KLIWAS 
Seite 23 
4,2,3 Sta tistic a 1 Ro nt Products - SSTand OC 
KLIWAS 
Climatology 
of North Sea 
Fronts 
The following section and Equations 1-4 provide an overview and a definition on 
the measures using the example of SST. The first parameter is the mean of SST 
gradient magnitude for frontal zone over a defined time interval per pixel: 
VSSTI 
V N front_obs 
IV SST), 
N fronlobs 
(1) 
with Nfronts_obs the number of front observations over a defined time interval per pixel. 
The second measure is the magnitude of mean SST parameter gradient vector for 
frontal zone over a defined time interval per pixel: 
VSSTI = 
y~^Nfront_obs 
VSST t 
N front obs 
(2) 
The direction of mean SST parameter gradient vector for frontal zone over a defined 
time interval per pixel is defined as: 
Direction of V SST = 
\ ^front obs 
VSST, 
Nfront_ObS 
(3) 
One of the most important parameters is the front probability over a defined time 
interval per pixel 
Probability front = £f 
(4) 
with Nsst the number of SST observations per pixel over a defined time interval, i.e. 
reference period. It can therefore provide reliable information about the probability 
for observing a SST or OC front at this location. GRADHIST provides the possibility 
to derive not only the mean magnitudes but also the gradient vectors for a frontal 
zone. For regions which show a prevailing direction of the gradient vectors both 
measures are nearly in the same order of magnitude, i.e., the fronts have a high 
directional persistence. If the magnitude of mean SST/OC gradient vector is 
apparently smaller than the mean of SST/OC gradient magnitude, the frontal zone is 
characterized by a high directional variability. Fig. 7 shows the distribution of the 
gradient vectors as well as the resulting mean gradient vector for two selected 
locations marked by pins. Furthermore, the histogram of the direction of the SST 
front gradient vectors is also shown.