Improving the m₂ tide model over shallow waters using topex/poseidon and ers‐1 altimetry

The residual M₂ tide relative to the CSR 3.0 model over the Western Pacific was determined using TOPEX/POSEIDON (TIP) and ERS‐I altimetry. The sea surface heights (SSH) were crossover‐adjusted to remove the biases in satellite orbits. Including data over shallow waters, the averaged root‐mean‐square (RMS) crossover differences of SSH before adjustment are 20.5 and 32.9 cm for TIP and ERS‐1. respectively, which were reduced to 16.1 and 27.4 cm after adjustment. A harmonic analysis method, in which the cosine and sine components of a tidal constituent were represented by spherical harmonic expansions with transformed spherical coordinates, was adopted to estimate the residual M₂ tide. The transformed spherical coordinates increase, the spatial resolution of the spherical harmonic expansions and help to avoid ill‐conditioned systems in least‐squares. Using TIP data from cycles 2 to 36 and ERS‐1 data from cycles 6 to 15, we experimented with various expansion degrees and combinations of data. The best result is with the TIP‐ERS‐l degree 20 solution, which improves the M₂ tide of CSR 3.0 by 3.84 cm RMS over shallow waters compared to tide gauge data. Along the coast of China, CSR 3.0 was not improved due to large data gaps and bad data quality. Over the deep oceans, CSR 3.0 and gauge data agree to below 4.22 cm RMS, and the M₂ tide of CSR 3.0 is improved by 0.5 cm RMS.