Abstract. 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)/•035 km (SR) at •02 km height resolution and to be dominated by a priori knowledge above •055 km (AR)/•047 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.

Abstract. The feasibility of retrieving water vapor profiles from downlooking passive microwave sounder data is demonstrated by usage of a retrieval algorithm which extends Bayesian optimal estimation. Special Sensor Microwave T-2 (SSM/T-2) downlooking sounder data, consisting of brightness temperature measurements sensitive to water vapor, are used together with total water vapor content data for computing tropospheric water vapor profiles. The significant nonlinearity in the cost function, an implication of the corresponding (nonlinear) radiative transfer equation, necessitates several extensions of the well-known optimal estimation inversion scheme. We supplemented the scheme by simulated annealing and iterative a priori lightweighting and obtained a powerful physical-statistical hybrid algorithm. Retrievals based on SSM/T-2 data were compared to atmospheric analyses of the European Centre for MediumRange Weather Forecasts (ECMWF). A statistical validation of the retrieved profiles is presented. The comparisons indicate an approximate accuracy of about 15 to 20 percent for relative humidity.

Abstract. An error analysis for mesospheric profiles retrieved from absorptive occultation data has been performed, starting with realistic error assumptions as would apply to intensity data collected by available high-precision UV photodiode sensors. Propagation of statistical errors was investigated through the complete retrieval chain from measured intensity profiles to atmospheric density, pressure, and temperature profiles. We assumed unbiased errors as the occultation method is essentially self-calibrating and straight-line propagation of occulted signals as we focus on heights of 50-100 km, where refractive bending of the sensed radiation is negligible. Throughout the analysis the errors were characterized at each retrieval step by their mean profile, their covariance matrix and their probability density function (pdf). This furnishes, compared to a variance-only estimation, a much improved insight into the error propagation mechanism. We applied the procedure to a baseline analysis of the performance of a recently proposed solar UV occultation sensor (SMAS -Sun Monitor and Atmospheric Sounder) and provide, using a reasonable exponential atmospheric model as background, results on error standard deviations and error correlation functions of density, pressure, and temperature profiles. Two different sensor photodiode assumptions are discussed, respectively, diamond diodes (DD) with 0.03% and silicon diodes (SD) with 0.1% (unattenuated intensity) measurement noise at 10 Hz sampling rate. A factor-of-2 margin was applied to these noise values in order to roughly account for unmodeled cross section uncertainties. Within the entire height domain (50-100 km) we find temperature to be retrieved to better than 0.3 K (DD) / 1 K (SD) accuracy, respectively, at 2 km height resolution. The results indicate that absorptive occultations acquired by a SMAS-type sensor could provide mesospheric profiles of fundamental variables such as temperature with unprecedented accuracy and vertical resolution. A major part of the error analysis also applies to refractive (e.g., Global Navigation Satellite System based)Correspondence to: G. Kirchengast (gottfried.kirchengast@kfunigraz.ac.at) occultations as well as to any temperature profile retrieval based on air density or major species density measurements (e.g., from Rayleigh lidar or falling sphere techniques).

Abstract. This paper proposes effective extensions to the well-known Bayesian optimal estimation, allowing one to cope not only with the ill-posedness but also with the intrinsic nonlinearity of many geophysical inversion problems. We developed a physical-statistical retrieval algorithm, which combines nonlinear optimal estimation with further optimization techniques. Profiling of water vapor based on (synthetic) downlooking microwave sounder data as an example for a typical geophysical nonlinear optimization problem is used to demonstrate the skills of the algorithm. Starting with a nonlinear scalar penalty function derived from a Bayesian approach, the sensible guess of a priori information, the selection of useful probability density functions, the advantages of simulated annealing, and the utility of Monte Carlo methods are discussed. These techniques together furnish capability for retrieving state vectors, which depend on the data in a (highly) nonlinear manner. The sensible combination as implemented in the introduced hybrid algorithm can provide solutions to problems that could not be tackled with standard (linearized) inversion methods properly.

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