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The prediction of the mean hourly average maximum ground level concentration of sulphur dioxide at Tilbury
Armosphcric Enriron,ncv:
Vol. 8. pp. 543-554. Pergamon
Press 1974. Prmted in Great Britain
THE PREDICTION OF THE MEAN HOURLY AVERAGE MAXIMUM GROUND LEVEL CONCENTRATION OF SULPHUR DIOXIDE AT TILBURY D. J. MOORE Central Electricity Research Laboratories, Leatherhead. Surrey KT22 7SE (First receiued 26 June and injinalform
11 December 1973)
Abstract-Measurements of the maximum hourly average concentration of sulphur dioxide at Tilbury, grouped according to wind speed and vertical temperature profile, are compared with values calculated from an expression developed by Moore (1972). It is concluded that the expression can be used to predict Tilbury concentrations without change in the parameters derived from Northfleet data. The expression still applies, even in conditions when chimney down-wash has been observed, indicating that the fraction of the plume material involved in down-wash is fairly small. NOMENCLATURE m’SO,/m~‘air x 10’ efflux velocity m s- 1 wind speed m s-l stack height + plume rise m parameter appearing in the expression for C, representing the effect of mechanical turbulence s parameter appearing in the expression for C, representing the effect of convective turbulence m s- ’ rate of emission of SO2 from stacks (total for station) m3 s- ’ at N.T.P. rate of emission of heat from stack MW total rate of generation of electricity by station MW.
I
INTRODUCTION
In Moore (1972), henceforth referred to as Paper I, a dispersion model was developed for predicting the hourly average SO2 concentration in various stability conditions and applied to measurements made at Northfleet power station. As that paper had limited circulation and reprints are not available, an abridged and re-edited version is appended below. In the present paper, the model developed in Paper I is applied to measurements made at Tilbury. Both Tilbury and Northfleet are power stations located on the river Thames about 20 miles east of central London (see Lucas, James and Davies (1967) for details). The principal differences between the plants are: (i) Tilbury is an oil-fired station with a considerable variation in the ratio (SO2 emitted/MW generated) while Northfleet was coal-fired and there was so little variation in the above ratio that SO2 emission could be assumed to be directly proportional to MW generated. In this analysis, the SO2 emission has been calculated from the station fuel quality data. (ii) The efflux velocity on full load at Tilbury is 7.5 m s- ’ (with two-stack operation) compared with 20 m s- ’ at Northfleet, consequently down-wash effects became important at much lower wind speeds. For this reason, the data are not only divided into groups 543
D. J. MOORE
544
of limited ranges of wind speed and vertical temperature profile, as in the Northfleet analysis, but a further sub-division according to the ratio (efflux velocity/wind speed) is also made. The new groupings are w/U > 1 (no downwash expected) 1 2 w/U 2 l/2 (downwash sometimes observed) w/U < l/2 (downwash always observed). (iii) During the period when the measurements were made, Northfleet was a base load station, normally operating for 24 h a day, while Tilbury was normally closed down from 24:00 h until about 06:OOh and sometimes on summer afternoons. This, coupled with the extra sub-division of the data according to the ratio w/U mentioned in (ii) above, means that there are fewer data in each group than there were from Northfleet. Consequently some of the less frequently occurring sub-divisions do not have sufficient data for an accurate mean observed concentration to be determined. It is therefore necessary to combine some of the data groups. The occasions when such groupings are necessary are noted in the Tables of Results, and the actual mean wind speed for the group is given. 2.
CALCULATION
OF
THE
GROUND
LEVEL
MAXIMUM
CONCENTRATION
The dispersion model developed in Paper I resulted in the following expression for the maximum hourly average ground level concentration: (i) For all data groups except those containing occasions with unstable lapse rates only (but including data grouped according to wind speed only, with no sub-division according to lapse rate): C, = [(M/H) + Wf-Jz)1W~2).
(1)
(ii) For unstable lapse rates only: C, = [(M/H)2 + (C/U2)2]1'2(Q/H2).
(2)
Values of H should be calculated from the expression proposed by Lucas (1967) which for Tilbury, which has a 100 m tall stack, is:
H = 100 + 475 Qh114/U.
(3)
The values of A4 and C for each stability division were determined from the Northfleet data in Paper I by obtaining the best fit between the observed values of C, and those calculated from equations (1) or (2). Four sub-divisions of stability were used in Paper I, but in two of them (“slightly stable” and “stable above slightly unstable”) the differences between the values of A4 for the two groups, although significant, were relatively small and the values of C were the same. It was therefore decided to calculate simple values of M and C for both these sets of Northfleet data. These were M = 1.64 + 0.10 s and C = 021.k 003 m s-i. With the above exception, the values of M and C used to calculate the Tilbury concentrations are those derived from the Northfleet data in Paper I. In addition, values of M and C which give best fit to the Tilbury data are determined. The physical reasoning behind equations (1) and (2) was that downward dispersion from very high sources (effective stack height above about 150 m) takes place through an environment which is always stably stratified to some degree. When unstable lapse rates are observed, these arise from a combination of measurements inside and outside thermals, but in the environment of the thermals the lapse rate is always slightly stably stratified. Horizontal inhomogeneities in temperature, which always exist over typical English countryside, result in local bursts of convective activity even when the mean observed lapse
545
Concentration of sulphur dioxide at Tilbury
is stable. The diffusivity can therefore be considered to consist of two terms, one resulting from mechanical stirring of the boundary layer [giving rise to the term containing M in equations (1) and (2)] and one resulting from convective activity [giving rise to the term containing C in equations (1) and (2)]. The different forms of equations (1) and (2) follow from the assumption that the convective turbulence is of a more intermittent nature when the observed lapse rate is stable. One would expect the value of C to change with the observed lapse rate and to be small in stable conditions and large in unstable conditions. M, on the other hand, should vary only slowly with lapse rate. It should be possible to calculate values of M and C from observations of the scales and intensity of the vertical and lateral components of the atmospheric turbulence and their variation with height, but in Paper I and in this study the values of M and C are obtained from the observed maximum surface SO2 concentrations. In a later paper the treatment will be extended to cover calculation of the distance of maximum concentration and to relate the values of M and C to meteorological observations. rate
3. COMPARISON
OF THE GROUND
OBSERVED AND CALCULATED LEVEL CONCENTRATIONS
MAXIMUM
Table 1 shows the observed and calculated mean concentrations for wind speed groups containing 10 or more hourly observations for each of the three ranges of w/U mentioned Table 1. All stabilities: equation (1) used in calculations Wind speed
w/u >
O-2
2-4
4-6
&8
8-10
lC-12
12-14
48 205 5.9 5.5 5.5
65 250 5.3 4.1 4.8
98 231 5.1 5.2 5.6
131 248 6.7 6.1 6.9
132 216 7.1 8.2 9.5
59 319 12.9 10.8 12.1
39* 346 17.1 14.0 16.5
lit 43 5.3 1.7 2.6
32 98 3.2 3.9 5.0
60 128 4.5 4.3 4.9
122 166 1.7 6.3 6.7
114 213 9.6 8.1 8.2
60 246 11.0 10.5 10.2
1st 21 3.5 2.8 21
28 43 4.4 4.8 4.6
45
28 II 5.1 5.2 5.9
20 83 5.1 3.9 4.4
14-16
>16
ms-’
I
Hours Mean load Observed Calculated (N) Calculated (T) 0.5 < w/Li < 1 Hours Mean load Observed Calculated (N) Calculated (T) w/u < 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
IO
3.9 3.1 3.9
MW Concentration pphm 26 254 16.4 14.6 13.9 123 95 10.2 8.4 9.8
14 319 15.4 16.1 16.8
MW Concentration pphm
MW Concentration pphm
*Mean wind speed 13,4ms-‘. t Mean wind speed, 2.45 m s- ‘. j Mean wind speed t3.9 and $15.7 m s-l. Key to Tables 1-5 Tables l-5 show the mean values of maximum hourly average surface concentration of SO2 downwind of Tilbury power station in various ranges of wind speed and of the ratio (efflux velocity)/(wind speed). These mean concentrations are compared with concentrations calculated from the expressions derived in Paper I. Each table contains data in a particular range of lapse rate conditions. These conditions, together with the expression used to calculate the surface concentrations are given in the individual table headings. Values of the parameters M and C appearing in the expressions are given in Table 6. Calculated(N) concentrations use M and C derived from the Northfleet data and calculated (T) concentrations used M and C values obtained from a least squares fit to the Tilbury data.
D. J. M~C~RE
546
Table 2. Unstable (sub-division (i) of Paper I): equation (2) used in calculations Wind soeed
tk2
2-4
46
6-8
8-10
17* 28 199 248 10.1 7.6 10.8 8.8 10.2 8.4
36 236 64 66 6.3
43 268 7.7 8.2 7.8
2Ot 322 10.5 10.2 9.7
0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T)
25f 122 5.3 5.2 4.9
39 173 6.9 6.4 6.1
47 216 8.0 7.8 7.4
w/v < 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
811 40 4.8 1.9 2.5
9 64 5.0 4.2 6.5
IO-12
-
12-14
1416
216
ms-’
w/cl > 1
Hours Mean load Observed Calculated (N) Calculated (T)
MW Concentration pphm
2Q 252 9.1 10.7 10.2
MW Concentration pphm 1F 100 6.1 4.9 6.5
MW Concentration pphm
Mean wind speed * 2.29 and t 11.4 m s- ‘. Mean wind speed $6.5 and 5 13.7 m s- ‘. Meanwindspeed1)6.2msF’andql43ms-’. in (ii) of section 1 above, with 2 shows a similar comparison slightly above slightly unstable, sub-divisions of Paper 1. Each
no subdivision of the data according to stability. Table for occasions with unstable lapse rates, Table 3 for the Table 4 for the slightly stable and Table 5 for the stable group in Tables 2-5 contains at least eight observations.
Table 3. Stable above slightly unstable (sub-division (ii) of Paper I): equation (1) used in calculations Wind speed
l&l2
12-14
o-2
2-4
46
6-8
8-10
9 239 48 3.9 4.5
11 248 4.1 3.9 4.4
24 231 4,3 5.0 5.5
39 232 8.1 6.1 6.3
35 272 8.1 8.0 8.0
12% 306 11.0 11.9 11.5
15 130 3.7 4.5 5.7
42 165 9.5 6.3 7.9
44 217 12.0 8.7 106
22$ 227 12.4 11.3 13.6
13 65 3.2 3.8 3.7
10 91 7.5 5.2 5.5
76 4.7 5.4 61
1416
>16
ms-’
w/u > 1 Hours Mean load Observed Calculated (N) Calculated (T) 0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T) \1.:c.:< 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
11t 71 4.9 3.5 4.8
195: 31 3.9 5.9 4.0
* Mean wind speed 11.3 m s- ‘. Mean wind speed t 3.7 and $ 13.4 m s- ‘. Mean wind speed $ 5.8 and I( 13.2 m s- ‘.
MW Concentration pphm
MW Concentration pphm
1011 MW Concentration pphm
547
Concentration of sulphur dioxide at Tilbury. Table 4. Slightly stable conditions (sub-division (iii) of Paper I): equation (1) used in calculations Wind speed
O-2
2-4
4-6
68
8-10
l&l2
12-14
12 254 5.1 4.7 5.8
14 225 7.2 3.7 46
25 218 4.5 3.3 4.1
34 261 5.7 6.2 7.8
30 295 8.7 8.4 10.6
29 324 15.7 10.8 13.6
33* 349 18.1 14.3 18.1
13t 174 3.8 3.2 5.4
9 130 6.1 4.9 6.8
25 162 6.7 5.9 7.1
12 191 10.2 7.9 8.7
22 250 13.9 11.5 11.9
121 40 4.0 3.2 3.6
12 76 4.3 3.6 4.2
1% 59 2.7 3.9 4.6
14-16
>16
m s-’
w/u > 1 Hours Mean load Observed Calculated (N) Calculated (T) 0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T) w/u < 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
MW Concentration pphm 15 247 19.2 15.9 15.8
13 324 140 18.9 18.1
MW Concentration pphm
911 80 11.5 8.9 10.9
MW Concentration pphm
* Mean wind speed 13.4 m s- ‘. t Mean wind speed 4.9 m s- i. Mean wind speeds $63, $11.8 and 1117 m s- ‘.
3.1 Efict of downwash The values of M and C derived from the Tilbury data are compared with the Northfleet values in Table 6. From Table 6 it can be seen that there are no significant differences between the Tilbury M and C values for the w/U sub-divisions in each of the stability Table 5. Stable lapse conditions (sub-division (iv) of Paper I): equation (1) used in calculations Wind speed
o-2
2-4
4-6
6-8
8-10
21 175 5.5 5.0 4.4
29 242 3.2 4.6 4.1
21 222 3.2 4.8 4.4
22 277 6.0 5.5 5.1
28* 280 62 6.8 6.3
14t 84 3.0 3.0 3.1
16 123 2.4 2.3 2.5
16 160 6.3 5.3 5.8
11 204 6.6 6.1 6.9
MW Concentration pphm
9 47 5.0 5.4 5.8
11 57 3.4 2.7 2.5
7 73 5.1 6.1 5.0
MW Concentration pphm
lo-12
12-14
1416
>16
ms-’
w/u > 1 Hours Mean load Observed Calculated (N) Calculated (7’) 0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T) w/u < 0.5 Hours Mean load Observed Calculated (N) Calculated (T) *Meanwindspeed9.3ms-‘. t Mean wind speed 4.3 m s- r. $ Mean wind speed 3.3 m s-i.
71 25 2.7 1.0 1.5
MW Concentration pphm
D. J. MOORE
548
groups, indicating that the effect of downwash on the maximum ground level concentration is not very large. Table 6 also shows the observed and calculated mean concentrations (not weighted according to the number of observations in each data group). The largest difference between the observed concentrations and those calculated using the Northfleet parameters occurs in the lowest w/U group in unstable conditions, where it is 1.5 pphm. This is not significant and from Table 2 it can be seen to be mainly due to the rather high average concentration (4.9 pphm) observed in 8 h with light winds and a mean load of only 40 MW, when the estimate of SO1 emission from electricity generated would be least accurate. Considering the results for all the data, the ratio of the observed to calculated (from the Northfleet parameters) Tilbury concentrations are 1.11 for w/U > 1, 1.09 for w/U between 0.5 and 1 and 1.12 for w/U < 005. The standard errors given in Table 6 are calculated by taking the square root of the sum of the squares of the differences between the observed and calculated values divided by the number of degrees-of-freedom, are also shown. The number of degrees-of-freedom is taken as the number of observation sets when the values of M and C are taken from the independent (Northfleet) data and the number of observations minus two where the values of M and C are calculated from the Tilbury data. 3.2 Use of Northjleet
parameters
to predict the Tilbury concentrations
In view of the apparent lack of any systematic effect due to down-wash, values of M and C are calculated for each of the stability groups taking all three sets of data (wU/ > 1, 0.5 Q w/U < 1, w/U < 0.5) together. Table 7 shows the ratios of the optimum values of M and C to the Northfleet values of M and C. None of the ratios are different from 1.0 at the 5 per cent level of significance. Any real small difference which does exist could as easily result from the different fuel usage at the two stations as from small variations in M and C. 3.3 True mean concentrations
In calculating the unweighted means given in Tables 6 and 7 equal weighting is given to each data group, irrespective of the number of observations included in the calculation of the mean concentration for that particular range of wind speed, stability and w/U. It follows that the actual values of the mean maximum concentration are different from these values, because to calculate the true mean value, the individual means should be weighted according to the number of hours of observation in each group. Thus in the first line of Table 6, where the observed unweighted mean is 8.67, the true mean is 7.78 (Table 8). The true mean calculated from the Northfleet values of the parameters is 7.23 as opposed to 7.78, the calculated unweighted mean given in Table 6. Equal weighting was given to the various data groups in this analysis because the intention was to produce a model which gave a good fit to the observed readings in the extreme conditions, e.g. very high wind speeds or very light winds in unstable conditions. If the data points had been weighted according to the frequency of observation, the low concentration, medium wind speed data would have been dominant in the least squares analysis, resulting in a relatively poor fit to the extreme data. The equal weighting given to each wind speed group in the various stability sub-divisions is the reason for the apparent slight inconsistencies in the mean values and values
(iv)
Stable
(ii) + (iii)
Slightly stable
Unstable (i)
All
Stability
>1 0.5-l <0.5 >I 0.51 < 0.5 >l O.>l <@5 >I O..%l <0.5
W/U
8.67 9.13 5.36 8.47 I.34 5.32 8.11 9.70 5.24 4.84 4.57 4.05
Observed unweighted mean (pphm) 4.58 4.93 2.47 1.76 1.60 0.67 4.44 4.81 2.92 1.50 2.17’ 1.21
7.78 8.36 4.80 8.92 7.52 3.65 6.97 8.55 5.01 5.36 4.16 3.82 1.46 1.70 0.96 0.67 0.84 1.91 2.13 2.47 2.12 1.02 0.57 1.04
8.63 9.00 5.34 8.49 7.71 4.87 8.09 9.64 5.26 4.88 4.58 3.71
Northfeet valuca Tilbury values Unweighted Unweighted Sample mean mean SD. S.E. (pphm) (pphm) 0.89 1.70 0.79 0.56 0.87 1.74 1.85 2.33 1.45 1.16 0.43 0.58
S.E. 1.86 1.48 1.85 1.54 1.55 2.16 1.92 144 2.04 1.19 1.44 0.73
+ f f * * f + f f f f f
: 0.10 0.16 0.16 0.04 0.09 0.42 0.17 0.25 0.35 0.30 0.14 0.46
Tilbury
0.26 0.41 0.22 0.57 057 0.80 0.23 0.46 0.19 0.21 0.24 040
f f f f f f f + ) f f f
PO3 0.12 O-08 0.02 0.03 0.20 0.04 0.21 026 0.04 0.05 0.18
C (m s-‘)
values Northfleet values
together
with
M = 1.26 + 0.10 C = 0.16 f 002
M = 164 * 0.10 c = 0.21 f 0.03
M = 1.63 f 010 c = 060 f 0.02
M = 1.54 f DO5 C = 0.25 f 0.02
Table 6. Unweighted mean values of observed and calculated maximum hourly average concentration in each of the stability groups, the Tifbury and Northfleet values and tolerances of M and C, and standard errors of the calculated concentrations
& ” g. % 2 4 r: P 4
n B 8 e G $ 3 r: 2 5
D. J. MOORE
550
Table 7. Tilbury/Northfleet
Stability
values of M and C for various stability groupings, combining all ratios of w/U
Tilbury/Northfleet value of M
All Unstable Slightly stable Stable
1.08 * 0.98 f 1.07 + 1.02 +
Tilbury/Northfleet value of C
Observed unweighted mean (pphm)
1.14 _+0.14 0.98 & 0.05 1.24 + 0.20 1.34 * 0.20
005 0.05 006 0.12
Calculated unweighted mean Northfleet Tilbury
7.90 7.3 I 7.99 4.51
7.1 I 7.14 7.09 3.81
7.79 6.97 7.81 4.34
of M and C for each of the sub-divisions and the values for “all stabilities”, which are obviously not exactly means of the values for the sub-divisions. True mean values of observed and calculated concentrations for each of the groups of data appearing in Table 6 are given in Table 8. Taking the observations as a whole, the true means are about 10 per cent lower than the unweighted means, but where the data are sub-divided into stability groups this difference is less marked and is even reversed in some cases. Table 8. True means of observed and calculated concentrations Stability All
Unstable
Slightly stable Stable
W/U >l 0.51 <0.5 >I 0.5- 1 <0.5 >I 0.51 < 0.5 >l 0.5-l 10.5
Observed mean
Northfleet parameters mean
Tilbury parameters mean
Hours
7.78 8.58 4.83 8.04 7.44 5.39 8.82 10.20 4.96 4.83 4.45 4.02
7.23 7.60 4.48 8.51 7.52 3.80 7.52 8.52 4.80 5.39 4.03 3.78
8.17 7.87 4.79 8.09 7.17 5.38 8.79 9.80 5.13 4.92 4.43 3.69
572 439 151 144 139 28 307 243 89 121 57 34
4. CONCLUSIONS
(i) The expression for calculating maximum hourly average surface concentrations developed from the Northfleet data appears to be applicable to the Tilbury data, using the same values of the experimentally determined parameters. (ii) No corrections appear to be required in conditions when downwash was observed to occur (see e.g. Hamilton, 1967) unless one is aiming with an unrealistically high degree of accuracy in the calculations. The second of the above conclusions appears to be at variance with the results quoted by Moore (1967), as in that paper it was found that the ratio of observed to calculated concentrations for the Tilbury plume increased as the ratio w/U decreased. However, the model used in those calculations was the classical expression in which maximum concentration is inversely proportional to the square of the plume height. The expression developed in Paper I contains the cube of the plume height in the denominator of one of the terms from which the maximum concentration is calculated. This results in relatively higher concentrations with low loads (lower plume heights) and hence this model is in
551
Concentration of sulphur dioxide at Tilbury
agreement with the observations without additional corrections. The implication of this result is that visual (or instrumental) observations of down-wash probably give a pessimistic picture of the quantitative effect of the phenomenon. The actual proportion of the plume material involved is probably small. (iii) The method of estimating the rate of emission of SO2 for the two stations, one oilfired (Tilbury) and one coal-fired (Northfleet) appears to be satisfactory, with the possible exception of very low loads. (iv) The model ignores the variation of plume rise with atmospheric stability at a given wind speed and attempts to introduce this effect into the model produced a poorer agreement with the data. This would appear to indicate that the effects of the stability on H and on the two dispersion parameters M and C are largely self compensating. Acknowledgements-The analysis described in this paper was carried out at the Central Electricity Research Laboratories, Leatherhead and this paper is published by permission of the Central Electricity Generating Board. REFERENCES Hamilton P. M. (1967) Plume height measurements at Northfleet and Tilbury power stations. Atmospheric Environment 1, 379388. Hamilton P. M. (1969) Use of lidar in the study of chimney plumes. Phil. Trans. R. Sot. 265, 153-172. Lucas D. H. (1967) Application and evaluation of the results of the Tilbury plume rise and dispersion experiment. Atmospheric Environment 1, 421-424. Moore D. J. (1969) The distribution of surface concentration of sulphur dioxide emitted from tall chimneys. Phil. Trans. R. Sot. 265, 245-260.
Moore D. J. (1972) The effects of atmospheric stability and wind speed on the l-h average ground centrations of sulphur dioxide emitted from tall stacks, 1Oe Colloque sur les Atmospheres Poll&es, par L’Institut National de Recherche Chimique Appliquee (IRCHA) Paris, 1972 (Abridged version to this paper). Pasquill F. (1962) Atmospheric Diffusion. Van Nostrand, London. Striven R. A. (1969) Variability and upper bounds for ground level concentration. PM. Trans. R. Sot.
level conOrganise appended 265, 20%
220.
APPENDIX Abridged version of Moore (1972). Imroduction
In Moore (1969) it was shown that the ground level 1h average maximum concentrations of Northfleet generating station were well represented by the following expression.
of SOz down-wind
C, = 2QF/enUH2,
(A.1)
F = dimensionless adjustment factor H = stack height (h) + plume rise (z,) (m)
z, = G(Qh’14/LT...(2) (Hamilton, 1967) (A.2) a = 5@)m2 s-’ MW-‘j4 Qh = rate of heat emission per stack in MW, was obtained by dividing the rate of electricity generations (Q,) by an experimentally determined factor (12 for Northfleet, a two stack station). Moore (I 969) also showed that the cross-wind spread (g),)of plume material was given by the expression ey = B.u(m) where B is constant for a given plume and has an average value of 0.08 for wind speeds greater than 5 m s- I. Striven (1969) has pointed out that the solution to the two-dimensional (time or distance from the source and height above the ground) diffusion equation in cases where the vertical diffusion coefficient K(z) is a function of z, the height above the ground, is, in the region of maximum surface concentration, nearly equal to the solution to the equation with a constant diffusion coefficient (K). The assumed constant value is equal to a weighted mean of the value of K(z) over the height range O-H. The vertical spread (a,), is then given by us = 2 Kx/U (mz).
(A.3)
D. J. MCI~RE
552
If we make the further assumption of a gaussian distribution of material within the plume the ground, the expression for the maximum surface concentration of material becomes C, = (3/&‘*R
and reflection
QL/(nBUH’)
at
(A.4)
where L = 2K/U
i.e. f7t = Lu.
The factor R takes account of differences in the diffusivity If the plume rise is given by equation (2) it follows that:
(A.5)
of the atmosphere
above and below the plume level.
H = h(U + U,)/U
(A.6)
where U, = the wind speed at which the plume rise equals the stack height. We may therefore combine equations (1. 2 and 4) to give: F = (3)3’2 RL/(2Br”‘H),
which becomes
F = F,[2U/(U
+ U,)]
(A.7)
if RL/B is not a function of wind speed. F, is the value of F when U = U,. It is assumed that L is not varying with wind speed. In Table lA, empirical values of F given by Moore (1969) for moderate and strong winds (F,) are compared with the values given by equation (7) (F,). They are in fair agreement. The variation of observed maximum concentration It had been demonstrated in Moore the concentration observed at a given for RL/B (equation 4) would therefore the turbulence, which would be large be increasing more rapidly with wind which would be large in strong winds. Table
IA. Comparison
between
with wind speed
(1969) that stability, as indicated by time of day, wind speed when the wind speed fell below about be expected to contain a term representing the in light winds. Also, in view of the fact that F,, speed than F,, a term representing the effect of
values of F given by the expression C2U/(U +
F1 = 025 + @03 (U - 5) and F2 = 0.4
lOI1
u
5
I
9
I1
13
15
F,
0.25
0.31
0.37
0.43
0.49
0.55
F,
@27
0.33
0.38
0.42
0.45
0.48
Equation
(4) was therefore
replaced
had a marked effect on 5 m s-i. The expression effect of convection on in Table 1, appears to mechanical turbulence,
ms-’ F, = 0.4 at U, = 1OmsK’ for both expressions
by the expression C, = (Q/H*)(M/H
which represents the naturally stable state of the atmosphere produced turbulence. Alternatively. the expression C, = (Q/H2)[(M/H)’
+ C/U’), interrupted
64.8) either by convective
or by mechanically
+ (C/U2)2]“2
(A.9)
which represents interruption by turbulence resulting from a combination of the two effects, was used.* One would expect M and C to vary with different lapse rate configurations but (hopefully) to remain constant in conditions with similar lapse profiles relative to the height of the plume. Table 2A shows the results of comparing the whole of the available Northfleet data with equation (8) with the values of M and C optimized by determining the line of best fit which passed throughthe origin. The values of M and C derived by fitting equation (8) to the data are M = 1.54 s and C = 0.25 m s- I. The standard error of the estimate in Table 2A was 0.6 pphm and the errors in the estimates of M and C were 3 and 6 per cent respectively. Equation (9) gave a poorer representation of the data. In calculating the above and following values of SO, concentration, the Lucas (1967) value of G(.viz 515 in the units given above, was used to determine the plume height H. The variation of the observed concentration with stability Determination of category number. Each of the wind speed groups were further gories designated by a two digit category number determined as follows:
sub-divided
into stability
(a) Potential temp. decrease greater than 0.5” C 100 m- ’ over the whole of the meteorological 1967) or over either half (up to 114 or 114187 m). Category No. 22. * In Moore
(1972) Q, rather
than Q was used in equations
cate-
tower (Moore,
(8) and (9) and C, was in units of pphm
voljvol.
553
Concentration of sulphur dioxide at Tilbury
(b) Otherwise the category number was determined as follows over either half of the tower: lapse rate of potential temperature 0+0.5”C 100 m- ’ digit 3; increase of potential temperature OGO.5”C 100 m- ’ digit 4; increase of potential temperature 0.5l.o”C 100 m- 1digit 5; temperature inversions digit 6. With the exception ofcategory 22 above, the category number ascribed to the lower half of the meteorological tower temperature measurement determined the first digit in the category number, e.g. category 34 would be an occasion when the air was slightly unstable (0 to -0.5”C lOOm_‘) up to 114 m and slightly stable (0 to +@5”C 100 m- ‘) above that level.
Table 2A. Comparison of observed SO2 concentrations (all stabilities) grouped according to wind speed, with equation (8) Wind speed No. of obs. Mean load Obs. concn. Equation (8)
t&2
2-4
46
68
66 373 6.3 7.1
122 405 7.0 5.9
270 404 5.6 5.7
403 403 6.4 6.3
8-10
lo-12
12-14
1416
421 426 7.4 7.7
290 466 10.0 9.6
187 494 12.1 11.5
54 530 13.3 13.3
>16
ms-’
51 466 14.9 15.8
MW pphm
Important stability divisions
Inspection of the maximum concentration data showed the more important divisions appeared to be: (i) unstable, comprising categories 22, 33, 43, 53 and 63 (there were only 1 or 2 h within the last two groups); (ii) a stable layer above a slightly unstable layer (comprising categories 34, 35 and 36); (iii) slightly stable, comprising categories 44,45,54,55, 64, 65 (i.e. only a shallow inversion or no inversion of temperature); (iv) stable, comprising categories 46, 56 and 66 (i.e. an inversion layer which either extended to the ground or had still stable, although less stable, air below it). These sub-divisions (i-iv) were used in the analysis. Calculated
and observed maximum concentrations
as,finctions
of wind speed and stability
Table 3A shows the mean concentrations, numbers of hours of readings, and concentrations equation (8) and, in the unstable case, calculated from equation (9) as well.
calculated from
Discussion
Table 3 indicates that equation (9) gave a better representation of the data in unstable conditions. In all other stability configurations equation (8) gave a much better fit.
Table 3A. The observed and calculated mean hourly maximum concentrations speed and stability categories Wind speed
1
3
5
at Northfleet, in various wind
7
9
11
13
15
110 7.1 9.6 8.5
121 7.9 9.8 8.4
81 10.8 10.7 9.5
57 10.1 11.5 10.8
12 12.8 12.2 12.3
Sub-division (i), unstable 24 58 11 No. of ohs. 13.4 7.8 16.7 Mean concn. Equation (8) 11.8 10.2 14.7 12.6 10.0 16.3 Equation (9) Sub-division (ii), stable above slightly unstable 18 58 9 No. of obs. 6.2 5.1 4.0 Mean concn. 5.1 5.1 5.4 Equation (8) Sub-division (iii), slightly stable 48 86 12 No. of obs. 6.0 5.4 5.2 Mean concn. 4.9 5.0 6.5 Equation (8)
92 6.9 6.4
104 8.2 8.5
83 11.3 10.4
47 13.5 12.8
8 13.0 14.6
100 6.4 5.8
111 7.4 6.7
96 9.0 9.6
83 12.6 11.7
34 13.6 14.3
Sub-division (iv), stable No. of obs. Mean concn. Equation (8)
101 5.1 4.3
85 5.8 5.8
30 6.2 6.7
34 4.0 4.4
32 3.7 3.8
68 4.2 3.8
>I6 6 15.8 13.9 15.1
ms-’ h pphm
h pphm 45 14.8 15.0
h pphm h pphm
D. J. MOORE
554
Table 4A. The best-fit values of the parameters M and C in equations (8 and 9) for stability division (i) and for equation (8) in stability divisions (ii, iii and iv), together with the standard errors of the estimates Stability
Value of M (s)
Value of C (m s- ‘)
(i) equation (8) (i) equation (9) (ii) (iii) (iv)
1.24(13) 1.63 (3) 1.89 (6) 1.58 (9) 1.26 (8)
0.54 (9) @60 (3) 0.20 (16) 0.20 (11) 0.16 (9)
Error of estimate 2,013 (pphm) 1.888 1.199 0.921 0.516
The values in parentheses are the percentage standard errors of the estimates of M and C. In categories (ii), (iii) and (iv), where the air above 114 m was stable, equation (9) gave a good representation of the data. Relatively slight differences in the values of A and C were required to represent the data (Table 4A). The value of C was about three times greater in unstable conditions than in any of the other categories, indicating that the convective component of the turbulence was far more effective, as one would have expected. The presence of the convective term in the best fit expressions for categories (iii) and (iv) may appear rather surprising, especially as it has almost the same weight as in category (ii). Conclusions
The fairly simple models of plume behaviour presented in this paper give a good representation of the maximum surface SO, concentration. Most of the features listed in Moore (1969) are explained and the physics of the processes described are qualitatively realistic,
Vol. 8. pp. 543-554. Pergamon
Press 1974. Prmted in Great Britain
THE PREDICTION OF THE MEAN HOURLY AVERAGE MAXIMUM GROUND LEVEL CONCENTRATION OF SULPHUR DIOXIDE AT TILBURY D. J. MOORE Central Electricity Research Laboratories, Leatherhead. Surrey KT22 7SE (First receiued 26 June and injinalform
11 December 1973)
Abstract-Measurements of the maximum hourly average concentration of sulphur dioxide at Tilbury, grouped according to wind speed and vertical temperature profile, are compared with values calculated from an expression developed by Moore (1972). It is concluded that the expression can be used to predict Tilbury concentrations without change in the parameters derived from Northfleet data. The expression still applies, even in conditions when chimney down-wash has been observed, indicating that the fraction of the plume material involved in down-wash is fairly small. NOMENCLATURE m’SO,/m~‘air x 10’ efflux velocity m s- 1 wind speed m s-l stack height + plume rise m parameter appearing in the expression for C, representing the effect of mechanical turbulence s parameter appearing in the expression for C, representing the effect of convective turbulence m s- ’ rate of emission of SO2 from stacks (total for station) m3 s- ’ at N.T.P. rate of emission of heat from stack MW total rate of generation of electricity by station MW.
I
INTRODUCTION
In Moore (1972), henceforth referred to as Paper I, a dispersion model was developed for predicting the hourly average SO2 concentration in various stability conditions and applied to measurements made at Northfleet power station. As that paper had limited circulation and reprints are not available, an abridged and re-edited version is appended below. In the present paper, the model developed in Paper I is applied to measurements made at Tilbury. Both Tilbury and Northfleet are power stations located on the river Thames about 20 miles east of central London (see Lucas, James and Davies (1967) for details). The principal differences between the plants are: (i) Tilbury is an oil-fired station with a considerable variation in the ratio (SO2 emitted/MW generated) while Northfleet was coal-fired and there was so little variation in the above ratio that SO2 emission could be assumed to be directly proportional to MW generated. In this analysis, the SO2 emission has been calculated from the station fuel quality data. (ii) The efflux velocity on full load at Tilbury is 7.5 m s- ’ (with two-stack operation) compared with 20 m s- ’ at Northfleet, consequently down-wash effects became important at much lower wind speeds. For this reason, the data are not only divided into groups 543
D. J. MOORE
544
of limited ranges of wind speed and vertical temperature profile, as in the Northfleet analysis, but a further sub-division according to the ratio (efflux velocity/wind speed) is also made. The new groupings are w/U > 1 (no downwash expected) 1 2 w/U 2 l/2 (downwash sometimes observed) w/U < l/2 (downwash always observed). (iii) During the period when the measurements were made, Northfleet was a base load station, normally operating for 24 h a day, while Tilbury was normally closed down from 24:00 h until about 06:OOh and sometimes on summer afternoons. This, coupled with the extra sub-division of the data according to the ratio w/U mentioned in (ii) above, means that there are fewer data in each group than there were from Northfleet. Consequently some of the less frequently occurring sub-divisions do not have sufficient data for an accurate mean observed concentration to be determined. It is therefore necessary to combine some of the data groups. The occasions when such groupings are necessary are noted in the Tables of Results, and the actual mean wind speed for the group is given. 2.
CALCULATION
OF
THE
GROUND
LEVEL
MAXIMUM
CONCENTRATION
The dispersion model developed in Paper I resulted in the following expression for the maximum hourly average ground level concentration: (i) For all data groups except those containing occasions with unstable lapse rates only (but including data grouped according to wind speed only, with no sub-division according to lapse rate): C, = [(M/H) + Wf-Jz)1W~2).
(1)
(ii) For unstable lapse rates only: C, = [(M/H)2 + (C/U2)2]1'2(Q/H2).
(2)
Values of H should be calculated from the expression proposed by Lucas (1967) which for Tilbury, which has a 100 m tall stack, is:
H = 100 + 475 Qh114/U.
(3)
The values of A4 and C for each stability division were determined from the Northfleet data in Paper I by obtaining the best fit between the observed values of C, and those calculated from equations (1) or (2). Four sub-divisions of stability were used in Paper I, but in two of them (“slightly stable” and “stable above slightly unstable”) the differences between the values of A4 for the two groups, although significant, were relatively small and the values of C were the same. It was therefore decided to calculate simple values of M and C for both these sets of Northfleet data. These were M = 1.64 + 0.10 s and C = 021.k 003 m s-i. With the above exception, the values of M and C used to calculate the Tilbury concentrations are those derived from the Northfleet data in Paper I. In addition, values of M and C which give best fit to the Tilbury data are determined. The physical reasoning behind equations (1) and (2) was that downward dispersion from very high sources (effective stack height above about 150 m) takes place through an environment which is always stably stratified to some degree. When unstable lapse rates are observed, these arise from a combination of measurements inside and outside thermals, but in the environment of the thermals the lapse rate is always slightly stably stratified. Horizontal inhomogeneities in temperature, which always exist over typical English countryside, result in local bursts of convective activity even when the mean observed lapse
545
Concentration of sulphur dioxide at Tilbury
is stable. The diffusivity can therefore be considered to consist of two terms, one resulting from mechanical stirring of the boundary layer [giving rise to the term containing M in equations (1) and (2)] and one resulting from convective activity [giving rise to the term containing C in equations (1) and (2)]. The different forms of equations (1) and (2) follow from the assumption that the convective turbulence is of a more intermittent nature when the observed lapse rate is stable. One would expect the value of C to change with the observed lapse rate and to be small in stable conditions and large in unstable conditions. M, on the other hand, should vary only slowly with lapse rate. It should be possible to calculate values of M and C from observations of the scales and intensity of the vertical and lateral components of the atmospheric turbulence and their variation with height, but in Paper I and in this study the values of M and C are obtained from the observed maximum surface SO2 concentrations. In a later paper the treatment will be extended to cover calculation of the distance of maximum concentration and to relate the values of M and C to meteorological observations. rate
3. COMPARISON
OF THE GROUND
OBSERVED AND CALCULATED LEVEL CONCENTRATIONS
MAXIMUM
Table 1 shows the observed and calculated mean concentrations for wind speed groups containing 10 or more hourly observations for each of the three ranges of w/U mentioned Table 1. All stabilities: equation (1) used in calculations Wind speed
w/u >
O-2
2-4
4-6
&8
8-10
lC-12
12-14
48 205 5.9 5.5 5.5
65 250 5.3 4.1 4.8
98 231 5.1 5.2 5.6
131 248 6.7 6.1 6.9
132 216 7.1 8.2 9.5
59 319 12.9 10.8 12.1
39* 346 17.1 14.0 16.5
lit 43 5.3 1.7 2.6
32 98 3.2 3.9 5.0
60 128 4.5 4.3 4.9
122 166 1.7 6.3 6.7
114 213 9.6 8.1 8.2
60 246 11.0 10.5 10.2
1st 21 3.5 2.8 21
28 43 4.4 4.8 4.6
45
28 II 5.1 5.2 5.9
20 83 5.1 3.9 4.4
14-16
>16
ms-’
I
Hours Mean load Observed Calculated (N) Calculated (T) 0.5 < w/Li < 1 Hours Mean load Observed Calculated (N) Calculated (T) w/u < 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
IO
3.9 3.1 3.9
MW Concentration pphm 26 254 16.4 14.6 13.9 123 95 10.2 8.4 9.8
14 319 15.4 16.1 16.8
MW Concentration pphm
MW Concentration pphm
*Mean wind speed 13,4ms-‘. t Mean wind speed, 2.45 m s- ‘. j Mean wind speed t3.9 and $15.7 m s-l. Key to Tables 1-5 Tables l-5 show the mean values of maximum hourly average surface concentration of SO2 downwind of Tilbury power station in various ranges of wind speed and of the ratio (efflux velocity)/(wind speed). These mean concentrations are compared with concentrations calculated from the expressions derived in Paper I. Each table contains data in a particular range of lapse rate conditions. These conditions, together with the expression used to calculate the surface concentrations are given in the individual table headings. Values of the parameters M and C appearing in the expressions are given in Table 6. Calculated(N) concentrations use M and C derived from the Northfleet data and calculated (T) concentrations used M and C values obtained from a least squares fit to the Tilbury data.
D. J. M~C~RE
546
Table 2. Unstable (sub-division (i) of Paper I): equation (2) used in calculations Wind soeed
tk2
2-4
46
6-8
8-10
17* 28 199 248 10.1 7.6 10.8 8.8 10.2 8.4
36 236 64 66 6.3
43 268 7.7 8.2 7.8
2Ot 322 10.5 10.2 9.7
0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T)
25f 122 5.3 5.2 4.9
39 173 6.9 6.4 6.1
47 216 8.0 7.8 7.4
w/v < 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
811 40 4.8 1.9 2.5
9 64 5.0 4.2 6.5
IO-12
-
12-14
1416
216
ms-’
w/cl > 1
Hours Mean load Observed Calculated (N) Calculated (T)
MW Concentration pphm
2Q 252 9.1 10.7 10.2
MW Concentration pphm 1F 100 6.1 4.9 6.5
MW Concentration pphm
Mean wind speed * 2.29 and t 11.4 m s- ‘. Mean wind speed $6.5 and 5 13.7 m s- ‘. Meanwindspeed1)6.2msF’andql43ms-’. in (ii) of section 1 above, with 2 shows a similar comparison slightly above slightly unstable, sub-divisions of Paper 1. Each
no subdivision of the data according to stability. Table for occasions with unstable lapse rates, Table 3 for the Table 4 for the slightly stable and Table 5 for the stable group in Tables 2-5 contains at least eight observations.
Table 3. Stable above slightly unstable (sub-division (ii) of Paper I): equation (1) used in calculations Wind speed
l&l2
12-14
o-2
2-4
46
6-8
8-10
9 239 48 3.9 4.5
11 248 4.1 3.9 4.4
24 231 4,3 5.0 5.5
39 232 8.1 6.1 6.3
35 272 8.1 8.0 8.0
12% 306 11.0 11.9 11.5
15 130 3.7 4.5 5.7
42 165 9.5 6.3 7.9
44 217 12.0 8.7 106
22$ 227 12.4 11.3 13.6
13 65 3.2 3.8 3.7
10 91 7.5 5.2 5.5
76 4.7 5.4 61
1416
>16
ms-’
w/u > 1 Hours Mean load Observed Calculated (N) Calculated (T) 0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T) \1.:c.:< 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
11t 71 4.9 3.5 4.8
195: 31 3.9 5.9 4.0
* Mean wind speed 11.3 m s- ‘. Mean wind speed t 3.7 and $ 13.4 m s- ‘. Mean wind speed $ 5.8 and I( 13.2 m s- ‘.
MW Concentration pphm
MW Concentration pphm
1011 MW Concentration pphm
547
Concentration of sulphur dioxide at Tilbury. Table 4. Slightly stable conditions (sub-division (iii) of Paper I): equation (1) used in calculations Wind speed
O-2
2-4
4-6
68
8-10
l&l2
12-14
12 254 5.1 4.7 5.8
14 225 7.2 3.7 46
25 218 4.5 3.3 4.1
34 261 5.7 6.2 7.8
30 295 8.7 8.4 10.6
29 324 15.7 10.8 13.6
33* 349 18.1 14.3 18.1
13t 174 3.8 3.2 5.4
9 130 6.1 4.9 6.8
25 162 6.7 5.9 7.1
12 191 10.2 7.9 8.7
22 250 13.9 11.5 11.9
121 40 4.0 3.2 3.6
12 76 4.3 3.6 4.2
1% 59 2.7 3.9 4.6
14-16
>16
m s-’
w/u > 1 Hours Mean load Observed Calculated (N) Calculated (T) 0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T) w/u < 0.5 Hours Mean load Observed Calculated (N) Calculated (T)
MW Concentration pphm 15 247 19.2 15.9 15.8
13 324 140 18.9 18.1
MW Concentration pphm
911 80 11.5 8.9 10.9
MW Concentration pphm
* Mean wind speed 13.4 m s- ‘. t Mean wind speed 4.9 m s- i. Mean wind speeds $63, $11.8 and 1117 m s- ‘.
3.1 Efict of downwash The values of M and C derived from the Tilbury data are compared with the Northfleet values in Table 6. From Table 6 it can be seen that there are no significant differences between the Tilbury M and C values for the w/U sub-divisions in each of the stability Table 5. Stable lapse conditions (sub-division (iv) of Paper I): equation (1) used in calculations Wind speed
o-2
2-4
4-6
6-8
8-10
21 175 5.5 5.0 4.4
29 242 3.2 4.6 4.1
21 222 3.2 4.8 4.4
22 277 6.0 5.5 5.1
28* 280 62 6.8 6.3
14t 84 3.0 3.0 3.1
16 123 2.4 2.3 2.5
16 160 6.3 5.3 5.8
11 204 6.6 6.1 6.9
MW Concentration pphm
9 47 5.0 5.4 5.8
11 57 3.4 2.7 2.5
7 73 5.1 6.1 5.0
MW Concentration pphm
lo-12
12-14
1416
>16
ms-’
w/u > 1 Hours Mean load Observed Calculated (N) Calculated (7’) 0.5 < w/u < 1 Hours Mean load Observed Calculated (N) Calculated (T) w/u < 0.5 Hours Mean load Observed Calculated (N) Calculated (T) *Meanwindspeed9.3ms-‘. t Mean wind speed 4.3 m s- r. $ Mean wind speed 3.3 m s-i.
71 25 2.7 1.0 1.5
MW Concentration pphm
D. J. MOORE
548
groups, indicating that the effect of downwash on the maximum ground level concentration is not very large. Table 6 also shows the observed and calculated mean concentrations (not weighted according to the number of observations in each data group). The largest difference between the observed concentrations and those calculated using the Northfleet parameters occurs in the lowest w/U group in unstable conditions, where it is 1.5 pphm. This is not significant and from Table 2 it can be seen to be mainly due to the rather high average concentration (4.9 pphm) observed in 8 h with light winds and a mean load of only 40 MW, when the estimate of SO1 emission from electricity generated would be least accurate. Considering the results for all the data, the ratio of the observed to calculated (from the Northfleet parameters) Tilbury concentrations are 1.11 for w/U > 1, 1.09 for w/U between 0.5 and 1 and 1.12 for w/U < 005. The standard errors given in Table 6 are calculated by taking the square root of the sum of the squares of the differences between the observed and calculated values divided by the number of degrees-of-freedom, are also shown. The number of degrees-of-freedom is taken as the number of observation sets when the values of M and C are taken from the independent (Northfleet) data and the number of observations minus two where the values of M and C are calculated from the Tilbury data. 3.2 Use of Northjleet
parameters
to predict the Tilbury concentrations
In view of the apparent lack of any systematic effect due to down-wash, values of M and C are calculated for each of the stability groups taking all three sets of data (wU/ > 1, 0.5 Q w/U < 1, w/U < 0.5) together. Table 7 shows the ratios of the optimum values of M and C to the Northfleet values of M and C. None of the ratios are different from 1.0 at the 5 per cent level of significance. Any real small difference which does exist could as easily result from the different fuel usage at the two stations as from small variations in M and C. 3.3 True mean concentrations
In calculating the unweighted means given in Tables 6 and 7 equal weighting is given to each data group, irrespective of the number of observations included in the calculation of the mean concentration for that particular range of wind speed, stability and w/U. It follows that the actual values of the mean maximum concentration are different from these values, because to calculate the true mean value, the individual means should be weighted according to the number of hours of observation in each group. Thus in the first line of Table 6, where the observed unweighted mean is 8.67, the true mean is 7.78 (Table 8). The true mean calculated from the Northfleet values of the parameters is 7.23 as opposed to 7.78, the calculated unweighted mean given in Table 6. Equal weighting was given to the various data groups in this analysis because the intention was to produce a model which gave a good fit to the observed readings in the extreme conditions, e.g. very high wind speeds or very light winds in unstable conditions. If the data points had been weighted according to the frequency of observation, the low concentration, medium wind speed data would have been dominant in the least squares analysis, resulting in a relatively poor fit to the extreme data. The equal weighting given to each wind speed group in the various stability sub-divisions is the reason for the apparent slight inconsistencies in the mean values and values
(iv)
Stable
(ii) + (iii)
Slightly stable
Unstable (i)
All
Stability
>1 0.5-l <0.5 >I 0.51 < 0.5 >l O.>l <@5 >I O..%l <0.5
W/U
8.67 9.13 5.36 8.47 I.34 5.32 8.11 9.70 5.24 4.84 4.57 4.05
Observed unweighted mean (pphm) 4.58 4.93 2.47 1.76 1.60 0.67 4.44 4.81 2.92 1.50 2.17’ 1.21
7.78 8.36 4.80 8.92 7.52 3.65 6.97 8.55 5.01 5.36 4.16 3.82 1.46 1.70 0.96 0.67 0.84 1.91 2.13 2.47 2.12 1.02 0.57 1.04
8.63 9.00 5.34 8.49 7.71 4.87 8.09 9.64 5.26 4.88 4.58 3.71
Northfeet valuca Tilbury values Unweighted Unweighted Sample mean mean SD. S.E. (pphm) (pphm) 0.89 1.70 0.79 0.56 0.87 1.74 1.85 2.33 1.45 1.16 0.43 0.58
S.E. 1.86 1.48 1.85 1.54 1.55 2.16 1.92 144 2.04 1.19 1.44 0.73
+ f f * * f + f f f f f
: 0.10 0.16 0.16 0.04 0.09 0.42 0.17 0.25 0.35 0.30 0.14 0.46
Tilbury
0.26 0.41 0.22 0.57 057 0.80 0.23 0.46 0.19 0.21 0.24 040
f f f f f f f + ) f f f
PO3 0.12 O-08 0.02 0.03 0.20 0.04 0.21 026 0.04 0.05 0.18
C (m s-‘)
values Northfleet values
together
with
M = 1.26 + 0.10 C = 0.16 f 002
M = 164 * 0.10 c = 0.21 f 0.03
M = 1.63 f 010 c = 060 f 0.02
M = 1.54 f DO5 C = 0.25 f 0.02
Table 6. Unweighted mean values of observed and calculated maximum hourly average concentration in each of the stability groups, the Tifbury and Northfleet values and tolerances of M and C, and standard errors of the calculated concentrations
& ” g. % 2 4 r: P 4
n B 8 e G $ 3 r: 2 5
D. J. MOORE
550
Table 7. Tilbury/Northfleet
Stability
values of M and C for various stability groupings, combining all ratios of w/U
Tilbury/Northfleet value of M
All Unstable Slightly stable Stable
1.08 * 0.98 f 1.07 + 1.02 +
Tilbury/Northfleet value of C
Observed unweighted mean (pphm)
1.14 _+0.14 0.98 & 0.05 1.24 + 0.20 1.34 * 0.20
005 0.05 006 0.12
Calculated unweighted mean Northfleet Tilbury
7.90 7.3 I 7.99 4.51
7.1 I 7.14 7.09 3.81
7.79 6.97 7.81 4.34
of M and C for each of the sub-divisions and the values for “all stabilities”, which are obviously not exactly means of the values for the sub-divisions. True mean values of observed and calculated concentrations for each of the groups of data appearing in Table 6 are given in Table 8. Taking the observations as a whole, the true means are about 10 per cent lower than the unweighted means, but where the data are sub-divided into stability groups this difference is less marked and is even reversed in some cases. Table 8. True means of observed and calculated concentrations Stability All
Unstable
Slightly stable Stable
W/U >l 0.51 <0.5 >I 0.5- 1 <0.5 >I 0.51 < 0.5 >l 0.5-l 10.5
Observed mean
Northfleet parameters mean
Tilbury parameters mean
Hours
7.78 8.58 4.83 8.04 7.44 5.39 8.82 10.20 4.96 4.83 4.45 4.02
7.23 7.60 4.48 8.51 7.52 3.80 7.52 8.52 4.80 5.39 4.03 3.78
8.17 7.87 4.79 8.09 7.17 5.38 8.79 9.80 5.13 4.92 4.43 3.69
572 439 151 144 139 28 307 243 89 121 57 34
4. CONCLUSIONS
(i) The expression for calculating maximum hourly average surface concentrations developed from the Northfleet data appears to be applicable to the Tilbury data, using the same values of the experimentally determined parameters. (ii) No corrections appear to be required in conditions when downwash was observed to occur (see e.g. Hamilton, 1967) unless one is aiming with an unrealistically high degree of accuracy in the calculations. The second of the above conclusions appears to be at variance with the results quoted by Moore (1967), as in that paper it was found that the ratio of observed to calculated concentrations for the Tilbury plume increased as the ratio w/U decreased. However, the model used in those calculations was the classical expression in which maximum concentration is inversely proportional to the square of the plume height. The expression developed in Paper I contains the cube of the plume height in the denominator of one of the terms from which the maximum concentration is calculated. This results in relatively higher concentrations with low loads (lower plume heights) and hence this model is in
551
Concentration of sulphur dioxide at Tilbury
agreement with the observations without additional corrections. The implication of this result is that visual (or instrumental) observations of down-wash probably give a pessimistic picture of the quantitative effect of the phenomenon. The actual proportion of the plume material involved is probably small. (iii) The method of estimating the rate of emission of SO2 for the two stations, one oilfired (Tilbury) and one coal-fired (Northfleet) appears to be satisfactory, with the possible exception of very low loads. (iv) The model ignores the variation of plume rise with atmospheric stability at a given wind speed and attempts to introduce this effect into the model produced a poorer agreement with the data. This would appear to indicate that the effects of the stability on H and on the two dispersion parameters M and C are largely self compensating. Acknowledgements-The analysis described in this paper was carried out at the Central Electricity Research Laboratories, Leatherhead and this paper is published by permission of the Central Electricity Generating Board. REFERENCES Hamilton P. M. (1967) Plume height measurements at Northfleet and Tilbury power stations. Atmospheric Environment 1, 379388. Hamilton P. M. (1969) Use of lidar in the study of chimney plumes. Phil. Trans. R. Sot. 265, 153-172. Lucas D. H. (1967) Application and evaluation of the results of the Tilbury plume rise and dispersion experiment. Atmospheric Environment 1, 421-424. Moore D. J. (1969) The distribution of surface concentration of sulphur dioxide emitted from tall chimneys. Phil. Trans. R. Sot. 265, 245-260.
Moore D. J. (1972) The effects of atmospheric stability and wind speed on the l-h average ground centrations of sulphur dioxide emitted from tall stacks, 1Oe Colloque sur les Atmospheres Poll&es, par L’Institut National de Recherche Chimique Appliquee (IRCHA) Paris, 1972 (Abridged version to this paper). Pasquill F. (1962) Atmospheric Diffusion. Van Nostrand, London. Striven R. A. (1969) Variability and upper bounds for ground level concentration. PM. Trans. R. Sot.
level conOrganise appended 265, 20%
220.
APPENDIX Abridged version of Moore (1972). Imroduction
In Moore (1969) it was shown that the ground level 1h average maximum concentrations of Northfleet generating station were well represented by the following expression.
of SOz down-wind
C, = 2QF/enUH2,
(A.1)
F = dimensionless adjustment factor H = stack height (h) + plume rise (z,) (m)
z, = G(Qh’14/LT...(2) (Hamilton, 1967) (A.2) a = 5@)m2 s-’ MW-‘j4 Qh = rate of heat emission per stack in MW, was obtained by dividing the rate of electricity generations (Q,) by an experimentally determined factor (12 for Northfleet, a two stack station). Moore (I 969) also showed that the cross-wind spread (g),)of plume material was given by the expression ey = B.u(m) where B is constant for a given plume and has an average value of 0.08 for wind speeds greater than 5 m s- I. Striven (1969) has pointed out that the solution to the two-dimensional (time or distance from the source and height above the ground) diffusion equation in cases where the vertical diffusion coefficient K(z) is a function of z, the height above the ground, is, in the region of maximum surface concentration, nearly equal to the solution to the equation with a constant diffusion coefficient (K). The assumed constant value is equal to a weighted mean of the value of K(z) over the height range O-H. The vertical spread (a,), is then given by us = 2 Kx/U (mz).
(A.3)
D. J. MCI~RE
552
If we make the further assumption of a gaussian distribution of material within the plume the ground, the expression for the maximum surface concentration of material becomes C, = (3/&‘*R
and reflection
QL/(nBUH’)
at
(A.4)
where L = 2K/U
i.e. f7t = Lu.
The factor R takes account of differences in the diffusivity If the plume rise is given by equation (2) it follows that:
(A.5)
of the atmosphere
above and below the plume level.
H = h(U + U,)/U
(A.6)
where U, = the wind speed at which the plume rise equals the stack height. We may therefore combine equations (1. 2 and 4) to give: F = (3)3’2 RL/(2Br”‘H),
which becomes
F = F,[2U/(U
+ U,)]
(A.7)
if RL/B is not a function of wind speed. F, is the value of F when U = U,. It is assumed that L is not varying with wind speed. In Table lA, empirical values of F given by Moore (1969) for moderate and strong winds (F,) are compared with the values given by equation (7) (F,). They are in fair agreement. The variation of observed maximum concentration It had been demonstrated in Moore the concentration observed at a given for RL/B (equation 4) would therefore the turbulence, which would be large be increasing more rapidly with wind which would be large in strong winds. Table
IA. Comparison
between
with wind speed
(1969) that stability, as indicated by time of day, wind speed when the wind speed fell below about be expected to contain a term representing the in light winds. Also, in view of the fact that F,, speed than F,, a term representing the effect of
values of F given by the expression C2U/(U +
F1 = 025 + @03 (U - 5) and F2 = 0.4
lOI1
u
5
I
9
I1
13
15
F,
0.25
0.31
0.37
0.43
0.49
0.55
F,
@27
0.33
0.38
0.42
0.45
0.48
Equation
(4) was therefore
replaced
had a marked effect on 5 m s-i. The expression effect of convection on in Table 1, appears to mechanical turbulence,
ms-’ F, = 0.4 at U, = 1OmsK’ for both expressions
by the expression C, = (Q/H*)(M/H
which represents the naturally stable state of the atmosphere produced turbulence. Alternatively. the expression C, = (Q/H2)[(M/H)’
+ C/U’), interrupted
64.8) either by convective
or by mechanically
+ (C/U2)2]“2
(A.9)
which represents interruption by turbulence resulting from a combination of the two effects, was used.* One would expect M and C to vary with different lapse rate configurations but (hopefully) to remain constant in conditions with similar lapse profiles relative to the height of the plume. Table 2A shows the results of comparing the whole of the available Northfleet data with equation (8) with the values of M and C optimized by determining the line of best fit which passed throughthe origin. The values of M and C derived by fitting equation (8) to the data are M = 1.54 s and C = 0.25 m s- I. The standard error of the estimate in Table 2A was 0.6 pphm and the errors in the estimates of M and C were 3 and 6 per cent respectively. Equation (9) gave a poorer representation of the data. In calculating the above and following values of SO, concentration, the Lucas (1967) value of G(.viz 515 in the units given above, was used to determine the plume height H. The variation of the observed concentration with stability Determination of category number. Each of the wind speed groups were further gories designated by a two digit category number determined as follows:
sub-divided
into stability
(a) Potential temp. decrease greater than 0.5” C 100 m- ’ over the whole of the meteorological 1967) or over either half (up to 114 or 114187 m). Category No. 22. * In Moore
(1972) Q, rather
than Q was used in equations
cate-
tower (Moore,
(8) and (9) and C, was in units of pphm
voljvol.
553
Concentration of sulphur dioxide at Tilbury
(b) Otherwise the category number was determined as follows over either half of the tower: lapse rate of potential temperature 0+0.5”C 100 m- ’ digit 3; increase of potential temperature OGO.5”C 100 m- ’ digit 4; increase of potential temperature 0.5l.o”C 100 m- 1digit 5; temperature inversions digit 6. With the exception ofcategory 22 above, the category number ascribed to the lower half of the meteorological tower temperature measurement determined the first digit in the category number, e.g. category 34 would be an occasion when the air was slightly unstable (0 to -0.5”C lOOm_‘) up to 114 m and slightly stable (0 to +@5”C 100 m- ‘) above that level.
Table 2A. Comparison of observed SO2 concentrations (all stabilities) grouped according to wind speed, with equation (8) Wind speed No. of obs. Mean load Obs. concn. Equation (8)
t&2
2-4
46
68
66 373 6.3 7.1
122 405 7.0 5.9
270 404 5.6 5.7
403 403 6.4 6.3
8-10
lo-12
12-14
1416
421 426 7.4 7.7
290 466 10.0 9.6
187 494 12.1 11.5
54 530 13.3 13.3
>16
ms-’
51 466 14.9 15.8
MW pphm
Important stability divisions
Inspection of the maximum concentration data showed the more important divisions appeared to be: (i) unstable, comprising categories 22, 33, 43, 53 and 63 (there were only 1 or 2 h within the last two groups); (ii) a stable layer above a slightly unstable layer (comprising categories 34, 35 and 36); (iii) slightly stable, comprising categories 44,45,54,55, 64, 65 (i.e. only a shallow inversion or no inversion of temperature); (iv) stable, comprising categories 46, 56 and 66 (i.e. an inversion layer which either extended to the ground or had still stable, although less stable, air below it). These sub-divisions (i-iv) were used in the analysis. Calculated
and observed maximum concentrations
as,finctions
of wind speed and stability
Table 3A shows the mean concentrations, numbers of hours of readings, and concentrations equation (8) and, in the unstable case, calculated from equation (9) as well.
calculated from
Discussion
Table 3 indicates that equation (9) gave a better representation of the data in unstable conditions. In all other stability configurations equation (8) gave a much better fit.
Table 3A. The observed and calculated mean hourly maximum concentrations speed and stability categories Wind speed
1
3
5
at Northfleet, in various wind
7
9
11
13
15
110 7.1 9.6 8.5
121 7.9 9.8 8.4
81 10.8 10.7 9.5
57 10.1 11.5 10.8
12 12.8 12.2 12.3
Sub-division (i), unstable 24 58 11 No. of ohs. 13.4 7.8 16.7 Mean concn. Equation (8) 11.8 10.2 14.7 12.6 10.0 16.3 Equation (9) Sub-division (ii), stable above slightly unstable 18 58 9 No. of obs. 6.2 5.1 4.0 Mean concn. 5.1 5.1 5.4 Equation (8) Sub-division (iii), slightly stable 48 86 12 No. of obs. 6.0 5.4 5.2 Mean concn. 4.9 5.0 6.5 Equation (8)
92 6.9 6.4
104 8.2 8.5
83 11.3 10.4
47 13.5 12.8
8 13.0 14.6
100 6.4 5.8
111 7.4 6.7
96 9.0 9.6
83 12.6 11.7
34 13.6 14.3
Sub-division (iv), stable No. of obs. Mean concn. Equation (8)
101 5.1 4.3
85 5.8 5.8
30 6.2 6.7
34 4.0 4.4
32 3.7 3.8
68 4.2 3.8
>I6 6 15.8 13.9 15.1
ms-’ h pphm
h pphm 45 14.8 15.0
h pphm h pphm
D. J. MOORE
554
Table 4A. The best-fit values of the parameters M and C in equations (8 and 9) for stability division (i) and for equation (8) in stability divisions (ii, iii and iv), together with the standard errors of the estimates Stability
Value of M (s)
Value of C (m s- ‘)
(i) equation (8) (i) equation (9) (ii) (iii) (iv)
1.24(13) 1.63 (3) 1.89 (6) 1.58 (9) 1.26 (8)
0.54 (9) @60 (3) 0.20 (16) 0.20 (11) 0.16 (9)
Error of estimate 2,013 (pphm) 1.888 1.199 0.921 0.516
The values in parentheses are the percentage standard errors of the estimates of M and C. In categories (ii), (iii) and (iv), where the air above 114 m was stable, equation (9) gave a good representation of the data. Relatively slight differences in the values of A and C were required to represent the data (Table 4A). The value of C was about three times greater in unstable conditions than in any of the other categories, indicating that the convective component of the turbulence was far more effective, as one would have expected. The presence of the convective term in the best fit expressions for categories (iii) and (iv) may appear rather surprising, especially as it has almost the same weight as in category (ii). Conclusions
The fairly simple models of plume behaviour presented in this paper give a good representation of the maximum surface SO, concentration. Most of the features listed in Moore (1969) are explained and the physics of the processes described are qualitatively realistic,