Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows.

The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.

On polarimetric radar signatures of deep convection for model evaluation: columns of specific differential phase observed during MC3E.

The representation of deep convection in general circulation models is in part informed by cloud-resolving models (CRMs) that function at higher spatial and temporal resolution; however, recent studies have shown that CRMs often fail at capturing the details of deep convection updrafts. With the goal of providing constraint on CRM simulation of deep convection updrafts, ground-based remote-sensing observations are analyzed and statistically correlated for four deep convection events observed during the Midlatitude Continental Convective Clouds Experiment (MC3E). Since positive values of specific differential phase (KDP) observed above the melting level are associated with deep convection updraft cells, so-called "KDP columns" are analyzed using two scanning polarimetric radars in Oklahoma: the National Weather Service Vance WSR-88D (KVNX) and the Department of Energy C-band Scanning Atmospheric Radiation Measurement (ARM) Precipitation Radar (C-SAPR). KVNX and C-SAPR KDP volumes and columns are then statistically correlated with vertical winds retrieved via multi-Doppler wind analysis, lightning flash activity derived from the Oklahoma Lightning Mapping Array, and KVNX differential reflectivity (ZDR). Results indicate strong correlations of KDP volume above the melting level with updraft mass flux, lightning flash activity, and intense rainfall. Analysis of KDP columns reveals signatures of changing updraft properties from one storm event to another as well as during event evolution. Comparison of ZDR to KDP shows commonalities in information content of each, as well as potential problems with ZDR associated with observational artifacts.