A holistic framework to estimate the origins of atmospheric moisture and heat using a Lagrangian model

Despite the existing myriad of tools and models to assess atmospheric source–receptor relationships, their uncertainties remain largely unexplored and arguably stem from the scarcity of observations available for validation. Yet, Lagrangian models are increasingly used to determine the origin of precipitation and atmospheric heat, scrutinizing the changes in moisture and temperature along air parcel trajectories. Here, we present a holistic framework for the process-based evaluation of atmospheric trajectories to infer source–receptor relationships of both moisture and heat. The framework comprises three steps: (i) the diagnosis of moisture and heat from Lagrangian trajectories using multi-objective criteria to evaluate the accuracy and reliability of the fluxes, (ii) the attribution of sources following mass- and energy-conserving algorithms in order to establish source–receptor relationships, and (iii) the bias correction of diagnosed fluxes and the corresponding source–receptor relationships. Applying this framework to simulations from the Lagrangian model FLEXPART, driven with ERA-Interim reanalysis data, allows us to quantify the errors and uncertainties associated with the resulting source–receptor relationships for three cities in different climates (Beijing, Denver and Windhoek). Our results reveal large uncertainties inherent in the estimation of heat and precipitation origin with Lagrangian models, but they also demonstrate the synergistic impacts of source- and sink bias-corrections. The proposed framework paves the way for a cohesive assessment of the dependencies in source–receptor relationships.

A Coupled Eulerian–Lagrangian Model for Sliding Inception of Elastic–Plastic Spherical Contact

Currently existing finite element (FE) Lagrangian models of elastic–plastic spherical contact are costly in terms of computing time to reach vanishing tangential stiffness at sliding inception. A coupled Eulerian–Lagrangian (CEL) model with explicit dynamic analysis and power-law hardening is proposed to resolve this problem. The CEL model also avoids convergence problem caused by excessive distortion of elements in Lagrangian models. Static friction coefficient at sliding inception is investigated and compared with available experimental results. It is found that the proposed new CEL model is more efficient and accurate compared to previously published results of Lagrangian models.