Microphysical aerosol parameters from multiwavelength lidar

The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill-posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400, 710, 800 nm, additionally) and the same two extinction coefficients. For known complex refractive index and up to 20% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30%, and the imaginary part of the refractive index stays below 35% for input noise up to 10% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case.     

Retrieval of stratospheric aerosol size distributions and integral properties from simulated lidar backscatter measurements

A new approach for retrieving aerosol properties from extinction spectra is extended to retrieve aerosol properties from lidar backscatter measurements. In this method it is assumed that aerosol properties are expressed as a linear combination of backscatters at three or fewer wavelengths commonly used in lidar measurements. The coefficients in the weighted linear combination are obtained by minimization of the retrieval error averaged for a set of testing size distributions. The formulas can be used easily by investigators to retrieve aerosol properties from lidar backscatter measurements such as the Lidar In-Space Technology Experiment and Pathfinder Instruments for Clouds and Aerosols Spaceborne Observations.     

Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements

The use of powerful Raman backscatter lidars enables one to measure the stratospheric aerosol extinction profile independently of the backscatter, thereby obtaining additional information to aid in retrieving the physical characteristics of the sampled aerosol. We used principal component analysis to construct a self-consistent method for the retrieval of aerosol bulk physical and optical properties from multiwavelength elastic and/or inelastic Raman backscatter lidar signals. The procedure is applied to synthetic and actual lidar signals. We found that aerosol surface area and volume can be usefully estimated and that the use of Raman-derived extinction data leads to a notable improvement in the accuracy of the estimations.     

Bayesian assessment of uncertainty in aerosol size distributions and index of refraction retrieved from multiwavelength lidar measurements

We investigate the assessment of uncertainty in the inference of aerosol size distributions from backscatter and extinction measurements that can be obtained from a modern elastic/Raman lidar system with a Nd:YAG laser transmitter. To calculate the uncertainty, an analytic formula for the correlated probability density function (PDF) describing the error for an optical coefficient ratio is derived based on a normally distributed fractional error in the optical coefficients. Assuming a monomodal lognormal particle size distribution of spherical, homogeneous particles with a known index of refraction, we compare the assessment of uncertainty using a more conventional forward Monte Carlo method with that obtained from a Bayesian posterior PDF assuming a uniform prior PDF and show that substantial differences between the two methods exist. In addition, we use the posterior PDF formalism, which was extended to include an unknown refractive index, to find credible sets for a variety of optical measurement scenarios. We find the uncertainty is greatly reduced with the addition of suitable extinction measurements in contrast to the inclusion of extra backscatter coefficients, which we show to have a minimal effect and strengthens similar observations based on numerical regularization methods.     

Optical properties and size distribution of aerosols derived from simultaneous measurements with lidar, a sunphotometer, and an aureolemeter

A new method is proposed to derive the optical properties and size distribution of aerosol in an air column from simultaneous measurements of the backscattering coefficient, the optical thickness, and the solar aureole intensity with lidar, a sunphotometer, and an aureolemeter. Inasmuch as the backscattering properties and the optical thickness depend on both the complex refractive index and the size distribution, whereas the forward-scattering properties depend mainly on the size distribution, real and imaginary indices of refraction and size distributions of aerosol are retrieved from these measurements. The real and the imaginary parts of the complex refractive index of an aerosol at a wavelength of 500 nm during the period from November 1991 to March 1992 obtained in Tsukuba, Japan, were estimated to be 1.46-1.48 and 0.005-0.014, respectively. It is inferred from the size distribution and an optical thickness fraction of stratospheric aerosols in the total columnar aerosols that these results reflect the influences of stratospheric aerosols that originated from the Mt. Pinatubo eruption.     

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

We present the theory of inversion with two-dimensional regularization. We use this novel method to retrieve profiles of microphysical properties of atmospheric particles from profiles of optical properties acquired with multiwavelength Raman lidar. This technique is the first attempt to the best of our knowledge, toward an operational inversion algorithm, which is strongly needed in view of multiwavelength Raman lidar networks. The new algorithm has several advantages over the inversion with so-called classical one-dimensional regularization. Extensive data postprocessing procedures, which are needed to obtain a sensible physical solution space with the classical approach, are reduced. Data analysis, which strongly depends on the experience of the operator, is put on a more objective basis. Thus, we strongly increase unsupervised data analysis. First results from simulation studies show that the new methodology in many cases outperforms our old methodology regarding accuracy of retrieved particle effective radius, and number, surface-area, and volume concentration. The real and the imaginary parts of the complex refractive index can be estimated with at least as equal accuracy as with our old method of inversion with one-dimensional regularization. However, our results on retrieval accuracy still have to be verified in a much larger simulation study.     

Inversion with regularization for the retrieval of tropospheric aerosol parameters from multiwavelength lidar sounding

We present an inversion algorithm for the retrieval of particle size distribution parameters, i.e., mean (effective) radius, number, surface area, and volume concentration, and complex refractive index from multiwavelength lidar data. In contrast to the classical Tikhonov method, which accepts only that solution for which the discrepancy reaches its global minimum, in our algorithm we perform the averaging of solutions in the vicinity of this minimum. This averaging stabilizes the underlying ill-posed inverse problem, particularly with respect to the retrieval of number concentration. Results show that, for typical tropospheric particles and 10% error in the optical data, the mean radius could be retrieved to better than 20% from a lidar on the basis of a Nd:YAG laser, which provides a combination of backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm. The accuracy is improved if the lidar is also equipped with a hydrogen Raman shifter. In this case two additional backscatter coefficients at 416 and 683 nm are available. The combination of two extinction coefficients and five backscatter coefficients then allows one to retrieve not only averaged aerosol parameters but also the size distribution function. There was acceptable agreement between physical particle properties obtained from the evaluation of multiwavelength lidar data taken during the Lindenberg Aerosol Characterization Experiment in 1998 (LACE 98) and in situ data, which were taken aboard aircraft.     

Determination of stratospheric aerosol microphysical properties from independent extinction and backscattering measurements with a Raman lidar

An algorithm that permits the retrieval of profiles of particle mass and surface-area concentrations in the stratospheric aerosol layer from independently measured aerosol (particle and Rayleigh) and molecule (Raman or Rayleigh) backscatter signals is developed. The determination is based on simultaneously obtained particle extinction and backscatter profiles and on relations between optical and microphysical properties found from Mie-scattering calculations for realistic stratospheric particle size distributions. The size distributions were measured with particle counters released on balloons from Laramie, Wyoming, between June 1991 and April 1994. Mass and surface-area concentrations can be retrieved with relative errors of 10-20% and 20-40%, respectively, with a laser wavelength of 355 nm and with errors of 20-30% and 30-60%, respectively, with a laser wavelength of 308 nm. Lidar measurements taken within the first three years after the eruption of Mt. Pinatubo in June 1991 are shown. Surface-area concentrations around 20 μm(2) cm(-3) and mass concentrations of 3 to 6 μg m(-3) were found until spring 1993.     

Synergetic technique combining elastic backscatter lidar data and sunphotometer AERONET inversion for retrieval by layer of aerosol optical and microphysical properties

We present a so-called lidar and almucantar (LidAlm) algorithm that combines information provided by standard elastic backscatter lidar (i.e., calibrated attenuated backscatter coefficient profile at one or two wavelengths) and sunphotometer AERONET inversion of almucantar like measurements (i.e., column-integrated aerosol size distribution and refractive index). The purpose of the LidAlm technique is to characterize the atmospheric column by its different aerosol layers. These layers may be distinct or partially mixed, and they may contain different aerosol species (e.g., urban, desert, or biomass burning aerosols). The LidAlm synergetic technique provides the extinction and backscatter coefficient profiles, particle size distributions, and backscatter-to-extinction ratios for each aerosol layer. We present the LidAlm procedure and sensitivity studies. The applications are illustrated with examples of actual atmospheric conditions encountered in the Paris area.     

Tropospheric aerosol optical properties derived from lidar, sun photometer, and optical particle counter measurements

Tropospheric aerosols have been observed for the period from November 1990 to April 1992 with a lidar, a sun photometer, and an optical particle counter. Variations of aerosol optical thickness derived from the lidar and the sun photometer data and measurements are presented. The simultaneous measurements of these instruments also allowed us to estimate the extinction-to-backscatter ratio (S(1)), which ranged from 20 to 70. Comparison of optical thicknesses derived from both instruments clearly shows the effect of Mt. Pinatubo's eruption and the temporal variation of optical thickness in the stratosphere over 12 km. The possible range of the complex refractive index for the columnar mean aerosols can be deduced from the probable range of S(1) derived by the use of an S(1) diagram as a function of complex refractive index (m). The imaginary part of m can be estimated provided that the real part of m is known.     

Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution

We report on the feasibility of deriving microphysical parameters of bimodal particle size distributions from Mie-Raman lidar based on a triple Nd:YAG laser. Such an instrument provides backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm. The inversion method employed is Tikhonov's inversion with regularization. Special attention has been paid to extend the particle size range for which this inversion scheme works to approximately 10 microm, which makes this algorithm applicable to large particles, e.g., investigations concerning the hygroscopic growth of aerosols. Simulations showed that surface area, volume concentration, and effective radius are derived to an accuracy of approximately 50% for a variety of bimodal particle size distributions. For particle size distributions with an effective radius of < 1 microm the real part of the complex refractive index was retrieved to an accuracy of +/- 0.05, the imaginary part was retrieved to 50% uncertainty. Simulations dealing with a mode-dependent complex refractive index showed that an average complex refractive index is derived that lies between the values for the two individual modes. Thus it becomes possible to investigate external mixtures of particle size distributions, which, for example, might be present along continental rims along which anthropogenic pollution mixes with marine aerosols. Measurement cases obtained from the Institute for Tropospheric Research six-wavelength aerosol lidar observations during the Indian Ocean Experiment were used to test the capabilities of the algorithm for experimental data sets. A benchmark test was attempted for the case representing anthropogenic aerosols between a broken cloud deck. A strong contribution of particle volume in the coarse mode of the particle size distribution was found.     

Retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion method

We regard the problem of differentiation occurring in the retrieval of aerosol extinction coefficient profiles from inelastic Raman lidar signals by searching for a stable solution of the resulting Volterra integral equation. An algorithm based on a projection method and iterative regularization together with the L-curve method has been performed on synthetic and measured lidar signals. A strategy to choose a suitable range for the integration within the framework of the retrieval of optical properties is proposed here for the first time to our knowledge. The Monte Carlo procedure has been adapted to treat the uncertainty in the retrieval of extinction coefficients.     

Iterative method for the inversion of multiwavelength lidar signals to determine aerosol size distribution

Two iterative methods of inverting lidar backscatter signals to determine altitude profiles of aerosol extinction and altitude-resolved aerosol size distribution (ASD) are presented. The first method is for inverting two-wavelength lidar signals in which the shape of the ASD is assumed to be of power-law type, and the second method is for inverting multiwavelength lidar signals without assuming any a priori analytical form of ASD. An arbitrary value of the aerosol extinction-to-backscatter ratio (S(1)) is assumed initially to invert the lidar signals, and the ASD determined by use of the spectral dependence of the retrieved aerosol extinction coefficients is used to improve the value of S(1) iteratively. The methods are tested for different forms of altitude-dependent ASD's by use of simulated lidar-backscatter-signal profiles. The effect of random noise on the lidar backscatter signals is also studied.     

Derivation of Mount Pinatubo stratospheric aerosol mean size distribution by means of a multiwavelength lidar

A multiwavelength lidar operated in Sodankyla, Finland, during the European Arctic Stratospheric Ozone Experiment (December 1991-March 1992). It produced vertical profiles of stratospheric aerosols at four wavelengths. The determination of aerosol mean size distribution has been performed by use of extinction/backscattering ratios as obtained from lidar data processing at 355, 352, and 750 nm. Lognormal distributions of sulfuric particles with mode radius of r(m) = 0.12-0.25 μm and corresponding widths of s = 2-1.6 have been retrieved as best fits of experimental data, in good agreement with in situ measurements. A successful attempt to derive bimodal log-normal distributions is also described, together with the experimental and theoretical problems involved.     

High-efficiency aerosol scatterometer that uses an integrating sphere for the calibration of multiwavelength lidar data

For the purpose of calibrating multiwavelength lidar data, we developed a scatterometer to measure the aerosol scattering coefficient at the ground level. The system is based on an integrating sphere, cw lasers (532 and 633 nm), and a controlled flow of the ambient air, including aerosol particles. The simulation study and experimental results indicate that the detection efficiency of this instrument is approximately 10%-40% better than that of an integrating nephelometer, because of the wider acceptance angle of the scattered light. The scattering coefficients measured at the two wavelengths, as well as the resulting value of the angstrom exponent, show good correlation with the results simultaneously measured with an integrating nephelometer and an optical particle counter.     

Retrieval of aerosol properties over land surfaces: capabilities of multiple-viewing-angle intensity and polarization measurements

We investigate the capabilities of different instrument concepts for the retrieval of aerosol properties over land. It was found that, if the surface reflection properties are unknown, only multiple-viewing-angle measurements of both intensity and polarization are able to provide the relevant aerosol parameters with sufficient accuracy for climate research. Furthermore, retrieval errors are only little affected when the number of viewing angles is increased at the cost of the number of spectral sampling points and vice versa. This indicates that there is a certain amount of freedom for the instrument design of dedicated aerosol instruments. The final choice on the trade-off between the spectral sampling and the number of viewing angles should be made taking other factors into account, such as instrument complexity and the ability to obtain global coverage.     

Information content of multiwavelength lidar data with respect to microphysical particle properties derived from eigenvalue analysis

The multiwavelength Raman lidar technique in combination with sophisticated inversion algorithms has been recognized as a new tool for deriving information about the microphysical properties of atmospheric aerosols. The input optical parameter sets, provided by respective aerosol Raman lidars, are at the theoretical lower limit at which these inversion algorithms work properly. For that reason there is ongoing intense discussion of the accuracy of these inversion methods and the possibility of simultaneous retrieval of the particle size distribution and the complex refractive index. We present results of the eigenvalue analysis, used to study the information content of multiwavelength lidar data with respect to microphysical particle properties. Such an analysis provides, on a rather mathematical basis, more insight into the limitations of these inversion algorithms regarding the accuracy of the retrieved parameters. We show that the effective radius may be retrieved to 50% accuracy and the real and imaginary part of the complex refractive index to +/- 0.05 and +/- 0.005i, if the imaginary part is < 0.02i. These results are in accordance with the classic approach of simulation studies with synthetic particle size distributions. Major difficulties are found with a particle effective radius of < 0.15 microm. In that case the complex refractive index may not be derived with sufficient accuracy. The eigenvalue analysis also shows that the accuracy of the derived parameters degrades if the imaginary part is > 0.02i. Furthermore it shows the importance of the simultaneous use of backscatter and extinction coefficients for the retrieval of microphysical parameters.     

Hybrid regularization method for the ill-posed inversion of multiwavelength lidar data in the retrieval of aerosol size distributions

A specially developed method is proposed to retrieve the particle volume distribution, the mean refractive index, and other important physical parameters, e.g., the effective radius, volume, surface area, and number concentrations of tropospheric and stratospheric aerosols, from optical data by use of multiple wavelengths. This algorithm requires neither a priori knowledge of the analytical shape of the distribution nor an initial guess of the distribution. As a result, even bimodal and multimodal distributions can be retrieved without any advance knowledge of the number of modes. The nonlinear ill-posed inversion is achieved by means of a hybrid method combining regularization by discretization, variable higher-order B-spline functions and a truncated singular-value decomposition. The method can be used to handle different lidar devices that work with various values and numbers of wavelengths. It is shown, to my knowledge for the first time, that only one extinction and three backscatter coefficients are sufficient for the solution. Moreover, measurement errors up to 20% are allowed. This result could be achieved by a judicious fusion of different properties of three suitable regularization parameters. Finally, numerical results with an additional unknown refractive index show the possibility of successfully recovering both unknowns simultaneously from the lidar data: the aerosol volume distribution and the refractive index.