Spurr, RJD (2004). A new approach to the retrieval of surface properties from earthshine measurements. JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 83(1), 15-46.

Instruments such as the MODIS and MISR radiometers on EOS AM-1, and POLDER on ADEOS have been deployed for the remote sensing retrieval of surface properties. Typically, retrieval algorithms use linear combinations of semi-empirical bidirectional reflectance distribution function (BRDF) kernels to model surface reflectance. The retrieval proceeds in two steps; first, an atmospheric correction relates surface BRDF to top-of-atmosphere (TOA) reflectances, then regression is used to establish the linear coefficients used in the kernel combination. BRDF kernels may also depend on a number of physical or empirical non-linear parameters (e.g. ocean wind speed for a specular BRDF); such parameters are usually assumed known. A major source of error in this retrieval comes from lack of knowledge of planetary boundary layer (PBL) aerosol properties. In this paper, we present a different approach to surface property retrieval. For the radiative transfer simulations, we use the discrete ordinate LIDORT model, which has the capability to generate simultaneous fields of radiances and weighting functions in a multiply scattering multi-layer atmosphere. Surface-atmosphere coupling due to multiple scattering and reflection effects is treated in full; the use of an atmospheric correction is not required. Further, it is shown that sensitivities of TOA reflectances to both linear and non-linear surface BRDF parameters may be established directly by explicit analytic differentiation of the discrete ordinate radiative transfer equations. Surface properties may thus be retrieved directly and conveniently from satellite measurements using standard non-linear fitting methods. In the fitting for BRDF parameters, lower-boundary aerosol properties can either be retrieved as auxiliary parameters, or they can be regarded as forward model parameter errors. We present examples of simulated radiances and surface/aerosol weighting functions for combinations of multi-angle measurements at several different wavelengths, and we perform some examples of self-consistent non-linear fitting to demonstrate feasibility for this kind of surface property retrieval.