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Piercing the clouds
5/5/11

The use of the EOF methodology requires observations of the system to be studied at every position and at every instant. Yet observations in oceanology are generally complete, as explains Aida Alvera-Azcárate, a FNRS postdoctoral researcher in the ULg’s Geo-hydrodynamic and Environmental Research Department (GHER): ‘a whole section of oceanology works on the basis of satellite data taken in infrared or within the field of the visible. Yet the presence of clouds in the atmosphere from time to time prevents the ocean surface from being observed, introducing holes in the data and preventing a direct application of the EOF methodology. To overcome this incompleteness Professor Jean-Marie Beckers has adapted the EOF methodology, in such a way to fill in the holes before its application properly speaking. We thus speak of the principle of DINEOF (Data Interpolating Empirical Orthogonal Functions).'

Méhode DINEOF

The DINEOF method is iterative. It at first tries to judge the functions or principal components on the basis of incomplete data. Starting from these approximate functions the missing data is reconstructed as average values. They round out the sample of real data, which enables the EOF methodology to be used, and through it a more precise calculation of the principal components which will themselves subsequently provide a better estimation of the missing data. This process is repeated until sufficient consistency between the functions and all the data (real and reconstructed) is obtained. It is possible to consider certain real data as missing in such a way to only bring them out at the end of the process, in order to test the method.

The optimal reconstruction of missing data is the innovative part of the DINEOF methodology. Its development by Professor Beckers dates back to 2003. It was subsequently Aida Alvera-Azcárate who took responsibility for validating it and setting it up for real cases, a lot more complicated than theoretical cases: ‘to validate the method I carried out reconstructions of raw and incomplete data concerning surface temperature, then concerning chlorophyll, winds, suspended matter in the Mediterranean and other domains. I then compared my results with independent in situ data, gathered by boat or buoys in the sea. It is the MEDAR atlas which gathers the on site observations for the Mediterranean over the past fifty years. Already at root the real satellite data is not exactly identical to the in situ data: the gap is due to the fact that the satellite takes its measurements at the air-sea interface, whilst the on-site instruments must be placed in the water and thus take underwater measurements. That can take place at a depth of one metre. On a very sunny day the gap can reach 0.5° for the North Sea or even more for the Mediterranean. To be acceptable, the error bar for my reconstructed data must be of the same order of size as this gap.’

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