GHER contribution - Methodology


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Mediterranean Data Archaeology and Rescue
GHER contribution - Methodology


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The Mediterranean Sea and the Black Sea have been studied actively for several decades, generating huge amounts of data which remain in danger to be lost if not archived. New multivariate sensors, in growing number and spatio-temporal resolution produce crucial information which require careful and but efficient integration.. This information is becoming an essential part of the numerous toolkits used by oceanographers, engineers, managers, navies and authorities to continuously monitor the ocean state and variability, to infer possible climate changes, etc.


The aim of the MEDAR/MEDATLAS II project is to archive and rescue multi-disciplinary in-situ hydrographic and bio-chemical data of the Mediterranean and the Black Seas through a wide cooperation of countries. The growing interplay between scientific disciplines requires multi-disciplinary integration of this information which includes, among many other parameters, temperature and salinity, dissolved oxygen, hydrogen sulfure, alkalinity, phosphate, ammonium, nitrite, nitrate, silicate, chlorophyll and pH.


The project was divided into several tasks. First, a global inventory was compiled using existing data sets of the core parameters and their cruise reports from the WDC-A, the WDC-B, the ICES and the MEDATLAS I inventories. Duplicates were eliminated by careful cross-checking. Secondly, the data sets were assembled regionally for the Western, Central and Eastern Region and the Black Sea sub-areas., trans-coded in the common ASCII human readable MODB/MEDATLAS format and quality checked by regional experts. Finally, a global integration ensured the assembling and consistency of the regional data sets. The vertical profiles were interpolated on 25 standard vertical levels, chosen according to the vertical distribution of the data: 0, 5, 10, 20, 30, 50, 75, 100, 125, 150, 200, 250, 300, 400, 500, 600, 800, 1000, 1200, 1500, 2000, 2500, 3000, 3500 and 4000m. which build the data set on standard levels.


Raw in-situ data sets are difficult to interpret and higher level products are required to offer a more complete and synthetic view of the Mediterrenean and Black Sea bio-chemical systems. The computation of climatological or gridded fields is also justified by the need to provide initial or boundary conditions to numerical models (Beckers et al. 2001) and is subject to the choice of an adequate analysis method.


Instead of using the classical objective analysis scheme (OA) (e.g. Bretherton 1976), gridded fields have been computed using the Variational Inverse Model (Brasseur 1991, Brasseur and Haus 1991, Brasseur et al. 1996, Brankart and Brasseur 1996, Brankart and Pinardi, 2001, Rixen et al. 2001), shown to be statistically equivalent to OA.

The basic idea of variational analysis is to determine a continuous field approximating the data and exhibiting small spatial variations. In other words, the target of the analysis f is defined as the smoothest field that respects the consistency with the observed values over the domain of interest. It is also referred to as a spline interpolation method. Expressed in mathematical terms, the analysis is obtained as the minimum of a variational principle (in a two-dimensional, horizontal space)



The integral extends over the whole domain. The first contribution in J represents the distance between the data and the target field at the exact position of the observations. The weights mi are determined according to the confidence in the data. In principle, the weights could be adjusted to every observation individually, but in practice it is impossible to decide whether one observation is more reliable than another.


The second contribution in J is a measure of the smoothness of the target field. The coefficients a1 and a2 fix the weights of the lower derivatives in the smoothing operator. In practice, all observation at a given level are selected to perform the minimization in a horizontal plane. The reconstruction of a three-dimensional  scalar field is then obtained as a superposition of several analyses at different depths. This reduction is made possible because the data profiles describe the vertical structure of the sea reasonably well and do not produce hydrostatic instabilities.

The reference field fb (or background field) has been computed by a semi-normed analysis (leaving out the underived term in J) (Brankart and Brasseur 1996). It has indeed been shown that in data-void areas this method produces more realistic fields than using a simple constant value or a linear regression of the data. The variational principle is solved using a finite element technique. The main advantage is a numerical cost almost independent of the number of data analysed. The mesh also easily takes into account the complexity of the basin geometry by automatically prohibiting correlations across land barriers. In preliminary versions of the climatology, a preprocessing quality check was applied to the raw data in order to eliminate values out of 3 standard deviations on bins 10 times bigger than the analysis grid. This method however was not able to remove a significant part of the bull’s eyes in the analyses. Therefore it was decided not to consider coastal data close than 15 km from the coast nor data over sounding depth shallower than 50m. For this purpose, we used the Sandwell 1' bathymetry, corrected in the Adriatic Sea with ETOPO1 data (Zavatarelli, personal communication). We are aware that there are still some problems with the bathymetry, but to our knownledge, this is the most accurate information we had at the time of the computations.


By converting the dimensional weights into non-dimensional quantities, and imposing that the correlation function be the Modified Bessel function of order 1, the calibration of the free parameters m, a1 and a2 reduces to the choice of a characteristic length scale L and a signal-to-noise ratio (S/N=e2/s2), which represents the ratio of the standard deviation of the signal e to the standard deviation of observational errors s. A Generalized Cross-Validation (GCV) technique has been implemented to compute the statistical parameters L and S/N out of the raw data (Brankart and Brasseur 1996). The method consists in successively eliminating one measurement from the full data base and performing analyses with the remaining data. The variance of the misfits between these reconstructed fields and the corresponding eliminated data is then considered as a statistical indicator of the quality of the analysis, with respect to S/N and L. In practice, for climatological analyses, the quality of the analysis is not very sensitive to the correlation length and has thus been fixed a priori, according to a reasonable choice of features to be represented in the domain of interest.


By analogy with OA, the statistical error field is obtained by using the stiffness matrix K of the analysis and two transfer operators T1 and T2 (Rixen et al. 2001)



where c is the correlation function, i.e. the Modified Bessel  function of order 1.


Gridded fields have been produced for both entire Mediterranean and Black Seas basins and several additional sub-basins including the Alboran Sea, the Balearic Sea, the Gulf of Lions and the Ligurian Sea, the Sicily Strait, the Adriatic Sea, the Aegean Sea, the Marmara Sea and the Danube shelf area at climatic, seasonal and monthly scale when relevant. Inter-annual and decadal variability of T/S for both basins has been computed as well. It should be noted that for a given temporal scale, all data have been used, but the observational error standard deviation has been modified according to Brankart and Pinardi (2001), by imposing a temporal correlation length: 3 months for a seasonal analysis, 1 month for a monthly analysis, 10 years for a decadal analysis and 1 year for an annual analysis. Spatial correlation length have been increased somewhat (see atlas) to ensure that the fields in data-void areas are correctly extrapolated.


The resulting atlas is made available free of charge at and on CD-Rom, where the fields are found in Netcdf format (compressed with the gzip tool), and figures in Jpeg format. The atlas contains a selection of figure and 3D fields in NetCDF format (compressed with the gzip utility). The value NaN was assigned to land grid points and those horizontal levels at which there were no data. Some hints to read netcdf files can be found here . Please check carefully the conditions of use. Results are organised in a 'tree' way: first identify the domain, then the parameter, then the relevant period.. Colorbar ranges for analysis fields have been set using the corresponding range for the section of the climatological field. Colorbars for error fields are simply bounded by the corresponding climatic field range of values. Vertical sections go down to the deepest level where data were available. Stations plots are only indicative, as ALL the data are used, but weighted according to the temporal scale of the analysis period. The blue stations are those which effectively correspond to the period under study; i.e. when the associated weight is greater than 0.2. The red stations are those which are temporally close to the period under study, i.e. when the associated weight in the analysis is greater than 0.01. Two examples of the Mediterranean and the Black Sea are shown below.




This work benefits from the input of many individuals and organizations, including scientists, technicians and crew members who spent a wealth of their time to collect data at sea. The present climatology would not exist without the efforts of data managers who realized the incredible value of measurements at sea, assembling and quality checking the historical data sets with the most dedicated care. Many thanks to Catherine Maillard for the coordination of the project. IOC support is deeply acknowledged, encouraging continuously the best scientific and technical collaboration within the international oceanographic community.





·       Beckers, J.-M., Rixen, M., Brasseur, P., Brankart, J.-M., Elmoussaoui, A., Crepon, M., Herbaut, C., Martel, F., Van den Berghe, F., Mortier, L., Lascaratos, A., Drakopoulos, P., Korres, P., Pinardi, N., Masetti, E., Castellari, S., Carini, P., Tintore, J., Alvarez, A., Monserrat, S., Parrilla, D., Vautard, R., and Speich, S. (2001). Model intercomparison in the Mediterranean. The MedMEx simulations of the seasonal cycle. Journal of Marine Systems. Accepted.

·       Brankart, J.-M. and Brasseur, P. (1996). Optimal analysis of in situ data in the Western Mediterranean using statistics and cross-validation. Journal of Atmospheric and Oceanic Technology, 13(2):477-491.

·       Brankart, J.-M. and Brasseur, P. (1998). The general circulation in the Mediterranean Sea: a climatological approach. Journal of Marine Systems, 18:41-70.

·       Brankart, J.-M. and Pinardi, N. (2001). Abrupt cooling of the Mediterranean Levantine Intermediate Water at the beginning of the 1980s: observational evidence and model simulation. Journal of Physical Oceanography, 31:2307-2320.

·       Brasseur, P. (1991). A Variational Inverse Method for the reconstruction of general circulation fields in the Northern Bering Sea. Journal of Geophysical Research, 96(C3):4891-4907.

·       Brasseur, P., Beckers, J.-M., Brankart, J.-M., and Schoenauen, R. (1996). Seasonal temperature and salinity fields in the Mediterranean Sea: Climatological analyses of an historical data set. Deep-Sea Research, 43(2):159-192.

·       Brasseur, P. and Haus, J. (1991). Application of a 3-D variational inverse model to the analysis of ecohydrodynamic data in the Northern Bering and Southern Chuckchi seas. Journal of Marine Systems, 1:383-401.

·       Bretherton, F. P., Davis, R. E., and Fandry, C. B. (1976). A technique for objective analysis and design of oceanographic experiment applied to MODE-73. Deep-Sea Research, 23:559-582.

·       Karafistan, A., Martin, J.-M., Rixen, M., and Beckers, J. (2001). Space and time distributions of phosphates in the Mediterranean sea. Deep-Sea Research, 49(1), 105-120.

·       Rixen, M., Beckers, J.-M., Brankart, J.-M., and Brasseur, P. (2001). A numerically efficient data analysis method with error map generation. Ocean Modelling, 2(1-2):45-60.









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  Last modified 06/28/02