## 4 Deriving mission requirements for ocean meso-scale applications
### Analysis from a data assimilation perspective  
Data assimilation is a powerful means for a dynamical interpolation of data and may be used to assess the spatial and temporal requirements of a satellite system (e.g. using a model forecast as an a priori knowledge instead of climatology). Demonstrating the value of data assimilation is the central objective of GODAE, the Global Ocean Data Assimilation Experiment [17]. Providing general requirements from a data assimilation perspective is, however, a difficult issue. Since the first steps in these directions [18-20], much progress has been made, and much more consistent results are today displayed regardless of the data assimilation techniques or/and the numerical models used.  
In the following, we refer to data assimilation experiments based on the SEEK (Singular Evolutive Extended Kalman) filters, a family of reduced order Kalman filters in which the estimation error is expressed in terms of a sub-space that evolves with time according to the ocean dynamics [21-23]. These experiments were performed in the frame of the GAMBLE (Global Altimeter Measurements By Leading Europeans) project [24]. The model configuration is that of a simplified double-gyre system driven by surface wind, which includes a western boundary current zonally propagating across the ocean basin and generating mesoscale eddies. This mimics with a very good statistical similarity the eddy-active general circulation of the ocean in the mid-latitudes, such as the Gulf-Stream system. The general strategy of the numerical experiments is that of the Observing System Simulation Experiments (OSSE). Twin assimilation experiments are realized using several observing systems based on one, two and three altimeters flying simultaneously. The assumed satellite mission parameters are those of T/P, Jason and ERS. Data collected along tracks are pooled together at regular interval (typically a few days) to perform the analyses synoptically. Observation errors consistent with those of real data are added as a random signal to the pseudo-observations.  
The comparison between error statistics calculated for the various multi-satellite relative phasing scenarios (time offset only, space offset only, space/time offset, parallel flights) and other mission parameters such as altitude, allows to draw a number of conclusions:  
* The addition of a second altimeter improves the reconstruction of the mesoscale circulation by an amount comprised between 18% and 28% depending on the mission parameters. The addition of a third satellite makes an additional improvement which is between 10% and 16%, again depending on the flight configuration.
* A three-day interval between successive analyses appears to be better than smaller (one day) or longer assimilation periods (ten or twenty days).
* The observing scenarios in favour of spatial sampling (interleaved tracks, or space offset) compete very well with those in favour of temporal sampling (time offset).
* The \"best\" observing scheme may be different if the variable of interest is related to the surface circulation, or to the deep fields.
* The dynamical modes intensified at intermediate depth require more than two satellites to be determined without ambiguity; in a dynamical context, the lack of information concerning these modes might affect the three-dimensional flow field globally, and therefore limit the quality of the estimation near the surface as well.
* In a three satellite constellation with a specified inclination, the increase of altitude has a negative effect on the performances.  
Overall, the results using three satellites confirm other studies indicating that a third satellite is necessary to control the mesoscale features satisfactorily. However, the selection of the optimal configuration is not trivial.