Escape rate: a Lagrangian measure of particle deposition from the atmosphere

Abstract

Abstract. Due to rising or descending air and due to gravity, aerosol particles carry out a complicated, chaotic motion and move downwards on average. We simulate the motion of aerosol particles with an atmospheric dispersion model called the Real Particle Lagrangian Trajectory (RePLaT) model, i.e., by solving Newton's equation and by taking into account the impacts of precipitation and turbulent diffusion where necessary, particularly in the planetary boundary layer. Particles reaching the surface are considered to have escaped from the atmosphere. The number of non-escaped particles decreases with time. The short-term and long-term decay are found to be exponential and are characterized by escape rates. The reciprocal values of the short-term and long-term escape rates provide estimates of the average residence time of typical particles, and of exceptional ones that become convected or remain in the free atmosphere for an extremely long time, respectively. The escape rates of particles of different sizes are determined and found to vary in a broad range. The increase is roughly exponential with the particle size. These investigations provide a Lagrangian foundation for the concept of deposition rates.

The joy of transient chaos

“…It has an initially columnar shape of size 1 Â 1 Â 400 hPa (in the vertical, pressure coordinates are used), containing n 0 ¼ 2:16 Â 10 5 particles of radius r ¼ 5 lm centered at Mount Merapi at the height of about 5 km (p 0 ¼ 500 hPa), and is emitted at 00 UTC on 1 November 2010. 39 The particles spread and reach very different regions in the atmosphere since, entering into different vertical levels, they become subject to different horizontal winds. 20 days after the hypothetical emission, the particles cover a huge area and are well mixed in the midlatitudes of the Southern Hemisphere.…”

“…Scale analysis reveals that the horizontal velocity of a small aerosol particle takes over the actual local wind speed practically instantaneously, whereas vertically the terminal velocity w should be added to the vertical velocity component of air. 39,40 w depends on the radius r and density q p of the particle, as well as, on the density q and viscosity of the air at the location of the particle r_ ¼ vðrðtÞ; tÞ þ wn; (6) where vðr; tÞ is the wind field at point r and time t, and n is the vertical unit vector pointing downwards. Realistic aerosol particles not falling out within hours are of radius of at most 12 lm, and have a density of about q p ¼ 2000 kg/m 3 .…”

Time-Reversibility in Atmospheric Dispersion

“…If the particles represent not passive tracers, rather aerosol particles with realistic radius r and density ρ p (e.g., r = 1 µm, ρ p = 2000 kg·m −3 ), Equation (1) contains an additional term describing the gravitational settling of the particles [25]. In this case, particles can deposit on the ground in both the forward and the backward simulation, and during the backward one, particles that deposited in the forward run are treated as particles emitted from the surface in the appropriate time instant and location.…”

“…The RePLaT (Real Particle Lagrangian Trajectory) dispersion model, first formulated in [25], is used to calculate the trajectories of particles that compose the pollutant clouds. RePLaT is a Lagrangian model tracking aerosol particles with a realistic radius and density.…”

Escape dynamics through a continuously growing leak

“…Simple nonlinear dynamical systems in which trajectories may escape through an artificial leak [1] placed in the phase space play an important role in recent studies. Various fields of physics deal with either the escape dynamics of the particles or the decay rate of other physical quantities such as sound intensity, light rays, or fractal eigenstates [2][3][4][5][6][7][8]. It has been pointed out that the escape dynamics strongly depends on the leak size, position, and orientation [9][10][11][12][13][14][15] as well as on other pre-defined properties of the leak, for instance, the reflection coefficient [16].…”