Christine Böckmann

Aerosol lidar intercomparison in the framework of the EARLINET project. 2.Aerosol backscatter algorithms

An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height-dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height-dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well.

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.

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.

Iterative regularization method for lidar remote sensing

Abstract In this paper we present an inversion algorithm for ill-posed problems arising in atmospheric remote sensing. The proposed method is an iterative Runge–Kutta type regularization method. Those methods are better well known for solving differential equations. We adapted them for solving inverse ill-posed problems. The numerical performances of the algorithm are studied by means of simulations concerning the retrieval of aerosol particle size distributions from lidar observations.

Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET

We present a summary on the current status of two inversion algorithms that are used in EARLINET (European Aerosol Research Lidar Network) for the inversion of data collected with EARLINET multiwavelength Raman lidars. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. Development of these two algorithms started in 2000 when EARLINET was founded. The algorithms are based on a manually controlled inversion of optical data which allows for detailed sensitivity studies. The algorithms allow us to derive particle effective radius as well as volume and surface area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light absorption needs to be known with high accuracy. It is an extreme challenge to retrieve the real part with an accuracy better than 0.05 and the imaginary part with accuracy better than 0.005–0.1 or±50 %. Single-scattering albedo can be computed from the retrieved microphysical parameters and allows us to categorize aerosols into highand low-absorbing aerosols. On the basis of a few exemplary simulations with synthetic optical data we discuss the current status of these manually operated algorithms, the potentially achievable accuracy of data products, and the goals for future work. One algorithm was used with the purpose of testing how well microphysical parameters can be derived if the real part of the complex refractive index is known to at least 0.05 or 0.1. The other algorithm was used to find out how well microphysical parameters can be derived if this constraint for the real part is not applied. The optical data used in our study cover a range of Ångström exponents and extinction-to-backscatter (lidar) ratios that are found from lidar measurements of various aerosol types. We also tested aerosol scenarios that are considered highly unlikely, e.g. the lidar ratios fall outside the commonly accepted range of values measured with Raman lidar, even though the underlying microphysical particle properties are not uncommon. The goal of this part of the study is to test the robustness of the algorithms towards their ability to identify aerosol types that have not been measured so far, but cannot be ruled out based on our current knowledge of aerosol physics. We computed the optical data from monomodal logarithmic particle size distributions, i.e. we explicitly excluded the more complicated case of bimodal particle size distributions which is a topic of ongoing research work. Another constraint is that we only considered particles of spherical shape in our simulations. We considered particle radii as large as Published by Copernicus Publications on behalf of the European Geosciences Union. 5008 D. Müller et al.: EARLINET inversion algorithms 7–10 μm in our simulations where the Potsdam algorithm is limited to the lower value. We considered optical-data errors of 15 % in the simulation studies. We target 50 % uncertainty as a reasonable threshold for our data products, though we attempt to obtain data products with less uncertainty in future work.

Ill-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.

Parallel software for retrieval of aerosol distribution from LIDAR Data in the framework of EARLINET-ASOS

We present new software for the retrieval of the volume distribution – and thus, other relevant microphysical properties such as the effective radius – of stratospheric and tropospheric aerosols from multiwavelength LIDAR data. We consider the basic equation as a linear ill-posed problem and solve the linear system derived from spline collocation. We consider as well the technical implications of the algorithm implementation. In order to reduce runtime which is incurred by the vast theoretical search space, experiments on the MareNostrum Supercomputer were made to understand the significance of the different search space dimensions on the quality of the solution with the goal of restricting or eliminating entirely certain dimensions of the search space, to massively reduce calculation time for later production runs. Results show that the search space can be reduced according to available computation power to still yield reasonable results. Also, the scalability of the parallel software proved to be good.

Boundary value method for inverse Sturm-Liouville problems

In this paper we present a method to recover symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. The linear multistep method coupled with suitable boundary conditions known as boundary value method (BVM) is the main tool to approximate the eigenvalues in each iteration step of the used Newton method. The BVM was extended to work for Neumann-Neumann boundary conditions. Moreover, a suitable approximation for the asymptotic correction of the eigenvalues is given. Numerical results demonstrate that the method is able to give good results for both symmetric and non-symmetric potentials.

Regularized inversion of microphysical atmospheric particle parameters: Theory and application

Retrieving the distribution of aerosols in the atmosphere via remote sensing techniques is a highly complex task that requires dealing with a wide range of different problems stemming both from Physics and Mathematics. We focus on retrieving this distribution from multi-wavelength lidar data for aerosol ensembles consisting of spherical particles via an iterative regularization technique. The optical efficiencies for spherical scatterers are examined to account for the behavior of the underlying integral equation. The ill-posedness of the problem and the conditioning of the discretized problem are analyzed. Some critical points in the model, like the assumed wavelength-independence of the refractive index and the fixed grid of investigated refractive indices, are studied with regard to their expected impact on the regularized solution. A new Monte-Carlo type method is proposed for retrieval of the refractive index. To validate the results, the developed algorithm is applied to two measurement cases of burning biomass gained from multi-wavelength Raman lidar.

EARLINET correlative measurements for CALIPSO

The European Aerosol Research Lidar Network (EARLINET) was established in 2000 to derive a comprehensive, quantitative, and statistically significant data base for the aerosol distribution on the European scale. At present, EARLINET consists of 25 stations: 16 Raman lidar stations, including 8 multi-wavelength Raman lidar stations which are used to retrieve aerosol microphysical properties. EARLINET performs a rigorous quality assurance program for instruments and evaluation algorithms. All stations measure simultaneously on a predefined schedule at three dates per week to obtain unbiased data for climatological studies. Since June 2006 the first backscatter lidar is operational aboard the CALIPSO satellite. EARLINET represents an excellent tool to validate CALIPSO lidar data on a continental scale. Aerosol extinction and lidar ratio measurements provided by the network will be particularly important for that validation. The measurement strategy of EARLINET is as follows: Measurements are performed at all stations within 80 km from the overpasses and additionally at the lidar station which is closest to the actually overpassed site. If a multi-wavelength Raman lidar station is overpassed then also the next closest 3+2 station performs a measurement. Altogether we performed more than 1000 correlative observations for CALIPSO between June 2006 and June 2007. Direct intercomparisons between CALIPSO profiles and attenuated backscatter profiles obtained by EARLINET lidars look very promising. Two measurement examples are used to discuss the potential of multi-wavelength Raman lidar observations for the validation and optimization of the CALIOP Scene Classification Algorithm. Correlative observations with multi-wavelength Raman lidars provide also the data base for a harmonization of the CALIPSO aerosol data and the data collected in future ESA lidar-in-space missions.