Error analysis and characterization of atmospheric profiles retrieved from GNSS occultation data


  • Markus J. Rieder,

  • Gottfried Kirchengast


The performance of the Global Navigation Satellite System (GNSS) based radio occultation method for providing retrievals of atmospheric profiles up to the mesosphere was investigated by a rigorous Bayesian error analysis and characterization formalism. Starting with excess phase profile errors modeled as white Gaussian measurement noise, covariance matrices for the retrieved bending angle, refractivity/density, pressure, and temperature profiles were derived in order to quantify the accuracy of the method and to elucidate the propagation of statistical errors through subsequent steps of the retrieval process. We assumed unbiased phase errors (the occultation method is essentially self-calibrating), spherical symmetry in the occultation tangent point region (reasonable for most atmospheric locations), and dry air (disregarding humidity being of relevance below 10 km in the troposphere only) in this baseline analysis. Because of the low signal-to-noise ratio of occultation data at mesospheric heights, which causes instabilities in case of direct inversion from excess phase profiles to atmospheric profiles, a Bayesian approach was employed, objectively combining measured data with a priori data. For characterization of the retrievals we provide, in addition to covariance estimates for the retrieved profiles, quantification of the relationship between the measured data, the retrieved state, the a priori data, and the true state, respectively. Averaging kernel functions, indicating the sensitivity of the retrieval to the true state, contribution functions, indicating the sensitivity of the retrieval to the measurement, and the ratio of retrieval errors to a priori errors are shown. Two different sensor scenarios are discussed, respectively, an advanced receiver (AR) scenario with 2 mm and a standard receiver (SR) scenario with 5 mm unbiased RMS error on excess phase data at 10 Hz sampling rate. The corresponding bending angle, refractivity, pressure, and temperature retrieval properties are shown. Temperature, the final data product, is found to be accurate to better than 1 K below ∼40 km (AR)/∼35 km (SR) at ∼2 km height resolution and to be dominated by a priori knowledge above ∼55 km (AR)/∼47 km (SR), respectively. For all data products the use of a Bayesian framework allowed for a more complete and consistent quantification of properties of profiles retrieved from GNSS occultation data than previous work.