Application of the cos-Fourier expansion to data transformation between different latitude–longitude grids

In geodesy and geophysics, data of global coverage are often given on a latitude–longitude grid of constant intervals in latitude and longitude, that we call the gridded data (GD), or as a spherical harmonic expansion (SHE). Generally, as the total number of SHE coefficients is only about half of that of the GD, the GD and the SHE do not have one-to-one correspondence, i.e. the GD can be recovered from the SHE computed using the GD. However, in the case when the GD can be exactly represented using a SHE, like the geoid computed from a geopotential model given in terms of a SHE, the GD and the SHE do have one-to-one correspondence. But this is just a special case. Hence, the SHE does not always preserve the complete resolution of the GD. In fact, the GD may have higher resolution than the SHE at higher latitudes. In this paper, we suggest to use the tensor-product of the cosine series over colatitude and the Fourier series over longitude, referred to as the cos-Fourier expansion (CFE), to represent the GD. The CFE always has a one-to-one correspondence with the GD, and preserves the resolution of the GD. The CFE is then applied for transforming GD between different grids. The results of a particular application for generating the ocean function (OF) over a 2 . 5 ∘ × 2 . 5 ∘ grid from that originally given over a 5 ′ × 5 ′ grid are presented to show the feasibility of the method. Furthermore, a comparison between the CFE and SHE is made using digital land and sea-floor elevation data that demonstrates the above-mentioned characteristics of the CFE and SHE.