From the range of low-Earth orbit (already several 100 km), it is not hard to design lidar systems with large enough footprints that essentially all orders of scattering are included in the signal returned from a typical cloud layer. This signal is therefore the temporal Green function of the cloud excited by a distributed pulse of photons. We will survey the basic time-dependent photon diffusion theory that replaces the standard lidar/radar equation for such active observation systems. We will show how to extract physical cloud parameters (physical and optical thicknesses, possibly stratification and horizontal variability) from the data using either the temporal moments or the time-decay rate. We will illustrate the proposed retrievals using pulses from LITE (Lidar-In-space Technology Experiment), the ground-breaking 1994 Shuttle mission. Finally, more cloud information —or improved parameter determinations— can be obtained if there is also a spatial component in the data (e.g., a narrow and large field-of-view).

We will draw an important parallel between large-footprint lidar observations of clouds and oxygen-band/line spectroscopy of solar photons propagating in said clouds. The high-resolution differential absorption spectroscopy can be used to reconstruct the Laplace transform of the pathlength distribution of the solar photons in the cloud, precisely what would be observed in the time-domain if the Sun were pulsed! So the same physical cloud information is present in the spectroscopic signal and the same moment-based methods apply. However, we do have to distinguish the case of transmitted light (ground-based instruments) and reflected light (airborne and satellite-based systems). Things get even more interesting when there are multiple layers of clouds and/or unresolved broken clouds: the classic photon diffusion problem becomes “anomalous” (i.e., nontrivial mixtures of large and small steps between scatterings or reflections). We will present a phenomenological theory for this more complex case.