116
H.E.M. Meier and A. Höglund
rivers have been implemented (Meier et al. 2003). These 29 rivers represent about
84 % of the total runoff. Monthly river runoff data were taken from the Baltic Sea
Experiment (BALTEX) Hydrological Data Center (BHDC) at SMHI (Bergström
and Carlsson 1994). Large-scale hydrological models are used to update the runoff
in recent years where the runoff data are not available (Graham 1999).
When the topography, initial and boundary conditions, and the atmospheric and
hydrological forcing are prepared the ocean model is ready to be integrated forward
in time with a baroclinic time step, which amounts in case of the RCO model to
150 s. Hence, the model resolves the advection of matter with the currents and fast
travelling baroclinic waves, as long as the baroclinic Rossby radius (see Chap. 2,
Sect. 2.3.2 and Chap. 3, Sect. 3.3.1.1) is larger than at least two grid cells of the
model. As the RCO model was designed to study past and future climate variability
of the Baltic Sea on a centennial time scale, a horizontal resolution higher than 2
nautical miles was technically impossible (Meier et al. 2003). As baroclinic Rossby
radii in the Baltic Proper amount to 3–10 km approximately (Fennel et al. 1991), the
RCO model and other models with similar set-up (e.g., Lehmann 1995; Neumann
et al. 2002; Je ¸drasik et al. 2008) are considered to be eddy-permitting but not eddyresolving.
4.2.2.8 Numerical Implementation and Shortcomings
All subgrid scale processes, like internal gravity waves and boundary layer turbulence, are parameterized which means that the impact of subgrid scale processes
on the resolved motion is taken into account using empirical relationships. Some of
these parameterizations might be used to calibrate the models using available observations because many of the mechanisms are still unknown. Processes important
for the calculation of currents for that we lack detailed knowledge today are, for
instance, bottom friction, vertical mixing and surface fluxes of momentum.
However, even if the mathematical equations describing the relevant processes
are known, the numerical treatment may cause biases of the solution of the problem
under consideration. For instance, test experiments showed that in long simulations
the modified SPLIT-QUICK advection scheme (Webb et al. 1998), which was earlier
embedded within the RCO model, does not guarantee numerical stability of passive
tracers released at point sources. SPLIT-QUICK is of third order accuracy but does
not preserve monotonicity. At large gradients overshooting due to numerical dispersion is observed. Hence, for the study of tracers a flux-corrected, monotonicity
preserving transport (FCT) scheme following (Gerdes et al. 1991) was embedded
(Meier 2007). In the simulations by Meier (2007) no explicit horizontal diffusion
was applied.
Due to the lack of knowledge about proper parameterizations of subgrid-scale
processes, insufficient horizontal and vertical grid resolution, biases of atmospheric
and hydrological forcing fields, too coarse topographical data sets, and insufficient
numerical schemes, Baltic Sea models suffer from uncertainties. For instance, in
case of the RCO model these shortcomings are a too shallow halocline (Meier 2007),
H.E.M. Meier and A. Höglund
rivers have been implemented (Meier et al. 2003). These 29 rivers represent about
84 % of the total runoff. Monthly river runoff data were taken from the Baltic Sea
Experiment (BALTEX) Hydrological Data Center (BHDC) at SMHI (Bergström
and Carlsson 1994). Large-scale hydrological models are used to update the runoff
in recent years where the runoff data are not available (Graham 1999).
When the topography, initial and boundary conditions, and the atmospheric and
hydrological forcing are prepared the ocean model is ready to be integrated forward
in time with a baroclinic time step, which amounts in case of the RCO model to
150 s. Hence, the model resolves the advection of matter with the currents and fast
travelling baroclinic waves, as long as the baroclinic Rossby radius (see Chap. 2,
Sect. 2.3.2 and Chap. 3, Sect. 3.3.1.1) is larger than at least two grid cells of the
model. As the RCO model was designed to study past and future climate variability
of the Baltic Sea on a centennial time scale, a horizontal resolution higher than 2
nautical miles was technically impossible (Meier et al. 2003). As baroclinic Rossby
radii in the Baltic Proper amount to 3–10 km approximately (Fennel et al. 1991), the
RCO model and other models with similar set-up (e.g., Lehmann 1995; Neumann
et al. 2002; Je ¸drasik et al. 2008) are considered to be eddy-permitting but not eddyresolving.
4.2.2.8 Numerical Implementation and Shortcomings
All subgrid scale processes, like internal gravity waves and boundary layer turbulence, are parameterized which means that the impact of subgrid scale processes
on the resolved motion is taken into account using empirical relationships. Some of
these parameterizations might be used to calibrate the models using available observations because many of the mechanisms are still unknown. Processes important
for the calculation of currents for that we lack detailed knowledge today are, for
instance, bottom friction, vertical mixing and surface fluxes of momentum.
However, even if the mathematical equations describing the relevant processes
are known, the numerical treatment may cause biases of the solution of the problem
under consideration. For instance, test experiments showed that in long simulations
the modified SPLIT-QUICK advection scheme (Webb et al. 1998), which was earlier
embedded within the RCO model, does not guarantee numerical stability of passive
tracers released at point sources. SPLIT-QUICK is of third order accuracy but does
not preserve monotonicity. At large gradients overshooting due to numerical dispersion is observed. Hence, for the study of tracers a flux-corrected, monotonicity
preserving transport (FCT) scheme following (Gerdes et al. 1991) was embedded
(Meier 2007). In the simulations by Meier (2007) no explicit horizontal diffusion
was applied.
Due to the lack of knowledge about proper parameterizations of subgrid-scale
processes, insufficient horizontal and vertical grid resolution, biases of atmospheric
and hydrological forcing fields, too coarse topographical data sets, and insufficient
numerical schemes, Baltic Sea models suffer from uncertainties. For instance, in
case of the RCO model these shortcomings are a too shallow halocline (Meier 2007),