-3]. The following operators appear in the equations above: ? = ? ? ?? , ? ?? ? (IV-6) ? ?? = ? ?? + ??? ? + ? ? ?? (IV-7) In the horizontal direction SELFE uses unstructured triangular grids, while in the vertical direction the model uses hybrid coordinates, i.e. terrain following ?-coordinates and partly Z-coordinates. However, inside the numerical code all model equations are written in a Z-coordinate system. The valid representation of horizontal derivatives in ?-system is achieved by vertical interpolation of required variables. The calculation mesh for the Pacific Ocean simulations contains 49 700 nodes and 97 989 triangular elements and has resolution from approximately 500 m near the Fukushima Daiichi NPP to 10 km in the Northwest Pacific. The surface forcing is obtained from ERA-Interim reanalysis. The lateral boundary conditions for KIOST/IMMSP calculations were obtained from HYCOM nowcast/forecast system. The KIOST/IMMSP temperature was nudged towards the HYCOM fields. The tidal forcing is imposed at open boundaries using the NAO.99b tidal prediction system.