- Email: [email protected]
A study of the contribution of pollution to visibility in a radiation fog∗
Atmospheric
Enwronment
Vol. 8. pp. 669-674.
PergamonPress1974.Printedin GreatBrititin.
DISCUSSIONS A STUDY OF THE CONTRIBUTION OF POLLUTION VISIBILITY IN A RADIATION FOG*
TO
I wish to congratulate the authors to their comprehensive experimental study of a fog-situation. Nevertheless some remarks on their theoretical evaluations (Section 4.3. of their article) seem to be suitable. (I) It is mentioned a supersaturation of 0.003 per cent during most of the fog. The existence of a supersaturation was derived from the shape of the size distributions being measured, in combination with the calculational results of Neiburger and Chien (1960). The assumption of the authors “that such a small deviation from saturation has a negligible effect on the equilibrium size of the droplets forming on hygrdscopic nuclei” can lead to incorrect results. The increase from saturation to OQO3per cent supersaturation of the extinction coefficient has been estimated (compare the extinction coefficients versus relative humidity by Hiinel, 1972a). The result was an increase by more than 100 per cent in each case. Moreover it has been calculated, that at a particle concentration of 8500 cm - 3 in four of the six cases studied the value 65 km-’ for the extinction coefficient is attained at relative humidities below saturation. Indeed there are two possibilities explaining the size distributions which have been measured without assumption of a supersaturation: (a) a fraction of the particles consists of considerably more water soluble substance than the remaining ones; (b) the aerosol size distribution in dry state has a secondary peak. (2) The authors derive an approximation for the equilibrium radius of solution droplets at saturation (equation 5 in section 4.3). They state that this equation gives errors smaller than 1 per cent for ammonium sulphate particles with radii larger than 0.05 pm in dry state. For ammonium sulphate the approximation formula has been proved using the exact thermodynamic theory (Dufour and Defay, 1963) and the thermodynamic properties of aqueous solutions of ammonium sulphate (compare the data of Low, 1969 and Robinson and Stokes, 1959). Equilibrium radii r cf = 1) for ammonium sulphate particles rCf=
0) (cm)
lo- 5
1om4
1o-3
2.12. 1o-6
7.64. 1O-5
2.53 lo- 3
8.20. 1O-2
2.61. 1O-6
8.21 IO-’
2.60. lo- 3
8.20. 1O-2
2.59. 1O-6
8.20. 1O-5
2.59. 1O-3
8.20. 1O-2
1om6 rCf=
Exact thermodynamic theory in combination with measured van’t Hoff factors Exact thermodynamic theory with constant van’t Hoff factor equal to 3 Approximation formula of the authors with constant van? Hoff factor equal to 3
1) (cm)
As it can be seen from the preceding table, the errors of the approximation formula stated by the authors, are valid only with the unrealistic assumption of a van’t Hoff factor being independent of concentration of ammonium sulphate in aqueous solution. However, it is evident from the measured data, that the van’t Hoff factor increases from the value 2.306 for a 0.1 molal solution to 3 for an infinitely diluted solution. A further proof of the approximation formula with NaCl particles gave smaller errors due to the smaller increase of the van? Hoff factor from the concentration 0.1 molal to infinite dilution. For particles containing only a small fraction of soluble material the approximation formula can produce even a shrinking of particles. * GARLAND
J. A., BRANSCIN J. R.
and Cox L. C. (1973) Atmospheric Environment 7, 1079-1092. 669
670
Discussions
Thus it can be said, that the approximation formula must lead to significant errors of the extinction coefficient, when those particles are optically predominant for which the approximation formula gives erroneous results. (3) Deriving their approximation formula, equation (6) for the extinction coefficient at saturation, the authors use a mean value K = 2 for the efficiency factor of extinction. Comparison with the results mentioned above showed that the assumption I( = 2 leads to an underesti~tion up to 63 per cent at saturation and of up to 20 per cent at f = 0.998. (4) Combining the results of HInel(1972a,b) it is possible to check the whole approximation formula, equation (6) for the extinction coefficient at saturation. The resulting errors were up to -8~1 per cent. This indicates that the assumption K = 2 makes the largest contribution to the error. However in literature there has been reported on size distributions containing more of the smallest particles than those used for the proof. For these cases the validity of the approximation formula has not been checked. (5)The authors derive a further approximation formula, equation (7), for the extinction coefficient at ~turation. The main part of this formula is a sum of the concentrations of formula weights per unit volume of all ions within all of the particles. As the authors believe this equation is valid only for those cases where the hygroscopic particles consist totally of electrolytes, an analogous formula has been derived for the case where the particles can be composed ofelectrolytes together with water insoluble material. It has been found that even this more general formula theoretically is restricted to those cases where the particles growing only due to adsorption or due to other water soluble material than electrolytes have a negligible contribution to the extinction coefficient at saturation. From the considerations above (section 2) it can be seen that this formula moreover is restricted to those cases where the amount of water soluble substance within the particles is not too small.
SUMMARY
As it is seen from the foregoing discussion the theoretical approximations of the authors do not give reliable results in each case. Moreover the assumption the air would be saturated during fog can give rise to errors. Therefore, it is not astonishing that the calculated contribution of soluble material to visibility in fog (compare Table 2 within the authors’ paper) cannot be correlated with the measured extinction coefficients, lnstitut ftir Meteorologic,
G.
H~NEL
Mainz, West Germany
REFERENCES
Dufour L. and Defay R. (1963) thermodynamics of Clouds. Int. Geoph. Ser. No. 6, Academic Press. New York. HLnel G. (1972a) Computation of the extinction of visible radiation by atmospheric aerosol particles as a function of the relative humidity, based upon measured properties. J. Aerosol Sci. 3, 377-386. Hanel G. (197213)The ratio of the extinction coefficient to the mass of atmospheric aerosol particles as a function of the relative humidity. J. Aerosol Sci. 3, 455460. Low R. D. H. (1969) A generalized equation for the solution effect in droplet growth. J. Atmos. Sci. 26, 60&611. Neiburger M. and Chien C. W. (1960) Computations of the growth of cloud drops by condensation using an electronic digital computer. Monograph No. 5, Amer. Geoph. Union, Physics of precipi~ti~n. Robinson R. A. and Stokes R. H. (1959) E~ek~oiyte Seditions. Butterworths, London.
AUTHORS
REPLY
HInet has raised several points in his careful evaluation of the theoretical ~eatment in Section 4.3 of the paper. His remarks prompt me first to emphasise that the purpose of this approximate theory is: (i) To make it possible to calculate how large a contribution soluble air pollutants can make to the extinction coefficent in fog; (ii) To provide a test for the hypothesis that the smaller droplets in fog are haze particles which have grown to their equilibrium size at saturation. (In spite of Hanel’s remarks about the possibility that the air did not reach saturation in the fog discussed, the authors argue below that the droplets above about 5 pm radius must have resulted from larger nuclei which grew to sixes greater than their equilibrium size during a period of supersaturation). Since the size distribution of various constituents was not available in the fog studied and is only rarely reported in the literature, an approximate approach such as the one formulated is the only possibility. The errors in the approximations made are probably smaller than the errors involved in the field measurements necessary to obtain the extinction due to the smaller droplet sire range. They are not so great as to reduce the usefulness of predictions about the importance of pollutants in reducing visibility in fog,
Enwronment
Vol. 8. pp. 669-674.
PergamonPress1974.Printedin GreatBrititin.
DISCUSSIONS A STUDY OF THE CONTRIBUTION OF POLLUTION VISIBILITY IN A RADIATION FOG*
TO
I wish to congratulate the authors to their comprehensive experimental study of a fog-situation. Nevertheless some remarks on their theoretical evaluations (Section 4.3. of their article) seem to be suitable. (I) It is mentioned a supersaturation of 0.003 per cent during most of the fog. The existence of a supersaturation was derived from the shape of the size distributions being measured, in combination with the calculational results of Neiburger and Chien (1960). The assumption of the authors “that such a small deviation from saturation has a negligible effect on the equilibrium size of the droplets forming on hygrdscopic nuclei” can lead to incorrect results. The increase from saturation to OQO3per cent supersaturation of the extinction coefficient has been estimated (compare the extinction coefficients versus relative humidity by Hiinel, 1972a). The result was an increase by more than 100 per cent in each case. Moreover it has been calculated, that at a particle concentration of 8500 cm - 3 in four of the six cases studied the value 65 km-’ for the extinction coefficient is attained at relative humidities below saturation. Indeed there are two possibilities explaining the size distributions which have been measured without assumption of a supersaturation: (a) a fraction of the particles consists of considerably more water soluble substance than the remaining ones; (b) the aerosol size distribution in dry state has a secondary peak. (2) The authors derive an approximation for the equilibrium radius of solution droplets at saturation (equation 5 in section 4.3). They state that this equation gives errors smaller than 1 per cent for ammonium sulphate particles with radii larger than 0.05 pm in dry state. For ammonium sulphate the approximation formula has been proved using the exact thermodynamic theory (Dufour and Defay, 1963) and the thermodynamic properties of aqueous solutions of ammonium sulphate (compare the data of Low, 1969 and Robinson and Stokes, 1959). Equilibrium radii r cf = 1) for ammonium sulphate particles rCf=
0) (cm)
lo- 5
1om4
1o-3
2.12. 1o-6
7.64. 1O-5
2.53 lo- 3
8.20. 1O-2
2.61. 1O-6
8.21 IO-’
2.60. lo- 3
8.20. 1O-2
2.59. 1O-6
8.20. 1O-5
2.59. 1O-3
8.20. 1O-2
1om6 rCf=
Exact thermodynamic theory in combination with measured van’t Hoff factors Exact thermodynamic theory with constant van’t Hoff factor equal to 3 Approximation formula of the authors with constant van? Hoff factor equal to 3
1) (cm)
As it can be seen from the preceding table, the errors of the approximation formula stated by the authors, are valid only with the unrealistic assumption of a van’t Hoff factor being independent of concentration of ammonium sulphate in aqueous solution. However, it is evident from the measured data, that the van’t Hoff factor increases from the value 2.306 for a 0.1 molal solution to 3 for an infinitely diluted solution. A further proof of the approximation formula with NaCl particles gave smaller errors due to the smaller increase of the van? Hoff factor from the concentration 0.1 molal to infinite dilution. For particles containing only a small fraction of soluble material the approximation formula can produce even a shrinking of particles. * GARLAND
J. A., BRANSCIN J. R.
and Cox L. C. (1973) Atmospheric Environment 7, 1079-1092. 669
670
Discussions
Thus it can be said, that the approximation formula must lead to significant errors of the extinction coefficient, when those particles are optically predominant for which the approximation formula gives erroneous results. (3) Deriving their approximation formula, equation (6) for the extinction coefficient at saturation, the authors use a mean value K = 2 for the efficiency factor of extinction. Comparison with the results mentioned above showed that the assumption I( = 2 leads to an underesti~tion up to 63 per cent at saturation and of up to 20 per cent at f = 0.998. (4) Combining the results of HInel(1972a,b) it is possible to check the whole approximation formula, equation (6) for the extinction coefficient at saturation. The resulting errors were up to -8~1 per cent. This indicates that the assumption K = 2 makes the largest contribution to the error. However in literature there has been reported on size distributions containing more of the smallest particles than those used for the proof. For these cases the validity of the approximation formula has not been checked. (5)The authors derive a further approximation formula, equation (7), for the extinction coefficient at ~turation. The main part of this formula is a sum of the concentrations of formula weights per unit volume of all ions within all of the particles. As the authors believe this equation is valid only for those cases where the hygroscopic particles consist totally of electrolytes, an analogous formula has been derived for the case where the particles can be composed ofelectrolytes together with water insoluble material. It has been found that even this more general formula theoretically is restricted to those cases where the particles growing only due to adsorption or due to other water soluble material than electrolytes have a negligible contribution to the extinction coefficient at saturation. From the considerations above (section 2) it can be seen that this formula moreover is restricted to those cases where the amount of water soluble substance within the particles is not too small.
SUMMARY
As it is seen from the foregoing discussion the theoretical approximations of the authors do not give reliable results in each case. Moreover the assumption the air would be saturated during fog can give rise to errors. Therefore, it is not astonishing that the calculated contribution of soluble material to visibility in fog (compare Table 2 within the authors’ paper) cannot be correlated with the measured extinction coefficients, lnstitut ftir Meteorologic,
G.
H~NEL
Mainz, West Germany
REFERENCES
Dufour L. and Defay R. (1963) thermodynamics of Clouds. Int. Geoph. Ser. No. 6, Academic Press. New York. HLnel G. (1972a) Computation of the extinction of visible radiation by atmospheric aerosol particles as a function of the relative humidity, based upon measured properties. J. Aerosol Sci. 3, 377-386. Hanel G. (197213)The ratio of the extinction coefficient to the mass of atmospheric aerosol particles as a function of the relative humidity. J. Aerosol Sci. 3, 455460. Low R. D. H. (1969) A generalized equation for the solution effect in droplet growth. J. Atmos. Sci. 26, 60&611. Neiburger M. and Chien C. W. (1960) Computations of the growth of cloud drops by condensation using an electronic digital computer. Monograph No. 5, Amer. Geoph. Union, Physics of precipi~ti~n. Robinson R. A. and Stokes R. H. (1959) E~ek~oiyte Seditions. Butterworths, London.
AUTHORS
REPLY
HInet has raised several points in his careful evaluation of the theoretical ~eatment in Section 4.3 of the paper. His remarks prompt me first to emphasise that the purpose of this approximate theory is: (i) To make it possible to calculate how large a contribution soluble air pollutants can make to the extinction coefficent in fog; (ii) To provide a test for the hypothesis that the smaller droplets in fog are haze particles which have grown to their equilibrium size at saturation. (In spite of Hanel’s remarks about the possibility that the air did not reach saturation in the fog discussed, the authors argue below that the droplets above about 5 pm radius must have resulted from larger nuclei which grew to sixes greater than their equilibrium size during a period of supersaturation). Since the size distribution of various constituents was not available in the fog studied and is only rarely reported in the literature, an approximate approach such as the one formulated is the only possibility. The errors in the approximations made are probably smaller than the errors involved in the field measurements necessary to obtain the extinction due to the smaller droplet sire range. They are not so great as to reduce the usefulness of predictions about the importance of pollutants in reducing visibility in fog,