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.     

Two-wavelength lidar inversion algorithm for a two-component atmosphere with variable extinction-to-backscatter ratios

This numerical study addresses the boundary value determination of the aerosol extinction coefficient from backscatter lidar measurements by use of the simultaneous evaluation of signals at 532 and 1064 nm. The basic equations are formulated for the most common case of a two-component atmosphere with variable aerosol extinction-to-backscatter ratios along the lidar line. The method proved to be quite stable for optically thick atmospheres even if the true profiles of the lidar ratios are not known exactly.     

Validation of wind profiles measured with incoherent Doppler lidar

A high-resolution incoherent Doppler lidar has been constructed at the University of Michigan Space Physics Research Laboratory. The primary purpose of this lidar is to measure vertical profiles of the horizontal wind field with high spatial and temporal resolution. In mid-1994 a rawinsonde system was used to assess the performance of the lidar. The resulting comparisons of profiles from the balloons and the lidar are shown. The comparisons show an ~2-m/s rms error between the two systems. The reasons for this error are discussed, and a sensitivity study is shown to illustrate the sensitivity of the lidar wind measurements to various system parameters. Finally, steps that are being taken to improve the systematic errors are discussed.     

Measurements of density and temperature profiles in the middle atmosphere with a XeF lidar

Density and temperature profiles in the 30-70-km altitude range are measured with a XeF lidar system using Rayleigh scattering. With a 16-W XeF laser at wavelengths 351 and 353 nm, density and temperature accuracies of less than +/-3% and +/-10 K are obtained up to 60 km for an observation time of 15 min. The overall performances are now competitive with and superior to those of traditional Nd:YAG SHG lidars at 532 nm.     

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.     

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

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

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.     

Vertical versus scanning lidar measurements in a horizontally homogeneous atmosphere

This study compares the aerosol backscatter and extinction coefficients retrieved from vertical elastic and Raman channels with those derived from measurements with multiangle elastic channels. Retrievals from simulated vertical signals at 355 nm, 387 nm, 532 nm, and 607 nm are compared with those from multiangle measurements (at 15 elevation angles) at 355 nm and 532 nm. The atmosphere is considered horizontally homogeneously stratified. For the backscatter coefficient, the Raman backscatter solution and the multiangle solution are considered. For the extinction coefficient, retrievals from the Raman channel and multiangle measurements are compared. The comparison shows that in the presence of horizontal homogeneity, multiangle measurements provide more reliable results, especially for the aerosol extinction coefficient. The uncertainty in the measured signals is considered in an alternative approach to quantify the relative error of the retrieved profiles with respect to the models (linear regression between retrieval and model).     

Nonlinear-approximation technique for determining vertical ozone-concentration profiles with a differential-absorption lidar

A new technique is presented for the retrieval of ozone-concentration profiles (O(3)) from backscattered signals obtained by a multiwavelength differential-absorption lidar (DIAL). The technique makes it possible to reduce erroneous local fluctuations induced in the ozone-concentration profiles by signal noise and other phenomena such as aerosol inhomogeneity. Before the O(3) profiles are derived, the dominant measurement errors are estimated and uncertainty boundaries for the measured profiles are established. The off- to on-line signal ratio is transformed into an intermediate function, and analytical approximations of the function are then determined. The separation of low- and high-frequency constituents of the measured ozone profile is made by the application of different approximation fits to appropriate intermediate functions. The low-frequency constituents are approximated with a low-order polynomial fit, whereas the high-frequency constituents are approximated with a trigonometric fit. The latter fit makes it possible to correct the measured O(3) profiles in zones of large ozone-concentration gradients where the low-order polynomial fit is found to be insufficient. Application of this technique to experimental data obtained in the lower troposphere shows that erroneous fluctuations induced in the ozone-concentration profile by signal noise and aerosol inhomogeneity undergo a significant reduction in comparison with the results from the conventional technique based on straightforward numerical differentiation.     

Particle backscatter, extinction, and lidar ratio profiling with Raman lidar in south and north China

Aerosol Raman lidar observations of profiles of the particle extinction and backscatter coefficients and the respective extinction-to-backscatter ratio (lidar ratio) were performed under highly polluted conditions in the Pearl River Delta (PRD) in southern China in October 2004 and at Beijing during a clear period with moderately polluted to background aerosol conditions in January 2005. The anthropogenic haze in the PRD is characterized by volume light-extinction coefficients of particles ranging from approximately 200 to 800 Mm(-1) and lidar ratios mostly between 40 and 55 sr (average of 47+/-6 sr). Almost clean air masses were observed throughout the measurements of the Beijing campaign. These air masses originated from arid desert-steppe-like regions (greater Gobi area). Extinction values usually varied between 100 and 300 Mm(-1), and the lidar ratios were considerably lower (compared with PRD values) with values mostly from 30 to 45 sr (average of 38+/-7 sr). Gobi dust partly influenced the observations. Unexpectedly low lidar ratios of approximately 25 sr were found for a case of background aerosol with a low optical depth of 0.05. The low lidar ratios are consistent with Mie-scattering calculations applied to ground-based observations of particle size distributions.     

Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles

A new method is considered that can be used for inverting data obtained from a combined elastic-inelastic lidar or a high spectral resolution lidar operating in a one-directional mode, or an elastic lidar operating in a multiangle mode. The particulate extinction coefficient is retrieved from the simultaneously measured profiles of the particulate backscatter coefficient and the particulate optical depth. The stepwise profile of the column-integrated lidar ratio is found that provides best matching of the initial (inverted) profile of the optical depth to that obtained by the inversion of the backscatter-coefficient profile. The retrieval of the extinction coefficient is made without using numerical differentiation. The method reduces the level of random noise in the retrieved extinction coefficient to the level of noise in the inverted backscatter coefficient. Examples of simulated and experimental data are presented.     

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.     

Determination of stratospheric aerosol microphysical properties from independent extinction and backscattering measurements with a Raman lidar

An algorithm that permits the retrieval of profiles of particle mass and surface-area concentrations in the stratospheric aerosol layer from independently measured aerosol (particle and Rayleigh) and molecule (Raman or Rayleigh) backscatter signals is developed. The determination is based on simultaneously obtained particle extinction and backscatter profiles and on relations between optical and microphysical properties found from Mie-scattering calculations for realistic stratospheric particle size distributions. The size distributions were measured with particle counters released on balloons from Laramie, Wyoming, between June 1991 and April 1994. Mass and surface-area concentrations can be retrieved with relative errors of 10-20% and 20-40%, respectively, with a laser wavelength of 355 nm and with errors of 20-30% and 30-60%, respectively, with a laser wavelength of 308 nm. Lidar measurements taken within the first three years after the eruption of Mt. Pinatubo in June 1991 are shown. Surface-area concentrations around 20 μm(2) cm(-3) and mass concentrations of 3 to 6 μg m(-3) were found until spring 1993.     

Experimental determination of a geometric form factor in a lidar equation for an inhomogeneous atmosphere

We experimentally determine a geometric form factor for an inhomogeneous atmosphere by using the polynomial regression method in a lidar equation.     

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.     

Self-aligning lidar for the continuous monitoring of the atmosphere

In a lidar system an accurate transmitter-receiver alignment is essential for correct results. Usually this optical adjustment is time consuming and requires the intervention of highly qualified personnel. As a solution to this problem, a fast and precise automatic alignment procedure is presented, based on a simple model of the transmitter-receiver overlap. The lidar mounted at the Naples University is used to test this method. A centering precision of few microradians is obtained through dedicated software controlling a gimbal-mounted mirror. The automatic alignment procedure is then assessed. In particular, the correctness of the center and of its error is determined. Finally, the system is applied to the monitoring of tropospheric aerosols, leading to the continuous retrieval of profiles with fine spatiotemporal resolution.