Simultaneous estimation of aerosol cloud concentration and spectral backscatter from multiple-wavelength lidar data

We present a sequential algorithm for estimating both concentration dependence on range and time and backscatter coefficient spectral dependence of optically thin localized atmospheric aerosols using data from rapidly tuned lidar. The range dependence of the aerosol is modeled as an expansion of the concentration in an orthonormal basis set whose coefficients carry the time dependence. Two estimators are run in parallel: a Kalman filter for the concentration range and time dependence and a maximum-likelihood estimator for the aerosol backscatter wavelength and time dependence. These two estimators exchange information continuously over the data-processing stream. The state model parameters of the Kalman filter are also estimated sequentially together with the concentration and backscatter. Lidar data collected prior to the aerosol release are used to estimate the ambient lidar return. The approach is illustrated on atmospheric backscatter long-wave infrared (CO2) lidar data.     

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%.     

Estimate optimization parameters for incoherent backscatter heterodyne lidar

Heterodyne lidar estimates are a function of a number of experimental parameters, some of which can be adjusted or tuned to optimize statistical precision. Here we refer the precision to the theoretical limit for optical measurements of return power and Doppler shift and investigate the conditions for optimization using established theoretical expressions for the standard deviation of various estimates. Tuning is characterized by a degeneracy parameter (the photocount per fade). For estimators that filter or resolve the return, it is shown that optimal tuning is achieved at wideband signal-to-noise ratios less than 0 dB and detected signal levels corresponding to more than a single effective photocount. Estimators that do not filter are predictably at a disadvantage when the signal bandwidth range gate product is low. The minimum standard deviation available from an optimally tuned heterodyne system is found to be greater than twice the limit.     

Method for reconstructing atmospheric optical parameters from the data of polarization lidar sensing

Inversion of polarization lidar sensing data based on the form of the lidar sensing equation with allowance for contributions from multiple-scattering calls for a priori information on the scattering phase matrix. In the present study the parameters of the Stokes vectors for various propagation media, including those with the scattering phase matrices that vary along the measuring range, are investigated. It is demonstrated that, in spaceborne lidar sensing, a simple parameterization of the multiple-scattering contribution is applicable and the polarization signal's characteristics depend mainly on the lidar and depolarization ratios, whereas differences in the angular dependences of the matrix components are no longer determining factors. An algorithm for simultaneous reconstruction of the profiles of the backscattering coefficient and depolarization and lidar ratios in an inhomogeneous medium is suggested. Specific features of the methods are analyzed for the examples of interpretation of lidar signal profiles calculated by the Monte Carlo method and are measured experimentally.     

Measurements of cirrus cloud backscatter color ratio with a two-wavelength lidar

We present observations of cirrus clouds from June 2006 to July 2007 performed by using a two-wavelength lidar located at Hampton University. For this time period, cirrus clouds were observed mostly in 7-13.5 km altitudes. Data analyses have been performed focusing on a color-ratio retrieval. In total, 86,369 samples from 1,689 profiles (1 min average and 15 m range resolution) containing cirrus clouds with attenuated backscatter ratio (ratio of attenuated total backscatter to the molecular backscatter) larger than 10 have been selected. The cirrus color ratio distribution shows a peak value at about 0.88 and a full width at half-maximum of 0.12.     

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.     

Retrieval of physical particle properties from lidar observations of extinction and backscatter at multiple wavelengths

Tropospheric height profiles of five particle backscatter coefficients between 355 and 800 nm and particle extinction coefficients at 355 and 532 nm measured with a multiple-wavelength backscatter lidar and a dual-wavelength Raman lidar are presented. From these data microphysical particle parameters are determined by a specifically designed inversion algorithm.     

Potential of lidar backscatter data to estimate solar aerosol radiative forcing

The potential to estimate solar aerosol radiative forcing (SARF) in cloudless conditions from backscatter data measured by widespread standard lidar has been investigated. For this purpose 132 days of sophisticated ground-based Raman lidar observations (profiles of particle extinction and backscatter coefficients at 532 nm wavelength) collected during two campaigns [the European Aerosol Research Lidar Network (EARLINET) and the Indian Ocean Experiment (INDOEX)] were analyzed. Particle extinction profiles were used as input for radiative transfer simulations with which to calculate the SARF, which then was plotted as a function of the column (i.e., height-integrated) particle backscatter coefficient (beta(c)). A close correlation between the SARF and beta(c) was found. SARF-beta(c) parameterizations in the form of polynomial fits were derived that exhibit an estimated uncertainty of +/-(10-30)%. These parameterizations can be utilized to analyze data of upcoming lidar satellite missions and for other purposes. The EARLINET-based parameterizations can be applied to lidar measurements at mostly continental, highly industrialized sites with limited maritime influence (Europe, North America), whereas the INDOEX parameterizations rather can be employed in polluted maritime locations, e.g., coastal regions of south and east Asia.     

Airborne CO(2) coherent lidar for measurements of atmospheric aerosol and cloud backscatter

An airborne CO(2) coherent lidar has been developed and flown on over 30 flights of the NASA DC-8 research aircraft to obtain aerosol and cloud backscatter and extinction data at a wavelength near 9μm. Designed to operate in either zenith- or nadir-directed modes, the lidar can be used to measure vertical profiles of backscatter throughout the vertical extent of the troposphere and the lower stratosphere. Backscatter measurements in absolute units are obtained through a hard-target calibration methodology. The use of coherent detection results in high sensitivity and narrow field of view, the latter property greatly reducing multiple-scattering effects. Aerosol backscatter profile intercomparisons with other airborne and ground-based CO(2) lidars were conducted during instrument checkout flights over the NASA Ames Research Center before extended depolyment over the Pacific Ocean. Selected results from data taken during the flights over the Pacific Ocean are presented, emphasizing intercom arisons with backscatter profile data obtained at 1.06 μm with a NASA Goddard Space Flight Center Nd:YAG lidar on the same flights.     

Determination by spaceborne backscatter lidar of the structural parameters of atmospheric scattering layers

Spaceborne active lidar systems are under development to give new insight into the vertical distribution of clouds and aerosols in the atmosphere and to provide new information on variables required for improvement of forecast models and for understanding the radiative and dynamic processes that are linked to the dynamics of climate change. However, when they are operated from space, lidar systems are limited by atmospheric backscattered signals that have low signal-to-noise ratios (SNRs) on optically thin targets. Therefore specific methods of analysis have to be developed to ensure accurate determination of the geometric and optical properties of scattering layers in the atmosphere. A first approach to retrieving the geometric properties of semitransparent cloud and aerosol layers is presented as a function of false-alarm and no-detection probabilities for a given SNR. Simulations show that the geometric properties of thin cirrus clouds and the altitude of the top of the unstable atmospheric boundary layer can be retrieved with standard deviations smaller than 150 m for a vertical resolution of the lidar system in the 50-100-m range and a SNR of 3. The altitudes of the top of dense clouds are retrieved with a precision in altitude of better than 50 m, as this retrieval corresponds to a higher SNR value. Such methods have an important potential application to future spaceborne lidar missions.     

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.     

Variational method for the retrieval of the optical thickness and the backscatter coefficient from multiangle lidar profiles

A variational method for retrieving the aerosol optical thickness and backscatter coefficient profiles from multiangle lidar measurements is presented and discussed. A monostatic single-wavelength low-energy lidar system was operated at different zenith angles during the Indian Ocean Experiment (INDOEX) campaign in 1999 to characterize the aerosol plumes in the Indian monsoon. The variational method was applied to lidar data to retrieve profiles of optical thickness and the backscatter coefficient for nighttime and daytime measurements. Results are obtained with an uncertainty of 10% below 3 km (nighttime) and 2.8 km (daytime) and a bias of less than 0.01. During daytime the retrieval of optical parameters is indeed limited to a lower altitude owing to the sky background signal and the atmospheric inhomogeneity. In both cases the total aerosol optical thickness is consistent (+/- 10%) with the integrated value derived from sunphotometer measurements. Backscatter-to-extinction ratios estimated in different regions by two distinct methods compared well, which proves the capability of the method to assess optical measurements and account for the altitude dependence of the phase function.     

Sensitivity of a lidar inversion algorithm to parameters relating atmospheric backscatter and extinction

A solution of the single-scattering lidar equation requires a relationship between the coefficients of backscatter beta(r) and extinction sigma(r) to be of the form beta(r) = C2sigma(r)k, where C2 and k are parameters independent of range r. The sensitivity of a particular lidar inversion algorithm to uncertainties in C2 and k is investigated using a measured lidar return which indicated the atmosphere to be essentially horizontally homogeneous during a reduced visibility condition. Starting with the measured power returned as a function of range, extinction coefficients and average visibilities are calculated using the inversion algorithm for different values of C2 and k and compared with those inferred from the lidar return using the slope method. The calculated extinction coefficients (and visibilities) were found to be extremely sensitive to uncertainties in C2. This questions the usefulness of the lidar inversion algorithm for aerosol extinction applications when the air mass characteristics change along the measurement path.     

Estimate of the incoherent-scattering contribution to lidar backscatter from clouds

Lidar backscatter from clouds in the Delft University of Technology experiment is complicated by the fact that the transmitter has a narrow beam width, whereas the receiver has a much wider one. The issue here is whether reception of light scattered incoherently by cloud particles can contribute appreciably to the received power. The incoherent contribution can come from within as well as from outside the transmitter beam but in any case is due to at least two scattering processes in the cloud that are not included in the coherent forward scatter that leads to the usual exponentially attenuated contribution from single-particle backscatter. It is conceivable that a sizable fraction of the total received power within the receiver beam width is due to such incoherent-scattering processes. The ratio of this contribution to the direct (but attenuated) reflection from a single particle is estimated here by means of a distorted-Born approximation to the wave equation (with an incident cw monochromatic wave) and by comparison of the magnitude of the doubly scattered to that of the singly scattered flux. The same expressions are also obtained from a radiative-transfer formalism. The ratio underestimates incoherent multiple scattering when it is not small. Corrections that are due to changes in polarization are noted.     

Multiple-scattering effect on ozone retrieval from space-based differential absorption lidar measurements

Single-scattering and multiple-scattering lidar signals are calculated for a spaceborne differential absorption lidar system for global ozone measurements at the on and off wavelength pair at 305 and 315 nm. The effect of multiple scattering is found to be negligible on stratospheric and tropospheric ozone retrieval under background stratospheric aerosol. Under low-visibility conditions in the planetary boundary layer the presence of multiple scattering causes an overestimation in maritime aerosol and an underestimation in urban as well as in rural aerosol. This effect is also examined in three cirrus models. The multiple scattering does not permit accurate ozone retrieval within cirrus; however, below it the solution recovers somewhat with generally an underestimation depending on the type and density of cirrus. The effect of aerosol and Rayleigh extinction on the ozone retrieval is also discussed.     

Estimate optimization parameters for incoherent backscatter heterodyne lidar including unknown return signal bandwidth

The conditions for optimizing the precision of heterodyne atmospheric lidar measurements using extended (deep) targets are investigated. The minimum standard deviation of each unknown (return power, Doppler shift, and signal bandwidth) is approximately twice the optical limit at best and is only weakly dependent on knowledge of the other parameters at optimal power levels. Somewhat stronger signal power levels are needed for bandwidth estimation. Results are displayed as a function of a time-bandwidth product to clarify the trade-off between estimate precision and range weighting. Realization under ideal conditions is confirmed by use of simulations.