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Random uncertainties and vertical error correlations are estimated for three independent data sets. The three collocated data sets are (1) refractivity profiles of radio occultation measurements retrieved from the Metop-A and B and COSMIC-1 missions, (2) refractivity derived from GRUAN-processed RS92 sondes, and (3) refractivity profiles derived from ERA5 forecast fields. The analysis is performed using a generalization of the so-called three-cornered hat method to include off-diagonal elements such that full error covariance matrices can be calculated. The impacts from various sources of representativeness error on the uncertainty estimates are analysed. The estimated refractivity uncertainties of radio occultations, radiosondes, and model data are stated with reference to the vertical representation of refractivity in these data sets. The existing theoretical estimates of radio occultation uncertainty are confirmed in the middle and upper troposphere and lower stratosphere, and only little dependence on latitude is found in that region. In the lower troposphere, refractivity uncertainty decreases with latitude. These findings have implications for both retrieval of tropospheric humidity from radio occultations and for assimilation of radio occultation data in numerical weather prediction models and reanalyses.

Temperature changes in the lower and middle stratosphere during 2001-2016 are evaluated using measurements from GPS Radio Occultation (RO) and Advanced Microwave Sounding Unit (AMSU) aboard the Aqua satellite. After downsampling of GPS-RO profiles according to the AMSU weighting functions, the spatially and seasonally resolved trends from the two data sets are in excellent agreement. The observations indicate that the middle stratosphere has cooled in the time period 2002-2016 at an average rate of –0.14±0.12 to –0.36±0.14 K/decade, while no significant change was found in the lower stratosphere. The meridionally and vertically resolved trends from high-resolution GPS-RO data exhibit a marked inter-hemispheric asymmetry and highlight a distinct boundary between tropospheric and stratospheric temperature change regimes matching the tropical thermal tropopause. The seasonal pattern of trend reveals significant opposite-sign structures at high and low latitudes, providing indication of seasonally varying change in stratospheric circulation.

We here present results from an evaluation of the Radio Occultation Meteorology Satellite Application Facility (ROM SAF) gridded monthly mean climate data record (CDR v1.0), based on Global Positioning System (GPS) radio occultation (RO) data from the CHAMP (CHAllenging Minisatellite Payload), GRACE (Gravity Recovery and Climate Experiment), COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate), and Metop satellite missions. Systematic differences between RO missions, as well as differences of RO data relative to ERA-Interim reanalysis data, are quantified. The methods used to generate gridded monthly mean data are described, and the correction of monthly mean RO climatologies for sampling errors, which is essential for combining data from RO missions with different sampling characteristics, is evaluated. We find good overall agreement between the ROM SAF gridded monthly mean CDR and the ERA-Interim reanalysis, particularly in the 8–30 km height interval. Here, the differences largely reflect time-varying biases in ERA-Interim, suggesting that the RO data record has a better long-term stability than ERA-Interim. Above 30–40 km altitude, the differences are larger, particularly for the pre-COSMIC era. In the 8–30 km altitude region, the observational data record exhibits a high degree of internal consistency between the RO satellite missions, allowing us to combine data into multi-mission records. For global mean bending angle, the consistency is better than 0.04 %, for refractivity it is better than 0.05 %, and for global mean dry temperature the consistency is better than 0.15 K in this height interval. At altitudes up to 40 km, these numbers increase to 0.08 %, 0.11 %, and 0.50 K, respectively. The numbers can be up to a factor of 2 larger for certain latitude bands compared to global means. Below about 8 km, the RO mission differences are larger, reducing the possibilities to generate multi-mission data records. We also find that the residual sampling errors are about one-third of the original and that they include a component most likely related to diurnal or semi-diurnal cycles.

Instrument GRAS (Global Navigation Satellite System Receiver for Atmospheric Sounding) on-board of the Metop-A satellite was activated on 27 October 2006. Currently, Metop-A is a fully operational satellite with GRAS providing from 650–700 occultations per day. We describe our processing of GRAS data based on the modification of our OCC software, which was modified to become capable of reading and processing GRAS data. We perform a statistical comparison of bending angles and refractivities derived from GRAS data with those derived from ECMWF analyses. We conclude that GRAS data have error characteristics close to those of COSMIC data. In the height range 10–30 km, the systematic refractivity difference GRAS–ECMWF is of the order of 0.1–0.2 %, and the standard deviation is 0.3–0.6 %. In the lower troposphere GRAS refractivity and bending angle indicate a negative bias, which reaches its maximum value in the tropics. In particular the retrieved refractivity is biased by up to 2.5 %. The negative bias pattern is similar to that found in the statistical validation of COSMIC data. This makes it probable that the bias should not be attributed to the instrument design or hardware.

A radio occultation data processing system (OCC) was developed for numerical weather prediction and climate benchmarking. The data processing algorithms use the well-established Fourier integral operator–based methods, which ensure a high accuracy of retrievals. The system as a whole, or in its parts, is currently used at the Global Navigation Satellite System Receiver for Atmospheric Sounding (GRAS) Satellite Application Facility at the Danish Meteorological Institute, German Weather Service, and Wegener Center for Climate and Global Change. A statistical comparison of the inversions of the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) data by the system herein, University Corporation for Atmospheric Research (UCAR) data products, and ECMWF analyses is presented. Forty days of 2007 and 2008 were processed (from 5 days in the middle of each season) for the comparison of OCC and ECMWF, and 20 days of April 2009 were processed for the comparison of OCC, UCAR, and ECMWF. The OCC and UCAR inversions are consistent. For the tropics, the systematic difference between OCC and UCAR in the retrieved refractivity in the 2–30-km height interval does not exceed 0.1%; in particular, in the 9–25-km interval it does not exceed 0.03%. Below 1 km in the tropics the OCC – UCAR bias reaches 0.2%, which is explained by different cutoff and filtering schemes implemented in the two systems. The structure of the systematic OCC – ECMWF difference below 4 km changes in 2007, 2008, and 2009, which is explained by changes in the ECMWF analyses and assimilation schemes. It is estimated that in the 4–30-km height range the OCC occultation processing system obtains refractivities with a bias not exceeding 0.2%. The random error ranges from 0.3%–0.5% in the upper troposphere–lower stratosphere to about 2% below 4 km. The estimate of the bias below 4 km can currently be done with an accuracy of 0.5%–1% resulting from the structural uncertainty of the radio occultation (RO) data reflecting the insufficient knowledge of the atmospheric small-scale structures and instrumental errors. The OCC – UCAR bias is below the level of the structural uncertainty.

[1] To examine the claim that Global Positioning System (GPS) radio occultation (RO) data are useful as a benchmark data set for climate monitoring, the structural uncertainties of retrieved profiles that result from different processing methods are quantified. Profile-to-profile comparisons of CHAMP (CHAllenging Minisatellite Payload) data from January 2002 to August 2008 retrieved by six RO processing centers are presented. Differences and standard deviations of the individual centers relative to the inter-center mean are used to quantify the structural uncertainty. Uncertainties accumulate in derived variables due to propagation through the RO retrieval chain. This is reflected in the inter-center differences, which are small for bending angle and refractivity increasing to dry temperature, dry pressure, and dry geopotential height. The mean differences of the time series in the 8 km to 30 km layer range from −0.08% to 0.12% for bending angle, −0.03% to 0.02% for refractivity, −0.27 K to 0.15 K for dry temperature, −0.04% to 0.04% for dry pressure, and −7.6 m to 6.8 m for dry geopotential height. The corresponding standard deviations are within 0.02%, 0.01%, 0.06 K, 0.02%, and 2.0 m, respectively. The mean trend differences from 8 km to 30 km for bending angle, refractivity, dry temperature, dry pressure, and dry geopotential height are within ±0.02%/5 yrs, ±0.02%/5 yrs, ±0.06 K/5 yrs, ±0.02%/5 yrs, and ±2.3 m/5 yrs, respectively. Although the RO-derived variables are not readily traceable to the international system of units, the high precision nature of the raw RO observables is preserved in the inversion chain.

We discuss the processing of GRAS radio occultation (RO) data done at the GRAS Satellite Application Facility. The input data consists of operational near-real time bending angles from December 2010 from the Metop-A satellite operated by EUMETSAT. The data are processed by an Abel inversion algorithm in combination with statistical optimization based on a two-parameter fit to an MSIS climatology. We compare retrieved refractivity to analyses from ECMWF. It is found that for global averages, the mean differences to ECMWF analyses are smaller than 0.2% below 30 km (except near the surface), with standard deviations around 0.5% for altitudes between 8 and 25 km. The current processing is limited by several factors, which are discussed. In particular, the penetration depth for rising occultations is generally poor, which is related to the tracking of the L2 signal. Extrapolation of the difference between the L1 and L2 signals below the altitude where L2 is lost is possible and would generally allow deeper penetration of retrieved refractivity profiles into the lower troposphere.

[1] Processing of radio occultation data requires filtering and quality control for the noise reduction and sorting out corrupted data samples. We introduce a radio holographic filtering algorithm based on the synthesis of canonical transform (CT2) and radio holographic focused synthesized aperture (RHFSA) methods. The field in the CT2-transformed space is divided by a reference signal to subtract the regular phase variation and to compress the spectrum. Next, it is convolved with a Gaussian filter window and multiplied by the reference signal to restore the phase variation. This algorithm is simple to implement, and it is numerically efficient. Numerical simulation of processing radio occultations with a realistic receiver noise indicates a good performance of the method. We introduce a new technique of the error estimation of retrieved bending angle profiles based on the width of the running spectra of the transformed wavefield multiplied with the reference signal. We describe a quality control method for the discrimination of corrupted samples in the L2 channel, which is most susceptible to signal tracking errors. We apply the quality control and error estimation techniques for the processing of data acquired by Challenging Minisatellite Payload (CHAMP) and perform a statistical comparison of CHAMP data with the analyses of the German Weather Service (DWD). The statistical analysis shows a good agreement between the CHAMP and DWD error estimates and the observed CHAMP–DWD differences. This corroborates the efficiency of the proposed quality control and error estimation techniques.

This paper has been withdrawn., Comment: This paper has been withdrawn. Its final version will be published in Journal of Geophysical Research

We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of these models, we devote the main part of this review to analyzing the impact of walls on their critical behavior. We discuss the possible boundary universality classes for the DP and BARW models, which can be described by a general scaling theory which allows for two independent surface exponents in addition to the bulk critical exponents. Above the upper critical dimension $d_c$, we review the use of mean field theories, whereas in the regime $d, Comment: 37 pages (including figures); journal-ref + ref added