Internal solitary wave parameters from SWOT KaRIn sea surface topography: a case study in the Tropical Atlantic

Satellite remote sensing has revolutionized the study of Internal Solitary Waves (ISWs), revealing wave characteristics that are hardly obtainable through traditional in situ instrumentation. It enables the observation of their full two-dimensional horizontal structure, crest lengths, propagation direction, and phase speed, all on a global scale. However, some essential ISW parameters such as their amplitude and wavelength have been more difficult to assess from their surface manifestations. In this paper we employ an inversion method based on the quantitative relationship between sea surface current and ISW surface topography measured from SWOT KaRIn. The inversion method employs a fully nonlinear equation with continuous stratification to account for the strongly nonlinear nature of ISWs and uses the sea surface height anomaly from KaRIn measurements as a constraint to determine a unique solution. The method is tested on a case study in deep waters off the Amazon shelf in the Tropical Atlantic where in situ measurements quasi-coincident with a SWOT overpass allow evaluation of its accuracy. By directly contrasting the DJL retrievals with estimates from weakly nonlinear KdV theory, we show that KdV underestimates wave amplitudes and fits poorly surface expressions, whereas DJL yields accurate fits to both SWOT and mooring observations. We address a new possibility to calculate ISW parameters such as amplitude, wavelength, phase speed and wave induced velocity field based on fully nonlinear theory and discuss typical error margins that must be dealt with by researchers willing to use SWOT KaRIn in ISW studies. • Sea surface topography from SWOT KaRIn converted to ISW amplitudes • A fully nonlinear inversion method validated for Tropical Atlantic deep waters • Dubreil-Jacotin-Long theory is necessary for accurate ISW parameters retrieval