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Dispersion of pollutants in convective low wind: a case study of Delhi
Atmospheric Environment 36 (2002) 2071–2079
Dispersion of pollutants in convective low wind: a case study of Delhi P. Goyal*, T.V.B.P.S. Rama Krishna Centre for Atmospheric Sciences, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Received 9 January 2001; accepted 18 July 2001
Abstract The transport and dispersion of pollutants becomes weak under low wind conditions resulting in large ground level concentrations (g.l.c.’s). Largest mean g.l.c.’s due to elevated sources are typically found under daytime convective conditions with moderate to weak winds in the earlier studies. Similar cases have been studied here by using three different dispersion models, i.e. Gaussian plume model (GPM) and two low wind models (LWM1 and LWM2) at few vulnerable places in Delhi. The models compute the hourly g.l.c.’s of SO2 due to industrial and power plant sources. The performance of these models has been compared against observed data to identify one of the model, appropriate for dispersion of pollutants in low wind convective conditions, which are frequently occurring meteorological conditions in Delhi and also in urban cities of India. This evaluation has been performed at four receptors by using three different methods: (i) comparison of hourly concentrations of the models against observed data, (ii) Q–Q-plots (Quantile–Quantile) and (iii) statistical measures. On the basis of the results and discussion of above methods, it has been concluded that GPM is always overpredicting and LWM2 is consistently underpredicting the concentrations, whereas, LWM1 is performing better than GPM and LWM2. Thus LWM1 may be recommended for studying dispersion of pollutants from elevated point sources in low wind convective conditions. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Low wind; Dispersion model; Ground level concentration; Convective condition
1. Introduction The deterioration of air quality in urban areas due to the continuous growth of industries and the day to day increase in vehicular traffic has provided the impetus for comprehensive monitoring/modeling of air quality. It is not always feasible to monitor/measure the concentrations of species at various vulnerable points of a city due to high cost and the experimental difficulties involved. However, an insight in this regard could be achieved with the help of suitable mathematical models.
*Corresponding author. Tel.: +91-11-659-11309; fax: +9111-686-2037. E-mail address: [email protected] (P. Goyal).
Low winds pose a particular problem in Gaussian models, since concentration is inversely proportional to wind speed, resulting in overprediction of concentration when wind speed approaches zero. The wind is defined as low wind when the surface wind at 10 m level is p2 m s1 (Sagendorf and Dickson, 1974; Cirrilo and Poli, 1992; Arya, 1995). The lack of reliable wind data itself creates problems because most conventional anemometers cease to function below the threshold wind speed. Other difficulties include both the inadequacy of the classical methods for modeling the transport and dispersion as the wind approaches zero and in describing the spatial and temporal character of the low winds in a stably stratified boundary layer. This latter problem requires special attention for very low level sources, because under these conditions, large
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ground level concentrations (g.l.c.’s) are likely to be experienced. Large pollutant concentrations might occur under convective low wind conditions due to elevated point sources (Moore, 1969; Deardorff, 1984). The study on the dispersion of air pollutants under convective low wind conditions assumes significance as these occur frequently in Indian environment. Several studies (Goyal et al., 1994; Arya, 1995; Sharan and Yadav, 1998) have investigated the dispersion of air pollutants in low wind conditions. Some of these studies have shown that the standard steady-state Gaussian plume models (GPMs) generally overpredict ground level pollutant concentrations in low wind conditions. The limitations of GPMs are discussed in literature (Arya, 1999; Zannetti, 1990; Seinfield, 1986). The model produces unreasonable results when applied to diffusion in low wind cases (Bass et al., 1979; Zannetti, 1986) because (1) downwind diffusion is neglected in comparison to the advection (2) the concentration is inversely proportional to wind speed and therefore, the concentration approaches infinity as the wind tends to zero and (3) the average concentrations are stationary (Anfossi et al., 1990). In addition the assumption of constant diffusivities seems reasonable in the far field and become questionable for describing near-source dispersion (Batchelor, 1949; Taylor, 1959; Csanady, 1973; Sharan et al., 1996). A study of Okamoto and Shiozawa (1978) for ground level sources showed that high g.l.c.’s might occur due to weak horizontal dispersion. The structure of the boundary layer is not yet sufficiently known under the low wind conditions. The classical conventional models such as Gaussian plume or based on K-theory with suitable assumptions, are known to work reasonable under most of the meteorological regimes except the weak wind conditions. Thus it becomes important to study the dispersion of pollutant under such conditions. In the present study we propose to fill up some of these gaps through modeling of dispersion in low wind convective conditions. Delhi, one of the most polluted capital cities of the world, has been considered for the case study. Major sources of air pollutants in Delhi are vehicles, industries, power plants, and domestic coal burning. An estimated 3000 metric tones of air pollutants are emitted daily (MOEF, 1997). Sulphur dioxide (SO2) is recognized as one of the major pollutant from elevated sources of industries and power plants in Delhi. These sources are known to produce high concentrations under low wind conditions. Thus, the objective of the present study is to study the dispersion of air pollutants emitting from elevated point sources in Delhi under convective low winds by using different models in order to identify a suitable model for dispersion of pollutants under same conditions. A GPM and two different models for treating low winds in
convective conditions have been used for estimating the g.l.c.’s. The models’ description is given in Section 2. The emissions and meteorological data and the computational methodology are given in the following Sections 3 and 4, respectively. The results and conclusions are discussed in the subsequent sections.
2. Models’ description 2.1. Gaussian plume model (GPM) The g.l.c.’s of the pollutants due to elevated point source (Wark et al., 1998) is given by " # Q y2 H2 Cðx; y; 0Þ ¼ ð1Þ exp 2 exp 2 ; pusy sz 2sy 2sz where Q is the source strength (g s1), u is the mean wind speed (m s1), sy ; sz are the horizontal and vertical dispersion parameters (m) respectively, y is the cross wind distance (m), H is the effective stack height (m) which is given as H ¼ hs þ Dh; where, Dh is the plume rise (m) and hs is the physical stack height (m). The wind profile law (Wark et al., 1998) has been used to estimate the wind speed at the stack level. Briggs (1969, 1975) plume rise formulae for hot plumes are used for evaluating the concentrations of SO2 from elevated point sources. These plume rise formulae are summarized below: For unstable or neutral atmospheric conditions, the downwind distance of final plume rise is Xf ¼ 3:5 X ; where X ¼ 14 F 5=8 for Fo55 m4 s–3 and X ¼ 13F 2=5 for F > 55 m4 s3. The effective stack height under these conditions is H ¼ hs þ ½1:6F 1=3 ð3:5X Þ2=3 uðhÞ;
ð2Þ 4 3
where, F is the buoyancy flux parameter (m s ), uðhÞ is the wind speed at the top of the stack (m s1), Xf is the distance to the final rise (m) and X is the distance at which atmospheric turbulence begins to dominate entrainment (m). The dispersion parameters sy and sz were estimated through the Briggs (1973) formulae for urban areas. 2.2. Low wind model 1 (LWM1) This model, incorporating series of puffs to simulate dispersion pattern under low wind conditions, is based on Deardorff’s work (Deardorff, 1984). Estimation of the g.l.c.’s is made for a point source, by puff diffusion in a thoroughly mixed convective boundary layer, under low winds (up2 m s1). This study incorporates a series of mean circular puffs emanating
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from a point source, with each spreading puff having a standard deviation of spread sr represented by Eq. (3) as given below and travel time t: 2 sr ð0:6TÞ2 s2R ¼ þ s2R0 ; ¼ ð3Þ zi ð1 þ 2TÞ where sR0 is the initial spread of the puff at t ¼ 0 and T ¼ w * t=zi ; where w * is the convective velocity scale and zi is the boundary layer height. This model assumes a Gaussian distribution radially within each mean puff and, hence, does not treat concentration fluctuations. Now consider a single puff spreading outwards from a nearly point source in accordance with Eq. (3) and well mixed in the region 0ozozi : Thus, the mean incremental concentration dC, a function of time t0 is given by dM r2 dC ¼ : ð4Þ exp 2ps2r ðt0 ÞZi 2s2r ðt0 Þ where dM is the mass of net contaminant. The mean concentration C% for a continuous succession of puffs can be obtained by integrating Eq. (4) over time t: Z t Z t Q r2 % ¼ CðtÞ dt0 ; dC ¼ exp ð5Þ 2 0 2s2r ðt0 Þ 0 0 2psr ðt ÞZi where dM=dt0 ¼ Q is the source emission rate, assumed constant after emissions commence at time t ¼ 0: Using the mixed layer scaling with w * as the only velocity scale, the concentration can be written as Z w 1 T 1 R2 2 * % C * ¼ Czi ¼ exp 2 0 dT 0 ; ð6Þ 2p 0 s2R ðT 0 Þ Q 2sR ðT Þ where
R2 ¼
ðx2 þ y2 Þ r2 ¼ 2 zi z2i
and
T0 ¼
w* 0 t: zi
Finally, the effect of finite mean wind of speed u along x is to cause x in (6) to be replaced by x ut0 : Eq. (6) then becomes ! Z T x y u 1 1 C* ¼ ; ; T; zi zi w* 2p 0 s2R ðT 0 Þ 3 2 !2 x uT 0 y2 6 þ 27 6 zi w * zi 7 7 6
exp6 7 dT 0 : 7 6 2s2R ðT 0 Þ 5 4 ð7Þ The integral in Eq. (7) is solved numerically for a period of 1 h.
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2.3. Low wind model 2 (LWM2) LWM2 assumes that the source material is released from the source in the form of a series of puffs with a drift velocity (u; v) to carry the source material from the source to the receptor. The puff released at a time t will have a standard deviation of s and centroid at (ut; vt). All the variables are normalized by the mixed layer scaling parameters, w * and zi : The g.l.c.’s of the pollutants under low wind convective conditions may be estimated by Z T Q d2 Cðx; TÞ ¼ exp dt ð8Þ 2 2s2 0 2ps zi when tXt * ; where t * ¼ zi =w * ; the convective time scale. Z T 2Q d2 h2 Cðx; TÞ ¼ exp dt ð9Þ exp 3=2 3 2s2 2s2 s 0 ð2pÞ when tot * : In the above equations, Q is the pollutant source strength and d is the distance from the centroid of the puff to the receptor which is given by d ¼ ½ðx utÞ2 þ y2 ð1=2Þ ; where h is source height. The diffusion is assumed to be isotropic (same in all directions). The standard deviation is given by Batchelor’s formula, s2 ¼ et3 þ s20 (Hanna et al., 1982), where e is the eddy dissipation rate (m2 s3) and s0 is the initial spread. Eqs. (8) and (9) are applicable for short and intermediate travel times of the puff.
3. Emissions and meteorological data The following input data are required for all the models considered in the present study. The location of various industrial and power plant sources and receptor points are shown on the map of Delhi (Fig. 1). Source characteristics include stack’s height, diameter, exit velocity, temperature and emission rates as given in Table 1. The meteorological data of hourly wind speed, wind direction, surface temperature and atmospheric stability of year 1992 has been obtained from India Meteorological Department (IMD), Delhi. Atmospheric stabilities (Pasquill’s classification of six stabilities, A–F) are compiled from the hourly wind speeds, cloud cover and solar insolation following Turner’s (1969) table. The hourly values of model parameters i.e. wind speed, mixing height and stabilities have been substituted in models formulae to obtain g.l.c.’s But in view of a brief graphical presentation, the variation of hourly wind speed and mixing height averaged over the month has been shown in Fig. 2a and b. The variability of wind data during 1100–1800 h have been shown through error bars in Fig. 2a which are representative of deviation
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Fig. 1. Study area (26 24 km2) of Delhi city. Receptors K; Point sources m.
from the mean values of wind. The boundary layer height is assumed to be the same as the mixing height (Arya, 1988), which starts building up at 11 a.m. attaining a maximum at 1 p.m. and decreasing thereafter till 6 p.m. (Fig. 2b).
4. Computational methodology
The convective velocity scale is given by w* ¼
gzi u y y% * *
ð10Þ
where u * is the surface friction velocity, y * is friction temperature scale, g is the acceleration due to gravity, y% is the mean temperature between ground and 10 m level and zi is the mixed layer height. The surface layer parameters u * and y * are calculated by
4.1. Model parameters The model parameters w * and e are calculated by using the similarity theory with the hourly meteorological data such as wind speed (u) at 10 m, temperature at ground (T0 ) and temperature at 10 m (T1 ). The surface temperatures are obtained by extrapolating 10 m level temperature to ground using the relation T0 ¼ T1 þ Gz; where G is the dry adiabatic lapse rate and z is the height (10 m).
ku ; u* ¼ lnðz=z0 Þ cm y* ¼
kðT T0 Þ 1 ; 0:74 lnðz=z0 Þ ch
where k is the Von Karman constant, z0 is the surface roughness length, cm and ch are the stability functions (Businger et al., 1971) which are
P. Goyal, T.V.B.P.S. Rama Krishna / Atmospheric Environment 36 (2002) 2071–2079 Table 1 Source strengths and stacks characteristics of the point sources Source (m)
Q (g s1)
Hs (m)
D (m)
Vs (m s1)
Ts (K)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
16.6 11.53 19.5 9.23 7.39 50.1 37.1 24.82 20.7 20.7 30.0 37.1 26.0 10.23 24.6 25.4 28.0 90.0 82.0 20.0 79.0 5.0 12.7
15 25 25 25 25 50 25 25 25 25 25 50 20 20 25 20 61 61 61 160 50 25 25
0.3 0.6 0.6 0.6 0.6 0.4 0.6 0.6 0.6 0.6 0.6 0.4 0.35 0.4 0.4 0.4 3.28 3.96 3.96 3.3 0.4 0.6 0.6
18.9 4.32 4.32 4.32 4.32 5.75 18.9 4.32 4.32 4.32 4.32 5.75 1.37 2.94 1.37 2.94 7.3 14.5 13.7 20.0 5.75 4.32 4.32
548 523 523 523 523 473 523 523 523 523 523 473 523 523 523 523 423 383 398 403 523 523 523
Wind Speed
8 6
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1 þ 0:74j1 h ch ¼ 2 ln ; 2 where jm ¼ ð1 15zÞ1=4 and jh ¼ ð1 9zÞ1=2 in which z ¼ z=L; is the nondimensional stability parameter, L is the Monin–Obukhov length which is given by L ¼ yu2 =kgy * : * The parameters u * ; y * and L are calculated by using an iterative method with the stability functions and the wind speed and temperatures at the ground and 10 m’s level. The eddy dissipation rate (e) is calculated by e ¼ w3 =zi : * The model parameters, as defined above, have been used for computing the hourly concentrations. 4.2. Computation of concentrations The dispersion of the pollutants have been studied through GPM, LWM1 and LWM2 on hourly basis during 1100–1800 h in the month of January as representative of winter season. Out of the total 31 days, 6 days were selected on the basis of frequent occurrence of low wind convective conditions, which means 48 h during convective conditions, which include low and moderate winds. The models’ concentrations are obtained for each hour individually by using the hourly meteorological data for 48 h in the month. Finally, the hourly concentrations, averaged over the days of the month have been obtained for 1100–1800 h.
4
4.3. Statistical errors
2 0 11
12
13
14
Mixing Height
(a)
15
16
17
18
17
18
Time (LST) 1800 1400 1000 600 11
(b)
12
13
14
15
16
Time (LST)
Fig. 2. Variation of hourly (a) wind speed (m s1) and (b) mixing height (m) in January 1992 at Delhi.
given by 1 þ j1 1 þ j2 m m þ ln cm ¼ 2 ln 2 2 p 1 1 2 tan ðjm Þ þ ; 2
A quantitative evaluation of models performance has been studied through various statistical measures as follows: (a) Root mean square error (RMSE) The RMSE is given by " #1=2 n X ðln Cp ln Co Þ2 RMSE ¼ exp ; n i¼1 where Cp and Co are the computed and observed concentrations respectively and n is the total number of samples. (b) Fractional bias (FB) The fractional bias is given by C% p C% o FB ¼ 2 ; C% p þ C% o where C% p and C% 0 are the averages of the computed and observed concentrations which are given by C% p ¼
n n 1X 1X Cp and C% o ¼ Co n i¼1 n i¼1
P. Goyal, T.V.B.P.S. Rama Krishna / Atmospheric Environment 36 (2002) 2071–2079
where Cp0 i ¼ Cpi C% o and Co0 i ¼ Coi C% o ; Cpi ; Coi are the computed and observed concentrations of each sample (i), Cp0 i ; Co0 i are the deviations of computed and observed concentrations of each sample (i), from the mean observed concentrations ðC% o Þ: (d) Normalized mean square error (NMSE) The NMSE is given by NMSE ¼
80 Concentration
(c) Index of agreement (IOA) The IOA is given by Pn ðCpi Coi Þ2 IOA ¼ 1 Pi¼1 n 0 0 2 i¼1 ðCpi Coi Þ
40 20
11
12
13
14
15
16
17
18
16
17
18
Time (LST)
(a)
ðCo Cp Þ2 ; C% o C% p
where ðCo Cp Þ2 is the average of the square of the deviations of the computed concentrations from the observed concentrations. (e) Correlation coefficient (r) The correlation coefficient is given by 1 Pn ðCp C% p ÞðCo C% o Þ n i¼1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Pn 1 Pn 2 % ðC C Þ ðCo C% o Þ2 p p i¼1 n n i¼1
60
0
40 Concentration
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30 20 10 0 11
(b)
12
13
14
15
Time (LST)
5. Results and discussion
Fig. 3. Comparison of hourly computed and observed SO2 concentrations (mg m3) at (a) Darya Ganj and (b) Maharani Bagh in Delhi. GPM -E-E-E-; LWM1 -’-’-’-; LWM2 m-m-m-; Observed -K-K-K-.
The performance of the models were evaluated by using three different methods (i) comparison of hourly concentrations obtained from GPM, LWM1 and LWM2 at four receptors in the month of January during 1100–1800 h with observed data of SO2 concentrations monitored at same time and same places, (ii) Q– Q (Quantile–Quantile) plots and (iii) statistical measures. The first method of evaluation is presented through Figs. 3a–4b. It is worth noting that SO2 concentrations obtained from LWM2 are consistently underpredicted as compared to observed concentrations. This is possibly due to mixing height parameter, lying in the denominator of the model’s formulation. This can be ascertained by the variation of concentrations of LWM2, follow the same trend as that of the mixing height, as shown in Fig. 2b. On the other hand, the concentrations of GPM were overpredicted compared to the observed values at all receptors. But, deviation from the observed concentrations of the above models, are always within acceptable limits quoted by Hanna et al. (1982). Their correlation for assessing model performance is that natural variability of computed deviation must be within a factor of 2–3 times the actual values. Although computed values from both the models (GPM and LWM2) are higher and lower than the corresponding observations, they remain
within a factor of two. In broad sense, LWM1 is performing better than other two models but not following a regular pattern at all the receptors. Thus it is difficult to arrive at any conclusion. Therefore, it is essential to assess the performance of these models further. The performance of the models have been examined with the help of Q–Q plots in Fig. 5a–c. These figures plot ranked model predictions against ranked observations, if the distributions of model predictions and observations were identical, the points would lie on the one-to-one line (Venkataram, 1999). It is observed that many of the concentrations of GPM (Fig. 5a) are scattered and lie far from the one-to-one line, which are showing the overpredictions of the model. However, the concentrations of LWM1 (Fig. 5b) are closer to the one-to-one line and showing slightly overprediction whereas the LWM2 values (Fig. 5c) though close to the one-to-one line showing both underprediction and overprediction, which reflects the fact, that LWM1 and LWM2 are performing better than GPM. To determine if one model is significantly better than another, it is necessary to use performance measures. Performance measures estimate the discrepancy between computations and observations and provide the means
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150
120
Observed
Concentration
160
80 40
100
50
0 11
12
13
14
15
16
17
18
0 0
Time (LST)
(a)
100
150
Calculated
(a)
40
50
20
Observed
Concentration
150 30
10
100
50
0 12
(b)
13
14
15
16
17
18
Time (LST)
Fig. 4. Comparison of hourly computed and observed SO2 concentrations (mg m3) at (a) Parliament Street and (b) Pahar Ganj in Delhi. GPM -E-E-E-; LWM1 -’-’-’-; LWM2 -m-m-m-; Observed -K-K-K-.
for comparing the models performance. According to the desired values of the statistical measures for a good model, the LWM1 ranks better than the GPM and LWM2 for three out of five measures (Table 2). The above discussion based on different methods of evaluation of models performance provides that LWM1 is performing better compared to GPM and LWM2.
0 0
150
100
50
0 0
The main objective of this study is to determine the dispersion of pollutants under low wind convective conditions. Two models have been developed for treating the low wind under convective conditions. The three models including GPM and two LWM have been used to predict the g.l.c.’s of SO2 due to point sources in Delhi. The low wind conditions occur very frequently in urban cities like Delhi in India. With low winds (p2 m s1), it is difficult to predict the concentrations under these conditions from Gaussian models. In the present study, attention has been given to low wind convective conditions.
100 Calculated
150
(c)
6. Conclusions
50
(b)
Observed
11
50
100
150
Calculated
Fig. 5. Q–Q plots of (a) GPM, (b) LWM1 and (c) LWM2 with respect to observed values.
A comparison of the results of three models with observed concentrations has been made at few vulnerable places in Delhi. Based on the above section of results and discussion, it can be concluded that GPM is always overpredicting. LWM2 is consistently underpredicting, but LWM1 is performing better than GPM and LWM2 under low wind convective conditions. The analysis of the relevant statistical parameters (Table 2) shows that the performance of LWM1 against observations is better than the GPM and LWM2. Thus, on the basis of the present study and present available
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Table 2 Statistical error analysis of different models Error
GPM
LWM1
LWM2
Ideal
RMSE FB IOA NMSE r
3.58 1.03 0.302 106.4 0.6
3.0 0.86 0.64 55.9 0.6
3.74 0.062 0.54 28.8 0.3
0 0 1 Least value 1
data, one can say that LWM1 may be used for studying the dispersion of air pollutants in low wind convective conditions. It may be mentioned here that in Delhi, major sources of SO2 are industries and power plants. The steady increase of industries has resulted in increase of SO2 emissions. Hence, new strategies should be undertaken to reduce emission of SO2 from industries and power plants to a safe and accepted level. In addition to emissions, the meteorological conditions, e.g., low wind convective conditions increases the g.l.c.’s which requires an appropriate model to give an assessment of actual situation of ambient air quality. In these regards, the above study may provide a useful tool in the form of model to predict SO2 concentrations under low wind convective conditions. However, more scientific studies are required with more observed data to find out best fit model for studying the dispersion of pollutants in urban cities like Delhi.
Acknowledgements The authors are grateful to Prof. F.B. Smith for his valuable discussions about dispersion of pollutants under low wind conditions. The authors would like to thank the anonymous reviewers for the critical comments and suggestions of the manuscript.
References Anfossi, D., Brusasca, G., Tinarelli, G., 1990. Simulation of atmospheric diffusion in low wind speed meandering conditions by Monte-Carlo dispersion model. II Nuovo Cimento 13c, 995–1006. Arya, S.P., 1988. Introduction to Micro Meteorology. Academic Press Inc., New York. Arya, S.P., 1995. Modeling and parameterization of nearsource diffusion in weak winds. Journal of Applied Meteorology 34, 1112–1122. Arya, S.P., 1999. Air Pollution and Meteorology. Oxford University Press, Oxford. Bass, A., Benkley, C.W., Scire, J.S., Mories, C.S., 1979. Development of mesoscale air quality simulation models, Vol. 1. Comparative sensitivity studies of puff, plume and
grid models for long-distance dispersion. US Environmental Protection Agency, EPA 600/7-80-056, Research Triangle Park, NC. Batchelor, G.K., 1949. Diffusion in a field of homogeneous turbulence, I. Eulerian analysis. Australian Journal of Science Research. 2, 437–450. Briggs, G.A., 1969. Plume Rise. USAEC Critical Review Series, TID-25075, Clearinghouse for Federal Scientific and Technical Information. Briggs, G.A., 1973. Diffusion estimation for small emissions in environmental research laboratories, Air Resources Atmospheric Turbulence and Diffusion Laboratory, 1973. Annual Report of the USAEC, Report ATDL-106, National Oceanic and Atmospheric Administration, Oak Ridge, TN. Briggs, G.A., 1975. Plume Rise Predictions. In Lectures on Air Pollution and Environmental Impact Analyses. Workshop Proceedings, Boston, MA, 29 September–8 October 1975. American Meteorological Society, Boston, Massachusetts, pp. 59–111. Businger, J.A., Wyngaard, J.C., Izumi, Y., Bradley, E.F., 1971. Flux profile relationships in the atmospheric surface layer. Journal of Atmospheric Science 28, 181–189. Cirrilo, A.C., Poli, A.A., 1992. An intercomparison of semiempirical diffusion models under low wind speed stable conditions. Atmospheric Environment 26A, 765–774. Csanady, G.T., 1973. Turbulent Diffusion in the Environment. D. Reidel Publishing, Dordrecht, pp. 248. Deardorff, J.W., 1984. Upstream diffusion in the convective boundary layer with weak or zero mean wind. In Fourth Joint Conference on Application of Air Pollution Meteorology. American Meteorological Society, Boston Massachusetts, USA Goyal, P., Singh, M.P., Bandyopadhyay, T.K., 1994. Environmental studies of SO2, SPM and NOx over Agra with various methods of treating calms. Atmospheric Environment 28, 3113–3123. Hanna, S.R., Briggs, G.A., Hosker, Jr. R.P., 1982. Handbook on Atmospheric Diffusion, Atmospheric Turbulence and Diffusion Laboratory, NOAA. USA Technical Information Centre, US Department of Energy. MOEF, 1997. White paper on pollution in Delhi with action plan, Government of India, Ministry of Environment and Forests (MOEF). Moore, D.J., 1969. The distributions of surface concentrations of sulphur dioxide emitted from tall chimneys. Philosophical Transactions of the Royal Society A 265. Okamoto, S., Shiozawa, K., 1978. Validation of an air pollution model for the Keihin area. Atmospheric Environment 12, 2139–2149. Sagendorf, J.F., Dickson, C.R., 1974. Diffusion under low wind speed inversion conditions, NOAA Technical Memo-ERLARL-52. Air Resources Laboratories, Silver Spring. Seinfield, J.H., 1986. Atmospheric chemistry and physics of air pollution. Wiley, New York. Sharan, M., Singh, M.P., Yadav, A.K., 1996. A mathematical model for the atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance. Atmospheric Environment 30, 1137–1145. Sharan, M., Yadav, A.K., 1998. Simulation of diffusion experiments under light wind, stable conditions by a
P. Goyal, T.V.B.P.S. Rama Krishna / Atmospheric Environment 36 (2002) 2071–2079 variable K-theory model. Atmospheric Environment 32, 3481–3492. Taylor, G.I., 1959. The present position in the theory of turbulent diffusion. Advances in Geophysics. 6, 101–111. Turner, D.B., 1969. Workbook of Atmospheric Dispersion Estimates, Washington, DC. Venkataram, A., 1999. Applying a Framework for Evaluating the Performance of Air Quality Models. Sixth International Conference on Harmonisation within Atmospheric
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Dispersion Modelling for Regulatory Applications, 11–14 October 1999, Rouen, France. Wark, K., Warner, C.F., Davis, W.T., 1998. Air Pollution: Its Origin and Control. Addission-Wesley Longman Inc., Reading, MA. Zannetti, P., 1986. A new mixed segmented-puff approach for dispersion modeling. Atmospheric Environment 20, 1121–1130. Zannetti, P., 1990. Air Pollution Modelling. Van Nostrand Reinhold, New York, pp 444.
Dispersion of pollutants in convective low wind: a case study of Delhi P. Goyal*, T.V.B.P.S. Rama Krishna Centre for Atmospheric Sciences, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Received 9 January 2001; accepted 18 July 2001
Abstract The transport and dispersion of pollutants becomes weak under low wind conditions resulting in large ground level concentrations (g.l.c.’s). Largest mean g.l.c.’s due to elevated sources are typically found under daytime convective conditions with moderate to weak winds in the earlier studies. Similar cases have been studied here by using three different dispersion models, i.e. Gaussian plume model (GPM) and two low wind models (LWM1 and LWM2) at few vulnerable places in Delhi. The models compute the hourly g.l.c.’s of SO2 due to industrial and power plant sources. The performance of these models has been compared against observed data to identify one of the model, appropriate for dispersion of pollutants in low wind convective conditions, which are frequently occurring meteorological conditions in Delhi and also in urban cities of India. This evaluation has been performed at four receptors by using three different methods: (i) comparison of hourly concentrations of the models against observed data, (ii) Q–Q-plots (Quantile–Quantile) and (iii) statistical measures. On the basis of the results and discussion of above methods, it has been concluded that GPM is always overpredicting and LWM2 is consistently underpredicting the concentrations, whereas, LWM1 is performing better than GPM and LWM2. Thus LWM1 may be recommended for studying dispersion of pollutants from elevated point sources in low wind convective conditions. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Low wind; Dispersion model; Ground level concentration; Convective condition
1. Introduction The deterioration of air quality in urban areas due to the continuous growth of industries and the day to day increase in vehicular traffic has provided the impetus for comprehensive monitoring/modeling of air quality. It is not always feasible to monitor/measure the concentrations of species at various vulnerable points of a city due to high cost and the experimental difficulties involved. However, an insight in this regard could be achieved with the help of suitable mathematical models.
*Corresponding author. Tel.: +91-11-659-11309; fax: +9111-686-2037. E-mail address: [email protected] (P. Goyal).
Low winds pose a particular problem in Gaussian models, since concentration is inversely proportional to wind speed, resulting in overprediction of concentration when wind speed approaches zero. The wind is defined as low wind when the surface wind at 10 m level is p2 m s1 (Sagendorf and Dickson, 1974; Cirrilo and Poli, 1992; Arya, 1995). The lack of reliable wind data itself creates problems because most conventional anemometers cease to function below the threshold wind speed. Other difficulties include both the inadequacy of the classical methods for modeling the transport and dispersion as the wind approaches zero and in describing the spatial and temporal character of the low winds in a stably stratified boundary layer. This latter problem requires special attention for very low level sources, because under these conditions, large
1352-2310/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 1 ) 0 0 4 5 8 - 7
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ground level concentrations (g.l.c.’s) are likely to be experienced. Large pollutant concentrations might occur under convective low wind conditions due to elevated point sources (Moore, 1969; Deardorff, 1984). The study on the dispersion of air pollutants under convective low wind conditions assumes significance as these occur frequently in Indian environment. Several studies (Goyal et al., 1994; Arya, 1995; Sharan and Yadav, 1998) have investigated the dispersion of air pollutants in low wind conditions. Some of these studies have shown that the standard steady-state Gaussian plume models (GPMs) generally overpredict ground level pollutant concentrations in low wind conditions. The limitations of GPMs are discussed in literature (Arya, 1999; Zannetti, 1990; Seinfield, 1986). The model produces unreasonable results when applied to diffusion in low wind cases (Bass et al., 1979; Zannetti, 1986) because (1) downwind diffusion is neglected in comparison to the advection (2) the concentration is inversely proportional to wind speed and therefore, the concentration approaches infinity as the wind tends to zero and (3) the average concentrations are stationary (Anfossi et al., 1990). In addition the assumption of constant diffusivities seems reasonable in the far field and become questionable for describing near-source dispersion (Batchelor, 1949; Taylor, 1959; Csanady, 1973; Sharan et al., 1996). A study of Okamoto and Shiozawa (1978) for ground level sources showed that high g.l.c.’s might occur due to weak horizontal dispersion. The structure of the boundary layer is not yet sufficiently known under the low wind conditions. The classical conventional models such as Gaussian plume or based on K-theory with suitable assumptions, are known to work reasonable under most of the meteorological regimes except the weak wind conditions. Thus it becomes important to study the dispersion of pollutant under such conditions. In the present study we propose to fill up some of these gaps through modeling of dispersion in low wind convective conditions. Delhi, one of the most polluted capital cities of the world, has been considered for the case study. Major sources of air pollutants in Delhi are vehicles, industries, power plants, and domestic coal burning. An estimated 3000 metric tones of air pollutants are emitted daily (MOEF, 1997). Sulphur dioxide (SO2) is recognized as one of the major pollutant from elevated sources of industries and power plants in Delhi. These sources are known to produce high concentrations under low wind conditions. Thus, the objective of the present study is to study the dispersion of air pollutants emitting from elevated point sources in Delhi under convective low winds by using different models in order to identify a suitable model for dispersion of pollutants under same conditions. A GPM and two different models for treating low winds in
convective conditions have been used for estimating the g.l.c.’s. The models’ description is given in Section 2. The emissions and meteorological data and the computational methodology are given in the following Sections 3 and 4, respectively. The results and conclusions are discussed in the subsequent sections.
2. Models’ description 2.1. Gaussian plume model (GPM) The g.l.c.’s of the pollutants due to elevated point source (Wark et al., 1998) is given by " # Q y2 H2 Cðx; y; 0Þ ¼ ð1Þ exp 2 exp 2 ; pusy sz 2sy 2sz where Q is the source strength (g s1), u is the mean wind speed (m s1), sy ; sz are the horizontal and vertical dispersion parameters (m) respectively, y is the cross wind distance (m), H is the effective stack height (m) which is given as H ¼ hs þ Dh; where, Dh is the plume rise (m) and hs is the physical stack height (m). The wind profile law (Wark et al., 1998) has been used to estimate the wind speed at the stack level. Briggs (1969, 1975) plume rise formulae for hot plumes are used for evaluating the concentrations of SO2 from elevated point sources. These plume rise formulae are summarized below: For unstable or neutral atmospheric conditions, the downwind distance of final plume rise is Xf ¼ 3:5 X ; where X ¼ 14 F 5=8 for Fo55 m4 s–3 and X ¼ 13F 2=5 for F > 55 m4 s3. The effective stack height under these conditions is H ¼ hs þ ½1:6F 1=3 ð3:5X Þ2=3 uðhÞ;
ð2Þ 4 3
where, F is the buoyancy flux parameter (m s ), uðhÞ is the wind speed at the top of the stack (m s1), Xf is the distance to the final rise (m) and X is the distance at which atmospheric turbulence begins to dominate entrainment (m). The dispersion parameters sy and sz were estimated through the Briggs (1973) formulae for urban areas. 2.2. Low wind model 1 (LWM1) This model, incorporating series of puffs to simulate dispersion pattern under low wind conditions, is based on Deardorff’s work (Deardorff, 1984). Estimation of the g.l.c.’s is made for a point source, by puff diffusion in a thoroughly mixed convective boundary layer, under low winds (up2 m s1). This study incorporates a series of mean circular puffs emanating
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from a point source, with each spreading puff having a standard deviation of spread sr represented by Eq. (3) as given below and travel time t: 2 sr ð0:6TÞ2 s2R ¼ þ s2R0 ; ¼ ð3Þ zi ð1 þ 2TÞ where sR0 is the initial spread of the puff at t ¼ 0 and T ¼ w * t=zi ; where w * is the convective velocity scale and zi is the boundary layer height. This model assumes a Gaussian distribution radially within each mean puff and, hence, does not treat concentration fluctuations. Now consider a single puff spreading outwards from a nearly point source in accordance with Eq. (3) and well mixed in the region 0ozozi : Thus, the mean incremental concentration dC, a function of time t0 is given by dM r2 dC ¼ : ð4Þ exp 2ps2r ðt0 ÞZi 2s2r ðt0 Þ where dM is the mass of net contaminant. The mean concentration C% for a continuous succession of puffs can be obtained by integrating Eq. (4) over time t: Z t Z t Q r2 % ¼ CðtÞ dt0 ; dC ¼ exp ð5Þ 2 0 2s2r ðt0 Þ 0 0 2psr ðt ÞZi where dM=dt0 ¼ Q is the source emission rate, assumed constant after emissions commence at time t ¼ 0: Using the mixed layer scaling with w * as the only velocity scale, the concentration can be written as Z w 1 T 1 R2 2 * % C * ¼ Czi ¼ exp 2 0 dT 0 ; ð6Þ 2p 0 s2R ðT 0 Þ Q 2sR ðT Þ where
R2 ¼
ðx2 þ y2 Þ r2 ¼ 2 zi z2i
and
T0 ¼
w* 0 t: zi
Finally, the effect of finite mean wind of speed u along x is to cause x in (6) to be replaced by x ut0 : Eq. (6) then becomes ! Z T x y u 1 1 C* ¼ ; ; T; zi zi w* 2p 0 s2R ðT 0 Þ 3 2 !2 x uT 0 y2 6 þ 27 6 zi w * zi 7 7 6
exp6 7 dT 0 : 7 6 2s2R ðT 0 Þ 5 4 ð7Þ The integral in Eq. (7) is solved numerically for a period of 1 h.
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2.3. Low wind model 2 (LWM2) LWM2 assumes that the source material is released from the source in the form of a series of puffs with a drift velocity (u; v) to carry the source material from the source to the receptor. The puff released at a time t will have a standard deviation of s and centroid at (ut; vt). All the variables are normalized by the mixed layer scaling parameters, w * and zi : The g.l.c.’s of the pollutants under low wind convective conditions may be estimated by Z T Q d2 Cðx; TÞ ¼ exp dt ð8Þ 2 2s2 0 2ps zi when tXt * ; where t * ¼ zi =w * ; the convective time scale. Z T 2Q d2 h2 Cðx; TÞ ¼ exp dt ð9Þ exp 3=2 3 2s2 2s2 s 0 ð2pÞ when tot * : In the above equations, Q is the pollutant source strength and d is the distance from the centroid of the puff to the receptor which is given by d ¼ ½ðx utÞ2 þ y2 ð1=2Þ ; where h is source height. The diffusion is assumed to be isotropic (same in all directions). The standard deviation is given by Batchelor’s formula, s2 ¼ et3 þ s20 (Hanna et al., 1982), where e is the eddy dissipation rate (m2 s3) and s0 is the initial spread. Eqs. (8) and (9) are applicable for short and intermediate travel times of the puff.
3. Emissions and meteorological data The following input data are required for all the models considered in the present study. The location of various industrial and power plant sources and receptor points are shown on the map of Delhi (Fig. 1). Source characteristics include stack’s height, diameter, exit velocity, temperature and emission rates as given in Table 1. The meteorological data of hourly wind speed, wind direction, surface temperature and atmospheric stability of year 1992 has been obtained from India Meteorological Department (IMD), Delhi. Atmospheric stabilities (Pasquill’s classification of six stabilities, A–F) are compiled from the hourly wind speeds, cloud cover and solar insolation following Turner’s (1969) table. The hourly values of model parameters i.e. wind speed, mixing height and stabilities have been substituted in models formulae to obtain g.l.c.’s But in view of a brief graphical presentation, the variation of hourly wind speed and mixing height averaged over the month has been shown in Fig. 2a and b. The variability of wind data during 1100–1800 h have been shown through error bars in Fig. 2a which are representative of deviation
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Fig. 1. Study area (26 24 km2) of Delhi city. Receptors K; Point sources m.
from the mean values of wind. The boundary layer height is assumed to be the same as the mixing height (Arya, 1988), which starts building up at 11 a.m. attaining a maximum at 1 p.m. and decreasing thereafter till 6 p.m. (Fig. 2b).
4. Computational methodology
The convective velocity scale is given by w* ¼
gzi u y y% * *
ð10Þ
where u * is the surface friction velocity, y * is friction temperature scale, g is the acceleration due to gravity, y% is the mean temperature between ground and 10 m level and zi is the mixed layer height. The surface layer parameters u * and y * are calculated by
4.1. Model parameters The model parameters w * and e are calculated by using the similarity theory with the hourly meteorological data such as wind speed (u) at 10 m, temperature at ground (T0 ) and temperature at 10 m (T1 ). The surface temperatures are obtained by extrapolating 10 m level temperature to ground using the relation T0 ¼ T1 þ Gz; where G is the dry adiabatic lapse rate and z is the height (10 m).
ku ; u* ¼ lnðz=z0 Þ cm y* ¼
kðT T0 Þ 1 ; 0:74 lnðz=z0 Þ ch
where k is the Von Karman constant, z0 is the surface roughness length, cm and ch are the stability functions (Businger et al., 1971) which are
P. Goyal, T.V.B.P.S. Rama Krishna / Atmospheric Environment 36 (2002) 2071–2079 Table 1 Source strengths and stacks characteristics of the point sources Source (m)
Q (g s1)
Hs (m)
D (m)
Vs (m s1)
Ts (K)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
16.6 11.53 19.5 9.23 7.39 50.1 37.1 24.82 20.7 20.7 30.0 37.1 26.0 10.23 24.6 25.4 28.0 90.0 82.0 20.0 79.0 5.0 12.7
15 25 25 25 25 50 25 25 25 25 25 50 20 20 25 20 61 61 61 160 50 25 25
0.3 0.6 0.6 0.6 0.6 0.4 0.6 0.6 0.6 0.6 0.6 0.4 0.35 0.4 0.4 0.4 3.28 3.96 3.96 3.3 0.4 0.6 0.6
18.9 4.32 4.32 4.32 4.32 5.75 18.9 4.32 4.32 4.32 4.32 5.75 1.37 2.94 1.37 2.94 7.3 14.5 13.7 20.0 5.75 4.32 4.32
548 523 523 523 523 473 523 523 523 523 523 473 523 523 523 523 423 383 398 403 523 523 523
Wind Speed
8 6
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1 þ 0:74j1 h ch ¼ 2 ln ; 2 where jm ¼ ð1 15zÞ1=4 and jh ¼ ð1 9zÞ1=2 in which z ¼ z=L; is the nondimensional stability parameter, L is the Monin–Obukhov length which is given by L ¼ yu2 =kgy * : * The parameters u * ; y * and L are calculated by using an iterative method with the stability functions and the wind speed and temperatures at the ground and 10 m’s level. The eddy dissipation rate (e) is calculated by e ¼ w3 =zi : * The model parameters, as defined above, have been used for computing the hourly concentrations. 4.2. Computation of concentrations The dispersion of the pollutants have been studied through GPM, LWM1 and LWM2 on hourly basis during 1100–1800 h in the month of January as representative of winter season. Out of the total 31 days, 6 days were selected on the basis of frequent occurrence of low wind convective conditions, which means 48 h during convective conditions, which include low and moderate winds. The models’ concentrations are obtained for each hour individually by using the hourly meteorological data for 48 h in the month. Finally, the hourly concentrations, averaged over the days of the month have been obtained for 1100–1800 h.
4
4.3. Statistical errors
2 0 11
12
13
14
Mixing Height
(a)
15
16
17
18
17
18
Time (LST) 1800 1400 1000 600 11
(b)
12
13
14
15
16
Time (LST)
Fig. 2. Variation of hourly (a) wind speed (m s1) and (b) mixing height (m) in January 1992 at Delhi.
given by 1 þ j1 1 þ j2 m m þ ln cm ¼ 2 ln 2 2 p 1 1 2 tan ðjm Þ þ ; 2
A quantitative evaluation of models performance has been studied through various statistical measures as follows: (a) Root mean square error (RMSE) The RMSE is given by " #1=2 n X ðln Cp ln Co Þ2 RMSE ¼ exp ; n i¼1 where Cp and Co are the computed and observed concentrations respectively and n is the total number of samples. (b) Fractional bias (FB) The fractional bias is given by C% p C% o FB ¼ 2 ; C% p þ C% o where C% p and C% 0 are the averages of the computed and observed concentrations which are given by C% p ¼
n n 1X 1X Cp and C% o ¼ Co n i¼1 n i¼1
P. Goyal, T.V.B.P.S. Rama Krishna / Atmospheric Environment 36 (2002) 2071–2079
where Cp0 i ¼ Cpi C% o and Co0 i ¼ Coi C% o ; Cpi ; Coi are the computed and observed concentrations of each sample (i), Cp0 i ; Co0 i are the deviations of computed and observed concentrations of each sample (i), from the mean observed concentrations ðC% o Þ: (d) Normalized mean square error (NMSE) The NMSE is given by NMSE ¼
80 Concentration
(c) Index of agreement (IOA) The IOA is given by Pn ðCpi Coi Þ2 IOA ¼ 1 Pi¼1 n 0 0 2 i¼1 ðCpi Coi Þ
40 20
11
12
13
14
15
16
17
18
16
17
18
Time (LST)
(a)
ðCo Cp Þ2 ; C% o C% p
where ðCo Cp Þ2 is the average of the square of the deviations of the computed concentrations from the observed concentrations. (e) Correlation coefficient (r) The correlation coefficient is given by 1 Pn ðCp C% p ÞðCo C% o Þ n i¼1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Pn 1 Pn 2 % ðC C Þ ðCo C% o Þ2 p p i¼1 n n i¼1
60
0
40 Concentration
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30 20 10 0 11
(b)
12
13
14
15
Time (LST)
5. Results and discussion
Fig. 3. Comparison of hourly computed and observed SO2 concentrations (mg m3) at (a) Darya Ganj and (b) Maharani Bagh in Delhi. GPM -E-E-E-; LWM1 -’-’-’-; LWM2 m-m-m-; Observed -K-K-K-.
The performance of the models were evaluated by using three different methods (i) comparison of hourly concentrations obtained from GPM, LWM1 and LWM2 at four receptors in the month of January during 1100–1800 h with observed data of SO2 concentrations monitored at same time and same places, (ii) Q– Q (Quantile–Quantile) plots and (iii) statistical measures. The first method of evaluation is presented through Figs. 3a–4b. It is worth noting that SO2 concentrations obtained from LWM2 are consistently underpredicted as compared to observed concentrations. This is possibly due to mixing height parameter, lying in the denominator of the model’s formulation. This can be ascertained by the variation of concentrations of LWM2, follow the same trend as that of the mixing height, as shown in Fig. 2b. On the other hand, the concentrations of GPM were overpredicted compared to the observed values at all receptors. But, deviation from the observed concentrations of the above models, are always within acceptable limits quoted by Hanna et al. (1982). Their correlation for assessing model performance is that natural variability of computed deviation must be within a factor of 2–3 times the actual values. Although computed values from both the models (GPM and LWM2) are higher and lower than the corresponding observations, they remain
within a factor of two. In broad sense, LWM1 is performing better than other two models but not following a regular pattern at all the receptors. Thus it is difficult to arrive at any conclusion. Therefore, it is essential to assess the performance of these models further. The performance of the models have been examined with the help of Q–Q plots in Fig. 5a–c. These figures plot ranked model predictions against ranked observations, if the distributions of model predictions and observations were identical, the points would lie on the one-to-one line (Venkataram, 1999). It is observed that many of the concentrations of GPM (Fig. 5a) are scattered and lie far from the one-to-one line, which are showing the overpredictions of the model. However, the concentrations of LWM1 (Fig. 5b) are closer to the one-to-one line and showing slightly overprediction whereas the LWM2 values (Fig. 5c) though close to the one-to-one line showing both underprediction and overprediction, which reflects the fact, that LWM1 and LWM2 are performing better than GPM. To determine if one model is significantly better than another, it is necessary to use performance measures. Performance measures estimate the discrepancy between computations and observations and provide the means
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150
120
Observed
Concentration
160
80 40
100
50
0 11
12
13
14
15
16
17
18
0 0
Time (LST)
(a)
100
150
Calculated
(a)
40
50
20
Observed
Concentration
150 30
10
100
50
0 12
(b)
13
14
15
16
17
18
Time (LST)
Fig. 4. Comparison of hourly computed and observed SO2 concentrations (mg m3) at (a) Parliament Street and (b) Pahar Ganj in Delhi. GPM -E-E-E-; LWM1 -’-’-’-; LWM2 -m-m-m-; Observed -K-K-K-.
for comparing the models performance. According to the desired values of the statistical measures for a good model, the LWM1 ranks better than the GPM and LWM2 for three out of five measures (Table 2). The above discussion based on different methods of evaluation of models performance provides that LWM1 is performing better compared to GPM and LWM2.
0 0
150
100
50
0 0
The main objective of this study is to determine the dispersion of pollutants under low wind convective conditions. Two models have been developed for treating the low wind under convective conditions. The three models including GPM and two LWM have been used to predict the g.l.c.’s of SO2 due to point sources in Delhi. The low wind conditions occur very frequently in urban cities like Delhi in India. With low winds (p2 m s1), it is difficult to predict the concentrations under these conditions from Gaussian models. In the present study, attention has been given to low wind convective conditions.
100 Calculated
150
(c)
6. Conclusions
50
(b)
Observed
11
50
100
150
Calculated
Fig. 5. Q–Q plots of (a) GPM, (b) LWM1 and (c) LWM2 with respect to observed values.
A comparison of the results of three models with observed concentrations has been made at few vulnerable places in Delhi. Based on the above section of results and discussion, it can be concluded that GPM is always overpredicting. LWM2 is consistently underpredicting, but LWM1 is performing better than GPM and LWM2 under low wind convective conditions. The analysis of the relevant statistical parameters (Table 2) shows that the performance of LWM1 against observations is better than the GPM and LWM2. Thus, on the basis of the present study and present available
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Table 2 Statistical error analysis of different models Error
GPM
LWM1
LWM2
Ideal
RMSE FB IOA NMSE r
3.58 1.03 0.302 106.4 0.6
3.0 0.86 0.64 55.9 0.6
3.74 0.062 0.54 28.8 0.3
0 0 1 Least value 1
data, one can say that LWM1 may be used for studying the dispersion of air pollutants in low wind convective conditions. It may be mentioned here that in Delhi, major sources of SO2 are industries and power plants. The steady increase of industries has resulted in increase of SO2 emissions. Hence, new strategies should be undertaken to reduce emission of SO2 from industries and power plants to a safe and accepted level. In addition to emissions, the meteorological conditions, e.g., low wind convective conditions increases the g.l.c.’s which requires an appropriate model to give an assessment of actual situation of ambient air quality. In these regards, the above study may provide a useful tool in the form of model to predict SO2 concentrations under low wind convective conditions. However, more scientific studies are required with more observed data to find out best fit model for studying the dispersion of pollutants in urban cities like Delhi.
Acknowledgements The authors are grateful to Prof. F.B. Smith for his valuable discussions about dispersion of pollutants under low wind conditions. The authors would like to thank the anonymous reviewers for the critical comments and suggestions of the manuscript.
References Anfossi, D., Brusasca, G., Tinarelli, G., 1990. Simulation of atmospheric diffusion in low wind speed meandering conditions by Monte-Carlo dispersion model. II Nuovo Cimento 13c, 995–1006. Arya, S.P., 1988. Introduction to Micro Meteorology. Academic Press Inc., New York. Arya, S.P., 1995. Modeling and parameterization of nearsource diffusion in weak winds. Journal of Applied Meteorology 34, 1112–1122. Arya, S.P., 1999. Air Pollution and Meteorology. Oxford University Press, Oxford. Bass, A., Benkley, C.W., Scire, J.S., Mories, C.S., 1979. Development of mesoscale air quality simulation models, Vol. 1. Comparative sensitivity studies of puff, plume and
grid models for long-distance dispersion. US Environmental Protection Agency, EPA 600/7-80-056, Research Triangle Park, NC. Batchelor, G.K., 1949. Diffusion in a field of homogeneous turbulence, I. Eulerian analysis. Australian Journal of Science Research. 2, 437–450. Briggs, G.A., 1969. Plume Rise. USAEC Critical Review Series, TID-25075, Clearinghouse for Federal Scientific and Technical Information. Briggs, G.A., 1973. Diffusion estimation for small emissions in environmental research laboratories, Air Resources Atmospheric Turbulence and Diffusion Laboratory, 1973. Annual Report of the USAEC, Report ATDL-106, National Oceanic and Atmospheric Administration, Oak Ridge, TN. Briggs, G.A., 1975. Plume Rise Predictions. In Lectures on Air Pollution and Environmental Impact Analyses. Workshop Proceedings, Boston, MA, 29 September–8 October 1975. American Meteorological Society, Boston, Massachusetts, pp. 59–111. Businger, J.A., Wyngaard, J.C., Izumi, Y., Bradley, E.F., 1971. Flux profile relationships in the atmospheric surface layer. Journal of Atmospheric Science 28, 181–189. Cirrilo, A.C., Poli, A.A., 1992. An intercomparison of semiempirical diffusion models under low wind speed stable conditions. Atmospheric Environment 26A, 765–774. Csanady, G.T., 1973. Turbulent Diffusion in the Environment. D. Reidel Publishing, Dordrecht, pp. 248. Deardorff, J.W., 1984. Upstream diffusion in the convective boundary layer with weak or zero mean wind. In Fourth Joint Conference on Application of Air Pollution Meteorology. American Meteorological Society, Boston Massachusetts, USA Goyal, P., Singh, M.P., Bandyopadhyay, T.K., 1994. Environmental studies of SO2, SPM and NOx over Agra with various methods of treating calms. Atmospheric Environment 28, 3113–3123. Hanna, S.R., Briggs, G.A., Hosker, Jr. R.P., 1982. Handbook on Atmospheric Diffusion, Atmospheric Turbulence and Diffusion Laboratory, NOAA. USA Technical Information Centre, US Department of Energy. MOEF, 1997. White paper on pollution in Delhi with action plan, Government of India, Ministry of Environment and Forests (MOEF). Moore, D.J., 1969. The distributions of surface concentrations of sulphur dioxide emitted from tall chimneys. Philosophical Transactions of the Royal Society A 265. Okamoto, S., Shiozawa, K., 1978. Validation of an air pollution model for the Keihin area. Atmospheric Environment 12, 2139–2149. Sagendorf, J.F., Dickson, C.R., 1974. Diffusion under low wind speed inversion conditions, NOAA Technical Memo-ERLARL-52. Air Resources Laboratories, Silver Spring. Seinfield, J.H., 1986. Atmospheric chemistry and physics of air pollution. Wiley, New York. Sharan, M., Singh, M.P., Yadav, A.K., 1996. A mathematical model for the atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance. Atmospheric Environment 30, 1137–1145. Sharan, M., Yadav, A.K., 1998. Simulation of diffusion experiments under light wind, stable conditions by a
P. Goyal, T.V.B.P.S. Rama Krishna / Atmospheric Environment 36 (2002) 2071–2079 variable K-theory model. Atmospheric Environment 32, 3481–3492. Taylor, G.I., 1959. The present position in the theory of turbulent diffusion. Advances in Geophysics. 6, 101–111. Turner, D.B., 1969. Workbook of Atmospheric Dispersion Estimates, Washington, DC. Venkataram, A., 1999. Applying a Framework for Evaluating the Performance of Air Quality Models. Sixth International Conference on Harmonisation within Atmospheric
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Dispersion Modelling for Regulatory Applications, 11–14 October 1999, Rouen, France. Wark, K., Warner, C.F., Davis, W.T., 1998. Air Pollution: Its Origin and Control. Addission-Wesley Longman Inc., Reading, MA. Zannetti, P., 1986. A new mixed segmented-puff approach for dispersion modeling. Atmospheric Environment 20, 1121–1130. Zannetti, P., 1990. Air Pollution Modelling. Van Nostrand Reinhold, New York, pp 444.