# Solving the mesoscale and internal tide sea surface height signatures in a single massive inversion using a variational approach

**CoAuthors**

**Event: **2017 Ocean Surface Topography Science Team Meeting

**Session: **Tides, internal tides and high-frequency processes

**Presentation type: **Type Oral

Presently, the gridded solutions of Sea Surface Height (SSH) mesoscales (e.g. CMEMS) and stationary Internal Tidal Wav (ITW) signatures (e.g. Ray or Zhao solutions) are estimated separately from the same along-track observation datasets. However, it is known that they both leak in each other’s estimation. In particular, the mesoscale solution subtracted before computing the ITW may remove a non-negligible part of the original ITW signal leading to underestimated ITW solutions.

To mitigate this problem, we are currently investigating the feasibility of solving the mesoscale and ITW in a single massive inversion covering a multi-decadal period. If the standard OI approach presently used for mesoscale mapping could not invert such a volume of observations, it is possible to perform an inversion using a variational approach. Following a wavelet basis in time and space for the mesoscale and a plane wave basis for ITW, we can solve for more than O(108) parameters iteratively by computing cost function gradients. The standard covariance models used in mesoscale mapping are converted in equivalent wavelet parameter prescribed variance.

After presenting the method, we will show the results of first implementations in the Hawaii and Azores regions covering the 1995-2013 period. The ITW solutions will be compared with existing solutions, by looking at a variance reduction diagnostic of an independent (2014-2017) set of altimetry observations. The results may suggest a significant gain of performing the global mesoscale-ITW inversion, providing more energetic and variance-reductive ITW solutions. Running the analysis globally would be very costly, but not impossible in the future. The possibility of considering non-stationary ITW in the same inversion will be also discussed.

To mitigate this problem, we are currently investigating the feasibility of solving the mesoscale and ITW in a single massive inversion covering a multi-decadal period. If the standard OI approach presently used for mesoscale mapping could not invert such a volume of observations, it is possible to perform an inversion using a variational approach. Following a wavelet basis in time and space for the mesoscale and a plane wave basis for ITW, we can solve for more than O(108) parameters iteratively by computing cost function gradients. The standard covariance models used in mesoscale mapping are converted in equivalent wavelet parameter prescribed variance.

After presenting the method, we will show the results of first implementations in the Hawaii and Azores regions covering the 1995-2013 period. The ITW solutions will be compared with existing solutions, by looking at a variance reduction diagnostic of an independent (2014-2017) set of altimetry observations. The results may suggest a significant gain of performing the global mesoscale-ITW inversion, providing more energetic and variance-reductive ITW solutions. Running the analysis globally would be very costly, but not impossible in the future. The possibility of considering non-stationary ITW in the same inversion will be also discussed.