4. atmospheric chemical transport models 4.1 introduction 4.2 box model 4.3 three dimensional...
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4. Atmospheric chemical transport models
4.1 Introduction4.2 Box model4.3 Three dimensional atmospheric chemical transport model
4.1 Introduction
Questions
• What is the contribution of source A to the concentration of pollu-tants at site B?
• What is the most cost-effective strategy for reducing pollutant concentrations below an air quality standard?
• What will be the effect on air quality of the addition of the reduc-tion of a specific air pollutant emission flux?
• What should one place a future source to minimize its environ-mental impacts?
• What will be the air quality tomorrow or the day after?
The atmosphere is an extremely reactive system in which nu-merous physical and chemical processes occur simultaneously.
Mathematical models provide the necessary framework for in-tegration of our understanding of individual atmospheric pro-cesses and study of their interaction.
Three basic components of an atmospheric model are species emission, transport and physiochemical transformations
① Eulerian model: describes the concentrations in an array of fixed computational cells② Lagrangian model: simulates concentration change of air parcel as it is advected in the atmosphere.
출처 : http://www.romair.eu/model-description.php?lang=en
출처 : http://www.shodor.org/os411/courses/411f/module03/unit05/page01.html
Classification based on dimension① box model( 상자 모델 ): zero-dimensional
Concentrations are functions of time only. C(t) ② column model: one-dimensional
Horizontally homogeneous layersConcentrations are functions of height and time. C(z, t)
③ two dimensional model: often used in description of global atmospheric chemistry ④ three dimensional model: c(x,y,z,t)
4.2 Box model (상자모델 )
4.1.1 Eulerian box modelAssume that the height (H) of the box equal the mixing layer height.
: background concentration : mass emission rate kg/h-1
: chemical production rate (kg m-3 h-1) : removal rate(dry deposition, wet deposition)
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Problem 1
Ex1) An inert species has as initial concentration and is emitted at a rate . Assuming that its background concentration is , calculate its steady-state concentration over a city characterized by an average wind speed of 3m/s. Assume that the city has dimensions and a constant mixing height of 1000m.
2) For changing mixing height with time① For decreasing mixing height No direct change of the concentration inside the mixed layer Because the box will be smaller, surface sources and sinks will have a more significant effect.② For increasing mixing height Entrainment and subsequent dilution will change the concentration. : the concentration above the box.
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4.1.2 Lagrangian Box model
• No advection term
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Problem 2
Ex 2) SO2 is emitted in an urban area with a flux of 2000 g m-
3 . The mixing height over the area is 1000m, the atmospheric residence time 20h, and SO2 reacts with an average rate of 3 % h-1. Rural areas around the city are characterized by a SO2
concentration equal to 2 g m-3 . What is the average SO2 con-centration in the urban airshed for the above conditions? As-sume an SO2 dry deposition velocity of 1cms-1 and a cloud/ fog-free atmosphere
4.3 Three dimensional atmospheric chemical model
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Input data: three dimensional meteorological field, emission data, initial and boundary condition of pollutantsExample of three dimensional model RADM(Regional Acid Deposition Model)UAM(Urban Airshed Model), CMAQ (Community Multiscale air quality) Chemical transport model
: eddy diffusivity
: emission rate: removal flux : Reactionrate
4.2.1 Coordinate system
Terrain following coordinates
4.2.2 Initial conditions
Start atmospheric simulations some period of time. At the end of start up period the model should have estab-lished concentration fields that do not seriously reflect the ini-tial conditions.
4.2.3 Boundary conditionSide boundary conditiona function of time.
• Unlike initial condition, boundary conditions, especially at the upwind boundaries, continue to affect predictions throughout the simulations.
• Therefore, one should try to place the limits of the modeling domain in relatively clean areas where boundary conditions are relatively well know and have a relatively small effect on model predictions.
• Uncertainty of side boundary conditions in urban air pollu-tion model prediction may be reduced by use of larger scale models to provide the boundary condition to the urban scale model.
: nesting technique
Upper boundary condition• Total reflection condition at the upper boundary of the com-
putation domain
• Alternative boundary condition (Reynolds et al., 1973)• for • for • : the concentration above the modeling region.
Lower boundary condition
: deposition velocity of species: ground-level emission rate of the species.
4.2.4 Numerical solution of chemical transport models
• A: Adevection operator• D: Diffusion operator• C: cloud operator• G: Gas-phase chemistry operator• P : Aerosol operator• S: source/sink operator
Operator splitting
• Instead of solving the full equation at once, basic idea is to solve independently the pieces of the problem correspond-ing to the various processes and then couple the various changes resulting from the separate partial calculations.
• The other alternatives
• Order of operator application is another issue.• McRae et al. (1982a)
T: transport operator : advection and diffusion
Diffusion
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• : stable