Michael A. Box

Forwardscattering corrections for optical extinction measurements in aerosol media. 2: Polydispersions

This paper, second of two parts, presents a parametric study of the forwardscattering corrections for experimentally measured optical extinction coefficients in polydisperse particulate media, since some forward scattered light invariably enters, along with the direct beam, into the finite aperture of the detector. Forwardscattering corrections are computed by two methods: (1) using the exact Mie theory, and (2) the approximate Rayleigh diffraction formula for spherical particles. A parametric study of the dependence of the corrections on mode radii, real and imaginary parts of the complex refractive index, and half-angle of the detectors view cone has been carried out for three different size distribution functions of the modified Gamma type. In addition, a study has been carried out to investigate the range of these parameters in which the approximate formulation is valid. The agreement is especially good for small-view cone angles and large particles, which improves significantly for slightly absorbing aerosol particles. Also discussed is the dependence of these corrections on the experimental design of the transmissometer systems.

The Scaling Group of the Radiative Transfer Equation

Abstract We show that the equation of radiative transfer is invariant under a group of simultaneous transformations of the scale (i.e., the optical thickness) and the phase function. In this way, we provide a unified explanation of various empirical scaling laws, similarity relations and other approximations (especially delta-function approximations) which have been proposed in the literature. Connections with critical-point behavior in statistical mechanics are also indicated.

A linearized radiative transfer model for ozone profile retrieval using the analytical forward-adjoint perturbation theory approach

For the retrieval of ozone profiles from space-borne radiance measurements, a new linearized radiative transfer model LIRA is presented. The model enables an effective linearization of the reflectance at the top of the atmosphere with respect to both the ozone density in the different layers of the model atmosphere and the Lambertian surface albedo in the UV of the solar spectrum. The linearization of the model is based on the forward-adjoint perturbation theory, where the forward and adjoint solution of the scalar radiative transfer equation in its plane-parallel form are achieved by employing the Gauss-Seidel iteration technique. For clear sky and aerosol-loaded atmospheres the model provides the reflectance as well as its derivatives with respect to ozone density with an accuracy of better than 0.02%. The derivatives with respect to surface reflection can be calculated with an error of less than 0.05%. The suitability of the model for ozone profile retrieval is demonstrated. Therefore ozone profiles are retrieved from 156 modeled radiance measurements, simulating real radiance measurements of the Global Ozone Monitoring Experiment (GOME) spectrometer in the UV. The comparison of the retrieved profiles using the proposed model LIRA with a reference retrieval shows small deviations in the stratosphere and upper troposphere of less than 1% and tolerable differences in the middle and lower troposphere of up to 10% in the mean profile at ground level.

Retrieval of aerosol size distributions by inversion of simulated aureole data in the presence of multiple scattering.

Inversion of solar almucantar data is a simple and practical method of obtaining aerosol size distributions. In this paper, we have inverted a number of sets of simulated data, using the standard single scattering approximation, to test the errors involved in ignoring multiple scattering. We have also inverted the data using two techniques: one, a modification of the method proposed by Deirmendjian and Sekera; and the other that of McPeters and Green. Inversion results strongly suggest that the accuracy of the retrieved size distribution can be significantly improved by use of our modified Deirmendjian-Sekera approach, in which multiple scattering by molecules is included along with single scattering by molecules and aerosols.

Multi year satellite remote sensing of particulate matter air quality over Sydney, Australia

Particulate matter (PM) air‐quality information is usually derived from ground‐based instruments. These measurements, while valuable, are not well suited to provide air‐quality information over large spatial scales. In this study, using 4 years of satellite aerosol optical thickness (AOT) at 0.55 µm derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board NASAs Terra and Aqua satellites, we present a multi‐year air analysis of PM air quality over Sydney, Australia. We then compare the satellite data with PM2.5 mass concentration measurements from six ground‐based stations in the area. Our results indicate significant diurnal variations and an overall increase in PM2.5 during Southern Hemisphere spring and summer seasons due to bush fires. The air quality in Sydney, Australia is good throughout the year except during major bushfires when PM2.5 mass loading can increase from normal (<20 µg m−3) to unhealthy conditions (>70 µg m−3). The satellite data also show corresponding AOT changes from less than 0.1 to greater than 1.0 during bushfire events. We conclude that satellite data are an excellent tool for studying PM air quality over large areas, especially when ground measurements are not available. While this is the first multi‐year combined satellite and ground‐based air quality analysis over Sydney, ancillary information from lidars, sun photometers, and size‐resolved chemistry measurements will further enhance our capability to monitor and forecast air quality in and around Sydney.

Inversion of Mie extinction measurements using analytic eigenfunction theory

Abstract We have employed the analytic eigenfunction technique, first developed by McWhirter and Pike, to obtain aerosol columnar size distributions from realistic Mie extinction measurements. The theory was tested out and its range of validity established using synthetic data. After that, the method was applied to several sets of volcanic ash cloud data, and the results compared with those for a constrained linear inversion. The technique is extremely easy to apply once the Mellin transform of the kernel has been obtained.

Information content analysis of aerosol remote-sensing experiments using an analytic eigenfunction theory: anomalous diffraction approximation.

An important step in any planned remote-sensing experiment is an analysis of the information content of the equations which will finally be inverted. In this paper we show the value of performing such an analysis using a recently developed analytic eigenfunction theory. So that we may fully utilize the analytic nature of this technique, we have applied it first to the anomalous diffraction approximation to the Mie theory extinction efficiency. Analytical expressions for the eigenfunctions and eigenvalues are derived. The effects of ill-conditioning, and their amelioration due to the inclusion of certain a priori knowledge, are then investigated.

Analytic inversion of multispectral extinction data in the anomalous diffraction approximation.

We obtain a simple integral formula for the radius distribution function or polydispersion n(r) in terms of the multispectral extinction τ(k), where k is the wavenumber. This formula is valid when the extinction coefficient is given by the anomalous diffraction approximation and n(r) vanishes faster than r∊ as r → 0 for some positive ∊.

Radiative effects of absorbing aerosols and the impact of water vapor

The radiative effects (both forcing at the tropopause and absorption in the lower troposphere) of standard aerosol models are examined as a function of relative humidity. Several of the models are also modified by the inclusion of additional soot, in line with recent observations. Increasing relative humidity causes many aerosol types to expand and also increases their single-scattering albedo. We have examined the impacts of these changes and also the interaction between aerosol growth and absorption of solar radiation by water vapor. These effects are seen not to be additive, especially in the case of flux divergence due to absorbing aerosols.

Radiative perturbation theory: a review

Abstract Radiative perturbation theory is a computational technique which can greatly ease the burden of repeated solution of the radiative transfer equation for model atmospheres which differ from one another by only relatively small changes in some of the optical parameters. It requires the solution of both the radiative transfer equation, and its adjoint, followed by some usually straightforward integrations of these solutions. In this work we review the theoretical structure of the technique, and discuss a series of applications which have already demonstrated its utility. Future developments of the theory, and new applications currently under consideration, are also discussed.