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Sensitivity of the Gaussian plume model
84
Discussions
SENSITIVITY
OF THE GAUSSIAN
PLUME
MODEL”?
Editor’s comments:
p. 550 line 4 “0.1-0.4 H” should be “O.lH-0.4H”; paragraph 3 “rr” should be in lower case. p. 551 second line after Table 1 “u,/H = ld? should be “a,/H = I/,,~?“. “Mr. Horne” should read “Dr. Horne” throughout.
their statement is severely limited by restricting values of B, within a fixed range. But 6, adopts a continuum of values and of course all plumes have a region of high sensitivity where 0.1 < az/H < 0.4 (the region where the underside of the plume reaches ground level). Thus the high sensitivity of ground level concentrations to variation in cri in this region of the plume is in no way enhanced for plumes from a high source. It is a mathematical property of their dimensionless equation (3) (my equation 2, p. 550) that predicted ground level concentrations from all plumes are equally sensitive to or at identical values of a,/H. The scale of the source and the plume is irrelevant. Last paragraph. The restriction imposed on the apphcability of my equation (3) is merely a restatement of what I said in my Discussion. It relates to neutral atmospheric conditions, not an “isotropic” atmosphere. In any case, the restriction does not affect my conclusion, as pointed out in my Discussion.
Dr. Horne’s original comments concerning the authors’ reply (p. 551) were:
Department of Chemical Engineering, University College London, Torrington Place, London WClE 7JE
I received Dr. Horne’s manuscript in May 1974 and proofs
of the discussion and the authors’ reply were sent to Dr. Horne and Professor Bohac in January 1975. At this stage Dr. Horne sent me a list of criticisms of the authors’ reply. Rather than prolong the discussion in print, I suggested to the participants that it might be possible to amend their contributions by mutual agreement. Unfortunately, at this point I left on an extended tour and during my absence the discussion was inadvertently published in the original form without proof corrections. I apologise to the participants for this unfortunate lapse. The corrections are:
Line 1. The content of their Note is correctly and carefully summarised in the first sentence and second paragraph of my Discussion. Unless the authors can fault what is written there, surely they cannot suggest that I have missed the point of their Note. Line 1. I did not even suggest that it is the sensitivity of the model that implies a range of values for er. Line 3. I did not conclude that there are only six sets of parameters for cz. (Of course I am aware that (i) intermediate atmospheric conditions exist and (ii) the experimental data for 0: have associated error limits.) Paragraph 2, line 4. This defence of their previous conclusion-that the sensitivity of predicted ground level concentrations to errors in er becomes more pronounced for large effective stack heights-is untenable. Though correct
Original Paper: * Bohac R. L., Derrick W. R. and Sosebee J. B. (1974)
LABORATORY
We have carefully read the comments of Dr. Horne concerning our reply to his discussion. We wish to call his attention to the first two lines of his discussion where he says: “. that x(x) is extremely sensitive to the value of u, when gr is in the range O.lH-0.4H. However, they are incorrect to conclude from this that ,“. This statement not only suggests, but states that we conclude that the sensitivity of the model implies a range of values of cr. We made no such conclusion. Indeed, by quoting us out of context, he has attributed comments to us that we never made nor believe. We cannot allow these comments to go unchallenged. Mathematics Department, University of Montana, Missoula, MT 59801, U.S.A.
DIOXIDE
EUROPEAN Shepherd (1974) suggests that the nature of the soil could influence the deposition velocity of SO, on grass growing in the soil. If the example given by Fisher on the basis of Shepherd’s and our results are correct, one must explain how SO2 reaches the soil when its resistance is greater than the resistance of the grass and the soil. The decrease in flux under a canopy depends on the foliage area density. When the soil is hidden under a * Payrissat M. and Beilke S. (1975) Atmospheric Environment 9. 211-217. t Discussion of Paper: Fisher B. E. A. (1975) Atmospheric Environment 9. 553.
ROBERTL. BOHAC, WILLIAM R. DERRICK
This discussion is now closed. D. J.
MOORE
REPLY
MEASUREMENTS
SULPHUR
HORNE
and Professor Bohac replied:
Atmospheric Environment 8. 291-293. t Discussion: Horne D. G. (1975) Atmospheric Environment 9. 550-552.
AUTHOR’S
D. G.
OF THE UPTAKE
OF
BY DIFFERENT SOILS*? canopy of dense grass it seems unlikely that much SO, will reach the soil directly by transfer between the grass leaves. When the soil resistance is not very high, diffusion of SO2 may occur when the grass is short and has a low leaf density. This diffusion may be explained by the air boundary layer resistance along the grass leaves. In this case, the transfer to the soil would be more important with a vegetation having a greater roughness than grass. Some prior fumigation experiments led us to think that the deposition velocity was influenced by the amount of SOz previously deposited. The observed decrease in the deposition velocity may arise either due to an increase of the soil resistance or to a high value of the air resistance. Complementary experiments, introducing SO2 into the
Discussions
SENSITIVITY
OF THE GAUSSIAN
PLUME
MODEL”?
Editor’s comments:
p. 550 line 4 “0.1-0.4 H” should be “O.lH-0.4H”; paragraph 3 “rr” should be in lower case. p. 551 second line after Table 1 “u,/H = ld? should be “a,/H = I/,,~?“. “Mr. Horne” should read “Dr. Horne” throughout.
their statement is severely limited by restricting values of B, within a fixed range. But 6, adopts a continuum of values and of course all plumes have a region of high sensitivity where 0.1 < az/H < 0.4 (the region where the underside of the plume reaches ground level). Thus the high sensitivity of ground level concentrations to variation in cri in this region of the plume is in no way enhanced for plumes from a high source. It is a mathematical property of their dimensionless equation (3) (my equation 2, p. 550) that predicted ground level concentrations from all plumes are equally sensitive to or at identical values of a,/H. The scale of the source and the plume is irrelevant. Last paragraph. The restriction imposed on the apphcability of my equation (3) is merely a restatement of what I said in my Discussion. It relates to neutral atmospheric conditions, not an “isotropic” atmosphere. In any case, the restriction does not affect my conclusion, as pointed out in my Discussion.
Dr. Horne’s original comments concerning the authors’ reply (p. 551) were:
Department of Chemical Engineering, University College London, Torrington Place, London WClE 7JE
I received Dr. Horne’s manuscript in May 1974 and proofs
of the discussion and the authors’ reply were sent to Dr. Horne and Professor Bohac in January 1975. At this stage Dr. Horne sent me a list of criticisms of the authors’ reply. Rather than prolong the discussion in print, I suggested to the participants that it might be possible to amend their contributions by mutual agreement. Unfortunately, at this point I left on an extended tour and during my absence the discussion was inadvertently published in the original form without proof corrections. I apologise to the participants for this unfortunate lapse. The corrections are:
Line 1. The content of their Note is correctly and carefully summarised in the first sentence and second paragraph of my Discussion. Unless the authors can fault what is written there, surely they cannot suggest that I have missed the point of their Note. Line 1. I did not even suggest that it is the sensitivity of the model that implies a range of values for er. Line 3. I did not conclude that there are only six sets of parameters for cz. (Of course I am aware that (i) intermediate atmospheric conditions exist and (ii) the experimental data for 0: have associated error limits.) Paragraph 2, line 4. This defence of their previous conclusion-that the sensitivity of predicted ground level concentrations to errors in er becomes more pronounced for large effective stack heights-is untenable. Though correct
Original Paper: * Bohac R. L., Derrick W. R. and Sosebee J. B. (1974)
LABORATORY
We have carefully read the comments of Dr. Horne concerning our reply to his discussion. We wish to call his attention to the first two lines of his discussion where he says: “. that x(x) is extremely sensitive to the value of u, when gr is in the range O.lH-0.4H. However, they are incorrect to conclude from this that ,“. This statement not only suggests, but states that we conclude that the sensitivity of the model implies a range of values of cr. We made no such conclusion. Indeed, by quoting us out of context, he has attributed comments to us that we never made nor believe. We cannot allow these comments to go unchallenged. Mathematics Department, University of Montana, Missoula, MT 59801, U.S.A.
DIOXIDE
EUROPEAN Shepherd (1974) suggests that the nature of the soil could influence the deposition velocity of SO, on grass growing in the soil. If the example given by Fisher on the basis of Shepherd’s and our results are correct, one must explain how SO2 reaches the soil when its resistance is greater than the resistance of the grass and the soil. The decrease in flux under a canopy depends on the foliage area density. When the soil is hidden under a * Payrissat M. and Beilke S. (1975) Atmospheric Environment 9. 211-217. t Discussion of Paper: Fisher B. E. A. (1975) Atmospheric Environment 9. 553.
ROBERTL. BOHAC, WILLIAM R. DERRICK
This discussion is now closed. D. J.
MOORE
REPLY
MEASUREMENTS
SULPHUR
HORNE
and Professor Bohac replied:
Atmospheric Environment 8. 291-293. t Discussion: Horne D. G. (1975) Atmospheric Environment 9. 550-552.
AUTHOR’S
D. G.
OF THE UPTAKE
OF
BY DIFFERENT SOILS*? canopy of dense grass it seems unlikely that much SO, will reach the soil directly by transfer between the grass leaves. When the soil resistance is not very high, diffusion of SO2 may occur when the grass is short and has a low leaf density. This diffusion may be explained by the air boundary layer resistance along the grass leaves. In this case, the transfer to the soil would be more important with a vegetation having a greater roughness than grass. Some prior fumigation experiments led us to think that the deposition velocity was influenced by the amount of SOz previously deposited. The observed decrease in the deposition velocity may arise either due to an increase of the soil resistance or to a high value of the air resistance. Complementary experiments, introducing SO2 into the