Pathfinder: applying graph theory to consistent tracking of daytime mixed layer height with backscatter lidar

The height of the atmospheric boundary layer or mixing layer is an important parameter for understanding the dynamics of the atmosphere and the dispersion of trace gases and air pollution. The height of the mixing layer (MLH) can be retrieved, among other methods, from lidar or ceilometer backscatter data. These instruments use the vertical backscatter lidar signal to infer MLHL, which is feasible because the main sources of aerosols are situated at the surface and vertical gradients are expected to go from the aerosol loaded mixing layer close to the ground to the cleaner free atmosphere above. Various lidar/ceilometer algorithms are currently applied, but accounting for MLH temporal development is not always well taken care of. As a result, MLHL retrievals may jump between different atmospheric layers, rather than reliably track true MLH development over time. This hampers the usefulness of MLHL time series, e.g. for process studies, model validation/verification and climatology. Here, we introduce a new method pathfinder, which applies graph theory to simultaneously evaluate time frames that are consistent with scales of MLH dynamics, leading to coherent tracking of MLH. Starting from a grid of gradients in the backscatter profiles, MLH development is followed using Dijkstra's shortest path algorithm (Dijkstra, 1959). Locations of strong gradients are connected under the condition that subsequent points on the path are limited to a restricted vertical range. The search is further guided by rules based on the presence of clouds and residual layers. After being applied to backscatter lidar data from Cabauw, excellent agreement is found with wind profiler retrievals for a 12-day period in 2008 (R2 = 0.90) and visual judgment of lidar data during a full year in 2010 (R2 = 0.96). These values compare favourably to other MLHL methods applied to the same lidar data set and corroborate more consistent MLH tracking by pathfinder.