Modelling of Pollutant Transport in the Atmosphere - MANHAZ

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II Diffusion Theories and associated Atmospheric Dispersion Models In the following a short review is given on the diffusion theories and model categories from which most practical dispersion models used today are based. Fixed and moving frames of reference In this chapter, the word "plume" will be used to designate a continuous release of pollutant from a point source, while the word "puff" will be used about an instantaneous released quantity of pollutant. So while the different segments of pollutants belonging to a plume all have different travel times since their release from the source point, all pollutants belonging to a single puff have one, and only one age since their start of release, namely the puffs travel time t. Two fundamental different types of atmospheric dispersion must be discriminated: 1. Fixed frame concentrations 2. Moving frame concentrations The fixed frame averaged concentration is measured at, or is referred to, at fixed points (on the ground), while the instantaneous concentration refers to a moving frame of reference, which follows with the cloud or puff's centre of mass. For this reason, averaged (whether time averaged or ensemble-averaged), dispersion is often referred to as " fixed frame" dispersion or absolute dispersion- while instantaneous dispersion often is referred to as "moving frame dispersion, or "relative dispersion". The physical mechanisms behind the two types of dispersion are quite different: While the averaged mean concentration and its associated dispersion, process phenomenologically can be described by single and independent fluid particle's trajectory ensemble statistics; the instantaneous puff dispersion process involves at least the joint statistics of two fluid particles or more at the same time. Much fundamental research and theoretical formation has during the past century been devoted to model and describe the turbulent diffusion process within the atmosphere The field has in particular been dominated 12
y Russian and British researchers the Twentieth century. A short review is given next: The classical distinctions among diffusion theories as used in the atmosphere have traditional been (in historical order): 1. diffusion equation methods (stability classes) 2. statistical methods (Random walk models – Kinematic simulation methods); 3. Lagrangian similarity scaling Ad. 1 Diffusion equation methods (stability classes) Anomalous Diffusion The classical approach to describe the atmospheric diffusion process was based on a generalization of the heat diffusion process known from solid-state physics, and the molecular diffusion process known from gas diffusion. In the beginning of last century, atmospheric physicists such as Prandl referred to the atmospheric diffusion process as "anomalous" diffusion, because it was much faster than the hitherto known "nomalous" (molecular) Brownian diffusion. The Diffusion Equation The classical diffusion equation emerges as a direct and simple consequence of the conservation of mass principia (dc/dt =0), that is, the rate (d /dt) of changing the total mass c within a closed system is zero. In Cartesian coordinates, where the concentration c is locally distributed, c(xi,t) can change locally as function of both space coordinates xi (i = 1,2,3), and time t. This conservation principle implies that the conservation equation now reads, neglecting a small term due to molecular diffusivity dc ct c u dt dc = i dx ∂ + = 0 (2) i where ui is the instantaneous, mass advecting wind speed. By here introducing mean and fluctuations parts c = c + c′ ; ui = ui + ui′ defined in such a way that the fluctuating parts averages to zero c′= 0 ; u′ i = 0 13 (3) (4)
Page 1 and 2: MANHAZ position paper on: Modelling
Page 3 and 4: Troposphere. Trapped between the st
Page 5 and 6: The importance of the local wind fi
Page 7 and 8: Figure 2. Typical vertical wind spe
Page 9 and 10: Notice that this source of turbulen
Page 11: dient winds can approximate the reg
Page 15 and 16: σ () t = 2K t + σ () 0 2 2 z z z
Page 17 and 18: Figure 3 Pasquill stability classif
Page 19 and 20: Monin-Obukhov similarity scaling (z
Page 21 and 22: With Richardson's diffusivity KDN i
Page 23 and 24: The corresponding predicted puff gr
Page 25 and 26: The cyclic variation of the stabili
Page 27 and 28: Dispersion modelling has also high
Page 29 and 30: structure of the diffusion. In prin
Page 31 and 32: Atmospheric dispersion module for n
Page 33 and 34: LSP is a local scale pre-processing
Page 35 and 36: It consists of nested modules, whic
Page 37 and 38: land uses the nearest land-based Me
Page 39 and 40: Another example, showing the effect
Page 41 and 42: Density calculations. Numerical dis
Page 43 and 44: cloud is expected to cover a larger
Page 45 and 46: Auxiliary parameters like concentra
Page 47 and 48: Variable atmospheric wind condition
Page 49 and 50: Busch, N.E., On the Mechanics of At
Page 51 and 52: Monin A.S. (1959) Smoke propagation
Page 53 and 54: Goldwire, H. C., McRae, T. G., John
Page 55: Table of Content Modelling of Pollu

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