Error caused by using a constant extinction/backscattering ratio in the lidar solution

Lidar AOD inversion and aerosol extinction profile correction method based on GA-BP neural network

Lidar is an effective remote sensing method to obtain the vertical distribution of aerosols, and how to select the aerosol extinction-backscattering ratio (AE-BR) during the inversion process is a key step to guarantee the accuracy of the lidar inversion of aerosol optical thickness (AOD) and aerosol extinction coefficient profile (AECP). In this paper, an inversion algorithm for AOD and AECP based on a genetic BP (GA-BP) neural network is proposed. Simultaneous measurements are carried out using CE318 sun photometer and lidar, and the mapping relationship between the lidar echo signal and AOD is established based on the genetic BP (GA-BP) neural network method, which achieves the accurate inversion of AOD with an absolute error mean value of 0.0156. Based on the AOD output from the GA-BP neural network, the real-time best AE- BR to improve the inversion accuracy of AECP. Finally, practical tests show that the method achieves accurate inversion of AOD, determines the range of AE-BR from 20-50sr, realizes real-time dynamic correction of AECP, and has strong generalization ability and applicability in practical situations.

Raman lidar at 355 nm using low dead time photon counting for atmospheric aerosol measurements

Photon counting is an effective way to enhance the dynamic range of the data acquisition system (DAQ) in Raman lidars. However, there exists a deficiency of relatively high dead times among current options, which necessitates an additional calibration procedure for the nonlinearity of the photon counting signal, thus leading to unanticipated errors. A field programmable gate array (FPGA)-based photon counting module has been proposed and implemented in a Raman lidar, offering two operational channels. Through observational experiments, it was determined that this module has an overall dead time of 1.13 ns taking advantage of the high-speed amplifier/discriminator pair and the logic design, a significant improvement compared to the 4.35 ns of a commercially used Licel transient recorder within the same counting rate range. This notably low dead time implies that its output maintains sufficient linearity even at substantially high counting rates. As a result, the need for a dead time calibration procedure prior to signal integration with the analog signal is eliminated, reducing uncertainty in the final integrated signal, and even in the retrieval result. The backscattering result of the comparison between this module and a transient recorder indicates that a more precise performance can be acquired benefiting from this hardware upgrading.

Correct(ed) Klett-Fernald algorithm for elastic aerosol backscatter retrievals: a sensitivity analysis

Retrieval algorithms for aerosol elastic backscatter lidars are most commonly based on a signal inversion known as the Klett solution. While often used, a sign error in the original publication has barely been mentioned or recognized in the scientific community. In this study, we present a corrected Klett inversion and a sensitivity analysis of its implementation under different atmospheric conditions. We show that the error's dimension depends on multiple factors, thus preventing trivial a posteriori corrections on the results calculated with the original, uncorrected Klett solution. Comparing the uncorrected with the corrected Klett solution, long integration pathways in combination with low aerosol concentrations lead to substantial relative deviations of more than 100%, whereas short integration pathways with high aerosol concentrations considerably reduce the relative deviations to magnitudes around 15%. The higher the altitude of layers with increased aerosol concentrations, the higher the deviations due to the incorrect usage of Klett's inversion, however on a slight level (≈1%).

Numerical Weather Predictions and Re-Analysis as Input for Lidar Inversions: Assessment of the Impact on Optical Products

The atmospheric molecular number density can be obtained from atmospheric temperature and pressure profiles and is a significant input parameter for the inversion of lidar measurements. When measurements of vertical profiles of temperature and pressure are not available, atmospheric models are typically considered a valid alternative option. This paper investigates the influence of different atmospheric models (forecast and reanalysis) on the retrieval of aerosol optical properties (extinction and backscatter coefficients) by applying Raman and elastic-only methods to lidar measurements, to assess their use in lidar data processing. In general, reanalyzes are more accurate than forecasts, but, typically, they are not delivered in time for allowing near-real-time lidar data analysis. However, near-real-time observation is crucial for real-time monitoring of the environment and meteorological studies. The forecast models used in the paper are provided by the Integrated Forecasting System operated by the European Centre for Medium-Range Weather Forecasts (IFS_ECMWF) and the Global Data Assimilation System (GDAS), whereas the reanalysis model is obtained from the fifth-generation European Centre for Medium-Range Weather Forecasts ReAnalysis v5 (ERA5). The lidar dataset consists of measurements collected from four European Aerosol Research Lidar Network (EARLINET) stations during two intensive measurement campaigns and includes more than 200 cases at wavelengths of 355 nm, 532 nm, and 1064 nm. We present and discuss the results and influence of the forecast and reanalysis models in terms of deviations of the derived aerosol optical properties. The results show that the mean relative deviation in molecular number density is always below ±3%, while larger deviations are shown in the derived aerosol optical properties, and the size of the deviation depends on the retrieval method together with the different wavelengths. In general, the aerosol extinction coefficient retrieval is more dependent on the model used than the aerosol backscatter retrievals are. The larger influence on the extinction retrieval is mainly related to the deviation in the gradient of the temperature profile provided by forecast and reanalysis models rather than the absolute deviation of the molecular number density. We found that deviations in extinction were within ±5%, with a probability of 83% at 355 nm and 60% at 532 nm. Moreover, for aerosol backscatter coefficient retrievals, different models can have a larger impact when the backscatter coefficient is retrieved with the elastic method than when the backscatter coefficient is calculated using the Raman method at both 355 nm and 532 nm. In addition, the atmospheric aerosol load can also influence the deviations in the aerosol extinction and backscatter coefficients, showing a larger impact under low aerosol loading scenarios.

Measuring the Vertical Profiles of Aerosol Extinction in the Lower Troposphere by MAX-DOAS at a Rural Site in the North China Plain

Ground-based multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements were performed during the summer (13 June–20 August) of 2014 at a rural site in North China Plain. The vertical profiles of aerosol extinction (AE) in the lower troposphere were retrieved to analyze the temporal variations of AE profiles, near-surface AE, and aerosol optical depth (AOD). The average AOD and near-surface AE over the period of study were 0.51 ± 0.26 and 0.33 ± 0.18 km−1 during the effective observation period, respectively. High AE events and elevated AE layers were identified based on the time series of hourly AE profiles, near-surface AEs and AODs. It is found that in addition to the planetary boundary layer height (PBLH) and relative humidity (RH), the variations in the wind field have large impacts on the near-surface AE, AOD, and AE profile. Among 16 wind sectors, higher AOD or AE occur mostly in the directions of the cities upstream. The diurnal variations of the AE profiles, AODs and near-surface AEs are significant and influenced mainly by the source emissions, PBLH, and RH. The AE profile shape from MAX-DOAS measurement is generally in agreement with that from light detection and ranging (lidar) observations, although the AE absolute levels are different. Overall, ground-based MAX-DOAS can serve as a supplement to measure the AE vertical profiles in the lower troposphere.

Forest fire smoke layers observed in the free troposphere over Portugal with a multiwavelength Raman lidar: optical and microphysical properties

Vertically resolved optical and microphysical properties of biomass burning aerosols, measured in 2011 with a multiwavelength Raman lidar, are presented. The transportation time, within 1-2 days (or less), pointed towards the presence of relatively fresh smoke particles over the site. Some strong layers aloft were observed with particle backscatter and extinction coefficients (at 355 nm) greater than 5 Mm⁻¹ sr⁻¹ and close to 300 Mm⁻¹, respectively. The particle intensive optical properties showed features different from the ones reported for aged smoke, but rather consistent with fresh smoke. The Ångström exponents were generally high, mainly above 1.4, indicating a dominating accumulation mode. Weak depolarization values, as shown by the small depolarization ratio of 5% or lower, were measured. Furthermore, the lidar ratio presented no clear wavelength dependency. The inversion of the lidar signals provided a set of microphysical properties including particle effective radius below 0.2 μm, which is less than values previously observed for aged smoke particles. Real and imaginary parts of refractive index of about 1.5-1.6 and 0.02i, respectively, were derived. The single scattering albedo was in the range between 0.85 and 0.93; these last two quantities indicate the nonnegligible absorbing characteristics of the observed particles.

North-south cross sections of the vertical aerosol distribution over the Atlantic Ocean from multiwavelength Raman/polarization lidar during Polarstern cruises

Shipborne aerosol lidar observations were performed aboard the research vessel Polarstern in 2009 and 2010 during three north-south cruises from about 50°N to 50°S. The aerosol data set provides an excellent opportunity to characterize and contrast the vertical aerosol distribution over the Atlantic Ocean in the polluted northern and relatively clean southern hemisphere. Three case studies, an observed pure Saharan dust plume, a Patagonian dust plume east of South America, and a case of a mixed dust/smoke plume west of Central Africa are exemplarily shown and discussed by means of their optical properties. The meridional transatlantic cruises were used to determine the latitudinal cross section of the aerosol optical thickness (AOT). Profiles of particle backscatter and extinction coefficients are presented as mean profiles for latitudinal belts to contrast northern- and southern-hemispheric aerosol loads and optical effects. Results of lidar observations at Punta Arenas (53°S), Chile, and Stellenbosch (34°S), South Africa, are shown and confirm the lower frequency of occurrence of free-tropospheric aerosol in the southern hemisphere than in the northern hemisphere. The maximum latitudinal mean AOT of 0.27 was found in the northern tropics (0- 15°N) in the Saharan outflow region. Marine AOT is typically 0.05 ± 0.03. Particle optical properties are presented separately for the marine boundary layer and the free troposphere. Concerning the contrast between the anthropogenically influenced midlatitudinal aerosol conditions in the 30- 60°N belt and the respective belt in the southern hemisphere over the remote Atlantic, it is found that the AOT and extinction coefficients for the vertical column from 0-5km (total aerosol column) and 1-5km height (lofted aerosol above the marine boundary layer) are a factor of 1.6 and 2 higher at northern midlatitudes than at respective southern midlatitudes, and a factor of 2.5 higher than at the clean marine southern-hemispheric site of Punta Arenas. The strong contrast is confined to the lowermost 3km of the atmosphere.

Statistical analysis of the spatial-temporal distribution of aerosol extinction retrieved by micro-pulse lidar in Kashgar, China

The spatial-temporal distribution of dust aerosol is important in climate model and ecological environment. An observation experiment of the aerosol vertical distribution in the low troposphere was made using the micro-pulse lidar system from Sept. 2008 to Aug. 2009 at the oasis city Kashgar, China, which is near the major dust source area of the Taklimakan desert. The monthly averaged temporal variation of aerosol extinction profiles are given in the paper. The profile of aerosol extinction coefficient suggested that the dust aerosol could be vertically transported from the ground level to the higher altitude of above 5 km around the source region, and the temporal distribution showed that the dust aerosol layer of a few hundred meters thick appeared in the seasons of early spring and summer near the ground surface.

Lower Troposphere Observation over Urban Area with Lidar at 1064 nm

An episode of relatively thick (till 3 km) aerosol formation over the urban area of Sofia city was observed by lidar at a wavelength of 1064 nm. The lidar is part of Sofia lidar station at the Institute of Electronics of Bulgarian Academy of Sciences. Analysis of the weather conditions during the measurement period explains the stable persistence of such formation of human-activity aerosol over the town for the days of observation 20, 21, 23, and 24 June, 2011. The estimated top of the Planetary Boundary Layer for the measurement dated 23 June showed unusually high altitude 2200 m above ground. The results are presented in terms of vertical atmospheric backscatter coefficient profiles and color maps of the aerosol stratification evolution.

Infrared lidar overlap function: an experimental determination

The most recent works demonstrate that the lidar overlap function, which describes the overlap between the laser beam and the receiver field of view, can be determined experimentally for the 355 and 532 nm channels using Raman signals. Nevertheless, the Raman channels cannot be used to determine the lidar overlap for the infrared channel (1064 nm) because of their low intensity. In addition, many Raman lidar systems only provide inelastic signals with reasonable signal-to-noise ratio at nighttime. In view of this fact, this work presents a modification of that method, based on the comparison of attenuated backscatter profiles derived from lidar and ceilometer, to retrieve the overlap function for the lidar infrared channel. Similarly to the Raman overlap method, the approach presented here allows to derive the overlap correction without an explicit knowledge of all system parameters. The application of the proposed methodology will improve the potential of Raman lidars to investigate the aerosol microphysical properties in the planetary boundary layer, extending the information of 1064 nm backscatter profiles to the ground and allowing the retrieval of microphysical properties practically close to the surface.

Practical analytical backscatter error bars for elastic one-component lidar inversion algorithm

We present an analytical formulation to compute the total-backscatter range-dependent error bars from the well-known Klett's elastic-lidar inversion algorithm. A combined error-propagation and statistical formulation approach is used to assess inversion errors in response to the following error sources: observation noise (i.e., signal-to-noise ratio) in the reception channel, the user's uncertainty in the backscatter calibration, and in the (range-dependent) total extinction-to-backscatter ratio provided. The method is validated using a Monte Carlo procedure, where the error bars are computed by inversion of a large population of noisy generated lidar signals, for total optical depths tau < or = 5 and typical user uncertainties, all of which yield a practical tool to compute the sought-after error bars.

Lidar beams in opposite directions for quality assessment of Cloud-Aerosol Lidar with Orthogonal Polarization spaceborne measurements

We present the "lidar beams in opposite directions" (LIBOD) technique and applications for quality assessment of spaceborne observations made by Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) onboard the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation satellite. LIBOD is applicable to standard total backscatter lidar because it does not require a priori knowledge of the particle extinction-to-backscatter ratio. In this paper, we present (i) an objective assessment of the lidar signal quality and representativity of correlative ground-based lidar and CALIOP measurements only using normalized range-corrected lidar signals and (ii) a numerical filtering and optimization technique for reducing the spurious oscillations induced by noisy signal differentiation as needed for retrieval of particle extinction coefficients and extinction-to-backscatter ratio profiles. Numerical simulations and Monte Carlo tests are conducted for assessing the performance of the LIBOD technique. The applications are illustrated with examples of actual correlative 532 nm lidar profiles from CALIOP and a ground-based lidar deployed in Tamanrasset in the heart of Sahara in 2006 and near Strasbourg, France, in 2007.

Systematic error of lidar profiles caused by a polarization-dependent receiver transmission: quantification and error correction scheme

Signals of many types of aerosol lidars can be affected with a significant systematic error, if depolarizing scatterers are present in the atmosphere. That error is caused by a polarization-dependent receiver transmission. In this contribution we present an estimation of the magnitude of this systematic error. We show that lidar signals can be biased by more than 20%, if linearly polarized laser light is emitted, if both polarization components of the backscattered light are measured with a single detection channel, and if the receiver transmissions for these two polarization components differ by more than 50%. This signal bias increases with increasing ratio between the two transmission values (transmission ratio) or with the volume depolarization ratio of the scatterers. The resulting error of the particle backscatter coefficient increases with decreasing backscatter ratio. If the particle backscatter coefficients are to have an accuracy better than 5%, the transmission ratio has to be in the range between 0.85 and 1.15. We present a method to correct the measured signals for this bias. We demonstrate an experimental method for the determination of the transmission ratio. We use collocated measurements of a lidar system strongly affected by this signal bias and an unbiased reference system to verify the applicability of the correction scheme. The errors in the case of no correction are illustrated with example measurements of fresh Saharan dust.

Particle size distribution retrieval from multiwavelength lidar signals for droplet aerosol

A method of retrieval of the aerosol particle size distribution (APSD) from multiwavelength lidar signals is presented. Assumed distribution (usually a bimodal combination of lognormal functions) with a few free parameters is directly substituted into the lidar equations. The minimization technique allows one to find the parameters that provide the best fit of the assumed APSD by comparison of theoretically generated and experimental signals. Prior knowledge of the lidar ratio is not required. The approach was tested on a typical synthetic APSD consisting of spherical droplets. Comparison of lidar measurements with results from a condensation particle counter was also performed. For signals registered at 3-5 wavelengths from the UV to the near IR a satisfactory retrieval of synthetic APSD is possible for the particles within the 100-3000 nm range.

Quasi-analytical determination of noise-induced error limits in lidar retrieval of aerosol backscatter coefficient by the elastic, two-component algorithm

The elastic, two-component algorithm is the most common inversion method for retrieving the aerosol backscatter coefficient from ground- or space-based backscatter lidar systems. A quasi-analytical formulation of the statistical error associated to the aerosol backscatter coefficient caused by the use of real, noise-corrupted lidar signals in the two-component algorithm is presented. The error expression depends on the signal-to-noise ratio along the inversion path and takes into account "instantaneous" effects, the effect of the signal-to-noise ratio at the range where the aerosol backscatter coefficient is being computed, as well as "memory" effects, namely, both the effect of the signal-to-noise ratio in the cell where the inversion is started and the cumulative effect of the noise between that cell and the actual cell where the aerosol backscatter coefficient is evaluated. An example is shown to illustrate how the "instantaneous" effect is reduced when averaging the noise-contaminated signal over a number of cells around the range where the inversion is started.

Particle backscatter and extinction profiling with the spaceborne high-spectral-resolution Doppler lidar ALADIN: methodology and simulations

The European Space Agency will launch the Atmospheric Laser Doppler Instrument (ALADIN) for global wind profile observations in the near future. The potential of ALADIN to measure the optical properties of aerosol and cirrus, as well, is investigated based on simulations. A comprehensive data analysis scheme is developed that includes (a) the correction of Doppler-shifted particle backscatter interference in the molecular backscatter channels (cross-talk effect), (b) a procedure that allows us to check the quality of the cross-talk correction, and (c) the procedures for the independent retrieval of profiles of the volume extinction and backscatter coefficients of particles considering the height-dependent ALADIN signal resolution. The error analysis shows that the particle backscatter and extinction coefficients, and the corresponding extinction-to-backscatter ratio (lidar ratio), can be obtained with an overall (systematic+statistical) error of 10%-15%, 15%-30%, and 20%-35%, respectively, in tropospheric aerosol and dust layers with extinction values from 50 to 200 Mm(-1); 700-shot averaging (50 km horizontal resolution) is required. Vertical signal resolution is 500 m in the lower troposphere and 1000 m in the free troposphere. In cirrus characterized by extinction coefficients of 200 Mm(-1) and an optical depth of >0.2, backscatter coefficients, optical depth, and column lidar ratios can be obtained with 25%-35% relative uncertainty and a horizontal resolution of 10 km (140 shots). In the stratosphere, only the backscatter coefficient of aerosol layers and polar stratospheric clouds can be retrieved with an acceptable uncertainty of 15%-30%. Vertical resolution is 2000 m.

Ground-truth aerosol lidar observations: can the Klett solutions obtained from ground and space be equal for the same aerosol case?

Upcoming multiyear satellite lidar aerosol observations need strong support by a worldwide ground-truth lidar network. In this context the question arises as to whether the ground stations can deliver the same results as obtained from space when the Klett formalism is applied to elastic backscatter lidar data for the same aerosol case. This question is investigated based on simulations of observed cases of simple and complex aerosol layering. The results show that the differences between spaceborne and ground-based observations can be as large as 20% for the backscatter and extinction coefficients and the optimum estimates of the column lidar ratios. In cases with complex aerosol layering, the application of the two-layer approach can lead to similar results (space, ground) and accurate products provided that horizontally homogeneous aerosol conditions are given.

Influence of atmospheric and system parameters on multiple scattering in spaceborne backscatter lidar measurements

We have simulated backscatter signals of spaceborne lidar systems with the help of a Monte Carlo model. Calculations were performed for various combinations of system parameters. As typical examples of atmospheric observation targets, two kinds of cirrus cloud and two kinds of aerosol were considered. Both total multiple scattering and the significance of individual higher scattering orders are discussed. For all cases, an approximate multiple scattering factor F was calculated that can be used to correct the single-scattering lidar equation to account also for multiple scattering.

Distortions of the extinction coefficient profile caused by systematic errors in lidar data

The influence of lidar data systematic errors on the retrieved particulate extinction coefficient profile in clear atmospheres is investigated. Particularly, two sources of the extinction coefficient profile distortions are analyzed: (1) a zero-line offset remaining after subtraction of an inaccurately determined signal background component and (2) a far-end incomplete overlap due to poor adjustment of the lidar system optics. Inversion results for simulated lidar signals, obtained with the near- and far-end solutions, are presented that show advantages of the near-end solution for clear atmospheres.

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.

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.

Aerosol lidar intercomparison in the framework of the EARLINET project. 1. Instruments

In the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET), 19 aerosol lidar systems from 11 European countries were compared. Aerosol extinction or backscatter coefficient profiles were measured by at least two systems for each comparison. Aerosol extinction coefficients were derived from Raman lidar measurements in the UV (351 or 355 nm), and aerosol backscatter profiles were calculated from pure elastic backscatter measurements at 351 or 355, 532, or 1064 nm. The results were compared for height ranges with high and low aerosol content. Some systems were additionally compared with sunphotometers and starphotometers. Predefined maximum deviations were used for quality control of the results. Lidar systems with results outside those limits could not meet the quality assurance criterion. The algorithms for deriving aerosol backscatter profiles from elastic lidar measurements were tested separately, and the results are described in Part 2 of this series of papers [Appl. Opt. 43, 977-989 (2004)]. In the end, all systems were quality assured, although some had to be modified to improve their performance. Typical deviations between aerosol backscatter profiles were 10% in the planetary boundary layer and 0.1 x 10(-6) m(-1) sr(-1) in the free troposphere.

Effect of multiple scattering on depolarization measurements with spaceborne lidars

An analytical model based on the integration of the scattering-angle and light-path manifold has been developed to quantify the effect of multiple scattering on cirrus measurements obtained with elastic polarization lidars from space. Light scattering by molecules and by a horizontally homogeneous cloud is taken into account. Lidar parameter, including laser beam divergence, can be freely chosen. Up to 3 orders of scattering are calculated. Furthermore, an inversion technique for the retrieval of cloud extinction profiles from measurements with elastic-backscatter lidars is proposed that explicitly takes multiple scattering into account. It is found that for typical lidar system parameters such as those of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) instrument multiple scattering does not significantly affect depolarization-ratio measurements in cirrus clouds with small to moderate optical depths. For all simulated clouds, the absolute value of the difference between measured and single-scattering volume depolarization ratio is < 0.006. The particle depolarization ratio can be calculated from the measured volume depolarization ratio and the retrieved backscatter ratio without degradation of accuracy; thus characterization of the various cirrus categories in terms of the particle depolarization ratio and retrieval of cloud microphysical properties is feasible from space. The results of this study apply to polar stratospheric clouds as well.

Stable inversion method for a polarized-lidar: analysis and simulation

A new inversion inhomogeneous atmosphere (IA) method that is more stable than Fernald's method for two-component (molecule and aerosol) scattering analysis of polarized Mie lidar signals is proposed and examined. The backscattering coefficient and the extinction-to-backscattering ratio (EBR) can be calculated for specified regions at which the depolarization ratio is less than that of molecule without further assumptions. The inversion procedure can be extended to both inward stepwise and outward stepwise integration algorithms. Simulation results indicate that a higher precision was achieved with the IA method than with Fernald's method in terms of error and random noise in estimating boundary value and EBR. Experimental results were also better with the IA method than with Fernald's method.

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.

Error analysis for the lidar backward inversion algorithm

Here we depart from the inhomogeneous solution of a lidar equation using the backward inversion algorithm that is nowadays generally referred to as the Klett method. In particular, we develop an error sensitivity study that relates errors in the user-input parameters boundary extinction and exponential term in the extinction-to-backscatter relationship to errors in the inverted extinction profile. The validity of the analysis presented is limited only by the validity of application of the inversion algorithm itself, its numerical performance having been tested for optical depths in the 0.01-10 range. Toward this end, we focus on an introductory background about how uncertainties in these two parameters can apply to a family of inverted extinction profiles rather than a single profile and on its range-dependent behavior as a function of the optical thickness of the lidar inversion range. Next, we performed a mathematical study to derive the error span of the inverted extinction profile that is due to uncertainties in the above-mentioned user calibration parameters. This takes the form of upper and lower range-dependent error bounds. Finally, appropriate inversion plots are presented as application examples of this study to a parameterized set of atmospheric scenes inverted from both synthesized elastic-backscatter lidar signals and a live signal.

Errors in the retrieval of thin-cloud optical parameters obtained with a two-boundary algorithm

The effect of various errors on the retrieval of optical depth, integrated backscatter, and extinction-to-backscatter ratio in optically thin clouds by use of a two-boundary algorithm is discussed. Uncertainties regarding aerosol loading at the cloud base and top lead to relevant errors that are often larger than those produced by signal noise. Formulas expressing the errors in the lidar-derived optical quantities dependent on optical depth and aerosol uncertainties at the base and top are derived for different fitting procedures. A method for the reduction of errors in the case of consecutive cloud measurements is explored, consisting of the fitting of the retrieved optical-depth-integrated backscatter data to obtain a correct extinction-to-backscatter ratio.

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.

Effect of speckle on lidar pulse-pair ratio statistics

The ratio of temporally adjacent lidar pulse returns is commonly used in differential absorption lidar (DIAL) to reduce correlated noise. These pulses typically are generated at different wavelengths with the assumption that the dominant noise is common to both. This is not the case when the mean number of laser speckle integrated per pulse by the lidar receiver is small (namely, less than 10 speckles at each wavelength). In this case a large increase in the standard deviation of the ratio data results. We demonstrate this effect both theoretically and experimentally. The theoretical value for the expected standard deviation of the pulse-pair ratio data compares well with the measured values that used a dual CO(2) laser-based lidar with a hard target. Pulse averaging statistics of the pulse-pair data obey the expected varsigma(1)/ radicalN reduction in the standard deviation, varsigma(N), for N-pulse averages. We consider the ratio before average, average before ratio, and log of the ratio before average methods for noise reduction in the lidar equation. The implications of our results are discussed in the context of dual-laser versus single-laser lidar configurations.

Optical properties of tropospheric aerosols determined by lidar and spectrophotometric measurements (Photochemical Activity and Solar Ultraviolet Radiation campaign)

We present the results of the aerosol measurements carried out over the Aegean Sea during the Photochemical Activity and Solar Ultraviolet Radiation campaign held in Greece during June 1996. Simultaneous observations performed with a lidar and a double-monochromator spectrophotometer allowed us to retrieve the optical depth, the Angström coefficient, and the backscatter-to-extinction ratio. The Sun photometric data can be used to improve quantitative aerosol measurements by lidar in the Planetary Boundary Layer. Systematic errors could arise otherwise, because the value of the backscatter-to-extinction ratio has to be supplied. Instead this ratio can be retrieved experimentally by use of an iterative solution of the lidar equation.

Two-wavelength lidar inversion algorithm for a two-component atmosphere

A method for the boundary-value determination of aerosol extinction profiles from backscatter lidar measurements is presented. Artificially generated lidar signals from two-component inhomogeneous model atmospheres are inverted with the information from two wavelengths (532 and 1064 nm) simultaneously. The solution for the vertical aerosol extinction profile is formulated with Klett's far-end solution. The boundary value is expressed in terms of aerosol transmission along the lidar line according to Fernald's solution of the lidar equation. The aerosol transmission is determined iteratively with a transcendental equation on the assumption that a linear relationship exists between the extinction coefficients at both wavelengths. Inversion calculations are applied to model atmospheres with range-dependent lidar ratios representing the growth of aerosol particles caused by increasing relative humidity in the planetary boundary layer. For the inversion constant lidar ratios are assumed that vary between 40 and 70 sr. The numerical procedure turns out to be stable enough to provide meaningful results even in cases of misestimated lidar ratios. The application of the method is of less use for misestimated background radiation and low aerosol concentrations.

Tropospheric aerosol extinction coefficient profiles derived from scanning lidar measurements over Tsukuba, Japan, from 1990 to 1993

Mie scattering lidar was used to observe aerosol extinction coefficient profiles in the troposphere over Tsukuba (140 E, 36 N), Japan, for three years from March 1990 to February 1993, and data obtained in fair weather were analyzed. The lidar measurements were made by a vertical scanning mode to generate profiles of extinction coefficients from the lidar level to a 12-km altitude. The extinction coefficients were derived from the lidar signals using a two-component (air molecule and aerosol) lidar equation, in which the ratio of aerosol extinction to backscattering was assumed to be constant. Seasonal average profiles were derived from individual profiles. Three-year average profiles were also calculated and modeled using mathematical expressions. The model profile assumed (1) a constant extinction ratio in the atmospheric boundary layer (ABL), (2) an exponentially decreasing extinction ratio above the ABL, and (3) a constant extinction ratio in the upper troposphere where the extinction ratio can be defined as the ratio of the aerosol extinction coefficient to the air molecule extinction coefficient. The extinction ratios both in the ABL and in the upper troposphere and the scale height that was used to express the exponential decrease were used as three unknown parameters. Seasonal variation of optical thickness that was obtained by integrating extinction coefficients with height was also investigated.

Transmission as an input boundary value for an analytical solution of a single-scatter lidar equation

Single-scatter lidar signals carry information on the spatial atmospheric backscatter coefficient, attenuated by the path-integrated extinction. Assuming that the relationship between the backscatter and the extinction is known, the inverted extinction profile and the path-integrated extinction are uniquely related to the input boundary value. The integrated extinction over a certain range interval is a measure of the optical transmission along that path. In reverse, for a given transmission over the path of interest, the input boundary value is uniquely defined. An analytical expression is derived that describes the input boundary condition for the inversion of the single-scatter lidar equation in terms of the transmission losses over the path of interest. The proposed method is useful in situations in which independent transmission measurements are carried out or in situations in which targets such as multiple cloud layers or beam stops are available in the lidar path. Equations for both the forward and the backward integration method are presented. Compared with the widely accepted inversion schemes that are based on single-point reference extinction values, the proposed method is less sensitive to noise.

Measurements of stratospheric aerosols with a combined elastic-Raman-backscatter lidar

Improvements made to the NASA Goddard Space Flight Center Stratospheric Ozone Lidar system have extended its atmospheric-aerosol-measuring capabilities. The methods by which aerosol-scattering ratio, aerosol backscatter, and aerosol extinction are simultaneously derived from lidar data are reported, and results obtained during several intercomparison campaigns at worldwide locations are shown. The results track the evolution of the Mt. Pinatubo aerosol cloud from 1991 to 1994 and report wavelength-dependence information for aerosol backscatter between 308 and 351 nm. Two analysis techniques, a more common inversion method and a combined elastic-Raman-backscatter approach, are also compared.

Sensitivity of the lidar solution to errors of the aerosol backscatter-to-extinction ratio: influence of a monotonic change in the aerosol extinction coefficient

Unlike other errors in the lidar equation solution for the two-component atmosphere, the error of the measured aerosol extinction coefficient caused by inaccuracies in the assumed aerosol backscatter-to-extinction ratios significantly depends on the aerosol spatial inhomogeneity. In a slightly nonhomogeneous atmosphere, an incorrect value in the assumed aerosol backscatter-to-extinction ratio does not significantly corrupt the measurement result, whereas in an atmosphere with a large monotonic change of the aerosol extinction [e.g., in the lower troposphere], the incorrect value yields a large distortion of the retrieved extinction-coefficient profile. In the latter case, even the far-end solution can produce a large error in the retrieved extinction coefficient. The analytical formulas for the determination of the range errors, obtained for the Klett and the optical-depth solutions, show that these errors significantly depend on the method of the boundary-condition determination. Distortions of the retrieved aerosol extinction profiles are, in general, larger if the assumed aerosol backscatter-to-extinction ratio is underestimated in relation to the real value.

Lidar measurement of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios

An iterative lidar-signal inversion method is presented that is valid for two-component (molecular andaerosol) scattering atmospheres. The iterative procedure transforms the original lidar signal, thereby making it possible to use the lidar-equation solution for a single-component atmosphere. In a manner analogous to Fernald's approach, the molecular extinction profile is used as a foundation for the boundary-condition determination, but the inversion procedure can be performed with either constant or variable (range-dependent) phase functions. A specific region in the measured range is located at which the ratio of the aerosol to molecular extinction coefficients is a minimum as determined by an examinationof the lidar-signal profile; for this region boundary conditions are specified.

Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar

Height profiles of the extinction and the backscatter coefficients in cirrus clouds are determined independently from elastic- and inelastic- (Raman) backscatter signals. An extended error analysis is given. Examples covering the measured range of extinction-to-backscatter ratios (lidar ratios) in ice clouds are presented. Lidar ratios between 5 and 15 sr are usually found. A strong variation between 2 and 20 sr can be observed within one cloud profile. Particle extinction coefficients determined from inelastic-backscatter signals and from elastic-backscatter signals by using the Klett method are compared. The Klett solution of the extinction profile can be highly erroneous if the lidar ratio varies along the measuring range. On the other hand, simple backscatter lidars can provide reliable information about the cloud optical depth and the mean cloud lidar ratio.

Measurement of atmospheric aerosol extinction profiles with a Raman lidar

A method is presented that permits the determination of atmospheric aerosol extinction profiles from measured Raman lidar signals. No critical input parameters are needed, which could cause large uncertainties of the solution, as is the case in the Klett method for the inversion of elastic lidar returns.