Abstract. 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.

Abstract. 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.

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.

Abstract. 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.

Abstract. The upcoming Ice Cloud Imager (ICI) radiometer, to be launched on board the second generation of European operational meteorological satellites (Metop-SG), will be the first microwave imager to provide sub-millimeter observations of the atmosphere. The Microwave Imager (MWI) radiometer will be flown on the same satellites and complement the ICI sensor with observations at traditional millimeter wavelengths. The addition of these two new passive microwave sensors to the global system of earth observation satellites opens up opportunities for synergistic satellite missions aiming to maximize the scientific return of the Metop-SG program. This study analyzes the potential benefits of combining observations of the MWI and ICI radiometers with a 94-GHz cloud radar for the retrieval of frozen hydrometeors. Starting from a simplified numerical experiment, it is shown that the complementary information content in the radar and radiometer observations can help to better constrain the particle size distribution of ice particles in the atmosphere. The feasibility of the combined retrieval is demonstrated by applying a one-dimensional, variational cloud-retrieval algorithm to simulated observations from a high-resolution atmospheric model. Comparison of the results with passive- and radar-only versions of the retrieval algorithm confirms that synergies between the active and passive observations allow an improved retrieval of microphysical properties of frozen hydrometeors. The effect of the assumed ice particle shape on the results is analyzed and found to be critical for obtaining good retrieval performance. In addition to this, the synergistic retrieval shows improved sensitivity to liquid water in both warm and supercooled clouds. The results of this study clearly demonstrate the potential of the combined observations to constrain the microphysical properties of ice hydrometeors which can help to reduce errors in retrieved profiles of mass- and number densities.