Ocean Dynamics
4) Springer
2.3.3 Regional pattern in forecast deviation for sea surface
current
The daily PVDs of the North Sea and Baltic Sea are evaluated
by determining the final displacements between the MME
PVD and the PVD of each forecast separately. The result is
a matrix for each forecast showing distances in kilometers for
each day at the points covered by the model grids. Moreover,
the temporal mean of final displacement is calculated for every
forecast at the corresponding transects. Another way to
display the deviation between the forecasts is to determine
the temporal mean of standard deviations of SSC magnitude
(c). The mean standard deviation between the forecasts over
the 48-h time period (insclf is normalized by the mean of
forecast standard deviations (msd Si ) to get comparable relative
values independent of the transect location. The temporal
mean of the resulting daily deviations (SD) was calculated at
each transect T\
SD(T) _ 1 V 7 ' msdf(i)
{ ] j E=i msdsfl) ’
with
msdf(I)
and
Sn(t) = -
msdsi(l) = - V” ! A(0,
n z —' l ~ l
and
S t (i) = <
where 1= 1,2,.../ for number of days, /= 1,2,.. .n for number of
forecast, and t—l,2,...k for each hourly output of the 48-h
forecast. Results are presented in Sect. 4.3
2.3.4 Regional pattern in forecast deviation for water
transport
Statistical analyses are only performed for surface water transport
for a better comparison to the surface fields of the other
parameters. To estimate regional differences in model consistency,
the occurrence of every CV category in percent (see
Sect. 2.2.3) at each transect is determined. Since not all
models included in the MME provide transport data for all
transects, the number of products and thus the resulting percentages
of complete data sets differ accordingly between
transects. To detect differences in daily transport patterns,
the correlations between each time series were determined
and the mean of all correlations was calculated. This was done
for each transect separately. The results were compared to the
mean of the correlations between the MME time series and
each product time series, also computed for each transect. To
determine which product deviates most from the others, the
RMSD between the time series of each product and the MME
median is normalized by the standard deviation of the MME
median at each transect. Normalization is done to have relative,
comparable results similar to the SSC analysis. This measure
allows comparison of regions with different transport
values. Results are presented in Sect. 4.4.
3 Daily results of the MME and ensemble statistics
3.1 Sea surface temperature and sea surface salinity
Examples of graphical daily output of the MME for SST in the
North Sea and for SSS in the Baltic Sea are shown in Figs. 2
and 3, respectively, reflecting obvious differences among the
forecasts. The number of ensemble members displays the actual
number of forecasts used by the MME system on the
current day. The ensemble minimum and maximum of the
forecasts indicate the plausible range of simulated SST and
SSS. For instance, in Fig. 2, the differences of SST among
the forecasts are approximately up to 3 °C in the English
Channel. The standard deviation displays the variability
among the forecasts. In the Skagerrak and Kattegat, high standard
deviation is the dominant characteristic in the SSS field
indicating large differences among the forecasts in these areas
(Fig. 3). Moreover, the ensemble median is calculated as additional
information in order to provide a more robust estimate
of the ensemble mean less prone to outliers.
For example, the ensemble mean of SST in the northern
North Sea close to the British coast is slightly higher than the
ensemble median (Fig. 2). In this case, SST of one forecast
might be much higher compared to the other forecasts on the
chosen day. This is also reflected by the wide range between
ensemble minimum and ensemble maximum where the differences
between the individual forecasts are shown. Along
the boundaries, where the number of ensemble members
changes, discontinuous transitions can often be found in all
fields. This characteristic is obvious approximately along 59°
N in the North Sea, where the analysis number drops from 6 to
5 and further to 4 northward. This form of discontinuity cannot
be found in the Baltic Sea, since most of models in this
region cover the same area.
3.2 Sea surface current
The PVD (see Sect. 2.2.2) and the 48-h time series for the u
and v components as well as a feather plot are displayed on
daily figures for each transect separately. An example of transect
7 (Tr7) in the North Sea is shown in Fig. 4. As the tides
are present in the surface currents, the time series at the North
Sea transects are dominated by a strong tidal signal which is
also visible in the resulting PVD. Surface currents in the Baltic
Sea also have a tidal signal which is much weaker, and the
strength of currents is in general lower than in the North Sea.
Flowever, comparatively strong currents occur also in the
Danish Straits. In this example, BSF1HBM seems to be out
of phase and overestimates the magnitude of u velocity while
it underestimates the magnitude of v velocity, the latter similar
to DMI DKSS. This is reflected in the PVD, where those
forecasts exhibit the largest distances from the starting point.
Although it is not obvious in the time series, the PVD of
