Analyzing the Diurnal Cycle by Bayesian Interpolation on a Sphere for Mapping GNSS Radio Occultation Data

Bayesian interpolation has previously been proposed as a strategy to construct maps of radio occultation (RO) data, but that proposition did not consider the diurnal dimension of RO data. In this work, the basis functions of Bayesian interpolation are extended into the domain of the diurnal cycle, thus enabling monthly mapping of radio occultation data in synoptic time and analysis of the atmospheric tides. The basis functions are spherical harmonics multiplied by sinusoids in the diurnal cycle up to arbitrary spherical harmonic degree and diurnal cycle harmonic. Bayesian interpolation requires a regularizer to impose smoothness on the fits it produces, thereby preventing the overfitting of data. In this work, a formulation for the regularizer is proposed and the most probable values of the parameters of the regularizer determined. Special care is required when obvious gaps in the sampling of the diurnal cycle are known to occur in order to prevent the false detection of statistically significant high-degree harmonics of the diurnal cycle in the atmosphere. Finally, this work probes the ability of Bayesian interpolation to generate a valid uncertainty analysis of the fit. The postfit residuals of Bayesian interpolation are dominated not by measurement noise but by unresolved variability in the atmosphere, which is statistically nonuniform across the globe, thus violating the central assumption of Bayesian interpolation. The problem is ameliorated by constructing maps of RO data using Bayesian interpolation that partially resolve the temporal variability of the atmosphere, constructing maps for approximately every 3 days of RO data.

Estimation of Winds from GPS Radio Occultations

GPS radio occultations (RO) offer the possibility to map winds in the upper troposphere and lower stratosphere (UTLS) region because geopotential height is the independent coordinate of retrieval. Most other sounders do not offer this possibility because their independent coordinate of retrieval is pressure. To estimate the precision with which GPS radio occultation data can map winds, dry pressure profiles are simulated from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) at the actual locations of the Challenging Minisatellite Payload (CHAMP) and the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) soundings for the year 2007. Monthly wind maps were created by using Bayesian interpolation on subsampled ERA-Interim data in 3–5-day bins and subsequent averaging over a month. Mapping winds in this approach requires that 1) geostrophy approximates winds; 2) dry pressure approximates pressure in the UTLS; and 3) geopotential height can be mapped accurately given sparse, nonuniform distributions of data. This study found that, under these conditions, it is possible to map monthly winds near the tropopause with an accuracy of 5.6 m s−1 with CHAMP alone and 4.5 m s−1 with COSMIC alone. The dominant contributors to uncertainty are undersampling of the atmosphere and ageostrophy, particularly at the leading and trailing edges of the subtropical jet. The former is reduced with increased density of GPS RO soundings. The latter cannot be reduced even after iteration for balanced winds. Nevertheless, it is still possible to capture the general wind pattern and to determine the position of the subtropical jet despite the uncertainty in its magnitude. COSMIC radio occultation measurements from 2006 through 2011 were used to estimate monthly geostrophic winds maps in UTLS. The resultant wind dataset is posted online.

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 ≃2-day 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.