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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.

Many studies have by now demonstrated the accuracy of GNSS Radio Occultation (RO) data, and their usefulness as a stable climate reference. Homogeneity of the data records are obtained by reprocessing of the data using uniform processing software throughout the length of the climate record. Version 1 of the ROM SAF Climate Data Record (CDR), based on Metop, CHAMP, GRACE, and COSMIC data, covers a continuous 15-year period from 2002 to 2016. The CDR is extended in time by an Interim CDR (ICDR) which is regularly updated nearly up to present time, and the combined time series is now long enough (20 years) to begin detection of climate trends. We here present results from recent climate applications of RO data: bending angle and temperature trends in the upper troposphere and stratosphere, including the first RO contribution to the IPCC 6th Assessment Report. Furthermore, we outline ROM SAF plans for generating RO climate data records. This includes calculating uncertainty estimates and generating homogenized water vapour climate data records based on a one-dimensional variational retrieval using detrended background data.The Radio Occultation Meteorology Satellite Application Facility (ROM SAF) is a decentralized operational processing facility under EUMETSAT. The main objective of the ROM SAF is to generate and deliver operational radio occultation products from GNSS RO instruments onboard Metop, Metop-SG, Sentinel-6 Michael Freilich and other satellites for NWP and climate applications. The ROM SAF CDR and ICDR is publically available from: http://www.romsaf.org. Further information about the ROM SAF products and services are available at this website.

The Radio Occultation (RO) technique is based on measurements of phase shifts of GNSS radio waves by an instrument onboard a low-Earth orbiting satellite. The processing of the measurements yields the refractive index of the Earth’s atmosphere, from which the temperature, pressure, and humidity fields can be retrieved. It is a limb-sounding technique, with a high vertical resolution, and with observational information retrieved from near-surface to the upper stratosphere. Numerous studies have demonstrated the accuracy of GNSS Radio Occultation (RO) data, and their usefulness as a stable climate reference. Homogeneity of the data records are obtained by reprocessing of the data using uniform processing software and a priori data throughout the length of the climate record. We here present results from a validation of the 17-year ROM SAF RO Climate Data Record (CDR), based on a new reprocessing of Metop, CHAMP, GRACE, and COSMIC data using excess-phase and amplitude data from EUMETSAT (the Metop mission) and UCAR/CDAAC (the CHAMP, GRACE, COSMIC, and Metop missions).A central issue for the generation of RO-based CDRs is whether data from different satellite missions can be combined to form long time series of multi-mission data. This presentation explores the consistency of gridded monthly-mean data from different RO missions through comparison with ERA-Interim reanalysis data, and through a study of mission differences during mission overlap periods. It is shown that within a core region from the upper troposphere to the middle stratosphere, roughly 8 to 35-40 kilometers (depending on latitude and geophysical variable), there is a high consistency amongst the RO missions, allowing for the construction of long-term stable data sets for use in climate studies and climate monitoring.

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.

The fact that fluctuations of refractivity may result in a systematic negative shift of the phase of waves propagating in a random medium is known for a long time. Tatarskii was the first to reveal it, and von Eshleman put this into the context of the radio occultation sounding of planetary atmospheres. In this paper, we show that this effect may also be one of the causes of the negative bias of refractivity retrieved for radio occultation observations of the Earth's atmosphere. We perform theoretical estimates of this effect based on the Rytov approximation. These estimates, however, do not consider the regular refraction, which may significantly change the magnitude of this effect. We perform numerical simulations of radio occultations, based on the Kolmogorov-von Karman isotropic spectrum of refractivity fluctuations, with the internal and external scales and magnitude tuned so as to reproduce the realistic level of the variance of retrieved refractivity and the amplitude fluctuations of the modeled signals. The model of the regular atmosphere is based on analyses of the European Centre for Medium-Range Weather Forecasts. We show that it is possible to set up a vertical profile of the structural constant of the fluctuation spectrum such that it will result in a systematic shift and variances of the retrieved refractivity consistent with those observed for COSMIC measurements.

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] The multiple phase screens technique is often used for modeling wave propagation and radio occultation sounding of the atmosphere. The last step of this procedure is the propagation from the last phase screen to the observation orbit of the spaceborne receiver. This step was formerly performed by the computation of multiple diffractive integrals, which impairs the numerical efficiency of the algorithm. We introduce an asymptotic method of wave propagation in vacuum from the last phase screen to a generic observation path. The exact solution is written in the form of the Zverev Transform, which belongs to the class of Fourier Integral Operators (FIO). The phase function of such an operator can be derived from the geometric optical equations. We construct an approximation for the Zverev Transform, utilizing the linearization of the equation of the geometric optical ray propagation in the vicinity of a smooth model of the ray structure. This permits the design of a fast numerical algorithm based on an FFT. Numerical simulations are performed for microwave propagation through a model atmosphere based on realistic gridded global fields of meteorological parameters. The new method based on the Linearized Zverev Transform is compared with the standard combination of multiple phase screens and diffractive integrals and with the asymptotic forward modeling for the propagation of centimeter waves in the atmosphere on limb paths. This method is especially useful for modeling LEO–LEO microwave occultations at frequencies of 9–30 GHz. The simulations demonstrate a high accuracy and numerical efficiency of the proposed method.

[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

The developments of an operational system for processing of radio occultations from the GRAS (Global navigation satellite system Receiver for Atmospheric Sounding) receiver onboard the future Metop satellite is the primary scope of the EUMETSAT project: GRAS Satellite Application Facility (SAF). The planned GRAS SAF data products and processing system is discussed together with a preliminary product validation based on statistical analysis of retrieved refractivity and temperature using radio occultation data from the German CHAMP (CHAllenging Minisatellite Payload) satellite. The CHAMP data from the first 8 weeks of 2003 have been processed using the GRAS SAF retrieval system and we present the results as compared to the ECMWF. The mean difference in refractivity is approx. 0.5% with standard deviations less than 1% between 8–25 km and approximately 2% both close to the surface and at 35 km.

We discuss the application of canonical transform (CT) methods for analyzing radio occultations with multipath behavior. In the present work we discuss a mapping to the representation of approximate impact parameter. This method generalizes the full spectrum inversion (FSI) method for the case of noncircular orbits. The method is based on mapping the field by a Fourier integral operator that maps directly from the measured time-dependent field to the impact parameter representation without first doing a back propagation. Furthermore, our method allows for simple, asymptotic direct modelling of wave propagation. We perform processing of simulated radio occultations and show that our method provides the same accuracy and resolution as the standard CT method.

[1] Fourier integral operators (FIOs) are used for constructing asymptotic solutions of wave problems and for the generalization of the geometrical optics. Geometric optical rays are described by the canonical Hamilton system, which can be written in different canonical coordinates in the phase space. The theory of FIOs generalizes the formalism of canonical transforms for solving wave problems. The FIO associated with a canonical transform maps the wave field to a different representation. Mapping to the representation of ray impact parameter was used in the formulation of the canonical transform (CT) method for processing radio occultation data. The full-spectrum inversion (FSI) method can also be looked at as an FIO associated with a canonical transform of a different type. We discuss the general principles of the theory of FIOs and formulate a generalization of the CT and FSI techniques. We derive the FIO that maps radio occultation data measured along the low Earth orbiter orbit without first applying back propagation. This operator is used for the retrieval of refraction angles and atmospheric absorption. We give a closed derivation of the exact phase function of the FIO obtained in the “phase matching” approach by Jensen et al. [2004] We derive a novel FIO algorithm denoted CT2, which is a modification and improvement of FSI. We discuss the use of FIOs for asymptotic direct modeling of radio occultation data. This direct model is numerically much faster then the multiple phase screen technique. This is especially useful for simulating LEO-LEO occultations at frequencies of 10–30 GHz.

The EUMETSAT network of Satellite Application Facilities (SAFs) will, to­gether with the EUMETSAT central facilities, constitute the future ground segments for the Meteosat Second Generation and EUMETSAT Polar System (EPS)/Metop satellites. SAFs are located in national meteorological offices or other approved institutes of EUMETSAT member states. The scope of the SAF activities will be to deliver products and/or software to derive these products, at the level of meteorological parameters, based primarily on the satellite data. The GRAS (Global Navigation Satellite System Receiver for Atmospheric Sounding) SAF will receive raw and pre-processed GPS radio occultation data from the GRAS instrument onboard the EPS/Metop satellite, process these into vertical profiles of refractivity, temperature, pressure, and humidity, and distribute these products continuously to numerical weather prediction and climate monitoring users. The GRAS SAF products promise globally distributed high-vertical resolution data on a 24 hour-basis, forming a considerable improvement on today’s measurement methods regarding coverage, vertical resolution, frequency, and cost. The accuracy requirements of the products vary with height. The expected root mean square error on temperature will be between 0.5 and 5 K, on pressure between 0.5 and 2 hPa, on specific humidity between 0.025 and 1 g/kg, and on refractivity between 0.1 and 2 %. Vertical resolution will be between 0.3 and 3 km in the vertical range covered from surface up to 50 km. A second objective of the GRAS SAF is to supply software for 4D-VAR assimilation of radio occultation data into Numerical Weather Prediction (NWP) models. The GRAS SAF is expected to distribute and archive atmospheric products from around 500 occultations per day at least through the expected project lifetime of 15 years. The main users of the GRAS SAF products will be meteorolo­gists doing NWP data assimilation, and users from the climate research and atmospheric science communities, needing comprehensive, globally distributed temperature, pressure, and humidity information. The products will come in two types: Near-Real Time Products (for NWP), disseminated less than three hours after acquisition, Offline Products (im­proved, for climate research), available less than 30 days after acquisition. The focus of this paper is on the design of the operational GRAS SAF facility. The GRAS SAF processing system and data products will be described and the user requirements for both Numerical Weather Prediction (NWP) and climate monitoring will be presented.

We have analyzed radio occultation simulations containing atmospheric multipath behavior. In the case where the medium and the satellite orbits are spherically symmetric the multipath behavior can be unfolded by a Fourier transform of the measured signal. However, small deviations from circular orbits may imply that the multipath behavior cannot be completely unfolded due to the fact that a given instantaneous frequency may occur at more than one time instant. In order to resolve the multipath behavior for realistic satellite orbits, we use the full-spectrum inversion approach and modify the measured signal by a phase model before carrying out a Fourier transform. For certain models, which depend on the measured phase of the simulated signal, we find that multipath behavior can be successfully unfolded. Even very strong multipath behavior, leading to critical refraction, can in some cases also be handled. The combined effect of applying a model and a Fourier transform can be viewed as a specific type of a canonical transform.

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