Piercing the clouds

The conditions which reign over the surface of the oceans are crucial for the climate, even for that which reigns at the other end of the planet. They are also an open door onto the physics of the oceans. But the majority of observations in physical oceanography are carried out by satellite. Thus what is to be done when clouds come between the satellites and the oceans? Aida Alvera-Azcárate has validated a statistical method which allows this cloud cover to be pierced.

Are we always aware of the influence the conditions which reign at the surface of the oceans at the other end of the planet can have on our climate? In particular the temperature of the oceans’ surfaces is one of the most important hydrodynamic parameters: it influences the atmosphere and the climate. It is for example the surface temperature at the Tropics which conditions the Gulf Stream current, and through it the climate in Europe. It is because the Gulf Stream has its source in the Tropics that the Winters in Europe are milder than those of the United States, which is on the same latitude.

Scientists have an interest in the oceans’ surface in multiple ways. It is the most variable section of the oceans and thus contains much more information than a layer situated at depths of 1000m. It also has more influence on the climate than the oceans’ interiors. Finally, and in a more practical manner, satellites only have access to the surface of the oceans. Nevertheless measurements taken at the surface allow deeper layers to be scanned, thanks to hydrodynamic models of the oceans built on the basis of the laws of physics.

The continuous observation of the oceans’ surface by different satellites generates a quantity of data whose management is a heavy task, even when dynamic models are used. Models, empirical ones in this case, can be used beforehand in the process to reduce the quantity of data. The principal components (EOF) methodology has for example been much used for a hundred years or so in every scientific field. It offers the advantage of being able to reduce a large quantity of data to several very simplified functions.

To understand its principle let us consider a basin filled with water whose surface is oscillating. To describe this surface wave we can note the position of every point at every moment, which rapidly generates a colossal amount of data. On the basis of this it is possible to find simple and empirical functions which allow the system to be described simply: a spatial function which gives the form of the wave at a given moment and a temporal function which characterises the variation of the wave over time. The determining of these functions then allows one to bypass an accumulation of data.

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).'

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.’

There exist other methods to reconstruct an incomplete ensemble of data. Optimal interpolation is the best known and the most classical. Its big problem is its calculating time: for a typical ensemble of data, DINEOF is 30 times more rapid than optimal interpolation. This gap mainly reflects a different statistical methodology between the two different methods.

If the reconstruction of data allows a more judicious use of dynamic ocean models a practical problem needed to be resolved. In effect a researcher who for example studies anchovies in the Mediterranean will not throw herself into reconstructing satellite data related to the oceans’ surface temperature. She wants a finished product, and possibly ready made daily images.

The majority of these ‘non-specialists’ of satellite images use either raw data which thus has holes in the place of clouds or composite images provided by specialized institutions. The sum of consecutive data, these composite images have the advantage of being spatially complete…even if this artificial reconstruction can produce artifacts, traces of clouds or maintain holes if the clouds have remained for several days.

‘Our idea is to place on the market another high frequency product,’ continues Aida Alvera-Azcárate. ‘Thus my website produces a complete an daily image of the Mediterranean’s surface temperature, reconstructed on the basis of the data covering the six preceding months, obtained through the American satellites of the NOAA (National Oceanic and Atmospheric Administration). These satellites provide on a daily basis high resolution images of the whole of the North East Atlantic, including the Mediterranean. My programme receives them and reconstructs them, to eliminate the clouds. It can also be downloaded free of charge from my site, which offers a forum where the users can ask questions. Some twenty or so are already registered on this platform. This opportunity was very greatly welcomed. It also offers transparency which allows others to check our results and compare them to their own.’

If the DINEOF method has mainly today been used to reconstruct data concerning the Mediterranean, it has also been applied elsewhere. The Liège team has been contacted by researchers at the University of Madeira in the Canaries, who were interested in obtaining complete data for one of their sea campaigns. The ocean in the Canaries zone in effect has strong spatial and temperature variations. Incomplete of composite data cannot allow these areas where the temperature varies brutally to be precisely detected.

More recently it was the Management Unit of the North Sea Mathematical Models which contacted the GHER. This federal institution is responsible for daily surveillance of the North Sea. It works on the basis of dynamic models which use biological laws and the laws of physics. One of their applications is calculating the evolution of algae in the North Sea. Yet the presence of suspended matter, as it absorbs the available light, strongly influences the dynamic of algae and phytoplankton. It was Damien Sirjacobs, when he was a researcher at the GHER (he now works in the Department of Life Sciences / Algolgy, mycology and experimental systematic), who applied the DINEOF method more specifically to the case of suspended matter in the North Sea (1). To do so he used data recorded between 2003 and 2006 by two satellites: the MERIS spectrometer installed on the European Space Agency’s (ESA) ENVISAT satellite and the MODIS radio-spectrometer on board NASA’s AQUA satellite.

‘One field of application for the DINEOF methodology which will still be much made use of is the study of the evolution of local structures,’ concludes our oceanologist. ‘In effect we talk of a global warming of the planet, but we know very little about how climate change acts at the level of local structures. And yet their existence and their movements are easier to detect than an average global warming which is, as we know, very small in relations to daily or seasonal variations.’