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The validity of a Gaussian plume model when applied to elevated releases at a site on the Canadian shield
Atmospheric
Enoiromnf
Vol. 23, No. 2. pp. 351-362,
1989. 0
Printed in Great Britain.
ooo&6981/89 s3.oo+o.w 1989 Pergiunon Ras pk
THE VALIDITY OF A GAUSSIAN PLUME MODEL WHEN APPLIED TO ELEVATED RELEASES AT A SITE ON THE CANADIAN SHIELD E. ROBERTSON and P. J. BARRY Atomic Energy of Canada Ltd., Environmental Research Branch, Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada KOJ 1JO (First received 28 January 1988 and in final form 3 August 1988)
Abstract-It is shown that while a standard Gaussian plume model can predict annual mean concentrations of a gas released from a tall stack on the Canadian Shield within a factor of two, the probability of achieving this level of agreement for hourly averages is 20-30% with no significant correlation between individual hourly observations and predictions (rZ = 0.08). The probability, however, increases to 50% with an averaging time of 12 h and the correlation coefficient increases to 0.44. An analysis of concentrations observed during narrowly defined meteorological conditions demonstrates the wide range of actual concentrations that is observed during conditions that can, given the models and parameterizations available, only result in one predicted concentration. The results demonstrate that atmospheric dispersion can only be adequately estimated for relatively long averaging periods when standard dispersion parameters that have been derived from averages of many experiments are used. The sources of uncertainties associated with short term atmospheric modelling required for emergency response are discussed and illustrated by measurements made at Chalk River. It is concluded that dispersivity is not uniquely associated with weather class. ‘Taere are very good reasons for believing that vertical dispersion is correlated with stability and it seems likely therefore that the weakness in the model arises from the assumption that horizontal dispersion is also a simple function of stability. Key word index: Dispersion, Gaussian plume models, stability, validity.
INTRODUCTION Gaussian plume models
Gaussian plume models are widely used to estimate downwind concentration distributions of contaminant gases released to the atmosphere. The fundamental limitations of all such models are associated with:
(1) temporal and spatial changes in the wind, (2) extrapolating parameterizations beyond their empirical basis, i.e. use of dispersion parameters derived from other sites, and (3) the statistical nature of a turbulent atmosphere. The reliability depends on:
of the Gaussian
plume model thus
(1) the accuracy of the meteorological measurements, (2) the applicability of the measurements within the scales of space and time being modelled, (3) an accurate assessment of stability and its relationship to horizontal and vertical dispersion, and (4) the sample averaging time. The last two points are discussed below.
Atmospheric
stability
Six stability classes are most often inferred from wind speed and insolation (Pasquill-Gifford), (Pasquill, 1962) or from wind speed and vertical temperature gradient. The equations for dispersion parameters for each class as a function of distance derived by Briggs (B&s, 1974) from Pasquill’s experimental data represent average values for smooth terrain. The Hosker equations for vertical dispersion equations include parameters that account for surface roughness (Hosker, 1974). Use of Briggs or Hosker equations implies a fixed relationship between horizontal (a,) and vertical (a,) dispersion parameters for each class. Dispersion, or turbulence, components can also be inferred from direct measurement of the standard deviation of the horizontal or vertical wind direction. Since vertical wind measurements are difficult and costly, values of uY estimated from measurements of standard deviation of wind direction, CT~may be coupled with O, values derived from stability class estimated from wind speed and temperature gradient (split-sigma method), giving an independent estimate for each dispersion parameter. Many workers have recently concluded that conventional schemes used for stability classification are often not applicable. For example, Atwater and Lon351
E. ROBERTSON and P. J. BARRY
352
dergan (1985) state: “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 classification was most correlated with the observed vertical dispersion, while the Turner sigma theta methods were most correlated with observed horizontal dispersion. Observed horizontal and vertical dispersion classes often differed from one another by two or more classes.” This statement raises the question whether horizontal and vertical dispersion parameters are related to stability in the same way, as is assumed by some classification schemes. To illustrate the magnitude of the uncertainty introduced by an uncertainty in stability classification, Table 1 lists Briggs values for b,, and IT, for each Pasquill class at a distance of 5 km. Differences in class choice or combination of cY and u, can lead to differences in concentration estimates of factors of 2-10 or even more.
SITE AND DATA DESCRIPTION
The Chalk River Nuclear Laboratories are situated about 200 km west of Ottawa on the Ottawa river which flows roughly from northwest to southeast. A series of low ridges runs approximately parallel to the southwest shore of the river while steep rocky cliffs rise from the northeast shore and the country beyond is generally higher (Fig. 1). The river and terrain tend to channel the winds. The land to the northeast is unpopulated and both sides of the river are well covered with trees about 30 m high.
Averaging time
Gaussian plume models are used over a range of averaging times depending on the application. For example, annual averages of estimated hourly concentrations may be used to assess the effects of chronic releases from existing or proposed stacks, in which case the accuracy of the estimate for each individual hour may not be crucial. In such cases, it will however be of interest to know the distribution of concentrations within the average and, in particular, the occurrence frequency of extremely high concentrations. The same models are used to assess the effects of gases released accidentally over periods of hours or minutes, in which case a greater degree of accuracy is required. However, since the dispersion parameters used in the Gaussian equation are averages of ensembles of experimental results, the application of these parameters to individual short averaging periods can result in uncertainties of 1-2 orders of magnitude. The objective of the Chalk River data analysis is to study the extent and effect of the Gaussian plume model limitations on model applications at the Chalk River site, and to estimate model reliability as a function of averaging time using archived data collected between 1963 and 1976.
Table 1. Briggs values of op and cr as a function of stability class for a distance of 5 km Class A B c D E F
OY
0,
905 659 453 329 246 165
1110 606 285 103 60 32
Fig. 1. Map showing river shores, stack and sampling stations.
353
Validity of Gaussian plume model Argon-41 concentrations were measured at four ground-level sites referred to as stations 5,6,9 and 10. The first two lie along the top of the ridge to the northwest of the stack at distances of 1.5 and 6 km, respectively. Station 9 is to the southeast at a distance of 1.1 km. These three stations lie along the axis of the most prevalent wind direction. Elevation profiles along and across the prevailing wind direction are shown in Fig. 2. The effective stack height used in model calculations is the difference between the elevations of the stack orifice and of the sampling station. No further correction is made for stack height since little or no buoyant plume rise occurs (Barry and Robertson, 1986). The methods of assaying the source strength and the concentrations in the samples have been described by Barry (1971). All concentration data are normalized to unit source strength. The meteorological data at the time consisted of wind directions and speeds measured with a Bendix-Friez aerovane and vertical differences of temperature measured by two resistance bulb thermometers. The elevation of the aerovane was about 15 m lower than that of the stack orifice. The temperature sensors were installed about 10 m above the ground surface and at about the same distance below the top of the tower. The height interval between them was 70 m. The archived meteorological and Ar data are in two sets: for the first set (1963-1969), the signals from the sensors were recorded on strip charts. Hourly average values were abstracted manually, screened for data quality and stored on computer cards. Wind directions were estimated to the nearest lo”, wind speeds to unit m.p.h. Temperature difference was directly recorded on the chart and abstracted to O.l”F. The argon concentrations are integrated over 6 min but in this set the 10 measurements were combined to form a l-h average corresponding to the hourly averaged
meteorological data. For the second data set, (1970-1976) signals from the meteorological sensors were automatically stored on paper tape every 6 min so that the recorded data corresponds to an instantaneous observation taken every 6 min rather than an average as before. The Ar concentrations however, continued to be integrals over 6 min. The data were subsequently stored on 28 magnetic tapes. Up to 16 variables were stored on the same paper tape and thus the system was not interrupted when some of the sensors were not operating correctly and there was no possibility of immediate data quality control. Thus there are frequent periods when one or more of the stored variables was incorrect or missing. Retrospective quality control of the data was difficult and time consuming. For example it was concluded that the orientation of the aerovane changed several times during the period of record. This conclusion is based on the assumption that, on average, when Ar concentrations were high at a given sampler the wind was in the direction of that sampler. Measured directions had to be corrected by as much as 30”. Explanations for these discrepancies are the possible inconsistent use of a site-specific grid system and the difficulties associated with aligning instruments on the top of high towers. Changes of orientation could be correlated with dates of instrument repairs or checks noted in old log books, thus giving confidence in the validity of the applied corrections. Stability classes for both data sets were estimated according to the scheme shown in Table 2. A report of meteorological data summaries is in preparation. It is of interest to note here that the occurrence frequency of Pasquill-Gifford stability classes estimated from the CRNL wind and temperature data and the classification scheme in Table 2 is significantly different from that obtained using data from the nearby Class-A meteorological station at Petawawa and the STAR
250
E -
z c z
200
Y
,’
150
100
I 1
1 0
DISTANCE
I
I
I
2
4
6
FROM STACK
(km )
Fig. 2. Terrain profile along the line of stack and samplers.
354
E. ROBERTSON and P. J. BARRY Table 3. Pasquill weather class relative frequencies Class A B C D E F
Petawawa Star
Chalk River
0.01 0.06 0.10 0.55 0.12 0.16
0.14 0.20 0.14 0.28 0.13 0.11
AT/AZ-U
classification scheme (Table 3). The relatively high frequency of unstable classes in the former scheme applies to both sets of archived data as well as to current measurements from a 65 m meteorological tower. Model description
nnnnnn
Two versions of a straight line Gaussian plume model are used for the work described in this report. They are referred to as the Predictive and the Statistical models. The Predictive model is used to estimate concentrations at the measurement sites from the meteorological data files and the results are then compared with measured concentrations stored on the same files. This allows comparison of individual measurements as well, after appropriate averaging, as longer term averages. For the Statistical model, ensembles of concentrations are calculated from repeated Monte Carlo simulations by drawing input data at random from the observed frequency distributions of the meteorological variables. Data from both Chalk River and the network meteorological station at Petawawa about 18 km down river have been used for this model. Results are used for comparison with observed long term averages and concentration frequency distributions. Both variants use a standard Gaussian equation to predict concentrations as a function of x, y, and z co-ordinates and unit release rate from the equation: C
~x.Y.O)=~[exP(I::)exp (1)
whereCcx,y,o) = ground concentration at distance x and crosswind displacement y, Q = source release rate (s- ‘), H = effective stack height (m), u = wind speed (m s-r) 15 m below stack orifice, x = distance (m), ci = vertical dispersion parameter (m), and oY= horizontal dispersion parameter (m).
NCcl’C)r-
vvvv
When wind direction data are only available as 16 compass points, as is the case in the data files from Petawawa and other meteorological stations, Equation (1) is modified to calculate the average concentration within a 22.5” sector so that
c(.r,my
y within
-(i>“‘--&[exP($)] (2)
8.0)-
where 8 = 2~116 radians.
355
Validity of Gaussian plume model
Concentrations estimated from Equation (2) are later referred to as “sector averages”. A form of this equation is used to estimate the effect of prolonged releases, in which case it may include the frequencies of each stability class and wind direction in each sector. In addition to meteorological data, input to both models includes distance between source and receptor, effective stack height relative to each receptor, and flags to allow a choice of dispersion equation parameters. Stability class is estimated from wind and temperature gradient data using the scheme shown in Table 2. Unless otherwise stated, Briggs (1974) equations were used for oYand Hosker (1974) equations with surface roughness parameter (z,,) = 0.4 m were used for 6,.
RESULTS
Statistical
model
The statistical model and its applications to CRNL data have been reported previously (Barry and Robertson, 1986). Long term averages of predicted concentrations agreed within a factor of 2 with observations and the frequency distributions of calculated concentrations were also found to be in reasonable agreement with those observed. The model is therefore useful to estimate the environmental impact of stack releases during the planning stages of industrial sites, or to test output sensitivity to parameter changes as will be shown later. Predictive model
The Predictive model was used with input data read from hourly data filles for 1963-1968 to compare predicted concentrations with measurements made at stations 5,6 and 9. Predictions were not attempted for hours with mean wind speeds x0.5 m s- ’ since wind speed and direction measurements are not reliable at very low speeds and cannot be determined during calms which are relatively frequent at CRNL. Furthermore, the assumption of a homogeneous wind field is least likely to be valid under low wind speed conditions. Three methods are used to assess model reliability, sensitivity to choice among standard dispersion equations and effect of averaging time. (1) One-to-one comparison between observed and predicted concentrations for various averaging times of hourly values. (2) The frequency distribution of the ratios of observed to predicted concentrations (obs/pred). For this comparison, the frequency of values for obs/pred within 15 ranges between + 10 and - 10 is calculated. Only those cases where both the observed and predicted concentration values were above the detection limit are used. A plot of the cumulative frequency of these ratios against the ratio shows the relative frequency of over and under predictions in each range. Such plots are used to give a qualitative picture of the relative ability of models using different parameters
and/or averaging times to predict observed concentrations. (3) Comparison of the cumulative frequency distributions of observed and predicted concentrations. The results described below are typical of all the CRNL data. The annual average of hourly predicted and observed concentrations are compared in Table 4. Agreement is within a factor of 2. On the other hand, one-toone agreement between observed and predicted concentrations was poor as shown in Fig. 3 which shows a plot of the cumulative frequency of occurrences of values for the ratio obs/pred between - 10 and + 10 for 1968 data. Only 30% of the sample pairs agreed within 10% and 80% within a factor of 10. However, the numbers of over and under predictions are almost equal suggesting that bias is absent-an important conclusion already evident from the closeness of predicted and observed annual mean concentrations. The dotted line is an ideal situation where 90% of predictions are within 10% of observed values. Sensitivity to dispersion parameters
Model sensitivity to choice of dispersion equation was tested. Figure 4 shows the frequency distribution of values obtained for obs/pred for 1968 data for models using (a) Briggs equations for u, and (b) Hosker equations with z,, = 0.4 m in one case and (c) 1.0 m in the other. The result shows that the predictive capability of the model is not very sensitive to these parameter changes. Effect of averaging time
When the hourly values are averaged for periods > 72 h, however, the frequency of agreement between observations and predictions within a factor of 10 or less is significantly increased as is shown in Fig. 5. Furthermore, the greatest change in error factor distribution is for averaging times between 1 and 12 h. Table 5 shows observed and predicted concentrations for five averaging times together with the corresponding correlation coefficients (r’). The values listed as
Table 4. Summary of mean observed and predicted concentrations of Argon-41 Year
Station
Mean observed concentration
Mean predicted concentration
1963
9 5
0.78 x 1O-6 0.49 x 10-e
0.40 x 10-e 0.61 x 1O-6
1966
9 5 6 9 5 6 9 5 6
0.71 x 10-6 0.35 x 10-e 0.06 x lo- 6
0.41 x 1o-6 0.40 x 10-e 0.06 x 10-e
0.40 x 0.90 x 0.21 x 0.64 x 0.77 x 0.28 x
0.56 x 0.74 x 0.15 x 0.61 x 0.66 x 0.14 x
1967
1968
10-6 10-6 10-h 10-e 10-e 1O-6
1O-6 10-e 10-6 1O-6 lo- 6 10-e
356
E. Cumulative
ROBERTSON and P. J. BARRY
fractions
of observed
values
FACTOR - OVER ESTIMATED
- UNDER ESTIMATED 10
5
-5
-10
of CobslCpred
1.0
-Le.
“ideal”
0.8
z .z z 0.6 2 : g u.l 0 0.4 .z LI 4’
: Ir 0.2
/ I I
0.1
l-
c
c
C. -
-
t
0. I 0.5
0.1
1.0
i
Cobs/Cpred
Fig. 3. Cumulative frequency of values for obs/pred for station 5 with 1968 data and an ideal situation.
UNDER ESTIMATED
FACTOR - OVER ESTIMATED 0 -
O -
0 -
Lo-
0
0.8
0.6
CobslCpred Fig. 4. Cumulative
of values for obs/pred’for predictions for station 5 1968 data using Briggs equations for o, (x), Hosker equations for 0, with z,, = 0.4 (curve) and z,, = 1.0 (0).
frequency
351
Validity of Gaussian plume model - UNDER ESTIMATED
FACTOR - OVER ESTIMATED 1.0
0.8
-
4.0
10.0
5.0
CobslCpred
Fig. 5. Cumulative frequency of values for obs/pred for station 5 with 1967-1968data for averaging times of 1, 12,24 and 72 h. Table 5. Effect of averaging time on model predictions Averaging time (h) Number of samples Observed mean cont. Predicted mean cont. Correlation (rZ)
$1) 6937 0.82 x 10e6 0.78 x 10S6 0.08
1 (in plume) 1515 0.33 x 1o-5 0.25 x 1O-s 0.16
12 247 0.19 x 10-S 0.14 x 10-S 0.44
“within the plume” are for cases when both observed and predicted concentration were above detection limits. The decreasing averages with longer averaging time reflect the occurrence of zero concentrations within the averaging period. The very substantial increase of rz even at 12 h testifies to the validity of long-term average concentrations. This is encouraging for operators of nuclear stations that have containment and thus an option of prolonged controlled releases even in accidents. It also provides some assurance for predicting effects of prolonged releases of any toxic gas. It may be that the improved correlation is due mainly to the increased number of hours within the averaging period when the wind is not toward the receptor. The cumulative frequency distributions (c.f.d.) of predicted and observed concentrations vs concentra-
24 149 0.15 x 1o-5 0.11 x 1o-5 0.54
48 85 0.13 x 1o-5 0.88 x 1o-6 0.66
72 49 0.12 x 1o-5 0.87 x 1O-6 0.77
tion for stations 5 and 6’during 1968 are plotted in Fig. 6. Two sets of observed data are shown. One is for all the data and the other is for cases for which predictions were made, i.e. all necessary meteorological data were available and the wind speed was > 0.5 m s- ‘. Assuming that the c.f.d. for those times when the meteorological data are missing is the same as that for the rest of the time, the difference between the two sets is the contribution to the c.f.d. during calms. This is seen to be small. The model tends to over predict the frequency of high concentrations by about a factor of 2. This is possibly due to the difficulties associated with low wind speeds.
Both the hourly and 6 min data were studied in an effort to identify conditions that are associated with
358
E.
I
ROBERTSON and
P. J.
BARR?
STATION 5, 1968
STATION 6. 1968 Is OBSERVED n= 8205 v OBSERVED n= 5557 . PZDICTCD
c/Q ( ~10
6
s.m.
-3 )
Fig. 6. Cumulative frequency distribution ofpredicted and observed concentrations vs normal-
ized concentration of stations 5 and 6 during 1968.
particularly high observed concentrations, or with small or large differences between observations and predictions. Qualitative examination of the data indicated that apparently similar conditions frequently coincide with a wide range of concentrations. This suggests that either: (a) the method for classifying stability is poor, (b) the dispersivity is not so uniquely tied to stability as the model supposes, or (c) both. In order to test (b), the data were sorted according to six stability classes and a wind direction toward each sampling station. The concentrations observed during periods with the same conditions, for which the model predicts a single value for the concentration, were then
examined. Table 6 shows mean observed and calculated concentrations for A, B, D and F class stability and the one recorded direction that is directly toward stations 5 and 6. Both plume centre and sector average calculated concentrations are shown since the direction data were abstracted to 10” for the first data set. Data for more than one period of record are listed to show that differences between observed and predicted means are not due to temporal measurement problems. Again, even though the data sets for these narrow ranges are small, there is reasonable agreement between observed concentration means and calculated.
Table 6. Summary of observed and predicted normalized concentrations within stability classes Mean observed Station 5
6
Class A B B* D F A B B* D F
196551968 0.14 x lo-4 0.18 x 1o-4
0.83 x 1o-5
1967-1968 0.50 x 0.16 x 0.14x 0.18 x 0.60 x
10-s lo-‘+ 1o-4 1O-4 1o-5
0.72x 0.43 x 0.42 x 0.95 x 0.23x
lo-’ 10-5 1O-5 10-5 lo-’
Predicted 1972-1973 0.68 x 1o-5 ---0.12 x 1o-4 -------------
Centre
Sector
0.34 x 10-s 0.77 x 10-5
0.45 x 10-s 0.73 x lo-5
0.39 x 1o-4 0.12 x 1o-4
0.19 x 1o-4 0.28 x 1O-5
0.38 x W6 0.87 x 1o-6 ____ 0.82 x 10-s 0.81 x 1o-5
0.44 x lo-6 0.73 x lo-6 ____ 0.34 x 1o-5 0.17 x 10-s
359
Validity of Gaussian plume model For the most stable class (i.e. narrower plumes) observations are in better agreement with sector averaged concentrations. This is especially true for station 6 which is furthest from the stack. This may be due to the averaging effect of the oscillation of the plume centre about both sides of the receptor during the sampling time. The biggest anomaly is for B class weather which occurs more frequently than expected with the classification scheme used, particularly in winter. However, when the data were further sorted into a B* class, which omits winter data, observed concentrations were marginally lower but higher than would be predicted for class B. Thus, concentrations usually predicted for stable classes are often observed during periods with no temperature inversions. The distribution of concentrations observed at station 5 within each stability classification was also determined. Figures 7a and b show the distribution of concentrations observed during D and B class stabilities at station 5 during the 196551968 period when the wind directions were recorded to the nearest lo”. Figures 7c and d are for 1972-1973 data. The number of samples is bigger because of the short sampling time. In this case the wind direction data are recorded to the nearest degree, and so the distribution is for a lo” interval in the direction of the receptor. The mean observed concentraton, centre plume and sector average predictions are indicated on the figure. The letters A, B, D and F show the predicted plume centre concentrations for those classes. The numbers in the bar on the left of the histogram is the number of zeros and that on the right is the number outside the range of the figure. Figure 7 shows that results are similar for the two data sets. It is interesting to note the large number of zeros compared to the few high concentrations that contribute to a mean that is acceptably close to the predicted concentration. Also the range of observed concentrations is wider than the range that would be predicted for station 5 regardless of choice of stability class. This could be largely due to the wide range of by and or occurring within each stability class reported by Geiss et al. (1981), and observed at Chalk River where the standard deviation of horizontal wind direction varies between 2 to 30” within each class (report in preparation). Also, it should be noted that these predictions are for a stack height of 43 m which is about right for the CRNL stack relative to station 5. Down draughts could reduce the effective stack height and account for some of the high concentrations. Although the tabulation of means in Table 6 implies some skill in estimating class, Fig. 7 demonstrates the wide range of concentrations that does occur during apparently similar conditions. From this we conclude that dispersivity is not uniquely associated with stability class. The above results lead to the question: is the observed uncertainty in model predictions due to use of one of six distinct stability classes for estimating both uY and a,?
To answer this question, the concepts of the statistical and predictive models were combined. Measured concentrations were compared with Gaussian plume model predictions based on real time wind speed and direction as before but with stability class chosen at random from its distribution observed at CRNL. The ensemble of observed/predicted ratios was almost identical to that found when real time stability based on dT/dz and wind speed was used. Increasing the averaging time for these predictions gives a similar improvement in the correlation between observations and predictions as was shown in Fig. 5. The stability was chosen at random for each hour in the averaging classes, (e.g. A could follow F). These results suggest that there is little to be gained from using the observed stability classes for the calculation even during prolonged periods of apparently constant conditions. Figure 8 compares the c.f.d. of concentrations predicted from random classes with that for observed concentrations. Although the agreement is not as good as that shown in Fig. 6, where real time stability classes were used for the predictions, the distributions are similar. The prediction from random stabilities increases the frequency of high concentrations by a factor of about 3. This may be due to a mismatch between stability and wind speed since the latter was chosen from its observed distribution. The results of the random stability class model explain why the calculated long term averages and probability distribution function of the concentrations agree reasonably well with their observed counterparts although on a one-to-one basis the comparison is poor.
CONCLUSION
This study has shown that while a standard Gaussian plume model can predict annual mean concentrations of a gas released from a tall stack on the Canadian Shield within a factor of 2, the probability of achieving this level of agreement for hourly averages is 20-30% with no significant correlation between individual hourly observations and predictions (r2 = 0.08). The probability, however, increases to 50% with an averaging time of 12 h and the correlation increases to 0.44. An analysis of concentrations observed during narrowly defined meteorological conditions has demonstrated the wide range of actual concentrations that is observed during conditions that can, given the models and parameterizations available, only result in one predicted concentration. However, the average of these observations is in reasonable agreement with the prediction. These results demonstrate that atmospheric dispersion can only be adequately estimated for relatively long averaging periods when standard dispersion parameters that have been derived from averages of many
360
E. ROBERTSONand P. J. BARRY
Cl 201 19ISL71615-
0 lb.-< 1312w 11z c lo: ii :: Q 7% 6s $6
532lO-
2.0 c/q
.(xN5
Fig. 7feb).
3.0 s.n.
-3
1
361
Validity of Gaussian plume mode1 Class
B
A
F
26 2&-T
18 : 16 -2
t4-
x z 12M x:
lo-
“0
8-
j
6 42O-
Class
A
B
D
F
(4
t
n
I,,
i
2.0
c/g
(
x10-S s.lL3
I,
3.0
24.0
)
Fig. 7. Distribution of concentrations observed at station 5 (a) 1968, D class (b) 1968, B class (c) 1972, D class (d) 1972, B class. The arrows are at predicted values of C/Q calculated for stability class A, B, F and D.
362
E.
ROBERTSONand
P. J.
BARRY
Fig. 8. Cumulative frequency distribution of concentrations predicted for station 5 with 1967-1968 wind data (b) and random stability classes compared with observations (a).
are used. The sources of uncertainties associated with short term atmospheric modelling required for emergency response that have been discussed and illustrated by measurements made at Chalk. River are probably general, but the magnitude of their effect will depend on site specific characteristics such as topography. Work is required to determine whether direct measurement of both horizontal and vertical turbulence will improve our capability to estimate concentrations due to short term releases. We conclude that dispersivity is not uniquely associated with weather class. There are very good reasons for believing that 0, is correlated with stability and it seems likely therefore that the weakness in the model arises from the assumption that eYis also simple and a unique function of stability. experiments
REFERENCES
Atwater M. A. and Londergan R. J. (1985) Differences caused by stability class on dispersion in tracer experiments. Atmospheric Erwironment 19, 1045-1051. Barry P. J. (1971) Use of Argon 41 to study the dispersion of
effluents from stacks in use of nuclear techniques in the measurement and control of environmental pollution. Int. Atomic Energy Agency, Vienna. Barry P. J. and Robertson E. (1986) llse of Meteorological Data to Parameterize Statistical Dispersion Models in Air Pollution Modelling and Its Application V. Plenum Press,
New York. Briggs G. A. (1974) Diffusion estimated for small emissions. Environmental Research Laboratories Air Resources, Atmosphere, Turbulence and Diffusion Laboratory, Annual Report 1973 USAFC Report ATDL-106, National Oceanic and Atmospheric Administration. Geiss H., Nester K., Thomas P. and Vogt K. J. (1981) In der Bundesrepublik Deutschland Experimentell ermittelte Ausbreitungsparameter fiir 100 m Emissionshohe, Jul1707. Hosker R. P. Jr. (1974) Estimates of dry deposition and plume depletion over forests and grasslands. In Physical Behauiour of Radioactive Contaminants in the Atmosphere. Int. Atomic Energy Agency, Vienna. IAEA (1980) A&ospher& dispersion in nuclear power plant siting-A safetv guide. Safetv Series No. 50-59-53.. ht. Atmiic Energy- Aiency, Vienna. Lewellen W. S. and Sykes R. I. (1985) Scientific critique of avaitable models for real-time simulations of dispersion. NUREG/CR-4157. Pasquill F. (1962) Atlnospheric Difision. Van Nostrand, Princeton, New Jersey.
Enoiromnf
Vol. 23, No. 2. pp. 351-362,
1989. 0
Printed in Great Britain.
ooo&6981/89 s3.oo+o.w 1989 Pergiunon Ras pk
THE VALIDITY OF A GAUSSIAN PLUME MODEL WHEN APPLIED TO ELEVATED RELEASES AT A SITE ON THE CANADIAN SHIELD E. ROBERTSON and P. J. BARRY Atomic Energy of Canada Ltd., Environmental Research Branch, Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada KOJ 1JO (First received 28 January 1988 and in final form 3 August 1988)
Abstract-It is shown that while a standard Gaussian plume model can predict annual mean concentrations of a gas released from a tall stack on the Canadian Shield within a factor of two, the probability of achieving this level of agreement for hourly averages is 20-30% with no significant correlation between individual hourly observations and predictions (rZ = 0.08). The probability, however, increases to 50% with an averaging time of 12 h and the correlation coefficient increases to 0.44. An analysis of concentrations observed during narrowly defined meteorological conditions demonstrates the wide range of actual concentrations that is observed during conditions that can, given the models and parameterizations available, only result in one predicted concentration. The results demonstrate that atmospheric dispersion can only be adequately estimated for relatively long averaging periods when standard dispersion parameters that have been derived from averages of many experiments are used. The sources of uncertainties associated with short term atmospheric modelling required for emergency response are discussed and illustrated by measurements made at Chalk River. It is concluded that dispersivity is not uniquely associated with weather class. ‘Taere are very good reasons for believing that vertical dispersion is correlated with stability and it seems likely therefore that the weakness in the model arises from the assumption that horizontal dispersion is also a simple function of stability. Key word index: Dispersion, Gaussian plume models, stability, validity.
INTRODUCTION Gaussian plume models
Gaussian plume models are widely used to estimate downwind concentration distributions of contaminant gases released to the atmosphere. The fundamental limitations of all such models are associated with:
(1) temporal and spatial changes in the wind, (2) extrapolating parameterizations beyond their empirical basis, i.e. use of dispersion parameters derived from other sites, and (3) the statistical nature of a turbulent atmosphere. The reliability depends on:
of the Gaussian
plume model thus
(1) the accuracy of the meteorological measurements, (2) the applicability of the measurements within the scales of space and time being modelled, (3) an accurate assessment of stability and its relationship to horizontal and vertical dispersion, and (4) the sample averaging time. The last two points are discussed below.
Atmospheric
stability
Six stability classes are most often inferred from wind speed and insolation (Pasquill-Gifford), (Pasquill, 1962) or from wind speed and vertical temperature gradient. The equations for dispersion parameters for each class as a function of distance derived by Briggs (B&s, 1974) from Pasquill’s experimental data represent average values for smooth terrain. The Hosker equations for vertical dispersion equations include parameters that account for surface roughness (Hosker, 1974). Use of Briggs or Hosker equations implies a fixed relationship between horizontal (a,) and vertical (a,) dispersion parameters for each class. Dispersion, or turbulence, components can also be inferred from direct measurement of the standard deviation of the horizontal or vertical wind direction. Since vertical wind measurements are difficult and costly, values of uY estimated from measurements of standard deviation of wind direction, CT~may be coupled with O, values derived from stability class estimated from wind speed and temperature gradient (split-sigma method), giving an independent estimate for each dispersion parameter. Many workers have recently concluded that conventional schemes used for stability classification are often not applicable. For example, Atwater and Lon351
E. ROBERTSON and P. J. BARRY
352
dergan (1985) state: “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 classification was most correlated with the observed vertical dispersion, while the Turner sigma theta methods were most correlated with observed horizontal dispersion. Observed horizontal and vertical dispersion classes often differed from one another by two or more classes.” This statement raises the question whether horizontal and vertical dispersion parameters are related to stability in the same way, as is assumed by some classification schemes. To illustrate the magnitude of the uncertainty introduced by an uncertainty in stability classification, Table 1 lists Briggs values for b,, and IT, for each Pasquill class at a distance of 5 km. Differences in class choice or combination of cY and u, can lead to differences in concentration estimates of factors of 2-10 or even more.
SITE AND DATA DESCRIPTION
The Chalk River Nuclear Laboratories are situated about 200 km west of Ottawa on the Ottawa river which flows roughly from northwest to southeast. A series of low ridges runs approximately parallel to the southwest shore of the river while steep rocky cliffs rise from the northeast shore and the country beyond is generally higher (Fig. 1). The river and terrain tend to channel the winds. The land to the northeast is unpopulated and both sides of the river are well covered with trees about 30 m high.
Averaging time
Gaussian plume models are used over a range of averaging times depending on the application. For example, annual averages of estimated hourly concentrations may be used to assess the effects of chronic releases from existing or proposed stacks, in which case the accuracy of the estimate for each individual hour may not be crucial. In such cases, it will however be of interest to know the distribution of concentrations within the average and, in particular, the occurrence frequency of extremely high concentrations. The same models are used to assess the effects of gases released accidentally over periods of hours or minutes, in which case a greater degree of accuracy is required. However, since the dispersion parameters used in the Gaussian equation are averages of ensembles of experimental results, the application of these parameters to individual short averaging periods can result in uncertainties of 1-2 orders of magnitude. The objective of the Chalk River data analysis is to study the extent and effect of the Gaussian plume model limitations on model applications at the Chalk River site, and to estimate model reliability as a function of averaging time using archived data collected between 1963 and 1976.
Table 1. Briggs values of op and cr as a function of stability class for a distance of 5 km Class A B c D E F
OY
0,
905 659 453 329 246 165
1110 606 285 103 60 32
Fig. 1. Map showing river shores, stack and sampling stations.
353
Validity of Gaussian plume model Argon-41 concentrations were measured at four ground-level sites referred to as stations 5,6,9 and 10. The first two lie along the top of the ridge to the northwest of the stack at distances of 1.5 and 6 km, respectively. Station 9 is to the southeast at a distance of 1.1 km. These three stations lie along the axis of the most prevalent wind direction. Elevation profiles along and across the prevailing wind direction are shown in Fig. 2. The effective stack height used in model calculations is the difference between the elevations of the stack orifice and of the sampling station. No further correction is made for stack height since little or no buoyant plume rise occurs (Barry and Robertson, 1986). The methods of assaying the source strength and the concentrations in the samples have been described by Barry (1971). All concentration data are normalized to unit source strength. The meteorological data at the time consisted of wind directions and speeds measured with a Bendix-Friez aerovane and vertical differences of temperature measured by two resistance bulb thermometers. The elevation of the aerovane was about 15 m lower than that of the stack orifice. The temperature sensors were installed about 10 m above the ground surface and at about the same distance below the top of the tower. The height interval between them was 70 m. The archived meteorological and Ar data are in two sets: for the first set (1963-1969), the signals from the sensors were recorded on strip charts. Hourly average values were abstracted manually, screened for data quality and stored on computer cards. Wind directions were estimated to the nearest lo”, wind speeds to unit m.p.h. Temperature difference was directly recorded on the chart and abstracted to O.l”F. The argon concentrations are integrated over 6 min but in this set the 10 measurements were combined to form a l-h average corresponding to the hourly averaged
meteorological data. For the second data set, (1970-1976) signals from the meteorological sensors were automatically stored on paper tape every 6 min so that the recorded data corresponds to an instantaneous observation taken every 6 min rather than an average as before. The Ar concentrations however, continued to be integrals over 6 min. The data were subsequently stored on 28 magnetic tapes. Up to 16 variables were stored on the same paper tape and thus the system was not interrupted when some of the sensors were not operating correctly and there was no possibility of immediate data quality control. Thus there are frequent periods when one or more of the stored variables was incorrect or missing. Retrospective quality control of the data was difficult and time consuming. For example it was concluded that the orientation of the aerovane changed several times during the period of record. This conclusion is based on the assumption that, on average, when Ar concentrations were high at a given sampler the wind was in the direction of that sampler. Measured directions had to be corrected by as much as 30”. Explanations for these discrepancies are the possible inconsistent use of a site-specific grid system and the difficulties associated with aligning instruments on the top of high towers. Changes of orientation could be correlated with dates of instrument repairs or checks noted in old log books, thus giving confidence in the validity of the applied corrections. Stability classes for both data sets were estimated according to the scheme shown in Table 2. A report of meteorological data summaries is in preparation. It is of interest to note here that the occurrence frequency of Pasquill-Gifford stability classes estimated from the CRNL wind and temperature data and the classification scheme in Table 2 is significantly different from that obtained using data from the nearby Class-A meteorological station at Petawawa and the STAR
250
E -
z c z
200
Y
,’
150
100
I 1
1 0
DISTANCE
I
I
I
2
4
6
FROM STACK
(km )
Fig. 2. Terrain profile along the line of stack and samplers.
354
E. ROBERTSON and P. J. BARRY Table 3. Pasquill weather class relative frequencies Class A B C D E F
Petawawa Star
Chalk River
0.01 0.06 0.10 0.55 0.12 0.16
0.14 0.20 0.14 0.28 0.13 0.11
AT/AZ-U
classification scheme (Table 3). The relatively high frequency of unstable classes in the former scheme applies to both sets of archived data as well as to current measurements from a 65 m meteorological tower. Model description
nnnnnn
Two versions of a straight line Gaussian plume model are used for the work described in this report. They are referred to as the Predictive and the Statistical models. The Predictive model is used to estimate concentrations at the measurement sites from the meteorological data files and the results are then compared with measured concentrations stored on the same files. This allows comparison of individual measurements as well, after appropriate averaging, as longer term averages. For the Statistical model, ensembles of concentrations are calculated from repeated Monte Carlo simulations by drawing input data at random from the observed frequency distributions of the meteorological variables. Data from both Chalk River and the network meteorological station at Petawawa about 18 km down river have been used for this model. Results are used for comparison with observed long term averages and concentration frequency distributions. Both variants use a standard Gaussian equation to predict concentrations as a function of x, y, and z co-ordinates and unit release rate from the equation: C
~x.Y.O)=~[exP(I::)exp (1)
whereCcx,y,o) = ground concentration at distance x and crosswind displacement y, Q = source release rate (s- ‘), H = effective stack height (m), u = wind speed (m s-r) 15 m below stack orifice, x = distance (m), ci = vertical dispersion parameter (m), and oY= horizontal dispersion parameter (m).
NCcl’C)r-
vvvv
When wind direction data are only available as 16 compass points, as is the case in the data files from Petawawa and other meteorological stations, Equation (1) is modified to calculate the average concentration within a 22.5” sector so that
c(.r,my
y within
-(i>“‘--&[exP($)] (2)
8.0)-
where 8 = 2~116 radians.
355
Validity of Gaussian plume model
Concentrations estimated from Equation (2) are later referred to as “sector averages”. A form of this equation is used to estimate the effect of prolonged releases, in which case it may include the frequencies of each stability class and wind direction in each sector. In addition to meteorological data, input to both models includes distance between source and receptor, effective stack height relative to each receptor, and flags to allow a choice of dispersion equation parameters. Stability class is estimated from wind and temperature gradient data using the scheme shown in Table 2. Unless otherwise stated, Briggs (1974) equations were used for oYand Hosker (1974) equations with surface roughness parameter (z,,) = 0.4 m were used for 6,.
RESULTS
Statistical
model
The statistical model and its applications to CRNL data have been reported previously (Barry and Robertson, 1986). Long term averages of predicted concentrations agreed within a factor of 2 with observations and the frequency distributions of calculated concentrations were also found to be in reasonable agreement with those observed. The model is therefore useful to estimate the environmental impact of stack releases during the planning stages of industrial sites, or to test output sensitivity to parameter changes as will be shown later. Predictive model
The Predictive model was used with input data read from hourly data filles for 1963-1968 to compare predicted concentrations with measurements made at stations 5,6 and 9. Predictions were not attempted for hours with mean wind speeds x0.5 m s- ’ since wind speed and direction measurements are not reliable at very low speeds and cannot be determined during calms which are relatively frequent at CRNL. Furthermore, the assumption of a homogeneous wind field is least likely to be valid under low wind speed conditions. Three methods are used to assess model reliability, sensitivity to choice among standard dispersion equations and effect of averaging time. (1) One-to-one comparison between observed and predicted concentrations for various averaging times of hourly values. (2) The frequency distribution of the ratios of observed to predicted concentrations (obs/pred). For this comparison, the frequency of values for obs/pred within 15 ranges between + 10 and - 10 is calculated. Only those cases where both the observed and predicted concentration values were above the detection limit are used. A plot of the cumulative frequency of these ratios against the ratio shows the relative frequency of over and under predictions in each range. Such plots are used to give a qualitative picture of the relative ability of models using different parameters
and/or averaging times to predict observed concentrations. (3) Comparison of the cumulative frequency distributions of observed and predicted concentrations. The results described below are typical of all the CRNL data. The annual average of hourly predicted and observed concentrations are compared in Table 4. Agreement is within a factor of 2. On the other hand, one-toone agreement between observed and predicted concentrations was poor as shown in Fig. 3 which shows a plot of the cumulative frequency of occurrences of values for the ratio obs/pred between - 10 and + 10 for 1968 data. Only 30% of the sample pairs agreed within 10% and 80% within a factor of 10. However, the numbers of over and under predictions are almost equal suggesting that bias is absent-an important conclusion already evident from the closeness of predicted and observed annual mean concentrations. The dotted line is an ideal situation where 90% of predictions are within 10% of observed values. Sensitivity to dispersion parameters
Model sensitivity to choice of dispersion equation was tested. Figure 4 shows the frequency distribution of values obtained for obs/pred for 1968 data for models using (a) Briggs equations for u, and (b) Hosker equations with z,, = 0.4 m in one case and (c) 1.0 m in the other. The result shows that the predictive capability of the model is not very sensitive to these parameter changes. Effect of averaging time
When the hourly values are averaged for periods > 72 h, however, the frequency of agreement between observations and predictions within a factor of 10 or less is significantly increased as is shown in Fig. 5. Furthermore, the greatest change in error factor distribution is for averaging times between 1 and 12 h. Table 5 shows observed and predicted concentrations for five averaging times together with the corresponding correlation coefficients (r’). The values listed as
Table 4. Summary of mean observed and predicted concentrations of Argon-41 Year
Station
Mean observed concentration
Mean predicted concentration
1963
9 5
0.78 x 1O-6 0.49 x 10-e
0.40 x 10-e 0.61 x 1O-6
1966
9 5 6 9 5 6 9 5 6
0.71 x 10-6 0.35 x 10-e 0.06 x lo- 6
0.41 x 1o-6 0.40 x 10-e 0.06 x 10-e
0.40 x 0.90 x 0.21 x 0.64 x 0.77 x 0.28 x
0.56 x 0.74 x 0.15 x 0.61 x 0.66 x 0.14 x
1967
1968
10-6 10-6 10-h 10-e 10-e 1O-6
1O-6 10-e 10-6 1O-6 lo- 6 10-e
356
E. Cumulative
ROBERTSON and P. J. BARRY
fractions
of observed
values
FACTOR - OVER ESTIMATED
- UNDER ESTIMATED 10
5
-5
-10
of CobslCpred
1.0
-Le.
“ideal”
0.8
z .z z 0.6 2 : g u.l 0 0.4 .z LI 4’
: Ir 0.2
/ I I
0.1
l-
c
c
C. -
-
t
0. I 0.5
0.1
1.0
i
Cobs/Cpred
Fig. 3. Cumulative frequency of values for obs/pred for station 5 with 1968 data and an ideal situation.
UNDER ESTIMATED
FACTOR - OVER ESTIMATED 0 -
O -
0 -
Lo-
0
0.8
0.6
CobslCpred Fig. 4. Cumulative
of values for obs/pred’for predictions for station 5 1968 data using Briggs equations for o, (x), Hosker equations for 0, with z,, = 0.4 (curve) and z,, = 1.0 (0).
frequency
351
Validity of Gaussian plume model - UNDER ESTIMATED
FACTOR - OVER ESTIMATED 1.0
0.8
-
4.0
10.0
5.0
CobslCpred
Fig. 5. Cumulative frequency of values for obs/pred for station 5 with 1967-1968data for averaging times of 1, 12,24 and 72 h. Table 5. Effect of averaging time on model predictions Averaging time (h) Number of samples Observed mean cont. Predicted mean cont. Correlation (rZ)
$1) 6937 0.82 x 10e6 0.78 x 10S6 0.08
1 (in plume) 1515 0.33 x 1o-5 0.25 x 1O-s 0.16
12 247 0.19 x 10-S 0.14 x 10-S 0.44
“within the plume” are for cases when both observed and predicted concentration were above detection limits. The decreasing averages with longer averaging time reflect the occurrence of zero concentrations within the averaging period. The very substantial increase of rz even at 12 h testifies to the validity of long-term average concentrations. This is encouraging for operators of nuclear stations that have containment and thus an option of prolonged controlled releases even in accidents. It also provides some assurance for predicting effects of prolonged releases of any toxic gas. It may be that the improved correlation is due mainly to the increased number of hours within the averaging period when the wind is not toward the receptor. The cumulative frequency distributions (c.f.d.) of predicted and observed concentrations vs concentra-
24 149 0.15 x 1o-5 0.11 x 1o-5 0.54
48 85 0.13 x 1o-5 0.88 x 1o-6 0.66
72 49 0.12 x 1o-5 0.87 x 1O-6 0.77
tion for stations 5 and 6’during 1968 are plotted in Fig. 6. Two sets of observed data are shown. One is for all the data and the other is for cases for which predictions were made, i.e. all necessary meteorological data were available and the wind speed was > 0.5 m s- ‘. Assuming that the c.f.d. for those times when the meteorological data are missing is the same as that for the rest of the time, the difference between the two sets is the contribution to the c.f.d. during calms. This is seen to be small. The model tends to over predict the frequency of high concentrations by about a factor of 2. This is possibly due to the difficulties associated with low wind speeds.
Both the hourly and 6 min data were studied in an effort to identify conditions that are associated with
358
E.
I
ROBERTSON and
P. J.
BARR?
STATION 5, 1968
STATION 6. 1968 Is OBSERVED n= 8205 v OBSERVED n= 5557 . PZDICTCD
c/Q ( ~10
6
s.m.
-3 )
Fig. 6. Cumulative frequency distribution ofpredicted and observed concentrations vs normal-
ized concentration of stations 5 and 6 during 1968.
particularly high observed concentrations, or with small or large differences between observations and predictions. Qualitative examination of the data indicated that apparently similar conditions frequently coincide with a wide range of concentrations. This suggests that either: (a) the method for classifying stability is poor, (b) the dispersivity is not so uniquely tied to stability as the model supposes, or (c) both. In order to test (b), the data were sorted according to six stability classes and a wind direction toward each sampling station. The concentrations observed during periods with the same conditions, for which the model predicts a single value for the concentration, were then
examined. Table 6 shows mean observed and calculated concentrations for A, B, D and F class stability and the one recorded direction that is directly toward stations 5 and 6. Both plume centre and sector average calculated concentrations are shown since the direction data were abstracted to 10” for the first data set. Data for more than one period of record are listed to show that differences between observed and predicted means are not due to temporal measurement problems. Again, even though the data sets for these narrow ranges are small, there is reasonable agreement between observed concentration means and calculated.
Table 6. Summary of observed and predicted normalized concentrations within stability classes Mean observed Station 5
6
Class A B B* D F A B B* D F
196551968 0.14 x lo-4 0.18 x 1o-4
0.83 x 1o-5
1967-1968 0.50 x 0.16 x 0.14x 0.18 x 0.60 x
10-s lo-‘+ 1o-4 1O-4 1o-5
0.72x 0.43 x 0.42 x 0.95 x 0.23x
lo-’ 10-5 1O-5 10-5 lo-’
Predicted 1972-1973 0.68 x 1o-5 ---0.12 x 1o-4 -------------
Centre
Sector
0.34 x 10-s 0.77 x 10-5
0.45 x 10-s 0.73 x lo-5
0.39 x 1o-4 0.12 x 1o-4
0.19 x 1o-4 0.28 x 1O-5
0.38 x W6 0.87 x 1o-6 ____ 0.82 x 10-s 0.81 x 1o-5
0.44 x lo-6 0.73 x lo-6 ____ 0.34 x 1o-5 0.17 x 10-s
359
Validity of Gaussian plume model For the most stable class (i.e. narrower plumes) observations are in better agreement with sector averaged concentrations. This is especially true for station 6 which is furthest from the stack. This may be due to the averaging effect of the oscillation of the plume centre about both sides of the receptor during the sampling time. The biggest anomaly is for B class weather which occurs more frequently than expected with the classification scheme used, particularly in winter. However, when the data were further sorted into a B* class, which omits winter data, observed concentrations were marginally lower but higher than would be predicted for class B. Thus, concentrations usually predicted for stable classes are often observed during periods with no temperature inversions. The distribution of concentrations observed at station 5 within each stability classification was also determined. Figures 7a and b show the distribution of concentrations observed during D and B class stabilities at station 5 during the 196551968 period when the wind directions were recorded to the nearest lo”. Figures 7c and d are for 1972-1973 data. The number of samples is bigger because of the short sampling time. In this case the wind direction data are recorded to the nearest degree, and so the distribution is for a lo” interval in the direction of the receptor. The mean observed concentraton, centre plume and sector average predictions are indicated on the figure. The letters A, B, D and F show the predicted plume centre concentrations for those classes. The numbers in the bar on the left of the histogram is the number of zeros and that on the right is the number outside the range of the figure. Figure 7 shows that results are similar for the two data sets. It is interesting to note the large number of zeros compared to the few high concentrations that contribute to a mean that is acceptably close to the predicted concentration. Also the range of observed concentrations is wider than the range that would be predicted for station 5 regardless of choice of stability class. This could be largely due to the wide range of by and or occurring within each stability class reported by Geiss et al. (1981), and observed at Chalk River where the standard deviation of horizontal wind direction varies between 2 to 30” within each class (report in preparation). Also, it should be noted that these predictions are for a stack height of 43 m which is about right for the CRNL stack relative to station 5. Down draughts could reduce the effective stack height and account for some of the high concentrations. Although the tabulation of means in Table 6 implies some skill in estimating class, Fig. 7 demonstrates the wide range of concentrations that does occur during apparently similar conditions. From this we conclude that dispersivity is not uniquely associated with stability class. The above results lead to the question: is the observed uncertainty in model predictions due to use of one of six distinct stability classes for estimating both uY and a,?
To answer this question, the concepts of the statistical and predictive models were combined. Measured concentrations were compared with Gaussian plume model predictions based on real time wind speed and direction as before but with stability class chosen at random from its distribution observed at CRNL. The ensemble of observed/predicted ratios was almost identical to that found when real time stability based on dT/dz and wind speed was used. Increasing the averaging time for these predictions gives a similar improvement in the correlation between observations and predictions as was shown in Fig. 5. The stability was chosen at random for each hour in the averaging classes, (e.g. A could follow F). These results suggest that there is little to be gained from using the observed stability classes for the calculation even during prolonged periods of apparently constant conditions. Figure 8 compares the c.f.d. of concentrations predicted from random classes with that for observed concentrations. Although the agreement is not as good as that shown in Fig. 6, where real time stability classes were used for the predictions, the distributions are similar. The prediction from random stabilities increases the frequency of high concentrations by a factor of about 3. This may be due to a mismatch between stability and wind speed since the latter was chosen from its observed distribution. The results of the random stability class model explain why the calculated long term averages and probability distribution function of the concentrations agree reasonably well with their observed counterparts although on a one-to-one basis the comparison is poor.
CONCLUSION
This study has shown that while a standard Gaussian plume model can predict annual mean concentrations of a gas released from a tall stack on the Canadian Shield within a factor of 2, the probability of achieving this level of agreement for hourly averages is 20-30% with no significant correlation between individual hourly observations and predictions (r2 = 0.08). The probability, however, increases to 50% with an averaging time of 12 h and the correlation increases to 0.44. An analysis of concentrations observed during narrowly defined meteorological conditions has demonstrated the wide range of actual concentrations that is observed during conditions that can, given the models and parameterizations available, only result in one predicted concentration. However, the average of these observations is in reasonable agreement with the prediction. These results demonstrate that atmospheric dispersion can only be adequately estimated for relatively long averaging periods when standard dispersion parameters that have been derived from averages of many
360
E. ROBERTSONand P. J. BARRY
Cl 201 19ISL71615-
0 lb.-< 1312w 11z c lo: ii :: Q 7% 6s $6
532lO-
2.0 c/q
.(xN5
Fig. 7feb).
3.0 s.n.
-3
1
361
Validity of Gaussian plume mode1 Class
B
A
F
26 2&-T
18 : 16 -2
t4-
x z 12M x:
lo-
“0
8-
j
6 42O-
Class
A
B
D
F
(4
t
n
I,,
i
2.0
c/g
(
x10-S s.lL3
I,
3.0
24.0
)
Fig. 7. Distribution of concentrations observed at station 5 (a) 1968, D class (b) 1968, B class (c) 1972, D class (d) 1972, B class. The arrows are at predicted values of C/Q calculated for stability class A, B, F and D.
362
E.
ROBERTSONand
P. J.
BARRY
Fig. 8. Cumulative frequency distribution of concentrations predicted for station 5 with 1967-1968 wind data (b) and random stability classes compared with observations (a).
are used. The sources of uncertainties associated with short term atmospheric modelling required for emergency response that have been discussed and illustrated by measurements made at Chalk. River are probably general, but the magnitude of their effect will depend on site specific characteristics such as topography. Work is required to determine whether direct measurement of both horizontal and vertical turbulence will improve our capability to estimate concentrations due to short term releases. We conclude that dispersivity is not uniquely associated with weather class. There are very good reasons for believing that 0, is correlated with stability and it seems likely therefore that the weakness in the model arises from the assumption that eYis also simple and a unique function of stability. experiments
REFERENCES
Atwater M. A. and Londergan R. J. (1985) Differences caused by stability class on dispersion in tracer experiments. Atmospheric Erwironment 19, 1045-1051. Barry P. J. (1971) Use of Argon 41 to study the dispersion of
effluents from stacks in use of nuclear techniques in the measurement and control of environmental pollution. Int. Atomic Energy Agency, Vienna. Barry P. J. and Robertson E. (1986) llse of Meteorological Data to Parameterize Statistical Dispersion Models in Air Pollution Modelling and Its Application V. Plenum Press,
New York. Briggs G. A. (1974) Diffusion estimated for small emissions. Environmental Research Laboratories Air Resources, Atmosphere, Turbulence and Diffusion Laboratory, Annual Report 1973 USAFC Report ATDL-106, National Oceanic and Atmospheric Administration. Geiss H., Nester K., Thomas P. and Vogt K. J. (1981) In der Bundesrepublik Deutschland Experimentell ermittelte Ausbreitungsparameter fiir 100 m Emissionshohe, Jul1707. Hosker R. P. Jr. (1974) Estimates of dry deposition and plume depletion over forests and grasslands. In Physical Behauiour of Radioactive Contaminants in the Atmosphere. Int. Atomic Energy Agency, Vienna. IAEA (1980) A&ospher& dispersion in nuclear power plant siting-A safetv guide. Safetv Series No. 50-59-53.. ht. Atmiic Energy- Aiency, Vienna. Lewellen W. S. and Sykes R. I. (1985) Scientific critique of avaitable models for real-time simulations of dispersion. NUREG/CR-4157. Pasquill F. (1962) Atlnospheric Difision. Van Nostrand, Princeton, New Jersey.