Reconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the Adriatic Sea surface temperature

Abstract

A method for the reconstruction of missing data based on an EOF decomposition has been applied to a large data set, a test case of Sea Surface Temperature satellite images of the Adriatic Sea. The EOF decomposition is realised with a Lanczos method, which allows optimising computational time for large matrices. The results show that the reconstruction method leads to accurate reconstructions as well as a low cpu time when dealing with realistic cases. The method has been tested with different amounts of missing data, artificially adding clouds ranging from 40% to 80% of data loss, and then compared to the same data set with no missing data. A comparison with in situ data has also been made. These validation studies show that results are robust, even when the amount of missing data is very high. The reconstruction of the data from the Adriatic Sea shows realistic features and a reliable temperature distribution. In addition, the method is compared to an Optimal Interpolation reconstruction. The results obtained with both methods are very similar. The main difference is the computational time, which is reduced nearly 30 times with the method presented here. Once the reconstruction has been performed, the EOF decomposition is analysed to show

Cloud filling of ocean colour and sea surface temperature remote sensing products over the Southern North Sea by the Data Interpolating Empirical Orthogonal Functions methodology

“…Finally, the optimal set of EOFs and of missing data estimates are calculated by a last iterative SVD cycle decomposing the complete dataset into the predetermined optimal number of modes. DINEOF methodology has been successfully applied to univariate treatment of SST (Alvera-Azcárate et al, 2005). DINEOF products are suitable not only for filling gaps in databases or filtering the noise component of the signal, but also to produce a synthetic representation of the dynamics of a system by interpretation of the dominant retained modes and of the long term trends captured by their temporal signatures.…”

“…To avoid the production of artefacts in the EOF calculations and subsequent projections, some limitations have to be set on the acceptable spatio-temporal proportion of missing data as in Alvera-Azcárate et al (2005). Prior to DINEOF treatment, it was chosen to eliminate each image holding less than 5% of the expected data.…”

“…The number of EOFs retained is then naturally the one that leads to the minimal misfit. For more details we refer to Beckers and Rixen (2003) and Alvera-Azcárate et al (2005).…”

Filling in missing sea-surface temperature satellite data over the Eastern Mediterranean Sea using the DINEOF algorithm

“…The optimal number of EOF modes retained is calculated by cross-validation (i.e., a few valid data are set aside and the error of the reconstruction is assessed by comparing the reconstructed data to these cross-validation data). For an extended description of DINEOF, and recent developments, the reader is referred to Beckers and Rixen [2], Alvera-Azcárate et al [3,12] and Beckers et al [13].…”

“…Due to the iterative nature of the algorithm, any inhomogeneity or nonisotropic behavior is automatically taken into account, generating an interpolation effect, hence the name Data Interpolating Empirical Orthogonal Functions (DINEOF). An adaptation of handling large data sets (typical of satellite imagery) can be found in [3].…”