Multi-Variable Tensor Decomposition Analytics

Time evolving meteorological variables of daily observations from multiple sources can be represented as simple 3-node tensors. Powerful analytic tools such as canonical polyadic (cp) tensor decomposition are available to factor streaming tensors into tensor approximations associated with dominant components. We show the potential of tensor decomposition for meteorological analysis by presenting multi-year experiments for inferring Planetary Boundary Layer Heights (PBLH) by employing cp tensor decomposition analytics applied to streaming ceilometer base Lidar data sets. The experiment compares the PBLH obtained from the 3 nodes tensor consisting of 5 minutes streams of hourly Lidar based aerosol backscatter profiles each day from 3 distinctly located ceilometers distributed along the East coast for a 1.5 years period from May 7, 2021-June 30, 2022. We compare the PBLH derived from the ceilometers with those inferred from a WRF model simulation for the same period with two nested intervals over the CONUS at 2 deg. and 0.9 deg., interpolated to the same locations as the ceilometers. The WRF model integration is forced by the interpolated hourly NOAA GFS reanalysis data set and annual averaged aerosols distributions specified geographically over the CONUS grid. We present graphs of the time dependence of the dominant tensor components of PBLH as well as the error of the dominant tensors for various assumptions of tensor rank. These dominant components show the correlations of PBLH over 24 hours over multiple regions.