Abstract

We have designed and built a compact, low-cost automated system to measure the optical absorption coefficient of air. Because most of the light absorption is due to black carbon, this method is a direct measure of the amount of black carbon in the atmosphere. The equipment was used to measure absorption over a period of one year in a central area of Santiago. Our results show a strong correlation with the daily traffic pattern. The highest value of the absorption coefficient during most of the year occurs during the morning rush hour (0700–0800), and the lowest value either early in the morning (0300–0500) or in the afternoon (1400–1700). The absorption coefficient also shows a strong dependence with the season of the year, with values 10–20 times higher in winter than in summer. The data show that, during most of the year, the amount of black carbon present in the atmosphere is due to traffic. At night, during winter, the high concentration of black carbon is due to the temperature inversion effect.

© 2000 Optical Society of America

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References

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  1. C. Fröhlich, “Techniques for the measurement of spectral radiation,” in Climatology for Solar and Wind Energy, R. Guzzi, C. G. Justus, eds. (World Scientific, Singapore, 1988), pp. 401–411.
  2. H. Horvath, “Atmospheric light absorption: a review,” Atmos. Environ. 27, 293–317 (1993).
    [CrossRef]
  3. A. Wittemore, “Air pollution and respiratory diseases,” Ann. Rev. Public Health 2, 397–411 (1981).
    [CrossRef]
  4. C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
    [CrossRef]
  5. I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
    [CrossRef]
  6. P. Artaxo, P. Oyola, R. Martínez, “Aerosol composition and source apportionment in Santiago de Chile,” Nucl. Instrum. Methods Phys. Res. B 150, 409–416 (1999).
    [CrossRef]
  7. P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
    [CrossRef]
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  9. E. Guzmán, “Experimental study of the stability of the atmosphere in Santiago by means of a sensible anemometer,” Ph.D. dissertation (Faculty of Mathematics and Physics, University of Chile, Santiago, 1984).
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    [CrossRef] [PubMed]
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  13. W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurements of Airborne Particles (Wiley, New York, 1999).
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    [CrossRef]
  15. A. D. Clarke, “Effects of filter internal reflection coefficient on light absorption measurements made using the integrating plate method,” Appl. Opt. 21, 3021–3031 (1982).
    [CrossRef] [PubMed]
  16. H. Horvath, L. Catalán, A. Trier, “A study of the aerosol of Santiago de Chile III: light absorption measurements,” Atmos. Environ. 31, 3737–3744 (1997).
    [CrossRef]
  17. C. M. Rojas, P. Artaxo, R. van Grieken, “Aerosols in Santiago de Chile: a study using receptor modelling with XRF and single particle analysis,” Atmos. Environ. Part B 24, 227–241 (1990).
    [CrossRef]
  18. J. R. Rutlland, E. Garreaud, E. Campos, P. Aceituno, “Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting,” presented at the Fourth International Conference on Meteorology and Oceanography of the Southern Hemisphere, Hobart, Australia, March 1993.

1999 (3)

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

P. Artaxo, P. Oyola, R. Martínez, “Aerosol composition and source apportionment in Santiago de Chile,” Nucl. Instrum. Methods Phys. Res. B 150, 409–416 (1999).
[CrossRef]

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

1997 (4)

A. Trier, N. Cabrini, J. Ferrer, I. Olaeta, “Correlations between urban atmospheric light extinction coefficients and fine particle mass concentrations,” Atmósfera 10, 151–170 (1997).

H. Horvath, “Experimental calibration for aerosol light absorption measurement using the integrating plate method: summary of the data,” Aerosol Sci. 28, 1149–1161 (1997).
[CrossRef]

H. Horvath, L. Catalán, A. Trier, “A study of the aerosol of Santiago de Chile III: light absorption measurements,” Atmos. Environ. 31, 3737–3744 (1997).
[CrossRef]

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

1993 (1)

H. Horvath, “Atmospheric light absorption: a review,” Atmos. Environ. 27, 293–317 (1993).
[CrossRef]

1990 (1)

C. M. Rojas, P. Artaxo, R. van Grieken, “Aerosols in Santiago de Chile: a study using receptor modelling with XRF and single particle analysis,” Atmos. Environ. Part B 24, 227–241 (1990).
[CrossRef]

1983 (1)

J. Rutllant, H. Salinas, “Meteorological characterization of events with high contamination potential in Central Chile,” Meteorologica 14, 353–361 (1983).

1982 (1)

1981 (1)

A. Wittemore, “Air pollution and respiratory diseases,” Ann. Rev. Public Health 2, 397–411 (1981).
[CrossRef]

1973 (1)

Aceituno, P.

J. R. Rutlland, E. Garreaud, E. Campos, P. Aceituno, “Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting,” presented at the Fourth International Conference on Meteorology and Oceanography of the Southern Hemisphere, Hobart, Australia, March 1993.

Artaxo, P.

P. Artaxo, P. Oyola, R. Martínez, “Aerosol composition and source apportionment in Santiago de Chile,” Nucl. Instrum. Methods Phys. Res. B 150, 409–416 (1999).
[CrossRef]

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

C. M. Rojas, P. Artaxo, R. van Grieken, “Aerosols in Santiago de Chile: a study using receptor modelling with XRF and single particle analysis,” Atmos. Environ. Part B 24, 227–241 (1990).
[CrossRef]

Baker, M.

Bustamante, G.

L. Catalán, E. Gramsch, G. Bustamante, “Fundamentals of a new method for automatic monitoring of the absorption coefficient in the atmosphere,” in Proceedings of the First Latin–American Workshop on Environmental Chemistry, 19–22 October 1997 (University of Chile, Jahuel, Chile).

Cabrini, N.

A. Trier, N. Cabrini, J. Ferrer, I. Olaeta, “Correlations between urban atmospheric light extinction coefficients and fine particle mass concentrations,” Atmósfera 10, 151–170 (1997).

Campos, E.

J. R. Rutlland, E. Garreaud, E. Campos, P. Aceituno, “Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting,” presented at the Fourth International Conference on Meteorology and Oceanography of the Southern Hemisphere, Hobart, Australia, March 1993.

Castanho, A. D.

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

Catalán, L.

H. Horvath, L. Catalán, A. Trier, “A study of the aerosol of Santiago de Chile III: light absorption measurements,” Atmos. Environ. 31, 3737–3744 (1997).
[CrossRef]

L. Catalán, E. Gramsch, G. Bustamante, “Fundamentals of a new method for automatic monitoring of the absorption coefficient in the atmosphere,” in Proceedings of the First Latin–American Workshop on Environmental Chemistry, 19–22 October 1997 (University of Chile, Jahuel, Chile).

Charlson, R. J.

Clarke, A. D.

Dockery, C. A.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Fay, M. E.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Ferrer, J.

A. Trier, N. Cabrini, J. Ferrer, I. Olaeta, “Correlations between urban atmospheric light extinction coefficients and fine particle mass concentrations,” Atmósfera 10, 151–170 (1997).

Ferris, B. G.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Fröhlich, C.

C. Fröhlich, “Techniques for the measurement of spectral radiation,” in Climatology for Solar and Wind Energy, R. Guzzi, C. G. Justus, eds. (World Scientific, Singapore, 1988), pp. 401–411.

Garreaud, E.

J. R. Rutlland, E. Garreaud, E. Campos, P. Aceituno, “Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting,” presented at the Fourth International Conference on Meteorology and Oceanography of the Southern Hemisphere, Hobart, Australia, March 1993.

Gramsch, E.

L. Catalán, E. Gramsch, G. Bustamante, “Fundamentals of a new method for automatic monitoring of the absorption coefficient in the atmosphere,” in Proceedings of the First Latin–American Workshop on Environmental Chemistry, 19–22 October 1997 (University of Chile, Jahuel, Chile).

Guzmán, E.

E. Guzmán, “Experimental study of the stability of the atmosphere in Santiago by means of a sensible anemometer,” Ph.D. dissertation (Faculty of Mathematics and Physics, University of Chile, Santiago, 1984).

Hinds, W. C.

W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurements of Airborne Particles (Wiley, New York, 1999).

Horvath, H.

H. Horvath, “Experimental calibration for aerosol light absorption measurement using the integrating plate method: summary of the data,” Aerosol Sci. 28, 1149–1161 (1997).
[CrossRef]

H. Horvath, L. Catalán, A. Trier, “A study of the aerosol of Santiago de Chile III: light absorption measurements,” Atmos. Environ. 31, 3737–3744 (1997).
[CrossRef]

H. Horvath, “Atmospheric light absorption: a review,” Atmos. Environ. 27, 293–317 (1993).
[CrossRef]

Kavouras, I. G.

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

Koutrakis, P.

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

Lawrence, J.

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

Lin, C. I.

Longo, K. M.

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

Martínez, R.

P. Artaxo, P. Oyola, R. Martínez, “Aerosol composition and source apportionment in Santiago de Chile,” Nucl. Instrum. Methods Phys. Res. B 150, 409–416 (1999).
[CrossRef]

Martins, J. V.

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

Olaeta, I.

A. Trier, N. Cabrini, J. Ferrer, I. Olaeta, “Correlations between urban atmospheric light extinction coefficients and fine particle mass concentrations,” Atmósfera 10, 151–170 (1997).

Oyola, P.

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

P. Artaxo, P. Oyola, R. Martínez, “Aerosol composition and source apportionment in Santiago de Chile,” Nucl. Instrum. Methods Phys. Res. B 150, 409–416 (1999).
[CrossRef]

Pope, C. A.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Rojas, C. M.

C. M. Rojas, P. Artaxo, R. van Grieken, “Aerosols in Santiago de Chile: a study using receptor modelling with XRF and single particle analysis,” Atmos. Environ. Part B 24, 227–241 (1990).
[CrossRef]

Rutlland, J. R.

J. R. Rutlland, E. Garreaud, E. Campos, P. Aceituno, “Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting,” presented at the Fourth International Conference on Meteorology and Oceanography of the Southern Hemisphere, Hobart, Australia, March 1993.

Rutllant, J.

J. Rutllant, H. Salinas, “Meteorological characterization of events with high contamination potential in Central Chile,” Meteorologica 14, 353–361 (1983).

Salinas, H.

J. Rutllant, H. Salinas, “Meteorological characterization of events with high contamination potential in Central Chile,” Meteorologica 14, 353–361 (1983).

Speitzer, F. E.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Spengler, D. J.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Stephanou, E. G.

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

Trier, A.

A. Trier, N. Cabrini, J. Ferrer, I. Olaeta, “Correlations between urban atmospheric light extinction coefficients and fine particle mass concentrations,” Atmósfera 10, 151–170 (1997).

H. Horvath, L. Catalán, A. Trier, “A study of the aerosol of Santiago de Chile III: light absorption measurements,” Atmos. Environ. 31, 3737–3744 (1997).
[CrossRef]

van Grieken, R.

C. M. Rojas, P. Artaxo, R. van Grieken, “Aerosols in Santiago de Chile: a study using receptor modelling with XRF and single particle analysis,” Atmos. Environ. Part B 24, 227–241 (1990).
[CrossRef]

Ware, J. H.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Wittemore, A.

A. Wittemore, “Air pollution and respiratory diseases,” Ann. Rev. Public Health 2, 397–411 (1981).
[CrossRef]

Xu, X.

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Yamasoe, M. A.

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

Aerosol Sci. (1)

H. Horvath, “Experimental calibration for aerosol light absorption measurement using the integrating plate method: summary of the data,” Aerosol Sci. 28, 1149–1161 (1997).
[CrossRef]

Ann. Rev. Public Health (1)

A. Wittemore, “Air pollution and respiratory diseases,” Ann. Rev. Public Health 2, 397–411 (1981).
[CrossRef]

Appl. Opt. (2)

Atmos. Environ. (3)

H. Horvath, L. Catalán, A. Trier, “A study of the aerosol of Santiago de Chile III: light absorption measurements,” Atmos. Environ. 31, 3737–3744 (1997).
[CrossRef]

H. Horvath, “Atmospheric light absorption: a review,” Atmos. Environ. 27, 293–317 (1993).
[CrossRef]

I. G. Kavouras, J. Lawrence, P. Koutrakis, E. G. Stephanou, P. Oyola, “Measurement of particulate aliphatic and polynuclear aromatic hydrocarbons in Santiago de Chile: source reconciliation and evaluation of sampling artifacts,” Atmos. Environ. 33, 4977–4986 (1999).
[CrossRef]

Atmos. Environ. Part B (1)

C. M. Rojas, P. Artaxo, R. van Grieken, “Aerosols in Santiago de Chile: a study using receptor modelling with XRF and single particle analysis,” Atmos. Environ. Part B 24, 227–241 (1990).
[CrossRef]

Atmósfera (1)

A. Trier, N. Cabrini, J. Ferrer, I. Olaeta, “Correlations between urban atmospheric light extinction coefficients and fine particle mass concentrations,” Atmósfera 10, 151–170 (1997).

Meteorologica (1)

J. Rutllant, H. Salinas, “Meteorological characterization of events with high contamination potential in Central Chile,” Meteorologica 14, 353–361 (1983).

N. Engl. J. Med. (1)

C. A. Dockery, C. A. Pope, X. Xu, D. J. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, F. E. Speitzer, “An association between air pollution and mortality in six U.S. cities,” N. Engl. J. Med. 329, 1753–3744 (1997).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (2)

P. Artaxo, P. Oyola, R. Martínez, “Aerosol composition and source apportionment in Santiago de Chile,” Nucl. Instrum. Methods Phys. Res. B 150, 409–416 (1999).
[CrossRef]

P. Artaxo, A. D. Castanho, M. A. Yamasoe, J. V. Martins, K. M. Longo, “Analysis of atmospheric aerosols by PIXE: the importance of real time and complementary measurements,” Nucl. Instrum. Methods Phys. Res. B 150, 312–321 (1999).
[CrossRef]

Other (5)

E. Guzmán, “Experimental study of the stability of the atmosphere in Santiago by means of a sensible anemometer,” Ph.D. dissertation (Faculty of Mathematics and Physics, University of Chile, Santiago, 1984).

C. Fröhlich, “Techniques for the measurement of spectral radiation,” in Climatology for Solar and Wind Energy, R. Guzzi, C. G. Justus, eds. (World Scientific, Singapore, 1988), pp. 401–411.

L. Catalán, E. Gramsch, G. Bustamante, “Fundamentals of a new method for automatic monitoring of the absorption coefficient in the atmosphere,” in Proceedings of the First Latin–American Workshop on Environmental Chemistry, 19–22 October 1997 (University of Chile, Jahuel, Chile).

W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurements of Airborne Particles (Wiley, New York, 1999).

J. R. Rutlland, E. Garreaud, E. Campos, P. Aceituno, “Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting,” presented at the Fourth International Conference on Meteorology and Oceanography of the Southern Hemisphere, Hobart, Australia, March 1993.

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Figures (8)

Fig. 1
Fig. 1

Temperature profiles of the air for winter days in Santiago. The profiles lead to low air convection that was generated on days with high particle concentration: (a) temperature profile during the morning and (b) at night when the surface cools the surrounding air.

Fig. 2
Fig. 2

Diagram of the device that was used to measure the optical absorption coefficient.

Fig. 3
Fig. 3

(a) Raw experimental data from a summer day. (b) Analysis of the same data by use of the algorithm described in the text. The data are representative of a central area of Santiago during morning rush hour (a high peak) and during the evening and at night (a second smaller peak).

Fig. 4
Fig. 4

Optical absorption coefficient for winter days after a coastal trough event, showing that the highest values occur at night and not during morning rush hour.

Fig. 5
Fig. 5

(a) Weekly average for the summer month of January, showing that the morning rush hour peak is higher than the night value. (b) In winter, the influence of temperature inversion reverses the trend, and the average at night is similar or even higher than the morning average.

Fig. 6
Fig. 6

Coastal trough in the central part of Chile, which generated a stable temperature inversion with high particle concentration. The arrows show the direction of the winds.

Fig. 7
Fig. 7

Daily absorption coefficients from June 1998 through June 1999. The squares represent rush hour at 0800, which is usually the highest value of the day. Note the large variations from one day to the next. The dots represent the 0400 data, which is the lowest value, and remains constant from October through March. During winter, large fluctuations are observed.

Fig. 8
Fig. 8

Average of each day (day of the month average) for the period from June to December 1998. The data show the strong influence of traffic on the absorption coefficient during the whole year. However, in winter (June and July), the temperature inversion effect generates the highest values at night.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Φ1=ΦETfp exp-Δx σ1dx+Φ0,
Φ2=ΦETfp exp-Δxσ1+σ2dx+Φ0.
Φi+1=ΦETfp exp-Δxσ1+σ2++σi+1dx+Φ0, Φi+1=ΦETfp exp-Δxσ1+σ2++σidxΦi-Φ0×exp-Δx σi+1dx+Φ0.
Φi+1-Φ0Φi-Φ0=exp-Δx σi+1dxexp-fA Δtσi+1.
σi+1=AfΔtlogΦi-Φ0Φi+1-Φ0.
Φi=VD/VM,

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