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We present a new aerosol extinction profile retrieval algorithm for multi-axis differential optical absorption spectrometer (MAX-DOAS) measurements at high-altitude sites. The algorithm is based on the lookup table method. It is applied to retrieve aerosol extinction profiles from the long-term MAX-DOAS measurements (February 2012 to February 2016) at the Environmental Research Station Schneefernerhaus (UFS), Germany (47.417∘ N, 10.980∘ E), which is located near the summit of Zugspitze at an altitude of 2650 m. The lookup table consists of simulated O4 differential slant column densities (DSCDs) corresponding to numerous possible aerosol extinction profiles. The sensitivities of O4 absorption to several parameters were investigated for the design and parameterization of the lookup table. In the retrieval, simulated O4 DSCDs for each possible profile are derived by interpolating the lookup table to the observation geometries. The cost functions are calculated for each aerosol profile in the lookup table based on the simulated O4 DSCDs, the O4 DSCD observations, and the measurement uncertainties. Valid profiles are selected from all the possible profiles according to the cost function, and the optimal solution is defined as the weighted mean of all the valid profiles. A comprehensive error analysis is performed to better estimate the total uncertainty. Based on the assumption that the lookup table covers all possible profiles under clear-sky conditions, we determined a set of O4 DSCD scaling factors for different elevation angles and wavelengths. The profiles retrieved from synthetic measurement data can reproduce the synthetic profile. The results also show that the retrieval is insensitive to measurement noise, indicating the retrieval is robust and stable. The aerosol optical depths (AODs) retrieved from the long-term measurements were compared to coinciding and co-located sun photometer observations. High correlation coefficients (R) of 0.733 and 0.798 are found for measurements at 360 and 477 nm, respectively. However, especially in summer, the sun photometer AODs are systematically higher than the MAX-DOAS retrievals by a factor of ∼2. The discrepancy might be related to the limited measurement range of the MAX-DOAS and is probably also related to the decreased sensitivity of the MAX-DOAS measurements at higher altitudes. The MAX-DOAS measurements indicate the aerosol extinction decreases with increasing altitude during all seasons, which agrees with the co-located ceilometer measurements. Our results also show maximum AOD and maximum Ångström exponent in summer, which is consistent with observations at an AERONET station located ∼43 km from the UFS.

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 (O2) 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.

In this paper, we present neural network methods for predicting uncertainty in atmospheric remote sensing. These include methods for solving the direct and the inverse problem in a Bayesian framework. In the first case, a method based on a neural network for simulating the radiative transfer model and a Bayesian approach for solving the inverse problem is proposed. In the second case, (i) a neural network, in which the output is the convolution of the output for a noise-free input with the input noise distribution; and (ii) a Bayesian deep learning framework that predicts input aleatoric and model uncertainties, are designed. In addition, a neural network that uses assumed density filtering and interval arithmetic to compute uncertainty is employed for testing purposes. The accuracy and the precision of the methods are analyzed by considering the retrieval of cloud parameters from radiances measured by the Earth Polychromatic Imaging Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR).

In this paper we revisit the fundamentals of the null-field method with discrete sources. We prove the unique solvability of the null-field equations for the total field inside the particle and the internal field outside the particle, at all wavenumbers. For this purpose, we use the equivalence between the null-field and surface integral equations methods. Furthermore, we discuss the completeness property of different systems of discrete sources for a surface field approximation, and derive an infinite set of integral equations for the surface fields in a variety of discrete sources. Finally, we formulate the null-field scheme as an approach aiming to construct an approximate solution to the scattering problem. The way in which we introduce the T matrix of a particle is different from the standard approach relying on the assumption that the system of regular vector spherical wave functions for the interior problem is a basis.

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.