Spatial distribution of doubly scattered polarized laser radiation in the focal plane of a lidar receiver.

Depolarization lidars are widely used to study clouds and aerosols because of their ability to discriminate between spherical particles and particles of irregular shape. Depolarization of cloud backscattered radiation can be caused also by multiple scattering events. One of the ways to gain information about particle parameters in the presence of strong multiple scattering is the measurement of radial and azimuthal dependence of the polarization patterns in the focal plane of receiver. We present an algorithm for the calculation of corresponding polarized patterns in the frame of double scattering approximation. Computations are performed for various receiver field of views, for different parameters of the scattering geometry, e.g., cloud base and sounding depth, as well as for different values of cloud particle size and refractive index. As the spatial distribution of cross-polarized radiation is of cross shape and rotated at 45 degrees with respect to laser polarization, the use of a properly oriented cross-shaped mask in the receiver focal plane allows the removal of a significant portion of the depolarized component of the backscattered radiation produced by double scattering. This has been verified experimentally based on cloud depolarization measurements performed at different orientations of the cross-shaped mask. Results obtained from measurements are in agreement with model predictions.

Information content of data measured with a multiple-field-of-view lidar.

Lidars with multiple fields of view (MFOVs) are promising tools for gaining information on cloud particle size. We perform a study of the information content of MFOV lidar data with the use of eigenvalue analysis. The approach we have developed permits an understanding of the main features of MFOV lidars and provides a way to relate the accuracy of particle size estimation with the measurement uncertainty and the scattering geometry such as the cloud-base height and the lidar sounding depth. Second-order scattering computations are performed for an extended range of particle sizes and for a wide range of lidar fields of view (FOVs). The results obtained allow us to specify the areas of possible applications of these lidars in cloud studies. Comparison of results obtained with polarized and cross-polarized scattered components demonstrate that the cross-polarized signal should provide a more stable retrieval and is preferable when double scattering is highly dominant. Our analysis allows for the estimation of the optimal number of FOVs in the system and their angular distribution, so this work can be a useful tool for practical MFOV lidar design.

Numerical simulation of light backscattering by spheres with off-center inclusion. Application to the lidar case.

A Mie backscattering model for spherical particles with off-center inclusion has been developed and tested. The program is capable of dealing with size parameter values up to approximately 1000, thus allowing one to simulate the optical behavior of a large variety of atmospheric aerosols, as well as cloud and precipitation particles. On the basis of this model, we simulated the optical properties of polydisperse composite atmospheric particles as observed by ground-based and airborne lidar systems. We have characterized optical properties in terms of host and inclusion radii, considering water particles with different composition inclusions. The performed modeling provides some insight into the so-called lidar bright- and dark-band phenomenon.

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.

Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions.

A dipole model is used to simulate incoherent Raman and fluorescent scattering by microspheres. The use of the addition theorem for spherical harmonics circumvents the need to evaluate double sums in the final formulas, thereby drastically reducing computational effort. Special attention is paid to consideration of backscattering geometry, which is important for lidar applications. The formulas derived for backscattering geometry decrease the computation time for size parameter x approdximately 100 by a factor of 200 compared with the time for calculations performed at other angles.

Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 2. Numerical simulation.

The results of numerical simulation of inelastic scattering by microspheres with the use of a dipole model are presented. The formulas that are derived speed up the computation, thereby permitting larger-sized microspheres to be studied. The angular scattering cross section and depolarization are calculated for a wide range of size parameters as well as for different orientations of incident wave polarization. Calculations performed with small incremental changes in size permit the influence of morphology-dependent resonance (MDR) on the power and angular distribution of scattered radiation to be studied. TM and TE types of MDR produce enhanced scattering of the incident wave with vertical and horizontal polarization; the corresponding shape of the phase function becomes oscillatory. Special attention is paid to the simulation of backward scattering by water droplets, which is important for Raman lidar applications.

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.