Institute of Oceanogphy Gdańsk University Jan Jędrasik The Hydrodynamic Model of the Southern Baltic Sea

The hydrodynamic model Based on Princeton Ocean Model (Blumberg and Mellor 1987)Based on Princeton Ocean Model (Blumberg and Mellor 1987) Vertical mixing processes are parameterized by the scheme of second order turbulence closure (Mellor and Yamada 1982)Vertical mixing processes are parameterized by the scheme of second order turbulence closure (Mellor and Yamada 1982) In order to apply the model for the Baltic Sea some modifications were done (Kowalewski 1997)In order to apply the model for the Baltic Sea some modifications were done (Kowalewski 1997)

Description of the hydrodynamic model M3D_UG Equations and boundary cionditions where: u, v, w, components of velocity prędkości; f, Coriolis parameter; ,  0, density of sea water in situ and reference density; g, gravity acceleration; p, pressure; K M, A M, vertical and horizontal viscosity coefficients where: p atm, atmospheric preassure; , sea level elevations where: T, temperature of water; S, salinity; K H, A H, vertical and horizontal diffusivity coefficients;  T, sources of heat where: A C,, empirical coefficient;  x,  y, spatial steps in x and y direction. where: q 2, turbulent kinetic energy, turbulent macroscale; K q, coefficient of vertical exchange of turbulent energy; , Karman‘s constant; H, sea depth; B 1, E 1, E 2, empirical constants.

At the sea surface Heat fluxes Energy fluxes Kinematic condition at the surface At the bottom z = H Parametrised as Fluxes of energy at the bottom Kinematic condition at the bottom where:  ox,  oy, wind surface stresses; H 0, heat fluxes from atmosphere;  bx,  by, bottom stresses; C D, drag coefficient (C D =0.0025); friction velocity; u, u b, v, v b, w, w b, components of velocity at the surface (no index) and at the bottom (with b index). At the lateral boundary (rivers) Initial conditions u(x,y,z) = 0,v(x,y,z) = 0,w(x,y,z) = 0 T = T(x,y,z), S = S(x,y,z).

Application of the model Rotational criterium where: , angular velocity of Earth; , geographical latitude Horizontal diffusivity criterium where: A H, horizontal diffusivity coefficient Courant-Fridrichs-Levy’s condition where: C velocity of fundamental mode, U max, maxime current velocity; or C t = 2C i + u max, C i, velocity of fundamental internal mode, u max, maxime advection velocity. Radiation condition Sigma coordinates (x *, y *, , t * ), x * = x, y * = y,, t * = t, where: D = H + , dla z =   = 0, for z = -H  = -1

The modelled areas The inflows from 85 riversThe inflows from 85 rivers The fields of wind speed over the sea surface were taken from 48-hours ICM forecast modelThe fields of wind speed over the sea surface were taken from 48-hours ICM forecast model

Numerical grids Horizontal grid Model allows to define subareas with different grid density Area I Area II Area III Vertical grid based on  -transformation defined as:

Temporal and spatial steps in the modelled areas