## 3 The need for high resolution ocean topography measurements to observing ocean mesoscale dynamics  
Following [PERSON] and [PERSON] [6], the most problematic features of ocean circulation from the perspective of altimeter sampling are the mesoscale eddies and fronts that are of interest in the sea-surface height (SSH) and ocean velocity fields. These features are essential to understanding the dynamics of ocean circulation on all space and time scales. Theoretical studies of the cascade of energy over scales from 100-1000 km have always suffered from the lack of high-resolution observations. Numerical model simulations indicate that, in many regions of the world ocean, this mesoscale variability plays a key role in the large-scale ocean circulation and climate variability in the form of eddy transport of momentum in eddy-mean flow interaction and in the form of meridional eddy transport of heat. Global synoptic observations of the eddy field have never been available to test the accuracy of the model simulations.  
Despite all the progress made through the last decade, there is still much to learn from altimeter data for mesoscale variability studies. Following [PERSON] [7], investigations that could be carried out include:  
* More detailed comparisons of altimetry with eddy resolving models (including comparison of higher order statistics such as frequency/wavenumber spectra and Reynolds stresses);
* Regional characterization of the three dimensional frequency/wavenumber of sea level (and velocity) and relationship with forcing fields and dynamics; Relationship with turbulence theories;
* Better characterization of seasonal/interannual variations in eddy energy and relationship with forcing fields (mean current instabilities, winds);
* Phenomenological (global) characterization of eddies (eddy census): size, rotation, diameter, life time, propagation, etc. and relationship with theories and models.
* Detailed dynamical structure of eddies. Estimation of the vorticity field (in and out of the eddy), divergence and deformation fields. Use in synergy with high resolution sea-surfacetemperature (SST) and ocean color images. Estimation of vertical circulation and biogeochemical coupling.
* Relation and interaction between eddies and Rossby waves.
* Eddy heat fluxes (in combination with SST remote sensing data). Contribution to the total heat fluxes.
* Eddy mean flow interaction. Role of eddies on the general circulation and climate.  
All above studies would benefit from higher space and time resolution.  
One should note that the best use of high resolution altimetry data will be when they are assimilated with in-situ and other remote sensing data into global eddy resolving models (and nested shelf/coastal models). This will indeed open a large range of scientific (see above) and operational applications. In particular, the capability of providing precise velocity estimations will be of great importance for operational applications (offshore, fisheries, marine safety, etc.)  
Empirical analysis and data assimilation approaches will be used in the next section to derive and justify mission requirements in terms of ocean mesoscale observations.