S. Dick, E Kleine 
20 
Fig. 2. Model bathymetry and nesting of grid nets: 1: NE Atlantic (10 km). 2: North Sea + Baltic (5 km). 3: German 
Bight + western Baltic (900 m) 
3. Novel Design of the Vertical Coordinate 
The new version of the BSH’s circulation model 
is based on a special co-ordinate representation as the 
basic building block. It has been developed in order to 
improve the model’s effective numerical performance. 
A recurrent experience is that the effective 
resolution, used to capture flow features, is much 
lower than the resolution of the numerical grid. 
Common-type circulation models are prone to 
numerical diffusion. The worst effects occur in 
artificial vertical mixing, where the model’s 
stratification is systematically eroded or even ruined. 
Expectations are often disappointed, and the model’s 
value often has been greatly reduced. The trouble 
remains (to a considerable extent) even when a so- 
called high-resolution scheme is used to calculate 
transport. This type of scheme has its own effective 
resolution and at best allows the degradation to be 
partly compensated. Besides, additional expenses are 
incurred due to its considerable computational 
requirements, which are of limited efficiency though. 
A different strategy to cope with the problem is 
addressed here which is at a level closer to its roots. 
We will deal with the co-ordinate representation and 
will try to find a physically appropriate description 
suitable for capturing water masses. To keep 
numerical diffusion due to vertical transport 
modelling as low as possible, we will try to find a 
layer description which follows the vertical motion of 
water masses as closely as reasonable. However, the 
co-motion has to be limited in order to keep the 
description of water masses from degenerating, an 
effect typically observed in isopycnal models. The 
method is briefly described in the following. A more 
thorough explanation has been provided by Kleine 
(2003). 
In order to gain sufficient flexibility, we will use 
the calculus of a co-ordinate system with arbitrary 
representation of the vertical. The pertinent 
framework is found in Kasahara (1974), Johnson 
(1980), Burger & Riphagen (1990). 
A one-dimensional transformation is applied to 
replace the vertical (height), z , by another variable, ,v, 
whose relation to height is required to be invertible, 
i.e. ds/dz be non-zero, say ds/dz > 0. This 
transformation may vary over the horizontal, so that 
surfaces on which the new vertical co-ordinate is 
constant need not be horizontal. Partial derivatives 
with respect to a horizontal dimension should be 
understood to relate to such a non-horizontal surface. 
Therefore, it is not just the vertical which is affected 
by the transformation, but the entire co-ordinate 
system. Besides, the co-ordinate transformation may 
vary with time. 
The transformed vertical co-ordinate is known as 
a “generalised vertical co-ordinate’’, as long as no 
other condition except invertibility is assumed to