Beckers, J.-M.

Ouberdous, M.

Rixen, M.

Sirjacobs, D.

Troupin, C.

Open Marine Archive

Session  3 – User Oriented services and products 211
 International Marine Data and Information Systems, IMDIS - 2008
Hydrostatic and advection constraints in the software DIVA: theory and 
applications
Troupin Charles , University of Liège, ctroupin@ulg.ac.be, (Belgium)
Ouberdous Mohamed , GHER (University of Liège),
Rixen Michel , NURC - NATO Undersea Research Centre, Rixen@nurc.nato.int
Sirjacobs Damien , GHER (University of Liège), D.Sirjacobs@ulg.ac.be
Beckers Jean-Marie , GHER (University of Liège), JM.Beckers@ulg.ac.be
Griding data is a frequently demanded process in geophysics: it consists in determining the value of a given fi eld on a regular grid from the knowledge of this fi eld at sparse locations within the domain of sake. 
The most used methods are based on interpolation techniques with an assumption of isotropic behavior of the fi eld. 
However, such techniques are not well adapted to the intrinsic nature of geophysical data:
in situ measurements are always sullied with an uncertainty on the fi eld value, thus a strict interpolation is not suit-1. 
able;
the effects of currents and coastlines make obsolete the assumption of isotropy.2. 
Diva (Data-Interpolating Variational Analysis) aims at bridging over the mentioned defi ciencies
by implementing the Variational Inverse Method (VIM, Brasseur et al., 1996). The principle of the method consists in 
minimizing a variational principle which accounts for:
the differences between the observations and the reconstructed fi eld;• 
the relative weights of the data;• 
the infl uence of the gradients and• 
the variability of the reconstructed fi eld.• 
Its major assets over classical methods are: 1. the resolution by the fi nite-element method, which allows a great numeri-
cal effi ciency and the consideration of problems with arbitrarily complicated contours; 2. the additional tools designed 
in order to facilitate the the analysis and make it as objective as possible; 3. the error fi eld (Brankart and Brasseur, 1998; 
Rixen et al., 2000) based on the data coverage and noise, provided along with the analysis; 4. the readiness of utilisation, 
with only three input fi le required for a typical analysis (analysis parameters, specifi cation of the domain contours and 
data themselves).
Among the available tools, let us mention:
the advection constraint during the fi eld reconstruction through the specifi cation of a velocity fi eld on a regular grid, • 
forcing the analysis to align with the velocity vectors;
the Generalized Cross Validation for the determination of analysis parameters (signal-to-noise ratio);• 
creation of contours at the selected depths;• 
the detection of possible outliers.• 
The latest developments of Diva in the frame of the SeaDataNet project include:
the hydrostatic constraint for eliminating the potential hydrostatic instabilities arisen from the combined analysis of 1. 
temperature and salinity data in several horizontal planes independently.
the specifi cation of a variable correlation length over the domain, allowing one to consider different scales of interest 2. 
according to the location;
the computation of the error fi eld based on the real correlation function of the considered data.3. 
Data sets of temperature and salinity in the Eastern North Atlantic are analyzed for illustrating the new features of the 
software: after gathering data from several sources (World Ocean DataBase, Coriolis, HydroBase2, Canigo) in the se-
lected region (0-50°N, 0-50°W), we perform analysis at standard levels on annual, seasonal and monthly bases. 
The complexity of the analysis is progressively increased by the consideration of realistic coast-lines, bottom topography 
and advection constraint.
Results are then compared with widespread climatologies from the World Ocean Atlas, giving rise to meso-scale features 
not properly represented in the latter, due to its lack of resolution.
212 Session 3 – User Oriented services and products
 International Marine Data and Information Systems, IMDIS - 2008
References
Brankart, J.-M., Brasseur, P., 1998. The general circulation in the Mediterranean Sea: a climatological approach. Journal of 
Marine Systems 18, 41-70.
Brasseur, P., Beckers, J.-M., Brankart, J.-M., Schoenauen, R., 1996. Seasonal temperature and salinity fi elds in the Mediter-
ranean Sea: Climatological analyses of a historical data set. Deep-Sea Research I 43, 159-192.
Rixen, M., Beckers, J.-M., Brankart, J.-M., Brasseur, P., 2000. A numerically effi cient data analysis method with error map 
generation. Ocean Modelling 2, 45-60.


Hydrostatic and advection constraints in the software DIVA: theory and applications

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