STATISTICAL ELEMENTS OF PREDICTING ... evaluated by a combination of emission and dispersion ... dependent emissions can give an effective statistical.
Published in Water Science and Technology, Australia, 44: 9 pp 157-164 2001.
STATISTICAL ELEMENTS OF PREDICTING THE IMPACT OF A VARIETY OF ODOUR SOURCES Peter R. Best, Karen E. Lunney and Christine A. Killip Katestone Scientific, PO Box 2184, Toowong, Queensland, Australia 4066
Summary Two key elements in predicting odour response are the estimation of peak (few seconds) ground-level concentrations and the evaluation of the likelihood of a consequent adverse response. Peak rather than ensemble-average concentrations are not easily predicted by current dispersion models. The required peak-to-mean ratios depend on source characteristics, downwind distance and atmospheric stability. Using recent wind tunnel simulations for four types of sources and two atmospheric stabilities and various measures of intermittency and non-stationarity, different regimes of behaviour are resolvable. A set of peak-to-mean ratios for a specified probability of exceedance is recommended and their practicality discussed. Keywords:
Peak-to-mean ratio, intermittency, odour assessment.
1. Introduction There is increasing interest in evaluating the odour impact of various industrial and agricultural enterprises. Recent tribunal proceedings in Australia have involved disputes over the methods of estimating odour emissions and variability, the criteria for annoyance due to odours and the methods of predicting likely odour impact. These issues affect the siting of industry and the choice of odour control technology and suitable buffer zones. Short-term concentrations of odorous compounds are usually characterised by an intermittent time series of high peaks and periods of low concentrations. Previous field tests using trained observers have demonstrated strong intermittency for a tall stack, with odour recognition occurring sporadically in space and time. For an area source the odour was detected more regularly with a much lower centreline intermittency. Concentration time series for wind tunnel simulations of an area and point source in neutral conditions demonstrate the different structures of concentration bursts and gaps for the two source structures (Figure 1). Odour response is not just tied to mean concentration and intermittency of component concentrations but depends on the overall intensity (strength) of the odour (usually measured in odour units (OU/m3)), the frequency and duration of occurrence of various odour levels, the specific annoyance (offensiveness) of the constituent compounds of an odour and the composition, tolerance and past odour experience of the local population. Odour intensity and frequency are traditionally evaluated by a combination of emission and dispersion modelling. Duration and offensiveness are usually only known from experience or intensive odour surveys.
Community annoyance can be evaluated at various levels of complexity and involves a wide variety of physiological, psychological and sociological factors. Various experiments (see Woodfield and Hall 1994) have shown that the perceived odour response is not linearly related to the concentrations C(r,t) of the odorous compound. Odour response may be more related to the general characteristics of fluctuations of concentrations away from the mean value, rather than just the value of the peak concentration. A variation of odour response with ln C or C0.5 could reduce the importance of very high concentrations compared to the evaluation of toxic or inflammable releases. There are several general methods of assessing likely nuisance, annoyance and complaints due to odour exposure. Community surveys are particularly useful for existing sources but relatively expensive to perform well. The results from extensive European studies may not be readily transferred to the exposure patterns in the more open-air Australian environment. Industry codes of practice are particularly useful as screening techniques for likely odour impact. Semiempirical descriptions also have considerable utility, especially for estimating the influence of individual sources within complex configurations. The Warren Springs relationship between maximum distance dmax for odour complaints from a low-level source of strength E OU/s (dmax = (kE)0.6) can be extended to zones for perception, continuous perception, annoyance and complaint. The value of k varies by an order of magnitude between perception and complaint generation (with a resultant factor of 5 in dmax). Exercising this simple formula on a long-term meteorological database and including weatherdependent emissions can give an effective statistical analysis of likely community response.
0.2
0.008
0.18
0.007
0.16
0.006 Concentration
Concentration
0.14 0.12 0.1 0.08 0.06
0.005 0.004 0.003 0.002
0.04
0.001
0.02 0 0
3600
7200
10800
14400
Seconds
Figure 1:
0 0
3600
7200
10800
14400
Seconds
(a) (b) Concentration time-series from wind tunnel simulations of an (a) area and (b) elevated point source, for 1000 m downwind of the source in neutral stability.
The above approaches give little weighting to source characteristics and are of limited use for designing new facilities. Techniques for estimating and measuring concentration fluctuations over a short time period are in their infancy. Considerable short-range field work has been performed in recent years (mainly concerned with the dispersion of explosive or toxic compounds rather than odours). There is a growing recognition (e.g. Chatwin et al. 1997) that misleading results have been obtained by not fully incorporating the response time of any concentration sensor. Mathematical models are only beginning to come to grips with the forecasting of "average" concentrations (typically over 1 hour of steady-state meteorology); even then the natural variability caused by atmospheric turbulence and the imprecision of input parameters can limit the accuracy for a given hour to within 50-100%. However, standard regulatory models are often considered reasonable for predicting behaviour over a large number of like events (the ensemble of realisations). A useful adjunct to standard modelling techniques is then a set of rules to estimate "peak" concentrations from the prediction of ensemble averages. Odour guidelines in many Australian states often assume that current dispersion models can sensibly estimate hourly average concentrations under most atmospheric conditions in flat terrain. The profiles of concentration fluctuation parameters are assumed to mirror those of ensemble mean concentrations. A peakto-mean (P/M) ratio is used to estimate a few second odour level from the prediction of a 60-minute average. Environmental management plans are often based upon a threshold concentration that may be exceeded for a small proportion of the time (e.g. 0.5% of all hours in a year). This exceedance level should be estimated from a suitable meteorological file and “realistic” emission profiles. Odours from different sources are generally assumed to combine in an additive fashion. Odour thresholds are usually tied to
the median response of the population, not that of the most sensitive members. Guidelines may address either the lack of detectability of odours on the boundary of a site (most stringent) to levels unlikely to cause an annoyance (and/or register a complaint). Historically procedures have been based upon (a) odour not being detectable at the boundary of an installation and (b) a peak-to-mean ratio of 10 based upon measurements by Warren Springs Laboratory around an elevated point source (Hall and Kukadia, 1995). For surface extended sources frequently encountered in agricultural industries, this procedure is known to be very conservative. A recent project for the Environmental Protection Agency of New South Wales (Katestone Scientific 1995, 1998) investigated suitable strategies for estimating "peak" odour concentrations from predictions of mean concentrations for a variety of typical sources and atmospheric conditions. Specific tests in the Monash University environmental wind tunnel included fluctuation measurements at distance equivalent to 2 km downstream for an area source (100 x 100 m), representing extensive animal slurry spreading, waste ponds or large sheds and a line source (100 x 5 m) representing the disposal of animal slurry to land, long agricultural sheds or industrial buildings. Other studies have provided similar statistics for an elevated point source, either unaffected by turbulence from nearby buildings ("tall stacks") or well within the influence of building wakes ("short stacks"). All sources are usually assumed to be located in flat terrain. The project also included an extensive review of available information, numerical simulations, statistical analysis of the wind tunnel measurements and overall recommendations for the treatment of single and multiple sources. Table 1, summarising the type of information available for each source configuration, emphasises the lack of suitable studies for odour evaluation in stable conditions, especially in complex terrain.
Table 1:
Available information concentration fluctuations.
Source type
on
Atmospheric conditions Unstable Neutral Stable F,L,N,T F,L,N,T F F,L F,L F,L,N F,L,T F N,L N,L,T L N,L L L (point) F (point) L N,L L F, L -
Tall stack Short stack Surface point Line Area Terrain Building wake Clusters of sources Note: F = Field measurements N = Numerical modelling L = Laboratory studies T = Theoretical approaches
2.
Estimating peak-to-mean ratios
The following section restricts attention to the general estimation of peak concentrations and is applicable to a variety of problems. Odour design procedures require additional considerations. A peak concentration refers to the maximum concentration exceeded no more than a specified percentage of a given period (e.g. at roughly the 10-3 probability for all seconds in one hour). The mean concentration C refers to the more predictable concentration average for a period long enough to reduce stochastic variability to a reasonable level (i.e. the usual ensemble average predicted by sensible air dispersion models). The intermittency γ is the fraction of the time record with non-zero concentration. The second moment σc of the concentration series usually defines the intensity of fluctuations i(x) = σc/C. As mean concentrations are more amenable to estimation, peak-to-mean ratios are usually required; these depend on the specified frequency at which the “peak" is exceeded, the response time of receptor or instrument, the location, size and geometry of the source and the atmospheric state. The concentration characteristics at a given location are well represented by the probability distribution; this information is rarely available although the lower order moments (mean, variance, skewness and kurtosis) may be more easily measured. The form of the probability Table 2: Distribution Clipped normal Exponential Log-normal Gamma
distribution is often assumed from previous field and laboratory experiments to be a one parameter distribution such as the exponential distribution, a two parameter distribution (e.g. normal, log-normal, clipped-normal, clipped-gamma, Weibull) or a complex distribution (e.g. conjugate beta, K and generalised Pareto). More information on the "peakiness" of the concentration records is contained within the spectrum and in multifractal characteristics or simpler measures such as the recurrence interval and burst and gap lengths. Experimental and theoretical analyses often focus upon the overall intensity of fluctuations; if the form of the probability distribution is assumed, the likelihood of a concentration n times the mean can be estimated. Table 2 gives the P/M ratios at various probabilities of exceedance for a practical range of intensities of concentration fluctuations and for the more common probability distributions. Assuming that a 10-3 exceedance level provides suitable protection, the corresponding P/M ratios are 8-16, 5-10 and 3-5 for intensities of 1.5, 1 and 0.5 respectively. The change in fluctuation characteristics with downwind distance may be adequately handled by a specification of changes in the parameters of a sensible probability distribution, rather than a change in the choice of distribution. Although recent research (Yee and Chan 1997) suggests that a two-parameter form of the clipped-gamma distribution deals adequately with field data for a near-surface source in convective and stable conditions (by assuming 1 + i2 = 3/γ), similar data assimilation for other real-world situations is unavailable. Our approach uses the available previous studies to identify the centreline variation of i(x), the effects of source size and the applicability of laboratory and numerical studies to realistic situations. Each source type has been assessed to provide approximate prescriptions of the location and magnitude of the maximum centreline intensity of fluctuations (xmax and imax), the positions of "nearfield" and "far-field" behaviour, the downwind centreline and off-axis dependence i(x,y) and a suitable time averaging exponent p for the required distance and exposure ranges. Table 3 gives a general guidance to the source and atmospheric dependencies.
"Peak"-to-mean ratios for various fluctuation intensities and risks of exceedance.
Probability of 10-2 i = 1.5 i=1 i = 0.5 6.0 3.8 2.2
Probability of 10-3 i = 1.5 i=1 i = 0.5 8.0 4.8 2.6
Probability of 10-4 i = 1.5 i=1 i = 0.5 9.7 5.6 2.9
6.7 7.0 7.1
10.4 15.9 11.9
14 34.3 16.7
4.6 4.9 4.6
3.2 2.7 2.5
6.9 9.3 6.9
4.6 3.9 3.3
9.2 16.7 9.2
6.1 5.4 4.0
Table 3:
Recommended approximate factors for estimating peak concentrations for different source types, distances and stabilities for use in screening procedure for flat terrain situations.
Source type
Stability
Near-field xmax
imax
P/M60
Far-field P/M3
i
P/M60
p P/M3
Area
N S C
0.5 0.5 0.5
500-1000 300-800 500-1000
2.5 2.3 2.5
1.9 1.7 1.9
0.4 0.3 0.4
2.3 1.9 2.3
1.7 1.4 1.7
0.15 0.10 0.15
Line
N S C
1.0 1.0 1.0
350 250 350
6 6 6
2.8 2.8 2.8
0.75 0.65 0.75
6 6 6
2.8 2.8 2.8
0.25 0.25 0.25
Surface point
N S C
2.5 2.5 2
200 200 1000
25 25 12
10 10 7
1.2 1.2 0.6
5-7 5-7 3-4
3 3 2.5
0.2 0.2 0.15
Tall wake-free point
N S C
4.5 4.5 2.3
5h 5h 2.5 h
35 35 17
8 8 4
1.0 1.0 0.5
6 6 3
1.3 1.3 1.1
0.4 0.4 0.4
Wake-affected point
N/C
0.4
-
2.3
1.4
0.4
2.3
1.4
0.1
Volume
N/S/C
0.4
-
2.3
1.4
0.4
2.3
1.4
0.1
Note: N,S and C denote neutral, stable and convective atmospheric stabilities, P/Mn the best estimate of P/M ratio for n minute averages, at a probability of 10-3, and h the stack height. The averaging time exponent p is for time periods between several minutes and 1-2 hours.
3. Modifying dispersion models Short-term predictions (e.g. 3 minutes) for existing dispersion models use a power law dependence of concentration means and averaging time, Cp/Cm= A (tm/tp)p where tm can be chosen as a suitable time for predicting ensemble mean concentrations Cm to a chosen accuracy, Cp is the concentration averaged over a short time period tp and the constant A is expected to be close to 1. The values of p are assumed to be independent of downwind location and source type, and tp is taken to be in the range from minutes (instrument time resolution) to hours. Table 3 and other recent work (Hibberd 1998) suggest that p depends almost entirely on source type, not stability. Extrapolation to very short-time periods (e.g. seconds) cannot be recommended as there appear to be three regimes of behaviour with different values of p, suggesting that several physical processes may be important. Analysis of wind tunnel simulations has shown that the multifractal nature of concentration fluctuations gives a direct relationship between p, the exceedance threshold, an intermittency measure and the non-stationarity of the concentration record (Best et al 2000). Highly intermittent plumes such as from tall stacks give rise to large values of p; surface sources are less intermittent and give lower values of p. Borgas (2000) uses self-similarity arguments to show that
values of p = 6/17 and 3/14 can be expected for point and line sources respectively. Recommended more general improvements for dispersion models such as Ausplume include a functional form for i(x) for generic source types, the choice of an exceedance level and probability distribution to calculate “peak” from the ensemble average hourly concentration and interim recommendations on the treatment of overlapping sources. For several types of sources, the following centreline profile is considered appropriate:1 i ( x) = imax exp − 2 {ln ( x / xmax )}2 2b where
imax xmax b
= centreline maximum of i(x) = location of imax = constant for given source type and stability classification.
This is a three-parameter log-normal distribution that has the following suitable properties: (i) (ii) (iii)
i(0) = 0 i(xmax) = imax i(x) → if for x ≈ 10 xmax.
The asymptotic relationship is useful for most sources.
The recommended values of imax, b, if and xmax are given in Table 4. Table 4:
Initial recommendations for parameters of the log-normal distribution for i(x).
Source type/stability Area/stable, side length L Surface point/neutral, diameter L Line/neutral, length L, across-wind Elevated point source, convective/neutral - buoyant - non-buoyant
imax 0.5
b 0.95
if 0.25
xmax 6L
0.9
2
0.4
2L
0.8
2
0.5
6L
3-4 2-3
2 2
1.2 0.8
0.2Zi 0.2Zi
probability distribution P(x) and an exceedance rate, values of P/M can be used to estimate peak concentrations for a particular set of source and meteorological characteristics. For odour evaluations, the procedure can be repeated to obtain peak odour levels at each receptor for all times in the meteorological file (Figure 2). Response statistics can be generated from the number of events exceeding a chosen threshold (this can be made receptor-specific) or by more complex post-processing procedures. For example, optimisation of plant design should aim to satisfy a regulatory requirement that annoyance should occur for no more than a certain percentage of hours per year. This can use industry-specific annoyance relationships determined from laboratory exposures of representative observers or field studies (e.g. Miedema et al 2000).
Note: Zi is the mixing depth. In the absence of recommended values for other stability conditions, the above values can be used.
The choice of probability distribution is less critical in many cases and a gamma distribution will suffice. The definition of “peak 1 second concentration” is viewed statistically as that concentration unlikely to be exceeded more than 10-2 of events (e.g. 36 events in one hour), and the P/M ratio is 8.5 i - 1 for 0.5 < i < 3. The off-axis variability i(y) is relatively well established as a U-shaped from i(y) = i(0) exp 2
[y2/2σ y ] where σy is the dispersion parameter for a one-hour period. With this form of i(x,y) and estimates of C(x,y) for a given hour, peak concentrations or receptor response can be estimated for a single source. Odour evaluations require additional considerations. In practice, odour emissions from agricultural holdings, sewerage treatment plants, ponds and irrigated land may vary considerably due to fluctuations in wind, temperature and process or animal activity. Modelling of hourly odour concentrations should forecast mean concentrations for a constant source emission rate E and allow for the variability caused by σE in the P/M ratio. If the emission and meteorological/dispersive fluctuations are independent, the total intensity of fluctuations will be given by itot2 = i2 + iE2. The emission variability can be neglected unless iE becomes comparable to i; this exception is most likely for an area source under stable conditions.
4. Odour assessment The preceding results can be used as a design tool to estimate odour annoyance statistics for a given receptor over a suitably long meteorological dataset, at least for a relatively simple source structure. With suitable definitions of source type, a selection of the
YES NO
Figure 2:
Recommended procedure.
This procedure is relatively straightforward for individual sources; for multiple sources, the degree of correlation will influence the total intensity of concentration and the procedure may become more cumbersome. Overlapping odour sources may not give rise to additive effects due to the masking by one component.
An alternative and simpler prediction scheme for multiple sources multiplies the emission rate or level by the corresponding maximum P/M ratio for the midfield to give an effective source strength for use in dispersion modelling of hourly events. At each receptor, the model output for a given hour for each source can be used with assumptions of (a) taking the most prominent contribution or (b) adding the contributions if the odour source characteristics are similar and the source separation is less than a multiple of the downwind distance. Topographic effects are often important and may change both the intensity of concentration and the related intensity of turbulence in the boundary layer. There is little available evidence on which to base recommendations for P/M ratios. Detailed monitoring of vertical and cross-wind turbulence levels may be necessary for critical cases of complex situations such as well-defined valleys, major land-water interfaces and sources near major buildings. In reality, odour assessments often involve multiple and disparate sources in complex terrain and stable atmospheric conditions. At present, there is no scientifically-defensible method of evaluating odour impact in such cases and reliance should be placed on the above and a variety of screening procedures. Physical modelling and/or direct tracer gas experiments may also reduce the uncertainties.
5. Conclusions and discussion The concept of a peak-to-mean ratio is a convenient artefact but is not a statistically sound measure, unless associated with a defined risk of exceedance and an observation period. Interim values of i(x) and related parameters for different types of sources can be recommended from the available information for the simpler source types and provide a more rational methodology that can accommodate future advances in theory and experimentation. Although there are insufficient data to choose the most suitable probability distribution, the resulting P/M ratios are not significantly different; a log-normal or clipped-gamma distribution should characterise extreme concentrations. The corresponding P/M ratios can be used in conjunction with dispersion model predictions of hourly averages. Several studies show that P/M ratios and averaging time exponents depend more on source type and downwind distance than stability. Averaging time exponents should only be used within the time duration for which they have been established. The methodology is less clear at present for multiple sources or non-ideal terrain. A superposition of results from single source considerations is likely to be over-conservative, due to the smoothing of concentration fluctuations caused by separating the
sources and the response of the human nose to a mixture of odorous gases. As with odour measurements, odour modelling is in its infancy. However, the pressing legal and public search for simple procedures should encourage rather than restrict the development of rational assessment procedures for this very common type of air quality problem.
5. References Best P.R., Lunney K.E. & Killip C. 2000, ‘Averaging time corrections for estimating extreme air quality statistics’, 15th International Clean Air and Environment Conference, Sydney, Australia. Borgas M.S. 2000(a), ‘The mathematics of whiffs and pongs’, Proceedings of Enviro 2000 Towards Sustainability, Sydney, Australia.. Chatwin P.C., Lewis D.M. & Mole N. 1997, ‘Comments on the properties and uses of atmospheric dispersion datasets’, Il Nuovo Cimento, 20C: 475-489. Hall D.J. and Kukadia V. 1995, ‘Approaches to the calculation of discharge stack heights for odour control’, Clean Air, 24: 74-92. Hibberd M.F. 1998, ‘Peak-to-mean ratios for isolated tall stacks (for averaging times from minutes to hours)’, 14th International Clean Air Conference, Melbourne, pp 255-260. Katestone Scientific 1995, ‘Peak-to-mean ratios for odour assessments’, Report to the Environment Protection Authority of New South Wales. Katestone Scientific 1998, ‘Peak-to-mean ratios for odour assessments’, Report to Environmental Protection Agency New South Wales. Miedema H.M.E, Walpot J.I, Vou H. & Steunemberg C.F. 2000, ‘Exposure - annoyance relationships for odour from industrial sources’, Atmospheric Environment 34: 2927-2936. Woodfield M. and Hall D.J. 1994, ‘Odour measurement and control - an update’, AEA Technology Report. Yee E. and Chan R. 1997, ‘A simple model for the probability distribution function of concentration fluctuations in atmospheric plumes’, Atmospheric Environment, 31: 991-1002.
7. Acknowledgment The Katestone Scientific 1995 project included very significant components from Drs. Sawford and Borgas of CSIRO Atmospheric Research and Professor Melbourne and Dr Taylor of Monash University.
