## 4 Data Simulation  
A primary advantage of such a WSOA system is that data are collected in two dimensions, namely along-track and across-track. Then surface gradients and Laplacian can be computed, leading to computations of the geostrophic velocity and vorticity (see [20]). Furthermore, the intrinsic resolution (16*1 km) samples the ocean surface enough to determine the structure of most of the ocean eddies at Rossby radius of deformation scales (see [27]) as well as coastal processes (see [28]).  
A way to illustrate the usefulness of such a system has been to simulate the observations that could have been done at the time of an extreme ocean event. The case of the December 2004 tsunami over the Indian Ocean is such an example. Indeed, the Topex/Poseidon (T/P) and Jason satellites flew over the area of interest a few hours after the beginning of the seism. However, the direction of the tsunami, as well as an estimation of its power could not be derived from the acquired data. We simulated observations of such a tsunami assuming that an interferometer is implemented on the two platforms, based on CEA (Comite a l'Energie Atomique) outputs of a tsunami propagation model (which has been well validated using the real T/P and Jason-1 altimeter data).  
The tsunami started at 0 h 58 GMT at the top North of Sumatra Island. Jason went over the equator, at 85.7\({}^{\circ}\) East longitude 116 minutes later. Finally, Topex/Poseidon went over 7 minutes later, at 84.3\({}^{\circ}\) East longitude. For the purpose of the simulation, the SLA (Sea Level Anomaly), referring to the height of the water above the MSS (Mean Sea Surface), have been computed. Simulations were performed with post processing resolution of 16*4 km (21 pixels in each swath), which is the best compromise between quality of the height budget and minimal density of measurements to detect small-scale phenomena.  
The simulation takes into account the overall instrumental and external factors studied, with the worst cases in propagation errors and attitude errors.  
Figure 19: Global error budget of WSOA in worst and best cases for 16*14 kmThe direction of the tsunami wave can be easily determined from the height profiles derived from the simulated WSOA data on the Jason platform (see Figure 20 (a) and (b)), thanks to the added knowledge in the range direction perpendicular to the satellite velocity. The roll errors, which are correlated across track and along track, are well corrected, thus even in the worst case the residual errors (from 1 cm in the NR to 5 cm in the FR) don't prevent from a very good observation of the amplitude of the phenomenon.  
Figure 21: Simulated interferometer data on T/P platform with yaw steering and Poseidon 2 data to the right of it.  
Figure 20: (a) Simulated sea level anomaly as would have been observed by an interferometer onboard the Jason platform over December 2004 tsunami and determination of the wave direction (yellow arrow) (b) 3D view of the observations (azimuth, range, height).  
Figure 21 shows what kind of data a WSOA on Topex/Poseidon would have delivered given the unfavorable yaw angle at the time estimated between 99 and 101 degrees. On the right side of the T/P track, Poseidon 2 track is also plotted. The advantage provided by the large swaths has vanished, and the residual data look like nadir altimeter data..  
It confirms the strong advantage of getting rid of any platform rotation by moving to a sun synchronous orbit.