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.     

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.     

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.     

III-posed retrieval of aerosol extinction coefficient profiles from Raman lidar data by regularization

In the analysis of Raman lidar measurements of aerosol extinction, it is necessary to calculate the derivative of the logarithm of the ratio between the atmospheric number density and the range-corrected lidar-received power. The statistical fluctuations of the Raman signal can produce large fluctuations in the derivative and thus in the aerosol extinction profile. To overcome this difficult situation we discuss three methods: Tikhonov regularization, variational, and the sliding best-fit (SBF). Three methods are performed on the profiles taken from the European Aerosol Research Lidar Network lidar database simulated at the Raman shifted wavelengths of 387 and 607 nm associated with the emitted signals at 355 and 532 nm. Our results show that the SBF method does not deliver good results for low fluctuation in the profile. However, Tikhonov regularization and the variational method yield very good aerosol extinction coefficient profiles for our examples. With regard to, e.g., the 532 nm wavelength, the L2 errors of the aerosol extinction coefficient profile by using the SBF, Tikhonov, and variational methods with respect to synthetic noisy data are 0.0015(0.0024), 0.00049(0.00086), and 0.00048(0.00082), respectively. Moreover, the L2 errors by using the Tikhonov and variational methods with respect to a more realistic noisy profile are 0.0014(0.0016) and 0.0012(0.0016), respectively. In both cases the L2 error given in parentheses concerns the second example.     

Retrieval of aerosol properties from combined multiwavelength lidar and sunphotometer measurements

Simulation studies were carried out with regard to the feasibility of using combined observations from sunphotometer (SPM) and lidar for microphysical characterization of aerosol particles, i.e., the retrieval of effective radius, volume, and surface-area concentrations. It was shown that for single, homogeneous aerosol layers, the aerosol parameters can be retrieved with an average accuracy of 30% for a wide range of particle size distributions. Based on the simulations, an instrument combination consisting of a lidar that measures particle backscattering at 355 and 1574 nm, and a SPM that measures at three to four channels in the range from 340 to 1020 nm is a promising tool for aerosol characterization. The inversion algorithm has been tested for a set of experimental data. The comparison with the particle size distribution parameters, measured with in situ instrumentation at the lidar site, showed good agreement.     

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.     

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.     

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.     

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.     

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.     

Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: experiment

We present effective radius, volume, surface-area, and number concentrations as well as mean complex refractive index of tropospheric particle size distributions based on lidar measurements at six wavelengths. The parameters are derived by means of an inversion algorithm that has been specifically designed for the inversion of available optical data sets. The data were taken on 20 June and on 20 July 1997 during the Aerosol Characterization Experiment ACE 2 (North Atlantic/Portugal) and on 9 August 1998 during the Lindenberg Aerosol Characterization Experiment LACE 98 (Lindenberg/Germany). Measurements on 20 June 1997 were taken in a clean-marine boundary layer, and a large value of 0.64 mum for the effective radius, a low value of 1.45 for the real part, and a negligible imaginary part of the complex refractive index were found. The single-scatter albedo was 0.98 at 532 nm. It was derived from the particle parameters with Mie-scattering calculations. In contrast, the particles were less than 0.2 mum in effective radius in a continental-polluted aerosol layer on 20 July 1997. The real part of the complex refractive index was ~1.6; the imaginary part showed values near 0.03i. The single-scatter albedo was 0.84. On 9 August 1998 an elevated particle layer located from 3000 to 6000 m was observed, which had originated from an area of biomass burning in northwestern Canada. Here the effective radius was ~0.24 mum, the real part of the complex refractive index was above 1.6, the imaginary part was ~0.04i, and the single-scatter albedo was 0.81. Excellent agreement has been found with results based on sunphotometer and in situ measurements that were performed during the field campaigns.     

Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: simulation

A sensitivity study with an inversion scheme that permits one to retrieve physical parameters of tropospheric particle size distributions, e.g., effective radius, volume, surface-area, and number concentrations, as well as the mean complex refractive index from backscatter and extinction coefficients at multiple wavelengths is presented. The optical data for the analysis are derived from Mie-scattering calculations for monomodal and bimodal logarithmic-normal distributions in the particle size range between 0.01 and 10 microm. The complex refractive index is taken between 1.33 and 1.8 in the real part and between 0 and 0.1 in the imaginary part. The choice of these parameters takes account of properties of optically active atmospheric particles. The wavelengths were chosen at 355, 400, 532, 710, 800, and 1064 nm for the backscatter and at 355 and 532 nm for the extinction data, which are the available wavelengths of the two lidar systems at the Institute for Tropospheric Research. Cases of erroneous optical data of the order of as much as 20%, an unknown refractive index, which may also be wavelength and size dependent, as well as the a priori unknown modality of the particle size distribution were considered. It is shown that both extinction channels are necessary for determining the above-mentioned parameters within reasonable limits, i.e., effective radius, surface-area, and volume concentrations to an accuracy of +/-50%, the real part of the complex refractive index to +/-0.1, and the imaginary part to +/-50%. The number concentration may have errors larger than 50%. The overall performance of the inversion scheme permits the evaluation of experimental data on a routine basis.     

Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory

A method is proposed that permits one to retrieve physical parameters of tropospheric particle size distributions, e.g., effective radius, volume, surface-area, and number concentrations, as well as the mean complex refractive index on a routine basis from backscatter and extinction coefficients at multiple wavelengths. The optical data in terms of vertical profiles are derived from multiple-wavelength lidar measurements at 355, 400, 532, 710, 800, and 1064 nm for backscatter data and 355 and 532 nm for extinction data. The algorithm is based on the concept of inversion with regularization. Regularization is performed by generalized cross-validation. This method does not require knowledge of the shape of the particle size distribution and can handle measurement errors of the order of 20%. It is shown that at least two extinction data are necessary to retrieve the particle parameters to an acceptable accuracy. Simulations with monomodal and bimodal logarithmic-normal size distributions show that it is possible to derive effective radius, volume, and surface-area concentrations to an accuracy of +/-50%, the real part of the complex refractive index to +/-0.05, and the imaginary part to +/-50%. Number concentrations may have errors larger than +/-50%.     

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.     

Significance of multiple scattering from tropospheric aerosols for ground-based backscatter lidar measurements

The influence of multiple scattering on the retrieval of extinction coefficients of tropospheric aerosols from ground-based backscatter lidar measurements is numerically modeled. In a first step, lidar returns are computed by means of a Monte Carlo code for model atmospheres with different aerosol types and different extinction coefficient profiles. In so doing, synthetic lidar signals with and without multiple scattering can be simulated. In a second step, both types of signal are inverted by the most frequently used analytical solution, which, however, is based on the single-scatter assumption. From a comparison of the results, the error of the retrieved aerosol-extinction profiles can be quantitatively determined. It was found that the contribution of multiply scattered photons to the lidar signals is typically below 10% and never exceeds 20%. The relative errors of the retrieved aerosol-extinction profile in the planetary boundary layer are still smaller; they were determined to be less than 3% for all aerosol types, even for extinction coefficients as large as 3.9 km(-1). Thus, for ground-based lidar measurements and typical meteorological conditions, errors caused by neglecting multiple scattering are by far less significant than other errors in lidar data evaluation.     

Upper tropospheric temperature measurements with the use of a Raman lidar

Upper tropospheric temperature profiles were measured with the NASA Goddard Space Flight Center scanning Raman lidar five months after the eruption of Mt. Pinatubo. To derive temperatures in regions of high aerosol content, the aerosol transmission is calculated for the Raman N(2) return signals under cloud-free conditions. The lidar-derived aerosol backscattering ratio and an estimate of the aerosol extinction-to-backscatter ratio were used to compute the aerosol transmission. With a model reference temperature at 25 km, temperature profiles with a root-mean-square difference between the lidar and radiosonde temperatures of <2 K were obtained over an altitude range of 5-10 km for a 10-min integrated measurement with 300-m resolution.     

Assessment of the Moderate-Resolution Imaging Spectroradiometer algorithm for retrieval of aerosol parameters over the ocean

The Moderate Resolution Imaging Spectroradiometer aerosol algorithm over the ocean derives spectral aerosol optical depth and aerosol size parameters from satellite measured radiances at the top of the atmosphere (TOA). It is based on the adding of apparent optical properties (AOPs): TOA reflectance is approximated as a linear combination of reflectances resulting from a small particle mode and a large particle mode. The weighting parameter eta is defined as the fraction of the optical depth at 550 nm due to the small mode. The AOP approach is correct only in the single scattering limit. For a physically correct TOA reflectance simulation, we create linear combinations of the inherent optical properties (IOPs) of small and large particle modes, in which the weighting parameter f is defined as the fraction of the number density attributed to the small particle mode. We use these IOPs as inputs to an accurate multiple scattering radiative transfer model. We find that reflectance errors incurred with the AOP method are as high as 30% for an aerosol optical depth of 2 at 550 nm. The retrieved optical depth has a relative error of up to 8%, and the retrieved fraction eta has an absolute error of approximately 6%. We show that the use of accurate radiative transfer simulations and a bimodal fraction f yields accurate values for the retrieved optical depth and the fraction f.     

Differential absorption lidar system for routine monitoring of tropospheric ozone

A differential absorption lidar system for routine profiling of tropospheric ozone for daytime and nighttime operation is described. The system uses stimulated Raman scattering in hydrogen and deuterium of 266-nm radiation from a quadrupled Nd:YAG laser. Ozone profiles from altitudes of 600 m to approximately 5 km have been obtained with analog detection. Implementing corrections for differential Rayleigh scattering, differential absorption from oxygen, sulphur dioxide, and nitrogen dioxide, and differential aerosol extinction and backscatter can reduce the total system inaccuracy to 5-15% for a clear day and 20-30% for a hazy day, except at the top of the mixed layer. Photon counting must be installed to increase the measurement range from 5 to 15 km. An example of an application of routine measurements of tropospheric ozone profiles is given.     

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.     

Validation of the Raman lidar algorithm for quantifying aerosol extinction

To calculate aerosol extinction from Raman lidar data, it is necessary to evaluate the derivative of a molecular Raman signal with respect to range. The typical approach taken in the lidar community is to make an a priori assumption about the functional behavior of the data to calculate the derivative. It has previously been shown that the use of the chi-squared technique to determine the most likely functional behavior of the data prior to actually calculating the derivative eliminates the need for making a priori assumptions. Here that technique is validated through numerical simulation and by application to a significant body of Raman lidar measurements. In general, we show that the chi-squared approach for evaluating extinction yields lower extinction uncertainty than traditional techniques. We also use the technique to study the feasibility of developing a general characterization of the extinction uncertainty that could permit the uncertainty in Raman lidar aerosol extinction measurements to be estimated accurately without the need of the chi-squared technique.