In order to provide a typical and clearly defined physical environment for testing the NPZD model discussed in section , we use an annual simulation of the water column in the Northern North Sea. The setup is similar to the one described in section 12.2.2 and validated in detail by Bolding et al. (2002). The photosynthetically available radiation (PAR) has been simply taken as visible part of the short-wave radiation, a feedback of increased turbidity due to plankton blooms to the light absorption has not been considered for the heat budget. For further details of the physical model setup, see section 12.2.2.
As shown by Burchard et al. (2005), the explicit ODE solvers introduced in section 8.13 do not guarantee non-negative solutions for biogeochemical concentrations when the biogeochemical model is stiff, i.e. when time scales are involved which may be shorter than the time step. In order to make the NPZD model stiff, Burchard et al. (2005) chose a half-saturation nutrient concentration of 0.02 mmol N m, whereas the typical values for would be between 0.2 and 1.5 mmol N m. This has the consequence that nutrient is taken up by phytoplankton even at low concentrations, which strongly decreases the time scale of this process. The overall phytoplankton evolution over an annual cycle is not much affected by this manipulation, except from the fact that now the summer surface nutrient concentrations are much lower. It should be noted that such low half saturation concentrations for nutrients have actually been observed in the oceanic mixed layer. Harrison et al. (1996) calculated for the mixed layer of the North Atlantic mean half saturation concentrations for nitrate and ammonium as small as 0.02 mmol N m.
In order to demonstrate the advantages of the Modified Patankar schemes over the fully explicit schemes, the simulation carried out here is based on a time step of 2 h for the physical part. For the biogeochemical part, a time splitting is used (set split_factor in bio.nml) such that fractional time steps are possible for the biogeochemical part. Thus, by using a time step of s for the physical part and iterating the biogeochemical part 1,4 and 36 times per physical time step with unchanged physical forcing, biogochemical time steps of s, s and s, respectively, can be obtained. By doing so, it is possible to use exactly the same physical forcing for all ODE solvers and all biogeochemical time steps.
When using the explicit ODE solver (to do so, set ode_method in bio.nml to 1, 2 or 3), the summer nutrient concentration goes down to negative values. This does not happen for the other conservative methods 7 and 8 (first- and second-order Modified Patankar schemes) and 10 and 11 (first- and second-oder Extended Modified Patankar schemes).
Karsten Bolding 2012-12-28