ABSTRACT
The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.
ABSTRACT
Equations for Rayleigh scattering in a mixture of gases are derived and compared to frequent approximations in the literature. The traditional Rayleigh scattering equation as modified by King for scatter from a pure gas is correct, whereas another version sometimes appearing in modern literature is erroneous. Use of a mixture's refractive index, which is equivalent to assuming the isotropic molecular polarizabilities of the component gases are identical, is an approximation. Another common approximation is using only number-density weighting of the King factors. Approximation errors can be large when the major components of a mixture have disparate optical properties. Fortunately, the errors for Earth's air are much smaller and comparable to errors from other sources.
ABSTRACT
The Ozone Profiling Atmospheric Lidar is a scanning four-wavelength ultraviolet differential absorption lidar that measures tropospheric ozone and aerosols. Derived profiles from the lidar data include ozone concentration, aerosol extinction, and calibrated aerosol backscatter. Aerosol calibrations assume a clear air region aloft. Other products include cloud base heights, aerosol layer heights, and scans of particulate plumes from aircraft. The aerosol data range from 280 m to 12 km with 5 m range resolution, while the ozone data ranges from 280 m to about 1.2 km with 100 m resolution. In horizontally homogeneous atmospheres, data from multiple-elevation angles is combined to reduce the minimum altitude of the aerosol and ozone profiles to about 20 m. The lidar design, the characterization of the photomultiplier tubes, ozone and aerosol analysis techniques, and sample data are described. Also discussed is a double-gating technique to shorten the gated turn-on time of the photomultiplier tubes, and thereby reduce the detection of background light and the outgoing laser pulse.
ABSTRACT
Simulation studies were carried out with regard to the feasibility of using combined observations from sunphotometer (SPM) and lidar for microphysical characterization of aerosol particles, i.e., the retrieval of effective radius, volume, and surface-area concentrations. It was shown that for single, homogeneous aerosol layers, the aerosol parameters can be retrieved with an average accuracy of 30% for a wide range of particle size distributions. Based on the simulations, an instrument combination consisting of a lidar that measures particle backscattering at 355 and 1574 nm, and a SPM that measures at three to four channels in the range from 340 to 1020 nm is a promising tool for aerosol characterization. The inversion algorithm has been tested for a set of experimental data. The comparison with the particle size distribution parameters, measured with in situ instrumentation at the lidar site, showed good agreement.
