Optimum spatial analysis of monitoring data on temperature, salinity and nutrient concentrations in the Baltic Proper

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Abstract
In spite of the large number of monitoring data on hydrography and nutrients collected from the Baltic Sea, it is still difficult to describe large-scale distribution patterns of these variables. We therefore suggest a stochastic approach that allows the spatial reconstruction of the fields for the entire sea. The Baltic Sea monitoring data on temperature, salinity and nutrient concentrations from the years 1972–1991 are each divided into twenty data sets: five regions, times four seasons. The spatial regions are the Southern Baltic Proper, the Northern and Central Baltic Proper, both above and below halocline, and the region of the Gulf of Finland and the Gulf of Riga. The four seasons consist of three-month periods: January–March (winter), April–June (spring), July–September (summer) and October–December (fall). Each monthly subset of a regional and seasonal data set is modeled as a sample out of a monthly realization of a random field. The data sets are decomposed into mean and fluctuational components. The mean is determined as an average over the space cells with dimensions of standard sampling depth intervals vertically, 10′ in meridional (south-north), 20′ in zonal (west-east) directions and over five-year periods in time. The fluctuation fields are considered second-order stationary, homogeneous and horizontally isotropic. Estimated horizontal (surface) and vertical (depth) components of the spatial correlations are approximated by Gaussian functions. The correlation scales for the fields of the Baltic Proper are mostly larger than 100 nautical miles horizontally and 40 m vertically and their dependence on the sea region or season is relatively weak. The most probable noise-to-signal ratio values of the data lie in the interval 0.6 to 1.2. The estimated correlation functions and noise-to-signal ratios allow the optimum analysis technique to assess the correctness of each datum of a sample on the background of the field statistics. The outliers of each monthly sample are excluded from the analysis. The observed fluctuations are interpolated into locations with missing data by an optimum interpolation procedure. The discrete cell-and-five-year mean values are interpolated by a different, piece-wise linear technique. Since the data number for the mean interpolation considerably exceeds the data number for the fluctuation interpolation, the interpolation errors for the mean are assumed negligible compared to the interpolation errors for the fluctuation. The sums of the mean and fluctuation, interpolated into the withheld observation points, are compared to the actually observed values and to some other linear interpolation estimates. In all test cases the optimum interpolation procedure performs the best.