We have developed a three-dimensional Eulerian regional acid deposition model to calculate episodic chemical concentrations and dry and wet deposition of acids in North America. This transport, transformation, and deposition modeling system subdivides the troposphere over the eastern United States, southeastern Canada, and the western Atlantic Ocean into a six-level, 30 by 30 horizontal grid with a horizontal grid size of 80 x 80 km/sup 2/. Transport and vertical diffusion of 24 trace gases and particles are calculated using temporally and spatially varying meteorology, provided by a mesoscale meteorological model. A gas phase chemical reaction mechanism is used to simulate concentrations and chemical conversion rates for 36 species, including 14 stable organics and 11 short-lived radicals. Altitude-, latitude-, and season-dependent photolysis rates for nine reactions in the chemical mechanism are specified using a delta-Eddington radiative transfer model which includes O/sub 2/ and O/sub 3/ absorption, scattering and absorption by clouds and aerosols, Rayleigh scattering, and ground relections.

A three-dimensional Eulerian acid deposition model: Physical concepts and formulation

Lagrangian Probability Density Function (PDF) methods have arisen the past 10 years as a union between PDF methods and stochastic Lagrangian models, similar to those that have long been used to study turbulent dispersion. The methods provide a computationally-tractable way of calculating the statistics, of inhomogeneous turbulent flows of practical importance, and are particularly attractive if chemical reactions are involved. The information contained at this level of closure--equivalent to a multi-time Lagrangian joint pdf--is considerably more than that provided by moment closures. The computational implementation is conceptually simple and natural. At a given time, the turbulent flow is represented by a large number of particles, each having its own set of properties--position, velocity, composition etc. These properties evolve in time according to stochastic model equations, so that the computational particles simulate fluid particles. The particle-property time series contain information equivalent to the multi-time Lagrangian joint pdf. But, at a fixed time, the ensemble of particle properties contains no multi-point information: Each particle can be considered to be sampled from a different realization of the flow. (Hence two particles can have the same position, but different velocities and compositions.) It is generally acknowledged (e.g. Reynolds 1990) that many different approaches have important roles to play in tackling the problems posed by turbulent flows. Each approach has its own strengths and weaknesses.

/pdf/lagrangian-pdf-methods-for-turbulent-flows-3y4l7og1ri.pdf

Lagrangian PDF Methods for Turbulent Flows

The authors examine the sensitivity of ozone concentrations in rural areas of the US to emissions of NO{sub x} and hydrocarbons using a regional photochemical model. Ozone production in rural areas appears to be limited by the availability of NO{sub x}. Rural ozone is strongly dependent on emission rates for NO{sub x} but is almost independent of hydrocarbons. This relationship is quite different from that in urban air, where ozone levels depend on both NO{sub x} and hydrocarbons. The predicted relationship between ozone and nitrogen oxides appears to be consistent with observations in rural air. For the low NO{sub x} regime (< 2 ppb) in rural areas, increases in NO{sub x} lead to increases in OH and to corresponding increases in the oxidation rate of hydrocarbons and in levels of ozone. Ozone concentrations in urban plumes appear to be related to regional scale production in addition to production within the plume.

The sensitivity of ozone to nitrogen oxides and hydrocarbons in regional ozone episodes

https://www.math.nyu.edu/faculty/majda/pdfFiles/PhysRep%201999%20Majda%20Kramer.pdf

Simplified models for turbulent diffusion : theory, numerical modelling, and physical phenomena

A new stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence is proposed. The model is three-dimensional and its formulation takes account of recent improvements in the understanding of one-particle models. In particular the model is designed so that if the particle pairs are initially well mixed in the fluid, they will remain so. In contrast to previous models, the new model leads to a prediction for the particle separation probability density function which is in qualitative agreement with inertial subrange theory. The values of concentration variance from the model show encouraging agreement with experimental data. The model results suggest that, at large times, the intensity of concentration fluctuations (i.e. standard deviation of concentration divided by mean concentration) tends to zero in stationary conditions and to a constant in decaying turbulence.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112090001239

A stochastic model for the motion of particle pairs in isotropic high-reynolds-number turbulence, and its application to the problem of concentration variance

F.A. Gifford

Papers

Horizontal diffusion in the atmosphere: A Lagrangian-dynamical theory

The time-scale of atmospheric diffusion considered in relation to the universal diffusion function, ƒ1

The random force theory applied to regional scale tropospheric diffusion

Tropospheric relative diffusion to hemispheric scales

Free tropospheric ozone production after deep convection of dispersing tropical urban plumes