Development of a NOx Chemistry Module for EDMS/AEDT to Predict NO2 Concentrations (2017)

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29   Comparison  of Dispersion Without  Chemistry - The total NOx results from CALPUFF and SCICHEM are based solely on the effects of atmospheric dispersion (no chemistry). The comparisons for the morning hour indicate that total NOx concentrations generated by AERMOD (full conversion) are similar in maximum concentration to those generated by SCICHEM and CALPUFF. This indicates that in terms of near field peaks, the dispersion modeling capabilities of each model are comparable for the scenario modeled. However, for the afternoon hour, the AERMOD total NOx is noticeably different than those of the other models. The difference is likely due to the formulations between plume and puff models (i.e., the CALPUFF and SCICHEM dispersion show similar characteristics during the afternoon hour) and the atmospheric characteristics of the afternoon hour. This is also evident by how the concentrations predicted by the puff models fall- off noticeably quicker with distance than AERMOD predictions do.  Full Chemistry versus Simplified NOx in SCICHEM - The full chemistry (CB mechanism) and the simplified NOx conversion methods in SCICHEM produced very similar results. This indicates that at least for the airport layout that was modeled including the spatial domain (e.g., up to five miles), the simplified method appears to be adequate.  Impact  of  CALPUFF  Modeling  Limitations - The resulting CALPUFF NO2 predictions are noticeably different than those from other methods/models. In addition to the aforementioned differences in model formulations, these differences are also likely due to the use of four separate runs (one for each aircraft mode) in order to accommodate the 200-source limitation associated with this model. As such, interactions of the plume puffs across the runs were not possible. The quicker drop-off of NO2 concentrations indicate a potentially greater degree of dispersion and sensitivity to distance. Based upon the outcomes of this analysis, the AERMOD ARM2 Method performs the best in computing NO2/NOx ratios and estimating NO2 concentrations, with R2 values similar to the other AERMOD methods. Time-varying puff models may, in some instances, provide greater fidelity, one example being when closer to the source. However, for most practical applications, they offer little advantage over ARM2 when computing NO2/NOx ratios associated with airport sources. 6.0 NOX Chemistry Methods (Including the Photostationary State) As a means of further assessing methods that directly and indirectly reflect the photostationary state for predicting NO2/NOx ratios, a wide array of regression equations were developed and evaluated using detailed airport-related modeled vs.-measured data from the three case-study airports: ADL, LAX, YUL (see Section  4.1). Additionally, and based upon initial test results, the three airport datasets were combined to provide greater statistical strength. Supplementary data processing and screening were also aimed at (but not limited to) the following: (i.) a correction for the solar zenith angle for the ADL dataset and (ii.) filtering out spuriously low NO2 values.17 For ease of identification and assimilation, three methods were evaluated as entitled and described below in Table 8):   Method  1:  Simple  Regression  -  Method 1 uses a regression methodology similar to that employed in ARM2 but with “airport-centric” data to model different categories of diurnal conditions (e.g., day and night). Furthermore, different levels of diurnal categories (e.g., three- 17 For consistency, this work was also conducted using the previously-tested models and methods (e.g., ARM/ARM2, OLM, PVMRM, CALINE4, CALPUF, CMAQ and SCICHEM, see also Sections 3.0, 4.0 and 5.0). Modeled‐to‐Modeled Comparisons  Based upon the outcomes of this  modeling analysis, the AERMOD  ARM2 Method performs the best  overall in computing NO2/NOx ratios  and estimating NO2 concentrations.  

30  hour durations, etc.) are also assessed. Various “goodness-of-fit” criteria were then used to identity an appropriate form of the regressed equations. For this method, the equations were enhanced by including constraints with fixed points for a NOX concentration of 0 and a NO2/NOX ratio of 1.0. In brief, this involved the implementation of horizontal asymptotes of either 0.1 or 0.2, depending on the time period analyzed.  Method  2: Multivariable Regression  -  For this method, similar constraints as those described above for Method 1 were also implemented. However, Method 2 was considered an advancement over Method 1 as it takes into account various atmospheric variables (similar to those used to model the photostationary state in Method 3 to account for the effects of the photostationary state as part of the regressed equation.) Method 2 also represents a single equation (rather than the multiple equations associated with Method 1) that can take into account different diurnal conditions.  Method 3: Photostationary State - This method assumes that the air is at a photostationary state condition and it uses specific hourly data to calculate the NO2/NOX ratio. Taking into account atmospheric conditions, this method is most applicable to receptor locations far enough away from the emission source such that the photostationary state condition has been reached. For example, depending on the O3 concentration, photolysis rates, and mixing times, several minutes and more may be required for air masses to reach a photostationary state. Table 8. NO2/NOX Methods  Title  Method 1: Simple  Regression for separate  day/night categories  Method 2: Multivariable  Regression taking into account  atmospheric characteristics  Method 3: Photostationary  State equation18,19  Modeling Scheme  Day, Night, and 3‐hr  categories  NO2/NOX = f ([NOX])  Where  [NOX] = NOX conc. (ppb)  NO2/NOX = f ([NOX], T, [O3], θ, S)  Where  [NOX} = NOX conc. (ppb)  T = Atmospheric temperature (K)  [O3] = Ozone conc. (ppb)  θ = Zenith angle of the sun (rad)  S = Solar irradiation (watts/m2)  ܱܰଶ ܰ ௫ܱ ൌ ܭଵܭଷ ሺሾܱଷሿሻ 1 ൅ ܭଵܭଷ ሺሾܱଷሿሻ Where  K1 = Reaction rate for    NO + O3 ‐> NO2 + O2        = (15.33/T)exp(‐1450/T)  (1/ppb*s)  K3 = Reaction rate for    NO2 + uv ‐> NO + O        = (0.0167exp(‐ 0.575/cos(θ)) (1/s)  T = Atmospheric temperature  (K)  [O3] = Ozone concentration  (ppb)  θ = Zenith angle of the sun  (rad)  18 Hamson, R.F., Jr.; Garvin, D. Reaction Rate and Photochemical Data for Atmospheric Chemistry 1977; NBS Technical Note 513; U.S. Department of Commerce: Washington, DC, 1978. 19 Dickerson, R.R.; Stedman, D.H.; Delany, A.C. “Direct measurements of O3 and nitrogen dioxide photolysis rates in the troposphere,” J. Geophys. Resh. 1982, 87(C7), 4933-4946.

31    Method Summary  Single independent  variable regression  similar to ARM2 but  based on airport‐specific  data.  Multivariable regression based  on airport‐specific data that  empirically accounts for both NO  oxidation and NO2 photolysis  through inclusion of atmospheric  parameters: T, O3, θ, and S.  Assumes the air masses are in  a photostationary state and  analytically determines the  NO2/NOX ratio.  User  Requirements/Data  Needs  User must choose the  diurnal category to use  the appropriate  regression equation.  User determines hourly  NOX concentration using  AERMOD.  User determines hourly NOX  concentration using AERMOD,  and specifies T, O3, θ, and S from  available meteorological and  other datasets.  User supplies T, O3, and θ from  available meteorological and  other datasets.  Based upon detailed regression assessments, the sets of regressed equations in Table 9 were selected for further evaluations involving time-paired comparisons of modeled and measured NO2/NOx values.   Table 9: Selected Equations for Comparisons of Modeled and Measured NO2/NOx Values  Method 1: Simple  Regression  Equation 1: Unconstrained regressed equation  NO2/NOx=1‐0.8*exp(‐1/(b*cx))   Where: b = 0.57357, c = 1.02214, x = NOx  concentration  Equation 2: (also called “Constrained‐2”): Same as Equation 1 but with different  coefficients reflecting constraints.  NO2/NOx=1‐0.8*exp(‐1/(b*cx))   Where: b = 0.3361, c = 1.03062, x = NOx  Method 2:  Multivariable  Regression  Multivariable regressed equation  NO2/NOx = a*x1(1/3) + b*x2(1/3) + c*x3(1/3) + d*x4(1/3) + e*x5(1/3) + f                Where: x1 =  NOx, x2 = Temp., x3 = θ (zenith angle of the sun), x4 = O3 (ozone), x5 =  Solar Irradiation, a = ‐0.1377, b = 8.4309, c = 5.963, d = 2.0289, e = ‐2.7279, f = 0.60589  Method 3:  Photostationary  State  Equation 1: Analytically‐derived photostationary state equation               Equation 2: Adjusted photostationary state equation to include a solar irradiation  variable                        F1 = a*Exp(b/x1)/x1                        F2 = (c*Exp(d/(Cos(x2))))+e*x4^f                        NO2/NOx = F1*x3/(F2+F1*x3)  ܭଵ ൌ ൬15.33ܶ ൰ ൈ ݁ ିଵସହ଴ ் ܭଷ ൌ 0.0167 ൈ ݁ ି଴.ହ଻ହ ୡ୭ୱఏ ܱܰଶ ܰ ௫ܱ ൌ ܭଵܭଷ ൈ ܱଷ 1 ൅ ܭଵܭଷ ൈ ܱଷ

The asses values. G (RMSE), focus on were dee assessed f equations number o voluminou details of   6.1  Meth The “Unc overall pe force the e replicate worse fit validation The regre  2  Po  Lo  Ex Example M sments were oodness-of-f standard dev paired compa med unneces or biases. Th , both in an a f statistical te s. The acc the statistical od 1 (Simp onstrained E rformance. T quation to ap the curve of statistics tha assessments ssion work w nd‐Order Poly wer: y = a*x g: y = a*ln(x ponential: y  odeled vs. M Plots (10 ARM2  (Blue)  Where X1 = Te a = 93.4 conducted u it criteria ev iation of the risons to pro sary. Howev ese statistica bsolute sens sts conducte ompanying e analyses. le Regressio quation” wa he “Constrai proach the th the unconstr n the Uncon to allow perf as conducted nomial: y = a ^b  )+b  = a*exp(b*x) easured NO  to 12 hrs.)  : F1 = a*Exp(b/ mp, X2 = θ (zen 86, b = ‐2001 sing paired-in aluations ma percent error vide hour-by er, average l methods w e, as well as d was extens xample grap n—Uncons s selected fr ned-2” equat eoretical 0 N ained Equat strained Equ ormance com starting with *x^2+b  2/NOx Ratios 32  x1)/x1, F2 = (c ith angle of th .64, c = 5.2171 -time compa inly involved , and the line -hour perfor error percen ere aimed at comparing t ive and the hs are illust trained and om the deta ion represent Ox and 1.0 N ion 1. Even ation, the C parisons usin the followin   Example M *Exp(d/(Cos(x2 e sun), X3 = O 5, d = ‐3.3359 risons of mo reviewing ar fit (e.g., s mance asses tages and h determining heir results a outcomes in rative. The  Constrained iled regressi s the implem O2/NOx poin though the C onstrained-2 g the validat g basic equat odeled vs. M (19 ARM2 (Blue) ))))+e*x4^f,  3 (ozone), X4 = , e = 1.59125,  deled and m R2, Root Me lope and y-in sments, non- istograms o accuracies o gainst each o the forms of following su ) on assessme entation of w t (i.e., 0,1) w onstrained e equation wa ion datasets. ions: eaured NO2  to 23 hrs.)       Solar Irradiati f = 0.84217  easured NO2 an Squared tercept). Wi paired evalua f the errors f the method ther. The o tables and g bsections pr nts based on eighting poi hile also try quation prod s included i /NOx Ratios on  /NOx Error th the tions were s and verall raphs esent best nts to ing to uced n the Plots 

Plots of N Various m following behavior o O2/NOX vers 2nd Ord ore complex plots show f the tail end us NOX using er Polynomi Night  equations w several crite of the curve these equati al  ere also eva ria that wer s. 33  ons are prese Log luated, starti e used to re nted below: ng with a m ject equation Power  Day  ix of differen forms, mo t formations stly based o . The n the

Y = a+ (Increase Y = a*x^10+b (Tail i ch b*ln(x)+c*ln(x)^2 (Tail starts d Y = a+b*ln(x)+c*ln  tail end sim *x^9+c*x^8+d*x^7 s not smooth aracteristic o +d*ln(x)^3+e*ln( ecreasing ra (x)^2+d*ln(x)^3+ ilar to 2nd‐Ord +e*x^6+f*x^5+g*x  – does not a f the actual f x)^4+f*ln(x)^5 pidly) e*ln(x)^4 er Polynomi ^4+h*x^3+i*x^2+j* ppear to be  unction)  34  al)  x+k (Tail Y = a+b/ln(x)+c/ (Tail slope is  Y = a+ (Tail slope is  Y = a+  flattens out  NO2 ln(x)^2+d/ln(x)^3 too sharply n b*x^.5+c*exp(‐x) too sharply n b/x+c/x^2+d/x^3 too soon (or  /NOX level)) +e/ln(x)^4 egative)   egative)   at the wrong    

 Y = a (Head ch Most of th illustrate t summariz     The statis including 1/(b*c^x) few appro and the re 6 pm) sce +b/ln(x)+c/ln(x)^  has a kink t aracteristic o ese equation hat the equat e the regressi tics are over R2 and MS ) are clearly l priate candid jection criter nario: 2+d/ln (x)^3+e/ln( hat does not  f the actual  s produced re ions should on fits that w all similar to E values. Ho ess desirable ates were sel ia illustrated Day   x)^4+f/ln(x)^5  appear to be function) asonable stat not be judged ere conducte those for th wever, the (low R2 valu ected from th with the prev 35    istics with R based on ju d on potentia e simple eq statistics for es) – indicat e list of equ ious plots. T 2 values in th st the statisti lly viable com uations (e.g., some equat ing poor fits. ations taking hese were fir e 0.5 to 0.6 r cal results. T plex equatio 2nd Polyno ions such as To simplify into account st selected fo Nigh ange. They h he following ns. mial, Power, Y = 1-.2*E the assessme both the sta r the day (6 t   elp to plots etc.) XP(- nts, a tistics am to

As shown in negativ y= y= Plots of th , the equatio e NO2/NOX r (d*x^a)/(e*x a*x/((b+c*x ese equation Hou Hou ns for the nig atios. Remov ^b+c)  ^d)^e)  s for each of rs 0 – 3  rs 6 – 9 ht condition ing these equ the three-hou 36  have a tail en ations results r categories a d with a sha in the follow re also show Ho Ho rply decreas ing plot and n in the follo urs 3 ‐ 6  urs 9 ‐ 12 ing slope res equations. wing plots. ulting

The equat such as 1 early. Oth y y y y y y These equ and illust equations Hour ions appear t 2-15 will nee er suitable eq =a+b*x^.5*l =a+b*x^1.5+ =a+b*x*ln(x =a+b*x+c*x =a+b*x+c*x/ =‐1*z/(d+b* ations and pl rate the eval was conduct DAY  Equation  y=1‐a*exp y=1‐.9*exp y=1‐.8*exp y=1‐exp(‐1 s 12 – 15 o be adequat d a different uations are li n(x)+c*x/ln(x c*x^.5  )+c*x^.5*ln(x ^.5*ln(x)  ln(x)  exp(‐1*c*x)) ots provide p uation proce ed. Some equ (‐1/(b*c^x))  (‐10/x^a)  (‐1/(b*c^x))  0/x^a)  e for most of equation fo sted below a )  )  otential solut ss for the eq ations repres R2  0.523384 0.472451 0.522563 0.460521 37  the three-hou rm as the cu nd displayed ions for mod uations. A c ent constrain NIGHT Equat y=1‐a* y=1‐.9 y=1‐.8 y=1‐.9 Hou r categories rrent two hav in the next p eling NO2/NO loser review ts to the curv   ion  exp(‐1/(b*c^ *exp(‐10/x^a *exp(‐1/(b*c *exp(‐a/x^1. rs 15 ‐ 18 . However, so e tail ends t lot. X ratios for of some of e characterist R2  x))  0.523 ) 0.472 ^x))  0.522 5)  me hourly g hat flatten ou different scen the sigmoid ics: 384  451  563  0  roups t too arios -type

For simpl plots of th y=a*exp(1 y=1‐.9*exp ification, the ese equation y=1 y=1 y=1 y=1 y=a y=1 /(b*c^x)  (‐1/b*c^x)  first three eq s for each of t ‐a*exp(‐1/(b ‐.9*exp(‐10/ ‐.8*exp(‐1/(b ‐exp(‐10/x^a *exp(1/(b*c^ ‐.9*exp(‐1/b 0.526813 0.516824 uations for e he three-hou *c^x)) x^a)  *c^x))  )  x)  *c^x) 38  ach day and r categories a P y y y night conditi re shown in t Method 1 lots by Day & =1‐a*exp(‐1/ =1‐.9*exp(‐1 =1‐.8*exp(‐1 on were furt he following : Simple Reg  Night 3‐hou y=1‐a*exp(‐1 y=1‐.9*exp(‐ y=1‐.8*exp(‐ y=1‐.9*exp(‐ (b*c^x))  0/x^a)  /(b*c^x))  her evaluated plots. ression  r categories /(b*c^x))  10/x^a)  1/(b*c^x))  a/x^1.5)  . The  

Most of th y= In contras equation m y= Although provide an of coeffic NO2/NOx intervals. While som largely fi constraint point (0,1 was appro to that poi y= y= e hourly rang 1‐.9*exp(‐10 t, the overal ay be best s 1‐.8*exp(‐1/ different equ overall reas ients for the ratios since e of these e t according s were imple ). Theoretica ximately thr nt:  1‐.8*exp(‐1/ 0.2+(1/(1+b e plots appe /x^a)  l plots (espe uited to repre (b*c^x))  ations can po onable fit for aggregated the user w quations hav to the data ( mented in an lly, this wou ough the use (b*c^x))  *exp(‐(c*x)))) ar to show th cially 0-3, 3 sent the data tentially be u all intervals, datasets. Th ould not be e constraints i.e., followe effort to mak ld represent of a weightin 39  at the followi -6, and 9-12 : sed for each including bo is simplifies burdened w to the curve d the data) e the equatio the condition g scheme th ng equation m ) and statist 3-hr interval th day and ni the potentia ith using m characteristic to allow for ns go throug where all N at made the f ay be the le ics indicate , the above e ght condition l use of Me ultiple equat s (e.g., asym the best sta h the 0 NOx O has conve ollowing equ ast desirable: that the follo quation appe s with just o thod 1 to p ions for dif ptotes), they tistics. Addi and 1.0 NO2 rted to NO2 ations come wing ars to ne set redict ferent were tional /NOx . This close

The latter see if mor followed b Equation  NO2/NOx NO2/NOx NO2/NOx NO2/NOx NO2/NOx NO2/NOx equation is a e accurate fit y the corresp =1‐0.8*exp(‐ =1‐0.8*exp(‐ =1‐0.8*exp(‐ =0.2+(1/(1+b =0.2+(1/(1+b =0.2+(1/(1+b nother sigmo s could be ac onding day p 1/(b*c^x))  1/(b*c^x)) Co 1/(b*c^x)) Co *exp(‐(c*x))) *exp(‐(c*x))) *exp(‐(c*x))) id formulatio hieved. The r lots of the cu nstrained  nstrained2  )  ) Constrained ) Constrained 40  n that was in esulting coef rves: b  0.573 0.193 0.336 0.5134   0.250 2  0.288 cluded to ser ficient and R c  57 1.0221 53 1.0634 11 1.0306 7 ‐0.025 93 ‐0.050 18 ‐0.034 ve as a basis 2 statistics ar R2  4 0.52263 9 0.01881 2 0.25196 2 0.52198 8 0.29251 1 0.2651 for comparis e presented b             on, to elow,

41      The “Meas” day data points refers to the measured (monitored) data while the “Constrained” equation refers to the weighting that was implemented to force the equation to approximately approach the 0,1 point. The “Constrained2” equations refer to additional constraints that were approximated through weighting of NOx data points at the 50, 100, 150, and 200 ppb points in an effort to more closely follow the unconstrained equation which produced the best fit. In fact, the unconstrained equation produced R2 values (i.e., 0.52) that were significantly higher than those of the constrained equations. The relatively small differences between the curves of the “Constrained” and “Constrained2” equations indicate that the most significant constraint was the weighting to approach the 0,1 point. That is, even though the “Constrained2” equations more closely approximate the unconstrained curve, they still produce similar and much lower R2 values than the unconstrained equations. Also, the other sigmoid equation, y=0.2+(1/(1+b*exp(-(c*x)))), did not produce any noticeable differences. In addition to the regression solution presented for this equation, various perturbations were made to the equation resulting in either similar statistics or an unsolvable formulation. Therefore, it is recommended that the unconstrained equation, y=1-.8*exp(-1/(b*c^x)), be used to represent the solution for Method 1. However, it is also recommended that the “Unconstrained2” parameters also be tested as part of the validation work for comparison purposes. 6.2  Method 2 (Multivariable Regression) Equation  This regressed equation produced comparable regression fit statistics to those of Method 1 (Equation 1). Based on its independent variables, Method 2 is conceptually the most robust method as it can potentially cover all time intervals (day and night conditions) with one equation. Similar to the Method 1 evaluations, the starting point for the Method 2 evaluations involved assessing similar basic equations (e.g., 2nd-Order Polynomial, Log, etc.). Because there are five independent variables, a linear equation  (y=a*x1+b*x2+c*x3+d*x4+e*x5+f) was used as the starting point to specify different forms of the basic equations as shown below:   Code  Model Definition  x1Sqrd  y=a*x1^2+b*x2+c*x3+d*x4+e*x5+f  x2Sqrd  y=a*x1+b*x2^2+c*x3+d*x4+e*x5+f  x3Sqrd  y=a*x1+b*x2+c*x3^2+d*x4+e*x5+f  x4Sqrd  y=a*x1+b*x2+c*x3+d*x4^2+e*x5+f  x5Sqrd  y=a*x1+b*x2+c*x3+d*x4+e*x5^2+f  x1log  y=a*ln(x1)+b*x2+c*x3+d*x4+e*x5+f   x2log  y=a*x1+b*ln(x2)+c*x3+d*x4+e*x5+f  x3log  y=a*x1+b*x2+c*ln(x3)+d*x4+e*x5+f  x4log  y=a*x1+b*x2+c*x3+d* ln(x4)+e*x5+f  x5log  y=a*x1+b*x2+c*x3+d* x4+e* ln(x5)+f  x1Exp  y=a*exp(b*x1)+c*x2+d*x3+e*x4+f*x5+g  x2Exp  y=a*b*x1+ exp(c*x2)+d*x3+e*x4+f*x5+g  x3Exp  y=a*b*x1+ c*x2+ exp(d*x3)+e*x4+f*x5+g  x4Exp  y=a*b*x1+ c*x2+ d*x3+ exp(e*x4)+f*x5+g  x5Exp  y=a*b*x1+ c*x2+ d*x3+ e*x4+ exp(f*x5)+g  x1Pow  y=a*x1^b+c*x2+d*x3+e*x4+f*x5+g  x2Pow  y=a*x1 +c*x2^b +d*x3+e*x4+f*x5+g 

Each term illustrate t (e.g., a*x1 he regression x3Pow  y x4Pow  y x5Pow  y , b*x2, etc.)  fits using th =a*x1 +c*x2 =a*x1 +c*x2 =a*x1 +c*x2 was modifie ese equation 42  +d*x3^b +e* +d*x3+e*x4^ +d*x3+e*x4+ d based on s.   x4+f*x5+g b +f*x5+g  f*x5^b +g  the type of equation. The following plots

  43 

The avera that from results do linear cha this NO2/N others. It dependen variable a the predic ge Adjusted the correspo not appear t racteristic tai OX vs. NOX should be n t variables o t a time. The ted NO2/NOX Coefficient o nding Metho o follow the l, and the fir plotting sche oted that it n two dimen following pl ratio for the f Multiple D d 1 fits. Ho tail end of th st term appe me). is difficult sional plots ots exemplify linear equati 44  etermination wever, as th e measured ars to have th To in indepe was co time. T equati As illu notice Tempe Irradia to NO to visualize – they only the relation on. (Ra2) is app e plots show points. In ge e most sign vestigate th ndent variab nducted by r he basis for on (y=a*x1+b strated by th ably greater rature, Zenit tion. But the X which is c the relations show the e ship between roximately 0 , the tail en neral, most o ificant effect e relative le, a contrib emoving eac comparisons *x2+c*x3+d e bar chart, O impact on th h Angle of t most signifi learly greate hip between ffects of jus each indepe .6 - higher d of the pred f the plots sh (at least bas effects of ution assess h variable on was the full *x4+e*x5+f). 3 appears to e regression he Sun, and cant impact i r than that o independen t one indepe ndent variabl than icted ow a ed on each ment e at a linear have than Solar s due f the t and ndent e and

While the effects of of Tempe the predic of the oth other vari term repre formulatio below: se plots prov the other var rature, Zenith ted points to er variables. ables), most senting NOX ns from the ide indicatio iables. For ex Angle, Sola more closely However, b of the focus c ). The first s Method 1 e ns of the im ample, the N r Irradiation follow the m ased on the an be placed et of more co valuations. T 45  pacts of each O2/NOX vs. , and Ozone. easured poin much higher on evaluatin mplex equat he results o independen NOX plot do As such, eff ts are not stra contribution g formulatio ions was bas f regressing Meth Suc Equ t variable, th es not directl orts to curve ightforward from NOX ( ns of the firs ed on implem these equati od 2: Using  cessful Meth ations as Sta Point   ey each mas y show the e up the tail e due to the im as opposed t t term (i.e., t enting succ ons are pres the  od I  ring  k the ffects nd of pacts o the he x1 essful ented

46 

  Some of t Method 1 on the firs try to iden modified: Y    In contras Y  These equ the data, presented Although correspon Similarly, have nega equations Ra2 value on an und formulatio plots are p hese equatio evaluations) t term or wit tify suitable = a+b*x1^.5* t, equation M = a*ln(x1)+b ations repres and more clo . equation M2 ding plot doe many of the tive slopes M2Eq15 thro s that are com erstanding of ns further (a resented belo Y Y Y Y Y Y ns have just , while other h a different candidate eq ln(x1)+c*x1/ 2Eq13 is an *(x2^(1/3))+c ent an advan sely represen Eq11 produc s not appear other equatio that are too ugh M2Eq19 parable to t the characte s well as oth w:  = 1‐a*EXP(‐  = a*x1^(1/3  = a*x1^(1/3  = a*x1^(1/3 = a*x1^(1/3  = a*x1^(1/3 their first term s have severa formulation. uations. Equ ln(x1)+d*x2+ example of a *x3+d*x4+e* cement over t the charac ed the highes to fit the data ns, even thou sharp (i.e., appear to pr hose of the o ristic shape t ers), the foll 1/(b*c^x1))+ )+b*x2^(1/3 )+b*x2^(1/3 )+b*x2^(1/3 )+b*x2^(1/3) )+g*ln(x1)+b 47  modified ( l terms modi They illustrat ation M2Eq8 e*x3+f*x4+g n equation wh x5+f  the linear for teristics of th t Ra2 value o as well as it gh the tail en causing nega ovide adequa ther equation hat a power f owing equat d*x2^(1/3)+e )+c*x3+d*x4 )+c*x3^(1/3) )+c*x3^(1/3) +c*x3^(1/3)+ *x2^(1/3)+c* i.e., using th fied using ei e the experim is an examp *x5+h  ere more tha mulation in e data over f 0.7, the tai could. As su d curves to b tive NO2/NO te curvature s). These eq unction wou ions were reg *x3+f*x4+g* +e*x5+f  +d*x4+e*x5+ +d*x4^(1/3)+ d*x4^(1/3)+ x3+d*x4+e* e same formu ther the same entation tha le where just n one term w curving the t the basic eq l end of the ch, it was no etter fit the d X ratios too s with reason uations were ld provide. T ressed, and x5+h  f  e*x5+f  e*x5^(1/3)+f x5+f  lation used formulation t was conduc the first term as modified: ail end to bet uations previ fit as shown t considered ata, still app early). How able statistics formulated o investigate their statistic   in the used ted to was ter fit ously in the ideal. ear to ever, (i.e., based these s and

The focus As indica other term Based on recommen Y  However, cap of 0.1 horizontal appear to (e.g., NO2 in regressing ted, most of s showed sm the Ra2 va ded: = a*x1^(1/3) in order to p or 0.2 ppb is line. Althou improve the o /NOx versus these equat the fit is capt all but steadi lue (0.69) a +b*x2^(1/3)+ revent the pre recommende gh the first te verall fit as O3, NO2/NO ions was to tr ured by the ly increasing nd an appro c*x3^(1/3)+ dictions from d. This is ak rm (NOx) ha some curvatu x versus S, e 48  y different in first term (x1 Ra2 values. priate fit o d*x4^(1/3)+e being either in to using tw s the most im res are notice tc.). carnations o term), but a f the tail en *x5^(1/3)+f erroneously o equations: pact, the 1/3 d in the indiv Method Result Success Equatio f the 1/3rd–P pplying this d, the follo too low or n a curve inter rd power for t idual plots o  2: Other  s Using the  ful Method  ns as Staring Point   ower formul formulation wing M2Eq egative, a low secting with he other term f each variab I    ation. to the 29 is er a s le

 6.3  Meth An analyt compariso work (i.e. Equation irradiation regression included m Unlike M   1450, etc.     Essentiall The equat resulting o ܭଵ ൌ ൬15ܶ ܭଷ ൌ 0.01 ܱܰଶ ܰ ௫ܱ ൌ 1 od 3 (Phot ically-derived n purposes, e , from initial 2 is an adjust term to allow process to fi ainly for co ethods 1 and ) in the equat y, the regress ion above is verall statist .33൰ ൈ ݁ିଵସହ் 67 ൈ ݁ି଴.ହ଻ୡ୭ୱఏ ܭଵܭଷ ൈ ܱଷ ൅ ܭଵܭଷ ൈ ܱଷ ostationary  equation (E ven though i modeled-vers ed form of th for the effe nd solutions mparison pur 2, the overall ion:  ion process s identical to th ics and plots ଴ ହ State), Equ quation 1) re t did not app us-measured e photostatio cts of cloud c for their valu poses to show equation is p   olves the valu e original eq by each varia 49  ation 1 (Ana presents the p ear to fit the m plots). nary state equ over. Also, es using the n the potentia re-defined fo For the categoriz the abov presente Since th evaluatio overall equation improve involved e of the cons uation but ha ble are prese lytically‐de hotostationa easured dat ation, but in the constants ew equation l for modifyi r Method 3 a Method 3 ed as “day” e equation, th d (left). e solution eq ns were requ equation fo (the origina the fit to the generalizing F1 = a* F2 = c* Y = F1* tants to prov s been simpli nted below: rived) and 2 ry state and w a well during cludes the ad were genera form. Equat ng/adjusting s presented b evaluations, (6am to 6pm e modeled v uation is alr ired to ident r NO2/NOX l equation) c measured da the consta Exp(b/x1)/x1 Exp(d/Cos(x x3/(F2+F1*x ide the best f fied (slightly  (Adjusted) as included the regressio dition of the lized to allow ion 2 was Equation 1. elow: only the da ) were used. U s. measured p eady specifie ify the appro . However an be tweak ta. The first t nts (e.g., 15   2))  3)  it to this equa rearranged).   for n solar the tasets sing lot is d, no priate , the ed to weak .33, - tion. The

The Ra2 v Also, the contribute Because t prediction zero NO2/ the same r by the fol Me alues (about Prob(t) value to the predic he predicted z s were invest NOX predicti egressed resu lowing plots. thod 3: NO2  Atmosphe Coefficie Adjusted Variable a b c d Variance Source Regressi Error Total 0.35) are rela s for the a an tion of NO2/N ero values fo igated furthe ons are due t lts indicate t vs NOx Ratio ric Paramete nt of Multiple D  coefficient of m  Analysis on tively low co d c parameter OX ratios (a r NO2/NOX m r. Based on e o zero O3 val hat most of th s by  rs  etermination ( ultiple determ Value 143.8872 ‐1218.092 5.84 ‐5.66 DF 9 9.24E 50  mpared to th s (or constan t least based ay be contri xamining the ues. Also, sub e zero predic R^2) = 0.3519909 ination (Ra^2) = Standard E 644 133010 961 59.26 E‐02 5394.2 E‐02 1.5 Sum of Squ 3 98.043 239 180.49 +03 2.7 e solutions se ts) suggest th on the curren buting to the se plots and t set airport p tions occur i 591  0.3517805438 rror t‐ratio 05.77 1.08E‐05 14356 ‐20.5546 63491 1.08E‐05 9E‐03 ‐35.6524 ares Mean Sq 54649 32.68118 64101 1.95E‐0 9E+02 lected for M at they may t equation). lower Ra2 va he underlyin lots of NO2/N n the ADL d Prob(t) 0.99999 0 0.99999 0 u F Ratio Pro 1672.839 2 ethods 1 and not significan lues, these g data, most OX vs NOX ataset as indi b(F) 0 2. tly of the from cated

  An attemp not conve the ADL converge. and the nu For comp below: t was made rge to a solu dataset (57 re The failures mber of data leteness, the Coefficie Adjusted to regress the tion (i.e., the cords out of are due to th points result full ADL dat nt of Multipl  coefficient o NO2 vs NOx data for LA regressions f 1,469) and a e different da ing in non-co a was also re e Determinat f multiple de RATIOS BY 51  X (SPAS) an ailed). Simil regression s tasets which nvergence. gressed separ ion (R^2) = 0 termination  vs NOx CO M d YUL separ arly, the zero olution was cause differe ately with th .3977606931 (Ra^2) = 0.39 NC. BY AI ethod 3: NO ately, but the O3 values w attempted wi nt solutions e successful   65274385  RPORT 2 vs NOx Rat regression w ere removed th also a failu for the param solution pres ios by Airpo ould from re to eters ented rt   

52  The relatively small difference in Ra2 values between the full dataset and the ADL dataset may suggest the ADL dataset may contribute significantly to the overall fit. However, the number of data points (the YUL dataset has over 6,000 data points) and the MSE values also need to be considered for each dataset. While further detailed investigations can be conducted, these findings provide some indications of the potential sources of error for the regression on the initial, generalized equation. In addition to generalizations of the parameters (or constants), two types of modifications to the equation were also explored:  Modifications to the formulation of the K3 (or F2) sub-equation.  Addition of the Solar Irradiance (S) variable and/or removal of the Solar Zenith Angle (θ). These modifications were only conducted on the K3 sub-equation. No modifications were made to the overall NO2/NOX equation as it represents an analytically-derived equation based on balancing the forward and reverse NOX reaction equations. Also, the K1 (or F1) sub-equation was not modified as it represents a form of the Arrhenius equation. The table below provides a summary of the modifications that were attempted: Equation  Code  Equation  Variables  Regression Solution  Ra^2  M3Eq2  F1 = Exp(b/x1)/x1  x1 = T Solved 0.2765  F2 = Exp(d/Cos(x2))  x2 = Theta Y = F1*x3/(F2+F1*x3)  x3 = O3 M3Eq3  F1 = a*Exp(b/x1)/x1  x1 = T Failed F2 = c*x4*Exp(d/Cos(x2))  x2 = Theta Y = F1*x3/(F2+F1*x3)  x3 = O3 x4 = S M3Eq4  F1 = a*Exp(b/x1)/x1  x1 = T Failed F2 = c*(x4^e)*Exp(d/(Cos(x2)))  x2 = Theta Y = F1*x3/(F2+F1*x3)  x3 = O3 x4 = S M3Eq5  F1 = a*Exp(b/x1)/x1  x1 = T Failed F2 = (c*Exp(d/(Cos(x2))))+e*x4  x2 = Theta Y = F1*x3/(F2+F1*x3)  x3 = O3 x4 = S M3Eq6  F1 = a*Exp(b/x1)/x1  x1 = T Solved 0.604  F2 = (c*Exp(d/(Cos(x2))))+e*x4^f x2 = Theta Y = F1*x3/(F2+F1*x3)  x3 = O3 x4 = S M3Eq7  F1 = a*Exp(b/x1)/x1  x1 = T Failed F2 = c*Exp(d/Cos(x2))  x2 = S Y = F1*x3/(F2+F1*x3)  x3 = O3 M3Eq8  F1 = a*Exp(b/x1)/x1  x1 = T Failed F2 = c*x2^d  x2 = S Y = F1*x3/(F2+F1*x3)  x3 = O3

M3Eq9  M3Eq10  M3Eq11  M3Eq12  M3Eq13  M3Eq14  The additi those that Notwithst methods 1 solution a F1 = a*Exp(b F2 = c*d^(‐1* Y = F1*x3/(F2 F1 = a*Exp(b F2 = c*d^(e* Y = F1*x3/(F2 F1 = a*Exp(b F2 = c*exp(d/ Y = F1*x3/(F2 F1 = a*Exp(b F2 = c*x2^2+ Y = F1*x3/(F2 F1 = a*Exp(b F2 = (c*Exp(d Y = F1*x3/(F2 F1 = a*Exp(b F2 = (c*Exp(d Y = F1*x3/(F2 on of the Sol were tested: F1  F2  (c* Y = anding the lim and 2 (a littl nd the corres /x1)/x1  x2) +F1*x3)  /x1)/x1  x2) +F1*x3)  /x1)/x1  x2)  +F1*x3)  /x1)/x1  d*x2+e  +F1*x3)  /x1)/x1  /(Cos(x2))))+e +F1*x3)  /x1)/x1  /(Cos(x2))))+e +F1*x3)  ar Irradiation = a*Exp(b/x1 =  Exp(d/(Cos(x  F1*x3/(F2+F itation to ju e higher than ponding plots *exp(f/x4) *ln(f*x4) variable (S) )/x1  2))))+e*x4^f 1*x3)  st day events Method 1 bu for each var NO2 vs NO Parame M 53  x1 = T x2 = S x3 = O3 x1 = T x2 = S x3 = O3 x1 = T x2 = S x3 = O3 x1 = T x2 = S x3 = O3 x1 = T x2 = Theta x3 = O3 x4 = S x1 = T x2 = Theta x3 = O3 x4 = S in equation M , the Ra2 valu t lower than iable are pres x Ratios by A ters for Best  ethod 3 Equ Solved Failed Failed Failed Failed Failed 3Eq6 seeme e of 0.6 is co Method 2). T ented below tmospheric  Performing  ations   0.5332  d to provide mparable to he full set of : the best resu the results for statistics for lts of this

The high contribute Equations but these M3Eq6 w Solar Irra formation Since Equ to predict from Meth 6.4 Prefe Based upo in Section Method fo near airpo Prob(t) value significantly M3Eq13 an equations bo ith a Ra2 valu diation (S) t of the K3 (F ation M3Eq6 NO2/NOX rat od 1 or 2 be rred Metho n the assessm  1.3, it is re r inclusion i rts:  Coe Adj Reg Var a b c d e f Var Sou Reg Erro Tot s of the a, c, d to the regres d M3Eq14 w th failed in e of about 0 erm may pr 2) sub-equati was regresse ios for night used for nigh d Recomme ent outcome commended nto the EDM fficient of Mul usted coefficie ression Variab iable Value 93.4856 ‐2001.6 5.22E‐0 ‐3.34E‐0 1.59E‐0 0.84216 iance Analysis rce DF ressio r 923 al 924 , and e param sion. ere formulate their regress .5. M3Eq9 m oduce a viab on since the t d only for da hours (6 pm t hours. ndation s described a that the follo S/AEDT-AE tiple Determin nt of multiple d le Results Standard Et‐ 2 6061668 1 4 45.94008 ‐ 4 33.82835 1 4 3.90E‐04 ‐ 5 1.03178 1 9 1.76E‐02 4 Sum of Sq M 5 168.2976 3 7 110.2424 1 2 278.54 54  eters may in d as alternat ions. Equati ay suggest th le solution. able shows v ta points rep to 6 am). Rat bove, in com wing Method RMOD softw ation (R^2) = 0. etermination  ratio Prob(t .54E‐05 0.99 43.5707 .54E‐05 0.99 0.85598 0.39 .54E‐05 0.99 7.90037 ean Squ F Ratio 3.65951 2820. .19E‐02 dicate that th ives M3Eq6 on M3Eq9 i at replacing t However, it arious other resenting day her, it is reco bination with 1-Equation are package 6042133138 (Ra^2) = 0.6039 ) 999 0 999 203 999 0 Prob(F) 266 0 ese paramete (because of M ndicates com he Solar Zen depends on formulations conditions, mmended tha the “Key” T 1 be adopte for modelin 99074 rs do not 3Eq6’s suc parable resu ith Angle wi the specific that failed. it cannot be u t either equa argets identi d as the Pref g NO2/NOx cess), lts to th the , new sed tions fied erred ratios

55  Method 1 ‐ Equation 1 NO2/NOx=1‐0.8*exp(‐1/(b*c^x))  Where: b = 0.57357, c = 1.02214, x = NOx concentration  For the purposes of this Research, this method is entitled ARM2-Airport. Among the justifications for this proposal are the following:  Method  1  (Simple  Regression),  Equation  1  (Unconstrained  Regressed)  - This equation is preferred as it performed similarly to the other methods but with the simplicity of basing the NO2/NOx ratio predictions on NOx concentrations. In this way, the NO2/NOx emission ratios for all airport-related emission sources are inherently accounted for in this method. Also, the same equation form (same parameters) was found to perform similarly for each of the three-hour segments (i.e., no need for different formulations for different hourly periods). In addition, the equation has an NO2/NOx “natural” limit of 0.86 at an NOx level of 0 ppm (a consequence of following the data during the regression work) so an artificial upper limit similar to that used in ARM2 is not considered necessary. Similarly, a lower limit is unnecessary as the equation (by design) approaches an asymptote of 0.2 at high NOx concentrations. Such limits would have been necessary under Method 2 as multiple independent variables make it difficult to identify any “natural” limits.  Method  1  (Simple  Regression),  Equation  2 (Constrained‐2) - While this equation provides a more theoretically correct constraint at the zero NOx concentration level, its regression statistics (e.g., R2) are noticeably worse than those of Method 1 - Equation 1, since it does not follow the data near low NOx levels. The modeled-versus-measured comparisons were inconclusive as the filtering process (i.e., for low NO2 values) as part of the data QA/QC work resulted in similar fit statistics.  Method 2 (Multivariable Regression) Equation 1 - This single equation was initially preferred since it can conceptually account for all day and night conditions using just one equation. However, since it performed similar to Method 1 - Equation 1, but required more extensive input data, it was not considered as efficient to use. The similar performance to Method 1 – Equation 1 confirms the findings from the earlier regression assessments that NOx concentrations have the biggest impact on NO2/NOx estimations.  Method  3,  (Photostationary  State),  Equations  1  (Analytically‐derived)  -  This Photostationary State Equation did not perform well with either the full or reduced modeled-to-measured datasets. In both cases, the R2 values were less than 0.1. The comparisons with the regressions equations indicate that the analytically-derived structure of this method/equation combination may not be a good representation of the conditions under which the measured data were collected.  Method 3, (Photostationary State), Equations 2 (Adjusted) - This method/equation combination revealed that the basic form of the Equation 1 photostationary state could potentially be “fine- tuned” to include the effects of changing sunlight conditions (i.e., account for cloud cover) to allow for more accuracy in predicting NO2/NOx ratios. However, this concept equation deviates markedly from the analytically-derived photostationary state equation and does not have any significant advantages compared to Methods 1 and 2. Preferred Method  Based upon the outcomes of the  Research, it is recommended that  Method 1 (Simple Regression), ‐  Equation 1 (Unconstrained  Regressed) should be adopted as  the Preferred Method for accurate  computing of NO2/NOx ratios and  estimating NO2 in the vicinities of  airports. Further, the method  should be adapted for the  EDMS/AEDT‐AERMOD software  package. This model is called the  ARM2‐Airport Module.