Lagrangian Trajectories Research Articles

Lagrangian model for passive scalar gradients in turbulence

The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier–Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the chosen Lagrangian path: the pressure Hessian and the viscous Laplacian. A recent model handles these unclosed terms using a multi-level version of the recent deformation of Gaussian fields (RDGF) closure (Johnson & Meneveau, Phys. Rev. Fluids, vol. 2 (7), 2017, 072601). This model is in remarkable agreement with direct numerical simulations (DNS) data and works for arbitrary Taylor Reynolds numbers $\textit {Re}_\lambda$ . Inspired by this, we develop a Lagrangian model for passive scalar gradients in isotropic turbulence. The equation for passive scalar gradients also involves an unclosed term in the Lagrangian frame, namely the scalar gradient diffusion term, which we model using the RDGF approach. However, comparisons of the statistics obtained from this model with DNS data reveal substantial errors due to erroneously large fluctuations generated by the model. We address this defect by incorporating into the closure approximation information regarding the scalar gradient production along the local trajectory history of the particle. This modified model makes predictions for the scalar gradients, their production rates, and alignments with the strain-rate eigenvectors that are in very good agreement with DNS data. However, while the model yields valid predictions up to $\textit {Re}_\lambda \approx 500$ , beyond this, the model breaks down.

Wind-driven advection across temperature gradients enhances iron-induced phytoplankton blooms in the Antarctic Polar Front

We demonstrate how the wind-driven Ekman transport enhances the advection and mixing of cells from the colder waters of the Surface Antarctic Waters from the south to the warmer waters of the northern Polar Front (PF) belt. This mechanism provides cells a mean ambient temperature near optimum levels for specific species and, ultimately, for community growth rates high enough to develop blooms under non-light limiting macronutrients and iron conditions. A Lagrangian trajectory model was constructed for tracking plankton cells as tracers forced by winds and surface currents. Depending on the region along the circumpolar front, increased winds can enhance this process across temperature gradients, and further accelerate such temperature-controlled growth. These results indicate that favorable temperature may enhance the growth rate even further when iron is sufficiently available, and thus have far-reaching implications for increased productivity in a future warming climate.

A Lagrangian Trajectory Analysis of Azimuthally Asymmetric Equivalent Potential Temperature in the Outer Core of Sheared Tropical Cyclones

A Lagrangian Trajectory Analysis of Azimuthally Asymmetric Equivalent Potential Temperature in the Outer Core of Sheared Tropical Cyclones

Implications of Emission Sources and Biosphere Exchange on Temporal Variations of CO2 and δ13C Using Continuous Atmospheric Measurements at Shadnagar (India)

AbstractDiurnal variation of atmospheric CO2 and its driving factors are studied using high‐precision in situ mixing ratio measurements and stable carbon isotopic CO2 (δ13C‐CO2) for the first time over Shadnagar, a suburban site in India, from November 2018 to October 2019. The annual mean mixing ratios of atmospheric CO2 and δ13C‐CO2 are observed to be 414.76 ± 4.26 ppm and −11.19 ‰ ± 1.63 ‰. Maximum diurnal variability of atmospheric CO2 was observed in summer monsoon (17.30 ± 9.29 ppm), and the minimum was noticed in winter (7.19 ± 0.11 ppm), indicating strong seasonality in diurnal variability of amplitude. To characterize the atmospheric CO2 sources, the Miller‐Tans model was implemented separately using the CO2 and its δ13C‐CO2 isotopic data during day and night. However, a strong source signature of δ13C‐CO2 was observed during the night‐time of summer monsoon with a slope of −37.42‰ ± 0.73‰, obtained using a reduced major axis regression. The identified source indicates possible emissions from fossil fuel combustion. Further, a Lagrangian back trajectory analysis was performed to study the influence of transport on the observed CO2 mixing ratios. The model trajectory confirms the influence of the Indian summer monsoon on the variations of atmospheric CO2 mixing ratios. Our study shows that fossil fuel emissions are one of the major contributors of CO2 in the study location (about ∼2 to 4 ppm) with biogenic fluxes adding a clear seasonality ranging from −8 to 4 ppm.

Improving trajectory calculations by FLEXPART 10.4+ using single-image super-resolution

Abstract. Lagrangian trajectory or particle dispersion models as well as semi-Lagrangian advection schemes require meteorological data such as wind, temperature and geopotential at the exact spatiotemporal locations of the particles that move independently from a regular grid. Traditionally, these high-resolution data have been obtained by interpolating the meteorological parameters from the gridded data of a meteorological model or reanalysis, e.g., using linear interpolation in space and time. However, interpolation is a large source of error for these models. Reducing them requires meteorological input fields with high space and time resolution, which may not always be available and can cause severe data storage and transfer problems. Here, we interpret this problem as a single-image super-resolution task. That is, we interpret meteorological fields available at their native resolution as low-resolution images and train deep neural networks to upscale them to a higher resolution, thereby providing more accurate data for Lagrangian models. We train various versions of the state-of-the-art enhanced deep residual networks for super-resolution (EDSR) on low-resolution ERA5 reanalysis data with the goal to upscale these data to an arbitrary spatial resolution. We show that the resulting upscaled wind fields have root-mean-squared errors half the size of the winds obtained with linear spatial interpolation at acceptable computational inference costs. In a test setup using the Lagrangian particle dispersion model FLEXPART and reduced-resolution wind fields, we find that absolute horizontal transport deviations of calculated trajectories from “true” trajectories calculated with un-degraded 0.5∘ × 0.5∘ winds are reduced by at least 49.5 % (21.8 %) after 48 h relative to trajectories using linear interpolation of the wind data when training on 2∘ × 2∘ to 1∘ × 1∘ (4∘ × 4∘ to 2∘ × 2∘) resolution data.

The sources of extreme precipitation predictability; the case of the ‘Wet’ Red Sea Trough

Extreme precipitation events inflict detrimental socio-economic impacts in the Eastern Mediterranean. These are mainly associated with Mediterranean cyclones or the ‘Wet’ Red Sea Trough (WRST). The region's weather forecasters consider the second challenging to forecast, even just a few days in advance. Here, we study the dynamic and thermodynamic factors influencing the intrinsic predictability of WRST events. With this aim, we combine insights from traditional atmospheric analysis techniques, Lagrangian air-parcel backward trajectories, and dynamical systems theory. The latter describes atmospheric states via their local dimension (d) and inverse persistence (θ), which inform us of the intrinsic predictability of the atmosphere in phase space. We compare WRST events of low (upper decile of d and θ) with high (lower decile of d and θ) predictability. We argue that low-predictability events display a significantly different atmospheric pattern. Moreover, the low-predictability events show significantly higher daily precipitation rates, more extensive spatial spread, and greater precipitation variability among events than more predictable ones. On average, low predictability events are initiated by two distinct moisture sources with different water vapor content. We conclude that the dynamical systems framework may become a valuable tool to improve the forecast of extreme precipitation events associated with the WRST by providing a priori information on their intrinsic predictability. We foresee successfully implementing such a framework for other extreme weather events and regions.

A Lagrangian Study of Tidal Advection of Mesospheric Water Vapor

AbstractPrevious studies have demonstrated that the diurnal variability of mesospheric water vapor involves a non‐linear interplay between dynamics, photochemistry, and catalytic processes. The inherent difficulty in measurement of winds and water vapor in this region makes the study of mesospheric water vapor complex. Here we study the sources of diurnal variability of mesospheric water vapor with the help of the specified dynamics configuration of the Whole Atmosphere Community Climate Model (WACCM) with thermosphere‐ionosphere eXtension (SD‐WACCM‐X) for typical equinox conditions during the solar minimum year 2009. Special emphasis is given to the advective transport by the migrating diurnal tide and its impact on the mean water vapor in the mesosphere. To isolate the contribution from advective and non‐advective processes, a Lagrangian parcel trajectory model is employed. Using this model, we incorporated the effect of both vertical and horizontal tidal advection on the diurnal variability of mesospheric water vapor. Our results indicate that the vertical tidal advection dominates the transport of water vapor in the upper mesosphere and that there is a significant contribution from horizontal tidal advection below 70 km. Among non‐advective processes, chemical loss of water vapor has the largest contribution. The Lagrangian parcel trajectory approach is further extended using the recently released version 2.07 of water vapor observations from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument and dynamical tides from the empirical Climatological Tidal Model for the Thermosphere (CTMT). Differences in SD‐WACCM‐X and CTMT + SABER results are discussed in light of the veracity of SABER water vapor measurements.

A kind of Lagrangian chaotic property of the Arnold–Beltrami–Childress flow

Three-dimensional steady-state Arnold–Beltrami–Childress (ABC) flow has a chaotic Lagrangian structure, and also satisfies the Navier–Stokes (NS) equations with an external force per unit mass. It is well known that, although trajectories of a chaotic system have sensitive dependence on initial conditions, i.e. the famous ‘butterfly effect’, their statistical properties are often insensitive to small disturbances. This kind of chaos (such as governed by the Lorenz equations) is called normal-chaos. However, a new concept, i.e. ultra-chaos, has been reported recently, whose statistics are unstable to tiny disturbances. Thus, ultra-chaos represents higher disorder than normal chaos. In this paper, we illustrate that ultra-chaos widely exists in Lagrangian trajectories of fluid particles in steady-state ABC flow. Moreover, solving the NS equation when $Re=50$ with the ABC flow plus a very small disturbance as the initial condition, it is found that trajectories of nearly all fluid particles become ultra-chaotic when the transition from laminar to turbulence occurs. These numerical experiments and facts highly suggest that ultra-chaos should have a relationship with turbulence. This paper identifies differences between ultra-chaos and sensitivity of statistics to parameters. Possible relationships between ultra-chaos and the Poincaré section, ultra-chaos and ergodicity/non-ergodicity, etc., are discussed. The concept of ultra-chaos opens a new perspective of chaos, the Poincaré section, ergodicity/non-ergodicity, turbulence and their inter-relationships.

Rossby waves past the breaking point in zonally dominated turbulence

The spontaneous emergence of structure is a ubiquitous process observed in fluid and plasma turbulence. These structures typically manifest as flows which remain coherent over a range of spatial and temporal scales, resisting statistically homogeneous description. This work conducts a computational and theoretical study of coherence in turbulent flows in the stochastically forced barotropic$\beta$-plane quasi-geostrophic equations. These equations serve as a prototypical two-dimensional model for turbulent flows in Jovian atmospheres, and can also be extended to study flows in magnetically confined fusion plasmas. First, analysis of direct numerical simulations demonstrates that a significant fraction of the flow energy is organized into coherent large-scale Rossby wave eigenmodes, comparable with the total energy in the zonal flows. A characterization is given for Rossby wave eigenmodes as nearly integrable perturbations to zonal flow Lagrangian trajectories, linking finite-dimensional deterministic Hamiltonian chaos in the plane to a laminar-to-turbulent flow transition. Poincaré section analysis reveals that Lagrangian flows induced by the zonal flows plus large-scale waves exhibit localized chaotic regions bounded by invariant tori, manifesting as Rossby wave breaking in the absence of critical layers. It is argued that the surviving invariant tori organize the large-scale flows into a single temporally and zonally varying laminar flow, suggesting a form of self-organization and wave stability that can account for the resilience of the observed large-amplitude Rossby waves.

Dry air intrusions link Rossby wave breaking to large-scale dust storms in Northwest Africa: Four extreme cases

Large dust storms in the Saharan desert and the subsequent transport of airborne dust over large distances are a major meteorological hazard. Several mechanisms associated to dust emission, occurring on a range of scales, have been previously documented, notably involving Rossby wave breaking and a low-level jet. However, the mechanistic link between the different features and actual dust concentrations has not been coherently established. Here, using a Lagrangian approach, and the conceptual view of extratropical cyclone airstreams, the role of the dry intrusion airstream for translating the influence of the upper-tropospheric Rossby wave perturbation to near-surface flow conductive for the highest dust concentrations is examined. To this end, four large-scale dust storms that were accompanied by dry intrusions in west Africa are studied. Data from the Copernicus Atmospheric Monitoring Service (validated against AERONET station data) are combined with atmospheric data from reanalysis and objectively-identified Lagrangian trajectories of dry intrusions. Common, coherent structures highlighting the role of dry intrusions link the upper-tropospheric Rossby wave breaks with the lower-tropospheric dry and cold jets. These conditions favor dust uplift and transport along an arc-shaped cold front trailing from a Mediterranean cyclone. Consequently, the southwest side of the front is characterized by the highest near-surface dust concentrations ahead of the dry intrusion outflow, where the Intertropical Discontinuity shifts equatorward by 3 to 7°. The northeast part of the front is, however, accompanied by southerly, warm conveyor belt-like flow transporting the dust northward to the Mediterranean, Middle East and/or Europe at mid and upper-tropospheric levels. While case-to-case variations exists, the central role of dry intrusions in all cases calls for systematic investigation of its occurrence as a predictive tool for large dust transport events.

Convectively Transported Water Vapor Plumes in the Midlatitude Lower Stratosphere

AbstractDeep convective overshooting has been shown to transport water vapor into the midlatitude lower stratosphere. However, it has not been demonstrated how the convective water vapor plumes evolve after the overshoots collapse. Furthermore, there is a lack of characterization of the convective water vapor plumes, nor is it clear whether satellite instruments can observe the characteristics. We use a high‐resolution numerical weather prediction model to study a convective system over North America. Multiple overshoots transport water vapor in the overworld stratosphere, forming a moist layer between 16.2 and 16.8 km (389.8–399.7 K), with horizontal diameters of about 300–400 km, and a maximum water vapor mixing ratio of 10.0 ppmv (4.3 ppmv anomaly). Lagrangian trajectories and mass integrations show the overworld water vapor plumes are maintained after the convective system weakens. In the lowermost stratosphere (LMS), water vapor plumes are less stable and ice is present, because there is perturbation by ongoing convection. Lagrangian trajectories and mass integrations show the LMS parcels partly return to the troposphere, and that the LMS water vapor mass is reduced by half after the convection weakens. On average, the LMS moistening is between 15.0 and 15.8 km (362.6–382.0 K), with horizontal diameters of about 150 km, and a maximum water vapor mixing ratio of 31.1 ppmv (18.4 ppmv anomaly). Although current satellites have difficulty observing the fine structure of the convective water vapor plumes, a new satellite instrument under development (SHOW) with 1‐km vertical and 100‐km horizontal resolution will be able to verify the plume characteristics.

Surface cross-equatorial pathways of seawater from the Bay of Bengal

Cross-equatorial pathways of heat and salt in the Eastern Indian Ocean are analyzed using Lagrangian trajectories based on the ECCO2 model simulation and drifter-derived currents combined with Argo data. The results show that most of the particles released in the Bay of Bengal move across the equator near the eastern boundary of the upper Indian Ocean (< 50m) during the southwest monsoon season and join the South Equatorial Current of the wind-driven circulation. Meridional salt and heat transports associated with the cross-equatorial currents feature significant seasonal variations, with stronger southward transports during the southwest monsoon than northward transports during the northeast monsoon, which are correlated significantly with the surface Ekman transports. The estimated annual mean salt and heat transports, based on the model (observational) data, are -0.06×109 (-0.11×109) kg·s-1 and -0.20 (-0.38) PW (1PW = 1015 W), respectively, southward across the equator.

Atmospheric water transport connectivity within and between ocean basins and land

Abstract. The global atmospheric water transport from the net evaporation to the net precipitation regions has been traced using Lagrangian trajectories. A matrix has been constructed by selecting various group of trajectories based on their surface starting (net evaporation) and ending (net precipitation) positions to show the connectivity of the 3-D atmospheric water transport within and between the three major ocean basins and the global landmass. The analysis reveals that a major portion of the net evaporated water precipitates back into the same region, namely 67 % for the Indian Ocean, 64 % for the Atlantic Ocean, 85 % for the Pacific Ocean and 72 % for the global landmass. It has also been calculated that 58 % of the net terrestrial precipitation was sourced from land evaporation. The net evaporation from the subtropical regions of the Indian, Atlantic and Pacific oceans is found to be the primary source of atmospheric water for precipitation over the Intertropical Convergence Zone (ITCZ) in the corresponding basins. The net evaporated waters from the subtropical and western Indian Ocean were traced as the source for precipitation over the South Asian and eastern African landmass, while Atlantic Ocean waters are responsible for rainfall over North Asia and western Africa. Atlantic storm tracks were identified as the carrier of atmospheric water that precipitates over Europe, while the Pacific storm tracks were responsible for North American, eastern Asian and Australian precipitation. The bulk of South and Central American precipitation is found to have its source in the tropical Atlantic Ocean. The land-to-land atmospheric water transport is pronounced over the Amazon basin, western coast of South America, Congo basin, northeastern Asia, Canada and Greenland. The ocean-to-land and land-to-ocean water transport through the atmosphere was computed to be 2×109 and 1×109 kg s−1, respectively. The difference between them (net ocean-to-land transport), i.e. 1×109 kg s−1, is transported to land. This net transport is approximately the same as found in previous estimates which were calculated from the global surface water budget.

Lagrangian turbulence statistics using 3D-PTV: Realistic virtual experiment assessment

The outcome of a three-dimensional particle tracking velocimetry (3D-PTV) experiment can be significantly improved if the influence of the camera locations, calibration, and light volume can be determined before conducting the experiment. Such a-priory assessment will also reduce the time for troubleshooting a 3D-PTV experiment. In this paper, we report a “virtual experiment” approach. Multiple frames of synthetic particle images are generated using triangulation and optical spread functions based on the Lagrangian trajectories in 3D velocity fields with known spatio-temporal characteristics. We use an analytical 3D Burger’s vortex, and the homogeneous isotropic turbulence (HIT) data-set from the turbulence database hosted by Johns Hopkins University (JHU). The 3D particle positions are projected on two-dimensional (2D) images using artificial extrinsic and intrinsic camera matrices, depth of field, and volume illumination. These 2D images served as images taken by a four-camera 3D-PTV system in a virtual experiment. Blind test calibration using OpenPTV, an open source software, reconstructs the camera positions for a simulated experimental set-up and the calibrated set-up is used to create Lagrangian trajectories from the particle image sequences. Finally, we compare the turbulent statistics reconstructed from the virtual experiment with that of the ground truth data. We show that reconstruction from a virtual 3D-PTV experiment reproduces the mean flow and turbulent statistics faithfully; however, the disparity increases for higher order and multi-point statistics. The proposed approach can be used to fine-tune the camera parameters and the light volume in order to increase the fidelity of turbulent flow measurements using 3D-PTV.

Large eddy simulations of the accumulation of buoyant material in oceanic wind-driven and convective turbulence

Buoyant material such as microplastics accumulate near the ocean surface in regions with convergent surface currents where they can be harmful to marine life. Here, we use large eddy simulations to investigate the transport and accumulation of buoyant material in a turbulent ocean mixed layer under combined wind and convection forcing. We model non-inertial buoyant particles with a combination of buoyant tracers and Lagrangian surface particles, which allows us to explore a wide range of particle buoyancies. Surface cooling drives convection, and under this regime persistent convective vortices form that trap buoyant particles, leading to large concentrations. Despite their small size, the convective vortices exhibit a bias towards cyclonic vorticity that has not been reported previously. Based on an analysis of Lagrangian trajectories, the average time that a particle spends inside a convective vortex is long enough for planetary vorticity to become important and further vortex stretching causes an exponential increase in vorticity. When wind forcing is included, there is a transition from convective cells to longitudinal wind rolls with three distinct flow patterns observed under weak, moderate and strong wind forcing. For sufficiently weak winds, convective vortices survive but are less effective at trapping buoyant material. Under strong wind forcing, convective vortices no longer exist, but some clustering occurs in regions of high speed associated with longitudinal wind rolls. We quantify the degree of clustering using the Gini coefficient and find that clustering is strongly influenced by the relative size of the friction and convective velocities and the particle buoyancy.

Evaluation of the distribution of COVID-19 particles in an Isolation room to reduce the possibility of transmission via CFD simulation

The outbreak and prolonged COVID-19 pandemic has caused a population decline as well as a profound impact on the global economy, the COVID virus spreads highly in the air through the process of sneezing, contact leads to many dangers to the health and safety of people around the world. Many simulation studies have been carried out to predict the risk of spread, as well as to find solutions to limit the infection when spreading sneeze droplets in the air. In this study, the motion and distribution of droplets containing coronaviruses emitted by coughing or sneezing in the isolation room at Ho Chi Minh City, Vietnam National University were investigated using ANSYS Fluent software. The airflow in the isolation room was simulated by a 3D turbulence model and energy equation using the finite volume method (FVM) with a domain of isolation room solved for appropriate boundary conditions. The effect of ventilation airflow speed and the size of droplets on the distribution of particles in the air were investigated by the Lagrangian particle trajectory analysis method. The CFD analysis result showed that the velocity distribution, turbulent kinetic energy, and flow dynamics had strongly affected the reducing rate of average droplet concentration in the isolation room. Specifically, the study focused on the dispersion of liquid droplets containing the virus under fixed operating conditions of ventilation systems and exhaust fans, with a flow rate of 840 m3/h. Under these conditions, the retention time of liquid droplets was determined to be 37.5 seconds, corresponding to droplet diameters ranging from 5 to 100 micrometres. The results indicate that the presence of particles in the room gradually becomes diluted over time due to the continuous circulation of air. The ability of air to diffuse within the vicinity of the occupant's position and the limited spread of small particles within the room demonstrate that the operating conditions are suitable.

A data-driven machine learning framework for modeling of turbulent mixing flows

A novel computationally efficient machine learning (ML) framework has been developed for constructing the turbulent flow field of single-phase or two-phase particle-liquid flows in a mechanically agitated vessel by feeding a very short-term experimental Lagrangian trajectory. Using a supervised k-nearest neighbors regressor learning algorithm coupled with a Gaussian process, the framework predicts the mean flow and turbulent fluctuations by sharing the statistical features learned from experimental data. The capability of the ML framework is evaluated by comparing the flow dynamics of predicted trajectories to extensive Lagrangian particle tracking measurements under various flow conditions. Local velocity distributions, Lagrangian statistical analysis, solid concentration distributions, and phase flow numbers show very good agreement between ML-predictions and experiments. Being accurate, efficient, and robust, the ML framework is a powerful tool for analyzing and modeling multiphase flow systems using a minimal amount of driver data input, which can equally be provided from any reliable numerical simulation, thus avoiding costly experimental measurements.

Short Path Wind-Field Distance-Based Lagrangian Trajectory Model for Enhancing Atmospheric Dispersion Prediction Accuracy

Short Path Wind-Field Distance-Based Lagrangian Trajectory Model for Enhancing Atmospheric Dispersion Prediction Accuracy

Closed SPARSE—A predictive particle cloud tracer

A closed and predictive particle cloud tracer method is presented that models the mean motion and deformation of a cloud of inertial particles at a singular point in space and along its Lagrangian trajectory in time. The tracer builds upon the Subgrid Particle-Averaged Reynolds Stress Equivalent (SPARSE) formulation first introduced in Davis et al. (2017) for the tracing of particle clouds. It was later extended to a Cloud-In-Cell (CIC) formulation in Taverniers et al. (2019) using a Gaussian distribution of a cloud’s influence over a mesh-based, velocity field solution. SPARSE corrects the cloud’s trace to second order by combining a Taylor series expansion of the drag coefficient and Nusselt number correction factors around the mean relative velocity of a cloud of particles with a Reynolds decomposition of the particle equations to obtain a governing system for the first two statistical moments of the cloud’s position, velocity and temperature. Here, we close the thus far unclosed SPARSE formulation by determining the velocity field in the vicinity of the mean cloud location using a truncated Taylor series velocity representation and by combining that with averaging. The resulting tracer is predictive. It enables the tracing of a cloud of particles through a single point and so reduces the required degrees of freedom in the accurate tracing of groups of particles. We demonstrate the accuracy and convergence of the method in several one-, two- and three-dimensional test cases.

The Troposphere-to-Stratosphere Transport Caused by a Rossby Wave Breaking Event over the Tibetan Plateau in Mid-March 2006

Based on reanalysis data, satellite ozone concentration observations, and a Lagrangian trajectory simulation, a Rossby wave breaking (RWB) event and its effect on stratosphere–troposphere exchange (STE) over the Tibetan Plateau in mid-March 2006 were investigated. Results showed that the increased eddy heat flux from the subtropical westerly jet magnified the amplitude of the Rossby wave, which contributed to the occurrence of the cyclonic RWB event. The quasi-horizontal cyclonic motion of the isentropic potential vorticity in the RWB cut the tropical tropospheric air mass into the extratropical stratosphere, completing the stratosphere–troposphere mass exchange. Meanwhile, the tropopause folding zone extended polewards by 10° of latitude and the tropospheric air mass escaped from the tropical tropopause layer into the extratropical stratosphere through the tropopause folding zone. The particles in the troposphere-to-stratosphere transport (TST) pathway migrated both eastwards and polewards in the horizontal direction, and shifted upwards in the vertical direction. Eventually, the mass of the TST particles reached about 3.8 × 1014 kg, accounting for 42.2% of the particles near the tropopause in the RWB event. The rest of the particles remained in the troposphere, where they moved eastwards rapidly along the westerly jet and slid down in the downstream upper frontal zone.