dinrichs et al. 
The annual cycle does not have to be considered on all depth 
levels, but only in the upper layers with a distinct seasonal signal. 
For the creation of the BNSC, an adjustment is performed down 
to a depth of 200m. In preparation of creation of the time 
series of annual mean values (am), the procedure is applied as 
follows: daily anomalies of the long-term mean annual cycle with 
respect to the long-term annual mean are calculated based on the 
polynomial fit and are referred to as the adjustment terms; in the 
following shown exemplarily for temperature T: 
365 
, 1 
adjTom (d) = To.(d) — = 2 TR, (d) 
—1 
These adjustment terms form a set of 365 values. Each single 
observed value has a corresponding adjustment term, depending 
on the calendar day of the observation. The adjustment term is 
subtracted from the observed value. 
In case of the monthly mean values, it is not the seasonal 
variability that could lead to a bias, but the intra monthly 
variability. Consequently, Iy, the correction is applied to the 
observed values in preparation of creation of the time series 
af monthly mean values (mm) as follows: the long-term mean 
annual cycle is split into 12 sections, according to the months of a 
year. For each single section, a long-term monthly mean value is 
estimated and the corresponding daily anomalies are calculated, 
yielding for each month m an individual set of adjustment terms, 
exemplarily shown here for temperature T: 
31 
n 1 
adjTfrm (dm) = Tf.(dm) — zz Dr Th (dm) 
dn=1 
[n contrast to the adjustment term for the creation of the annual 
mean, only the days corresponding to the respective month m 
are considered here, denoted by d,„. Then, the adjustment term 
corresponding to the calendar day of observation is subtracted 
from the observed value. 
Creation of Mean Values 
Temporal mean averages are composed calculating the arithmetic 
mean of the corrected observational data in each box. Monthly 
and annual mean values are calculated. It has to be stressed, that 
boxes lacking observations are left empty. 
Horizontally Interpolated Fields 
Based on the fields of box averages (monthly and annual mean 
values), horizontally interpolated fields are composed, aiming 
at closing the gaps between populated grid boxes. The applied 
procedure is the method of optimal interpolation (also known as 
optimal analysis). It was introduced by Gandin (1965) and since 
then has been widely used in different hydro-meteorological 
applications, for instance for the World Ocean Circulation 
Experiment Climatology (Gouretski and Koltermann, 2004). A 
vast literature exists about the usage of the optimal interpolation, 
but we leave this beyond the scope to this paper and only crudely 
outline the optimal interpolation method below. 
rontiers in Earth Science | www.frontiersin.or 
Baltic and North Seas Climatology 
In this method, for the arbitrary point (0) the interpolated 
parameter value F, is represented as the sum of the parameter 
first guess value, Go, and the weighted sum of the parameter 
deviations from the first guess at N observation locations (i): 
Fo=Got4) m O- GO], i=1,.N 
The optimal weights wo, are defined by the spatial correlation 
structure of the analyzed field. Generally, the optimal 
interpolation is preferred when the true correlation function can 
be accurately estimated; otherwise, other methods can provide 
comparable results. In many applications, the isotropic Gaussian 
<bell shaped) correlation function C (r) is used with the e-folding 
correlation length scale: 
2 
Cn=eR 
where r denotes the horizontal spatial distance and R being the 
correlation length scale. 
As noted by Sokolov and Rintoul (1999), the intrinsic 
correlation length scale for the optimal interpolation will be 
dictated more by the size of the data-void region than by the 
actual estimate. 
The BNSC region is characterized by strong variations in data 
density with the central part (central North Sea and Skagerrak, 
Kattegat, Belt Sea) being much better sampled than the adjacent 
Atlantic regions and the Gulfs of the Baltic Sea. As a trade- 
off, we used the e-folding correlation scale of 166 km in all our 
calculations. The interpolated fields produced by the optimal 
interpolation procedure may be considered as the result of 
applying a filter to the data. The optimal interpolation produces 
a spatial average of the data where smoothing length scales are 
in dependent on the data configuration, with the small scale 
oscillations being filtered uniformly, resulting in interpolated 
fields with homogeneous statistics. In data-poor regions, the 
optimal interpolation relaxes to the first-guess field. 
it needs to be taken into account that the interpolation errors 
are higher for the data poor time periods. Especially in the 
starting years of the BNSC time series, the spatial coverage 
is very low, however. The same refers to greater depths. In 
the following, the number of populated boxes on each depth 
level is analyzed and set into relation to the maximum number 
of possibly populated (“wet”) boxes. The maximum coverage 
accounts to a little more than 14%; large areas in time and depth, 
however, show values of 5% and less. Based on this analysis and 
taking into account the frequency of observations as a function 
of time (see Figure 1), it was chosen to perform interpolation on 
all depth levels in monthly resolution for the period 1950-2015. 
Additionally, the spatial coverage can be improved when box- 
averaged fields for wider time-windows (e.g., several years) are 
used. For a time window of 10 years from 1955 on, the maximum 
value of horizontal coverage improves to more than 50% and 
large areas show more than 20% horizontal coverage. Still, the 
coverage in the deeper layers remains rather poor. A monthly 
resolution is applied to the standard depth levels of up to 101 m. 
For greater depths, the annual mean is applied. 
Jahr 2019 LValıme 7.1 Article 15$£