A neural-network-based method, quantile regression neural networks (QRNNs), is proposed as a novel approach to estimating the a posteriori distribution of Bayesian remote sensing retrievals. The advantage of QRNNs over conventional neural network retrievals is that they learn to predict not only a single retrieval value but also the associated, case-specific uncertainties. In this study, the retrieval performance of QRNNs is characterized and compared to that of other state-of-the-art retrieval methods. A synthetic retrieval scenario is presented and used as a validation case for the application of QRNNs to Bayesian retrieval problems. The QRNN retrieval performance is evaluated against Markov chain Monte Carlo simulation and another Bayesian method based on Monte Carlo integration over a retrieval database. The scenario is also used to investigate how different hyperparameter configurations and training set sizes affect the retrieval performance. In the second part of the study, QRNNs are applied to the retrieval of cloud top pressure from observations by the Moderate Resolution Imaging Spectroradiometer (MODIS). It is shown that QRNNs are not only capable of achieving similar accuracy to standard neural network retrievals but also provide statistically consistent uncertainty estimates for non-Gaussian retrieval errors. The results presented in this work show that QRNNs are able to combine the flexibility and computational efficiency of the machine learning approach with the theoretically sound handling of uncertainties of the Bayesian framework. Together with this article, a Python implementation of QRNNs is released through a public repository to make the method available to the scientific community.

This study assesses the global distribution of mean atmospheric ice mass from current state-of-the-art estimates and its variability on daily and seasonal timescales. Ice water path (IWP) retrievals from active and passive satellite platforms are analysed and compared with estimates from two reanalysis data sets, ERA5 (European Centre for Medium-range Weather Forecasts Reanalysis 5, ECMWF) and MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications 2). Large discrepancies in IWP exist between the satellite data sets themselves, making validation of the model results problematic and indicating that progress towards a consensus on the distribution of atmospheric ice has been limited. Comparing the data sets, zonal means of IWP exhibit similar shapes but differing magnitudes, with large IWP values causing much of the difference in means. Diurnal analysis centred on A-Train overpasses shows similar structures in some regions, but the degree and sign of the variability varies widely; the reanalyses exhibit noisier and higher-amplitude diurnal variability than borne out by the satellite estimates. Spatial structures governed by the atmospheric general circulation are fairly consistent across the data sets, as principal component analysis shows that the patterns of seasonal variability line up well between the data sets but disagree in severity. These results underscore the limitations of the current Earth observing system with respect to atmospheric ice, as the level of consensus between observations is mixed. The large-scale variability of IWP is relatively consistent, whereas disagreements on diurnal variability and global means point to varying microphysical assumptions in retrievals and models alike that seem to underlie the biggest differences.

Radiances from microwave temperature sounders have been assimilated operationally at ECMWF for two decades, but observations significantly affected by clouds and precipitation have been screened out. Extending successful assimilation beyond clear-sky scenes is a challenge that has taken several years of development to achieve. In this paper we describe the all-sky treatment of AMSU-A, which enables greater numbers of temperature sounding radiances to be used in meteorologically active parts of the troposphere. Successful all-sky assimilation required combining lessons learned from the clear-sky assimilation of AMSU-A with the approach initially developed for humidity-sensitive microwave radiances. This concerned particularly observation thinning, error modeling, and variational quality control. As a result of the move to all-sky assimilation, the forecast impact of AMSU-A now replicates and exceeds that of the previous clear-sky usage. This is shown via trials in comparison to the current ECMWF assimilation system, judged with respect to forecast scores and background fits to independent observations. Persistently cloudy regions and phenomena such as tropical cyclones are better sampled when assimilating AMSU-A in all-sky conditions, causing an increase of about 13% in used channel-5 radiances globally. These impacts are explored, with an emphasis on tropical cyclones in the 2019 season. Independent observations provide consistent evidence that representation of humidity is improved, for example, while extratropical Z500 forecasts are improved by about 0.5% out to at least day 2. On the strength of these results, assimilation of AMSU-A moved to all-sky conditions with the upgrade to IFS cycle 47R3 in October 2021.

Accurate measurements of ice hydrometeors are required to improve the representation of clouds and precipitation in weather and climate models. In this study, a newly developed, synergistic retrieval algorithm that combines radar with passive millimeter and sub-millimeter observations is applied to observations of three frontally generated, mid-latitude cloud systems in order to validate the retrieval and assess its capabilities to constrain the properties of ice hydrometeors. To account for uncertainty in the assumed shapes of ice particles, the retrieval is run multiple times while the shape is varied. Good agreement with in situ measurements of ice water content and particle concentrations for particle maximum diameters larger than 200 µm is found for one of the flights for the large plate aggregate and the six-bullet rosette shapes. The variational retrieval fits the observations well, although small systematic deviations are observed for some of the sub-millimeter channels pointing towards issues with the sensor calibration or the modeling of gas absorption. For one of the flights the quality of the fit to the observations exhibits a weak dependency on the assumed ice particle shape, indicating that the employed combination of observations may provide limited information on the shape of ice particles in the observed clouds. Compared to a radar-only retrieval, the results show an improved sensitivity of the synergistic retrieval to the microphysical properties of ice hydrometeors at the base of the cloud. Our findings indicate that the synergy between active and passive microwave observations may improve remote-sensing measurements of ice hydrometeors and thus help to reduce uncertainties that affect currently available data products. Due to the increased sensitivity to their microphysical properties, the retrieval may also be a valuable tool to study ice hydrometeors in field campaigns. The good fits obtained to the observations increase confidence in the modeling of clouds in the Atmospheric Radiative Transfer Simulator and the corresponding single scattering database, which were used to implement the retrieval forward model. Our results demonstrate the suitability of these tools to produce realistic simulations for upcoming sub-millimeter sensors such as the Ice Cloud Image or the Arctic Weather Satellite.

A fully physical, 1‐D variational inversion algorithm (1DVAR) has been developed to simultaneously retrieve total precipitable water (TPW), 10 m wind speed, and cloud liquid water path (CLWP) over ocean. Results presented are for the Global Precipitation Measurement Microwave Imager (GMI), but the algorithm is adaptable to any microwave imager. The Colorado State University 1DVAR is novel in that the observation error covariances are not assumed to be zero and empirical orthogonal functions are utilized to retrieve the structure of the water vapor profile, aided by GMI's high‐frequency channels. Validation against radiosonde and ocean buoy observations demonstrates a near zero bias for wind speed and a small positive bias for water vapor, respectively, with RMS errors that rival those of benchmark products. RMS errors against validation are 2.6 mm and 1.2 m/s for TPW and wind speed. No calibration adjustments were made to achieve these results, and no “truth” data were used to train the algorithm. The advantages of this fully physical inversion are its adaptability, transparency, and full description of retrieval errors. Sensitivities of the algorithm are explored in detail.

Remote sensing observations at sub-millimeter wavelengths provide higher sensitivity to small hydrometeors and low water content than observations at millimeter wavelengths, which are traditionally used to observe clouds and precipitation. They are employed increasingly in field campaigns to study cloud microphysics and will be integrated into the global meteorological observing system to measure the global distribution of ice in the atmosphere with the launch of the Ice Cloud Imager (ICI) radiometer on board the second generation of European operational meteorological satellites (Metop-SG). Observations at these novel wavelengths provide valuable information not only on their own but also in combination with complementary observations at other wavelengths. This study investigates the potential of combining passive sub-millimeter radiometer observations with a hypothetical W-band cloud radar for the retrieval of frozen hydrometeors. An idealized cloud model is used to investigate the information content of the combined observations and establish their capacity to constrain the microphysical properties of ice hydrometeors. A synergistic retrieval algorithm for airborne observations is proposed and applied to simulated observations from a cloud-resolving model. Results from the synergistic retrieval are compared to equivalent radar- and passive-only implementations in order to assess the benefits of the synergistic sensor configuration. The impact of the assumed ice particle shape on the retrieval results is assessed for all retrieval implementations. We find that the combined observations better constrain the microphysical properties of ice hydrometeors, which reduces uncertainties in retrieved ice water content and particle number concentrations for suitable choices of the ice particle model. Analysis of the retrieval information content shows that, although the radar contributes the largest part of the information in the combined retrieval, the radiometer observations provide complementary information over a wide range of atmospheric states. Furthermore, the combined observations yield slightly improved retrievals of liquid cloud water in mixed-phase clouds, pointing towards another potential application of combined radar–radiometer observations.