Developments in Environmental Science, Volume 6

C. Borrego and E. Renner (Editors)

Copyright r 2007 Elsevier Ltd. All rights reserved.

814

ISSN: 1474-8177/DOI:10.1016/S1474-8177(07)06826-X

Poster 26

An air pollution model applying a semi-analytical solution for

low wind conditions

Tiziano Tirabassi, Davidson Moreira, Daniela Buske and Antonio Goulart

Abstract

Aeolian dust from arid and semi-arid areas contributes significantlyto the global atmospheric aerosol mass and is expected to impactthe climate system by direct and indirect effects. The project Sa-haran Mineral dust experiment (SAMUM) aims at investigating theproperties of Saharan dust. Within this framework, a new regionalmodel system was developed for simulations of the Saharan dustcycle and radiative effects. The model performance is tested for twoSaharan dust outbreaks directed to Europe in August and October2001.

The importance of dispersion modelling in low wind conditionslies in the fact that such conditions occur frequently and are crucialfor air pollution episodes. The classical approach based on conven-tional models, such as Gaussian plume or the K-theory with suitableassumptions, are known to work reasonably well during mostmeteorological regimes, except for weak wind conditions.

A steady-state mathematical model for dispersion of contaminantsin low wind conditions that takes into account the along-wind diffu-sion is proposed. The solution of the advection–diffusion equationfor these conditions is obtained applying the Laplace transform,considering the planetary boundary layer (PBL) as a multilayer sys-tem. The eddy diffusivities used in the K-diffusion model were de-rived from the local similarity and Taylor’s diffusion theory. Theeddy diffusivities are functions of distance from the source and cor-rectly represent the near-source diffusion in weak winds.

The GILTT solution

The crosswind integration of the advection–diffusion equation (in sta-tionary conditions) considering the PBL as a multilayer system leads to

Air Pollution Model for Low Wind Conditions 815

(in any nth layer)

un@cn@x

¼@

@xKx

@cn@x

� �þ

@

@zKz

@cn@z

� �(1)

subject to the boundary conditions of zero flux at the ground and PBLtop, and a source with emission rate Q at height Hs.

c represents the average crosswind integrated concentration, u is themean wind speed in x direction and Kx and Kz are the eddy diffusivities.Bearing in mind the dependence of the, Kx and Kz coefficients and windspeed profile u on the height h of a PBL is discretized in N sub-intervalsin such a way that inside each interval Kx, Kz and u assume constantaverage values. The analytical solution proposed by Vilhena et al. (1998)is applied to Eq. (1) and results

cnðx; zÞ ¼P8j¼1

wjPj

xAne

�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

PjPe

� �Pj un

xKn

� �q� �z

24 þ Bne

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

PjPe

� �Pjun

xKn

� �q� �zþ

QHðz�HsÞ

2

1�PjPe

PjKnun

x

� �1=2

e�ðz�HsÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

PjPe

� �Pj un

xKn

� �q� �� e

ðz�HsÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

PjPe

� �Pj un

xKn

� �q� �0@

1A35

(2)

where wj and Pj are the weights and roots of the Gaussian quadraturescheme and H(z�Hs) is the Heaviside function and Pe ¼ unx/Kx is thewell-known Peclet number.

In Table 1, the performances of the model were evaluated against thefield experiments carried out at the Idaho National Engineering Labo-ratory (INEL) (Sagendorf and Dickson, 1974). Furthermore, the studysuggests that the inclusion of the along-wind diffusion can improve thedescription of the turbulent transport of atmospheric contaminants. Themodel has been used with and without the diffusion along the wind di-rection outlining so the performances due to the PBL parameterizationsand due the capability to represent low wind scenarios. The statisticalindices (see Hanna, 1989) point out that the model simulates the observedconcentrations satisfactorily.

Table 1. Statistical evaluation of models results for ground-level concentration

Experiment NMSE COR FA2 FB FS

K-diffusion (with Kx) 0.21 0.85 0.92 �0.02 0.21

K-diffusion (without Kx) 0.31 0.83 0.83 �0.09 0.26

Tiziano Tirabassi et al.816

REFERENCES

Hanna, S.R., 1989. Confidence limit for air quality models as estimated by bootstrap and

jacknife resampling methods. Atmos. Environ. 23, 1385–1395.

Sagendorf, J.F., Dickson, C.R., 1974. Diffusion under low wind-speed, inversion conditions.

National Oceanic and Atmospheric Administration Technical Memorandum ERL

ARL-52.

Vilhena, M.T., Rizza, U., Degrazia, G.A., Mangia, C., Moreira, D.M., Tirabassi, T., 1998.

An analytical air pollution model: Development and evaluation. Contrib. Atmos.

Phys. 71(3), 315–320.