Spatial large‐scale correlations for optimal interpolation of temperature, salinity and nutrient concentrations in the Gulf of Finland

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Abstract
Spatial correlations of temperature, salinity and nutrient concentrations in the Gulf of Finland are estimated for winter, spring, summer and fall. The correlation estimates are based on the results of observations in the Gulf of Finland for the period 1972–1991. The time and space resolution of the correlation model are determined by averaging the original data in time over each month and in space over the cells with horizontal dimensions equal to 10′ in the east–west and 20′ in the south–north direction and to the standard sampling depth intervals in the vertical direction. The fluctuations of the averaged data are defined as deviations of the month and cell average data values from the seasonal 20‐year overall mean values. The model of spatial correlation is based on the assumption that the fluctuations of the month‐and‐cell average data form a random sample out of a spatially homogeneous, horizontally isotropic and temporally stationary field. Most of the estimated correlations are positive, except for the vertical correlation component of salinity in summer, which shows considerable negative values at the distance lags exceeding 30 m. As an example of assimilation of the estimated correlations, the statistical (optimal) linear interpolation approach was applied for estimation of the optimal location of a measurement site, additional to the three currently used international monitoring stations, commonly known as LL12, LL7 and LL3A, in the Gulf of Finland. The optimal location of the additional fourth measurement site, which leads to the least average interpolation error, was found to be within the vertical column of cells with co‐ordinates 60° 00′ N 28° 10′ E for salinity and 60° 00′ N 28° 20′ E for total phosphorus concentration measurements. The same average error cannot be achieved by increasing the sampling frequency at the three present international monitoring stations.