Comparative Study of Gaussian Dispersion Formulas Within the Polyphemus Platform: Evaluation with Prairie Grass and Kincaid Experiments

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Comparative Study of Gaussian Dispersion Formulas within the Polyphemus Platform: Evaluation with Prairie Grass and Kincaid Experiments

IRE` NE KORSAKISSOK CEREA, Joint Laboratory ENPC-EDF R&D, Universite´ Paris-Est, Marne la Valle´e, France

VIVIEN MALLET Inria, Paris-Rocquencourt Research Center, Rocquencourt, France

(Manuscript received 19 November 2008, in ﬁnal form 15 June 2009)

ABSTRACT

This paper details a number of existing formulations used in Gaussian models in a clear and usable way, and provides a comparison within a single framework—the Gaussian plume and puff models of the air quality modeling system Polyphemus. The emphasis is made on the comparison between 1) the parameterizations to compute the standard deviations and 2) the plume rise schemes. The Gaussian formulas are ﬁrst described and theoretically compared. Their evaluation is then ensured by comparison with the observations as well as with several well-known Gaussian and computational ﬂuid dynamics model performances. The model results compare well to the other Gaussian models for two of the three parameterizations for standard deviations, Briggs’s and similarity theory, while Doury’s shows a tendency to underestimate the concentrations because of a large horizontal spread. The results with the Kincaid experiment point out the sensitivity to the plume rise scheme and the importance of an accurate modeling of the plume interactions with the inversion layer. Using three parameterizations for the standard deviations and the same number of plume rise schemes, the authors were able to highlight a large variability in the model outputs.

1. Introduction vironmental Protection Agency (EPA) models Industrial Source Complex Short Term, version 3 (ISCST3) and Gaussian models are widely used to model dispersion ‘‘AERMOD,’’ and the United Kingdom’s widely used at local scale, despite their well-known limits, since they Gaussian model Atmospheric Dispersion Modeling are based on simple analytical formulas and are com- System (ADMS). Since Polyphemus is not a single air putationally cheap to use. However, the use of empirical quality model but a platform aimed at handling dif- schemes to compute the Gaussian standard deviations ferent models, it provides an appropriate framework to involves large uncertainties—hence many different formulations exist. When plume rise occurs, additional pa- benchmark parameterizations and features of Gaussian rameterizations are introduced, which results in still more models, thus evaluating the spread in model outputs. In variability. In this paper, the Gaussian models developed addition, one of the aims of this paper is also to put on the Polyphemus platform (Mallet et al. 2007) are used together a number of different parameterizations that to evaluate the results’ sensitivity to the physical param- were previously described in many different contexts, eterizations for standard deviations and plume rise. This in a clear and usable way, which also makes com- evaluation is ensured by means of theoretical study, com- parisons easier. parison to experimental data, and comparison to other We first present the Polyphemus Gaussian models in well-known Gaussian model performances, like U.S. En- section 2, with an emphasis on the parameterizations for standard deviations and plume rise. A first comparison of the parameterizations is given in section 3. Corresponding author address: Ire`ne Korsakissok, CEREA, 6–8 Then, the model evaluation is carried out with Prairie avenue Blaise Pascal, Cite´ Descartes, 77455 Champs-sur-Marne, Marne la Valleé CEDEX 2, France. Grass (section 4) and Kincaid (section 5) field experi- E-mail: [email protected] ment datasets.

DOI: 10.1175/2009JAMC2160.1

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2. Description of the Polyphemus Gaussian models cay. In Polyphemus, full gaseous chemistry may also be handled by the Gaussian puff model. a. The Gaussian plume and puff models

Polyphemus hosts both a Gaussian plume model and b. Dispersion parameterization schemes a Gaussian puff model. Arya (1999) reviews the main assumptions for the relevance of the two models. A The expression of the total plume standard deviation is the sum of the spread due to turbulence (s , s ), Gaussian plume model assumes a Gaussian distribution yturb zturb the additional spread due to plume rise (s , s ), and of mean concentration in the horizontal (crosswind) and ypr zpr vertical directions, in steady-state and homogeneous the initial spread due to the diameter ds of the source meteorological conditions. The dispersion in the down- 2 2 2 2 2 2 2 sy 5 sy 1 sy 1 ds /4, sz 5 sz 1 sz . (2) wind direction is supposed to be negligible compared to turb pr turb pr the transport by the mean wind in the plume model. A For the sake of clarity, s and s are named in this Gaussian puff model discretizes the plume into a series yturb zturb of puffs, each of them having a Gaussian shape in all section sy and sz. These standard deviations are esti- three directions. The puff model can also take into ac- mated through empirical schemes, as functions of the count different meteorological data for each puff, there- downwind distance to the source and the stability, based fore allowing a more accurate simulation of nonstationary on a few dispersion field experiments. Here, three pa- and nonhomogeneous conditions. In Polyphemus, the rameterizations are described. Two of them are based plume and puff models share the same parameterizations. on a discrete description of the atmospheric boundary Thus, in stationary and homogeneous conditions—as as- layer: the Briggs formulas and the Doury formulas. The sumed in the Prairie Grass and Kincaid experiments—the third one is based on similarity theory, and involves Gaussian puff model gives the same solution as the parameters such as the wind velocity fluctuations, the Gaussian plume model, if averaged over a long enough Monin–Obukhov length, the mixing height, and the period. Henceforth, only the Gaussian plume model is friction velocity. therefore used (it was verified that the Gaussian puff model gave the same results). 1) BRIGGS FORMULAS For a stationary plume, the concentration C is given The Briggs formulas are based on the Pasquill–Turner by the Gaussian plume formula: stability classes (Turner 1969) and fitted on the Prairie "# Grass experiment. This parameterization is born from Q (y y )2 5 s an attempt to synthesize several widely used schemes by C(x, y, z) exp 2 2psyszu 2sy interpolating them for open country and for urban areas, ()"#"# 2 2 for which they are particularly recommended. The full (z z ) (z 1 z ) 3 p 1 p formulas can be found in Arya (1999), for instance. The exp 2 exp 2 , 2sz 2sz general form is given by (1) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiax g sy 5 p , sz 5 ax(1 1 bx) , (3) where Q is the source emission rate, given in mass per 1 1 bx second, u is the mean wind speed, and s and s are the y z with x as the downwind distance from source, and a, b, Gaussian plume standard deviations in the horizontal and g coefficients depending on the Pasquill stability (crosswind) and vertical directions. The coordinate y re- class. There are six stability classes corresponding to fers to the crosswind horizontal direction, and y is the s different states of the atmosphere (Pasquill 1961), from source coordinate in that direction. The coordinate z A (extremely unstable) to F (stable). refers to the vertical coordinate and zp is the plume height above ground—sum of the source height and the plume 2) DOURY FORMULAS rise (see section 2c). The second term of the last factor represents the ground reflection; similarly, additional An alternative parameterization is described in Doury terms can take into account the reflections on the ele- (1976). This parameterization has been developed for the vated inversion layer. Also, when the plume is mixed specific application of radionuclide dispersion, and fitted enough in the boundary layer (sz . 1.5zi), the formula is on a wider experimental field than the Prairie Grass field. modified to consider that the plume is vertically homo- The formulas use only two stability situations, corre- geneous. In addition, other factors can be applied to this sponding to ‘‘normal’’ and ‘‘low’’ dispersion, determined formula to take loss processes into account, such as dry by the vertical temperature gradient. By default, it is as- deposition, scavenging, and radioactive or biological de- sumed that low dispersion occurs during nighttime with

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rounding air: this difference in heights can be significant (up to a few hundred meters) and is called ‘‘plume rise’’ (see Fig. 1). Estimates of the plume rise can be provided, based on the source initial height, diameter, ejection temperature, and ejection velocity. In all formulas described below, it is assumed that the plume instanta- neously reaches its final height at the emission time, then travels downwind. More accurate formulations allow one to determine the plume rise as a function of the downwind distance, but are not investigated here. If the plume rise is Dh, the plume final height is given by

zp 5 zs 1Dh,withzs as the source height. The initial FIG. 1. Representation of an elevated source: zs is the source spread due to plume rise is added to the total standard height and zp is the effective source height, with plume rise. The deviations at the emission time according to Eq. (2). It is modeled point of emission is at zp but the downwind travel is ne- estimated following Irwin (1979) for the crosswind spread glected during plume rise. The initial plume spread due to plume rise is s . and Hanna and Paine (1989) for the vertical spread that zpr Dh Dh low wind speed (u # 3ms21). The standard deviations sy 5 and sz 5 . (6) are given in both cases in the general form pr 3.5 pr 2

K K Three different formulas to compute plume rise are de- s 5 (A t) h and s 5 (A t) z , (4) y h z z scribed in this section. While the Briggs–Hybrid Plume Dispersion Model (HPDM) formulas depend on the where t is the transfer time since release time. In the case stability of the atmosphere, the two other formulas de- of a steady-state plume, t 5 x/u, where x is the distance pend only on the source dynamics and buoyancy and are from the source and u is the wind speed. The formulas based on the source heat rate. for the normal situation can be found in Demae¨l and Carissimo (2008). 1) BRIGGS–HPDM PLUME RISE

3) SIMILARITY THEORY The plume rise computation is based on the Briggs formulas—detailed in Seinfeld and Pandis (1998)— If enough meteorological data are available, s and s y z assuming a buoyancy-driven plume rise [Eqs. (8)–(12)]. can be estimated using the standard deviations of wind In the formulas, Dh is the plume rise, u is the wind ve- velocity fluctuations in crosswind horizontal direction s y locity, w is the convective velocity, and u is the friction and in vertical direction s . Following Irwin (1979), * * w velocity. In addition, s is the Briggs static stability pa- dispersion coefficients are investigated in the form p rameter and Fb is the initial buoyancy flux parameter. They are defined as sy 5 sytFy and sz 5 swtFz, (5)

gdu/dz 2 Ts T where t is the time in seconds, and Fy and Fz are functions s 5 and F 5 gy d , (7) p T b s s T of a set of parameters that specify the characteristics of s the atmospheric boundary layer. These functions are determined from experimental data. Various expressions with g as the gravity acceleration, du/dz as the vertical gradient of potential temperature, T as the ambient tem- of Fy and Fz have been proposed (e.g., Irwin 1979; Weil 1988). Appendix A details the formulations used in perature, ys as the vertical velocity of the emission, ds as the source diameter, and Ts as the source temperature. Polyphemus for Fy, Fz, sy, and sw. A modified formulation from Hanna and Paine (1989) is also available for (i) Stable cases the case of elevated sources (above 100-m height). Two different formulations are also given for the standard The formulas for stable cases come from Seinfeld deviations above the boundary layer. and Pandis (1998) and are also used in the HPDM (Hanna and Paine 1989). The final plume rise is Dh 5 c. Plume rise schemes min(Dh1, Dh2), where ! When emissions are hotter than the ambient air, or 1/3 have a significant ejection speed, the plume generally Fb 1/4 3/8 Dh1 5 2.6 and Dh2 5 4Fb sp . (8) reaches a certain height before behaving like the sur- usp

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(ii) Unstable and neutral cases The following formulas come from Seinfeld and Pandis (1998) and are originally from Briggs:

F3/4 Dh 5 21.4 b if F , 55 and (9) u b

F3/5 Dh 5 38.71 b if F $ 55. (10) u b In the above formulas, ambient turbulence is supposed to be negligible, relative to the plume internal turbulence. However, in many unstable and neutral cases, the plume eventually reaches a point where ambient turbulence is large enough to stop the plume vertical FIG. 2. Partial penetration in the inversion layer: zs is the source progress. In Briggs (1971), this so-called breakup height height and zi is the inversion layer source height. The penetration factor is P. The initial plume rise is Dh and the plume rise of the is determined as the point where both the plume and the remnant part of the plume within the boundary layer is Dh9. Also, ambient eddy dissipation rates are equal. It is reported in Q is the total emission rate. Hanna (1984) and used here for neutral cases, whereas the unstable breakup formula comes from Hanna and Paine (1989). When there is the choice between a break- Here, the ejection heat rate is computed using the up formula and a Briggs formula, the one giving the source diameter, its ejection velocity, and the tempera- minimal plume rise is chosen: ture difference between the plume and ambient air: ! 3/5 Fb 2/5 2 Dh 5 4.3 z unstable (11) Qh 5 228.19 ys ds (Ts T). (15) uw2 i * ! This is an approximation, based on the assumption that 2/3 F the caloriﬁc capacity of the ejected gas is not too dif- Dh 5 1.54 b z1/3 neutral. (12) uu2 s ferent from that of air. * 4) PARTIAL PENETRATION IN THE INVERSION 2) HOLLAND FORMULA LAYER This plume rise formula is the same for all stabilities. In the case of an elevated source with a large plume It comes originally from Holland (1953) and was modi- rise, the plume can partially or totally penetrate the in- ﬁed by Stu¨ mke (1963): version layer (Fig. 2). Thus, the part of the plume that is above the inversion height is supposed to be trapped d y d1.5 T T 1/4 there and cannot reenter the boundary layer. Over- Dh 5 1.5 s s 1 65 s s . (13) u u T looking this phenomenon can lead to false estimations s of the ground concentration, either by overestimating concentrations if the plume is always trapped below the 3) CONCAWE FORMULA inversion layer or by underestimation if the plume is trapped above the inversion layer. A partial penetration In Brummage (1968), a comparison study was made of the plume is therefore assumed when the plume between several plume rise formulas, including the centerline (after plume rise) is close enough to the in- Holland–Stu¨mke formula, which was among the best. An version height. The formulas come from Hanna and attempt was made to synthesize the multiple formula- D 2 a b Paine (1989). If the plume rise h exceeds (zi zs)/1.5, tions into a relationship in the form Dh 5 K(Qh/u ), the top of the plume impacts the capping inversion, and where Qh is the source heat rate and K, a,andb are a partial or total penetration of the inversion layer oc- empirical constants. It resulted in the Concawe formulas: curs. The fraction of the plume that has penetrated the inversion layer, called the penetration factor, is equal to Q0.55 P 5 1.5 2Dz/Dh if 0.5 ,Dz/Dh , 1.5 (partial penetra- Dh 5 0.071 h . (14) u0.67 tion), and P 5 1ifDz/Dh # 0.5 (total penetration),

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FIG. 3. Evolution of the Gaussian standard deviations (a) sy and (b) sz against the travel time from the source, for Briggs’s formulas (six stability classes), Doury’s parameterization (normal diffusion), and the similarity theory scheme (stable, neutral, and unstable cases).

where Dz 5 zi 2 zs. In the case of a partial penetration, Grass z0 5 0.01 m. This leads to the value for unstable the fraction of the plume that remains within the bound- cases (corresponding to the B class) L 525.86 m, and for ary layer has a new emission rate Q(1 2 P)andanew stable cases (E class) L 5 11.5 m. The convective velocity D 95 1 2 3 52 3 value of plume rise h (0.62 0.38P)(zi zs) (shown is computed with the formula w* u*h/L.Theplume in Fig. 2). In the case of a total penetration, the remaining height is taken at z 5 1.5 m. emission rate is equal to zero and there is no plume left in the boundary layer. b. Evaluation of the standard deviations Figure 3a shows the evolution of the horizontal stan-

3. Comparison of the dispersion formulas dard deviations up to about 3 h. The values for sy at t 5 9000 s range from 100 m (similarity theory) to 3000 m a. Comparison setup (Doury) in stable cases. In unstable cases, there is less

The evolution of the Gaussian standard deviations variability, since sy ranges from 1200 to 3000 m. The (without a possible additional spread due to the diameter standard deviation computed with similarity theory is and/or plume rise) can be plotted for the parameteriza- the smallest in stable and neutral cases, but it compares tions described in the previous section, to evaluate the to the Briggs results in unstable cases. The Doury stan- spread. It must be noted that the Briggs formulas give sy dard deviations are comparable to the others in unstable and sz as a function of the downwind distance x from the cases, and give the largest values in the case of stable source, whereas the Doury and similarity theory param- situations. For larger travel times, it would grow above eterizations are expressed according to the travel time t. all other parameterizations. Also, if the wind speed is These two parameters are related through t 5 x/u,withu very low (about 0.5 m s21), the downwind distance re- as the wind speed. The evolution of the standard de- mains relatively small even for large travel times, viations against t is given in Fig. 3. The Briggs formulas therefore the Doury and similarity theory parameteriza- are computed for the six Pasquill stability classes, taking tions give larger standard deviations at a given distance a wind speed value representative of the stability class: than Briggs’s. The spread for the vertical standard de- 21 21 u 5 2ms for A and F classes, u 5 2.5 m s for B, viation is also very large (Fig. 3b). In stable cases sz u 5 4ms21 for C, u 5 5.5 m s21 for D, and u 5 3ms21 values range from about 20 m (similarity theory) to for E. To compute the standard deviations with similarity 400 m (Doury). In unstable cases, there are larger dif- theory, some other meteorological data are needed, and ferences, with sz ranging from 100 m (similarity theory) 5 the following values are taken: the friction velocity u* to 3500 m (Briggs, class A), so over 30 times larger. Of all 0.3 m s21 and the boundary layer height h 5 500 m. The parameterizations, only the Briggs formulas for the un- Monin–Obukhov length L is computed according to the stable classes A, B, and C show standard deviations above relationship between L and the roughness length z0 given 500 m. Similarity theory is the parameterization giving by Golder (1972), taking the roughness value for Prairie the smallest vertical standard deviation for all stabilities.

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These preliminary results highlight a large variability TABLE 1. Statistics for several Gaussian models: comparison of in the standard deviations, depending on the stability maximum arc concentration for simulation and observation. Poly- and the parameterization. Thus, a substantial variability phemus results are presented for three formulas for standard deviations and 43 trials in Prairie Grass experiment. Unit is (mg m23)/ can also be expected in the output results. Besides, be- (g s21), which is concentration normalized by the emission rate. cause of the differences in estimations of sz, the plume might penetrate the inversion layer with some parame- Model Mean FB NMSE Corr FAC2 terizations and not with others, which would increase the Obs 2.23 0.00 0.00 1.00 1.00 variability. It should also be pointed out that the stability ADMS4 1.56 0.36 3.01 0.63 0.66 diagnosis depends on the standard deviation formula AERMOD 2.14 0.04 1.83 0.75 0.73 ISCST3 2.01 0.11 1.78 0.72 0.61 used. For instance, in the Prairie Grass experiments, the Obs 2.32 0.00 0.00 1.00 1.00 Pasquill–Turner diagnosis used with the Briggs formulas Briggs 2.33 0.00 1.83 0.78 0.74 considers 30% of the experiments to be unstable, 20% Doury 1.74 0.29 2.58 0.67 0.29 stable, and 50% neutral, whereas the diagnosis based on Similarity theory 2.34 20.01 0.91 0.85 0.62 Monin–Obukhov length (Table A1, described below)— used for similarity theory—gives about 48% of unstable cases and 52% of stable cases. This might compensate typical performance measures for acceptable models. some of the differences in the standard deviation estima- Those criteria have been summarized in Chang and tions: for instance, similarity theory in unstable cases and Hanna (2004) and in Hanna et al. (2004) based on the Briggs’s formulas in neutral cases give similar estimations. evaluation of many models with many field datasets. A model is deemed acceptable if the mean bias is within 4. Evaluation with Prairie Grass experiment 630% of the mean (20.3 # FB # 0.3), if the random scatter is about a factor of 2–3 of the mean (NMSE # 4), a. Model evaluation criteria and if the fraction of predictions within a factor 2 of the The statistical evaluation method used for all models observations is about 50% (FAC2 $ 0.5). in this comparison is described in Chang and Hanna b. Experiment and modeling setup (2004). It is also the method used in the Model Valida- tion Kit (Olesen and Chang 2005), which has been de- The Prairie Grass experiment has become a standard veloped and tested during a series of workshops and database on which parameterizations have been fitted, conferences on harmonization within atmospheric dis- and has been used for many model evaluation studies. persion modeling for regulatory purposes. In many field The experiment took place in O’Neil, Nebraska, during experiments, the sensors are placed in arcs at various summer 1956. The site was a flat terrain of short-cut distances downwind of the source, and the maximum grass. A continuous plume of SO2 was released, without predicted and observed concentrations for each arc plume rise, near the ground (at 0.46 m). Measurements (‘‘maximum arcwise concentrations’’) are compared. were taken on five arcs at 50, 100, 200, 400, and 800 m Therefore, all other concentration values on the arc are from the source. A set of 43 of the 68 trials is usually used not used in the comparison. The maximum observed for model validations, including a wide range of stability value is determined on time-averaged concentration conditions during day and night. In our simulations, the measurements (the averaging time for Prairie Grass stability classes are taken from the database used in experiments is 10 min). The comparison study is carried Hanna et al. (2004) for Flame Acceleration Simulator out using maximum arcwise concentrations normalized (FLACS) evaluation, and the other experimental data by the emission rate Q—so-called centerline values. The are taken from the U.S. EPA database (http://www.epa. results are discussed using scatter diagrams as well as gov/scram001/dispersion_prefrec.htm). statistical performance measures such as the fractional c. Comparison with other Gaussian models bias (FB), the normalized mean square error (NMSE), the fraction of predictions within a factor 2 of observa- Many Gaussian models and a few computational fluid tions (FAC2), and the correlation coefficient (Corr). dynamics (CFD) models were evaluated with the Prairie The formulas to compute these statistics are given in Grass experiment. Three of the most used Gaussian appendix B. It should be noted that these formulas give models were compared in CERC (2007): ISCST3 and negative values of FB for model overprediction and AERMOD are recommended by the U.S. EPA, and positive values if the model tends to underpredict con- ADMS4 is developed in the United Kingdom and widely centrations. A perfect model would have Corr and FAC2 used in Europe. ISCST uses discrete categories to de- equal to 1.0 and FB and NMSE equal to 0.0. As there is scribe the atmospheric stability (Pasquill–Guifford pa- no such thing as a perfect model, it is useful to determine rameterization for rural areas and Briggs’s formulas for

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FIG. 4. Evolution of the statistics against the downwind distance from source for (top, left to right) Corr, FB, and FAC2, and (bottom) NMSE. The statistics are computed at five monitoring arcs (50, 100, 200, 400, and 800 m). The acceptable performance is situated between the dashed lines. urban area), whereas AERMOD and ADMS use good results, as expected since the parameterizations boundary layer depth and Monin–Obukhov length to they use for standard deviations are fitted on the Prairie describe the state of the atmospheric boundary layer. Grass experiment. On the contrary, the results for Poly- The CFD models FLACS (Hanna et al. 2004) and phemus with Doury’s formula and ADMS4 are hardly Mercure (Demae¨l and Carissimo 2008) were also eval- within the range of acceptable model performance for uated using Prairie Grass data. all indicators: ADMS4 underpredicts the mean con- Table 1 shows the Prairie Grass statistics for the centrations by about 30%, and only 29% of the values Polyphemus plume model with several parameteriza- predicted by the Doury model are within a factor 2 of the tions, along with the aforementioned Gaussian models. observations. Polyphemus with similarity theory shows Results for ADMS4, AERMOD, and ISCST3 come very good results—there is almost no bias, and the cor- from CERC (2007). The statistics for these three models relation and NMSE are the best of all models presented are computed with a subset from the usual set of 43 ex- here. A more detailed analysis of the results with Poly- periments (used for Polyphemus evaluation), hence the phemus Gaussian models is provided below. differences in the mean observed centerline values. The d. Statistics for each arc statistics presented here are computed for the center- lines of the five arcs. Most values in Table 1 are within The model performance is now analyzed for the five the acceptable range defined in section 4a. AERMOD, monitoring arcs, so as to compare the behavior of the ISCST3, and Polyphemus with the Briggs formulas show three standard deviation parameterizations. Figure 4

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FIG. 5. Scatterplot of maximum arc concentrations for observations and simulations with the (a) Doury, (b) Briggs, and (c) similarity theory parameterizations. Prairie Grass experiment, 43 trials. Unit is mg m23 (g s21)21. The results are shown at five monitoring arcs (50, 100, 200, 400, and 800 m). shows the statistical indicators, described in appendix B, these results, the FLACS results reported in Hanna et al. computed on the centerline values for each arc sepa- (2004) underestimated the concentrations at the shortest rately for the 43 experiments. The ‘‘acceptable range’’ as distances (up to 200 m), and slightly overpredicted the defined in section 4a is delimited by the dashed lines. results at the farthest arcs. Demae¨l and Carissimo (2008) Most indicators show a decreasing performance at far- also found the underestimation tendency for the Mercure ther distances from the source, except the correlation. CFD model at short distances. They attributed it to the Whereas Briggs’s and Doury’s parameterizations un- Eulerian dispersion,pffiffi which corresponds to a plume be- derpredict the concentrations—this tendency increases havior in s } t (with t the travel time), whereas the with the distance (FB grows higher)—similarity theory plume dispersion at short range should be in s } t. For C, overpredicts the concentrations, especially at the far- D, and E stability classes, the overall performance of the thest arcs (400 and 800 m). This can be related to the Mercure CFD model was shown to be between that of small standard deviation values given by this parame- the Briggs and Doury parameterizations. terization, pointed out in section 3. At the first two arcs Figure 5 shows the scatterplots for the three param- (50 and 100 m), similarity theory gives the best results eterizations. While the behavior of the model with the for all indicators. Finally, the Doury parameterization Briggs parameterization is quite well fitted to the ob- shows a poor performance in terms of FAC2, as well as servations, the overprediction tendency at the two fur- for NMSE and FB, for all distances. In comparison to ther arcs is clearly shown for similarity theory. The

Unauthenticated | Downloaded 09/26/21 09:05 PM UTC DECEMBER 2009 K O R S A K I S S O K A N D M A L L E T 2467 scatterplot for the Doury parameterization confirms its poor performance, especially in terms of FAC2: the results for one arc are almost flat, which means that the modeled concentrations at one arc do not vary much with the different experiments. This could come from the representation of the atmosphere stability in only two classes (normal and low diffusion), which may be insufficient in some meteorological situations. Section 3 also showed that the Doury parameterization can give a very high value of sy relative to the other two parameterizations at a given distance, especially at low wind speeds.

5. Evaluation with Kincaid experiment a. Experiment and modeling setup FIG. 6. Plume rise (m) computed by the different schemes for Kincaid experiments as a function of the wind speed. The Kincaid experiment took place at the Kincaid power plant in Illinois in 1980 and 1981. The plant stack is 187 m high with a diameter of 9 m and is surrounded ulations were carried out with three parameterizations by flat farmland and some lakes. Meteorological data for standard deviations (similarity theory, Briggs’s, and came from an instrumented tower, and the conditions Doury’s) and three parameterizations for plume rise during the experiments ranged from neutral to convec- described in section 2. The chimney diameter as well as tive. The tracer material was a buoyant plume of SF gas, 6 the initial plume spread due to plume rise was taken into released from the stack and measured by monitors de- account in the total standard deviations [Eq. (2)]. When ployed on arcs between 0.5 and 50 km from the source at similarity theory is used, the alternative HPDM for- ground level. There were 200 monitors that were shifted mulas for elevated release detailed in appendix A are day to day to correspond to the wind direction, and the used. Relative to the usual similarity theory parame- arcs distances also varied with the meteorological situ- terization, it slightly increases the overestimation but it ation. The recorded measurements are the arc maxi- also improves the correlation coefficient, especially with mum concentrations averaged over 1 h. The database Briggs–HPDM plume rise. The model evaluation con- contains 171 h of measurements. This dataset is often sists, first, in comparing the results with the different used to validate plume rise parameterizations because of parameterizations, with an emphasis on the plume rise the highly buoyant release that led to substantial plume description. Second, we compare the results with those of rise. All data used for the following simulations is given other models. with the Model Validation Kit (http://www.harmo.org/ kit/Download.asp). In this dataset, a quality indicator b. Model evaluation was assigned to each measurement value, denoting how 1) PLUME RISE reliable the maximum concentration should be consid- ered (Olesen 1995). Only the most reliable data, of A first analysis of the plume rise values is done in this quality 2 and 3, were used here. The statistics are com- section, so as to compare the plume rise formulations puted on 165 experiments. and to give an insight on the additional variability due to It has to be pointed out that in the following study the plume rise. Figure 6 shows the plume rise values com- simulations with the Polyphemus Gaussian model use the puted with the 3 parameterizations and 165 experi- observed inversion height when available and, for some ments, against the wind speed. As expected, the plume cases, the predicted height. On the contrary, other models rise decreases with higher wind speeds, smoothing dis- presented here like ADMS, AERMOD, and most likely crepancies between the different schemes. It was pointed Operationelle Meteorologiske Luftkvalitetsmodeller out, for example in Canepa et al. (2000), that the Briggs (OML) and HPDM recomputed the inversion height scheme has a tendency to overestimate plume rise at low with their own preprocessor. This could lead to significant wind speeds. Indeed, the plume rise given by the Briggs– differences, since this height is of great importance to HPDM scheme reaches very high values for low wind know whether the plume touches the ground or is trapped speeds. The Holland and Concawe plume rises are simi- above the inversion layer, as explained in section 2. Sim- lar, which is not surprising considering that the former

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TABLE 2. Proportion of cases with total or partial penetration in TABLE 3. Statistics for Polyphemus Gaussian models: comparison the inversion layer for all three plume rise parameterizations. of centerline values C/Q for simulations and observations—Kincaid Proportion with respect to 165 experiments. data of quality 2 and 3. There are 165 experiments. Unit: ng m23 (g s21)21. Plume rise is computed with Briggs–HPDM formulas. The Model Total penetration (%) Partial penetration (%) scheme for standard deviations that performs best is in boldface. Briggs–HPDM 29 28 Model Mean Std FB NMSE Corr FAC2 Holland 23 17 Concawe 24 23 Obs 39.89 39.22 0.00 0.00 1.00 1.00 Briggs 21.33 21.10 0.61 2.37 0.19 0.43 Doury 12.77 14.09 1.03 4.70 0.07 0.22 Sim.th. 42.02 34.73 20.05 1.33 0.19 0.45 was used in the design of the latter. Hence, we can sup- pose that the model behavior will be similar for those two schemes, whereas using Briggs–HPDM could lead trations, by a factor of 2 for the Briggs formulas and 3 for to a model underestimation, if the plume is predicted to the Doury formulas. On the contrary, the similarity the- be too high. In addition, Table 2 shows the proportion of ory parameterization performs quite well for all indicators cases in Kincaid experiments with total or partial pen- (since there is nearly no bias), except for the correlation, etration in the inversion layer: as expected, it is higher which is quite low for all standard deviations. for the Briggs–HPDM plume rise, with almost 60% of This is conﬁrmed by Fig. 7 where the scatterplot for the cases. The Holland and Concawe plume rises give the Briggs formulas clearly indicates the underestima- about the same number of cases with total penetration. tion tendency (Fig. 7b), whereas the one with similarity However, there are fewer cases with partial penetration theory (Fig. 7a) is much more centered. However, in both given by Holland than by the Concawe formulas. cases, one can observe ‘‘vanishing concentrations’’— Hereinafter, evaluation results are analyzed for each concentrations that are observed but are not reproduced of the three plume rise parameterizations (statistics on by the model. This can occur when the plume rise is too all arcs and experiments). For each plume rise parame- high, if the plume totally penetrates the inversion layer, terization, the scheme for standard deviations that per- or if it touches the ground later than the observed plume. forms best is in boldface in Tables 3–5. The similarity In the ﬁrst case, simulated concentrations are equal to theory parameterization is labeled ‘‘Sim.th.’’ zero at all arcs for the experiment, since there is no re- entering of the plume below the inversion layer. In the 2) RESULTS WITH BRIGGS–HPDM PLUME RISE second case, only the concentrations at the nearest arcs Table 3 shows the model results with Briggs–HPDM to the source are missing, that is, the highest concen- plume rise, for the three standard deviation schemes. As trations. This phenomenon could be responsible for the expected, the tendency is to underpredict the concen- low correlations that are globally observed.

FIG. 7. Scatterplots of centerline values C/Q for simulations and observations—Kincaid data of quality 2 and 3: (a) similarity theory and (b) Briggs. There are 165 experiments. Unit: ng m23 (g s21)21. Plume rise is computed with the Briggs–HPDM formulas. Standard deviations are computed with the Briggs and similarity theory formulas.

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TABLE 4. Statistics for Polyphemus Gaussian models: comparison TABLE 5. Statistics for Polyphemus Gaussian models: comparison of centerline values C/Q for simulations and observations—Kincaid of centerline values C/Q for simulations and observations—Kincaid data of quality 2 and 3. There are 165 experiments. Unit: ng m23 data of quality 2 and 3. There are 165 experiments. Unit: ng m23 (g s21)21. Plume rise is computed with Holland formulas. The (g s21)21. Plume rise is computed with Concawe formulas. The scheme for standard deviations that performs best is in boldface. scheme for standard deviations that performs best is in boldface.

Model Mean Std FB NMSE Corr FAC2 Model Mean Std FB NMSE Corr FAC2 Obs 39.89 39.22 0.00 0.00 1.00 1.00 Obs 39.89 39.22 0.00 0.00 1.00 1.00 Briggs 33.01 28.26 0.19 1.46 0.21 0.42 Briggs 32.88 32.75 0.19 1.49 0.27 0.48 Doury 15.87 13.27 0.86 3.55 0.04 0.28 Doury 16.87 17.74 0.81 3.29 0.12 0.31 Sim.th. 61.97 47.52 20.43 1.38 0.24 0.38 Sim.th. 61.82 53.79 20.43 1.57 0.24 0.43

3) RESULTS WITH HOLLAND PLUME RISE lower correlation. Results for the other models come from CERC (2007), as in the case of Prairie Grass, for Results with the Holland plume rise are given in Table 4. quality 2 and 3 (Table 6). As noted in section 5a, we used The modeled concentrations are globally higher than 165 experiments instead of 171, hence the slight differ- with the HPDM plume rise, since the estimated plume ences in the observed mean and standard deviations. rise is lower. However, the Doury parameterization still Results with Polyphemus models are between those of underestimates considerably the concentrations, as with AERMOD and ADMS4, except for the correlations that the Prairie Grass experiment. The bias and NMSE are are lower as already observed, and comparable to those of considerably improved for the Briggs parameterization ISCST3. whereas the concentrations’ overestimation with simi- Using data of quality 3 only, we can also compare with larity theory has increased, leading to a higher bias and HPDM (United States; Hanna and Paine 1989), OML NMSE than with HPDM plume rise. (Denmark), Simulation of Air Pollution from Emissions The vanishing concentrations can be seen for the above Inhomogeneous Regions (SAFE_AIR; Italy; scatterplots of all plume rise parameterizations (not Canepa et al. 2000), as well as the Lagrangian model shown here), not only for Briggs–HPDM. Hence, one Numerical Atmospheric-Dispersion Modelling Environ- cannot point out that a particular scheme overestimates ment (NAME; United Kingdom; Webster and Thomson the plume rise, and this may also come from an inaccurate 2002). The statistics for HPDM and OML come originally estimation of the observed boundary layer height. from Olesen (1995). Table 7 shows the results for all these 4) RESULTS WITH CONCAWE PLUME RISE models. ISCST3, AERMOD, and Polyphemus with the Doury formulas show a signiﬁcant underestimation of Results with the Concawe plume rise are shown in the mean values, hence the high bias and NMSE. All Table 5. Here, the best results are given by the Briggs other models slightly underestimate the mean values parameterization, as in the case of the Holland formulas. except SAFE_AIR and Polyphemus with similarity For the Briggs–HPDM plume rise, the best results were theory and Concawe plume rise, which slightly over- with similarity theory. As expected, the results with the predicts the observations. The correlation results are Concawe plume rise are not very different from the surprisingly against this trend: for instance, AERMOD Holland results, especially when looking at the mean has a correlation of 40%, which is comparable to the best concentrations and the biases. However, the correlation results. On the contrary, models that have an otherwise and the proportion of values within a factor 2 of the observation have increased. This slightly better performance is not surprising, considering that this formula TABLE 6. Statistics for several Gaussian models: comparison of was built from a set of different plume rise formulas, centerline values C/Q for simulations and observations—Kincaid data of quality 2 and 3. Unit: ng m23 (g s21)21. including Holland, and adjusted on a set of neutral and convective cases with buoyant plumes, as explained in Model Mean Std FB NMSE Corr FAC2 Brummage (1968). Obs 41.0 39.3 0.00 0.00 1.00 1.00 ADMS4 40.4 31.1 20.05 0.80 0.50 0.58 c. Comparison with other Gaussian models AERMOD 20.3 24.1 0.68 2.30 0.35 0.33 ISCST3 23.1 53.3 0.56 3.83 0.26 0.26 For this comparison, we use the results obtained with Obs 39.89 39.22 0.00 0.00 1.00 1.00 the Concawe parameterization that gives the best results Briggs–Concawe 32.83 32.80 0.19 1.50 0.27 0.47 for all standard deviation formulas. In addition, the re- Doury–Concawe 16.75 17.81 0.82 3.32 0.12 0.30 sults with similarity theory and Briggs–HPDM plume Sim.th.–Concawe 61.70 53.91 20.43 1.58 0.25 0.43 rise are also provided since they are good despite the Sim.th.–HPDM 41.99 34.76 20.05 1.33 0.19 0.44

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TABLE 7. Statistics for several Gaussian models: comparison of additional variability in the output results, especially centerline values C/Q for simulation and observation—Kincaid 23 21 21 since the plume might penetrate the inversion layer or data of quality 3. Unit: ng m (g s ) . might not, depending on the parameterization. Model Mean Std FB NMSE Corr FAC2 The model evaluation against Prairie Grass and Kincaid Obs 54.34 40.25 0.00 0.00 1.00 1.00 experiments gave very satisfactory overall results, com- ADMS4 48.5 31.5 0.11 0.60 0.45 0.68 pared to other well-known Gaussian models. Similarity AERMOD 21.8 21.8 0.86 2.07 0.40 0.29 theory is the best standard deviation scheme, which is not ISCST3 30.0 60.0 0.57 2.80 0.26 0.28 surprising since it relies on a more detailed description HPDM 44.84 38.55 0.19 0.75 0.44 0.56 of the atmosphere. However, the Briggs formulas also SAFE_AIR 59.73 52.54 20.09 1.10 0.20 0.50 OML 47.45 45.48 0.13 1.24 0.15 0.55 compare well with other model results, not only with the NAME 38.7 47.2 0.33 1.45 0.27 0.56 Prairie Grass experiment—on which they were adjusted— Obs 53.69 40.72 0.00 0.00 1.00 1.00 but also with Kincaid. Only the Doury parameterization Briggs–Concawe 37.95 33.06 0.34 1.20 0.21 0.58 appears to be unsatisfactory for the two experiments Doury–Concawe 17.36 14.21 1.02 3.19 0.18 0.30 used here, since it tends to overestimate the plume Sim.th.–Concawe 68.91 51.25 20.25 1.03 0.17 0.58 Sim.th.–HPDM 47.92 33.93 0.11 1.05 0.05 0.59 spread, leading to underestimation of the concentrations. There is no striking difference in performance—for these cases—between ‘‘old generation’’ schemes, based on a good performance such as SAFE_AIR, OML, and Poly- discrete representation of the stability (Briggs, Pasquill– phemus models with Concawe formulas have relatively Guifford used in ISCST3), and the ‘‘new generation’’ low correlations. The correlation for Polyphemus with estimations based on similarity theory, although the lat- similarity theory and HPDM plume rise is very low (5%) ter performs slightly better. but this conﬁguration is among the best models for all The results with the Kincaid experiment point out the other indicators. This correlation is not surprising since additional variability due to plume rise estimation. In the HPDM model evaluation in Hanna and Paine (1989) particular, the ‘‘best’’ standard deviation parameterization also showed low correlations with this experiment. Further depends on the plume rise scheme used (similarity theory improvements were made in HPDM, such as a correction with Briggs–HPDM plume rise, and Briggs’s standard to take into account the plume lofting at the inversion deviations with Concawe and Holland formulas). All layer during convective conditions, and this seems to have combinations perform well, except with the Doury for- greatly improved the results. Table 7 also shows that the mulas. The results also highlight the importance of some spread in the model outputs is very large: the predicted features such as a non-Gaussian shape for convective 23 mean concentrations range from about 20 to 70 ng m conditions as well as plume lofting at the inversion layer. 21 21 (g s ) , which means more than a factor of 3 between These missing features are most likely responsible for the some models. It is interesting to note that, with the dif- relatively low correlations. A meteorological preprocessor ferent parameterizations available in Polyphemus for that would recompute the inversion height could also help standard deviations and plume rise, we can reproduce to improve the results for the Kincaid experiment. the same spread, the model conﬁguration being other- With three parameterizations to compute the stan- wise unchanged. Only the correlations are still low, no dard deviations, and the same number of plume rise matter the formula used, which tends to prove that it schemes, we were able to show a large spread in the comes from the shared inversion-height modeling (plume model outputs, representative of the variability of the penetration and lofting). Gaussian models. The main perspective is now to extend that work to include more parameterizations and to 6. Conclusions compare with more datasets, providing a full compari- Polyphemus Gaussian plume and puff models were son between parameterizations in the same conditions. described, with an emphasis on the parameterizations This study also suggests that ensemble modeling with used to estimate the standard deviations and the plume Gaussian models could be interesting in the future. rise. The Gaussian plume model was then used to compare these various parameterizations within a single APPENDIX A framework, all other model features being equal. A preliminary study on the standard deviation values Formulas for Standard Deviations with (section 3) highlighted a large variability: the estimated Similarity Theory values could differ from up to a factor 30. Although the variability of the estimated plume rise is not so high, In all the formulas presented here, the stability is de- except for low wind speeds (section 5), it produces an termined from the Monin–Obukhov length, as given in

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TABLE A1. Matching between Monin–Obukhov length and stable and neutral cases and in Weil (1988) for con- stability, from Seinfeld and Pandis (1998). vective cases: L: Monin–Obukhov length (m) Stability Pasquill class s 5 0.6w unstable 2100 # L , 0 Unstable B w * 5 210 # L ,2100 Unstable C z 3/4 5 s 5 1.3u 1 stable neutral, jLj . 10 Neutral D w * h 10 # L , 105 Stable E 0 # L , 10 Stable F where w* is the convective velocity, u* is the friction velocity, h is the boundary layer height, and L is the Table A1, which also shows the corresponding Pasquill Monin–Obukhov length. class. The function Fz is given by Irwin (1979) for stable a. Within the boundary layer and neutral cases and by Weil (1988) for convective cases: 1) TRANSVERSE SPREAD sY d unstable cases: First, we have to determine the horizontal standard deviation of wind velocity fluctuations s . For that part y t 1/2 we use formulas given in Hanna et al. (1982): Fz 5 1 1 0.5 (A3) tLz h 1/3 sy 5 u 12 0.5 unstable * L d ! stable/neutral cases: fz 8hi s 5 1.3u exp 2 neutral < t 1 y * u 1 1 0.9 if z , 50 * F 5 hi z : 50 z 0.806 1 s 5 max 1.3u 1 , 0.2 stable, [1 1 0.945(0.1t) ] if z $ 50 y * h where h is the boundary layer height, L is the Monin– where h is the boundary layer height, L is the Monin– Obukhov length, f is the Coriolis parameter, and z is the Obukhov length, and z is the height where concentrations height where concentrations are computed. are computed. The following expression is advocated The function Fy is given by the general form by Hanna et al. (1982) for the vertical Lagrangian time t 1/2 scale t : F 5 1 1 0.5 , (A1) Lz y t L z where tL is the Lagrangian time scale. To compute this 1 exp 5 t 5 0.15h h unstable parameter, we use formulas given in Hanna (1984): Lz sw h z t 5 0.15 unstable 0.5 L s s y t 5 w !neutral z Lz 0.5 fz s 1 1 15 t 5 y !neutral u* L fz h z 0.8 1 1 15 t 5 0.10 stable. u* Lz s h rffiffiffi w h z tL 5 0.07 stable, (A2) sy h b. Alternative formulas for elevated sources where h is the boundary layer height, L is the Monin– In Hanna and Paine (1989), an alternative set of for- Obukhov length, u* is the friction velocity, f is the mulas is proposed for sources of height greater than Coriolis parameter, and z is the height where concen- 100 m, since the other formulations based on similarity trations are computed. theory were calibrated on experiments closer to the ground and did not give satisfactory results in the case of the 2) VERTICAL SPREAD s Z Kincaid experiment, for instance. These formulas are used The vertical wind standard deviation is computed for stable or neutral cases, where dispersion was found to using formulas given in Venkatram et al. (1984) for be greater than given by the classical formulation.

Unauthenticated | Downloaded 09/26/21 09:05 PM UTC 2472 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 48 d The wind vertical standard deviation is computed as They are applied for all stabilities. They ensure that the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dispersion parameters at least are always strictly positive s 5 0.5 1.2u2 1 0.35w2 L $ 100 values (no division by zero or square root of a negative w * * value). However, since in most case studies the observed s 5 1.3u 0 # L , 100 w * concentrations are inside the boundary layer, and there is no mixing through the inversion layer, these are not d The wind horizontal standard deviation is computed as the most used formulas in practice. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2) GILLANI FORMULA FOR VERTICAL STANDARD s 5 0.7 3.6u2 1 0.35w2 L $ 100 y * * DEVIATION qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 s 5 max(1.5 3.6u 1 0.35w , 0.5) 0 # L , 100 An alternative way to compute sz above the boundary y * * layer is given by Gillani and Godowitch (1999): ffiffi For the vertical standard deviation, the function Fz does p s2 5 s2 (1 1 2.3 t), (A8) not change, but the vertical time scale is computed with z zpr a different set of formulas for stable and slightly unstable cases. In the following formulas, sp stands for the assuming that t is the time travel of the plume, as usual, Briggs static stability parameter defined in section 2. and the initial time is equal to 0. One can note that this formula can be applied above the boundary layer for all d In the case of stable/neutral situations (L . 0): s parameterizations. The initial plume spread zpr due to z plume rise is computed differently from the formula tLz 5 if z # L sw given in section 2 since the initial spread is often over- pffiffiffiffi estimated that way. An alternative way proposed by tLz 5 0.27 sp if L # 10 pffiffiffiffi Gillani and Godowitch (1999) is (z/s )(L 10) 0.27 sp(z L) t 5 w 1 Lz (z 10) (z 10) s 5 max[15 exp(117dT/z), 3], (A9) zpr if 10 , L , z where dT/dz is the vertical ambient temperature gradient. d In the case of slightly unstable situations (jLj # 100): z 0.38 z APPENDIX B tLz 5 0.27 0.55 if z # jLj sw jLj (A4) Statistical Indicators h 5z 8z The statistical indicators are tLz 5 0.3 1 exp 0.0003 exp sw h h (C C ) if jLj , z , h (A5) FB 5 0 p (B1) 0.5(C0 1 Cp) c. Above the boundary layer 2 (C C ) NMSE 5 0 p (B2) 1) HPDM FORMULAS FOR WIND STANDARD C0Cp DEVIATIONS

All the formulas given by similarity theory are valid (C0 C0)(Cp Cp) only within the boundary layer. There are not many Corr 5 (B3) sC sC studies about the dispersion above the boundary layer, 0 p so the formulas used for that case are quite simple. They C come from Hanna and Paine (1989): FAC2 5 fraction of data that satisfies 0.5 # p # 2.0, C qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 s 5 0.1 3.6u2 1 0.35w2 and (A6) (B4) y * * qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where C and C are the predicted and measured maxi- s 5 0.1 1.2u2 1 0.35w2 . (A7) p 0 w * * mum arcwise concentrations, respectively, a is the average

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