Efficient single-scattering lookup table for lidar and polarimeter phytoplankton studies.

Coupled atmosphere and ocean remote sensing retrievals of aerosol, cloud, and oceanic phytoplankton microphysical properties, such as those carried out by the NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, involve single-scattering calculations that are time consuming. Lookup tables (LUTs) exist to speed up these calculations for aerosol and water droplets in the atmosphere. In our new Lorenz-Mie lookup table, we tabulate single scattering by an ensemble of coated isotropic spheres representing oceanic phytoplankton at wavelengths from 0.355 µm. The lookup table covers phytoplankton particles with radii in the range of 0.15-100 µm at an increase of up to 104 in computational speed compared to single-scattering calculations. The allowed complex refractive indices range from 1.05 to 1.24 for the shell's real part, from 10-7 to 0.3 for the shell's imaginary part, from 0 to 0.001 for the core's imaginary part, and equal to 1.02 for the core's real part. We show that we precisely compute inherent optical properties for the phytoplankton size distributions ranging up to 5 µm for the effective radius and up to 0.6 for the effective variance. We test wavelengths from 0.355 to 1.065 µm and find that all the inherent optical properties of interest agree with the single-scattering calculations to within 1% for 99.9% of cases. We also provide an example of using the lookup table to reproduce the phytoplankton optical datasets listed in the PANGAEA database for synthetic hyperspectral algorithm development. The table together with C++, Fortran, MATLAB, and Python codes to apply different complex refractive indices and phytoplankton size distributions is freely available online.

Efficient single-scattering look-up table for lidar and polarimeter water cloud studies.

Combined lidar and polarimeter retrievals of aerosol, cloud, and ocean microphysical properties involve single-scattering cloud calculations that are time consuming. We create a look-up table to speed up these calculations for water droplets in the atmosphere. In our new Lorenz-Mie look-up table we tabulate the light scattering by an ensemble of homogeneous isotropic spheres at wavelengths starting from 0.35 µm. The look-up table covers liquid water cloud particles with radii in the range of 0.001-500 µm while gaining an increase of up to 104 in computational speed. The covered complex refractive indices range from 1.25 to 1.36 for the real part and from 0 to 0.001 for the imaginary part. We show that we can precisely compute inherent optical properties for the particle size distributions ranging up to 100 µm for the effective radius and up to 0.6 for the effective variance. We test wavelengths from 0.35 to 2.3 µm and find that the elements of the normalized scattering matrix as well as the asymmetry parameter, the absorption, backscatter, extinction, and scattering coefficients are precise to within 1% for 96.7%-100% of cases depending on the inherent optical property. We also provide an example of using the look-up table with in situ measurements to determine agreement with remote sensing. The table together with C++, Fortran, MATLAB, and Python codes to interpolate the complex refractive index and apply different particle size distributions are freely available online.

Automated, unsupervised inversion of multiwavelength lidar data with TiARA: assessment of retrieval performance of microphysical parameters using simulated data.

We evaluate the retrieval performance of the automated, unsupervised inversion algorithm, Tikhonov Advanced Regularization Algorithm (TiARA), which is used for the autonomous retrieval of microphysical parameters of anthropogenic and natural pollution particles. TiARA (version 1.0) has been developed in the past 10 years and builds on the legacy of a data-operator-controlled inversion algorithm used since 1998 for the analysis of data from multiwavelength Raman lidar. The development of TiARA has been driven by the need to analyze in (near) real time large volumes of data collected with NASA Langley Research Center's high-spectral-resolution lidar (HSRL-2). HSRL-2 was envisioned as part of the NASA Aerosols-Clouds-Ecosystems mission in response to the National Academy of Sciences (NAS) Decadal Study mission recommendations 2007. TiARA could thus also serve as an inversion algorithm in the context of a future space-borne lidar. We summarize key properties of TiARA on the basis of simulations with monomodal logarithmic-normal particle size distributions that cover particle radii from approximately 0.05 µm to 10 µm. The real and imaginary parts of the complex refractive index cover the range from non-absorbing to highly light-absorbing pollutants. Our simulations include up to 25% measurement uncertainty. The goal of our study is to provide guidance with respect to technical features of future space-borne lidars, if such lidars will be used for retrievals of microphysical data products, absorption coefficients, and single-scattering albedo. We investigate the impact of two different measurement-error models on the quality of the data products. We also obtain for the first time, to the best of our knowledge, a statistical view on systematic and statistical uncertainties, if a large volume of data is processed. Effective radius is retrieved to 50% accuracy for 58% of cases with an imaginary part up to 0.01i and up to 100% of cases with an imaginary part of 0.05i. Similarly, volume concentration, surface-area concentration, and number concentrations are retrieved to 50% accuracy in 56%-100% of cases, 99%-100% of cases, and 54%-87% of cases, respectively, depending on the imaginary part. The numbers represent measurement uncertainties of up to 15%. If we target 20% retrieval accuracy, the numbers of cases that fall within that threshold are 36%-76% for effective radius, 36%-73% for volume concentration, 98%-100% for surface-area concentration, and 37%-61% for number concentration. That range of numbers again represents a spread in results for different values of the imaginary part. At present, we obtain an accuracy of (on average) 0.1 for the real part. A case study from the ORCALES field campaign is used to illustrate data products obtained with TiARA.

Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 3: case studies.

We conclude our series of publications on the development of the gradient correlation method (GCM), which can be used for an improved stabilization of the solution space of particle microphysical parameters derived from measurements with multiwavelength Raman and high-spectral-resolution lidar (3 backscatter +2 extinction coefficients). We show results of three cases studies. The data were taken with a ground-based multiwavelength Raman lidar during the Saharan Mineral Dust Experiment in the Cape Verde Islands (North Atlantic). These cases describe mixtures of dust with smoke. For our data analysis we separated the contribution of smoke to the total signal and only used these optical profiles for the test of GCM. The results show a significant stabilization of the solution space of the particle microphysical parameter retrieval on the particle radius domain from 0.03 to 10 µm, the real part of the complex refractive index domain from 1.3 to 1.8, and the imaginary part from 0 to 0.1. This new method will be included in the Tikhonov Advanced Regularization Algorithm, which is a fully automated, unsupervised algorithm that is used for the analysis of data collected with the worldwide first airborne 3 backscatter +2 extinction high-spectral-resolution lidar developed by NASA Langley Research Center.

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.

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" (3ß+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 3ß+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.

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 (ß)+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 "3ß+1α," "2ß+1α," and "3ß" 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 "3ß+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 "3ß+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 "3ß" configuration performs significantly poorer. The performance of the "3ß+1α" and "2ß+1α" configurations is intermediate between the "3ß+2α" and the "3ß."