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.     

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.     

Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio

An intercomparison of the algorithms used to retrieve aerosol extinction and backscatter starting from Raman lidar signals has been performed by 11 groups of lidar scientists involved in the European Aerosol Research Lidar Network (EARLINET). This intercomparison is part of an extended quality assurance program performed on aerosol lidars in the EARLINET. Lidar instruments and aerosol backscatter algorithms were tested separately. The Raman lidar algorithms were tested by use of synthetic lidar data, simulated at 355, 532, 386, and 607 nm, with realistic experimental and atmospheric conditions taken into account. The intercomparison demonstrates that the data-handling procedures used by all the lidar groups provide satisfactory results. Extinction profiles show mean deviations from the correct solution within 10% in the planetary boundary layer (PBL), and backscatter profiles, retrieved by use of algorithms based on the combined Raman elastic-backscatter lidar technique, show mean deviations from solutions within 20% up to 2 km. The intercomparison was also carried out for the lidar ratio and produced profiles that show a mean deviation from the solution within 20% in the PBL. The mean value of this parameter was also calculated within a lofted aerosol layer at higher altitudes that is representative of typical layers related to special events such as Saharan dust outbreaks, forest fires, and volcanic eruptions. Here deviations were within 15%.     

Validation of the Raman lidar algorithm for quantifying aerosol extinction

To calculate aerosol extinction from Raman lidar data, it is necessary to evaluate the derivative of a molecular Raman signal with respect to range. The typical approach taken in the lidar community is to make an a priori assumption about the functional behavior of the data to calculate the derivative. It has previously been shown that the use of the chi-squared technique to determine the most likely functional behavior of the data prior to actually calculating the derivative eliminates the need for making a priori assumptions. Here that technique is validated through numerical simulation and by application to a significant body of Raman lidar measurements. In general, we show that the chi-squared approach for evaluating extinction yields lower extinction uncertainty than traditional techniques. We also use the technique to study the feasibility of developing a general characterization of the extinction uncertainty that could permit the uncertainty in Raman lidar aerosol extinction measurements to be estimated accurately without the need of the chi-squared technique.     

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.     

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.     

Sensitivity of roots to errors in the coefficient of polynomialsobtained by frequency-domain estimation methods

Although the roots of a polynomial of high order are extremely sensitive to perturbations in its coefficients, experience has demonstrated that frequency-domain estimation techniques succeed in the determination of accurate poles and zeros, even in the case of high-order transfer function models. The authors prove that this is due to the correlations among the estimated coefficients. When the result of a measurement is a set of correlated values, they conclude that it is not justifiable to use the standard deviation to determine the number of significant digits. Additional digits have to be considered in order to maintain the information enclosed in the correlations     

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.     

Combined Raman lidar for the measurement of atmospheric temperature,water vapor,particle extinction coefficient,and particle backscatter coefficient

The lidar of the Radio Science Center for Space and Atmosphere (RASC; Kyoto, Japan) make use of two pure rotational Raman (MR) signals for both the measurement of the atmospheric temperature profile and the derivation of a temperature-independent Raman reference signal. The latter technique is new and leads to significant smaller measurement uncertainties compared with the commonly used vibrational Raman lidar technique. For the measurement of temperature, particle extinction coefficient, particle backscatter coefficient, and humidity simultaneously, only four lidar signal are needed the elastic Cabannes backscatter signal, two RR signals, and the vibrational Raman water vapor signal. The RASC lidar provides RR signals of unprecedented intensity. Although only 25% of the RR signal intensities can be used with the present data-acquisition electronics, the 1-s -statistical uncertainty of nighttime temperature measurements is lower than for previous systems and is < 1K up to 11-km height for, e.g., a resolution of 500 m and 9 min. In addition, RR measurements in daytime also have become feasible.     

Estimating the change point of a normal process mean with a monotonic change

One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. In this paper, we describe the behavior model of process mean and then obtain a maximum‐likelihood estimator (MLE) for the change point of the normal process mean without requiring the exact knowledge of the change type. Instead, we assume that the type of change present belongs to a family of monotonic changes. Finally, we study the performance of the proposed change‐point estimator relative to the MLEs for the process mean change point derived under a simple step change and linear trend change assumption. We do this for a number of monotonic change types following a signal from a Shewhart X̄ control chart. Copyright © 2008 John Wiley & Sons, Ltd.     

Distortion of particulate extinction profiles measured with lidar in a two-component atmosphere

Distortions of particular extinction-coefficient profiles measured with lidar in a two-component (molecular and aerosol) scattering atmosphere are analyzed. The error of the extinction coefficient measured at range r depends on the location of the point r(b), where a boundary value is specified, and the particulate optical depth of the atmosphere between r and r(b); the particulate backscatter-to-extinction ratio; and the ratio of particulate and molecular scattering extinction. If the near-end solution is used, small measurement errors can produce a significant divergence between the actual and the retrieved extinction-coefficient profiles, even if the boundary value and the particulate backscatter-to-extinction ratio are specified accurately. This effect is exacerbated at small values of the particulate scattering coefficient and the backscatter-to-extinction ratio. When reasonable criteria are used, feasible minimum and maximum boundary values can be specified to restrict the range of lidar equation solutions from below and from above.     

Iterative method for the inversion of multiwavelength lidar signals to determine aerosol size distribution

Two iterative methods of inverting lidar backscatter signals to determine altitude profiles of aerosol extinction and altitude-resolved aerosol size distribution (ASD) are presented. The first method is for inverting two-wavelength lidar signals in which the shape of the ASD is assumed to be of power-law type, and the second method is for inverting multiwavelength lidar signals without assuming any a priori analytical form of ASD. An arbitrary value of the aerosol extinction-to-backscatter ratio (S(1)) is assumed initially to invert the lidar signals, and the ASD determined by use of the spectral dependence of the retrieved aerosol extinction coefficients is used to improve the value of S(1) iteratively. The methods are tested for different forms of altitude-dependent ASD's by use of simulated lidar-backscatter-signal profiles. The effect of random noise on the lidar backscatter signals is also studied.     

Analysis of the performance of a coherent pulsed fiber lidar for aerosol backscatter applications

The antenna and the Doppler estimation characteristics of a coherent pulsed lidar intended for short-range aerosol backscatter applications have been analyzed. The system used fiber-optic interconnects and operated at a wavelength of 1.548 microm. The range dependence of the signal for various bistatic and monostatic antenna configurations has been determined. The system operated in a low-pulse-energy, high-pulse-repetition-rate mode, and the Doppler estimates from the return signal were achieved with a multipulse accumulation procedure. The expected performance of the accumulation in this low-photocount regime was compared with the data obtained from the system, and a reasonable level of agreement was demonstrated.     

Sensitivity analysis of differential absorption lidar measurements in the mid-infrared region

The availability of new laser sources that are tunable in the IR spectral region opens new perspectives for differential absorption lidar (DIAL) measurements. A region of particular interest is located in the near IR, where some of the atmospheric pollutants have absorption lines that permit monitoring of emissions from industrial plants and in urban areas. In DIAL measurements, the absorption lines for the species to be measured must be carefully chosen to prevent interference from other molecules, to minimize the dependence of the absorption cross section on temperature, and to optimize the measurements with respect to the optical depth. We analyze the influence of these factors and discuss a set of criteria for selecting the best pairs of wavelengths (lambda(on) and lambda(off)) to be used in DIAL measurements of several molecular species (HCl, CO, CO(2), NO(2), CH(4), H(2)O, and O(2)). Moreover, a sensitivity study has been carried out for selected lines in three different regimes: clean air, urban polluted air, and emission from an incinerator stack.     

Sensitivity of surface reflectance retrieval to uncertainties in aerosol optical properties

We formulate a procedure to investigate the sensitivity of surface reflectances retrieved from satellite sensor data to uncertainties in aerosol optical properties. Aerosol optical characteristics encompassed in the study include the aerosol optical depth, the Junge parameter (i.e., spectral dependence), and the imaginary part of the refractive index (i.e., aerosol absorption). The study includes both clear and hazy atmospheric conditions, wavelengths of 0.550 and 0.870 μm, three solar zenith angles, and five viewing geometries. Key results are presented graphically in terms of accuracy requirements on the aerosol property under consideration for a 5% uncertainty in predicted surface reflectance.