Mapping GPS Radio Occultation Data by Bayesian Interpolation

Bayesian interpolation for mapping GPS radio occultation data on a sphere is explored and its performance evaluated. Bayesian interpolation is ideally suited to the task of fitting data randomly and nonuniformly distributed with unknown error without overfitting the data. The geopotential height at dry pressure 200 hPa is simulated as data with theoretical distributions of the Challenging Mini-Satellite Payload (CHAMP) and of the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC). The simulated CHAMP data are found to be best fit with a spherical harmonic basis of 14th degree; the COSMIC data with a spherical harmonic basis of 20th degree. The best regularizer mimics a spline fit, and relaxing the penalty for purely meridional structures or for the global mean yields little advantage. Climatologies are most accurately established by binning in similar or equal to 2-days intervals to best resolve synoptic structures in space and time. Finally, Bayesian interpolation is shown to negate a source of systematic sampling error obtained in binning and averaging highly nonuniform data but to incur another systematic error due to incomplete resolution of the background atmosphere, notably in the Southern Hemisphere.