more closely. It was found that despite explicit stability 
checks like a check for the CFL-criteria and checks for 
(linear) stability in the von Neumann sense, in certain sit- 
uations, numerical instabilities occurred, which could only 
be avoided by additional non-linear stability and 
realizability checks within the turbulence closure scheme. 
Those checks are already described for turbulence closure 
schemes not using double diffusion in Umlauf and 
Burchardt (2005), so that these checks were extended to 
our turbulence model including double diffusion. 
The paper is organized as follows: Section 2 describes the 
used model HBM and the model setups in detail. Section 3 
gives an explanation of realizability in general (Section 3.1) 
and documents the added stability and realizability criteria 
(Section 3.2). In Section 4, both the physical and also the 
technical (£-tests) validation of model results with and without 
the new criteria are shown, and finally the impact of the en- 
hanced stability on the results of a downstream drift model is 
presented in Section 5. Main conclusions are provided in 
Section 6. 
2 Model and setups 
2.1 Numerical model 
The physical model used in this study is HBM (HIROMB- 
BOOS model) described in Berg and Poulsen (2012) which is 
used both for operational forecasts (e.g. by the CMEMS Baltic 
MFC or the BSH), for reanalysis (Fu et al. 2012) and for 
research projects at various institutes, especially for the 
North Sea and Baltic Sea region (e.g. MeRamo:Neumann 
et al. (2018, in review), CLAIM (n.d.)). 
HBM is a three-dimensional baroclinic ocean circulation 
model using Boussinesq approximations. The model is a fur- 
ther development of the operational circulation model 
BSHcmod (Dick et al. 2001). Like in BSHcmod, advection 
and diffusion are realized by a flux-corrected transport 
scheme, and the horizontal viscosity is parametrized by 
Smagorinsky (1963). In HBM the user has the choice between 
z-coordinates with free surface and so-called dynamical or 
generalized vertical coordinates (Dick et al. (2008), Kleine 
(2004)) and the possibility of a fully dynamical two-way 
nesting with any number of grids. The vertical mixing is real- 
ized by a two-equation k-w turbulence model accounting for 
buoyancy-affected geophysical flows (Umlauf et al. 2003). By 
parametrization, the shear due to internal waves (Axell 2002), 
an estimate production in the surface layer from below and 
unresolved bottom shear due to tides (Canuto et al. 2010) are 
also taken into account. A detailed description of the used 
parameters resp. the parameter-making could be found in 
Berg (2012). In this study, the turbulence model is coupled 
to an algebraic second order closure scheme either based on 
Ocean Dynamics 
Canuto et al. (2002) or based on Canuto et al. (2010). Both 
closure schemes consider double diffusion which is relevant in 
the Baltic Sea — one of the main application areas. For exam- 
ole, at the Baltic Sea Science Congress 2017, it was shown 
that double-diffusive instabilities may constitute a key mixing 
orocess in this region (Gillner et al. 2017). The latter scheme 
finally has been extended by additional stability and 
tealizability checks. A detailed description of this extension 
can be found in Chapter 3. 
2.2 Setups 
During this study, two setups both running in operational 
mode and both covering the entire North- and Baltic Sea 
were used. Both setups were forced by atmospheric data 
[rom the operational atmospheric model of the German 
Weather Service (DWD) and run-off data from the opera- 
(ional run-off model E-hype operated at the Swedish 
Meteorological and Hydrological Institute. At the open 
boundary in the northern North Sea and in the English 
Channel, the water level has been set to the sum of surge 
data generated by BSH’s operational North Atlantic model 
and tides based on 19 partial constituents. Temperature and 
salinity at the open boundary were taken from the Janssen 
st al. (1999) climatology. 
2.2.1 CMEMS setup 
The CMEMS setup is using z-coordinates with free surface 
and consists of four nested grids: 
“North Sea” with a horizontal resolution of 3 nautical 
miles and up to 50 vertical layers 
“Wadden Sea” with a horizontal resohıtion of 1 nautical 
mile and up to 24 vertical layers 
“Inner Danish Waters” with a horizontal resolution of 0.5 
nautical miles and up to 77 vertical layers 
“Baltic Sea” with a horizontal resolution of 1 nautical mile 
and up to 122 vertical layers 
2.2.2 BSH setup 
The BSH setup is using dynamical/generalized vertical coor- 
dinates and consists of two nested grids: 
“North Sea/Baltic Sea” with a horizontal resolution of 3 
hautical miles and up to 36 vertical layers 
“German Coastal Waters” with a horizontal resolution of 
0.5 nautical miles and up to 25 vertical layers 
A Sprins. --