Selection of an appropriate model to predict plume dispersion in coastal areas

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Atmospheric Environment 41 (2007) 6095–6101 www.elsevier.com/locate/atmosenv

Selection of an appropriate model to predict plume dispersion in coastal areas Ok-Hyun Park, Min-Gwang Seok Department of Environmental Engineering, Pusan National University, Busan 609-735, South Korea Received 25 October 2006; received in revised form 10 April 2007; accepted 11 April 2007

Abstract In order to suggest a new methodology for selecting an appropriate dispersion model, various statistical measures having respective characteristics and recommended value ranges were integrated to produce a new single index by using fuzzy inference where eight statistical measures for various model results, including fractional bias (FB), normalized mean square error (NMSE), geometric bias mean (MG), geometric bias variance (VG), within a factor of two (FAC2), index of agreement (IOA), unpaired accuracy of the peak concentration (UAPC), and mean relative error (MRE), were taken as premise part variables. The new methodology using a single index was applied to the prediction of ground-level SO2 concentration of 1-h average in coastal areas, where eight modeling combinations were organized with fumigation models, sy schemes for pre-fumigation, and modification schemes for sy during fumigation. As a result, the fumigation model of Lyons and Cole was found to have better predictability than the modified Gaussian model assuming that whole plume is immerged into the Thermal Internal Boundary Layer (TIBL). Again, a better scheme of sy (fumigation) was discerned. This approach, which employed the new integrated index, appears to be applicable to model evaluation or selection in various areas including complex coastal areas. r 2007 Elsevier Ltd. All rights reserved. Keywords: Atmospheric dispersion model; Statistical measures; Fuzzy inference; Model selection; Coastal area

1. Introduction Though statistical measures have been used to evaluate prediction performances of atmospheric dispersion models, it is difficult to discern the best model based on a single measure because each measure has its own functional characteristics and judging criteria. Thus, it is desirable to develop a methodology for selecting an appropriate model or a modeling scheme through comparison of a new index Corresponding author. Tel.: +82 51 510 2415; fax: +82 51 514 9574. E-mail address: [email protected] (O.-H. Park).

1352-2310/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2007.04.010

synthesized with various statistical measures. In this study, a model selection methodology was developed via two steps. In the first step, candidate dispersion modeling schemes applicable to complex coastal areas were organized by considering fumigation phenomena and the Thermal Internal Boundary Layer (TIBL), and then performances of each modeling scheme in the prediction of 1-h SO2 concentration in complex coastal terrain were roughly reviewed using statistical measures for application results of the candidate models or modeling schemes. In the second step, statistical score as a single index was calculated by applying fuzzy inference to premise part functions where various statistical measures were used as

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premise variables. Then, the best model or modeling scheme was finally determined through comparison of the indices. 2. Modeling 2.1. Acquisition of meteorology, environment, and terrain data The coastal area near the power plant in Boryeung, Korea (N361240 , E1261300 ) was selected as the modeling area, and associated meteorological data from 1.5 to 60 m height from January to December 2002, were obtained. Upper air data of pressure and temperature with altitude were also collected. Onehour average SO2 concentration data were obtained from the SONGHAK site located 4 km downwind from the power plant in the Northwestern wind direction leading to Boryeung. Numerical data of surface altitude above sea level for distributed grid sites with even spacing were generated from numerical maps (scale 1/25,000) by the Triangulate Irregular Network method using Arc view software. 2.2. Evaluated fumigation models In order to estimate high SO2 concentrations above ground level in complex coastal areas, the modified Gaussian plume model (1) of Lyons and Cole (1973), and a simple Gaussian model (2) as well as ISCST3 and ADMS3 were examined as candidate models. hi was calculated using Kouchi et al.’s (1999) equation. " R p  pffiffiffiffiffiffi # Q 1 1= 2p expð0:5p2 Þ dp pffiffiffiffiffiffi C ðx;yÞf ¼ ¯ i 2psyf Uh ( !) y2  exp  , ð1Þ 2s2yf

where C(x,y)f is ground-level concentration at (x, y) during fumigation (g m3), y is lateral departure from the plume axis at downwind distance x (m), syf is lateral dispersion coefficient at distance x during ¯ is mean wind speed within TIBL fumigation (m), U (m s1), hi is thickness of TIBL at distance x from shore line (m), and p is height difference between hi and He (effective stack height) normalized by sz (vertical dispersion coefficient). ( !) ! Q y2 C ðx;yÞf ¼ pffiffiffiffiffiffi , (2) exp  2s2yf 2psyf hi U where hi ¼ He+2sz (Engleman, 1996). 2.3. Preprocessing of dispersion coefficients Various relationships between downwind distance and sigma for the Boryeung coastal area were obtained using Park et al.’s (2001) work. When TIBL takes place over coastal land, plumes from tall stacks are released into an ‘‘F’’ class stable atmosphere, and then diffused by turbulence at an ‘‘A’’ class unstable condition after meeting TIBL (Venkatesan et al., 2002). Van Dop et al. (1979) and Misra (1980) proposed Eqs. (3) and (4), respectively, to correct the lateral variance of plume just before fumigation. s2y ¼ s2ysðx2 Þ þ s2ytðxÞ  s2ytðx2 Þ

(3)

s2y ¼ s2ysðx2 Þ þ s2ytðxx2 Þ ,

(4)

where sys is sy in the stable atmospheric layer (m), syt is sy in the unstable atmospheric layer (m), and x2 is the downwind distance for the plume to reach TIBL (m). Since the averaging times of sy and sz in the P–G scheme for a flat plain are 3 and 10 min, respectively, the values of sy and sz for each stability class

Table 1 Fumigation modeling schemes Fumigation model

hi

s2y Scheme

syf Scheme

Modeling scheme

Eq. (1)

Kouchi et al. (1999)

Van Dop’s Eq. (3)

Eq. Eq. Eq. Eq. Eq. Eq. Eq. Eq.

I II III IV V VI VII VIII

Misra’s Eq. (4) Eq. (2)

hi ¼ he+2sz

Van Dop’s Eq. (3) Misra’s Eq. (4)

(5) (6) (5) (6) (5) (6) (5) (6)

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were corrected for different averaging times by using the Angell and Pack (1965) equation. The effect of sigma enhancement during buoyant plume rising was corrected using the equations proposed by Hanna et al. (1997). Since turbulence intensity affecting plume dispersion decreases with height, sigmas for elevated plume were corrected by multiplying the ratios of syðz2 Þ =syðz1 Þ and sjðz2 Þ =sjðz1 Þ to syðz1 Þ and szðz1 Þ , respectively, where y and c are horizontal and vertical wind directions, z1 ¼ 60 m (reference height) in Boryeung coastal area, and z2 ¼ He. Dispersion coefficients for rolling terrain

fair (over)

poor

fair (under)

good

6097

were corrected from sigmas for flat plain (e.g. P–G system) by using the Terrain Factor Model (Okamoto et al., 1986). syf for fumigation plume was corrected using Eqs. (5) and (6). The correction factor of He/8 in Eq. (6) is based on Turner (1970). syf ¼ syðxÞ þ 0:47H e ðmÞ,

(5)

syf ¼ syðxÞ þ H e =8 ðmÞ,

(6)

where sy(x) is sy at downwind distance x just before fumigation.

poor

good

fair

poor

1

-1.33 -1.2 -1 fair poor (over)

-0.3

good

0

1 1.2 1.33

0.3 fair(under)

4

1.3

3

16

good

4

5

0

0

fair

1.6

3.34

good

fair

0

0.2

0.3

-4

-3

12

fair (over)

fair good (under) poor

poor

0.4

0.5

fair (over)

poor

poor

6.28

poor 1

25

poor

1

0.2 0.7 0.25 0.33

9

-4 fair good (under) poor

-2

-3

-2

-0.2 0.2 0.67 0.8 0.75

0.15 -0.15 0.67 0.8 0.75

Fig. 1. Membership function diagram for (a) FB, (b) NMSE, (c) MG, (d) VG, (e) FAC2 and IOA, (f) UAPC, and (g) MRE.

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2.4. Organization of modeling schemes for fumigation plume Eight modeling schemes were organized as shown in Table 1 by using fumigation dispersion models (Eqs. (1) and (2)), s2y (before fumigation) models (Eqs. (3) and (4)), and syf models (Eqs. (5) and (6)). The statistical measures of 1-h SO2 concentrations, from 10:00 to 11:00 h when the conditions of TIBL and low wind took place, were calculated using eight fumigation modeling schemes as well as ISCST3 and ADMS3 as reference models. The results revealed that fumigation models are superior to ISCST3 and ADMS3 in the prediction of high concentration at ground level; however, there does not exist any fumigation modeling scheme for which all the measures commonly show the best performance. The better predictability of fumigation models in coastal areas appears to be due to the fact that the fumigation models were specifically formulated to express the high ground-level concentrations occurring in coastal areas where TIBL and low wind conditions frequently take place. 3. Establishment of fuzzy models to integrate statistical measures Fuzzy inference was used to provide a single index based on various statistical measures for selecting an appropriate scheme among eight fumigation modeling schemes, and to reasonably explain uncertainties caused by vagueness associated with different recommended range of each measure. As an inference method, the Mamdani method was used, in which variables of consequent parts (e.g. model performance) are expressed in a triangle or trapezoid membership function to be quantified later. When a number of rules exist, the relationships between premise variable and consequent variable were obtained for each rule, and final relations were obtained by integrating those relationships. Inference results were quantified into statistical scores by defuzzyfication of the output (e.g. graphical map). 3.1. Establishment of membership functions for premise variable Statistical measures such as fractional bias (FB), normalized mean square error (NMSE), geometric bias mean (MG), geometric bias variance (VG), within a factor of two (FAC2), index of agreement (IOA), unpaired accuracy of the peak concentration

(UAPC), and mean relative error (MRE) were taken as the variables of the premise part. Membership functions of premise variables consisted of ‘‘good’’, ‘‘fair’’, and ‘‘poor’’ classified according to model performance level under consideration of judging criteria on the measures proposed by many investigators including Chang and Hanna (2004), Ziomas et al. (1998), and Zawar-Reza et al. (2005). Membership functions for various premise variables are shown in Fig. 1, based on Table 2. 3.2. Fuzzy inference A fuzzy model with eight inputs and one output structure was used where eight statistical measures were taken as premise part variables and model performance (statistical score) was a consequent part variable. Rules were established as shown in Table 2 Determining the membership function for various premise variables Measure

Range

FB

0.3oFBo0.3 1oFBo1.2 1.2oFBo1 FB41.33 or FBo1.33

NMSE

NMSEo4 9oNMSEo16 25oNMSE

MG

0.7oMGo1.3 3oMGo4 0.25oMGo0.33 MG45 or MGo0.2

Membership function

Fair

Good Underestimation Overestimation Poor Good Fair Poor

Fair

Good Underestimation Overestimation Poor

VG

VGo1.6 3.34oVGo6.82 12oVG

Good Fair Poor

FAC2

0.5oFAC2 0.3oFAC2o0.4 FAC2o0.2

Good Fair Poor

IOA

0.5oIOA 0.3oIOAo0.4 IOAo0.2

Good Fair Poor

UAPC

0.2oUAPCo0.2 0.67oUAPCo0.75 3oUAPCo2 UAPC40.8 or UAPCo4

MRE

0.15oMREo0.15 0.67oMREo0.75 3oMREo2 MRE40.8 or MREo4

Fair

Fair

Good Underestimation Overestimation Poor Good Underestimation Overestimation Poor

Membership and its frequency

Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule

G G G G G G G G G G G G G G G G G G G G G

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

5 4 4 4 5 5 3 3 3 4 4 4 5 5 2 2 3 2 3 3 3

OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF

0 1 0 0 0 0 2 0 1 1 0 0 0 0 3 2 2 0 1 0 1

F F F F F F F F F F F F F F F F F F F F F

2 2 3 2 1 1 2 4 2 1 2 1 0 0 2 2 1 5 2 3 1

UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF

0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1

P P P P P P P P P P P P P P P P P P P P P

1 1 1 1 2 2 1 1 1 2 2 2 3 3 1 1 2 1 2 2 2

Total score

Grade

Rule number

Membership and its frequency

55.5 53 52.5 52 52 52 50.5 49.5 49.5 49.5 49 48.5 48.5 48.5 48 47 47 46.5 46.5 46 46

A B C D D D E F F F G H H H I J J K K L L

Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule

G G G G G G G G G G G G G G G G G G G G

G: good, OF: fair overprediction, F: fair, UF: fair underprediction, P: poor.

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

4 3 4 4 2 2 3 2 2 3 3 3 3 4 2 2 2 2 2 3

OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF OF

1 0 0 0 3 2 2 0 1 1 0 1 0 0 3 2 2 0 1 1

F F F F F F F F F F F F F F F F F F F F

0 2 1 0 1 1 0 4 2 1 2 0 1 0 0 1 1 3 1 0

UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF UF

0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0

P P P P P P P P P P P P P P P P P P P P

3 2 3 3 2 2 3 2 2 3 3 3 3 4 3 3 3 3 3 4

Total score

Grade

46 45.5 45.5 45 44.5 43.5 43.5 43 43 43 42.5 42.5 42 42 41 40.5 40.5 39.5 39.5 39.5

L M M N O P P Q Q Q R R S S T U U V V V

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Table 3 Rules to select an appropriate prediction model

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Table 3 according to the respective number of ‘‘good’’, ‘‘fair’’, or ‘‘poor’’ memberships where the value of each statistical measure corresponded. The various statistical measures were classified into ‘‘good’’ when the measures corresponded to ‘‘FAC2 (1/2 measurements opredictionso2.0 measurements)’’, ‘‘fair’’ for a factor of 2–3, and ‘‘poor’’ for a factor of 3–4. To determine the order of rules, weight was given to each membership (i.e. 7–10 (average 8.5) to ‘‘good’’, 4–7 (average 5.5) to ‘‘fair’’, 6 to ‘‘fair (over)’’, 5 to ‘‘fair (under)’’, 1–4 (average 2.5) to ‘‘poor’’ membership). Fig. 2 displays that A–V orders were taken as a membership function of the consequent variable.

V UT

4. Selection of an appropriate modeling scheme The results of fuzzy inference (e.g. graphical maps) were quantified into statistical scores indicating the modeling performance. Table 4 summarizes the results of fuzzy inference based on statistical measures for 1-h SO2 concentrations calculated using eight schemes of fumigation modeling, where modeling scheme II is the best one for fumigation modeling. The formula expressing the lateral dispersion of fumigating plumes, syf ¼ sy (before deposition)+ He/8, appears to be superior to the other one, syf ¼ sy (before deposition)+0.47He.

S R Q P ONM L K J

I HGF

E

DCB

A

Function value

1

0 0

1 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 Score Fig. 2. Membership function of consequence part.

Table 4 Results of fuzzy inference based on statistical measures for various modeling schemes Scheme I

II

III

IV

V

VI

VII

VIII

FB NMSE MG VG FAC2 IOA UAPC MRE

Good fair Good Good fair Poor Fair poor Fair poor Good Fair Good: 4

Good Good Good fair Poor Fair Fair poor Good Good fair Good: 5

Good fair Good Good fair Poor Fair poor Fair poor Good Good fair Good: 5

Good fair Good Poor Poor Fair Fair poor Good Good fair Good: 4

Good fair Good Good fair Poor Fair poor Poor Good Poor Good: 4

Good fair Good Good fair Poor Fair poor Fair poor Good Good fair Good: 5

Good fair Good Good fair Poor Fair poor Poor Good Fair poor Good: 4

Good Good Good fair Poor Fair poor Fair poor Good Good fair Good: 5

Total

Fair: 5 Poor: 3

Fair: 4 Poor: 2

Fair: 5 Poor: 3

Fair: 4 Poor: 3

Fair: 3 Poor: 4

Fair: 5 Poor: 3

Fair: 4 Poor: 4

Fair: 4 Poor: 3

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5. Conclusions In order to select an appropriate model or a modeling scheme for predicting atmospheric pollution, a new methodology was established by producing statistical scores as an integrated single index through fuzzy inference of premise part membership functions, in which ‘‘good’’, ‘‘fair’’, and ‘‘poor’’ were defined considering the judging criteria for various statistical measures taken as premise variables. As a result of applying the methodology to the prediction of 1-h SO2 concentrations in coastal area, the fumigation model of Lyons and Cole (1973) was found to be superior to the modified Gaussian model, assuming that the whole plume from elevated sources traveling in stable atmospheric layer is fumigated and mixed thoroughly in vertical direction after meeting the TIBL. The equation expressing the lateral dispersion of fumigating plumes, syf ¼ sy (before deposition)+He/8, appears to be superior to the other scheme, syf ¼ sy (before deposition)+0.47He, where He is effective stack height. Gaussian fumigation models improved performance in 1-h SO2 concentration prediction in coastal areas rather than ISCST3 and ADMS3, which have generally been accepted in various terrains. References Angell, J.K., Pack, D.J., 1965. Atmospheric lateral diffusion estimates from tetroons. Applied Meteorology 4, 418–425. Chang, J.C., Hanna, S.R., 2004. Air quality model performance evaluation. Meteorology and Atmospheric Physics 87, 167–196.

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Engleman, I.R., 1996. Air Pollution Meteorology. Trimedia Publishing Company, USA, pp. 79–90. Hanna, S.R., Briggs, G.A., Deardorff, J.W., Egan, B.A., Gifford, F.A., Pasquill, F., 1997. Meeting review—AMS workshop on stability classification scheme and sigma curve summary of recommendations. Bulletin of the American Meteorological Society, 1305–1309. Kouchi, A., Ryoji, O., Yanping, S., 1999. Gas diffusion in a convection layer near a coastal layer. Wind Engineering and Industrial Aerodynamics 81, 171–180. Lyons, W.A., Cole, H.S., 1973. Fumigation and plume trapping on the shores of Lake Michigan during stable onshore flow. Journal of Applied Meteorology 12, 494–510. Misra, P.K., 1980. Dispersion from tall stacks into a shoreline environment. Atmospheric Environment 14, 495–510. Okamoto, H., Ohba, R., Kinoshita, S., 1986. Prediction of diffusion taking account of topographical effects. In: Proceedings of the 7th World Clean Air Congress, Sydney, Australia, pp. 34–41. Park, O.H., Lee, S.H., Chun, S.N., 2001. Improvement of atmospheric dispersion modeling in coastal areas under stable, low wind conditions. In: Proceedings of the 12th World Clean Air Congress, Seoul, Korea. Turner, D.B., 1970. Workbook of Atmospheric Dispersion Estimates (revised), US EPA, Number 999-AP-26. Research Triangle Park, NC. Van Dop, H., Steenkist, R., Nieuwstadt, F.T.M., 1979. Revised estimates for continuous shoreline fumigation. American Meteorological Society 18, 133–137. Venkatesan, A., Mathiyarasu, R., Somayaji, K.M., 2002. A study of atmospheric dispersion of radionuclides at a coastal site using a modified Gaussian model and a mesoscale sea breeze model. Atmospheric Environment 36, 2933–2942. Zawar-Reza, P., Kingham, S., Pearce, J., 2005. Evaluation of a year-long dispersion modeling of PM10 using the mesoscale model TAPM for Christchurch, New Zealand. Science of the Total Environment 349, 249–259. Ziomas, I.C., Tzoumaka, P., Balis, D., 1998. Ozone episodes in Athens, Greece. A modelling approach using data from the medcaphot-trace. Atmospheric Environment 32, 2313–2321.