Filtering noise from oceanographic data with some applications for the Kara and Black Seas

If a reconstruction process is reduced to the solution of ill-posed algebraic systems, we suggest several procedures to improve the accuracy of reconstruction from noisy and irregular data. These procedures transform ill-posed equations to their well-posed analogies, thereby reducing both the contribution of noise to the equation system and the condition number of the system matrix. One of the techniques, the so-called “regularizing filter”, can be applied to observation samples of limited size when the ratio of the number of estimated field parameters to the number of field observations and noise to signal ratio are under 0.5–0.6 and 4–5, respectively. Furthermore, the filter is constructed without any preliminary knowledge of low-order noise statistics. The regularizing filter combined with a conventional function fitting procedure is illustrated through linear mapping scalar oceanographic fields, such as the surface temperature in the Black Sea observed from the NOAA-11, SiO2 in the Kara Sea, cesium and chlorophyll in the Black Sea. Herein comparing our approach to optimal interpolation, generalized cross-validation and smoothing spline-interpolation is also given.