Ocean Dynamics
Ô Springer
domain. For the Baltic Sea, the maximal number of different
forecasts can be assembled in the Gulf of Finland. In most areas
of the Baltic Sea, there are up to nine forecasts used for the
current version of the MME for SST and SSS. For the MME,
only areas covered by more than three forecasts are taken into
account, resulting in a smaller region of the MME compared to
the area of the MyOcean product. The number of contributing
models, MME maximum, MME minimum, MME median, and
MME mean and standard deviation between the models of SST
and SSS are calculated at each grid point for each time step of
the 48-h forecast. These outputs are provided in the NetCDF-
files. On the NOOS and BOOS website, the figures of the first
forecast time are shown (i.e., 01:00 UTC).
2.2.2 Sea surface current
At present, up to seven forecasts of SSC are available for the
North Sea and up to ten forecasts for the Baltic Sea. A first
overview of the ensemble spread is given by progressive vec
tor diagrams (PVD) (Emery and Thomson 2001) ofthe hourly
surface currents calculated for each 48-h forecast at selected
points distributed over the whole study area (see example of
PVD in Fig. 4). Since the NOOS and BOOS transects are
situated in hydrodynamically important areas, i.e., English
Channel, Kattegat, or the Danish Straits, PVDs are calculated
at the centers of all transect (see Fig. 7 for transect locations
and numbering). The PVD is a type of water particle trajectory
calculated by summing up the travelled distance ofthe particle
using the hourly u and v velocities of the surface currents. In
addition, the ensemble mean and the standard deviation ofthe
velocity components are calculated on an hourly basis, and the
resulting mean PVD (MME PVD) is determined.
More recently, a MME and corresponding statistics ofthe 2D
SSC fields are produced on an hourly basis for the 48-h forecast
period. On the NOOS and BOOS websites, only figures for the
first 24 h are displayed. The MME and statistical values are
calculated as follows (where i—1,2,.. .n for number of forecast):
1. The mean current field of each velocity component and
the resulting magnitude, the vector mean current (VM), is
determined with
/ 1 ^^ n 1 ^ r n
VM = V if + v 2 , with Ti = — > Uj v = — > v,
?! ¿- 1 '=1 ?! ¿- 1 '=1
It should be noted that this definition may average out
current components of opposite directions, which means that
even though the models predict strong current of varying di
rections, the average VM may be small.
2. The standard deviation (Syg ), which represents the dis
persion between the models, is given by
s vm = (VM.-VM)" with VM, = ^/u?+v2
3. The stability (P) between the forecasts, expressed by the
ratio of the vector mean current VM to the mean magni
tude (MM ), is calculated with
p_Y_^L* too w ith MM = — M, Mj = \/ if + v?
MM "
Areas characterized by, i.e., low stability indicate that either
magnitude or directions of the forecasts are not consistent.
4. The angular difference, which is the difference between
the current fields of the MME mean and the MyOcean
(MyO) product, is displayed as angular degree (a) and
given by
lll*l?MyOj + (j’* v MyOJ / -
COSQ' = with VM Mv0 = \ II MvO 2 + VMvO 2
VM* VM My0 V
5. The difference-to-standard-deviation ratio (DSR), calcu
lated by dividing the difference between the MME mean
(VM ) and the MyOcean product (VM My0 ) by the stan
dard deviation of the MME, is expressed as
VM-VM Mv0
dsr = —
The ratio shows where the difference is smaller than the
standard deviation, i.e., if below 1.
2.2.3 Water transport
The MME of water transport is based on an ongoing project in
the NOOS and BOOS communities, which has been running
since 2004, focusing on the exchange of computed transport
to get a better understanding of the hydrodynamic situation in
the North Sea and Baltic Sea. In the project, heat transport, salt
transport, and water transport across several transects in the
North and Baltic Sea are calculated on a daily basis using the
outputs from different circulation models. The main tidal con
tribution is removed by averaging the transport at each grid
cell along the transect over a time interval of 24 h and 50 min
centered around noon of the first day of each forecast. The