Combining line-by-line spectral integration with three-dimensional Monte Carlo (MC) solvers is the most accurate approach for simulating radiative transfer in cloudy atmospheres. However, this method is one of the most computationally expensive. This work presents approaches to reduce this computational cost without any loss of accuracy. For this purpose, the proposed methodology jointly exploits two complementary acceleration techniques: gas model reformulation on the one hand, and the use of quasi-random low-discrepancy sampling, i.e. Quasi-Monte Carlo (QMC), on the other. The key observation is that different combinations of these two techniques lead to significantly different costs of radiative transfer calculations in cloudy atmospheres. Crucially, these two techniques do not act independently: their combination yields a synergy that exceeds the product of their individual gains and that depends strongly on the scattering regime. Transmissivity-based models of gas radiative properties (here the ℓ-distribution method) are shown to reduce the dimensionality of the radiative transfer problem by one unit compared to absorption-coefficient formulations (here the line-by-line and correlated k-distribution approaches). This allows QMC estimators to converge faster than standard MC sampling, especially in clear-sky conditions. In scattering scenarios, a forced scattering technique is additionally employed. This method increases the advantage of QMC compared to MC by partially fixing the number of random variables required to generate photon paths. All three strategies (gas model reformulation, quasi-random sampling, and forced scattering) are applied in the thermal infrared using the 3DMCPOL atmospheric radiative transfer model. They are then evaluated on three configurations: a cloud-free absorbing atmosphere, a thin cloud, and an optically thick cloud. Results demonstrate that the computational efficiency of the methods strongly depends on the scattering optical thickness: while the required photon count is reduced by up to a factor of 1700 in clear-sky conditions, the gain in terms of photon number remains significant in scattering configurations, with reduction factors exceeding 300 for high thin clouds and reaching nearly 100 for optically thick clouds.

Accurate models of gas radiation are required for the analysis of atmospheric remote sensing data. These models need to be CPU efficient in order to comply with the exponential growth of data provided by the most recent generations of satellite instruments. In this paper, we describe two methods to treat gaseous absorption in satellite-based remote sensing scenarios. The two approaches are founded on statistical/machine learning (SL/ML) strategies. Compared to most works that only focus on a single SL/ML model, a detailed comparison is provided in this paper between a physics-informed SL method founded on a double mathematical induction strategy, called the dependent ALD (Augmented L-Distribution) model, and a purely data driven ML model (DDML). Results of the two approaches are assessed against reference LBL calculations and compared with a Correlated K-Distribution (CKD) model both in terms of accuracy and CPU cost. The two SL/ML models are shown to reach an accuracy higher than 0.5% at a small fraction (three orders of magnitude below) of the CPU cost of high-resolution calculations. The two methods open new possibilities for fast though accurate forward modeling of satellite remote sensing data.

The French-Israeli space-borne C3IEL (Cluster for Cloud evolution, ClImate and Lightning) mission aims at providing new insights on convective clouds, at high spatial and temporal resolutions, close to the scales of the individual convective eddies. The mission will simultaneously characterize the convective cloud dynamics, the interactions of clouds with the surrounding water vapor, and the lightning activity. The C3IEL mission consists in a short-baseline (~150 km) train of 2 synchronized nano-satellites. Each nano-satellite carries a visible camera (670 nm) for cloud imagery at a spatial resolution of ~20 meters, near-infrared water vapor imagers (1.04, 1.13 et 1.37 µm) measuring in and near the water vapor absorption bands, and a lightning imager (777.4 nm) and at least one photometer (777.4 nm). The scientific objectives of the C3IEL mission, i.e. documenting the 3D evolution of the clouds’ surface, entrainment of water vapor, and electrification, will be first reminded. Then, we will introduce the satellite train configuration, the different sensors of the mission and the innovative and different observational strategy that will be applied during daytime and nighttime. We will then detail the expected observations and products, including the ones related to lightning.

A retrieval algorithm of integrated water vapor content above cloud, using shortwave infrared observations, is developed and evaluated through idealized and realistic atmospheric profiles, with its application currently limited to oceanic regions and latitudes within ±60°. Water vapor plays a crucial role in cloud formation and development, particularly in the formation of clouds resulting from convective processes. The resulting convective cloud locally influences the spatio-temporal variability of atmospheric water vapor content, through exchanges between cloud and its immediate environment. Therefore, a better understanding of the water vapor content above and around clouds is necessary to improve our comprehension of interactions between water vapor and cloud to better constrain Large-Eddy Simulations and numerical weather forecasting models. The algorithm was developed for the Cluster for Cloud evolution, ClImatE and Lightning space mission project. This mission, scheduled for 2028, aims to enhance our knowledge of the 3D convective cloud development velocities, the electrical activity associated with convective systems, and the water vapor content above and around the cloud. The retrieval algorithm presented in this study uses a Bayesian probabilistic approach, the optimal estimation method. The atmosphere is assumed to be composed of homogeneous plane-parallel layers, and synthetic radiance datasets were generated to test the developed retrieval algorithm. The feasibility of retrieving the integrated water vapor content above the cloud over the ocean from shortwave infrared radiances is shown to have, under idealized vertically homogeneous cloud profiles, absolute errors less than 2 kg m−2 for optically thick clouds or when the integrated water vapor content is below 20 kg m−2 and less than 1 kg m−2 for very thick clouds with an optical thickness exceeding 150. Tests using realistic water vapor and cloud extinction profiles that present non-homogeneous vertical distributions show that integrated water vapor content above water type clouds could be retrieved with a Root-Mean-Square Error related to cloud vertical penetration of approximately less than 1 kg m−2 except for optically thin and low-level clouds (cloud optical thickness less than 50 and cloud top height less than 2 km). For very low water vapor content encountered in the presence of high deep convective clouds, the retrieval algorithm tends to systematically overestimate the retrieved water vapor content due to an overestimation of the cloud extinction profile in the upper part of the cloud in the inversion model.

We performed Monte Carlo simulations of single-wavelength lidar signals from multi-layered clouds with special attention focused on the multiple-scattering (MS) effect in regions of the cloud-free molecular atmosphere (i.e. between layers or outside a cloud system). Despite the fact that the strength of lidar signals from the molecular atmosphere is much lower compared to the in-cloud intervals, studies of MS effects in such regions are of interest from scientific and practical points of view. The MS effect on lidar signals always decreases with the increasing distance from the cloud far edge. The decrease is the direct consequence of the fact that the forward peak of particle phase functions is much larger than the receiver field of view (RFOV). Therefore, the photons scattered within the forward peak escape the sampling volume formed by the RFOV (i.e. the escape effect). We demonstrated that the escape effect is an inherent part of MS properties within the free atmosphere beyond the cloud far edge. In the cases of the ground-based lidar, the MS contribution is lower than 5 % within the regions of the cloud-free molecular atmosphere with a distance from the cloud far edge of about 1 km or higher. In the cases of the space-borne lidar, the rate of decrease of the MS contribution is so slow that the threshold of 5 % can hardly be reached. In addition, the effect of non-uniform beam filling is extremely strong. Therefore, practitioners should employ, with proper precautions, lidar data from regions below the cloud base when treating data of a space-borne lidar. In the case of two-layered cloud, the distance of 1 km is sufficiently large so that the scattered photons emerging from the first layer do not affect signals from the second layer when we are dealing with the ground-based lidar. In contrast, signals from the near edge of the second cloud layer are severely affected by the photons emerging from the first layer in the case of a space-borne lidar. We evaluated the Eloranta model (EM) in extreme conditions and showed its good performance in the cases of ground-based and space-borne lidars. At the same time, we revealed the shortcoming that can affect practical applications of the EM. Namely, values of the key parameters – i.e. the ratios of phase functions in the backscatter direction for the nth-order-scattered photon and a singly scattered photon – depend not only on the particle phase function but also on the distance from a lidar to the cloud and the receiver field of view. Those ratios vary within a quite large range, and the MS contribution to lidar signals can be largely overestimated or underestimated if erroneous values of the ratios are assigned to the EM.

Obtaining accurate values of atmospheric transmissivities of non-uniform paths remains a challenging task for the forward modelling of satellite radiance as well as for radiative forcing calculations. In this work, we present a fast though accurate modelling approach called the Mixture L-distribution (MLD) method. This technique consists of the application of the L-distribution approach to spectral intervals over which gas spectra are scaled (linearly correlated). The method to construct intervals of scaling is founded on an adaptation of the "multispectral technique", initially proposed for high temperature engineering applications, to atmospheric paths.

The objective of the present work is to describe a technique to approximate atmospheric path transmissivities using a recurrent structure, following a method proposed recently but limited to date to high temperature applications. The physical model together with its underlying statistical assumptions is detailed. It is found to involve a rather simple analytical formula that applies both to two-layers systems and to more general multi-layers non-uniform configurations. This treatment of path non-uniformities uses several unknown parameters that are first trained on LBL reference data in two-layers configurations to illustrate the relevance of the proposed approximate model. Then, in a second time, model's parameters are trained on non-uniform path transmission curves representative of multi-layers atmospheres. The corresponding recurrent formulation is shown to provide accurate estimates of transmissivities of non-uniform atmospheric paths (maximum relative errors are below 0.35% in all the considered test cases) at a very low CPU cost.

This article presents a realistic and novel method to estimate the solar radiant flux collected by the receiver of a solar power tower (SPT) system, taking into account the detailed atmospheric radiative transfer. It describes how an atmospheric radiative transfer Monte Carlo code is modified to solve the radiative transfer both in the atmosphere and within the concentrating system consisting of the heliostat field and the receiver. To validate the geometric modeling of a complete SPT (624 heliostats with 24 facets) as well as the estimation of its optical efficiency (both independent of the atmosphere), a comparison with the reference ray-tracing code “Solstice” is presented for two times of the day, two solar disk half-angles, and two heliostat surface slope errors. This new model allows the estimation of not only the optical losses but also, as in Moulana (2019), the gains due to atmospheric and environmental contributions i.e., radiant flux from circumsolar, aerosol scattering, ground reflection, etc. Annual average results (with a numerical uncertainty less than 0.01%) under clear sky conditions (without clouds) show that the gains are not negligible and could reach up to 0.414 MW (1.08% of the radiant flux collected by the receiver) for a relatively small SPT located in a desert area.

Structural patterns of cloud effective radius (ER) and liquid water content (LWC) profiles are essential variables of cloud lifecycle and precipitation processes, while observing cloud profiles from passive remote-sensing sensors remains highly challenging. Understanding whether there are typical structural patterns of ER and LWC profiles in liquid clouds and how they are linked to cloud entrainment or precipitating status is critical in developing algorithms to derive cloud profiles from passive satellite sensors. This study aims to address these questions and provide a preliminary foundation for the development of liquid cloud profile retrievals for the Multi-viewing, Multi-channel and Multi-polarization Imaging (3MI) sensor aboard the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) Polar System-Second Generation (EPS-SG) satellite, which is scheduled to be launched in 2025. Firstly, we simulate a large ensemble of stratocumulus cloud profiles using the Colorado State University (CSU) Regional Atmospheric Modeling System (RAMS). The empirical orthogonal function (EOF) analysis is adopted to describe the shape of simulated profiles with a limited number of elemental profile variations. Our results indicate that the first three EOFs of LWC and ER profiles can explain >90 % of LWC and ER profiles. The profiles are divided into four prominent patterns and all of these patterns can be simplified as triangle-shaped polylines. The frequency of these four patterns is found to relate to intensities of the cloud-top entrainment and precipitation. Based on these analyses, we propose a simplified triangle-shaped cloud profile parameterization scheme allowing us to represent these main patterns of LWC and ER. This simple yet physically realistic analytical model of cloud profiles is expected to facilitate the representation of cloud properties in advanced retrieval algorithms such as those developed for the 3MI/EPS-SG.

This paper presents the Backscattering Lidar Signal Simulator (BLISS), an end-to-end lidar simulator developed by the Centre National d’Etudes Spatiales (CNES). We computed the constant multiple-scattering (MS) coefficient of BLISS with a Monte Carlo (MC) code in the framework of CALIOP/CALIPSO observations for different homogeneous and plane-parallel stratocumulus and cirrus cloud geophysical scenes. The MS coefficient varies from 0.46 to 0.63. Then we evaluated the Level 1 products of BLISS. Above and in-cloud relative difference between the attenuated backscattering coefficient vertical profile simulated by BLISS and by the MC code is smaller than 0.5% under single-scattering regime and smaller than 10% (30% if optical depth of cirrus is large) under multiple-scattering regime, thus confirming the robustness of BLISS.

Abstract. In remote sensing applications, clouds are generally characterized by two properties: cloud optical thickness (COT) and effective radius of water/ice particles (Reff). Most of the current operational passive remote sensing algorithms use a mono-angular bi-spectral method to retrieve COT and Reff. They are based on pre-computed lookup tables while assuming a homogeneous plane-parallel cloud layer and without considering measurement errors and the choice of ancillary data. We use the formalism of the optimal estimation method applied to near-infrared multi-angular measurements, to retrieve COT and Reff, and the corresponding uncertainties related to the measurement errors, the ancillary data, and the cloud model assumption. The used measurements were acquired by the airborne radiometer OSIRIS (Observing System Including PolaRization in the Solar Infrared Spectrum), developed by the Laboratoire d'Optique Atmosphérique. It provides multi-angular measurements at tens of meters resolution, very suitable for refining our knowledge of cloud properties and their high spatial variability. OSIRIS is based on the POLDER concept as a prototype of the future 3MI space instrument planned to be launched on the EUMETSAT-ESA MetOp-SG platform in 2023. The used approach allows the exploitation of all the angular information available for each pixel to overcome the radiance angular effects. More consistent cloud properties with lower uncertainty compared to operational mono-directional retrieval methods (MODIS-like methods) are then obtained. The framework of the optimal estimation method provides also the possibility to estimate uncertainties of different sources. Three types of errors were evaluated: (1) Errors related to measurement uncertainties, which reach 10 % for high values of COT and Reff, (2) errors related to an incorrect estimation of the ancillary data that remain below 0.5 %, (3) errors related to the simplified cloud physical model assuming homogeneous plane-parallel cloud and the independent pixel approximation. We show that not considering the in-cloud heterogeneous vertical profiles and the 3D radiative transfer effects lead to uncertainties on COT and Reff exceeding 10 %.

Abstract. We performed extensive Monte Carlo (MC) simulations of single-wavelength lidar signals from a plane-parallel homogeneous layer of atmospheric particles and developed an empirical model to account for the multiple scattering in the lidar signals. The simulations have taken into consideration four types of lidar configurations (the ground based, the airborne, the CALIOP, and the ATLID) and four types of particles (coarse aerosol, water cloud, jet-stream cirrus and cirrus). Most of simulations were performed with the spatial resolution of 20 m and the particles extinction coefficient εp between 0.06 km−1 and 1.0 km−1. The resolution was of 5 m for high values of εp (up to 10.0 km−1). The majority of simulations for ground-based and airborne lidars were performed at two values of the receiver field-of-view (RFOV): 0.25 mrad and 1.0 mrad. The effect of the width of the RFOV was studied for the values up to 50 mrad. The proposed empirical model is a function that has only three free parameters and approximates the multiple-scattering relative contribution to lidar signals. It is demonstrated that the empirical model has very good quality of MC data fitting for all considered cases. Special attention was given to the usual operational conditions, i.e., low distances to a particles layer, small optical depths and quite narrow receiver field-of-views. It is demonstrated that multiple scattering effects cannot be neglected when the distance to a particles layer is about 8 km or higher and the full RFOV is of 1.0 mrad. As for the full RFOV of 0.25 mrad, the single scattering approximation is acceptable for aerosols (εp ≲ 1.0 km−1), water clouds (εp ≲ 0.5 km−1), and cirrus clouds (εp ≤ 0.1 km−1). When the distance to a particles layer is of 1 km, the single scattering approximation is acceptable for aerosols and water clouds (εp ≲ 1.0 km−1, both RFOV = 0.25 and RFOV = 1 mrad). As for cirrus clouds, the effect of multiple scattering cannot be neglected even at such low distance when εp ≳ 0.5 km−1.

Abstract. As part of the EUREC4A (Elucidating the role of cloud-circulation coupling in climate) field campaign, which took place in January and February 2020 over the western tropical Atlantic near Barbados, the French SAFIRE ATR42 research aircraft conducted 19 flights in the lower troposphere. Each flight followed a common flight pattern that sampled the atmosphere around the cloud-base level, at different heights of the subcloud layer, near the sea surface and in the lower free troposphere. The aircraft's payload included a backscatter lidar and a Doppler cloud radar that were both horizontally oriented, a Doppler cloud radar looking upward, microphysical probes, a cavity ring-down spectrometer for water isotopes, a multiwavelength radiometer, a visible camera and multiple meteorological sensors, including fast rate sensors for turbulence measurements. With this instrumentation, the ATR characterized the macrophysical and microphysical properties of trade-wind clouds together with their thermodynamical, turbulent and radiative environment. This paper presents the airborne operations, the flight segmentation, the instrumentation, the data processing and the EUREC4A datasets produced from the ATR measurements. It shows that the ATR measurements of humidity, wind and cloud-base cloud fraction measured with different techniques and samplings are internally consistent, that meteorological measurements are consistent with estimates from dropsondes launched from an overflying aircraft (HALO), and that water isotopic measurements are well correlated with data from the Barbados Cloud Observatory. This consistency demonstrates the robustness of the ATR measurements of humidity, wind, cloud-base cloud fraction and water isotopic composition during EUREC4A. It also confirms that through their repeated flight patterns, the ATR and HALO measurements provided a statistically consistent sampling of trade-wind clouds and of their environment. The ATR datasets are freely available at the locations specified in Table 11.

A method to derive the 3D cloud envelope and the cloud development velocity from high spatial and temporal resolution satellite imagery is presented. The CLOUD instrument of the recently proposed C3IEL mission lends itself well to observing at high spatial and temporal resolutions the development of convective cells. Space-borne visible cameras simultaneously image, under multiple view angles, the same surface domain every 20 s over a time interval of 200 s. In this paper, we present a method for retrieving cloud development velocity from simulated multi-angular, high-resolution top of the atmosphere (TOA) radiance cloud fields. The latter are obtained via the image renderer Mitsuba for a cumulus case generated via the atmospheric research model SAM and via the radiative transfer model 3DMCPOL, coupled with the outputs of an orbit, attitude, and camera simulator for a deep convective cloud case generated via the atmospheric research model Meso-NH. Matching cloud features are found between simulations via block matching. Image coordinates of tie points are mapped to spatial coordinates via 3D stereo reconstruction of the external cloud envelope for each acquisition. The accuracy of the retrieval of cloud topography is quantified in terms of RMSE and bias that are, respectively, less than 25 and 5 m for the horizontal components and less than 40 and 25 m for the vertical components. The inter-acquisition 3D velocity is then derived for each pair of tie points separated by 20 s. An independent method based on minimising the RMSE for a continuous horizontal shift of the cloud top, issued from the atmospheric research model, allows for the obtainment of a ground estimate of the velocity from two consecutive acquisitions. The mean values of the distributions of the stereo and ground velocities exhibit small biases. The width of the distributions is significantly different, with higher a distribution width for the stereo-retrieved velocity. An alternative way to derive an average velocity over 200 s, which relies on tracking clusters of points via image feature matching over several acquisitions, was also implemented and tested. For each cluster of points, mean stereo and ground positions were derived every 20 s over 200 s. The mean stereo and ground velocities, obtained as the slope of the line of best fit to the mean positions, are in good agreement.

Clouds play a major role in Earth's energy budget and hydrological cycle. Clouds dynamical structure and mixing with the ambient air have a large impact on their vertical mass and energy fluxes and on precipitation. Most of the cloud evolution and mixing occurs at scales smaller than presently observable from geostationary orbit, which is less than 1 km. A satellite mission is planned for bridging this gap, named "Cluster for Cloud evolution, ClImatE and Lightning" (C3IEL). The mission is a collaboration between the Israeli (ISA) and French (CNES) space agencies, which is presently at the end of its Phase A. The planned mission will be constituted of a constellation of 2 to 3 nanosatellites in a sun synchronous early afternoon polar orbit, which will take multi-stereoscopic images of the field of view during an overpass. C3IEL will carry 3 instruments: (1) CLOUD visible imager at a spatial resolution of 20 m. The multi-stereoscopic reconstruction of the evolution of cloud envelops at a resolution better than 100 m and velocity of few m/s will provide an unprecedented information on the clouds dynamics and evolution. (2) WATER VAPOR imagers at 3 wavebands with different vapor absorption will provide vertically integrated water vapor around the cloud and possibly a 3-dimensional structure of the vapor around the clouds due to their mixing and evaporation with the ambient air. (3) Lightning Optical Imagers and Photometers (LOIP). The lightning sensors will provide a link between cloud dynamics and electrification at higher spatial resolution than previously available. C3IEL will provide presently missing observational evidence for the role of clouds at sub-km scale in redistributing the energy and water in the atmosphere, and of the relation between storm vigor and frequency of lightning activity.