In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an odd vector field $Q$ obeying $\{Q,Q\}=0$ and with $Q$-invariant odd symplectic structure. We study geometry of $QP$-manifolds. In particular, we describe some construction of $QP$-manifolds and prove a classification theorem (under certain conditions). We apply these geometric constructions to obtain in natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern-Simons theory in BV-formalism arises as a sigma-model with target space $\Pi {\cal G}$. (Here ${\cal G}$ stands for a Lie algebra and $\Pi$ denotes parity inversion.)Comment: 29 pages, Plain TeX, minor modifications in English are made by Jim Stasheff, some misprints are corrected, acknowledgements and references adde

The cloud droplet number concentration (N d) is of central interest to improve the understanding of cloud physics and for quantifying the effective radiative forcing by aerosol‐cloud interactions. Current standard satellite retrievals do not operationally provide N d, but it can be inferred from retrievals of cloud optical depth (τ c) cloud droplet effective radius (r e) and cloud top temperature. This review summarizes issues with this approach and quantifies uncertainties. A total relative uncertainty of 78% is inferred for pixel‐level retrievals for relatively homogeneous, optically thick and unobscured stratiform clouds with favorable viewing geometry. The uncertainty is even greater if these conditions are not met. For averages over 1° ×1° regions the uncertainty is reduced to 54% assuming random errors for instrument uncertainties. In contrast, the few evaluation studies against reference in situ observations suggest much better accuracy with little variability in the bias. More such studies are required for a better error characterization. N d uncertainty is dominated by errors in r e, and therefore, improvements in r e retrievals would greatly improve the quality of the N d retrievals. Recommendations are made for how this might be achieved. Some existing N d data sets are compared and discussed, and best practices for the use of N d data from current passive instruments (e.g., filtering criteria) are recommended. Emerging alternative N d estimates are also considered. First, new ideas to use additional information from existing and upcoming spaceborne instruments are discussed, and second, approaches using high‐quality ground‐based observations are examined.

We present an algorithm for the retrieval of cloud droplet size distribution parameters (effective radius and variance) from the Research Scanning Polarimeter (RSP) measurements. The RSP is an airborne prototype for the Aerosol Polarimetery Sensor (APS), which was on-board of the NASA Glory satellite. This instrument measures both polarized and total reflectance in 9 spectral channels with central wavelengths ranging from 410 to 2260 nm. The cloud droplet size retrievals use the polarized reflectance in the scattering angle range between 135°and 165°, where they exhibit the sharply defined structure known as the rain-or cloud-bow. The shape of the rainbow is determined mainly by the single scattering properties of cloud particles. This significantly simplifies both forward modeling and inversions, while also substantially reducing uncertainties caused by the aerosol loading and possible presence of undetected clouds nearby. In this study we present the accuracy evaluation of our algorithm based on the results of sensitivity tests performed using realistic simulated cloud radiation fields.