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Atmospheric Environment 44 (2010) 753e762

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Atmospheric Environment

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A new Lagrangian particle model for the simulation of dense gas dispersion

D. Anfossi a, G. Tinarelli b, S. Trini Castelli a,*, M. Nibart c, C. Olry c, J. Commanay d

a Institute of Atmospheric Sciences and Climate e ISAC/C.N.R., Corso Fiume 4, 10133 Torino, ItalybARIANET Srl, Milano, ItalycARIA Technologies, Boulogne-Billancourt, FrancedAPSYS-EADS, Suresnes, France

a r t i c l e i n f o

Article history:Received 23 July 2009Received in revised form20 November 2009Accepted 24 November 2009

Keywords:Dense gas dispersionLangevin equationsGravity spreadingField experimentsAccidental releases

* Corresponding author. Tel.: þ39 0113839828; faxE-mail address: S.TriniCastelli@isac.cnr.it (S. Trini

1352-2310/$ e see front matter � 2009 Elsevier Ltd.doi:10.1016/j.atmosenv.2009.11.041

a b s t r a c t

A Lagrangian stochasticmodel (MicroSpray), able to simulate the airbornedispersion in complex terrain andin presence of obstacles, was modified to simulate the dispersion of dense gas clouds. This is accomplishedby taking into account the following processes: negative buoyancy, gravity spreading and the particle'sreflection at the bottom computational boundary. Elevated and ground level sources, continuous andinstantaneous emissions, time varying sources, plumes with initial momentum (horizontal, vertical oroblique in any direction), plumeswithout initialmomentumare considered.MicroSpray is part of themodelsystem MSS, which also includes the diagnostic MicroSwift model for the reconstruction of the 3-D windfield in presence of obstacles and orography. To evaluate theMSS ability to simulate the dispersion of heavygases, its simulation performances are compared in detail to two field experiments (Thorney Island and KitFox) and to a chlorine railway accident (Macdona). Then, a comprehensive analysis considering severalexperiments of theModelers Data Archive is presented. The statistical analysis on the overall available datareveals that the performance of the newMicroSpray version for dense gas releases is generally reliable. Forinstance, the agreement between concentration predictions and observations iswithin a factor of two in the72% up to 99% of the occurrences for the case studies considered. The values of other performancemeasures,such as correlation coefficient, geometric mean bias and geometric variance, mostly set in the rangesindicated as good-model performances in the specialized literature.

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1. Introduction

Hazardous toxic substances are produced and transported inmodern industry. In case of accidents the release and dispersionof hazardous gases and vapours may cause severe problems to thepopulations living in the neighbourhood of industries and storageareas, where such materials are handled. Consequently, determiningthe possible distribution of the hazardous substances is importantfor evaluating the suitability of the safety measures to both preventaccidents andmitigate their effects. The hazardous gases and vapoursare often initially denser than the ambient air. This occurs becausethe emitted substance may have high molecular weight and/or lowrelease temperature, and/or because of high storage pressure andthe resulting generation of aerosols. The density effects will besignificant if the amount of the release and its excess density lead tothe exceedance of a critical dimensionless parameter, such as theRichardson number (Ri). Ri also depends on the initial cloud size andthe ambient velocity. In the first phase, if the critical parameter is

: þ39 0116600364.Castelli).

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exceeded, the emitted cloud (following Britter,1989,we use ‘cloud’ todefine both continuous releasee plumee and instantaneous releasee puff) begins to disperse under the action of its own negativebuoyancy and arbitrarily oriented momentum. In a second phase, itsexcess of density reduces as ambient air is entrained. Finally, at somedistance downwind, transition to passive dispersion takes place. Animportant issue is that dense clouds may disperse quite differentlyfrom a neutral gas and, therefore, additional effects are to be takeninto account, such as the horizontal gravity spreading and the cloudslumping in sloping terrain. As a result, the form of the dense cloudhas different characteristics compared to a neutral emission. Namely,it is flatter for the reduced vertical turbulent mixing and wider forthe enhanced amount of entrained air in the spreading. Thus, as alsoobserved by Britter (1989) and Kovalets and Maderich (2006), theground level concentration (g.l.c.) along the cloud axis of symmetry isonly slightly different from that of a neutral emission, because theenhancement in lateral spread counters the reduction in verticalspread. However, the 3-D shape of the concentration field is quitedifferent in the two emission situations. For instance, in case ofground level or near ground level sources the occurrence of a signif-icant upwind spread of dense gas is often observed. Furthermore, the

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762754

area of critical concentration levels, inwhich the populationmight beseriously injured, is much wider.

Besides understanding and predicting these processes, the realterrain dispersion simulation for risk analysis purposes poses specificdifficulties, related to inhomogeneous and complex terrain, presenceof buildings and other large roughness obstacles and possible occur-rences of lowwind speed and stable conditions. Dispersion simulationin these situations is generally performed by means of empiricalmodels or, in some specific cases, by computational fluid dynamics(CFD)models.Anotherway,hereproposed, isofferedbytheLagrangianparticle dispersion (LPD) models. The LPD approach is a compromisebetween the complexity and computational time demand of CFDmodels and the simpler integral models. In many cases, such as fastemergency response or scenarios in complex terrain and obstacles,a fast but reliable model could be very useful.

Thus, in this work we propose a new version of the LPD modelMicroSpray (Moussafir et al., 2004; Tinarelli et al., 2007) to be usedas a simulation tool in this framework, describing the dispersionbehaviour and the processes that occur in a dense gas cloud gener-ated from accidental releases, where the plume descent has to betreated. In the next Section the standard MicroSpray code is brieflydescribed and in the third Section the modifications to MicroSprayfor dealing with dense gases are presented. The fourth Sectionpresents the MicroSpray validation: its performances are comparedto two field experiments, Thorney Island (McQuaid, 1985) and KitFox (see Hanna and Chang, 2001) and to a chlorine railway accident,Macdona (see Hanna, 2007). A comprehensive evaluation of thenew model is finally carried out combining different subsets fromthe Modelers Data Archive (MDA, Hanna et al., 1991) and Rediphem(Nielsen and Ott, 1996) datasets.

2. Brief outline of standard MicroSpray

MicroSpray is part of the model system MSS (Moussafir et al.,2004), which includes MicroSwift and MicroSpray. MicroSwift(Moussafir et al., 2004; Tinarelli et al., 2007) is an analyticallymodifiedmass consistent interpolator over complex terrain. Given topography,land use data, meteorological data and buildings, a mass consistent3-D wind field is generated. It is also able to parameterize diagnosticturbulence parameters (namely the turbulent kinetic energy andits dissipation rate) to be used by MicroSpray inside the flow zonesmodified by obstacles. MicroSpray is an LPD model able to take intoaccount the presence of obstacles. It directly derives from SPRAY code(Anfossi et al., 1998; Carvalho et al., 2002; Ferrero et al., 2001; Ferreroand Anfossi, 1998; Kerr et al., 2001; Tinarelli et al., 1994, 2000; TriniCastelli et al., 2003). It is based on a 3-D form of the Langevin equationfor the random velocity (Thomson, 1987).

In MicroSpray, as in SPRAY, the displacement xi of each particleis given by

dxi ¼�uai þ u0i þ ubi

�dt; (1)

where the turbulent velocity u0i is computed by the followingLagrangian stochastic equation

du0i ¼ aiðx;u; tÞdt þ bijðx;u; tÞdWjðtÞ (2)

and where i; j ¼ 1;2;3, uai is the meanwind velocity vector (whosevertical component is equal to zero in flat terrain only), ubi is anadditional velocity accounting for the buoyancy effects, x is thevector of the particle position, u is the Lagrangian velocity vector. Forthe description of how the new version of MicroSpray accounts forthe density effects we refer to next section 3. aiðx;u; tÞdt is a deter-ministic term, bijðx;u; tÞdWjðtÞ is a stochastic term and the quantitydWjðtÞ is the incremental Wiener process. The deterministic coeffi-cient aiðx;u; tÞ depends on the Eulerian probability density function

(PDF) of the turbulent velocity and it is determined from the Fok-kerePlanck equation. In the two horizontal directions the PDF isassumed to be non-homogeneous Gaussian. In the vertical directionthe PDF is assumed to be non-Gaussian, to deal with non-uniformturbulent conditions and/or convection. In this case, two differentapproaches can be adopted in order to calculate the FokkerePlanckequation: a bi-Gaussian one (Luhar and Britter, 1989) and a Gram-Charlier one (Anfossi et al., 1997), truncated to the third or fourthorder. The diffusion term bijðx;u; tÞ is obtained from the Lagrangianstructure function and is related to the Kolmogorov constant, C0,for the inertial subrange. In SPRAY and, therefore, in the standardMicroSpray version, the rise of hot plumes if any, is accounted forin a simplified way (Anfossi et al., 1993). Input data, such aswind velocities, standard deviations and Lagrangian time scales areassigned to each particle, at each time step, through a 4-D interpo-lation: bilinear in the horizontal plane and linear in the verticalplane, among the eight closest Eulerian grid points, and in time,between two subsequent input meteorological files.

3. New MicroSpray modules for dense gas

The new version ofMicroSpraymodel here presented is especiallyoriented to deal with dense gas dispersion in an urban environmentand in industrial sites. It accounts for the following aspects:plume without initial momentum and with initially arbitrarilyorientedmomentum (horizontal, vertical or oblique in any direction),negative buoyancy, elevated and ground level emissions, instanta-neous and continuous emissions, time varying sources, cloud spreadat the ground due to gravity, bouncing against obstacles and, finally,particle reflection at the domain bottom in presence of a dense cloud.At present, no source emission modules, treating the phase changesliquidevapour that may occur at the source, are accounted for. Also,latent heat processes in the dispersing cloud, such as aerosol evapo-ration, are not accounted for.

In the new MicroSpray module for dense gas, the motion of thedense cloud is divided in various phases. When the emission doesnot occur at the ground level there is a first phase in which thedescent of the denser-than-air cloud is simulated. In the followingsecond phase (that is the first phase for a ground level emission) thecloud spreads and finally, in the third phase, the buoyancy effectsbecome negligible and the cloud is simply transported and diffusedas a passive substance.

It is worth mentioning that the inclusion in LPD models of thecloud rise or descent, due to the buoyancy effects, and of the gravityspreading and reflection at domain bottom processes, is not trivial.In fact, in these cases, the motion of each particle depends on thecharacteristics (buoyancy, dimension and ambient air entrainment)of the cloud as a whole, i.e. it depends on how density varies in the3-D ‘ensemble’ of particles, whereas in the so-called ‘single-particle’LPD models each particle trajectory is independent of the behaviourof the other cloud particles. The same problem, even if limited tothe inclusion of plume rise from high stacks in the LPD models, wasconsidered and solved, in similar ways as here proposed, bymany authors (Luhar and Britter, 1992; Anfossi et al., 1993; Hurleyand Physick, 1993; Hurley, 2005;Webster and Thomson, 2002). Alsoprevious authors, who proposed LPD for dense gas dispersion, usedsimilar approaches, see for instance Gopalakrishnan and Sharan(1997), who considered only marginally heavy gases, Lee et al.(2007) and Williams et al. (2005), both considering ground levelemissions only, and Gaffen et al. (1987) who considered elevatedemissions only. In particular, a comprehensive discussion of theproblems encountered in the insertion of plume rise into LPDmodelsand of possible solutions is presented by Webster and Thomson(2002) and Anfossi and Physick (2005). Basically, they identify fourpossibilities: i) a separate simple integral plume rise model (see, for

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762 755

instance, Briggs,1975), giving the final plume height, is used and theemission of particles, neutrally buoyant, occurs at that final height;ii) an integral plume rise model is used at each time step for eachparticle and the derived velocities (thus accounting for the localentrainment and atmospheric stability) are added to the Lagrangianparticle velocities; iii) a set of differential equations describing thetime and space evolution of bulk plume quantities are solved at eachtime step for each particle; and iv) a further stochastic equation forthe particle temperature is solved and the buoyancy of the particle isincluded in the stochastic equation for the particle velocity evolution(van Dop, 1992). Though having advantages from the turbulenceclosure point of view, this fourth approach has problems in theentrainment treatment. Thus, following Hurley (2005) andWebsterand Thomson (2002) we adopted the third approach, in order tosimulate the plume descent considering, in this case, the negativebuoyancy contribution due to its density excess.

To deal with the first plume phase, in which the emission heightand direction may be variable, five governing conservation equationsofmass, energy, verticalmomentumand two horizontalmomenta areintegrated for each particle at each time step, based on Glendeninget al. (1984), Hurley (2005) and Hurley and Manins (1995). Defining:

us ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2p þ v2p þw2

p

q; B ¼ gðra � rpÞ=ra;

E ¼ 2bue and ue ¼ ½a1jus � Uacosðjp � jaÞcosðfp � faÞjþ a2jUa½1� cos2ðjp � jaÞ� cos2ðfp � faÞ�

1=2j� ð3Þ

where a, p refer to air and particle plume, respectively, b is the plumeradius, B is the buoyancy, E represents the entrainment rate,Ua is thewind velocity and ue is the entrainment velocity, a1 and a2 are theentrainment constants, r is the density, f and j are the vertical andhorizontal angles. The following conservation equations are solved:

mass :ddt

�rprausb2

�¼ Eus (4a)

energy :ddt

husb2B

i¼ �rp

raN2uswpb2 (4b)

vertical momentum :ddt

�rprauswpb2

�¼ Bb2us (4c)

x horizontal momentum :ddt

�rprausb2up

�¼ Eusua (4d)

y horizontal momentum :ddt

�rprausb2vp

�¼ Eusva (4e)

where up, vp and wp are the particle velocity components, ua andva are the horizontal components of the wind velocity, N2 is theBrunteVaisala frequency. The first three equations (4a)e(4c) werederived by Hurley and Manins (1995) starting from Glendening et al.(1984) andpreviously proposed byHurley (2005). The two remainingequations (4d, 4e) were proposed by Anfossi et al. (in press),following the same procedure as in Hurley and Manins (1995).

At the emission, a normally distributed buoyancy flux isassigned to each particle, fixing the mean value equal to the meanbuoyancy flux B and the standard deviation equal to B/3. This is thesame procedure proposed by Anfossi et al. (1993), also used forbuoyant emissions in SPRAY.

When a dense plume reaches the ground a horizontalmomentum is generated by theweight of the plume itself that tendsto spread the plume. This heavy gas induced radial outflow velocitydepends on the density gradients, thus on the bulk properties of thedense plume, i.e. on how the plume density varies in the vertical.In this work the gravity spreading is simulated as described in thefollowing. Themagnitude of the horizontally spreading velocity, Ug,is computed as

Ug ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2gBbulkHbulk

p(5a)

where Hbulk ¼ ð1=NpÞPNp

i¼1 zpi, rbulk ¼ ð1=NpÞPNp

i¼1 rpi andBbulk¼ (rbulk� ra)/ra are themeanheight, density andbuoyancyof thecolumn above each particle. Equation (5a) is used inmanymodels, seefor instance Eidsvik (1980), and it represents the speed of a propa-gating edge of a cloud at the groundwith a certain vertical extent, dueto the effect of the weight of the vertical column. The two horizontalvelocity components ðUgs;VgsÞ due to the gravity spread are:

Ugs ¼ UgcosðgÞ and Vgs ¼ VgsinðgÞ (5b)

where g is a random angle picked up from an uniform distribution,i.e. 0 < g < 360. g is assigned to every particle and maintainedthe same until the gravity spreading process is ended or the particlehits an obstacle. In this latter case, the bounced particle has a finaldirection in the opposite sense with respect to the obstacle face,picked up from a uniform distribution in a straight angle.

Due to the weight of the dense cloud acting on each bouncingparticle, the boundary condition at the bottom of the computationdomainhadalso to bemodifiedwith respect to the oneusuallyappliedin SPRAY, where the reflected vertical velocitywr is set equal tominusthe incident vertical velocity wi. In fact, to avoid an unrealistic flat-tening of particles at the ground, caused by the continuing descentimposed by the plume descent equations (4), not only a reverse of signis needed, but also the value of the reflected velocity should becorrectly determined so as to account for a transfer of momentum tothe horizontal components. This transfer depends on the averagedensity of the plume column above the particle. Therefore, we set:

wr ¼ wif ðrbulk=raÞ (6a)

The expression for f ðrbulk=raÞ was entirely empirically deter-mined comparing dense gas dispersions in flat terrain and withoutobstacles, simulated with the present model and with a CFDmodel,MERCURE (Carissimo et al., 1997). It reads:

f ðrbulk=raÞ ¼ 12ftanh½ � 9:0ðrbulk=raÞ þ 11:3� þ 1:0g (6b)

Equation (6b) has the correct asymptotic behaviour: it tends to 1 asðrbulk=raÞ approaches 1 and tends to 0when ðrbulk=raÞ becomes large.

Summarizing, all the above equations (4)e(6) are solved foreach particle, at each time step, provided the density of the particleis greater than that of the ambient air, more precisely the ratioðrp � raÞ=rahas to be greater than zero. Then, the particle continuesits motion as a neutral particle, and the term in equation (1)accounting for the buoyancy effects vanishes. In detail, during thenon-neutral phase (i.e., during the cloud descent and the groundlevel spreading, both due to the excess density effect) the additionalvelocities ubi have the following expressions:

ubx ¼ Ugs þ up; uby ¼ Vgs þ vp; ubz ¼ wp (7)

In the following neutral dispersion phase, in which the densityeffects are no more effective, the ubi velocities are equal to zero.

In the method implemented in MicroSpray, the contribution tothe vertical velocity accounting for the plume descent automaticallyvanishes towards zero as the density of the particle attains the

Fig. 1. Thorney Island ti8 experiment. Time trend of the tracer concentration at sampler4 (top; locationwith respect to the source: x¼ 234.49m, y¼ 61.73m, z¼ 0.40m) and 19(bottom; location with respect to the source: x ¼ 371.56 m, y ¼ 55.38 m, z ¼ 4.40 m)Crosses: observations; dashed line: observed mean; solid line: predictions and calcu-lated mean.

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762756

environment air density. Therefore, in principle, it is not necessaryto introduce a threshold value, such as a critical value of Ri-number,after which to stop the plume descent. However, for optimizingthe computational aspects, we consider a threshold value for theparticle density, close enough to the air density like (rp � ra)/ra < 10�5, which determines when the density effects can beconsidered negligible. Analogously, the other processes relatedto the density excess, i.e. gravity spreading and bottom reflection,are stopped when the bulk density of the column approaches theambient air density. Moreover, inMicroSpray the algorithm treatingthe dense gas behaviour is activated only in an initial Ri-numberrange where the buoyancy contribution plays an important role.

4. Validation of MicroSpray version for dense gas

As anticipated in the Introduction, to verify the accuracy ofMicroSpray we performed numerical simulations of different densegas case studies. The newmodelwas tested against the Thorney Island(McQuaid, 1985) and Kit Fox (Hanna and Chang, 2001) field experi-ments and to Macdona chlorine railroad accident (Hanna, 2007).Moreover, we performed several simulations of further different casestudies from theMDA (Hanna et al.,1991) and Rediphem (Nielsen andOtt, 1996) datasets.

In the following Sections we present the main results from allthe case studies considered.

4.1. MSS application to Thorney Island field experiment

As first stage of the new Microspray validation, in this sectionwe present the results obtained versus the observed data from theThorney Island field experiment.

For a general description of the Thorney Island experiments werefer to McQuaid (1985) and to two Reports, Rediphem (Nielsen andOtt, 1996) and MDA (Hanna et al., 1991). Following the MDA docu-mentation, we considered 11 trials, 9 with instantaneous emissionand 2 with continuous release. In this section we examine in detailtrial 8, named ti8, which has been one of the most frequently-analyzed Thorney Island trials and is often discussed in the literature.

Therefore, here we describe only the basic information for thetrial. Further overall comparisons for Thorney Island experimentare presented in subsection 4.4.

A mixture of Freon-12 and Nitrogen (3958 kg) was instanta-neously emitted from a cylindrical-shaped tent-like structure(diameter¼ 14m, height¼ 13m)whose sideswere quickly dropped,without any initial momentum. An array of 42 samplers, located atdifferent heights (0.4, 2.4, 4.4 and 6.4 m) in the range 70e500 mdownwind the source, collected some tracer for 660 s. The initialtracer concentration was 1 mol/mol, while the relative initial emis-sion density ðrp=raÞ was equal to 1.63. Wind speed was 2.4 m s�1

at 10 m and the wind heading was about 18� to the left of the arraycentreline. The friction velocity characterising the experiment wasu*¼ 0.126m s�1 and the roughness length z0¼ 0.012m. The stabilitywas neutral, represented by Pasquill category D. No turbulence andwind profile data were given.

For the simulation of the local circulation with MicroSwift,a computational domain of 200m� 800m� 200mwas considered.MicroSwift had horizontal grid spacing of 2 m and a stretched gridin the vertical, where the meteorological data were computed.MicroSpray used the same gridded dataset to derive the neededinformation at each particle position. No obstacles have beenincluded in theMicroSwift simulation, since no exact information onthe dimensions of the obstacles there present (hangar and othersmall buildings) was available. As initial condition, a logarithmicwind profile, horizontally homogeneous,was inferred on the basis ofthe values of u* and z0, also used to determine the turbulence fields.

20 000 particles were released at t ¼ 0 uniformly distributed withinthe source cylinder centred at x¼ 200 m and y¼ 0 m and then theirtrajectories were calculated. The number of particles to be releasedwas determined after varying it in preliminary runs, until a conver-gent result in the concentration field was reached, paying a partic-ular attention to the higher concentration values. Finally, theaveraged simulated concentrations were computed at the samplerlocations on the same period of 3 s as for the observations. Then, themaximum and mean observed and predicted concentrations werecalculated over the 660 s observational time period.

Fig. 1 depicts, as an example, the time series of the tracerconcentration measured and predicted at samplers 4 and 19,respectively 71 and 180 m far from the source and located ata height of 0.4 and 4.4 m, sampled at 3 s intervals. It clearly showsthe arrival of the tracer cloud at the sampler and its passing over.As expected, a large concentration variability as a function of time isalso evident, due to the turbulence and wind field variation atvarious time scales. While the overall behaviour is correctly simu-lated, the simulated travel time or arrival time of the cloud is abouta factor of two less than the observed arrival time. This might alsobe due to the fact that, as above mentioned, no information on the

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762 757

variability of wind and turbulence and on the obstacles dimensionswas available.

To give an idea of the time evolution of the puff in the first stageof the dispersion process, in Fig. 2 we show a snapshot of the puff ofparticles at four times (1, 3, 6 and 27 s) starting from the emission,as simulated by MicroSpray. For a qualitative comparison withthe dynamics of the observed cloud, we refer to McQuaid (1985)book, where however similar pictures are available for other trials,number 7 and 13. The puff suddenly droops downward towardsthe ground, while the horizontal spread takes place emptyingthe internal part of the column and giving it a circular shape. Thiscircular puff is then transported along the mean flow direction. Theplots, where the plume spreading effect is evident, correctlyrepresent the behaviour observed during the experiment, wherethe centre of the plume emptied itself due to the horizontal spreadand the edges filled themselves. Also the movement of the puffalong the mean direction is correctly captured. Notice that thedownwind part of the cloud is larger and less dense than theupwind part, due to increased entrainment.

In the following Figs. 3e6 an analysis of the results is presented.Fig. 3 shows the scatter diagram of the mean concentrations (dia-monds) and of themaximum concentrations (crosses), both observedand prescribed at each sampler. From a qualitative point of view, wenotice that the agreement for the concentration means is satisfactory,but with a tendency of the simulated values to underestimate themeasurements. For the concentration maxima the scatter is symmet-rical with respect to the best-agreement line and the agreement looksrathergood,particularly for thehighestvalues. This is confirmedby the

Fig. 2. Thorney Island ti8 experiment, MicroSpray simulation. Sequence of dense gas cloud im

estimation of the sum of the ten maxima of concentrations atthe available locations (TOP10), which is 9.87 � 105 mg m�3 for theobserved data and 9.78 � 105 mg m�3 for the simulated data.

The cases of overprediction of the low values of concentrationoccur at different distances, but typically at the higher sampler verticallevel. This suggests that the vertical distribution of the simulatedconcentrations is not optimal. Moreover, we notice that the concen-trations span 2 order of magnitude and more. We were mainlyinterested in tracking the higher values over a relatively large distance(2 km). Therefore, we chose a number of particles large enough topursue this goal. The number of particles used however might be notenough large to optimize the discretization level for the lowerconcentration, inducing an overprediction of the measured values.

To evaluate the performance quantitatively, a statistical analysisfor the mean and maximum concentrations was also done. Theindexes considered are: correlation coefficient (CC), geometric meanbias (MG), geometric variance (VG), factor of 2 (FA2) and factor of 5(FA5). We recall that MG and VG are defined as follows:

MG ¼ exp�ln Co � ln Cp

�VG ¼ exp

��ln Co � ln Cp

�2� (8)

Thus, a “perfect” simulation would have MG ¼ VG ¼ 1. Wecomputed MG and VG since observed concentrations at the wholearray of samplers vary over three orders of magnitude and, inthese cases, the logarithmic indexes may be more appropriate(Hanna et al., 1991).

The performance measures for the concentration maxima ateach downwind arc were computed, as done in theMDA report, but

ages showing its outflowmotion, from top-left to bottom-right: at 1 s, 3 s, 6 s and 27 s.

Fig. 3. Thorney Island ti8 experiment. Scatterdiagramofmean (diamonds) andmaximum(crosses) observed (abscissa) and predicted (ordinate) concentrations (mg m�3).

Fig. 5. Thorney Island ti8 experiment. Scatter diagram of observed (abscissa) andpredicted (ordinate) arrival time (s) for maximum concentrations (mg m�3).

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762758

it is proper to bear in mind that only 7 pairs are available. Weobtained CC ¼ 0.97, MG ¼ 0.88, VG ¼ 1.25, FA2 ¼ 86%, FA5 ¼ 100%.These values set inside the “target ranges” for good models sug-gested by Chang and Hanna (2004), that is FA2 > 0.5 (50%),0.7 < MG < 1.3 and VG < 1.6. The general behaviour of the tracerexperiment is correctly captured: CC, FA2 and FA5 are satisfactory,the value of VG is rather good whereas MG is less satisfactory,indicating a trend to underestimate the observations.

To compute the statistical performance measures on a consis-tent number of data, we repeated the analysis for the concentrationmeans and maxima estimated at the single sampler, considering allthe samplers together even if they were at different heights(0.4, 2.4, 4.4 and 6.4 m), for a total of 42 pairs.

In this case we obtained for the mean values CC ¼ 0.63,MG ¼ 1.35, VG ¼ 2.32, FA2 ¼ 53%, FA5 ¼ 90%, and for the maximumvalues CC¼ 0.95, MG¼ 0.99, VG¼ 1.69, FA2¼ 71% and FA5¼ 95%. Inparticular, the MG index for the mean and the VG index for both themean and maximum values are greater than the good-model targetrange. As expected, evaluating the performance of the model bypairing concentration observations and predictions both in time and

Fig. 4. Thorney Island ti8 experiment. Maximum concentration (mg m�3) at the arcs(ordinate) as function of the distance from the source (abscissa): observations (crossesand dashed line) and predictions (diamonds and solid line).

space is a very severe approach, as largely discussed in Chang andHanna (2004). The computed statistics results to be very sensitive tothe time shifts between the observed and predicted cloud arrivals atthe single location (see also Fig. 5) and to even a small failure in theoverlap between the observed and simulated plumes.

When considering all these index values, it is also worthwhile torecall that no information on the turbulence characteristics of theexperiment and of the wind profile were available, but only thevalue of the upwind mean wind at 10 m was known.

The degree of agreement in the observed and simulatedconcentrationmaxima is also confirmed by Fig. 4, where their trendas a function of the various downwind arcs is shown. Most of thetime, the agreement is within a factor of two. The scatter diagram ofthe time of arrival of the cloud, defined as the time at which theconcentration maximum is observed or predicted, is reported inFig. 5. The travel time before arrival of the plume is generally aboutfactor of 2 too small in the simulations compared to the observa-tions. This could be related, at least in part, to the fact that theadvective wind speed is not known but it is prescribed, as antici-pated above, from a single average value at 10 m above ground andassuming a logarithmic profile. Thus a difference in the actual windspeed near the ground, where the dense cloud moves, greatly

Fig. 6. Thorney Island ti8 experiment. Scatter diagram of the observed (abscissa) andpredicted (ordinate) concentration standard deviation (mg m�3).

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762 759

influences the cloud travel speed. Another source of uncertaintymay be the variability of the roughness in the experimental field,while in the simulation it was kept constant and equal to the valueprovided in the MDA Report.

To conclude the detailed analysis of ti8 trial, we plotted Fig. 6, inwhich the scatter diagram between observed and predictedconcentration standard deviation is shown. Also this Figure suggeststhat the overall agreement is good,with67%of the predictionswithina factor of two of the observations and 95% within a factor of five.

4.2. MSS application to Kit Fox field experiment

Data and information on the Kit Fox (Hanna and Chang, 2001)dense gas experiment were mainly found in the MDA Database. The1995 Kit Fox dense gas field dataset consists of 52 trials during whichCO2 gas was released from a 1.5 m � 1.5 m ground level area sourceover a rough surface, in neutral and stable conditions. The relativeemissiondensity, re=ra,where re and ra are the emission and ambientdensities respectively, was equal to 1.52. About 2/3 of the trialsrepresented short-term transient puffs, while about 1/3 of the trialsrepresented continuous plumes. 84 fast-response concentrationmonitors were located at four downwind arrays (25, 50, 100 and225 m). Wind speeds and directions at 2 m levels, friction velocities,MonineObukhov lengths and PasquilleGifford stability classes wereprovided for each of the 52 trials. In order to study the effects ofincreased roughness, the experiments used two sets of artificialroughness arrays: the Uniform Roughness Array (URA), with a rough-ness length of about 0.01e0.02 m, and the Equivalent RoughnessPattern (ERP), with a roughness length of about 0.12e0.24 m. Theartificial roughness arrayswere constructed using rectangles of piecesof plywood placed perpendicular to themean flow direction. A sketchof the experiment configuration is plotted in Fig. 7.

For the model simulations, a computational domain of400 m � 240 m � 100 m was used. MicroSwift had horizontal gridspacing of 2 m and a stretched grid in the vertical. For the calcula-tion of the concentrations, in MicroSpray the same horizontal gridresolutionwas used, while the vertical grid spacing was 0.5 m up to2 m above the ground. 10,000 particles were released per secondfrom the 1.5 m � 1.5 m area source, whatever the duration ofrelease. Maximum concentrations at the four downwind distances(25, 50,100 and 225m)were computed. Uniform roughness lengthsof 0.015 m and 0.18 mwere used in the simulations respectively forthe URA and ERP sets of artificial arrays. The values of frictionvelocities, MonineObukhov lengths and PasquilleGifford stabilityclasses reported in the MDA for the different trials were directly

Fig. 7. Sketch of the Kit Fox site (from Kit Fox MDA database): downrange (abscissa, m)and crossrange (ordinate, m) directions.

used in input to MicroSwift. The mixing layer heights were esti-mated using the methodology suggested in the Yellow Book of TNO(1997). As regards the meteorological input, only a single datum at2 m above the ground level was used per trial. Vertical profiles ofwind speed were then generated using the Irwin (1979) powerlaws, based on this 2-m wind speed and PasquilleGifford stabilityclass. The Lagrangian turbulence was internally parameterized byMicroSpray on the basis of the input parameters.

Maximum predicted concentrations and observations werecompared, for a 20 s averaging time, at the different downwinddistances. As a consequence, 208 pairs were considered for thisexperiment. All available data were included in the statistics ofthe concentrations and no threshold values were considered. KitFox trials can be split into four groups, depending on the kind ofarray and emission, that is URA e continuous, URA e puff, ERP e

continuous and ERP e puff. An indication of the number of trials foreach group and of the classification of trials depending on thestability conditions is reported hereafter in Table 1.

Each of these groups was statistically evaluated in order todetermine the accuracy of MicroSpray model predictions with theobserved data. Geometric mean bias (MG), geometric variance (VG),as well as factor of 2 (FA2) are presented in the following Table 2.

The general behaviour of tracer experiment is correctlycaptured, the CC for the overall statistics was equal to 0.88 and theMG, VG and FA2 values set inside the “target ranges” for goodmodels suggested by Chang and Hanna (2004). This is true for allkind of array and emission duration, puff or continuous: only theURA continuous case has an MG slightly above the good-modellimit. MicroSpray results are thus well within the criteria for goodperformingmodels (Chang and Hanna, 2004). However, and even ifcontinuous emissions involve only 18 trials over 52, it is importantto mention that MG values show a trend to underestimate theobservations when modelling continuous emission, while theyindicate a slight overprediction for short-duration transient puffs.

The MicroSpray performance measures agree well with thoseobtained by three different versions of the model HEGADAS (Hannaand Chang, 2001), which best performance for the overall set gaveMG¼ 0.96, VG¼ 1.15 and FA2 ¼ 92%, and obtained by the CFD codeFLACS (Hanna et al., 2004), where the performance measures forthe overall set were MG ¼ 1.12, VG ¼ 1.20 and FA2 ¼ 94%.

The results obtained using the new modules for dense gas inMicroSpraygas are quite encouraging, since emissions are located atground level, within the roughness obstacles, where thewind speedis a key parameter. It is also important to recall that these releases ofdense gas were performed for neutral and stable atmosphericstratifications. In the latter critical and peculiar conditions, char-acterised by very low wind speed near the ground and stablecondition, it is generally quite difficult to properly predict concen-tration levels.

4.3. MSS application to Macdona chlorine railroad accident

After testing MSS for field experiments carried out undercontrolled conditions, we tested the model for an actual accidental

Table 1Details of the classification of Kit Fox trials in groups.

Group of trials Total n. of trials N. of trials in PasquillGifford stability class

D E F

URA continuous 12 2 7 3URA puff 21 8 5 8ERP continuous 6 1 1 4ERP puff 13 6 3 4

Table 2Statistical indexes related to maximum concentrations (20 s averaging time) for theevaluation of MicroSpray performance on Kit Fox experiment.

Kit Foxexperiment

URAcontinuous

URA puff ERPcontinuous

ERP puff Overall

12 trials(48 pairs)

21 trials(84 pairs)

6 trials(24 pairs)

13 trials(52 pairs)

52 trials(208 pairs)

MG 1.42 0.95 1.19 0.87 1.04VG 1.20 1.15 1.25 1.29 1.20FA2 92% 99% 83% 83% 88%

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762760

release scenario. We made use of a study that compared theperformances of six widely used hazardous gas models simulatingdownwind chlorine gas concentrations following three recentrailcar accidents (Hanna, 2007). Since the accidents occurred atremote locations, no meteorological and concentration observa-tions were available and also the source emission rates could just beestimated. As a consequence, in that study it was not possible toinvestigate which model was “best”. Plots and Tables of the resultsfrom the six models were produced and it was concluded that thesemodels agree in their estimate of the downwind dispersion withinan order of magnitude. Out of the three accidents we chose theMacdona (TX) scenario. The aim here was to run anMSS simulationwith the same input information provided to the six models, aspresented in Hanna (2007) and Hanna et al. (2008), to verify if our

a

c

Fig. 8. Macdona accident simulations intercomparison. Solid lines: MSS results; vertical bamaximum 10 min average Cl2 concentration (ordinate, ppmv) versus downwind distance (amodel-simulated concentration of 20 ppm, 400 ppm and 2000 ppm, versus distance (absc

prescribed concentrations were in agreement with those of theother models. Therefore, we computed the following quantities:maximummodel-simulated 10 min average chlorine concentrationat the downwind distances (0.1, 0.2, 0.5, 1 and 2 km), plume widthsand plume heights in correspondence to the model-simulatedconcentration of 2000, 400, and 20 ppm at the same distances.

A computational domain of 2200 m � 1400 m � 1000 m wasconsidered. MicroSwift had a horizontal grid spacing of 10 m anda stretched grid in the vertical. One hundred particles were releasedper second from the 1-m-high source. The emission lasted 136 s,whereas the dispersion simulation lasted 30 min. Concentrationwas computed at 60 fictitious samplers per arc, from which theabove quantities were estimated.

In Fig. 8 the simulation results obtained for the concentration,plume width and height is shown as a function of the downwinddistance. Fig. 8b, c and d refer to the prescribed concentration of20, 400 and 2000 ppm, respectively. The vertical bars indicate thevariability (min, max) of the six models and circles locate themedian of these models. It can be seen, in Fig. 8a, that all prescribedconcentrations laywithin the variability of the sixmodels ensembleand are close to the median. Excluding the case of cloud height of20 ppm (Fig. 8b), inwhich again the values laywithin the variabilityof the six models ensemble, generally our simulation results areclose to the minimum of the ensemble values. In MSS simulationsthe maxima of concentration tended to be displaced symmetrically

b

d

rs: six models ensemble variability (min, max); circles: median of the six models. (a):bscissa, m). (b), (c) and (d) Cl2 cloud width and height (ordinate, m) corresponding toissa, m).

Table 3Statistical indexes related to the maximum concentrations for the comprehensiveevaluation of MicroSpray performance on the MDA database, including ThorneyIsland (trials n. 6, 7, 8, 9, 12, 13, 18, 19 45, 47), Burro (trials n. 2, 3, 4, 5, 6, 7, 8, 9) andCoyote (trials n. 3, 5 and 6) field experiments.

Experiment Thorney Island Burro Coyote Overall

69 pairs 40 pairs 22 pairs 131 pairs

MG 0.78 0.92 1.21 0.89VG 1.34 1.26 1.29 1.31FA2 72% 78% 77% 75%

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762 761

towards the two edges of the cloud, at least in the initial phase of thedispersion. Comparing the results from Fig. 8a and the next 8b-c-d,we observe that, while at given distances the maximum values ofconcentration well agree with the other models' result, probablythe effectiveness of the dilution in the predicted cloud differed fromthe other set of models, leading to a displacement of the concen-tration contours' distribution.

It was also verified that the concentration, C, varies withdistance, x, according to the power law C2/C1 ¼ (x2/x1)�p withp ¼ 1.54, that is in the expected range: 1.5e2 (Hanna, 2007).

Because of the lack of direct observation it is not possible to rankthe seven e six plus MSS e model results. However, the resultsshown in Fig. 8 indicate that MSS performance has an accuracycomparable to the ensemble of six widely used models.

4.4. A comprehensive evaluation of MSS performance

To present a synthesis of MSS performances, we performedseveral simulations of different case studies again using datasetsdescribed in theMDA (Hanna et al.,1991) and the Rediphem (Nielsenand Ott, 1996) reports, to which we refer for the details of theexperiments.

In particular, we run MSS for multiple cases of Thorney Islandexperiment, considering both continuous and instantaneous puffemissions: experiment numbered as 6, 7, 8, 9, 12, 13, 18 and 19 forthe instantaneous releases and as 45 and 47 for the continuousreleases. Then, we used data from different trials performed in theframe of Burro (trials n. 2, 3, 4, 5, 6, 7, 8, 9) and Coyote (trials n. 3, 5and 6) field experiment campaigns. In Burro and Coyote experi-ments, carried out at the China Lake in California, liquefied naturalgas (LNG) was poured into a water basin (diameter: 58 m, averagedepth: 1 m, water level was 1.5 m below the terrain) and wasdirected radially outwards on the water surface. The LNG exittemperature was at the atmospheric boiling point.

In the Burro case, four arcs (distance from the source: 57, 140,400 and 800 m) of 10 m masts were equipped with thermocouplesand concentration sensors at three levels. In Coyote setup, thedisplacement of the measurement array was modified and it wasconcentrated between 140 m and 500 m, to better detail the highervalues of the concentration field (distance from the source: 140,200, 300, 400 and 500 m).

Fig. 9. Scatter plot of predicted (ordinate) and observed (abscissa) concentrations(ppm) for the set of MDA case studies including Thorney Island (trials n. 6, 7, 8, 9, 12,13, 18, 19 45, 47), Burro (trials n. 2, 3, 4, 5, 6, 7, 8, 9) and Coyote (trials n. 3, 5 and 6) fieldexperiments.

For simulating Burro and Coyote experiments,MSSwas configuredto run on a horizontal domain of 800 � 400 m2 with a vertical extentof 200 m. Meteorological data were computed by MicroSwift ona horizontal grid having resolution of Dx ¼ Dy ¼ 5 m, and a verticalstretched grid, with the first level above the ground set at 0.05 m andthe domain top at 200 m, for a total of 25 levels. For this compre-hensive analysis, also Thorney Island experiments were here simu-lated with the same configuration. To compute ground levelconcentrations, a horizontal grid having the same dimensions of themeteorological onewas chosen, to allowa good compromise betweenthe computational time demand and the quality of the concentrationfields. A vertical cell dimension of 2 m for Burro and Coyote and of1 m for Thorney Island experiments was chosen to be closer to the“receptor height for modelling”, suggested inside the databasedescription, which here corresponds to the centre of the cell. Micro-Swift was initialized with the wind vertical profile and the surfacelayer parameters of the experiment. The turbulence variables weredetermined using Hanna (1982) parameterization on the basis of thestability parameters. The emission was simulated using 100 particlesper second. For the full set of Burro and Coyote trials here considered,the concentrations were calculated both as ‘instantaneous’ (1 s aver-aging time) and as ‘average’ (from 40 to 140 s for Burro and from 50 to90 s for Coyote, depending on the experiment considered). For the setof Thorney Island trials, 1 s averaged concentrations were computedfor the instantaneous emissions and 30 s averages for continuousemissions. In Fig. 9 we plot the scatter diagram of MSS predictionsversus the observations collected for all the cases above cited. Datapoints represent concentration maxima at each downwind arc. Wenotice that the agreement of the simulated concentrations with themeasurements is fairly good, since the majority of the scatter points(75%) falls inside a factor of 2 with respect to the line of perfectagreement. The whole set of data falls inside a factor of 5 and thecorrelation coefficient of the overall statistics is 0.88. The performancemeasures for the three experiments, Thorney Island, Burro andCoyote, and for the overall data presented in Fig. 9 are reported inTable 3. We notice that MSS is not showing a systematic tendency tounder- or overestimating the observed data, sinceMG for the differentexperiments takes values both lower and higher than 1. The spread ofthe data around the best fit line is similar for all the experiments, sinceVG and FA2 do not vary substantially in the three case studies. Alsothese results satisfy the criteria for good performing models (Changand Hanna, 2004), suggesting that MSS, and in particular Microspray,can be used to simulate the release and dispersion of dense gaseswitha rather high confidence.

5. Conclusions

In this paper we have presented a new version of the Lagrangianstochastic model MicroSpray, designed to simulate the dense gasdispersion in complex terrain and in presence of obstacles. Micro-Spray is part of the model system MSS that also includes thediagnostic MicroSwift model for the reconstruction of the 3-Dwindfield in presence of obstacles and orography.

D. Anfossi et al. / Atmospheric Environment 44 (2010) 753e762762

MicroSpray was updated to deal with the negative buoyancy,gravity spreading and the modifications to the particle's reflectionat the bottom computational boundary. These processes are typicalof dense gas dispersion only. The model can account for elevatedand ground level sources, continuous and instantaneous emissions,time varying sources, plume without and with initial momentum,in any direction.

Following a brief overview of the standard MicroSpray model(Moussafir et al., 2004), the new MicroSpray modules, especiallydesigned for the dense gas application, were illustrated.

The MSS capability to accurately simulate the dense gasesdispersion was proven against two field experiments (ThorneyIsland and Kit Fox), a chlorine railway accident (Macdona) and a setof different experiments from MDA (Hanna et al., 1991) and Redi-phem (Nielsen and Ott, 1996) datasets. These comparisons suggestthat MSS is able to provide reliable and rather fast (from 1 to3 min run time) simulation of the dispersion of dense gases. MSSperformances show the same level of accuracy obtained by othermodels in the different case studies, as quantified by some statis-tical analysis. The performance measures of MicroSpray simula-tions mostly range inside the reference figures for good performingmodels suggested by Chang and Hanna (2004).

The approach of coupling a diagnostic meteorological processorto a Lagrangian model ensures a reliable description of the physicsof the atmospheric processes and, at the same time, demandsa smaller computational and time effort than more advanced andcomplex models, still producing a good quality of the dispersionsimulation. These two aspects together make MSS-type of model-ling systems suitable tools for applicative environmental assess-ment and emergency response.

Acknowledgment

The authors like to thank the anonymous Referee for his/herfocused comments and precious suggestions, which lead to largelyimprove the quality of this paper.

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