ALBERT

Notes: Summary This article analyzes the nature of the aerosol information that current or planned spacecraft measurements could contribute toward the required input data for studies of natural anthropogenic influences on the middle atmosphere, and their consequent effects on our weather and climate. The analysis is conducted with particular reference to the solar occultation sounding technique as applied by the SAGE I experiment on the Atmospheric Explorer Mission B spacecraft. Its conclusions should prove to be of use in both the interpretation of the SAGE I data, and in the design of the follow-on mission on the Earth Radiation Budget satellite. Our analysis shows, in particular, that further studies are required in: the choice and number of sounding channels; the data taking sequence in relation to the atmospheric regions probed; the accuracy and vertical resolution of the atmospheric profiling, and their dependence on both the instrument/spacecraft parameters and the data inversion techniques; and the data reduction procedures. Neither of the selected channels is in a one-to-one relationship with an atmospheric constituent; hence, unless further assumptions are introduced, inversion techniques based on such a property are not applicable. The aerosol wavelengths are not satisfactory as they are only sensitive to the large size tail of the aerosol size distribution rather than to the predominant sizes; for these, UV wavelengths would be required. Owing to the change of the Sun's shape due to atmospheric refraction as the Sun either sets or rises, the higher altitudes will be scanned fewer times than the lower altitudes. Also, because transmission approaches rapidly unity above ∼40 km, the same high altitudes are more sensitive to measurement errors-errors that will propagate to lower altitude determinations when inverted profiles are reconstructed from the top of the atmosphere. These two factors, combined with the small air mass values at the high altitudes, are the cause of the mathematical ill-conditioning of the inversion problem. They point toward the need for a data-taking sequence strategy that would trade off between data storage and transmission constraints, larger accuracy at the high altitudes, and proper division of the atmosphere in order to overcome the ill-conditioning. Likewise, and as a result of the above considerations, there is a need for a detailed trade off study between data accuracy and vertical resolution of the reconstructed profiles. This should take into account the seasonal and geographical variations in the distribution of atmospheric constituents, as well as a representative statistical set at any given location and time, appropriate error measures and their vertical profiles, and several inversions utilizing as initial guesses profiles that depart from the true ones. It is also shown that the aerosol and ozone number densities cannot be recovered simultaneously without introducing some formula for the aerosol extincition or assumptions on the form of the aerosol size distribution. This problem is not resolved by the addition of sounding channels because each such channel introduces an additional unknown aerosol extinction. Thus, one is led to a separate rather than a simultaneous determination of the various constituents by resorting to complementary measurements. For a future experiment, it is suggested to determine the ozone separately from measurements at a close pair of appropriate wavelengths between which the aerosol extinction varies slowly whereas that of ozone exhibits a rapid variation. A similar technique could also be used for the separate determination of NO2. The relaxation-type of inversion suggest byChu andMcCormick (1979) does not seem to be appropriate because each channel is not sensitive selectively to an individual constituent, the aerosol channels are not sensitive to the important sizes in the distribution, and the sensitivity of the channels to the constituents of interest varies greatly with altitude. In the retrieval of the vertical profiles, the cause of the ill-conditioning of the inversion is identified. Two approaches are suggested for overconing this problem: (i) build the profile starting from the top of the atmosphere (forward procedure) but with an initial layer of sufficient air mass, or preferably (ii) reconstruct the profile from the lowest altitude reached (backward procedure) with a renormalization at the top of the atmosphere. In this process, the minimization search method (Fymat, 1976) would appear to be a better technique than the onion-peeling technique, as demonstrated byMill andDrayson (1978). In order to maximize the scientific return of SAGE I, a data inversion procedure is proposed. It assumes that (i) there are no aerosols above ∼25 km, and no NO2 below this altitude (as suggested byChu andMcCormick, 1979), (ii) below ∼25 km, ozone (and NO2, if present) could be determined separately, and (iii) the aerosol has a known refractive index at all wavelengths of interest, is assumed to be spherical (or describable in terms of ‘equivalent spheres’), and the minimum and maximum radii of its size distribution are known a priori. Under these assumptions, it is possible to retrieve the neutral density, NO2 and O3 profiles above ∼25 km, by either the forward or the backward procedure described above. Taking into consideration the power law variation of the air density with altitude, it is further possible to reconstruct the corresponding profiles at all the lower altitudes from the determinations in the altitude range ∼30–40 km. Below ∼25 km, the four SAGE I channels would then all become available for the aerosol inversion. While the profile reconstruction could proceed as for the higher altitudes, the aerosol inversion at each individual altitude presents problems of its own. Results of numerical experiments for aerosol inversion using all four SAGE wavelengths and seven different inversion routines are presented. If good a priori information is available on the sought size distribution solution, reasonably satisfactory inversions can be performed (see line 1 of Table 2, and Fig. 3c and 3d). However, in the absence of such information, there are as many solutions as inversion methods tried, in complete conformity with the well-known ill-conditioning of the problem. Among methods providing physically meaningful solutions, no method could be singled out as preferable to the others. In these inversions, the data were assumed to be exact, and 99% of the distribution were used. Under different conditions, the nonuniqueness of the inversion would be further compounded. Lastly, based on the present study, a strategy is suggested for the design and data interpretation of a follow-on SAGE-type experiment. Considering the important advantages to this problem presented by forward scattering, as demonstrated byFymat andMease (1978), a composite (extinction-forward scattering) experiment is recommended for the future experiments.

Notes: Abstract Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing an arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities.

Notes: Abstract A complete set of transfer equations required for the order-of-scattering analysis of partially polarized radiation in inhomogeneous, anisotropically scattering atmospheres is provided. The equations have been derived for both a local study using the radiative transfer equation and its associated auxiliary equation for the source-matrix, and a global study in terms of the scattering and transmission matrices; they account for the polarity of the scattering medium. Their derivations for the finite order scattering and the finitely cumulative scattering, in particular, have yielded important new equations expressing the invariance principles and the integro-differential recurrences for the scattering and transmission matrices. These novel expressions contain as a special case Bellmanet al's (1972) equations for the simpler case of isotropic scattering of unpolarized light in homogeneous atmospheres.

Notes: Abstract Reciprocity and symmetry relationships, representing local invariants for the scattering phase-matrix, are derived for twelve cases of particle assemblies studied by van de Hulst (1957) including situations of scattering in an arbitrary direction, in the near forward and near backward directions. These relations are used to generate corresponding relations representing global invariants for the scattering and transmission matrices of atmospheres consisting of such assemblies. The latter relations are obtained from the matrix integro-differential equations for scattering and transmission; they apply to single scattering, any finite order of scattering, and after an arbitrary cumulation of scattering orders (finite or infinite). Our results are summarized in Tables I and II for general inhomogeneous atmospheres and for particular inhomogeneous atmospheres that are symmetrical with respect to their central level. The latter case includes homogeneous atmospheres as a special case. The largest set of local relations obtained contains three independent relations (called universal, reversal, exchange) which can further be combined to yield four additional dependent relations. This circumstance happens in three out of the above twelve cases. In the remaining cases fewer relations (both independent and dependent) remain valid. Likewise, a maximal set of three independent global relations is obtained for general inhomogeneous atmospheres; they too can be linearly combined to yield seven other dependent relations. For the symmetrically inhomogeneous atmospheres, three independent and seven dependent additional relations are obtained. On the basis of these tables, it becomes a trivial matter to provide the local and global invariants (both the independent and the dependent relations) for any assembly of particles and atmospheric inhomogeneity. A mixture of Rayleigh-Cabannes scattering by anisotropic molecules or extremely small particles and Mie scattering by large isotropic particles is considered for illustration. Lastly, the group properties of these invariants are studied.