PLPM (PHOTOCHEMICAL LAGRANGIAN PARTICLE MODEL): FORMULATION AND PRELIMINARY VALIDATION.

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1 8 th Int. Conf. on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purposes PLPM (PHOTOCHEMICAL LAGRANGIAN PARTICLE MODEL): FORMULATION AND PRELIMINARY VALIDATION. Gabrele ZANINI (1), Roberto BELLASIO (2), Roberto BIANCONI (2), Luca DELLE MONACHE (3), Mara Petrova KOLAROVA (4), Rta LORENZINI (1), Sona MOSCA (2), Fabo MONFORTI (1), Sara PEVERIERI (1) and Lna VITALI (1) (1) ENEA, PROT-INN secton - va Martr d Monte Sole 4, I Bologna, Italy. (2) ENVIROWARE srl - C.D. Colleon Andromeda 1, I Agrate Branza (MI), Italy. (3) Department of Meteorology, San Jose State Unversty, San Jose, CA 95192, USA. (4) Nat.Inst.for Meteorology and Hydrology, Blvd.Tsargradsko Chaussee, Sofa 1794, Bulgara. INTRODUCTION PLPM (Photochemcal Lagrangan Partcle Model) s a Lagrangan partcle model developed n last years by ENEA and ENVIROWARE Srl. In ths presentaton, we dscuss the physcal formulaton of PLPM, the man features of the kernel densty reconstructon methods and some prelmnary tests carred out to evaluate the model and the densty reconstructon methods. In partcular, the Kncad data set (Bowne e Loondergan, 1983), along wth the Model Valdaton Kt (Olesen, 1998), has been used to test the model on the dsperson of non reactve compounds. The results obtaned so far suggest brngng them to the attenton of the ar qualty modellng communty, together wth the questons that are stll open and would beneft of the efforts of other researchers. MODEL DESCRIPTION General features PLPM s a three-dmensonal dsperson model nterfaced to the dagnostc meteorologcal model CALMET (Scre et al., 1999). Wthn the model a fxed number of partcles s released by each source at each tme step. Each released partcle can be assumed to be composed by several pollutants (.e. each partcle contans nformaton regardng dfferent substances). In the complete verson of the model, the pollutants n each partcle wll vary qualtatvely and quanttatvely wth tme snce the chemcal reactons may result n the producton or loss of some speces. These portons of atmospherc pollutants are macroscopc snce nclude a large number of molecules, but they are small enough to be consdered as ponts. Partcles moton s the resultng effect of the mean wnd feld and the turbulent dffuson. The partcles' random walk nduced by turbulence s Markovan. Gven the poston of a partcle at tme t, ts poston at the tme t+ t s be gven by: ( + ) = ( ) + ( + ) x t t x t t u u (1) where =1,2,3 ndcates respectvely the x, y and z drecton, u s the mean wnd component along the -th drecton and u ' represents the turbulent velocty fluctuaton along the same -th drecton. The tme evoluton of the velocty fluctuaton s descrbed n the most general terms by the non-lnear Langevn equaton ntroduced by Thomson (1987): ( x, u', t) dt + b ( x, u', t) dξ ( t) du = a (2) j j Where a and b j are functons of space, velocty and tme, and dξ j (t) s a random ncrement of a Wener process wth ndependent components

2 8 th Int. Conf. on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purposes The fluctuatng turbulent term at tme t s correlated to the one at tme t+ t: turbulence remnds ts prevous state for a certan perod, and a Lagrangan tme scale can be defned as the value at whch the autocorrelaton coeffcent s equal to 1/e. The Lagrangan tme vares for dfferent turbulent regmes. Under convectve condtons two models can be alternatvely used to descrbe the turbulent vertcal moton: the homogeneous skewed model of Hurley and Physck (1993) and the quas-homogeneous model of Bancon et al. (1999), both based on Thomson (1987) model. The concentraton feld The most common method of computng the concentraton feld s the box countng. It smply conssts n defnng a grd, summng the partcles' masses n each cell and dvdng by the grd cell volume to obtan the concentraton value. Ths method has been shown to suffer of a major dsadvantage: the concentraton values depend on the cell volume and on the number of partcles used. For large volumes the concentraton feld s too smoothed, whle for small volumes the concentraton feld s perturbed by a hgh numercal nose, unless a very hgh number of partcle s used A dfferent numerc technque for computng concentratons n a Lagrangan partcle model s the kernel densty estmator, whch permts to reduce the number of partcles and to compute a completely grd-free and contnuous concentraton feld n each pont of the doman. The kernel estmator mplemented n PLPM has the followng form n m x x y y z z c( x, y, z, t) = d d d (3) = 1 λx λ y λz λx λ y λz where c ( x, y, z, t) s the concentraton n ( x, y, z) at tme t; n s the total number of partcles n the doman, ( x, y, z ) and m are the poston and the mass of -th partcle and d(u) s the Epanechnkov functon: 3 2 (1 u ) u 1 d ( u) = 4 (4) 0 u > 1 The λ parameters are the bandwdths (one for each space drecton). They states the ampltude of the volume n whch the mass of the partcle s spread n the doman. Bandwdths are the crtcal parameters for the good estmaton of the concentraton feld: too small bandwdths can lead to a largely rregular concentraton feld (large varance) whereas bandwdths overestmaton can result n a large bas of the reconstructed feld. Thus, an optmal method for bandwdth calculaton s needed, amed to mnmze both varance and bas. Bandwdth calculaton In the present verson of PLPM four dfferent methods are avalable for bandwdth calculaton: Kernel RL3 (Receptors-based, Locally-defned, three-dmensonally ordered) Bandwdths are assocated to the receptors,.e. the ponts where the concentraton has to be estmated. For each receptor all partcles are ordered by ther dstance from the receptor

3 8 th Int. Conf. on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purposes A group of nearest neghbours of the receptor s defned as contanng the closest partcles carryng one eghteth of the total partcles mass (for each chemcal speces) The bandwdth assocated to the receptor, n each drecton, s the maxmum projecton of the dstance of the nearest neghbours n that drecton. Kernel PG (Partcles-based and Globally-defned) Bandwdths are assocated to the partcles. The same set of bandwdth, one for each space drecton, s assocated to each partcle. Bandwdths are calculated, n each drecton as (De Haan,1999): 1 R d+ 4 λ = α A( K) n mn σ, wth =1,, d 1.34 where σ and R are the standard devaton and the nterquartle range of the partcles dstrbuton n each space drecton; n s the total number of partcles, d the number of space dmensons ;α s a tunng parameter (set equal to 0.85 by DeHaan) and A(K) s a parameter dependng on the partcle dstrbuton and the kernel functon. Kernel PL1 (Partcles -based, Locally-defned, one-dmensonally ordered). Bandwdths are assocated to the partcles and each partcle has a dfferent set of bandwdths. The neghbourhood for each partcle s defned agan as contanng the closest partcles carryng one eghteth of the total partcles mass (for each chemcal speces) but three dfferent neghbourhoods are defned for each space drecton, based on the projecton of partcles dstances on the three axs. For each drecton the bandwdth s set as the projected dstance of the frst partcle excluded from each of the neghbourhoods. Kernel PL3 (Partcles-based, Locally-defned, three-dmensonally ordered) Bandwdths are assocated to the partcles and each partcle has a dfferent set of bandwdths. A sngle neghbourhood for each partcle s defned agan as contanng the closest partcles carryng one eghteth of the total partcles mass (for each chemcal speces). Threedmensonal dstances are consdered n the orderng process. In each drecton the bandwdth s set as the maxmum projecton of the dstances of the nearest neghbours n that drecton. PRELIMINARY VALIDATION The performances of the nert verson of PLPM have been compared wth the data set of the well known Kncad release experment. Meteorologcal felds have been calculated by means of CALMET, startng from the data of the Natonal Weather Servce ncluded n the kt 1. The only source of the experment emts a plume of buoyant SF 6 nert gas. The present verson of PLPM does not nclude a gradual plume rse algorthm, thus the source heght has been corrected to an effectve heght h eff =h s + h. h has been calculated by means of the Brggs formulae as reported n Senfeld and Pands (1998), pag.932. Hourly emssons have been dvded n 120 puffs 1 Due to the smple orographc and meteorologcal features of the Kncad doman, usng CALMET s not strctly necessary and good results could be acheved also through smpler meteorologcal preprocessors. Anyway, the strct nterdependence of PLPM and CALMET suggested to proceed wth the complete model sute

4 8 th Int. Conf. on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purposes released every 30 seconds, each contanng 30 partcles, for a total emsson rate of 3600 partcles/hour. Performance ndexes In Table 1 the usual performance ndexes for model valdaton are shown. Selected data consst of the Kncad subset wth qualty ndex Q 2. The four kernel based approaches descrbed n prevous secton are analyzed together wth the box countng method for densty reconstructon. Table 1. Performance ndexes for dfferent concentraton calculaton approaches on the data set wth Q 2. Q=2,3 Average Sgma Bas NMSE R FAC2 FB FS (N=586) [ng/m 3 /(g/s)] [ng/m 3 /(g/s)] [ng/m 3 /(g/s)] Measures Box Countng Kernel RL Kernel PG Kernel PL Kernel PL In Table 2 smlar results are shown for the Kncad data wth Q = 3. Table 2. Performance ndexes for dfferent concentraton calculaton approaches on the data set wth Q = 3. Q=3 Meda Sgma Bas NMSE R FAC2 FB FS (N=338) [ng/m 3 /(g/s)] [ng/m 3 /(g/s)] [ng/m 3 /(g/s)] Measures Box Countng Kernel RL Kernel PG Kernel PL Kernel PL Performance ndexes clearly show that the kernel based method s largely preferable to the box countng. All the kernel methods lead to a postve bas,.e. a general underestmaton of the concentraton data. As far as the four bandwdths calculaton methods are concerned, partclesbased methods ( PG, PL1 and PL3) perform better than the RL3 receptor-based. Also local approaches (PL1 and PL3) seem preferable to the PG global approach. Performances of PLPM are comparable to performances of other regulatory models as AERMOD or ISCST3 on the same data set (CERC, 2001)

5 8 th Int. Conf. on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purposes Resdual analyss A resdual analyss 2 has been performed to evaluate model performances for dfferent values of some sgnfcant parameters (as emsson temperature or speed, stablty class, wnd speed and so on). Fve percentles (5 th, 25 th, 50 th, 75th and 95 th ) of the resdual dstrbutons for dfferent values of the emsson temperature and for the PL3 kernel approach are shown n fgure 1. Models perform better as much the 50 th percentle of the resdual dstrbuton s close to the unty and the dstrbuton s stff around the unty value. Fgure 1 shows as model performance s better for low temperature values, when the effect of the buoyant plume rse s smaller. All the other reconstructon methods (not reported here) show a smlar trend. Hgher emsson temperatures lead to a clear underestmaton of the predcted values confrmng the need for a detaled treatment of gradual plume to be mplemented n the next verson of PLPM. Fgure 1. Resdual analyss for PL3 concentraton reconstructon approach and varyng emsson temperature on the data set wth Q 2. CONCLUSIONS A frst prototype of a fully Lagrangan photochemcal partcle model, PLPM, has been presented and dscussed. Pecular features of ths model are the hgh resoluton, beng lnked to the CALMET meteorologcal model and the grd ndependence, obtaned by usng the kernel densty estmator. The man results of the model valdaton show as PLPM acheves the performances level of some well known regulatory models suggested by the EPA. Also ths valdaton exercse, has shown as densty reconstructon methods based on the kernel approach are preferable to the usual box countng method. A resdual analyss has suggested next steps n the model development, as the mplementaton of complete descrpton of the gradual plume rse. 2 Resduals are defned as the ratos C p /C o of predcted and observed values

6 8 th Int. Conf. on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purposes REFERENCES Bancon, R., Mosca, S., and Grazan, G., PDM: a Lagrangan Partcle Model for Atmospherc Dsperson. European Communtes report EN, Ispra, Italy. Bowne N.E. and Londergan R.J. (1983) Overvew, Results, and Conclusons for the EPRI Plume Model Valdaton and development Project: Plans Ste, EPRI Report EA Cambrdge Envronmental Research Consultants (2001) ADMS 3.1 Valdaton Summary. Avalable on Carter, W. P. L., A detaled mechansm for the gas-phase atmospherc reactons of organc compounds. Atmospherc Envronment, 24A, No. 3, de Haan P., (1999) On the use of densty kernels for concentraton estmatons wthn partcle and puff dsperson models. Atmospherc Envronment, 33, No. 13, Hurley, P., and Physck, W., A skewed homogeneous Lagrangan partcle model for convectve condtons, Atmospherc Envronment, 27A, Olesen H.R., (1998) Model Valdaton Kt-status and outlook. 5th workshop on Harmonsaton wthn Atmospherc Dsperson Modellng for Regulatory Purpose, Rhodes, Greece, May, Patankar, S. V., Numercal heat transfer and flud flow. McGraw-Hll, New York. Scre J.S., Strmats, D.G. and Yamartno, R.J., A User s Gude for the CALPUFF dsperson Model (Verson 5.0), Earth Tech, Inc Thomson, D. J., Crtera for the selecton of stochastc models of partcle trajectores n turbulent flows. J. Flud Mech., 180,