We present the Fourier-Space Spherical Harmonic Discrete Ordinate Method (FS-SHDOM), a deterministic solver of the full radiative transfer equation for horizontally homogeneous atmospheres illuminated by Gaussian beams. The method extends our previous Spectral Spherical Harmonic Discrete Ordinate Method (SSHDOM), developed for aircraft-based observations, to realistic spaceborne lidar geometries characterized by atmospheric domains extending over several tens of kilometers and Gaussian-beam footprints of only a few tens of meters. By exploiting the horizontal homogeneity of the atmosphere, the three-dimensional radiative transfer problem is reduced to a sequence of one-dimensional transport equations in Fourier space. This reduction yields a computationally efficient formulation while fully accounting for multiple scattering.Two independent numerical solution techniques are developed. The production algorithm is based on Picard iteration, whereas a Discrete Ordinate Method with Matrix Exponential (DOME) provides an independent direct solution of the discrete-ordinate equations for verification. Numerical results show excellent agreement between the two methods for allcloud optical thicknesses and observation geometries considered, while the Picard iteration reduces the computational cost by approximately a factor of 50. Excellent agreement is also obtained for off-axis observation geometries, in which the detector viewing direction deviates from the exact backscattering direction.The proposed formulation encompasses several classical radiative transfermodels as limiting cases, including the plane-parallel SHDOM formulation,the single-scattering approximation, and the Gaussian-beam lidar equation. In addition to providing an efficient tool for simulating multiple-scattering lidar observations, FS-SHDOM can serve as adeterministic reference solution for validating approximatemultiple-scattering models.

Shipping activities emit aerosols that can modify the microphysical and optical properties of low-level marine clouds. In the framework of the ESA ACtIon4Cooling (Aerosol Cloud Interactions for Cooling) project, marine clouds influenced by ship-track emissions are investigated as natural analogues to assess the monitoring capabilities of various Solar Radiation Modification (SRM) approaches, including Marine Cloud Brightening (MCB).In this study, we combine high-resolution satellite observations from SUOMI-NPP/VIIRS (Visible Infrared Imaging Radiometer Suite) and Sentinel-5p/TROPOMI (TROPOspheric Monitoring Instrument) with vessel density data from EMODNET (European Marine Observation and Data Network) to detect cloud anomalies in the shipping corridors and quantify the ship-relevant cloud perturbations. VIIRS-derived cloud variables include cloud top height, cloud top emissivity, effective radius, liquid water path, and optical depth, while TROPOMI provides similar cloud information in the Oxygen A-band. Additional TROPOMI L2 products such as the absorbing aerosol index, aerosol type, and tropospheric NO₂ columns can also provide suitable proxies for ship emissions. The detection of the ship-tracks can be further improved when actual AIS (Automatic Identification System) data are used instead of the monthly aggregated EMODNET vessel density maps.Cargo and tanker ships dominate the upper range of ship lengths, often between 150 and 300 meters, with some exceeding 400 meters, while passenger ships also include very large vessels over 200 meters, corresponding to cruise liners. Since ship length serves as a proxy for vessel capacity and engine power, larger ships generally consume more fuel and emit greater amounts of aerosol precursors. As a result, cargo, tanker, and passenger ships are more important for atmospheric emissions and ship track formation, even though smaller vessels might be more numerous.Perturbations of the cloud parameters due to ship emissions are detected using machine learning classifiers with Logistic Regression being the baseline and more advanced models like Random Forest Regressor and Gradient Boosting (XGBoost). To quantify the ship-relevant cloud perturbations, the detected perturbations are fed directly to the Radiative Transfer Model pyDOME, which returns the full radiance field together with TOA (top-of-the atmosphere) forcing, surface irradiance and heating‑rate profiles for every perturbation. In order to synthesize the observations-based results and to explore the large-scale implications of the perturbations in marine low-level clouds, simulations are conducted with the state-of-the-art atmospheric general circulation model ICON (the ICOsahedral Non-hydrostatic model).

Volcanic eruptions impact human populations and the environment, with volcanic ash contributing to these effects through its influence on air quality, agriculture, and air transportation. Traditional satellite observation methods for monitoring volcanic ash encounter several challenges, including distinguishing ash from other aerosols, coverage area limitations, frequency of observations, and the impact of adverse weather and atmospheric conditions. These issues highlight the need for supplementary satellite-based approaches to improve volcanic ash monitoring. This project introduces a new method that utilizes machine learning techniques to analyze UV and visible satellite data for detecting and classifying volcanic ash. The research focuses on exploring how satellite UV and visible light observations can be used to identify volcanic ash in the atmosphere. A classifier was developed using simulations from a radiative transfer model, which represents various atmospheric scenarios. This classifier is then applied to analyze spectral measurements obtained by the TROPOspheric Monitoring Instrument (TROPOMI) on the ESA Sentinel-5p satellite. The complexity of detecting and classifying volcanic ash arises not only from the presence of other aerosols in the atmosphere but also from the changing characteristics of the ash, influenced by the type of magma and ongoing alterations as the ash remains airborne. This research presents progress in tackling these challenges and in developing a complex algorithm that incorporates a wide range of parameters. The application of this method to the Raikoke eruption case study enables the identification of some volcanic ash, illustrating the potential of this approach. However, this case study also reveals the presence of misclassifications, highlighting the need for continuous improvement in the classifier. This research offers valuable insights into the detection and classification of volcanic ash, contributing to the enhancement of monitoring strategies for hazard mitigation.

This article introduces an innovative operational Bayesian neural network (BNN) framework for high-precision joint retrieval of aerosol optical depth (AOD) and aerosol layer height (ALH) with physically consistent uncertainty decomposition from TROPOMI hyperspectral measurements. Unlike conventional approaches, three different full-physics BNN architectures (implemented via Bayes-by-Backprop, Dropout, and Batch Norm (BN) techniques) are developed to simultaneously estimate target parameters and their heteroscedastic aleatoric uncertainties while preserving radiative transfer constraints. Epistemic uncertainties are quantified via Monte Carlo sampling of stochastic forward propagation, enabling systematic separation of data- versus model-driven uncertainties. A comprehensive validation demonstrates the following: 1) synthetic experiments show that epistemic uncertainties strongly correlate with retrieval errors, particularly for observing geometries outside the training data distribution, outperforming aleatoric estimates and 2) analyses using TROPOMI measurements demonstrate that the framework delivers comparable accuracy to operational products while providing unique uncertainty diagnostics. The framework's computational efficiency, combined with its probabilistic outputs, establishes a new paradigm for characterizing aerosol properties from satellite measurements, particularly valuable for climate and air quality applications.

The Ozone Monitoring Suite-Nadir (OMS-N), a state-of-the-art hyperspectral ultraviolet-visible (UV-VIS) sensor onboard China’s FengYun-3F (FY-3F) satellite, was launched in August 2023. Designed for a morning orbit, OMS-N represents a significant advancement in global atmospheric composition monitoring, offering an unprecedented spatial resolution of 7 km×7 km. The total ozone column (TOC) product derived from OMS-N is critical for climate modeling and UV radiation assessment. This study presents the first TOC retrievals from OMS-N, utilizing an adapted Differential Optical Absorption Spectroscopy (DOAS) algorithm. The retrieval algorithm overcomes traditional DOAS limitations by incorporating key innovations, including optimized radiative transfer calculations and refined a priori information on surface properties and ozone profiles, which are derived directly from OMS-N spectra rather than relying on external datasets or climatologies. Validation against ground-based measurements from Brewer, Dobson, and SAOZ instruments at 33 sites demonstrated strong agreement, with correlation coefficients mostly greater than 0.9. Comparisons with other well-established satellite instruments, including TROPOMI and GOME-2B, showed that OMS-N can consistently capture global seasonal ozone patterns, with biases typically within 2

This paper investigates the application of Physics-Informed Neural Networks (PINNs) for solving the inverse advection-diffusion problem to localize pollution sources. The study focuses on optimizing neural network architectures to accurately model pollutant dispersion dynamics under diverse conditions, including scenarios with weak and strong winds and multiple pollution sources. Various PINN configurations are evaluated, showing the strong dependence of solution accuracy on hyperparameter selection. Recommendations for efficient PINN configurations are provided based on these comparisons. The approach is tested across multiple scenarios and validated using real-world data that accounts for atmospheric variability. The results demonstrate that the proposed methodology achieves high accuracy in source localization, showcasing the stability and potential of PINNs for addressing environmental monitoring and pollution management challenges under complex weather conditions.

The two-LAyered snow Radiative Transfer (LART) model has been proposed for snow remote sensing applications. It is based on analytical approximations of the radiative transfer theory. The geometrical optics approximation has been used to derive the local snow optical parameters, such as the probability of photon absorption by ice grains and the average cosine of single light scattering in a given direction in a snowpack. The application of the model to the selected area in Antarctica has shown that the technique is capable of retrieving the snow grain size both in the upper and lower snow layers, with grains larger in the lower snow layer as one might expect due to the metamorphism processes. Such a conclusion is confirmed by ground measurements of the vertical snow grain size variability in Antarctica.

This paper presents an investigation into the use of a random forest (RF) model for retrieving chlorophyll content from Sentinel-3 satellite data. We train various RF regression models on available datasets and introduce a classifier to identify instances where predictions may be inaccurate. This classifier aids in filtering out less reliable cases, enhancing the overall accuracy of our models at the expense of reducing the amount of processed data. Additionally, we optimize the hyperparameters of this hybrid model to improve its performance further. Our findings illustrate the effectiveness of combining regression models with a classifier in environmental remote sensing, offering a promising method for improving the accuracy of satellite-derived chlorophyll measurements.

An advanced light scattering model for Total Internal Reflection Microscopy (TIRM) is presented. The model considers the specific TIRM geometry and deals with the scattering by an axisymmetric particle of arbitrary orientation placed in a stratified medium and the imaging of the scattered field. The scattered field is computed by truncating the scattered and internal field expansions and by using spherical and plane wave expansions for the free-space dyadic Green’s function. While the first expansion is valid outside a sphere enclosing the particle, the second one is valid outside the tangent planes bounding the particle from above and below. We demonstrate that in both cases, the results are the same, and thus, that the restrictive condition according to which the interface should not intersect the particle’s circumscribed sphere is not relevant. The image of the scattered field is computed by using the Debye diffraction integral and fast Fourier transform, while for a better reconstruction of the particle orientation, an image processing step consisting in a contour extraction and ellipse fitting is considered. The numerical simulations dealing with scattering by a prolate spheroid provide evidence of the remarkably sensitivity of the geometric parameters of the image ellipse to the particle orientation angles, as well as, of the integral response of the detector to the distance between the particle and the interface.

Photon transport within Earth’s atmosphere is a vital aspect of atmospheric science. The accurate modeling of radiative transfer is crucial for remote sensing data analysis. Yet, simulating the photon transport in multi-dimensional models poses a significant computational challenge. Monte Carlo simulations are a common approach, but they demand a large number of photons for reliable results. Parallelization techniques can be employed to accelerate Monte Carlo computations by using multi-core CPUs and GPUs. This research delves into a comparative analysis of different parallelization techniques for the Python version of the Monte Carlo model. We consider conventional photon transport simulations that rely on iterative loops, the multithreading technique, NumPy’s vectorization, and GPU acceleration via the CuPy library. It is shown that CuPy, harnessing GPU parallelism, significantly accelerates simulations, making them suitable for large-scale scenarios. It is shown that as the number of photons grows, the overhead from reading and retrieving data to the GPU decreases, making the CuPy library an effective and easy-to-use option for Monte Carlo simulations.

Convolution neural networks are widely used for image processing in remote sensing. Aquacultures have an important role in food security and hence should be monitored. In this paper, a novel lightweight neural network for in-terrestrial aquaculture field retrieval from high-resolution remote sensing images is proposed. The structure of this pond segmentation network is based on the UNet architecture, providing higher training speed. Experiments are performed on Gaofen satellite datasets in Shanghai, China. The proposed network detects the inland aquaculture ponds in a shorter time than stateof-the-art neural network-based models and reaches an overall accuracy of about 90 %.

Accurate computations of the radiance in the gaseous absorption bands typically require fine wavelength steps. In this paper, a fast technique for computing a radiance spectrum in the wavelength region of 400–2500 nm is proposed. Our approach draws inspiration from the established k-correlation distribution model, with k denoting the absorption coefficient. However, our method expands upon this by considering both the direct transmittance and the scattering coefficient as predictors. At selected spectral points, the full radiative transfer simulations are performed, and the mathematical relation between a predictor and the radiance is established. Then, the radiance is restored on a fine wavelength grid. This approach can be used to enhance the accuracy of the convolved spectrum computations based on precomputed approximately monochromatic lookup tables and reduce the size of lookup tables. Numerical analysis demonstrates the method’s applicability to scenarios characterized by aerosol optical thicknesses not exceeding two.

A cloud tomographic retrieval algorithm relying on (i) the spherical harmonics discrete ordinate method for radiative transfer calculation and (ii) the adjoint radiative transfer theory for computing the gradient of the objective function has been designed. In order to escape local minima and to increase the efficiency of the retrieval algorithm, the computation of the gradient of the objective function by the adjoint method has been combined with that of the gradient of a surrogate function. The retrieval algorithm uses regularization and accelerated projected gradient methods endowed with a step length procedure. The performances of the retrieval algorithm as compared to those of a retrieval algorithm based on the surrogate minimization method are analyzed on a few synthetic problems.

Sequential numerical methods for integrating the ordinary differential equations can be time consuming when high accuracy is required over the large time domain. One way to accelerate computations and to get use of parallel computing is to combine computationally cheap (coarse) and expensive (fine) solvers. This approach is often referred to as the Parareal algorithm, in which a time domain is divided into subintervals. A cheap solver is used to obtain the starting points for temporal subintervals, while the fine solver which runs in parallel is used to perform accurate simulations within each subinterval. In the classical implementation of the Parareal algorithm, both coarse and fine solvers are fix step methods. However, due to inaccurate initial values at the beginnings of the subintervals, Parareal may require several iterations until the required accuracy is achieved and be slower than a serial algorithm. In this paper we analyze the performance of the Parareal algorithm based on adaptive step solvers. It is shown that such modification is more robust, requires less number of iterations and overall faster than the classical implementation. We present an error analysis and discuss possible future improvements.

Single-mode optical fibers (SMFs) have become the backbone of modern communication systems. However, their throughput is expected to reach its theoretical limit in the nearest future. Utilization of multimode fibers (MMFs) is considered as one of the most promising solutions rectifying this capacity crunch. Nevertheless, differential equations describing light propagation in MMFs are a way more sophisticated than those for SMFs, which makes numerical modelling of MMF-based systems computationally demanding and impractical for the most part of realistic scenarios. Physics-informed neural networks (PINNs) are known to outperform conventional numerical approaches in various domains and have been successfully applied to the nonlinear Schr\"odinger equation (NLSE) describing light propagation in SMFs. A comprehensive study on application of PINN to the multimode NLSE (MMNLSE) is still lacking though. To the best of our knowledge, this paper is the first to deploy the paradigm of PINN for MMNLSE and to demonstrate that a straightforward implementation of PINNs by analogy with NLSE does not work out. We pinpoint all issues hindering PINN convergence and introduce a novel scaling transformation for the zero-order dispersion coefficient that makes PINN capture all relevant physical effects. Our simulations reveal good agreement with the split-step Fourier (SSF) method and extend numerically attainable propagation lengths up to several hundred meters. All major limitations are also highlighted.

Volcanic eruptions eject large amounts of ash and trace gases such as sulfur dioxide (SO2) into the atmosphere. A significant difficulty in mitigating the impact of volcanic SO2 clouds on air traffic safety is that these gas emissions can be rapidly transported over long distances. The use of space-borne instruments enables the global monitoring of volcanic SO2 emissions in an economical and risk-free manner. Within the European Space Agency (ESA) Sentinel-5p+ Innovation project, the S5P SO2 layer height (S5P+I: SO2LH) activities led to the improvements of the retrieval algorithm and generation of the corresponding near real-time S5P SO2 LH products. These are currently operationally provided, in near real-time, by the German Aerospace Center (DLR) within the framework of the Innovative Products for Analyses of Atmospheric Composition (INPULS) project. The main aim of this paper is to present its extensive verification, accomplished within the S5P+I: SO2LH project, over major recent volcanic eruptions, against collocated space-borne measurements from the IASI/Metop and CALIOP/CALIPSO instruments as well as assess its impact on the forecasts provided by the Copernicus Atmospheric Monitoring Service (CAMS). The mean difference between S5P and IASI observations for the Raikoke 2019, the Nishinoshima 2020 and the La Soufrière-St Vincent 2021 eruptive periods is ∼ 0.5 ± 3 km, while for the Taal 2020 eruption, a larger difference was found, between 3 ± 3 km and 4 ± 3 km. The comparison of the daily mean SO2 LH further demonstrates the capabilities of this near real-time product, with slopes between 0.8 and 1 and correlation coefficients ranging between 0.6 and 0.8. Comparisons between the S5P SO2 LH and the CALIOP/CALIPSO ash plumes revealed an expected bias at −2.5 ± 2 km, considering that the injected SO2 and ash plume locations do not always coincide over an eruption. Furthermore, the CAMS assimilation of the S5P SO2 LH product led to much improved model output against the non-assimilated IASI LH, with a mean difference of 1.5 ± 2 km, compared to the original CAMS analysis, and improved the geographical spread of the Raikoke volcanic plume following the eruptive days.

The Copernicus Atmosphere Monitoring Service (CAMS), operated by the European Centre for Medium-Range Weather Forecasts on behalf of the European Commission, provides daily analyses and 5 d forecasts of atmospheric composition, including forecasts of volcanic sulfur dioxide (SO2) in near real time. CAMS currently assimilates total column SO2 products from the GOME-2 instruments on MetOp-B and MetOp-C and the TROPOMI instrument on Sentinel-5P, which give information about the location and strength of volcanic plumes. However, the operational TROPOMI and GOME-2 data do not provide any information about the height of the volcanic plumes, and therefore some prior assumptions need to be made in the CAMS data assimilation system about where to place the resulting SO2 increments in the vertical. In the current operational CAMS configuration, the SO2 increments are placed in the mid-troposphere, around 550 hPa or 5 km. While this gives good results for the majority of volcanic emissions, it will clearly be wrong for eruptions that inject SO2 at very different altitudes, in particular exceptional events where part of the SO2 plume reaches the stratosphere. A new algorithm, developed by the German Aerospace Centre (DLR) for GOME-2 and TROPOMI, optimized in the frame of the ESA-funded Sentinel-5P Innovation–SO2 Layer Height Project, and known as the Full-Physics Inverse Learning Machine (FP_ILM) algorithm, retrieves SO2 layer height from TROPOMI in near real time (NRT) in addition to the SO2 column. CAMS is testing the assimilation of these products, making use of the NRT layer height information to place the SO2 increments at a retrieved altitude. Assimilation tests with the TROPOMI SO2 layer height data for the Raikoke eruption in June 2019 show that the resulting CAMS SO2 plume heights agree better with IASI plume height data than operational CAMS runs without the TROPOMI SO2 layer height information and show that making use of the additional layer height information leads to improved SO2 forecasts. Including the layer height information leads to higher modelled total column SO2 values in better agreement with the satellite observations. However, the plume area and SO2 burden are generally also overestimated in the CAMS analysis when layer height data are used. The main reason for this overestimation is the coarse horizontal resolution used in the minimizations. By assimilating the SO2 layer height data, the CAMS system can predict the overall location of the Raikoke SO2 plume up to 5 d in advance for about 20 d after the initial eruption, which is better than with the operational CAMS configuration (without prior knowledge of the plume height) where the forecast skill is much more reduced for longer forecast lead times.

In this article, we present three algorithms for aerosol parameters retrieval from TROPOspheric Monitoring Instrument measurements in the $\text {O}_{2}$ A-band. These algorithms use neural networks 1) to emulate the radiative transfer model and a Bayesian approach to solve the inverse problem, 2) to learn the inverse model from the synthetic radiances, and 3) to learn the inverse model from the principal-component transform of synthetic radiances. The training process is based on full-physics radiative transfer simulations. The accuracy and efficiency of the neural network based retrieval algorithms are analyzed with synthetic and real data.

Precise knowledge about aerosols in the lower atmosphere (optical properties and vertical distribution) is particularly important for studying the Earth’s climatic and weather conditions. Measurements from satellite sensors in sun-synchronous and geostationary orbits can be used to map distributions of aerosol parameters in global or regional scales. The new-generation sensor Tropospheric Monitoring Instrument (TROPOMI) onboard the Copernicus Sentinel-5 Precursor (S5P) measures a wide variety of atmospheric trace gases and aerosols that are associated with climate change and air quality using a number of spectral bands between the ultraviolet and the shortwave infrared. In this study, we perform a sensitivity analysis of the forward model parameters and instrument information that are associated with the retrieval accuracy of aerosol layer height (ALH) and optical depth (AOD) using the oxygen (O 2 ) A-band. Retrieval of aerosol parameters from hyperspectral satellite measurements requires accurate surface representation and parameterization of aerosol microphysical properties and precise radiative transfer calculations. Most potential error sources arising from satellite retrievals of aerosol parameters, including uncertainties in aerosol models, surface properties, solar/satellite viewing geometry, and wavelength shift, are analyzed. The impact of surface albedo accuracy on retrieval results can be dramatic when surface albedo values are close to the critical surface albedo. An application to the real measurements of two scenes indicates that the retrieval works reasonably in terms of retrieved quantities and fit residuals.