Wavelet analysis is applied to airborne infrared lidar data to obtain an objective determination of boundaries in aerosol backscatter that are associated with boundary layer structure. This technique allows high-resolution spatial variability of planetary boundary layer height and other structures to be derived in complex, multilayered atmospheres. The technique is illustrated using data from four different lidar systems deployed on four different field campaigns. One case illustrates high-frequency retrieval of the top of a strongly convective boundary layer. A second case illustrates the retrieval of multiple layers in a complex, stably stratified region of the lower troposphere. The method is easily modified to allow for varying aerosol distributions and data quality. Two more difficult cases, data that contain a great deal of instrumental noise and a cloud-topped convective layer, are described briefly. The method is also adaptable to model analysis, as is shown via application to large eddy simulation data.

S U M M A R YMantle convection models require an initial condition some time in the past. Because this initial condition is unknown for Earth, we cannot infer the geological evolution of mantle flow from forward mantle convection calculations even for the most recent Mesozoic and Cenozoic geological history of our planet. Here we introduce a fluid dynamic inverse problem to constrain unknown mantle flow back in time from seismic tomographic observations of the mantle and reconstructions of past plate motions using variational data assimilation. We derive the generalized inverse of mantle convection and explore the initial condition problem in high-resolution, 3-D spherical mantle circulation models for a time period of 100 Myr, roughly comparable to half a mantle overturn. We present a synthetic modelling experiment to demonstrate that mid-Cretaceous mantle structure can be inferred accurately from fluid dynamic inverse modelling, assuming present-day mantle structure is well-known, even if an initial first guess assumption about the mid-Cretaceous mantle involved only a simple 1-D radial temperature profile. We also demonstrate that convecting present-day mantle structure back in time by reversing the time-stepping of the energy equation is insufficient to model the mantle structure of the past. The difficulty arises, because such backward convection calculations ignore thermal diffusion effects, and therefore cannot account for the generation of thermal buoyancy in boundary layers as we go back in time. Inverse mantle convection modelling should make it possible to infer a number of flow parameters from observational constraints of the mantle.

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