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Weare and Strub [1981] counted the number of observations needed to minimize sampling uncertainty in a 5°x5° grid box by ensuring that the observations were evenly split between all areas of the grid box, month and diurnal cycle. From this, they concluded that even sampling could not be achieved with fewer than eleven observations, but that in practice more than eleven, sometimes many more, would be needed.
Rayner et al. [2006] estimated a combined measurement and grid-box sampling uncertainty by considering how the variance of the grid-box average changed as a function of the number of observations. The technique picked up spatial variations in grid-box sampling uncertainty associated with regions of high variability. Rayner et al. [2009] showed results from an unpublished analysis by Kaplan, in which spatially complete satellite data were used to estimate the variability within 1°x1° grid boxes. The same features were seen as in the Rayner et al. [2006] analysis, allowing for differences in resolution, although the uncertainties estimated by Kaplan tended to be higher. She et al. [2007] also used sub-sampling of satellite data to estimate grid-box sampling uncertainty for the Baltic Sea and North Sea. Kent and Berry [2005] showed that separately assessing measurement and sampling uncertainties can help to decide whether more, or better, observations are needed to reduce the average uncertainty in an individual grid box.
Morrissey and Greene [2009] developed a theoretical model for estimating grid-box sampling uncertainty that accounted for non-random sampling within a grid box. This was an extension of the method used to estimate sampling uncertainties in land temperature data and global temperatures by Jones et al. [1997]. Land temperatures are measured by stations at fixed locations that take measurements every day. Marine temperature measurements are taken at fixed times, but the ships and drifting buoys move during a particular month. Morrissey and Greene [2009] do not provide a practical implementation of their approach, only a theoretical framework. Kennedy et al. [2011b] extended the concept of the average correlation within a grid box developed in Jones et al. [1997] to incorporate a time dimension. Kent and Berry [2008] used a temporal autocorrelation model that took account of the days within the period that were sampled, and the days which were not, to estimate the temporal sampling uncertainty. An alternative to the Jones et al. [1997] method for land data was provided by Shen et al. [2007], but it has not yet been applied in SST analyses.
It is possible that the locations visited by ships and drifting buoys are related and, to an extent, dictated by meteorological and oceanographic conditions. Ships have long used the prevailing currents in the Atlantic to speed their progress and it is in the interest of almost all shipping to steer clear of hurricanes and other foul weather. Bad weather is also likely to have influenced how and when observations were made. Conversely, the conditions in which a sail ship might become becalmed could lead to over sampling of higher SSTs. Drifting buoys drift, and a drifter trapped in an eddy might persistently measure temperatures that are representative of only a very limited area. Drifters also tend to drift out of areas of upwelling and congregate in other areas.
The effect of uneven sampling can be reduced by the creation of "super observations" during the gridding process [Rayner et al., 2006], or data preparation stage [Ishii et al., 2003], but such processes cannot readily account for the situations where no observations are made at all.
As noted by Rayner et al. [2006], the grid-box sampling uncertainties are likely to be uncorrelated or only weakly correlated between grid boxes so the effect of averaging together many grid boxes will be to reduce the combined grid-box sampling uncertainty by a factor proportional to the square root of the number of grid boxes. Consequently the sampling component of the uncertainty will be of minor importance in the global annual average (Figure 8).
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