ADDING REALISM TO SOURCE CHARACTERIZATION USING A GENETIC ALGORITHM

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1 ADDING REALISM TO SOURCE CHARACTERIZATION USING A GENETIC ALGORITHM Luna M. Rodiguez*, Sue Ellen Haupt, and Geoge S. Young Depatment of Meteoology and Applied Reseach Laboatoy The Pennsylvania State Univesity, Univesity Pak, Pennsylvania. INTRODUCTION Ameica s National Stategy fo Homeland Secuity states that one of the nation s goals is to espond to and ecove fom hamful incidents that occu (Homeland Secuity Office 007). Such incidents include an intentional elease of hazadous chemical, biological, nuclea, o adioactive (CBNR) mateial into the atmosphee. It is impotant to be able to pedict the tanspot and dispesion of these mateials. Howeve, sometimes thee is inadequate souce infomation to pefom those pedictions; theefoe it becomes necessay to chaacteize the souce of an aibone contaminant fom emote measuements of the esulting concentation field. The chaacteization of a souce involves back-calculating the souce location and emission ate. Thee has been extensive wok backcalculating souce chaacteistics, fo example, Thompson et al (007) and Rao (007). Some pevious wok that uses genetic algoithms (GA s) to optimize souce chaacteistics include the wok done by Allen (006, 007), Haupt (005), Haupt et. al. (006, 007a, 007b, 007c), and Long et. al. (007). In addition to chaacteizing the souce some of these effots include back-calculating meteoological vaiables, such as wind speed, wind diection, and stability. Seveal of the pevious papes include adding noise to the data to simulate eos in the senso data, input paametes, and the inheent atmospheic tubulence. The goal of the pesent study is to pefom a sensitivity analysis to add an element of ealism to the likely senso constaints. It is done using an identical twin appoach with a Gaussian Puff model, which then optimizes a solution by means of a GA, and finally finds the global minimum with the Nelde-Mead downhill simplex algoithm (NMDS). The sensitivity analysis is needed because some of the sensos ae often limited in tems of satuation and detection levels. These ae taken into account because they make the obsevations non-gaussian, which means that the GA must be awae of the levels so that it can model the obseved data instead of the ideal Gaussian. *Coesponding autho addess: Luna M. Rodiguez, Depatment of Meteoology, The Pennsylvania State Univesity, Univesity Pak, PA 680; lm57@psu.edu. PROCEDURES C = exp The Gaussian puff model () is used to detemine Q t ( ) x Ut exp.5 ( ) π σ xσ yσ z σ x ( z H ) ( z + H ) σ e z + exp σ e x y exp σ y concentation obsevations ove five time steps and five gid sizes on a 6 km domain (Table ), whee C is the concentation at ecepto, (x, y, z ) ae the Catesian coodinates downwind of the puff, Q is the emission ate of the souce, t is the length of time of the elease itself, U is the wind speed, H e is the effective height of the puff centeline, and (σ x, σ y, σ z ) ae the dispesion coefficients that ae computed fom Beychok (994). Table. Chaacteistics of gids evaluated on a constant 6 km domain GRID SIZE NUMBER OF GRID POINTS Data is ceated by fist applying () to geneate concentation at gid points then clipping the data to simulate detection and satuation of the levels. A Pasquill stability class D is used in this study and Figue shows how the concentation stength vaies ove 5 time steps fo a 6X6 ecepto gid. This concentation data is then clipped to simulate satuation and detection levels of the sensos. The detection level is detemined with espect to the maximum concentation stength value and any data unde that level is set to zeo. The detection levels ae simulated by imposing a minimum level to ou data, i.e., fo a X0-6 cutoff, anything smalle than X0-6 of the maximum concentation is changed to 0 and similaly fo the X0 -, X0-8, X0-4 kg m -3 cases. Satuation level fo this study means that any value ove a detemined pecent of the maximum concentation stength is changed to that paticula value. Fo a satuation level of 00% of the maximum () SPACING BETWEEN GRID POINTS (KM) X X X X X

2 concentation stength, kg m -3 is used as the cutoff value. Fo satuation of 50% of the maximum concentation stength 0.5 kg m -3 is the cutoff so anything above this value is set equal to 0.5 kg m -3, likewise fo % (0. kg m -3 ) and 0.% (0.0 kg m -3 ). Examples of the detection and satuation cutoff levels ae given in Figue whee the maximum concentation in this illustation is kg m -3. Afte the data is clipped it seves as ou tue obsevations. The GA begins with a andom population of guesses to the vaiables that fall within the citeia descibed in Table. These ae then compaed to ou tue obsevations by means of a cost function (). t= cost function = 5 TR = ( log ( ac + ε ) log ( ar + ε )) 5 t= 0 TR ( log ( ar + ε )) = Whee, C is the concentation as pedicted by the dispesion model given by (), R is the obsevation data value at ecepto, TR is the total numbe of eceptos, a and ε ae constants added to avoid logaithms of zeo. Table. Vaiable Thesholds used to populate the GA PARAMETER MINIMUM VALUE MAXIMUM VALUE Location (x,y) (metes) Souce Stength (kg m -3 ) 0 0 Wind Diection ( ) GAs wok by evaluating an initial population via the cost function then selecting the best anking individuals to epoduce, foming a new geneation though the GA opeatos of cossove and mutation. These ae then in tun evaluated and the pocess iteation. We use a population of 40 chomosomes, 640 iteations, and a mutation ate of 0.3.The mean and standad deviations of 0 Monte Calo uns of the median of 0 uns fo each satuation level wee evaluated fo each detection level and gid size. The tue solutions fo all of these cases is a solution stength of kg/s, a location of (0,0), and a wind diection of RESULTS Figues 3-6 show the mean values of the 0 Monte Calo uns, each figue with a diffeent satuation level as a constant while vaying the detection levels acoss the abscissa and the diffeencing gid sizes indicated by the coloed lines. In the figues each paamete (wind diection, souce stength, & x,y location) is plotted sepaately. Fo the wind diection we ae seeking a value of 80, fo the concentation 0 0 () stength a value of kg/s, and fo the souce elease a location of 0,0 metes. Figues 3 and 4 show that the GA etieves the coect souce chaacteistics fo all the detection levels using the 8X8 and 6X6 gid. The othe gid sizes did not pefom as well and wee inconsistent. When loweing the satuation level, Figues 5 and 6, evey gid size smalle than a 6X6 becomes highly uneliable. Thesholding the data too seveely eliminates so much infomation that etieval quality goes down significantly, thus, moe dynamic ange in sensos lends to moe accuate invesion fo the vaiables. This dynamic ange poduces the most impact if it extends to the maximum concentation as is illustated in Figue 7. In this figue the detection level is X0-6 and the satuation levels vay along the abscissa with the diffeing gid sizes indicated by the coloed lines. In ageement with Figues 3-6, Figue 7 shows that the lage gid sizes, 8X8 and 6X6, ae successful in etieving the coect paamete values up to the 50% satuation level. The smalle gid sizes ae less eliable afte the 50% cutoff and none of the gid sizes ae able to coectly identify all of the paametes fo the lowest satuation levels. 4. CONCLUSION The hybid GA method used hee (with NMDS) is successful in back-calculating souce chaacteistics and wind diection with data that has been thesholded foming a clipped Gaussian. These thesholds simulate satuation and detection levels in sensos and if applied too seveely they eliminate so much infomation that etieval quality degades significantly. The invesion is most successful if the senso can detect the maximum concentations, which means that the most effective sensos have this chaacteistic. The next step in this poject is to etieve souce and meteoological data using a time-dependent computational fluid dynamics lage eddy simulation to ceate synthetic data. Such data inheently includes time-dependent behavio unique to each contaminant episode athe than the ensemble aveage pedicted by the tanspot and dispesion model used in pevious studies. Then a ealistic senso configuation will be consideed as well as vaying stability classes. Finally, we expect to use this model to back-calculate souce chaacteistics and meteoological paametes with eal field data obsevations ACKNOWLEDGEMENTS This wok was suppoted by DTRA unde gant numbe W9NF-06-C-06. REFERENCES Allen, C.T., G.S. Young, and S.E. Haupt, 006: Impoving Pollutant Souce Chaacteization by

3 Optimizing Meteoological Data with a Genetic Algoithm, Atmospheic Envionment, 4, Allen, C.T., S.E. Haupt, and G.S. Young, 007: Souce Chaacteization with a Recepto/Dispesion Model Coupled With A Genetic Algoithm, Jounal of Applied Meteoology and Climatology, 46, Beychok, M. R., 994: Fundamentals of Gas Stack Dispesion, 3PdP ed. Milton Beychok, pub., Ivine, CA, 93. Haupt, S.E., 005: A Demonstation of Coupled Recepto/Dispesion Modeling with a Genetic Algoithm, Atmospheic Envionment, 39, Haupt, S.E. G.S. Young, and C.T. Allen, 006: Validation Of A Recepto/Dispesion Model Coupled With A Genetic Algoithm, Jounal of Applied Meteoology, 45, Haupt, S.E., R.L. Haupt, and G.S. Young, 007: A Mixed Intege Genetic Algoithm used in Chem-Bio Defense Applications, submitted to Jounal of Soft Computing. Haupt, S.E., G.S. Young, and C.T. Allen, 007: A Genetic Algoithm Method to Assimilate Senso Data fo a Toxic Contaminant Release, Jounal of Computes,, Homeland Secuity Office, cited 007: National Stategy fo Homeland Secuity. [Available online at S.pdf.] Long, K.J., S.E. Haupt, and G.S. Young, 007: Impoving Meteoological Focing and Contaminant Souce Chaacteization Using a Genetic Algoithm. Submitted to Jounal of Envionmental Management. Rao, K.S., 007: Souce estimation methods fo atmospheic dispesion, Atmos. Env. 4, Thomson, L.C., Hist, B., G. Gibson, S. Gillespie, P. Jonathan, K.D. Skeldon, M.J. Padgett, 007: An impoved algoithm fo locating a gas souce using invese methods, Atmos. Env., 4, 8-34

4 FIGURE Figue. Concentation patten ove 5 time steps on a 6X6 ecepto gid. The panel on the left shows the concentation fo with a 80 wind diection and the panel on the ight fo a 5 wind diection. a) b) Figue. Data fit to a Gaussian. The maximum concentation nomalized to kg m -3. Panel a indicates the theshold detection levels of X0-6, X0 -, X0-8, and X0-4. Panel b shows the satuation levels, set as a pecentage of the full (00%, 50%, %, 0.%).

5 a) b) Figue. Results fo all gid sizes and detection levels of the satuation level that at 00% of the maximum concentation stength value. Panel a shows the mean value of θ (wind diection, 80 ), panel b indicates souce stength ( kg/s), and panels c and d show the location (0, 0) (in m) fo x and y espectfully. All of these esults ae of 0 Monte Calo uns of the median value of 0 individual uns. a) b) Figue. Results fo all gid sizes and detection levels of the satuation level that at 50% of the maximum concentation stength value. Panel a shows the mean value of θ (wind diection, 80 ), panel b indicates souce stength ( kg/s), and panels c and d show the location (0, 0) (in m) fo x and y espectfully. All of these esults ae of 0 Monte Calo uns of the median value of 0 individual uns.

6 a) b) Figue 3. Results fo all gid sizes and detection levels of the satuation level that at % of the maximum concentation stength value. Panel a shows the mean value of θ (wind diection, 80 ), panel b indicates souce stength ( kg/s), and panels c and d show the location (0, 0) (in m) fo x and y espectfully. All of these esults ae of 0 Monte Calo uns of the median value of 0 individual uns. a) b) Figue 4. Results fo all gid sizes and detection levels of the satuation level that at 0.% of the maximum concentation stength value. Panel a shows the mean value of θ (wind diection, 80 ), panel b indicates souce stength ( kg/s), and panels c and d show the location (0, 0) (in m) fo x and y espectfully. All of these esults ae of 0 Monte Calo uns of the median value of 0 individual uns.

7 a) b) Figue 7. Results fo all gid sizes and satuation levels of the detection level that at X0-6 of the maximum concentation stength value. Panel a shows the mean value of θ (wind diection, 80 ), panel b indicates souce stength ( kg/s), and panels c and d show the location (0, 0) (in m) fo x and y espectfully. All of these esults ae of 0 Monte Calo uns of the median value of 0 individual uns.