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Full text: Uncertainty estimation for operational ocean forecast products

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
	        
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