21 
the grid node are taken to obtain a field estimate. It means, that most of the observed data 
are actually lost for the analysis. In this case the climatic estimate is based on a number of 
observations which may not be representative of the regional long-term mean conditions. 
Chelton and Schlax (1991) analysing colour scanner satellite data introduced the notion of 
time averaging to the standard optimal interpolation method in recognition that some 
temporal averaging is desirable to reduce the aliasing of high-frequency variability in the 
signal. Time of observation is neglected in our interpolation and original data are subject to 
spatial averaging prior to optimal interpolation. The ocean was subdivided into 0.5-degree 
latitude zones between 80°S and 90°N. Each zone was in turn subdivided into boxes with the 
longitude size equal to 55 km for the zone mid-latitude. Thus the quantity that is estimated 
is not the signal at a particular estimation point but its average over a 55x55 km box. Data 
averaging was done within each box if at least 4 profiles were available. Similar averaging 
procedure was used by Levitus (1982) and in the later updates of the NOAA ocean 
climatology, where one-degree data averages served as input for the further analysis. 
However, unlike in NOAA climatologies we performed averaging on the potential density 
surfaces, referenced to the pressure of the respective standard level. Since diapycnal 
processes are assumed to be important in the near-surface layer, within the upper 100- 
meter layer averaging was performed on the isobaric (standard depth) surfaces. 
The averaging results in a 10-fold reduction of the input data, from 1,059,535 original profiles 
to only 106 330 profiles (for all data mean averaging), with the total number of the box- 
averaged profiles being 21311. Fig. 12 shows the distribution of the averaged and original 
profiles used finally for the optimal interpolation of temperature and salinity. 
4.3. Modelling spatial lag correlation 
The correlation structure for the increment field has a central and highly sensitive role in the 
optimal interpolation method. The optimal interpolation requires the knowledge of the spatial 
correlation function p, and the signal-to-noise ratio y 1 . Unfortunately, because of a general 
data paucity the determination of the spatial correlations for the fields of oceanographic 
parameters is a difficult task, compared with the situation in meteorology, where time series 
observations are often routinely available. Satellite observations however provide sufficient 
information to determine statistical characteristics of oceanographic fields but only at the 
ocean surface (Kuragano and Kamachi, 2000). Repeat XBT sections were also used to infer 
the spatial correlation structure. Meyers et al (1991) give an example of space-time scale 
determination of sea surface temperature and depth of the 20°C isotherm in the Tropical 
Pacific Ocean.