Differences caused by stability class on dispersion in tracer experiments

Atmospheric Environment Vol. 19, No. 7, pp. 1045-1051, 1985

0004-6981/85 $3.00 + 0.00 © 1985 Pergamon Press Ltd.

Printed in Great Britain.

DIFFERENCES CAUSED BY STABILITY CLASS ON DISPERSION IN TRACER EXPERIMENTS MARSHALL A. ATWATER a n d RICHARD J. LONDERGAN TRC Environmental Consultants, Inc., 800 Connecticut Boulevard, East Hartford, CT 06108, U.S.A. (First received 24 September 1984 and in final form 13 November 1984)

Abstract--A single source mass transfer technique by Hellums that provides a systematic method of fitting concentration data from a tracer dispersion experiment to determine horizontal and vertical dispersion coefficient values was used to determine revised dispersion estimates for tracer experiments. These revised coefficients were compared to results from standard analysis methods and to coefficients predicted by the Pasquill-Gifford curves. Differences in stability classification result in much larger differences in dispersion coefficients than the differences associated with the curve-fitting techniques. The stability class estimate inferred from the observed dispersion often differed by two or more classes from the estimate based on meteorology. The dT/dz stability classification method was most correlated with the observed vertical dispersion, while the Turner and ae methods were most correlated with observed horizontal dispersion. Observed horizontal and vertical dispersion classes often differed from one another by two or more classes. Key word index: Air pollution, dispersion coefficients, stability classification, tracer experiments.

INTRODUCTION

Since the passing of the Clean Air Act, the Environmental Protection Agency (EPA) has used numerous air quality models that relate source emissions and meteorological data to the expected air quality. The EPA has relied upon the predictive capability of air quality models to identify the levels of control required to solve industrial and urban air pollution problems. The models are mathematical representations of the complex physical and chemical processes involved in the dispersion, transformation and deposition of pollutants. Most of the models selected by the EPA are based on the steady-state Gaussian point-source formulae developed in the 1940s with numerous enhancements for transformation, deposition, decay, buildup, depletion, and multiple source and receptor configurations. These Gaussian models utilize empirical parameters derived from field experiments to predict dispersion behavior as a function of meteorological conditions. A number of tracer dispersion programs conducted during the 1950s and 1960s were used to estimate these dispersion parameters. Data from these tracer experiments were analyzed prior to wide-scale use of computers and of advanced numerical analysis routines. Hellums of Phillips Petroleum had hypothesized that improved dispersion parameters might result from the re-analysis of these tracer data with modern mathematical fitting techniques. He therefore developed a series of computer programs to analyze tracer experiments, using a non-linear least-squares optimization routine, called the Single Source Mass Transfer (SSMT)method (Hellums, 1982). The initial

objective of this study was to assess the feasibility of improving model performance through the use of the revised dispersion parameters. From a practical viewpoint, dispersion parameters from individual tracer experiments cannot be used to predict dispersion unless they are incorporated within a model framework keyed to meteorological, site, and source conditions. The general model development approach attempts to combine estimates of dispersion from experiments with similar types of conditions through an 'atmospheric stability class' that defines an index of atmospheric turbulence. Several stability classification schemes are used currently by the technical and regulatory community. Prediction schemes in existing air quality models utilize the atmospheric stability class to select appropriate empirical dispersion parameters for a particular event. A number of papers have examined various stability classification schemes. Sedefian and Bennett (1980) examined one year of data in New York City, and Gildart and Chang (1983) examined stability by different methods with four years of data at Sacramento, CA. The present study will use data from tracer experiments. Steps in assessing the SSMT results as a basis for improved models included a comparison with earlier estimates of dispersion parameters and examination of the SSMT dispersion coefficients as a function of several standard classification schemes. Dispersion coefficient estimates for a number of tracer experiments were also calculated by a relatively simple calculation scheme similar to the techniques from which current model parameters were derived. SSMT results have been compared to these simple estimates and to the generalized dispersion algorithms employed in existing models.

1045

1046

MARSHALL A. ATWATERand RICHARD J. LONDERGAN

<2)

THE SINGLE SOURCE MASS TRANSFER METHOD

~7z = Z 1 -t'- Z 2 x q.- Z 3 X2 -r- Z 4 x 3,

The Gaussian dispersion model provides a simple description of plume spread and transport. The model assumes straight-line steady-state plume transport and describes the crosswind plume spread as a bivariate normal distribution, characterized by the vertical and horizontal standard deviations (orz and try) of the concentration distribution. The Gaussian air quality models in current usage employ sets of empirical dispersion coefficients (more properly, dispersion coefficient curves, since ay and a~ vary with downwind distance) which were developed using measurements from tracer dispersion experiments. Since experimental data were available for only a limited range of downwind distances, the distance dependence of these empirical dispersion curves was based largely on theoretical considerations. Generally, the measurements from each arc of ground-level samplers were used to compute the center-of-mass, horizontal standard deviation (to estimate ay), and the crosswindintegrated concentration (CWIC), which was used to infer the vertical plume spread and to estimate a t. The ay and % estimates from individual experiments were then grouped according to atmospheric stability conditions, and a family of dispersion coefficient curves were constructed which encompassed the range of dispersion behavior observed. In general, these curves were developed in a subjective fashion, without resorting to mathematical fitting techniques or other objective methods. One previous attempt to analyze the total data set from a tracer experiment was undertaken by Cramer et al. (1972) who used a Marquardt non-linear leastsquares estimation technique to construct dispersion coefficient values from a set of tracer measurements taken at Dugway Proving Ground at distances of 20-183 m and at several elevations above the ground surface. The work showed the method to have great potential in fitting such large data sets. The SSMT method provides a technique for calculating 0"y and a~ values from tracer dispersion measurements using modern computational methods to derive self-consistent estimates of O'y and crz from these data. The method utilizes an optimization model to determine O'y and a z values simultaneously to obtain an optimal least-squares fit to the full set of measured data points for each experiment. Unlike the earlier, simpler techniques, which assumed that all measurements on a sampling arc were at the same downwind distance, the SSMT method takes into account the actual sampler locations. Also, unlike earlier techniques, the SSMT method can develop solutions (fly(X)and az(x)) for up to five sampling arcs simultaneously, instead of using the data from each arc separately. The SSMT method develops cubic polynomial equations for the horizontal and vertical dispersion coefficient curves. The basic equations used by the method are

where x is downwind distance and Y, and Z~ are the empirical constants which are determined by the SSMT optimizer. Best-fit solutions for cr+(x) and %(x) are developed by the SSMT program. In each instance, the optimizer minimizes the sum of squares of the 'residues' representing the differences between measured tracer concentration at each sampler location and Gaussian model concentrations estimated using ay and a 7 from (1) and (2). The solution defines the residue as a measure of relative difference

O'y= Yt + Y2x + Y3x2 + Y+x 3

(1)

Ci - Ei

D, : min (C~E,)'

13)

where E~ is the measured concentration at sampler i. C+ is the Gaussian estimate and the denominator represents the smaller of the measured and estimated concentration values. In addition to specifying a particular polynomial form of the dispersion coeffÉcientequations, the SSMT method also imposes two constraints on the solutions. The constraints are: I 1) The dispersion coefficients are positive (greater than zero) within the distance range of the samplers. i2) The coefficients increase with downwind distance within the range of interest. The constraints help to preclude physically unreasonable solutions (such as negative dispersion coefficients or plumes which shrink rather than expand). The SSMT method is not a foolproof system. The mathematical power of the fitting procedure is no guarantee that the results will properly describe the observed dispersion behavior for every tracer experiment. In fact, when the pattern of tracer measurements departs significantly from a Gaussian distribution, the method may give quite misleading results. In view of the possible misleading results, all experiments in which the average residue exceeds 1000 were eliminated from the analyses in this study. About 10,50 of the experiments were eliminated for this reason. The simpler methods used previously to estimate ay and a z from tracer experiments were less precise, but were also less susceptible to mathematical instabilities. DESCRIPTION OF TRACER EXPERIMENT DATA BASE

Tracer programs have been undertaken at a number of sites to examine dispersion for a variety of meteorological and topographical conditions. Four tracer programs at Hanford (Nichola, 1977), Prairie Grass (Barad, 1958), Green Glow (Barad and Fuquay, 1962) and Ocean Breeze (Haugen and Fuquay, 1963) were examined in this study. For each tracer experiment, the set of individual concentration measurements on a given arc were used to estimate the maximum concentration, the plume centerline location, the plume width and the crosswind integrated

Differences caused by stability class on dispersion in tracer experiments

category, as seen in Table 1. The Turner method has a larger number of neutral cases, with fewer cases in the extreme categories A and G. The dT/dz method has more cases in the extreme categories and fewer cases in the near neutral categories. The tr0 method indicates fewer stable cases and more unstable cases. The Turner and dT/dz methods relate primarily to vertical dispersion, while sigma theta is a direct measure o f the horizontal wind fluctuations. The results of Table 1 suggest that discrepancies between stability class values for the same experiment obtained using different methods o f classification are common, as evidenced by the results for Ocean Breeze, Hanford and Prairie Grass. All three methods indicated stable classifications for Green Glow.

concentration (CWIC). For the present study the plume width, as defined by the variance o f the crosswind concentration distribution, tr2, and the integral of ground-level concentration values for all crosswind positions (CWIC), will be used. The variance of the crosswind concentration is computed from R27t2

tr2--

N

N (180) 2 ~

Z E'(Oi-00)2'

(4)

Eii=:

i=1

where R is the arc distance from the source, 00 is the azimuth to the observed centerline location and E~ and 0~ are the measured concentration and azimuth for monitor i. The integral of ground level concentration provides a measure of vertical dispersion behavior independent of plume width. For an arc with equal azimuthal spacing 60 between samplers, the C W l C is estimated by

DISPERSION RATES A N D STABILITY CLASS

The dispersion coefficients computed by the S S M T were used to identify a 'plume dispersion class,' using the Pasquill--Gifford (P-G) dispersion curves. For each arc, the S S M T coefficient values were compared to values at that distance from the P - G curves. The stability class associated with the P - G coefficient value closest to the S S M T value was defined as the plume dispersion class. Treating horizontal and vertical dispersion separately, two plume dispersion classes were identified for each arc. The S S M T results were used to examine two aspects of observed plume behavior; (1) changes in plume behavior from arc to arc and (2) comparison of horizontal and vertical plume dispersion classes. Systematic changes in stability from arc to arc would indicate that the slope of the P - G dispersion curves

N

C W I C = ~, E, R60.

(5)

i=1

For ease of identification, these values calculated from observations on a given arc will be referred to as 'second moment values' of try and CWlC. The stability class is the indicator used by dispersion models to select the appropriate dispersion curve. Three stability classification methods that were considered include the Turner method (Turner, 1964), the dT/dz method (Nuclear Regulatory Commission, 1972) and the as method (Pasquill, 1961). Each of the methods determines stability in classes of A (very unstable) to G (very stable). Each of the classification methods considered places a different number of experiments in each stability

Table 1. Number of experiments within a given class for three methods of stability classification Experiment

A

B

Han ford Prairie Grass Ocean Breeze Green Glow Total

0 0 1 0 1

0 2 7 0 9

Hanford Prairie Grass Ocean Breeze Green Glow Total

5 1 1 0 7

Hanford Prairie Grass Ocean Breeze Green Glow Total

19 19 40 0 78

C

Class D

E

F

G

Total

29 9 7 10 55

19 2 7 17 45

0 0 0 0 0

142 46 68 37 293

theta method 49 28 49 17 4 16 3 24 28 12 0 10 81 56 103

0 3 0 2 5

0 0 0 0 0

142 43 58 26 269

16

46

1

6

11 2 30

5 35 92

48 12 0 0 60

146 38 68 37 289

Turner method 14 80 10 23 19 27 0 10 43 140

Sigma 11 2 2 2 17

dT/dz method 6 0 0 0 6

1047

0 0 3 0 3

11 0 9 0 20

1048

MARSHALL A. ATWATERand RICHARD J. LONDERGAN

differs f r o m t h e o b s e r v e d rate o f p l u m e s p r e a d w i t h distance. F o r tracer tests w i t h t h r e e o r m o r e s a m p l i n g arcs, h o r i z o n t a l p l u m e d i s p e r s i o n class v a l u e s o n t h e t h i r d a n d fifth arcs were c o m p a r e d w i t h v a l u e s f r o m t h e first arc. (Arc 1 is t h e c l o s e s t to t h e s o u r c e for e a c h e x p e r i m e n t . ) R e s u l t s o b t a i n e d for h o r i z o n t a l d i s p e r s i o n r a t e s a r e s u m m a r i z e d in T a b l e 2. T h e c h a n g e s f r o m a r c to a r c d o n o t indicate large d i s c r e p a n c i e s between observed horizontal dispersion rates and the

distance dependence of the P-G curves. In most i n s t a n c e s , t h e p l u m e d i s p e r s i o n class o n A r c 3 a n d A r c 5 w a s w i t h i n _ 1 class o f t h e A r c 1 value. T h e d i s t r i b u t i o n o f p l u m e d i s p e r s i o n class v a l u e s d o e s indicate a shift t o w a r d m o r e s t a b l e v a l u e s w i t h increasi n g distance. A r c 3 a n d A r c 5 r e s u l t s s h o w fewer C l a s s D values, a n d m o r e C l a s s E a n d C l a s s F, t h a n A r c 1. Vertical d i s p e r s i o n r a t e s s h o w s o m e w h a t d i f f e r e n t b e h a v i o r as s h o w n in T a b l e 3. A g a i n , in m o s t cases, t h e

Table 2. Comparison of horizontal plume dispersion class values on different arcs with the SSMT method Arc 3 Plume dispersion class

A

Arc 1 Plume dispersion class B C D E F

Total

A B C D E F

19 2 1 0 0 0

9 21 6 1 0 0

0 9 28 4 3 0

2 1 11 25 13 0

0 0 0 1 14 5

0 0 0 1 1 1

30 33 46 32 31 6

Total

22

37

44

52

20

3

178

Arc 5 Plume dispersion class

A

Arc 1 Plume dispersion class B C D E F

Total

A

7

4

3

0

0

0

B

1

12

3

0

I

0

C D E F

1 0 0 0

1 1 0 0

12 5 1 0

2 2 13 5

0 0 3 5

0 1 1 0

14 17 16 9 18 10

Total

9

18

24

22

9

2

84

Note: The five arc data are from Hanford and Green Glow. No data in this table are from Ocean Breeze. Table 3. The frequency of vertical plume dispersion class at Arcs 3 and 5 as a function of Arc 1 with the SSMT method Arc 3 Plume dispersion class

A

Arc 1 Plume dispersion class B C D E F

Total

A B C D E F

I0 19 3 0 0 0

2 22 8 1 0 0

2 8 38 17 0 0

0 4 8 10 4 0

0 0 2 6 3 0

0 0 1 1 3 6

14 53 60 35 10 6

Total

32

33

65

26

11

11

178

Arc 5 Plume dispersion class

A

Arc 1 Plume dispersion class B C D E F

A B C D E F

3 4 0 0 0 0

5 2 2 1 0 0

0 6 14 9 8 0

1 2 2 7 0 1

0 1 l 4 0 3

0 0 2 0 0 6

9 15 21 21 8 10

Total

7

10

37

13

9

8

84

Total

Note: Deposition may have been significant for Hanford and Green Glow.

Differences caused by stability class on dispersion in tracer experiments

1049

are compared via a joint-frequency contingency table. Less than 60 % of the horizontal and vertical dispersion categories agree within + 1 class of the other. The vertical dispersion estimates are more unstable (Classes B and C) while the horizontal dispersion estimates are shifted toward Classes D and E, although most estimates are in Classes A - D . The results in Table 4 indicate both a systematic difference between horizontal and vertical dispersion class values and relatively low correlation between horizontal and vertical dispersion class for the same experiment. Table 5 shows the frequency of occurrence of the horizontal and vertical plume dispersion classes as a function of the Turner stability class. An examination of Table 5 shows that the number of unstable plume dispersion classes, both vertical and horizontal, is much greater than indicated by the Turner stability classification. Linear correlation coefficients between plume dispersion class and various standard stability classifi-

plume dispersion class on Arc 3 and Arc 5 is within -t- 1 class of the Arc 1 value. The only systematic shifts between arcs apparent in Table 3, however, are a decrease in Class A values (and increase in Class B) between Arc 1 and Arc 3, plus a decrease in Class C values and an increase in Class D, from Arc 1 to both Arc 3 and Arc 5. Taken together, the results in Tables 2 and 3 indicate some systematic differences between the P - G curves and the observed (SSMT)dependence of dispersion on downwind distance. In several instances, plume dispersion class values tended to increase with arc distance, indicating that the S S M T dispersion rates were growing less rapidly than the P - G curves. Most air quality models in current use calculate horizontal and vertical dispersion rates using a single stability class. The implicit assumption that horizontal and vertical turbulence are coupled can also be examined via the S S M T coefficients. In Table 4, the plume dispersion class values determined from S S M T horizontal and vertical dispersion rates on the same arc

Table 4. The joint frequency of vertical and horizontal plume dispersion class on Arc 1 with the SSMT method Vertical plume dispersion class

A

A B C D E F Total

Horizontal plume dispersion class B C D E F Total

26 24 14 5 0 1 70

9 14 20 10 1 2 56

16 13 20 12. 7 6 74

8 21 35 6 2 4 76

4 3 19 4 1 1 32

1 5 2 2 0 0 10

64 80 110 39 11 14 318

Table 5. The frequency of the plume dispersion class as a function of Turner stability for Arc 1 1

Horizontal plume dispersion class 2 3 4 5 6 7

0

0

1

0

0

0

0

1

8 21 22 9 8 2 70

2 16 24 7 6 0 55

3 9 36 15 7 0 71

2 11 45 10 7 0 75

0 3 15 11 3 0 32

0 0 7 2 1 0 10

0 0 0 0 0 0 0

15 60 149 54 32 2 313

1

2

1

1

0

0

0

0

0

0

1

2 3 4 5 6 7 Total

7 18 21 8 4 2 61

6 24 41 5 3 0 79

1 15 61 18 14 0 109

1 3 15 11 9 0 39

0 0 4 7 0 0 11

0 0 7 5 2 0 14

0 0 0 0 0 0 0

15 60 149 54 32 2 313

Turner stability class 1

2 3 4 5 6 7 Total

Turner stability class

Vertical plume dispersion class 3 4 5 6 7

Total

Total

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MARSHALL A. ATWATERand RICHARD J. LONDERGAN

cations are summarized in Table 6. F o r the T u r n e r a n d dT/dz methods, the correlation coefficient value is significantly higher (at the 95~o level) for vertical dispersion, while for % the correlation is significantly higher (at the 95 ~0 level) for horizontal dispersion. These results would be expected on physical grounds, since the T u r n e r a n d dT/dz m e t h o d s are based on indicators o f radiative heating and cooling, which primarily affect vertical turbulence, while tr0 is a direct measure o f horizontal turbulence. The correlation coefficients in Table 6 indicate that the tr0 m e t h o d is a better indicator of horizontal dispersion than the T u r n e r method, a n d the T u r n e r a n d dT/dz m e t h o d s are comparable for vertical dispersion. Frequency contingency tables for these two m e t h o d s are presented in Table 7 for comparison with results for the T u r n e r m e t h o d in Table 5. Results in Table 7 show that the observed distribution o f horizontal plume dispersion class values is b r o a d e r than that predicted by the ae method, with fewer Class D a n d Class E values. By contrast, the dT/dz m e t h o d predicts more cases with extreme values, i.e. Class A, Class F a n d Class G, and fewer cases for Classes B - E

than the observed vertical dispersion distribution. Further, a bias toward stable cases exists for the T u r n e r m e t h o d and the dT/dz m e t h o d for vertical dispersion. F o r the T u r n e r method, the plume dispersion class was predicted to be more stable than observed 79 o~, of the time and more unstable 7 %0. F o r the dT/dz method, the plume dispersion class was more stable 64 ~0 a n d more unstable than observed in 24')~, of the cases. F o r the remainder of the cases, the S S M T (observed) plume dispersion class agreed with the predicted stability class. CONCLUSIONS These results indicate that representation o f stability is a higher priority for improved air quality model prediction than improved dispersion coefficients. In most instances, the horizontal or vertical dispersion class was consistent from one arc to another, within + one class, while present stability classification methods gave results which frequently differed from observed dispersion by two or more classes. F u r t h e r m o r e , the horizontal a n d vertical dispersion class values were

Table 6. The linear correlation between stability classification and plume dispersion class Stability classification Turner

dT/dz a0

Plume dispersion class

Correlation coefficient

Number of cases

Horizontal Vertical Horizontal Vertical Horizontal Vertical

0.14 0.31 0.19 0.36 0.52 0.09

313 313 238 238 245 245

Table 7. The frequency of horizontal and vertical plume dispersion class as a function of a0 and dT/dz stability a0 Stability class 1

1

Horizontal plume dispersion class 2 3 4 5 6 7

Total

5

0

0

0

0

0

0

5

6 4 6 0 0 0 21

7 13 14 2 0 0 36

0 16 31 16 2 0 65

2 8 35 29 0 0 74

0 1 13 17 1 t) 32

0 2 3 5 0 0 10

0 0 0 0 0 0 0

15 44 102 69 3 0 238

1

2

17 2 0

29 0 0

4

3

5 6 7 Total

3 12 3 40

2 3 4 5 6 7 Total

dT/dz Stability class 1

2 3

Vertical plume dispersion class 3 4 5 6 7 19 3 2

5

0

1

0

1 0

0 0

0 0

0 0

5

7

3

0

1

0

3 13 2 52

11 31 17 90

7 10 12 38

1 4 6 I1

1 5 6 14

0 0 0 0

Total 71 6 2 19 26 75 46 245

Differences caused by stability class on dispersion in tracer experiments often different. Differences in stability classification resulted in much larger differences in dispersion coefficient values than the uncertainties associated with curve-fitting techniques. Often the stability class estimate based on meteorology was different from the observed dispersion class by two or more categories. Acknowledoements--The authors gratefully acknowledge the support of this work by the American Petroleum Institute (API) and thank Lloyd Hellums, Phillips Petroleum and the AQ-7 Task Force of API for providing technical guidance during the course of this work.

REFERENCES

Barad M. L. (ed) (1958) Project Prairie Grass, a field program in diffusion (3 Volumes). Geophysical Research Papers No. 59, Air Force Cambridge Research Center, ASTIA Document AD-151572. Barad M. L. and Fuquay J. J. (eds) (1962) The Green Glow Diffusion Program. Geophysical Research Papers No. 73 (2 Volumes). Air Force Cambridge Research Laboratories-62-251.

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Cramer H. E., Bjorklund J. R., Dumbauld R. K., Faulkner J. , E., Record F. A., Swanson R. N. and Tingle A. G. (1972) Development of dosage models and concepts (Vol. 1 Details of Study)¢Final Rpt to U.S. Army Dugway Proving Ground, AD-893 341l~from GCA Corporation, Bedford, MA 01730, 1440194, February 1972. Gildart M. C. and Chang D. P. Y. (1983) A temporal comparison of stability typing methods. J. Air Pollut. Control Ass. 33, 491-493. Haugen D. A. and Fuquay J. J. (1963) The ocean breeze and dry gulch diffusion programs. Air Force Cambridge Research Laboratories. Contract AT (45-1)-1350. Hefiums L. (1982) Rigorous mathematical analysis for Gaussian plume representation of tracer field data. Phillips Petroleum, BartlesviUe, OK. Nichola P. W. (1977) The Hanford 67-Series; a volume of atmospheric field diffusion measurements, Report PNL2433 Battelle Pacific Northwest Laboratories. Nuclear Regulatory Commission (1972) Onsite meteorological programs. Safety Guide 23, Washington, D.C. Pasquill F. (1961) The estimation of the dispersion of windborne materials. Meteorology 90, 33-49. Sedefian L. and Bennett E. (1980)A comparison of turbulence classification schemes. Atmospheric Environment 14, 741-750. Turner D. B. (1964) A diffusion model for an urban area. J. appl. Met. 3, 83.