Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Corporate social performance and stock returns: UK evidence from disaggregate measures

This study examines the relation between corporate social performance and stock returns in the UK. We closely evaluate the interactions between social and financial performance with a set of disaggregated social performance indicators for environment, employment, and community activities instead of using an aggregate measure. While scores on a composite social performance indicator are negatively related to stock returns, we find the poor financial reward offered by such firms is attributable to their good social performance on the environment and, to a lesser extent, the community aspects. Considerable abnormal returns are available from holding a portfolio of the socially least desirable stocks. These relationships between social and financial performance can be rationalized by multi-factor models for explaining the cross-sectional variation in returns, but not by industry effects.