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 ev 
ery 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 trans 
port for a better comparison to the surface fields of the other 
parameters. To estimate regional differences in model consis 
tency, 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 per 
centages 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 rela 
tive, comparable results similar to the SSC analysis. This mea 
sure 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 ac 
tual 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 stan 
dard 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 ad 
ditional 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 dif 
ferences 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 can 
not 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 tran 
sect 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