91 ?? ???? ?? = 0 (III-24) ??????????? + ?? ???? ???? ? ?? = ???????? ? ???? ???? (III-25) The numerical algorithm was implemented in a horizontal curvilinear orthogonal coordinate system. Fitting of the coordinate system to the bottom topography by means of mixed z?coordinate transformation allows the accurate description of shallow water ?ow and steep slopes [III-2]. The governing equations, together with the boundary conditions, are solved by finite di?erence techniques. The model equations are solved on an Arakawa C grid with all scalars located at the cell centroid, while velocity components are defined at the center of the faces of cells. Temporal di?erencing is second order leap-frog scheme with the Asselin filter. The vertically integrated equations of continuity and momentum (external mode) are separated from the equations for the vertical structure of ?ow (internal mode). Splitting on the external and internal modes was applied [III-18]. The equations for the external mode were solved explicitly using a short time step to satisfy the Courant-Friedrichs-Lewy condition for fast barotropic long waves. The 3-D velocity and scalar fields (temperature, salinity, turbulent quantities) were computed semi-implicitly with a larger time step. An implicit treatment of the vertical viscosity and di?usion terms is used, whereas advective terms, horizontal viscosity and di?usion are computed on the previous time step. The advection of scalars is approximated by the high order Total Variation Diminishing scheme [III-19]. III-5. APPLICATION TO THE BALTIC SEA The THREETOX model was customized for the Baltic Sea. The bathymetry was obtained from the GEODAS database [III-20] with 2 minute resolution, both in longitude and latitude. The bathymetry was extended to describe Kattegat and the transport of 137Cs was modelled using spherical horizontal coordinates with a horizontal resolution of 1/15° along the parallels and 1/30° along the meridians, and by using 20 sigma layers in the vertical direction. Main rivers with seasonally varying discharge rates were included in the model, i.e, Neva, Vistula, Daugava, Oder, Neman, Kemijoki, Torne-Alv, Narva, Dalalven and other smaller rivers. The total freshwater discharge rate was 484 km3/year. The atmospheric forcing was obtained from ERA-Interim reanalysis data [III-21] and air temperature, wind speed and direction, relative humidity, cloudiness and air pressure were interpolated from ERA-Interim data to the computational grid. Temperature, salinity, water velocity and surface elevation were prescribed along Kattegat from MyOcean reanalysis [III-22] for the North Sea. The sediment grain size was defined as 30 µm. The simulation started on 1 October 1985 when it was assumed that initially only a homogeneous background concentration of 137Cs in water (15 Bq/m3) exists. After one year, the concentration of 137Cs in the surface layer after the Chornobyl accident was prescribed according to Figure 4 of the main report (see Section 2.2.2 of the main report) and calculations were performed for the period 31 October 1986 to 1 January 1991.