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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• : upwind finite difference scheme

• : stable