Theory of inversion with two-dimensional regularization: profiles of microphysical particle properties derived from multiwavelength lidar measurements

Comparison of Columnar, Surface, and UAS Profiles of Absorbing Aerosol Optical Depth and Single-Scattering Albedo in South-East Poland

The impact of absorbing aerosols on climate is complex, with their potential positive or negative forcing, depending on many factors, including their height distribution and reflective properties of the underlying background. Measurement data is very limited, due to insufficient remote sensing methods dedicated to the retrieval of their vertical distribution. Columnar values of absorbing aerosol optical depth (AAOD) and single scattering albedo (SSA) are retrieved by the Aerosol Robotic Network (AERONET). However, the number of available results is low due to sky condition and aerosol optical depth (AOD) limitation. Presented research describes results of field campaigns in Strzyżów (South-East Poland, Eastern Europe) dedicated to the comparison of the absorption coefficient and SSA measurements performed with on-ground in-situ devices (aethalomter, nephelometer), small unmanned aerial system (UAS) carrying micro-aethalometer, as well as with lidar/ceilometer. An important aspect is the comparison of measurement results with those delivered by AERONET. Correlation of absorption to scattering coefficients measured on ground (0.79) and correlation of extinction on ground to AOD measured by AERONET (0.77) was visibly higher than correlation between AOD and AAOD retrieved by AERONET (0.56). Columnar SSA was weakly correlated with ground SSA (higher values of columnar SSA), which were mainly explained by hygroscopic effects, increasing scattering coefficient in ambient (wet conditions), and partly high uncertainty of SSA retrieval. AAOD derived with the use of profiles from UAS up to PBL height, was estimated to contribute in average to 37% of the total AAOD. A method of AAOD estimation, in the whole troposphere, with use of measured vertical profiles of absorption coefficient and extinction coefficient profiles from lidars was proposed. AAOD measured with this method has poor correlation with AERONET data, however for some measurements, within PBL, AAOD was higher than reported by AERONET, suggesting potential underestimation in photometric measurement under particular conditions. Correlation of absorption coefficient in profile to on ground measurements decrease with altitude. Measurements of SSA from drones agree well with ground measurements and are lower than results from AERONET, which suggests a larger contribution of absorbing aerosols. As an alternative for AAOD estimation in case of lack of AERONET AAOD data simple models are proposed, which base on AOD scaling with SSA measured with different methods. Proposed solution increase potential of absorption coefficient measurements in vertical profiles and columns of the atmosphere. Presented solutions make measurements of absorption coefficients in vertical profiles more affordable and allow rough estimation of columnar values for the whole atmosphere.

Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 2: simulations with synthetic optical data

We developed a mathematical scheme that allows us to improve retrieval products obtained from the inversion of multiwavelength Raman/HSRL lidar data, commonly dubbed "3 backscatter+2 extinction" (3β+2α) lidar. This scheme works independently of the automated inversion method that is currently being developed in the framework of the Aerosol-Cloud-Ecosystem (ACE) mission and which is successfully applied since 2012 [Atmos. Meas. Tech.7, 3487 (2014)10.5194/amt-7-3487-2014; "Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas)," in International Laser Radar Conference, July 2015, paper PS-C1-14] to data collected with the first airborne multiwavelength 3β+2α high spectral resolution lidar (HSRL) developed at NASA Langley Research Center. The mathematical scheme uses gradient correlation relationships we presented in part 1 of our study [Appl. Opt.55, 9839 (2016)APOPAI0003-693510.1364/AO.55.009839] in which we investigated lidar data products and particle microphysical parameters from one and the same set of optical lidar profiles. For an accurate assessment of regression coefficients that are used in the correlation relationships we specially designed the proximate analysis method that allows us to search for a first-estimate solution space of particle microphysical parameters on the basis of a look-up table. The scheme works for any shape of particle size distribution. Simulation studies demonstrate a significant stabilization of the various solution spaces of the investigated aerosol microphysical data products if we apply this gradient correlation method in our traditional regularization technique. Surface-area concentration can be estimated with an uncertainty that is not worse than the measurement error of the underlying extinction coefficients. The retrieval uncertainty of the effective radius is as large as ±0.07  μm for fine mode particles and approximately 100% for particle size distributions composed of fine (submicron) and coarse (supermicron) mode particles. The volume concentration uncertainty is defined by the sum of the uncertainty of surface-area concentration and the uncertainty of the effective radius. The uncertainty of number concentration is better than 100% for any radius domain between 0.03 and 10 μm. For monomodal PSDs, the uncertainties of the real and imaginary parts of the CRI can be restricted to ±0.1 and ±0.01 on the domains [1.3; 1.8] and [0; 0.1], respectively.

Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory

Multiwavelength Raman/high spectral resolution lidars that measure backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm can be used for the retrieval of particle microphysical parameters, such as effective and mean radius, number, surface-area and volume concentrations, and complex refractive index, from inversion algorithms. In this study, we carry out a correlation analysis in order to investigate the degree of dependence that may exist between the optical data taken with lidar and the underlying microphysical parameters. We also investigate if the correlation properties identified in our study can be used as a priori or a posteriori constraints for our inversion scheme so that the inversion results can be improved. We made the simplifying assumption of error-free optical data in order to find out what correlations exist in the best case situation. Clearly, for practical applications, erroneous data need to be considered too. On the basis of simulations with synthetic optical data, we find the following results, which hold true for arbitrary particle size distributions, i.e., regardless of the modality or the shape of the size distribution function: surface-area concentrations and extinction coefficients are linearly correlated with a correlation coefficient above 0.99. We also find a correlation coefficient above 0.99 for the extinction coefficient versus (1) the ratio of the volume concentration to effective radius and (2) the product of the number concentration times the sum of the squares of the mean radius and standard deviation of the investigated particle size distributions. Besides that, we find that for particles of any mode fraction of the particle size distribution, the complex refractive index is uniquely defined by extinction- and backscatter-related Ångström exponents, lidar ratios at two wavelengths, and an effective radius.

Retrieval of aerosol parameters from multiwavelength lidar: investigation of the underlying inverse mathematical problem

We present an investigation of some important mathematical and numerical features related to the retrieval of microphysical parameters [complex refractive index, single-scattering albedo, effective radius, total number, surface area, and volume concentrations] of ambient aerosol particles using multiwavelength Raman or high-spectral-resolution lidar. Using simple examples, we prove the non-uniqueness of an inverse solution to be the major source of the retrieval difficulties. Some theoretically possible ways of partially compensating for these difficulties are offered. For instance, an increase in the variety of input data via combination of lidar and certain passive remote sensing instruments will be helpful to reduce the error of estimation of the complex refractive index. We also demonstrate a significant interference between Aitken and accumulation aerosol modes in our inversion algorithm, and confirm that the solutions can be better constrained by limiting the particle radii. Applying a combination of an analytical approach and numerical simulations, we explain the statistical behavior of the microphysical size parameters. We reveal and clarify why the total surface area concentration is consistent even in the presence of non-unique solution sets and is on average the most stable parameter to be estimated, as long as at least one extinction optical coefficient is employed. We find that for selected particle size distributions, the total surface area and volume concentrations can be quickly retrieved with fair precision using only single extinction coefficients in a simple arithmetical relationship.

Arrange and average algorithm for the retrieval of aerosol parameters from multiwavelength high-spectral-resolution lidar/Raman lidar data

We present the results of a feasibility study in which a simple, automated, and unsupervised algorithm, which we call the arrange and average algorithm, is used to infer microphysical parameters (complex refractive index, effective radius, total number, surface area, and volume concentrations) of atmospheric aerosol particles. The algorithm uses backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm as input information. Testing of the algorithm is based on synthetic optical data that are computed from prescribed monomodal particle size distributions and complex refractive indices that describe spherical, primarily fine mode pollution particles. We tested the performance of the algorithm for the "3 backscatter (β)+2 extinction (α)" configuration of a multiwavelength aerosol high-spectral-resolution lidar (HSRL) or Raman lidar. We investigated the degree to which the microphysical results retrieved by this algorithm depends on the number of input backscatter and extinction coefficients. For example, we tested "3β+1α," "2β+1α," and "3β" lidar configurations. This arrange and average algorithm can be used in two ways. First, it can be applied for quick data processing of experimental data acquired with lidar. Fast automated retrievals of microphysical particle properties are needed in view of the enormous amount of data that can be acquired by the NASA Langley Research Center's airborne "3β+2α" High-Spectral-Resolution Lidar (HSRL-2). It would prove useful for the growing number of ground-based multiwavelength lidar networks, and it would provide an option for analyzing the vast amount of optical data acquired with a future spaceborne multiwavelength lidar. The second potential application is to improve the microphysical particle characterization with our existing inversion algorithm that uses Tikhonov's inversion with regularization. This advanced algorithm has recently undergone development to allow automated and unsupervised processing; the arrange and average algorithm can be used as a preclassifier to further improve its speed and precision. First tests of the performance of arrange and average algorithm are encouraging. We used a set of 48 different monomodal particle size distributions, 4 real parts and 15 imaginary parts of the complex refractive index. All in all we tested 2880 different optical data sets for 0%, 10%, and 20% Gaussian measurement noise (one-standard deviation). In the case of the "3β+2α" configuration with 10% measurement noise, we retrieve the particle effective radius to within 27% for 1964 (68.2%) of the test optical data sets. The number concentration is obtained to 76%, the surface area concentration to 16%, and the volume concentration to 30% precision. The "3β" configuration performs significantly poorer. The performance of the "3β+1α" and "2β+1α" configurations is intermediate between the "3β+2α" and the "3β."

Feasibility study of integral property retrieval for tropospheric aerosol from Raman lidar data using principal component analysis

A method is introduced to derive integral properties of the aerosol size distribution, e.g., aerosol mass, from tropospheric multiwavelength Raman lidar aerosol extinction and backscatter data, using an adapted form of the principal component analysis (PCA) technique. Since the refractive index of general tropospheric aerosols is variable and aerosol types can vary within one profile, an inversion technique applied in the troposphere should account for varying aerosol refractive indices. Using PCA, if a sufficiently complete set of appropriate refractive index dependent kernels is used, no a priori information about the aerosol type is necessary for the inversion of integral properties. In principle, the refractive index itself can be retrieved, but this quantity is more sensitive to measurement errors than the various integral properties of the aerosol size distribution. Here, the PCA technique adapted for use in the troposphere is introduced, the refractive index information content of the kernel sets is investigated, and error analyses are presented. The technique is then applied to actual tropospheric Raman lidar measurements.

Vertical profiles of microphysical particle properties derived from inversion with two-dimensional regularization of multiwavelength Raman lidar data: experiment

Inversion with two-dimensional (2-D) regularization is a new methodology that can be used for the retrieval of profiles of microphysical properties, e.g., effective radius and complex refractive index of atmospheric particles from complete (or sections) of profiles of optical particle properties. The optical profiles are acquired with multiwavelength Raman lidar. Previous simulations with synthetic data have shown advantages in terms of retrieval accuracy compared to our so-called classical one-dimensional (1-D) regularization, which is a method mostly used in the European Aerosol Research Lidar Network (EARLINET). The 1-D regularization suffers from flaws such as retrieval accuracy, speed, and ability for error analysis. In this contribution, we test for the first time the performance of the new 2-D regularization algorithm on the basis of experimental data. We measured with lidar an aged biomass-burning plume over West/Central Europe. For comparison, we use particle in situ data taken in the smoke plume during research aircraft flights upwind of the lidar. We find good agreement for effective radius and volume, surface-area, and number concentrations. The retrieved complex refractive index on average is lower than what we find from the in situ observations. Accordingly, the single-scattering albedo that we obtain from the inversion is higher than what we obtain from the aircraft data. In view of the difficult measurement situation, i.e., the large spatial and temporal distances between aircraft and lidar measurements, this test of our new inversion methodology is satisfactory.