Baltic Sea Research Institute Warnemünde, Germany Some GOTM Numerics SOPRAN GOTM School Warnemünde: 10.-11.09.07 Hans Burchard Baltic Sea Research Institute Warnemünde, Germany

Spatial discretisation Discretisation into a user-defined number of vertical layers. Layers may be equi- distant or with zooming to bottom and/or surface: dl>0: bottom zooming du>0: surface zooming Mean flow variables: on cell centres, Turbulent quantities: on interfaces.

Time stepping: Time step Dt is constant. In principle, there are no stability criteria to be obeyed, since the vertical diffusion is implicit, and the vertical advection is iterated. However, physical time scale must be resolved, e.g., time step must Be much scmaller than tidal period (e.g. Dt < 1 h). In contrast to 3D models, results of 1D models must not be detoriated by numerical errors, you should always find high enough resolution. Test: decrease time step step-wise by factor of 2 (increase output interval by factor of 2), and look for convergence of results.

Some aspects of ecosystem model numerics: Ecosystem models should 1. conserve mass, and concentrations should be 2. non-negative. This must also be reflected by the numerical schemes. Ecosystem model equations may be stiff (i.e. cover a large Range of time scales, such as photo-chemistry vs. inter- annual variability). Classical schemes violate one or the other constraint. For GOTM, we have developed new schemes for the processes, the so-called Modified-Patankar schemes (MP, Burchard et al.) and the Extended Modified Patankar schemes (EMP, Bruggeman et al.).

Northern North Sea, NPZD model result.

Surface nutrient concentration with explicit schemes:

Surface nutrient concentration with MP schemes:

Surface nutrient concentration with MP schemes, blow-up: