Evaluation of the TUPOS air quality dispersion model using data from the EPRI Kincaid field study

Atmospheric Environment Vol. 25A, No. 10, pp. 2187-2201, 1991. Printed in Great Britain.

000~6981/91 $3.00+0.00 Pergamon Press pie

EVALUATION OF THE TUPOS AIR QUALITY DISPERSION MODEL USING DATA FROM THE EPRI KINCAID FIELD STUDY D. BRUCE TURNER,*]" LUCILLE W. BENDER,~ JAMES O. PAUMIER~ a n d PHILLIP F. BOONE~ +,Applied Modeling Research Branch, Atmospheric Sciences Modeling Division, Atmospheric Research and Exposure Assessment Laboratory, Environmental Protection Agency, Research Triangle Park, NC 2771 l, U.S.A. and ~:Computer Sciences Corporation, Research Triangle Park, NC 27709, U.S.A. (First received 5 September 1989 and in final form 27 December 1990) Abstract--Data from SF6 tracer studies conducted at the Kincaid power plant in central Illinois by the Electric Power Research Institute in 1980 and 1981 have been used to evaluate the TUPOS air quality dispersion model. Most of the 96 h data are from periods representing daytime convective conditions when the impact of an elevated buoyant source would be expected to be greatest at ground level. Since on the order of 200 tracer measurement stations on four to six arcs were in operation during each hour of the study, a reasonable estimate of the maximum concentration along each arc could be made. The maximum concentration on each arc was the principal value used for purposes of comparing tracer measurements with model estimates. In addition to making comparisons between tracer and TUPOS estimates, comparisons were also made using the regulatory model MPTER. Although the means of residuals (model concentration minus tracer concentration) from the hourly maxima are both negative, TUPOS with a mean residual of - 32.6 ppt (parts per trillion) shows improvement over MPTER with a mean residual of -50.3 ppt. Tracer concentrations show 4 hourly maxima exceed 500 ppt. TUPOS estimates 3 and MPTER estimates 2 concentrations above 500 ppt. The performance results were used to suggest further changes to the TUPOS model. These consisted primarily of determining the fluctuation statistics and wind speed and direction for a height midway between effective plume height and ground level rather than at plume height. These changes were implemented and shown to provide improvement when tested on the dependent data set used to evaluate the original model. The mean of the residuals for hourly maxima for the REVISED TUPOS is -0.2 ppt showing a shift to almost no bias. The REVISED TUPOS estimates 5 hourly maxima exceeding 500ppt. Although the significance of the results for the revised model are not as great as they would be if an independent data set were used, these results are still useful in indicating the proper direction of changes to be made that can improve modeling. Key word index: Rural air pollution models, model evaluation, model performance, atmospheric diffusion, TUPOS model. INTRODUCTION In the U.S. point source modeling used to satisfy regulations, regarding the criteria pollutants SO2 and particulate matter, needs to make good estimates of the second-highest concentration (3-h and 24-h) within a year. Therefore the emphasis is upon the highest concentrations in the frequency distribution. However, other features of model performance such as good estimates of the mean, predicting the distance and azimuth of maxima and estimating maxima under the correct meteorological condition are of interest. Wanting to use input data more closely related to plume dispersion than the commonly used Pasquill stability classes, the initial T U P O S model (Version 1) was made available in 1986 (Turner et al., 1986). T U P O S is derived from letters from the phrase turbulence profile sigmas and is a Gaussian plume model with the dispersion estimated by the turbulence stat* Present affiliation: Trinity Consultants, Inc., 12801 N. Central Expwy., Suite 1200, Dallas, TX 75243, U.S.A. 2187

istics of standard deviation of wind azimuth angle, a a, and the standard deviation of wind elevation angle, ae, at plume level. Partial loss of the plume from the mixing layer is estimated by assuming that the vertical distribution of tracer within the plume is fairly uniform and the proportion of the plume remaining within the mixed layer is given by (mixing height - p l u m e bottom)/(plume t o p - p l u m e bottom). Vertical profiles of air temperature, wind direction, wind speed, and the two standard deviations mentioned above were assumed available as input data. These vertical profiles were assumed to have sufficient detail so that linear interpolation between data points would reflect the proper character of the atmosphere. The profiles of temperature and wind speed were used to calculate the plume rise through the various layers. Following Briggs (1985), a modification was made to add a 'hesitant plume algorithm' to be applied in certain convective situations. This resulted in T U P O S (Version 2). The algorithm treats situations where the plume has sufficient buoyancy to reach the top of the mixing layer but insufficient buoyancy to penetrate it

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D. BRUCETURNER et al.

readily. The plume temperature excess keeps the plume from appreciable initial downward spreading (therefore the plume hesitates) but dissipates through additional crosswind spreading over that normally expected. This second version (2.0) of TUPOS became available in 1986 (Turner, 1986).

A D D I T I O N A L MODIFICATIONS TO TUPOS

Plume rise

algorithm and the non-buoyant mixed-layer algorithm is used. Let C h be the concentration calculated by the hesitant-plume algorithm and Cm be the concentration calculated by the non-buoyant mixed-layer algorithm. The concentration is calculated from: C = [F*/F*(critical)] C h + { 1 - [F*/F*(critical)]} Cm. This resulting model is referred to as TUPOS in the rest of the paper. APPLICATION OF MPTER

The plume rise algorithm (Turner, 1985) in the original TUPOS calculated the plume top under stable conditions, but calculated the plume centerline under unstable conditions. This produced some inconsistencies which were, in part, remedied at the time of the addition of the hesitant plume algorithm. The calculation of the plume rise through layers was reconsidered and reprogrammed to calculate the plume top only. A consistent set of plume rise equations from Briggs (1984) is used for this methodology (see appendix). Non-buoyant mixed-layer algorithm Following the suggestion [section 3. (c)] of Gryning et al. (1987), a non-buoyant mixed-layer model was added to TUPOS.

In order to compare the TUPOS performance with a model in use for regulatory applications, the MPTER model was applied to the same database. MPTER is a Gaussian-plume model which uses Pasquill-Gifford dispersion parameters as functions of Pasquill stability class and downwind distance from the source. The plume rise algorithm considers the wind speed estimated at stack top and the near ground stability but does not consider the variation of temperature or wind with height. The relation of the plume with the mixing height is 'all or nothing'. If the plume centerline is estimated to be above the mixing height, ground-level concentrations are assumed to be zero. If the plume centerline is below the mixing height, the entire plume is assumed available for mixing through the layer.

Coefficient in hesitant plume At the incorporation of the 'hesitant plume algorithm' into TUPOS, Briggs (1985) indicated that a value of 7 for one of the coefficients appeared about correct. The results of the tank studies of Willis and Deardorff (1987), supported a value of 13 for this coefficient. The value of 13 was used in the model. This has the effect of lowering the magnitude of the concentrations calculated by the hesitant-plume algorithm. Selection of algorithm The selection of the algorithm to be used was changed slightly from what was suggested in the addendum to TUPOS (Turner, 1986). For all cases when the ratio, zl/L (zi is mixing height; L is Monin-Obukhov length), is greater than or equal to 10 the Gaussian plume algorithm is applied: (1) for positive zi/L, the stable form is used; (2) for negative zi/L, the unstable form is used for the estimation of the plume dispersion parameter, az, from the fluctuation statistic for elevation angle, % For cases with z~/L less than - 10, a critical dimensionless buoyancy flux, F*(critical), is determined from : -

F* (critical) = [(2/9) (z i -h)/zi]

5/3,

where h is the physical stack height, If the dimensionless buoyancy flux, F* [which is Fo/(U w.2 zi) where Fo is initial buoyancy flux, u is the wind speed at stack top and w* is convective scaling velocity] exceeds F* (critical), the hesitant-plume algorithm is used. Otherwise, a combination of the calculated concentrations from the hesitant plume

F O R M U L A T I O N OF A REVISED TUPOS

Upon completion of various analyses (to be discussed below) using TUPOS, it was concluded that there was evidence that modifications to the TUPOS would result in improved model performance. A new model was created by replacing the coefficient that was 13 in the hesitant plume model with 7 (the original value in the hesitant-plume algorithm) and estimating the following variables at a height half-way between the ground and effective plume height: a,, ~ro,transport wind speed and direction. The resulting model will be referred to as REVISED TUPOS. Chronologically the REVISED TUPOS was suggested by the analysis of the TUPOS concentrations and the model was formulated, model runs made, and comparison analyses made as a last step. It should be understood that the modeling results for the REVISED TUPOS should be better than for TUPOS since the data set used to test the REVISED TUPOS is the same one from which the suggestions to change the model were derived. Therefore one cannot have the same confidence in the REVISED TUPOS results one would have if an independent data set was used for the evaluation.

DATA AVAILABLE FOR M O D E L EVALUATION

The data from the tracer portion of the study conducted at the Kincaid power plant in central

TUPOS air quality dispersion model Illinois by the Electric Power Research Institute (EPRI, 1983) are nearly ideal for evaluating a model such as TUPOS. The tracer SF6 was injected into the stack ductwork and released through the stack. The plant has a single stack 187 m high. The surrounding terrain near the plant is gently rolling (having an estimated roughness length, zo, of 0.2 m.) consisting mostly of farmland but also a lake, with three fingers from 6 to 12 km long, each no wider than 2 km. Tracer experiments were conducted on 49 days over a period of about 15 months. On days that tracer studies were conducted, tracer was released over periods on the order of 6-9 h and hourly samples were taken on four to six arcs downwind at distances appropriate to the expected meteorological conditions. Rather than being perfect arcs, the arcs were somewhat irregular due to the orientation of roads used to service the samplers. However, the distance from the source of individual sampling stations was generally within 5% of that of the desired arc. In the order of 200 tracer samples were taken for each hour. The meteorological data supporting the study consist of a 100-m meteorological tower instrumented with temperature difference sensors between loo and 10m and between 100 and 50m, as well as a temperature sensor at 10m. Measurements of temperature difference between 10 and 2 m were made on a nearby 10-m mast. Wind speed and direction were measured at 10, 30, 50, and IOO m. Five-minute average turbulent fluctuation statistics in the horizontal, aa, were obtained at the 10-, 30-, 50-, and 100-m levels. Fiveminute average vertical fluctuation statistics, tr+, were obtained only at the loo-m level using a u, v, w system. Winds and temperatures above tower top were obtained from T-sondes released at approximately 1-h intervals during the period of tracer release. Lidar measurements to determine plume height and Doppler acoustic soundings for wind and mixing height information were also part of the study. Hourly values of tracer release rate, stack gas exit temperature, and stack gas exit velocity were available and were used with each model. Because of the low release rates the emissions were scaled upward by a factor of 1 million to avoid computer round off and truncation errors.

2189

the vertical profile of ae, the standard deviation of the elevation angle, sometimes referred to as cry.

SELECTING DATA SET TO BE USED

Preliminary testing of the running of TUPOS was accomplished with a 3-day set of data. This 'pilot study' was conducted to ensure that the data analysis performed by the MPDA was adequate and that the model ran correctly. Data from the MPDA were insufficient to run TUPOS for seven of the tracer experiments. Primarily this was due to missing profiles of horizontal and vertical fluctuations. Those experiments having sufficient data from the MPDA to run TUPOS were noted after removing the 3 days of the pilot study. Half of the remaining data were selected for use in this evaluation. This leaves an independent data set for use at a later time for additional model evaluation. Since adjacent calendar days may have similar meteorological conditions, every other available experiment was selected, rather than using a random selection procedure. The resulting experiments and hours available for the evaluation are listed in Table 1. This results in 96 h in 19 experiments (19 separate calendar days) available for the evaluation.

TRACER STATIONS AND MODEl+ RUNS

Files of the station designation (number) and Universal Transverse Mercator (UTM) coordinates of the tracer stations were compiled for each experiment (calendar day). Since these did not vary much hourly but did vary daily, this seemed to minimize the number of receptors for which calculations had to be made. Thus the running of the model TUPOS could be done on a calendar day (experiment) basis. The TUPOS model runs for the 19 experiments were made using a Microvax II computer. A conversion [T/(1.758 p)] was included in the model program to convert the concentration in mass per volume, (pg m -3) as normally calculated by the dispersion model, to volume tracer to volume of air (ppt). T is ambient temperature in degrees K; p is atmospheric pressure in millibars.

PROCESSING M E T E O R O L O G I C A L DATA

The tower and T-sonde meteorological data were read from magnetic tapes and assembled for input to the meteorological processor MPDA (Paumier et al., 1986). The 5-min tower data were analysed externally so that hourly values of the variables were available for input to MPDA. T-sonde information was transformed so that plots of potential temperature as a function of height could be made. These were used in determining the hourly mixing height. Since vertical fluctuations from the tower were only available at 100m, these data were used to assist in determining

THE CHARACTERISTICS OF THE 96 h OF S I M U L A T I O N

Table 2 gives a breakdown of the 96 h by zi/L and by the calculated interaction of the plume with zi. For the 4 h of stable conditions (z+/L > 0), the Gaussian plume algorithm in TUPOS is used. For the 9 h of full plume penetration, where the bottom of the plume is calculated to be above z~, ground-level concentrations are expected to be zero and no model is selected. For the 36 h of unstable-neutral conditions ( - 10 < z+/L < 0), with less than full penetration, the Gaussian plume

D. BRUCETURNER et al.

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Table 1. List of time periods used for TUPOS evaluation Experiment 1 3 5 7 9 11 13 15 18 20 22 24 26 28 30 33 44 46 48

Year

Month

Day

80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 81 81 81

APR APR APR MAY MAY MAY MAY MAY JUL JUL JUL JUL JUL JUL JUL JUL MAY MAY MAY

22 25 28 1 4 6 8 10 11 13 15 19 21 23 25 28 25 28 31

Hours beginning at: 13 11 14 15 06 11 09 10 09 11 09 08 12 09 14 10 14 09 05

12 15 16 07 12 10 11 11 12 10 09 13 10 15 11 15 10 06

13 16 17 08 13 14 12 12 13 11 15 11 16 12 16 12 07

No. hours 1 4 6 3 5 4 3 6 7 7 9 2 3 5 4 7 5 7 8

14 17 18 19 09 10 14 13 13 14 12

14 14 15 13

13 17 13 17 13 08

15

15 15 16 16 17 14 15 16 17

15 16 17 18 14 15 16 09 10 11 12

Total

96

Table 2. Characteristics of simulated hours. This defines the labels (POS, H3, etc.) for the groupings of the data according to meteorology which will be used as a shorthand in labeling some of the figures. H groups are modeled using the hesitant-plume algorithm of the model; those labeled M use the mixed-layer procedures (a weighted average of the hesitant-plume and a nonbuoyant mixed-layer algorithm); and G groups are modeled with the Gaussian algorithm. Plume penetration refers to the relationship of the modeled plume height to the mixed-layer height

zffL from zffL<-lO

L>O 4 (POS)

No. consideration of zi FULL model plume penetration Partial penetration; < 50% of model plume below z~ Partial penetration; > 50% of model plume below z~ No penetration; all of model plume below z~

--lOtoO

1 F* > F*(cr) 8 (H3) 11 (H2) 19 (HI)

8 F* < F*(cr) 1 (M) 8 (M)

10 (G3) 9 (G2) 17 (G1)

POS--L is positive (stable). FULL--Full penetration. G l ~ a u s s i a n , all of plume beneath. G 2 ~ a u s s i a n , partial penetration, > 50% below zl. G3~Gaussian, partial penetration, < 50% below zi. M--Mixed l a y e r - F * less than critical. HI--Hesitant plume, all of plume beneath. H2--Hesitant plume, partial penetration, > 50% below z~. H3--Hesitant plume, partial penetration, < 50% below z~.

a l g o r i t h m is used. F o r the 47 h of mixed-layer conditions ( z f f L < - 10), with less t h a n full penetration, a b u o y a n t mixed-layer algorithm, the hesitant-plume algorithm, is used for 38 h where F* > F*(critical); a n d a weighted c o m b i n a t i o n of the hesitant-plume algorithm a n d a n o n - b u o y a n t mixed-layer algorithm is used for the o t h e r 9 h where F* < F* (critical). Some of the analysis will be d o n e using these groupings of the data, at times referring to the designations indicated in parentheses in Table 2 beside the n u m b e r of data hours.

CONSIDERATION OF CONCENTRATIONS TO BE COMPARED T h e tracer m e a s u r e m e n t locations a p p e a r e d to be of sufficient density t h a t a near centerline c o n c e n t r a t i o n b e n e a t h the plume o n nearly all sampling arcs could be determined. Figure 1 shows a plot of m e a s u r e d tracer c o n c e n t r a t i o n s (diamonds connected with solid lines), hereinafter referred to as tracer, a n d model c o n c e n t r a t i o n s (triangles connected with dashed lines) as a function of a z i m u t h from the source for a given

TUPOS air quality dispersion model arc. The top of Fig. 1 is an example of one of the hours with well-behaved tracer concentrations along an arc. The bottom of Fig. 1 shows a more typical situation with large variability of tracer concentrations at adjacent stations. The tracer data were examined for each arc and a subjective estimate of the quality on a 3point scale [from 3 (best) to 1 (poorest)] was assigned. In general this judgement was made by using a 3 for an arc with a number of non-zero concentrations showing a definite peak with lower concentrations to each side (the top part of Fig. 1 is an example), a 2 for a number of non-zero concentrations but with high and low concentrations (sometimes zero) intermittantly along the arc (the bottom part of Fig. 1 is an example), and a 1 for the highest concentration given by perhaps only a single non-zero measurement location. If the tracer concentration at all sampling stations on the arc was zero, a quality of 1 was also used. Some of the analyses are done partitioning the data according to this subjective quality. In addition a maximum concentration for each arc distance could be determined for the model. It was therefore decided early in the analysis that the emphasis would be on comparisons of concentration maxima for each sampling arc distance. Additional comparisons will be made in terms of the difference in azimuth from the source of the position of the tracer maximum and the model maximum. USE OF FRACTIONAL ERRORS

The fractional error, FE, can be used as a measure of comparison of model and tracer data. We have used the following definition letting M equal the model concentration and T equal the tracer concentration: F E = 2 ( M - T)/(M + T).

Sometimes F E is defined with the reverse sign of our definition here, that is, using T - M instead of M - T. We have used the above definition because it is intuitively satisfying for F E to be positive whenever the model overestimates the concentration compared to the tracer, and for F E to be negative whenever the model underestimates. The fractional error has the characteristics that it is zero if both concentrations are the same, it has a range from - 2 to +2, and is symmetrical for concentrations that are within a factor of each other. F o r example if the modeled concentration is double the tracer, F E = 0.67; if the modeled concentration is half the tracer, F E = 0 . 6 7 . F E is mathematically undefined if both concentrations are zero. F E is + 2 or - 2 if one of the concentrations is zero and the other is non-zero, regardless of its magnitude. Although F E can be a useful measure of performance, it does have limitations (such as any magnitude modeled concentration with zero tracer will result in an F E of 2; both concentrations of zero result in F E being undefined) and therefore will not be the only measure used.

2191

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EXAMINATION OF TUPOS PERFORMANCE Using data for each of the 580 arc-hours, plots of fractional error (from the arc maxima) as a function of the distance from the source were made with a separate plot for each meteorological condition. Although those plots were useful in seeing how the models performed for different meteorological conditions, they are not presented here. For the Gaussian cases (G 1, G2, G3) the T U P O S estimated the concentration to be zero at near distances (0.4-2.0km) and overestimated concentrations at the far distances (greater than 5.0km). Quite in contrast to this, the hesitant plume cases (HI, H2, H3) were characterized by a

2192

D. BRUCETURNER et al.

Table 3. Mean residuals and concentrations for TUPOS, MPTER and REVISED TUPOS by meteorological condition. See Table 2 for explanations of meteorological conditions Meteorological condition No. hours

Arc hours

All POS FULL GI G2 G3 M H1 H2 H3

Mean residuals

4 9 17 9 10 9 19 11 8

TUPOS

MPTER

580

-9.19

- 18.62

21 53 109 53 67 48 104 70 55

- 11.70 -46.28

- l 1.70 -46.28 30.61 5.12 - 39.86 13.74 -57.38 21.57 - 95.29

54.59

35.58 - 18.33 49.00 -61.84 -28.53 - 57.46

Mean concentrations REVISED TUPOS

Tracer

TUPOS

MPTER

REVISED TUPOS

13.53

73.53

64.35

54.91

87.07

- 11.69 -46.28 65.27 75.67 - 1.23 60.45 -21.86 6.78 - 29.05

11.70 46.28 60.86 64.09 39.86 89.54 119.59 75.34 95.29

0.00 0.00 115.44 99.66 21.53 138.54 57.74 46.80 37.83

0.00 0.00 91.47 69.20 0.00 103.28 62.20 96.91 0.00

0.01 0.00 126.13 139.75 38.63 149.99 97.73 82.12 66.24

Table 4. Mean residuals and concentrations for TUPOS, MPTER and REVISED TUPOS by distance Mean residuals Dist. (km)

Number

TUPOS

MPTER

Mean concentrations REVISED TUPOS

Tracer

TUPOS

MPTER

REVISED TUPOS

All

580

-9.19

- 18.62

13.53

73.53

64.35

54.91

87.07

0.4 0.5 1.0 2.0 3.0 5.0 7.0 10.0 15.0 20.0 30.0 40.0 50.0

7 29 47 50 91 78 78 62 55 39 20 5 19

--85.63 - 13.10 -34.39 -26.35 -29.18 - 12.96 - 20.63 12.18 26.42 41.48 -21.63 -19.26 29.69

-85.63 - 13.38 -31.66 -33.12 -40.13 - 9.08 - 1.24 -39.82 17.94 14.32 - 55.33 -21.38 - 3.93

-85.63 -3.70 0.34 14.79 7.82 19.94 3.28 26.98 34.43 39.57 - 14.64 -19.70 29.51

85.63 13.38 41.66 62.51 92.01 94.73 88.90 90.92 65.22 55.55 90.06 21.38 30.66

0.00 0.27 7.27 36.16 62.83 81.77 68.27 103.10 91.63 97.03 68.42 2.12 60.35

0.00 0.00 10.00 29.39 51.88 85.65 87.65 51.10 83.16 69.87 34.72 0.00 26.73

0.00 9.67 42.00 77.30 99.83 114.67 92.18 117.90 99.65 95.12 75.42 1.68 60.17

general underestimation, again with the model primarily estimating zero at the near distances. The relatively few overestimates were at the greater distances, but there were also a n u m b e r of underestimates at the far distances. The mixed-layer category with F* less than critical (M) is d o m i n a t e d by overestimates. Table 3, which displays the mean residuals and mean concentrations for all arc-hour maxima by meteorological condition shows the overestimation in the mean for G1, G2, and M and underestimation for HI, H2, H3 and also G3. Table 4 with mean residuals and mean concentrations with distance shows the general underestimation of T U P O S at closer distances and some overestimation at greater distances. It should be n o t e d that the highest tracer concentration was 706.0 ppt measured on the 30 km arc at hour 08 during experiment 24. This measurement was assigned a quality of 1 since concentrations along the arc are up and d o w n with the second highest concentration equal to 57.7 ppt at a receptor 10 ° azimuth away from the 706.0 ppt. F o u r other receptors between these two along the arc had lower concentrations (10.9-

32.2 ppt). Although this concentration of 706.0 ppt is suspiciously high (the m a x i m u m on the 20 k m arc was 85.1 ppt and the m a x i m u m on the 40kin arc was 59.1 ppt), there is certainly evidence that the tracer was reaching the sampling array at a n u m b e r of sampling sites. F o r this hour the T U P O S estimates full penetration of the plume t h r o u g h the 200-m mixing depth (only 13m above stack top). The T-sonde plot was examined to see if the mixing height estimate might be in error. There was a very strong inversion of potential temperature and no evidence that the mixing height might be any higher. In fact, the estimate for the next h o u r was also 200 m, so that the mixing height was not increasing rapidly with time. The 706.0ppt tracer concentration was retained and is included in all statistics and figures which use data of all qualities.

EXAMINATION OF MPTER PERFORMANCE

In applying the M P T E R to this database, the wind speeds at the lO-m height from the Kincaid data were used with cloud cover and ceiling height from the

TUPOS air quality dispersion model Peoria National Weather Service airport station (about l l 0 k m to the north) in order to estimate the Pasquill stability class. It was found that the model estimated zero ground-level concentrations for 45 of the 96h. This is due to two factors: (1) a plume rise algorithm is used which does not consider the variation of temperature or wind with height except to extrapolate the surface wind to stack top; and (2) the model employs an all-or-nothing principle for interaction of plume and mixing height--a plume centerline above the mixing height results in zero groundlevel concentrations. There are only 4 h with tracer concentrations equal to zero at all tracer measurement locations. Figure 2 displays the plume height estimates from both TUPOS (squares) and MPTER (triangles) related to the mixing height. It is obvious that there are many cases with plume rise estimated much higher with the MPTER. The plume height and the mixing height are quite critical to the estimates of concentration made by all the models. Verification of values of these two variables were not made as part of this study. Note that in Table 4, MPTER underestimates the mean concentration at all but two distances, 15 and 20km, but has means within 10ppt for three other distances: 5, 7, and 50 km. Looking at mean concentrations and residuals by meteorological condition (Table 3), MPTER estimates zero concentrations (as does TUPOS) for the cases POS and FULL. MPTER also estimates zero for the conditions G3 and H3, those that the TUPOS plume rise considers as partial penetration with less than 50% of the plume beneath the mixing height. It is also of interest that the highest mean concentration is estimated for the same condition, M, as the highest mean from TUPOS.

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2193 FRACTIONAL ERRORS

Table 5 shows the distribution of fractional errors calculated from the tracer maximum on an arc and the model maximum on the same arc for the same hour for tracer maxima considered as quality 3 or 2. By selecting the fractional error bounds shown it is easy to see what proportion of the model estimates are within 25 and 50% and within a factor of 2 or 3 of the tracer concentrations. Note from the information below the body of the table that for both TUPOS and MPTER about 10% of the estimates are within 25% and 18% are within 50%. Those estimates within a factor of 2 are 30% for TUPOS and 26% for MPTER. Estimates within a factor of 3 are 48% for TUPOS and 39% for MPTER.

CONSIDERATION

OF HOURLY MAXIMA

Some comparisons were made of the tracer maximum for each hour (independent of arc distance and azimuth) with the model maximum for the same hour. The resulting distribution of residuals are shown in Fig. 3. The entire rectangle for each 50 ppt interval is for data of all qualities. The hatched portion is for data of qualities 3 and 2. In spite of the large number of calculated zeros with the MPTER, the distribution of the residuals peak in the same interval and have outliers extending to approximately the same values as TUPOS. Although the mean residual for TUPOS (-32.62ppt) represents less underestimation than MPTER (with a mean residual of -50.38 ppt), the difference is not great. The distribution of the tracer and model concentrations (hourly maxima) are shown in Fig. 4. Since the 45 zeros are significant in the MPTER distribution, the TUPOS comes a bit closer in reproducing the tracer distribution and has an estimated highest maximum in the same 50ppt range as that of the highest maximum tracer. Table 6 shows the distribution of the distances of the hourly maxima. The tracer maxima are most frequent (18) at 3 km. The TUPOS maxima are most frequent (20) at 15 km; the MPTER maxima are most frequent at 7 km. Note that although there are 8 of the 96 h with tracer maxima at 1 km or less, there are no occurrences of model maxima at distances less than 2 km.

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UIXING HEIGHT(M)

Fig. 2. Plume height for TUPOS (squares) and MPTER (triangles)as a function of mixing height for the same hour.

Except for the 4 h with tracer concentrations equal to zero at all receptors, a receptor position with highest concentration for the hour and the azimuth of that receptor from the Kincaid stack can be determined. The azimuth of the model plume transport is also available. Figure 5 shows the distribution of the

2194

D. BRUCE TURNER et al. Table 5. Distribution of fractional errors for 316 arc-hours (includes only data of qualities 3 and 2. Note that by definition these qualities include no zero tracer concentrations. If a tracer concentration and model concentration are equal, the F E is assigned a value of 0)

Fractional error

TUPOS

=2.0 > 1.0, < 2.0 >0.667, < 1.0 >0.4, <0.667 >0.222, <0.4 >0.0, <0.222

MPTER

43 32 25 11 20

REVISED TUPOS

28 32 15 16 20

=0.0

58 32 34 10 25

1

> - 0 . 2 2 2 , <0.0 >-0.4, <-0.222 >-0.667, <-0.4 > - 1.0, < -0.667 > - 2.0, < - 1.0 = -2.0 Total

14 14 13 23 85 36

10 10 11 9 43 121

14 8 23 28 64 20

316

316

316

(Decimals below are frequencies in Within+and-25% (34) Within + a n d - 50% (59) Within a factor of 2 (97) Within a factor of 3 (152) Outside a factor of 3 Over Under Modeled as zero

parentheses divided by 316.) 0.108 (31) 0.098 0.187 (57) 0.180 0.307 (83) 0.263 0.481 (124) 0.392

(39) (57) (114) (174)

0.123 0.180 0.361 0.551

(164) 0.519 (43) 0.136 (121) 0.383

(192) 0.608 (28) 0.089 (164) 0.519

(142) 0.449 (58) 0.184 (84) 0.266

(36) 0.114

(121) 0.383

(20) 0.063

Note: FE of 0.222 = 25% error; 0.4 = 50% error; 0.667 = a factor of 2; 1.0 = a factor of 3; 2.0=model is non-zero, tracer is zero; - 2 . 0 = m o d e l is zero, tracer is non-zero.

Table 6. Frequency of distance of hourly maximum. The line, 'zero concentration' refers to the number of hours that concentrations at all receptors are modeled to be zero, hence the maximum concentration is also zero and no determination of the distance to the maximum can be made. Frequencies in parentheses are for qualities 3 and 2

Tracer Zero concentration Distance (km) 0.4

4

TUPOS

MPTER

REVISED TUPOS

15

45 (24)

12

2 (1) 11 (10) 5 (5) 12 (11) 18 (15) 20 (15) 5 (3) 3 (3) 5 (4) 96 (67)

2 (2) 3 (3) 10 (8) 11 (10) 6 (5) 8 (5) 7 (6) 4 (4)

7 (5) 14 (14) 11 (9) 10 (10) 11 (9) 20 (13) 4 (2) 3 (3) 4 (2) 96 (67)

4 (4)

0.5

2 (1)

1.0 2.0 3.0 5.0 7.0 10.0 15.0 20.0 30.0 50.0 Totals

2 (1) 6 (3) 18 (15) 13 (11) 14 (9) 12 (10) 9 (6) 5 (3) 6 (3) 1 (1) 96 (67)

differences o f t h e s e a z i m u t h s (model p l u m e a z i m u t h m i n u s a z i m u t h o f tracer m a x i m u m ) . F o r T U P O S the p l u m e t r a n s p o r t direction is d e t e r m i n e d using m e t e o r o l o g i c a l d a t a e s t i m a t e d at p l u m e level. F o r

96 (67)

T U P O S this difference has h i g h e s t f r e q u e n c y in the 10-20 ° r a n g e a n d 27 o f 92 h (29%) are within + 10 °. F o r M P T E R the p l u m e t r a n s p o r t d i r e c t i o n is determ i n e d using t h e onsite 10-m wind. F o r M P T E R this

TUPOS air quality dispersion model

2195

b) 15.

N

--

MPTER

g6

L,J 10 ¸

--750

--~00

--250

RESIDUALS

250

MODEL

(PPT)

25

- -

500

TRACER)

i

i

20

o) T U P O 5 N = 95 MEAN;

--32.62

I~1

~" ~o

--750

--500

--250

RESIDUALS

250

0

'MODEL

(PPT)

- -

500

7:,0

TRACER)

25

20 ~.~ 1 5

{-]

c)

I[ N -- 96 MEAN:

REVISED TUPOS

II --

o,

6

II

5

O

--750

--500

--250

RESIDUALS

0

(PPT)

250

(MODEL

- -

500

750

TRACER)

Fig. 3. Residual (model concentration minus tracer concentration) distributions from hourly maxima for (a) TUPOS; (b) M PTER; and (c) REVISED TUPOS. The entire rectangle is for data of all qualities. The hatched portion is for data of qualities 3 and 2. The statistics are for all qualities.

difference has highest frequency in the - 10 to 0 ° range and 30 of 92 h (33%) are within + 10 °. The means are greatly affected by the outliers in the less than - 5 0 range. We consider the modes to be of greatest interest. The position of the modes is consistent with the expected mean relations of wind direction with height, a general veering (turning clockwise) of the wind with height.

DISCUSSION OF RESULTS AND RECOMMENDATIONS FOR A REVISED MODEL

Both TUPOS and MPTER generally estimate maximum concentrations at greater distances than the distance of maximum shown by the tracer measurements and there is, in the mean, an underestimation of concentrations. It was felt that some modifications

D. BRUCE TURNER et al.

2196

CONCENTRATION DISTRIBUTIONOF HOURLY ~AXII,~

CONCENTRATIONDISTRIBUTIONOFHOURLYMAXIMA 50

50

o) TRACER

N=96

40

N=96

40

c) MPTER 134.7

MEAN: 173.7

MEAN:

STDDE-V:107.3

STD D~: 151.8 3O

3O Z

Z to D

w D

o

o

7,

to

E

~- 20

u. 20

10

10

n ZERO

0

250

500

750

ZERO

O

CONCENTRATION(PPT)

250

500

7~o

CONCENTRATION (PPT)

CONCENTRATION DISTRIBUTIONOF HOURLY I~II,~

CONCENTRATION DISTRIBUTIONOF HOURLY klAXlIdA 50.

S0

N=96 MEAN:

40¸

b) TUPOS

N = g6

40

~E~:

160.8

d) REVISED m971

TUPOS

STDDEv: 1794

STD DE'V: 156.2 3O

30 ¸ Z w D

Z w D

o

o

Lg OC

to

L 20

20

10

IO

ZERO

250

500

750

CONCENTRATION (PPT)

ZERO

0

250

500

750

C 0 N C EN T~ TK,-,-,-,-(PPT) ,-,-,-,-,-~

Fig. 4. Concentration distributions of the 96 h maxima for (a) tracer; (b) TUPOS; (c) MPTER; and (d) REVISED TUPOS. The entire rectangle is for data of all qualities. The hatched portion is for data of qualities 3 and 2. The statistics are for all qualities.

could be made to the T U P O S to shift results in the proper direction. In view of the underestimations in the mean for the three hesitant-plume conditions shown in Table 3, it would seem appropriate to return to the use of the coefficient 7 rather than 13 in the hesitant-plume model. This should increase concentrations for these meteorological conditions.

Since any diffusion of material from plume level to ground level must descend through those atmospheric layers between the plume centerline and the ground, it would seem quite reasonable to use dispersion parameters representative of the entire layer. Therefore determining ~r,, (re, and plume transport wind speed at the height half-way between the ground and plume centerline may be more representative of the actual

TUPOS air quality dispersion model

2197

N -- 9 2 MEAN: -- 1 5 . 4 STO DEV: 47.6

20"

13)

MPTER

~- 1 0 .

5"

<-~

MO~)EOL

~LUM-E3Oz~T-

N = 92 MEAN: STD DEV:

~ o_

AZIMUTH

20F

T R ' ~ C E " # M~'XOIMUM ~"

o)

--2.0 47,7

"

'

TOPOS

I i

15" Z

® < --:50

--~0

MODEL

--40

--130

PLUME

--.20

NNNNN

--1O

AZIMUTH

0

10

-- A Z I M U T H

20

OF

"tO

,L0

TRACER

~0

)~50

MAXIMUM

25

N -- 9 2 MEAN: --11.9 STEI D E V : ~ 1 . 1

¢)

~ ~

REVISED TUPOS

N N

'<--50

--~0

MOOEL

--40

130

PLUME

--20

--I0

AZIMUTH

0

10

-- A Z I M U T H

20

30

40

OF" T R A C E R

~0

~'*~0

MAXIMUM

Fig. 5. The distributions of model plume azimuth minus azimuth of tracer maximum (from the source for (a) TUPOS; (b) MPTER; and (c) REVISED TUPOS. The entire rectangle is for data of all qualities. The hatched portion is for data of qualities 3 and 2. The statistics are for all qualities.

atmospheric processes. Since tre is generally larger at a lower height, this will have the effect of increasing the ground-level concentration and moving the point of m a x i m u m closer to the source. Using the wind direction for the height half-way between the ground and plume centerline should also

improve the estimation of the azimuth of the maximum concentration. Using the above ideas a R E V I S E D T U P O S was created and executed using the 96 h of data. Results of using this model appear in all tables and figures already presented.

2198

D. BRUCETURNERet RESULTS OF THE REVISED TUPOS

For a model to be of greatest use for many regulatory purposes, it should not underestimate concentrations in the mean and it should estimate the magnitude of the highest concentrations reasonably well. Although the direction of the maximum concentration each hour is unimportant as models are used for regulation in the U.S., correctly estimating this azimuth is a desirable modeling characteristic. Table 3 shows that for arc maxima of all qualities both T U P O S and M P T E R underestimate in the mean, and the R E V I S E D T U P O S slightly overestimates (the mean residual is 13.53ppt). As might be expected, since the plume rise remains unchanged in the revised model, the performance for conditions POS and F U L L remain unchanged. For H conditions, mean concentrations are nearly double those of the original model which represents an improvement, although concentrations are still underestimated in the mean for two conditions. F o r the G conditions, concentrations for two conditions were overestimated in the mean for the T U P O S . The concentrations for these two conditions are overestimated to a greater extent with the R E V I S E D T U P O S . This is also true of the M condition. Table 4 shows that mean residuals for the five distances from 1 to 7 k m shifts from negative to positive in shifting from T U P O S to R E V I S E D T U P O S . Table 6 shows that there are now 3 fewer hours with zero concentrations at all receptors and there are higher frequencies of maximum concentration occurring at the closer distances, 32 h with maximum at distances from 2 to 5 k m compared to 18h with maximum at these distances with the original model. Therefore some shifts have occurred in the desirable direction.

al.

Table 5 which considers arc-hour concentrations of qualities 3 and 2, shows about the same proportion within 25% and within 50% (12% and 18%) for the original and revised models. However estimates within a factor of 2 increases from 31% to 36% and estimates within a factor of 3 increases from 48% to 55%. Figures 3, 4, and 5 consider only the comparison of hourly maxima. In Fig. 3 the distribution of the residuals for the R E V I S E D T U P O S is not greatly different from those for T U P O S but does have a mean much closer to zero. The concentration distribution for R E V I S E D T U P O S shown in Fig. 4 does match those for the tracer concentrations more closely than does T U P O S . The R E V I S E D T U P O S estimates 5 h with hourly maxima exceeding 500 ppt. The tracer measurements have 4 in this range and T U P O S estimated 3. The mode of the R E V I S E D T U P O S distribution has shifted away from zero, more in line with the tracer distribution. As shown by Fig. 5 the use of the wind information for the height half-way between plume height and the ground has shifted the mode to the 0-10 ° range (between T U P O S and MPTER). There are 34 of the 92 h with estimated plume transport directions within + 10 ° of the azimuth of the plume maximum, compared to 30 for M P T E R and 27 for T U P O S . The mean difference shifts more negative, - 1 1 . 9 ° for the R E V I S E D T U P O S compared to - 2 . 0 ° for T U P O S due to an increase in the frequency of values in the less than - 50 ° range. Table 7 show the frequency distributions of the arc maxima for each hour for all data and for data of qualities 3 and 2. Tracer measurements show four concentrations above 500 ppt, T U P O S estimates five and the R E V I S E D T U P O S nine with M P T E R three. Tracer measurements show 22 concentrations above

Table 7. Frequency distribution of arc maximum concentrations for tracer, TUPOS, MPTER, and REVISED TUPOS. Numbers are for all qualities; numbers in parentheses are for qualities 3 and 2 Concentration range (ppt)

Tracer

TUPOS

1 1

1 (1)

MPTER

REVISED TUPOS

750:800 700:750 650:700 600:650 550:600 500:550 450:500 400:450 350:400 300:350 250:300 200:250 150:200 100:150 50:100 0.1:50 0:

1 (1) 2 (2) 2 (2) 5 (3) 8 (6) 24 (23) 31 (28) 75 (71) 126 (88) 228 (90) 74

1 (1) 1 (1) 2 (2) 2 (2) 4 (4) 10 (10) 9 (9) 11 (9) 18 (16) 32 (26) 29 (26) 83 (60) 196 (113) 181 (36)

1 tl) 2 (1) 2 (2) 3 (3) 4 (2) 8 (6) 18 (13) 13 (8) 36 (25) 42 (34) 51 (40) 92 (60) 308 (121)

1 (1) 1 (1) 1 (1) 2 (2) 2 (2) 2 (1) 2 (2) 9 (7) 13 (9) 11 (9) 18 (16) 26 (23) 33 (25) 38 (28) 108 (81) 170 (88) 143 (20)

Totals

580 (316) 580 (316)

580 (316)

580 (316)

2 (2)

T U P O S air quality dispersion model

2199

Table 8. Comparison of T U P O S , M P T E R and REVISED T U P O S for all hours

MPTER

REVISED TUPOS

102.28 126.33

74.60 106.02

127.56 139.02

Mean fractional error Std. dev of FE

-0.443 1.172

-0.802 1.249

-0.166 1.113

Mean residual Std. dev. of residuals

-3.48 136.85

-31.16 131.36

21.80 145.22

64.35 106.27

54.91 97.21

87.07 125.17

-0.819 1.284

-0.310 1.319

Tracer

TUPOS

Select quality data 316 arc-hours Mean conc. (ppt) Std. dev. of conc.

105.76 84.72

Data of all qualities 580 arc-hours Mean conc. (ppt) Std. dev. of conc.

73.53 87.63

Mean fractional error Std. dev of FE

-0.574 1.286

Mean residual Std. dev. of residuals

-9.19 114.66

- 18.62 121.73

13.53 129.02

Table 9. Comparison of T U P O S , M P T E R and REVISED T U P O S for unstable Gaussian (36h) and mixed-layer (47 h) conditions on all arcs For unstable Gaussian hours (G1, G2, G3) REVISED TUPOS (Theor. Sigmas)

MPTER

REVISED TUPOS

130.97 141.86

62.07 98.24

151.46 144.47

Mean fractional error Std. dev of FE

-0.024 1.218

--0.820 1.235

Mean residual Std. dev. of residuals

59.58 127.16

--9.31 96.64

80.07 131.05

122.29 147.01

84.32 123.18

59.55 99.49

103.68 131.36

162.61 161.30

Mean fractional error Std. dev. of FE

-- 0.298 1.341

-- 0.729 1.321

- 0.036 1.360

Mean residual Std. dev. of residuals

28.86 108.92

4.09 103.09

48.22 118.01

MPTER

REVISED TUPOS

84.30 110.63

85.07 110.74

113.50 133.50

-0.704 1.040

-0.763 1.260

-0.382 0.971

Tracer

TUPOS

Select quality data 129 arc-hours Mean cone. (ppt) Std. dev. of cone.

71.39 43.86

0.198 1.182

193.68 150.75 0.583 1.021

Data of all qualities 229 arc-hours Mean cone. (ppt) Std. dev. of cone.

55.46 50.39

For mixed layer hours (M, HI, H2, H3) Tracer

TUPOS

Select quality data 183 arc-hours Mean cone. (ppt) Std. dev. of cone.

131.07 97.30

Mean fractional error Std. dev. of FE Mean residual Std. dev. of residuals

-46.77 127.11

-46.00 150.33

-17.57 142.09

65.03 98.32

65.74 103.26

96.59 127.26

-0.573 1.226

-0.730 1.295

-0.236 1.222

Data of all qualities 277 arc-hours Mean cone. (ppt) Std. dev. of cone. Mean fractional error Std. dev. of FE Mean residual Std. dev. of residuals

AE¢~)

25:10-J

98.37 101.55

-33.35 115.45

-32.63 138.28

-1.79 137.97

0.530 1.233 107.15 158.59

2200

D. BRUCETURNERet al.

250ppt; T U P O S estimates 41, REVISED T U P O S 62, and MPTER 38. In spite of the increased frequencies of these higher concentrations, the mean concentrations as shown in Table 8 are still lower than the tracer measurements for both T U P O S and M P T E R for both qualities. The REVISED T U P O S has a mean residual of 14 ppt for all data and 22 ppt for data of qualities 3 and 2.

TESTING OF THEORETICALFLUCTUATIONSTATISTICS Realizing that the estimation of a e has considerable effect on concentration estimates for the unstable Gaussian hours, a modified model was created that would estimate both the horizontal and vertical dispersion from the theoretical equations (Equations 7 and 18a) in Gryning et al. (1987). These were applied so that the estimates of a e and aa were for half-way from ground to plume height, similar to the REVISED TUPOS. For most hours this results in larger estimates of both horizontal and vertical dispersion and higher ground-level maxima. The summary results are given at the right side of Table 9. The mean concentration is about three times the tracer concentration for all arc maxima (REVISED T U P O S estimated concentrations are nearly double). Although the theoretical aa is generally somewhat larger than that derived from extrapolating the tower measurements to half-way between ground ar 1 plume level, the plume impact at the ground is large.' primarily because the theoretical (re estimates are greater. For select data (qualities 3 and 2) the estimated mean concentrations using the theoretical sigmas are nearly three times the tracer measurement mean (REVISED T U P O S is not quite double the tracer).

COMPARISON FOR GROUPINGS OF METEOROLOGICAL

1981 at the Kincaid power plant in central Illinois by the Electric Power Research Institute. Comparison is made with a model currently used for regulatory modeling, MPTER. Although the means of residuals from the hourly maxima (TUPOS: -32.6; MPTER: - 5 0 . 4 ) are not greatly different, the T U P O S shows subjective improvement. The performance results were used to suggest further changes to the T U P O S model. These consisted primarily of determining the fluctuation statistics and wind speed and direction for a height midway between effective plume height and ground level rather than at plume height. These changes were implemented and shown to provide improvement when tested on the dependent data set used to evaluate the original model. The REVISED T U P O S displays better performance with regard to the azimuth of the hourly maximum. The mean of the residuals for hourly maxima (model concentration minus tracer concentration) for the revised model was - 0.2 ppt; the mean of residuals for the original model was -32.6ppt. Using data of all qualities for the 580 arc maxima for all hours, the mean residual for T U P O S was - 9.2 ppt; for REVISED T U P O S was 13.5 ppt. This results in a shift from underestimation of the concentration for the original model to overestimation with the revised model, a more desirable trait for regulatory modeling. Although the significance of the results for the revised model are not as great as they would be if an independent data set were used and the authors may be accused of 'tuning the model', these results are still useful in indicating the proper direction of changes that can improve modeling. Acknowledgements--The authors want to thank Thomas E.

Pierce and David Dodd for their assistance in processing the meteorological, and tracer data from the magnetic tape data sources; John S. Irwin for his discussions and suggestions on analysis of the model results; and Sylvia B. Coltrane for her secretarial assistance.

CONDITIONS For those interested in the performance measures of Table 8 separated by meteorological conditions, Table 9 indicates the performance for mixed-layer hours and for unstable Gaussian hours. As indicated in the previous section, the REVISED T U P O S overestimates concentrations in the mean for the unstable Gaussian hours. For the mixed-layer hours all models underestimate concentrations but the REVISED T U P O S does better in the mean but not as well for the select data as for the entire data set.

CONCLUSION The performance of the model T U P O S has been examined using the maximum concentration on each arc as well as the maximum concentration for each hour. These are from data for 96 h, half of the available data, from the tracer studies conducted in 1980 and

Disclaimer Although the research described in this article has been supported by the U.S. Environmental Protection Agency, it has not been subjected to Agency review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.

REFERENCES

Briggs G. A. (1984) Plume rise and buoyancy effects. In Atmospheric Science and Power Production (edited by Randerson D). Chapter 8, pp. 327 366. DOE/TIC-27601. Technical Information Center. U.S. Department of Energy [available as DE84005177 (DOE/TIC-27601) from NTIS]. Briggs G. A. (1985) Analytical parameterizations of diffusion: the convective boundary layer. J. clim. appl. Met. 24, 1167-1186. Electric Power Research Institute (1983) Plume Model Validation Field Measurements--Flat Terrain Site Kincaid, Illinois. EPRI Report Number EA-3064. EPRI, Palo Alto,

CA 94304. Gryning S. E., Holtslag A. A. M., Irwin J. S. and Sivertsen B. (1987) Applied dispersion modeling based on meteorologi-

TUPOS air quality dispersion model cal scaling parameters. Atmospheric Environment 21, 7989. Paumier J., Stinson D., Kelly T., Bollinger C. and Irwin J. S. (1986) MPDA-I: A Meteorological Processor for Diffusion Analysis--User's Guide. EPA-600/8-86/011. U.S. Environmental Protection Agency, Research Triangle Park, NC (available only from NTIS, Accession Number PB 86-171 402/AS). Turner D. B. (1985) Proposed pragmatic methods for estimating plume rise and plume penetration through atmospheric layers (preliminary communication). Atmospheric Environment 19, 1215-1218. Turner D. B. (1986) Addendum to TUPOS--lncorporation of a Hesitant Plume Algorithm. EPA-600/8-86/027. U.S. Environmental Protection Agency, Research Triangle Park, NC (available only from NTIS, Accession Number PB86-241 031/AS). Turner D. B., Chico T. and Catalano J. A. (1986) T U P O S - - A Multiple Source Gaussian Dispersion Algorithm Using Onsite Turbulence Data. EPA-600/8-86-010. U.S. Environmental Protection Agency, Research Triangle Park, NC (available only from NTIS, Accession Number PB 86-181 310/AS). Willis G. E. and Deardorff J. W. (1987) Buoyant plume dispersion and inversion entrapment in and above a laboratory mixed layer. Atmospheric Environment 21, 1725-1735. APPENDIX: PLUME RISE USED IN TUPOS Assuming a top hat distribution of the plume with the plume thickness equal to the plume rise, the top of the plume, above the stack, is 1.5 times the plume rise and the plume bottom is 0.5 times the plume rise, also above the stack top. An initial estimate of the plume top, t, is determined using 1.5 times Equation 8.98, p. 351 in Briggs (1984): t = 1.5 {1.54 [fo/(UU*2)]2/ahl/3}. Using this estimate of the top of the plume above the stack top, an iterative estimate is made using 1.5 times Equation 8.97, p. 350: t = 1.5{ 1.2[Fo/(U u*2)]3/5(h q- 0.67 t) 2/5}.

(1)

If the convective scaling parameter, H*, (Turner, 1986) is positive, an additional estimate is made from 1.5 times

2201

Equation 8.101, p. 351:

t = 1.5{3[Fo/u]3/SH *- 2/5}.

(2)

For unstable conditions the lower of these two estimates is used for the plume top. For stable conditions where dO/dz exceeds 0.001 Km - t, the lower of the two estimates above are set aside and two further equations are evaluated. The first is 1.5 times Equation 8.71, p. 344:

t = 1.5 {2.6[Fo/(U s)] 1/3}.

(3)

where s = 9.806 (dO/dz)/T and d is the stack top diameter. The second is Equation 8.67, p. 343, with the coefficient set at 5.9 for estimating the plume top: t = 5.9 [Fo/s 3/2] 1/4 __3d.

(4)

The lower of these two estimates is then compared with the estimate set aside above and the lower value taken as the estimate of the stable plume top. If the estimate of the plume top is within the layer of meteorological conditions being considered, the plume rise is assumed to have been found and the plume top is t meters above the stack and the effective plume height is at 2/3 t. If t is above this layer, it is assumed to reach into the next layer. An estimate is made of the residual buoyancy flux, FR, existing at the top of this layer and is used for estimating the additional rise in the next layer. The FR is estimated from one of the following four equations depending upon which equation above produced the plume rise estimate. The four equations are, as follows, where L is the top of the layer above stack top:

FR = [(t - L) 5'3 u* 2u]/[2.66 H 2,'3],

( 1a)

where H = h + (0.67 t)

FR = [(t - L) 5/a H .2;3 u]/12.27,

(2a)

FR = [(t - L) 3 us]/59.3,

(3a)

F R = { [ ( t - L ) + 3d]2/Ss~/2}/1211.7.

(4a)

The plume rise estimation then proceeds in the next layer solving Equations (1) (4) with the residual buoyancy flux, FR, substituted for F 0 and using the wind speed and temperature for that layer. To obtain the new plume top estimate, the height of the bottom of this new layer above stack top is added to the result of each equation. This is continued layer by layer until the plume top estimate is contained within a layer.