Seasonal variations of mode-1 M2 internal tides observed by satellite altimetry

The seasonal variations of M₂ internal tides is investigated using 25 years of satellite altimetric sea surface height measurements from 1992--2017. The satellite data are divided into four seasonal subsets, from which four seasonal M₂ internal tide models are constructed. This study employs a new mapping technique that combines along-track spatial filtering, harmonic analysis, plane wave analysis, and two-dimensional spatial filtering. The vector mean of the four seasonal models yields the seasonal-mean model, which is equivalent to the 25-year-coherent model constructed directly using all the data. The seasonal models have larger errors than the seasonal-mean model, because the seasonally-subsetted data sets are short. Two seasonally-variable models are derived: The first model is a step function of the four seasonal models (phase-variable, amplitude-variable); The second model is same as the first one but that the amplitude is from the seasonal-mean model (phase-variable, amplitude-invariable). All these models are evaluated using independent CryoSat-2 data. Each seasonal model reduces most variance in its own season and least variance in its opposite season. Based on globally-integrated variance reductions, the two seasonally-variable models reduce 13% and 23% more variance than the seasonal models, respectively. The seasonal-mean model can reduce 27% more variance, thanks to its small model errors. However, the seasonally-variable models are better than the seasonal-mean model in the tropical zone, where the seasonal signals are larger than model errors. The satellite results reveal that M₂ internal tides are subject to seasonal variation in varying degrees and that the seasonal variation is a function of location. Large variations in amplitude and phase mainly occur in the tropical zone. The seasonal phase variations are mainly caused by the seasonal variations of ocean stratification and internal tide speed. Significant amplitude variations are usually associated with strong internal tides such as from the Luzon and Lombok Straits, and in the Amazon River plume, the western Pacific and the Arabian Sea. At higher latitudes such as the North Pacific and North Atlantic Oceans, the seasonal variations are weak but detectable. The seasonally-variable models can partly account for the seasonal variations of internal tides, in particular, in the tropical zone.  A major challenge is the large model errors, which will be further reduced with the accumulation of new altimeter missions and data (e.g., SWOT).