Salinity evaluation of Baltic Sea applying the simple and ordinary lognormal kriging

Abstract

The object of this study was ecological data observed at 10 stations in the coastal zone of the Baltic Sea. Here we analyze water salinity data collected in the period 1994–2001 in all seasons: in winter, in spring, in summer and in autumn. The Center of Marine Research in Klaipėda (Lithuania) provides us with data. Measurements are made at different depths. We do not investigate the influence of depth on factors, and therefore only deal with the observations made at the depth of 1 meter. The purpose of work was to predict the mean value at the randomly chosen station for a specific future moment applying the simple and ordinary lognormal kriging, and estimate the prediction in terms of mean square prediction error (MSPE). The lognormal kriging is used when the strong right asymmetry peculiar to data. Because the left asymmetry peculiar to our data so we applied the appropriate linear transformation. Such transformation did not influence for MSPE value. For every season a value of covariance function can be calculated. Then after joining all the empirical covariances we easily fit the parametrical model by using nonlinear regression (we applied the nlinfit function in Matlab). We considered 3 spatial covariance functions: spherical, exponential and Gaussian. For every covariance function can be calculated mean square error (MSE) value. The MSE is used as criteria for choosing the function which fits best the empirical data. The exponential covariance function for every season fits data best. We get four covariance functions in the first step. The second step is to find the combined covariance function using weighted average method described in [2]. Combined covariance function was used in spatial-temporal prediction applying simple and ordinary lognormal kriging methods — see [1]. Comparison of these two spatial — temporal prediction methods was implemented by using MSPE values calculated directly or by cross-validation method.