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Time series analysis of surface layer ozone in the Lower Fraser Valley of British Columbia Robeson, Scott Michael 1987

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TIME SERIES ANALYSIS OF SURFACE LAYER OZONE IN THE LOWER FRASER VALLEY OF BRITISH COLUMBIA by SCOTT MICHAEL ROBESON B.A., The University of Delaware, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Geography) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1987 © Scott Michael Robeson In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Geography The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date October 7, 1987 DE-6(3/81) ii Abstract Near the earth's surface, ozone is a highly toxic and reactive pollutant. In order to avoid potentially hazardous concentrations near densely populated areas, accurate forecasts of the temporal variability of ozone are necessary. Several statistical models which may be used to understand the temporal variability of ozone as well as to forecast short-term ozone fluctuations are developed. The models may be divided into two distinct categories: (1) those which forecast daily maximum one-hour average ozone concentrations and (2) those which forecast the diurnal behavior of one-hour average ozone concentrations. To assess the relative utility of each model, their forecast ability is evaluated by statistical comparison with data not used in model development. Most of the developed models appear to perform reasonably well; however, the utility of any forecast model is dependent upon the needs of the user. It is believed that the limits of the "pure time series" method (i.e., mathematical decomposition of time series into various elements) have been approached. Future investigations with these data should attempt to answer specific questions regarding the physical mechanisms governing ozone variability. iii T a b l e o f C o n t e n t s P a g e A b s t r a c t i i T a b l e o f C o n t e n t s i i i L i s t o f T a b l e s v L i s t o f F i g u r e s v i L i s t of S y m b o l s a n d A b b r e v i a t i o n s i x A c k n o w l e d g e m e n t s x i 1. I n t r o d u c t i o n 1 1.1 Photochemistry of Ozone 1 1.2 Rationale of Approach 2 1.3 Study Region 4 1.4 Data 6 1.4.1 Data Observation Methods 8 1.4.2 Stations Used for Analysis 8 2. M o d e l s o f A n n u a l V a r i a b i l i t y 12 2.1 Introduction 12 2.2 A Deterministic/Stochastic (D/S) Annual Model 15 2.2.1 Generation of Frequency Distributions 16 2.2.2 Interpolation of Missing Data Values 20 2.3 An Auto Regressive Integrated Moving Average (ARIMA) Model 22 2.4 A TEMperature and PERsistence Based Model (TEMPER) 25 2.5 Forecasts Using Annual Models 27 2.5.1 Model Evaluation Statistics 28 2.5.2 Time of Daily Maximum Ozone Concentrations 42 3. M o d e l s o f D i u r n a l V a r i a b i l i t y 44 3.1 Introduction 44 3.2 An Exponentially-Weighted Persistence Oriented Model (Daily Model 1) 46 3.3 Relationships Between Ozone and Other Variables 47 3.3.1 Variable Selection 48 3.2.2 Daily Model 2 50 3.4 Evaluation of Daily Model Forecasts 51 iv 4. C o n c l u s i o n s a n d R e c o m m e n d a t i o n s 58 4.1 Introduction 58 4.2 Investigative Summary and Conclusions 58 4.3 Recommendations for Further Work 59 R e f e r e n c e s 61 A p p e n d i x : S c a t t e r p l o t s a n d S u m m a r y S ta t i s t i cs f o r E v a l u a t i o n o f D a i l y M o d e l s 65 L i s t o f T a b l e s Table 1 Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Page Pollutants monitored in the lower Fraser Valley air quality monitoring network (1986) 6 Parameter estimates for deterministic/model 16 Correlation coefficients for daily maximum ozone and daily maximum air temperature (May-Sep) at T9 before and after interpolation with deterministic/ stochastic model 22 Parameter estimates for ARIMA( 1,1,0) model: May-September 25 Parameter estimates for TEMPER 27 Model evaluation statistics for annual models 39 Parameter estimates of b n for Daily Model 1 47 Ordinary correlation coefficients for ozone, air temperature, and nitrogen dioxide 49 Regression equations for Daily Model 2 51 Selected evaluation statistics for daily models: May-September, 1984 53 vi L i s t o f F i g u r e s Page Figure 1.1 Location of lower Fraser Valley 5 Figure 1.2 Location of pollutant monitoring stations in the lower Fraser Valley (1986) 7 Figure 1.3 Seven point moving average of daily maximum ozone at station T7 10 Figure 2.1 Seven point moving average of daily maximum ozone a) Station T9 13 b) Station T i l 14 Figure 2.2 Conditional pdfs for daily maximum ozone a) Station T9 18 b) Station T i l 19 Figure 2.3 Seven point moving average of daily maximum ozone at station T9 with interpolation 21 Figure 2.4 Amplitude spectra for differencing filters 24 Figure 2.5 Scatterplots of observed vs. predicted daily maximum ozone for annual models at station T9: May-September, 1986 a) D/S model 29 b) ARIMA( 1,1,0) 30 c) TEMPER 31 d) TEMPER with random error in temperature series 32 e) Pure persistence 33 Figure 2.6 Scatterplots of observed vs. predicted daily maximum ozone for annual models at station T i l : May-September, 1986 a) D/S model 34 b) ARIMA(1,1,0) 35 c) TEMPER 36 d) TEMPER with random error in temperature series 37 e) Pure persistence 38 Figure 2.7 Amplitude spectra of persistence and ARIMA( 1,1,0) models as filters 40 Figure 2.8 Hour of occurrence of daily maximum ozone: May-Sep, 1978-1985 43 Figure 3.1 Mean values of ozone throughout the day at stations T9 and T i l : May to September, 1978-1985 45 vii Figure A l Scatterplots of observed vs. predicted ozone concentrations for Daily Model la at station T9: May-September, 1986 a), b) Forecasts for 0900,1000 65 c), d) Forecasts for 1100,1200 66 e), f) Forecasts for 1300,1400 67 g), h) Forecasts for 1500,1600 68 i),j) Forecasts for 1700,1800 69 Figure A2 Scatterplots of observed vs. predicted ozone concentrations for Daily Model lb at station T9: May-September, 1986 a), b) Forecasts for 1000,1100 70 c), d) Forecasts for 1200,1300 71 e), f) Forecasts for 1400,1500 72 g), h) Forecasts for 1600,1700 73 i),j) Forecasts for 1700,1800 74 Figure A3 Scatterplots of observed vs. predicted ozone concentrations for Daily Model 2 at station T9: May-September, 1986 a), b) Forecasts for 0900,1000 75 c), d) Forecasts for 1100,1200 76 e), f) Forecasts for 1300,1400 77 g), h) Forecasts for 1500,1600 78 i),j) Forecasts for 1700,1800 79 Figure A4 Scatterplots of observed vs. predicted ozone concentrations for pure persistence at station T9: May-September, 1986 a), b) Forecasts for 0900,1000 80 c), d) Forecasts for 1100,1200 81 e), f) Forecasts for 1300,1400 82 g), h) Forecasts for 1500,1600 83 i),j) Forecasts for 1700,1800 84 Figure A5 Scatterplots of observed vs. predicted ozone concentrations for Daily Model 1 at station T i l : May-September, 1986 a), b) Forecasts for 1000,1100 85 c), d) Forecasts for 1200,1300 86 e), f) Forecasts for 1400,1500 87 g), h) Forecasts for 1600,1700 88 i),j) Forecasts for 1700,1800 89 viii Figure A6 Scatterplots of observed vs. predicted ozone concentrations for Daily Model 2 at station T i l : May-September, 1986 a), b) Forecasts for 0900,1000 90 c), d) Forecasts for 1100,1200 91 e), f) Forecasts for 1300,1400 92 g), h) Forecasts for 1500,1600 93 i),j) Forecasts for 1700,1800 94 Figure A7 Scatterplots of observed vs. predicted ozone concentrations for pure persistence at station T i l : May-September, 1986 a), b) Forecasts for 0900,1000 95 c), d) Forecasts for 1100,1200 96 e), f) Forecasts for 1300,1400 97 g), h) Forecasts for 1500,1600 98 i),j) Forecasts for 1700,1800 99 ix List of Symbols and Abbreviations K Constant in three parameter lognormal distribution M Stabilizing molecule in photochemical reactions MAE Mean Absolute Error O Mean of observed ozone concentrations P Mean of predicted ozone concentrations RMSE Root Mean Square Error RMSEs Systematic component of RMSE RMSEu Unsystematic component of RMSE T t Daily maximum one-hour average air temperature on day Y Daily maximum one-hour average ozone concentration on day Y n One-hour average ozone concentration on day Y at hour 'h' a^ Ordinary least-square regression coefficient at hour 'h' a^ Sequence of randomly distributed numbers bg,b^,b2 Ordinary least-square regression coefficients b^ Ordinary least-square regression coefficient at hour 'h' d Number of differencing operations performed, Index of agreement Residual ozone series h Plank's constant, hour of the day h* Hour of the day used for regression in Daily Model 1 k^^.kg Rate constants in photochemical reactions n Number of terms in exponentially-weighted moving average p Number of autoregressive parameters in an ARIMA model ppb/v Parts per billion by volume q Number of moving average parameters in an ARIMA model r Pearson product-moment correlation coefficient X s a Standard deviation of the sequence a t s Q Standard deviation of observed ozone concentrations s_ Standard deviation of predicted ozone concentrations t Day number wj Weights in exponentially-weighted moving average W j . An arbitrary time series zfc An arbitrary time series V Backward differencing operator 0 Moving average coefficient X Wavelength of electromagnetic radiation v Frequency of electromagnetic radiation 4> Autoregressive coefficient xi Acknowledgements Although this thesis is considered a monograph, its production could not have proceeded without the help and encouragement of many other individuals. The members of my committee have been thoughtful and patient during both the conception and execution of this work. My thesis supervisor, Dr. Douw G. Steyn, always had an open door, an open mind, and an attentive ear whenever I wished to discuss matters, academic or otherwise. Many ideas for both this thesis and future work came from our informal sessions. I also thank Dr. Timothy R. Oke for his insightful comments on many of my ill-formed ideas -- I often appreciated Dr. Oke's simple yet sophisticated approach to science. I also thank Dr. James Zidek for assuring me that what I was doing was proper in a statistical sense. Mr. Morris Mennell and Mr. Al Percival of the Pollution Control Section of the Greater Vancouver Regional District (GVRD) were responsible for the collection and provision of the data used in this thesis. I thank them for their willing consultation as well as allowing me to tour their observation network. It was essential to gain familiarity with site locations and observation techniques. Hu Wallis played a dual role as air quality meteorologist for the GVRD and fellow graduate student. I thank Hu for numerous discussions and for commenting on early drafts of sections of the text. While working on this thesis, my personal funding was provided by University of British Columbia Graduate Fellowships as well as Teaching Assistantships from the Department of Geography. I thank these institutions for considering me and my research worthy of their financial support. During the course of the past two years, many friends and fellow graduate students have influenced me greatly. I particularly want to thank Keith Ayotte, Matthias Roth, Hans Peter Schmid, Jeffrey Schmok, and James Voogt as well as all those who spent many late nights in room 210J. I also express my appreciation to Teresa Ho for making the last few months as pleasant as they were. Lastly, I thank my parents and family who have provided continual support during the two years that I have been on the other side of the continent. 1 Chapter 1 Introduction Near the earth's, surface, ozone is a highly toxic and reactive pollutant. Damage to human health (Goldsmith and Nadel, 1969; Bates et al., 1972; Mustafa and Lee, 1976) and vegetation (Heck et al., 1983; Reich and Amundson, 1985) has been clearly demonstrated. In order to avoid potentially hazardous ozone levels (particularly near densely populated areas), accurate forecasts of the atmospheric concentration of ozone are necessary. The description of the temporal variability of ozone and the assessment of the ability to forecast ozone concentrations using purely statistical techniques are the central aims of this research. 1.1 Photochemistry of ozone In order to understand the temporal variability of tropospheric ozone, one must first be aware of the chemical mechanisms which govern ozone formation. Environmental conditions which are conducive to production of ozone may then be identified and incorporated into forecasting models. Although there are no significant primary emissions of ozone into the atmosphere, concentrations near urban areas may reach dangerously high levels via photochemical production (Fishman and Crutzen, 1978). In the lower atmosphere the important chemical reactions are N0 2 + he - NO + O (1.1) O + 0 2 + M - 0 3 + M (1.2) 0 3 + NO N0 2 + 0 2 (1.3) where he represents a high energy photon ( X < 420 nm) and M is a molecule (usually N 2 or 0 2) which absorbs excess energy and stabilizes the ozone molecule. Reactions 1.1-1.3 2 m a y reach a steady state represented by [ 0 3 ] = k 1 C N 0 2 ] / k 3 [ N O ] (1.4) A s a result , in the polluted troposphere, the most common sink for ozone is associated w i th emissions of N O . However , the presence of certain species of hydrocarbons may al low ozone to accumulate. Reactive hydrocarbons become oxidized and form peroxy radicals wh ich then convert N O to N 0 2 (F ishman, 1985): R O x + N O • R O y + N 0 2 (1.5) Hence if N O is converted to N 0 2 by any process other than 1.3, concentrations of ozone wi l l surpass the steady state concentration given by 1.4. A t night, no ozone is produced and continuous emissions of N O wi l l decrease concentrations of ozone to undetectable levels. Contact w i th soil , vegetation, and other surfaces wi l l also rapid ly destroy ozone (Regener and A ldez , 1969). 1.2 Rationale of approach Throughout this work stat ist ical analys is (specifically, t ime series analysis) of historical data is employed to describe and forecast ozone var iabi l i ty . A l though stat ist ical methods may be seen as abstract and sometimes complex, the extreme inherent complexity of the physica l , chemical and anthropogenic processes which govern ozone format ion current ly l imits the use of deterministic methods in a forecasting mode. Indeed, the empir ical analys is of f ield observations is usual ly a necessary precursor to the development of more detailed determinist ic models. A l though it is usual ly beneficial to incorporate informat ion concerning sys tem behavior into a model, it m a y be advantageous to develop a crude model which s imply forecasts wel l . Fo r forecasting purposes, many of the assumptions important for statist ical 3 inference are not relevant (Gi lchr ist , 1976). Mul t icol l inear i ty and autocorrelation of residuals both pose problems (i.e., biased estimates) i n tradit ional regression analys is ; however, these properties are extremely useful in the development of good forecast models. Bennett (1981) states that "most of the causes of bias have no effect on forecasting accuracy, and biased models usual ly provide better forecasts." The presence of autocorrelated residuals, though, does make estimates of confidence intervals unrel iable; and, of course, errors in the measurement of sys tem var iables as wel l as the undetected presence of non-l inear relat ionships (assuming a l inear model) w i l l make forecasts less accurate. Severa l advantages of stat ist ical forecasting have been summar ized by Bennett (1981): - al l assumptions are c lear ly presented; - information concerning system behavior is revealed; - stat ist ical forecast models are crude approximations of real wor ld behavior; - stat ist ical forecast models "can be easi ly automated, readi ly updated, can take account of a large number of factors, and can incorporate complex models of system st ructure" (Bennett, 1981). Stat ist ical models of temporal var iabi l i ty are certainly not without problems. When these models are used to forecast a state var iable, one must be sure that future observations are taken f rom the same "populat ion" as those used in the development of the models (adaptive parameter models can be an exception; see Bennett , 1979). Th is is a par t icu lar ly interesting problem in the environmental sciences where exper imental controls and repetit ion are usual ly not possible. One must rely upon observations of past events which m a y or m a y not be representat ive of conditions which wi l l occur in the near future. It is extremely difficult, i f not impossible, to determine whether var iab i l i ty exist ing in histor ical data is typical or atypical of the present. Sophisticated mathemat ica l techniques often distance the forecaster f rom these data l imitat ions; however, the researcher must not adopt a false sense of certainty regarding forecasts which can only be tested against real-4 world observations. The ozone observations used in this study were taken in the lower F rase r Va l l ey region of B r i t i sh Columbia, Canada . The physiography of the study region is described in the fol lowing section. 1.3 Study Region The lower F r a s e r Va l l ey region of B r i t i sh Co lumbia (see F igure 1.1) extends f rom the St ra i t of Georgia in the west to the F rase r canyon in the east. The val ley is further bounded by the Coast Mounta ins to the north and the Cascade Range to the southeast. Previous studies of atmospheric pollutants in the lower F rase r Va l ley by Concord Scientif ic Corporat ion (CSC) (1982, 1985) indicated that ozone concentrations have often exceeded the m a x i m u m acceptable level (82 ppb/v) and have occasionally exceeded the m a x i m u m tolerable (153 ppb/v) level as defined by the Canad ian Nat iona l A i r Qual i ty Objectives. C S C (1982) determined that the greatest source of the precursor pol lutant emissions which lead to ozone format ion are motor vehicles although stat ionary sources (i.e., commercia l and industr ia l fuel combust ion, gasoline retai l ing, etc.) were found to be important as wel l . The most densely populated and industr ia l a rea of the lower F r a s e r Va l l ey lies in the Greater Vancouver Regional Dist r ic t ( G V R D , populat ion of approximately 1.5 mil l ion); therefore, most emissions are believed to originate there. When compared w i th other major urban areas in Canada , the quant i ty of emissions in the lower F rase r Va l l ey is not part icular ly great (Dickson and Quicker t , 1975); however, ozone concentrations reach very high levels due largely to the physiography of the area. The mountains act as a barr ier to a i r pollutants wh ich are channeled along the F rase r Va l ley . A l so , l ike many coastal regions, the lower F r a s e r Va l l ey experiences a sea-breeze circulation (see Steyn and Fau lkner , 1986) which advects cool mar ine air, thereby l imi t ing the depth of the planetary boundary layer (Steyn and Oke, 1982). Together, the Figure 1.1 Location of lower Fraser Valley (shaded) 6 topography and low boundary layer height l imi t the volume of atmosphere in which pollutants may disperse. Persistent summer anticyclones make the ozone problem severe by promot ing envi ronmental conditions conducive to the production and accumulat ion of photochemical pol lutants -- w a r m air temperatures, l ight winds, and intense solar input. 1.4 Data The data used in this study are d rawn f rom a network of air qual i ty and meteorological monitor ing stations in the lower F rase r Va l ley of B r i t i sh Columbia which are operated by the G V R D and the Br i t i sh Co lumbia M in i s t r y of Env i ronment and P a r k s (see F igure 1.2). The a r ray of pol lutants measured varies according to station; the current network is summar ized for al l monitor ing stations in Table 1. A digital archive of selected pollutant and meteorological var iables was established by Concord Scientif ic (1982) and is now avai lable f rom 1978 to the present t ime. The Pol lut ion Control Section of the G V R D current ly updates the archive on a monthly basis. Table 1. Pollutants Monitored in the Lower Fraser Valley A i r Quality Monitoring  Network (1986). Station ° 3 N 0 2 N O so 2 C O T H C C O H T S P T l x a X X X X X X T2 X X X X X X X X T3 x X X X X X T4 X X X X X X X X T5 X X X X X X X T6 X X X X X T7 X X X X X X X X T8 X X X X T9 X X X X X X X X T10 X X X X X X X T i l X X X X T12 X X X X T14 X X X T15 X X X X T16 X X X T17 X X X X X a) " x " denotes a pollutant which is monitored. MILES 0 1 2 3 4 5 Figure 1.2 Location of pollutant monitoring stations in the lower Fraser Valley (1986) 8 1.4.1 Data Observation Methods A i r qual i ty monitor ing stations observe each pol lutant instantaneously 60 t imes per hour at a height of approximately 2.5 meters above the ground surface. The instantaneous values are telemetered to a central computer operated by the G V R D where they are averaged each hour. The entire monitor ing network mainta ins a standard of 75% data recovery throughout — if less than 75% of a given averaging period's observations are not avai lable, data for that period are considered "not avai lab le" . L i kew ise , no dai ly m a x i m u m value is reported i f 75% of that day 's hourly observations are not avai lable. P r i m a r y cal ibrat ion is performed on each instrument three t imes per year . The ozone generator used for p r imary cal ibrat ion is sent to the Env i ronmenta l Protect ion Service of Env i ronment Canada for cal ibrat ion wi th a standard instrument. In addit ion, secondary cal ibrat ion is performed every four days (for a durat ion of one hour) between 0100-0400 hours when ozone concentrations are general ly quite low and the presence of miss ing data has less impact. Secondary cal ibrat ion of ozone sensors also requires that each inst rument is zeroed v i a an ozone-free sample and spanned using an ozone generator. Captured data are then automat ical ly adjusted according to instrument bias. Ozone measurements are made by us ing either the chemiluminescence f rom reaction wi th ethylene (Bendix Model 8002) or by ultra-violet photometry ( T E C O Model 49) - both methods are considered highly reliable ( O E C D , 1979) and meet U . S . E P A standards. 1.4.2 Stations Used for Analysis In order to describe the temporal var iabi l i ty of ozone in the lower F r a s e r Va l l ey , eight years (1978-1985) of data f rom two monitor ing stations have been analyzed. Stat ion T 9 at Rocky Point Pa rk and station T i l at Abbotsford A i rpor t (see Figure 1.2) were chosen on the basis of the severity of historical ozone concentrations, their spat ia l location and separat ion, and the qual i ty and length of their data records. These two stations are 9 roughly aligned paral le l to the w ind directions (i.e., wester ly sector) wh ich commonly produces the highest ozone concentrations ( C S C , 1985). In addit ion, they are crudely representat ive of two distinct atmospheric situations ~ an urban or " local t ransport" s i tuat ion (station T9) and a rura l or " regional t ransport " situation (station T i l ) . A local t ransport si tuation is characterized by strong local emissions which react for a few hours, causing high oxidant concentrations near emission sources. In contrast, a regional t ranspor t si tuation is one where emissions t ravel far f rom their sources and undergo extensive photochemical t ransformat ion before reaching a distant downwind location. His tor ica l ly , the highest ozone concentrations in the lower F rase r V a l l e y have occurred in the Por t Moody area at stations T 7 and T 9 ( C S C , 1985). G i ven these high levels, stat ion T 7 might seem to be an obvious choice for ana lys is ; however, this station's data record contains a clear change in magnitude and var iance structure which is noticeable between the summer seasons of 1982 and 1983 (Figure 1.3). A recent review of moni tor ing stations in the lower F rase r Va l l ey (Dann et al., 1987) noted the presence of a s tand of young deciduous (alder) trees near the ambient air intake mani fo ld a t T7 which m a y have negatively influenced recorded ozone values. Due to the undetermined influence of these trees, data f rom station T 9 (although histor ical ly less extreme than that f rom T7) is deemed much more reliable and therefore more amenable to quant i tat ive analys is . Stat ion T 9 , located in Rocky Point P a r k alongside Bu r ra rd Inlet in the Por t Moody B a s i n , was established in 1977 to monitor general community a i r qual i ty in the city of Por t Moody. The Env i ronmenta l Protect ion Service has since designated T 9 as a Nat iona l A i r Pol lut ion Survey Class 1 stat ion and offers f inancia l and technical support. Jus t to the west of the stat ion are wood processing and coal/sulphur loading terminals. Fa r the r to the west are four petroleum refineries and an intermit tent ly used natura l gas-f ired power generat ing plant (this plant was oil-f ired prior to 1977). Given these large local sources of S E V E N POINT MA O F DAILY MAXIMUM O Z O N E AT STATION T7 11 emissions, the heavi ly populated areas to the south and west, and the potential for local stagnation of air f low, there is obviously great concern for a i r qual i ty in this area. Ozone concentrations at station T i l (Abbotsford Airport ) have also been found to exceed air qual i ty standards ( C S C , 1985). In contrast to station T 9 , stat ion T i l is located near a l ightly-used airport and has no large local sources of emissions. Stat ion T i l is directly downwind of the major emissions source area (i.e., the greater Vancouver region) when ozone concentrations throughout the val ley are highest ( C S C , 1985). Hence, it is believed that the source of the photochemical pol lutants which reach stat ion T i l is the greater Vancouver area. 12 Chapter 2  Models of Annual Variability 2.1 Introduction Severa l studies of the annual var iabi l i ty of ozone in the urban troposphere have shown strong seasonal dependence (Merz et al., 1972; Chock et al., 1975; Horowi tz and Baraka t , 1979). T ime series plots of dai ly m a x i m u m one-hour average ozone values (Figure 2.1) clearly reveal this seasonal behavior for stations T 9 and T i l (the seven point moving average in F igure 2.1 is applied str ict ly for d isplay purposes). Since the Canad ian ambient air qual i ty objectives are stated in terms of one-hour average concentrations, the dai ly m a x i m u m of the one-hour average concentrations wi l l be used to describe and forecast annual var iat ions of ozone. A l though the marked seasonal dependence of ozone concentrations is wel l documented, very little research has attempted to describe and model the annua l var iat ion. The development of annua l models is important for a number of reasons: - A n n u a l models are a compact representat ion of system var iabi l i ty . - Frequency distributions exhibi t ing annua l var iabi l i ty may be computed. - Va luab le information for emissions control strategy is revealed. - Quant i tat ive forecasts m a y be made. In this chapter, three annua l models are described. Their comparat ive abi l i ty to forecast dai ly m a x i m u m one-hour average ozone concentrations is presented in the f inal section. A l though the term " a n n u a l " wi l l be used throughout, in str ict terms its use is only appropriate for the f irst model described. However , for simpl ic i ty and brevi ty, al l models in this chapter, whether they are used for only a port ion of the year or not, are referred to as "annua l models". SEVEN POINT MA OF DAILY MAXIMUM OZONE AT STATION T9 Figure 2.1 Seven point moving average of daily maximum ozone a) Station T9 S E V E N POINT MA O F DAILY MAXIMUM O Z O N E AT STATION T11 1978 1979 1980 1981 1982 1983 1984 1985 Y E A R Figure 2.1 b) As Figure 2.1a, for Station T i l 15 2.2 A Deterministic/Stochastic (D/S) Annual Model Horowi tz and Ba raka t (1979) have identif ied the general form of a non-stat ionary stochastic process which is able to simulate observed pollutant concentrations without assuming independence or first-order stat ionar i ty. They examined one year of ozone data f rom the St ; Lou is Regional A i r Pol lut ion S tudy to show the ut i l i ty of such a model. A l though a single year of data exhibi ts a large degree of non-stat ionari ty due to the seasonal var iab i l i ty of ozone, year- to-year var iat ions due to synoptic-scale weather conditions and/or emissions trends wi l l induce other types of non-stat ionari ty (Horowitz and Ba raka t , 1979). In order to reproduce the seasonal var ia t ion of ozone concentrations, Horowi tz and B a r a k a t (1979) fitted a second order polynomial to their data which first had been log-transformed. The use of a polynomial to describe annual var iabi l i ty is just i f ied since the least-squares procedure w i l l objectively determine the t iming of the seasonal m a x i m u m ; however, discontinuit ies may occur in the transi t ion f rom December 31 to J a n u a r y 1. To avoid this discontinuity, the polynomial m a y be replaced by a sinusoid only i f the peak of the sinusoid has not been specified a priori. The discontinuity is judged not to have serious repercussions wi th the data used here. Horowi tz and Baraka t (1979) appl ied a simple log transformat ion to their data before determining the least-squares coefficients of the polynomial ; here, the data are t ransformed v i a the 3-parameter log-normal procedure outlined by Ot t and Mage (1976) in order to obtain normal ly distr ibuted residuals. A f te r removal of the polynomial , a highly autocorrelated sequence of data remains: e t = l n ( Z t - K ) - [ b 0 + b j t + b 2 t 2 ] (2.1) A simple first-order autoregressive equation, 16 e t = * e t - l + a t > (2-2) removes the serial correlation, leaving a normally and independently distributed (NDD) sequence, a^., with a mean value of zero. Thus, the ozone concentration on Julian day 't', , may be described by Xt = exp { [ b Q + bjt + b 2 t 2 ] + *e t. 1 + a t } + K (2.3) Parameter estimates for stations T9 and T i l using data from 1978 to 1985 (1986 data was reserved to evaluate the model's performance) are presented in Table 2.1. In order to illustrate the utility of the D/S model, it will be used to simulate conditional probability distribution functions (Section 2.2.1) as well as to interpolate missing values (Section 2.2.2) in the ozone time series of station T9. The model's ability to forecast specific values of daily ozone maxima is presented in Section 2.5. Table 2.1 Parameter Estimates for Deterministic/Stochastic Model T9: D0 3.57 (.02)a 8.58 x (2 x 1(T IO"4) -2.45 x (6 x 10 -4 IO"7) 4> .526 (.02) s a .238 K -25 T i l : 3.81 .445 xlO" 2 -.133 x 10 - 4 .592 .187 -25 C01) (2 x IO"4) (5 x IO"7) (.02)  a) numbers in parentheses are standard deviations of estimates 2.2.1 Generation of Frequency Distributions When characterizing the frequency distribution of an atmospheric pollutant, a lognormal probability distribution function (pdf) has traditionally been employed (Bencala and Seinfeld, 1976). The use of ordinary pdfs requires data that are independent of one another and stationary. Since air pollutant concentrations are rarely independently distributed or stationary, the use of such frequency distributions is highly inappropriate. 17 Indeed, the inherent serial correlation of pollutant data should be used to develop stochastic models which can generate both ordinary (see Horowitz and Barakat, 1979) and conditional pdf s (i.e., given past values, determine the pdf for tomorrow's value). Although Horowitz and Barakat (1979) have shown that the presence of autocorrelation in sequences of pollutant data does not affect the computation of annual probability distributions for the daily maximum concentration, another objection may be made to the indiscriminant use of ordinary pdfs. Seinfeld (1986) has stated that one of the most important uses of such pdfs is to determine the "return period" for a given concentration level. If daily maximum concentrations are treated as independent of one another (as they are in ordinary frequency distributions) the return period will be grossly overestimated since a large degree of serial correlation exists in pollutant data. In other words, high concentrations tend to occur in sequence and at certain times during the year. Hence, the use of traditional extreme value analysis with non-stationary, autocorrelated data is not recommended. Methods for the analysis of extreme values when data contain trends (i.e., seasonality, autocorrelation, etc.) are outlined in Kinnison (1985). Ordinary pdfs for the daily maximum one-hour ozone concentration which include information concerning system behavior (i.e., seasonal trend and autocorrelation) are good descriptive devices. For annual pdfs, the method outlined by Horowitz and Barakat (1979) is recommended. If a long time series is not available, it may be necessary to increase sample size via simulation. For simulation purposes, Equation 2.3 is ideal; however, the large samples available here did not warrant such an approach. The conditional pdfs which may be developed using 2.3 are extremely useful for short-term emissions control strategies which are often based upon the probability of exceeding a given pollutant concentration. One simulated realization of a conditional pdf for a mid-summer day (e.g., July 1) when the previous day's ozone concentration is 82 ppb is presented in Figure 2.2. A stringent comparison of the simulated conditional pdf with CONDITIONAL PDF FOR DAILY MAX OZONE AT T9 (64 < X < 100) 30 25 20 co UJ o LU rr O o o u. 15 -o or ui m I 10 0 OBSERVED SIMULATED oo 20 40 60 80 100 120 OZONE CONCENTRATION (PPB) 140 160 180 Figure 2.2 Conditional pdfs for daily maximum ozone a) Station T9 CONDITIONAL PDF FOR DAILY MAX OZONE AT T11 (64 < X < 100) 2 0 15 10 -5 -0 OBSERVED SIMULATED CO 2 0 40 60 8 0 100 OZONE CONCENTRATION ( P P B ) 120 Figure 2.2 b) As Figure 2.2a, for Station T i l 20 observed values is not possible since a finite data sample has only a few mid-summer days w i th concentrations of precisely 82 ppb. Hence, the observed conditional pdf was developed over a range of concentrations (e.g., the range arb i t rar i ly chosen in F igure 2.2 is f rom 64 to 100 ppb, or 82 ± 1 8 ppb) on days in June to August , 1978-1985. The simulated conditional pdf used today's observed value to compute the e ^ te rm while the a^ series was generated using an N I D random number generator. The s imulated conditional pdf appears to match the observed values reasonably wel l . To summar ize , in order to develop a conditional pdf for tomorrow's dai ly ozone m a x i m u m , one uti l izes pert inent information: t ime of year (via a seasonal polynomial) and previous days ' ozone concentrations (via an autoregressive term). 2.2.2 I n t e r p o l a t i o n of M i s s i n g D a t a V a l u e s The deterministic/stochastic model was also used to interpolate miss ing dai ly ozone m a x i m a (22% of the total) in the data record of station T9 . F r o m the standpoint of univar iate t ime series analys is , the model contains important quant i tat ive information regarding seasonali ty, autocorrelat ion, and the magnitude of random fluctuations; therefore, one would expect interpolated values to be very representat ive of actual values. Indeed, interpolation is a very important task since many types of analys is (e.g., spectral , Box-Jenk ins , etc.) require t ime series to be continuous. A t least v isual ly the determinist ic/ stochastic model interpolates wel l ~ it is not obvious that an interpolation has been performed (compare F igure 2.1a wi th F igure 2.3). However , when viewed f rom the standpoint of mul t ivar iate t ime series ana lys is , the interpolation procedure m a y bias estimates of correlation and regression coefficients. A s an example, ordinary correlation coefficients of dai ly m a x i m u m ozone and dai ly m a x i m u m temperature are computed before and after the interpolation procedure. A s seen in Table 2.2, values which have been S E V E N POINT MA O F DAILY MAX O Z O N E : STATION T 9 ( I N T E R P O L A T E D ) o 1978 1979 1980 1981 1982 1983 1984 1985 Y E A R Figure 2.3 Seven point moving average of daily maximum ozone at station T9 with interpolation 22 T a b l e 2.2 C o r r e l a t i o n C o e f f i c i e n t s f o r D a i l y M a x i m u m O z o n e a n d D a i l y M a x i m u m  A i r T e m p e r a t u r e A t T 9 B e f o r e a n d A f t e r I n t e r p o l a t i o n w i t h  D e t e r m i n i s t i c / S t o c h a s t i c M o d e l (May -Sep tember ) Y e a r O r i g i n a l S e r i e s I n t e r p o l a t e d S e r i e s 1982: .485 (36 ) a .346 (46) 1983: .751 (86) .667 (96) 1984: .713 (120) .668 (143) 1985: .648 (96) .604 (122)  a) numbers in parentheses are sample sizes interpolated misrepresent the nature of the relationship between dai ly m a x i m u m ozone and dai ly m a x i m u m air temperature (a series f rom M a y to September of each year should have 153 values; the series used to generate Table 2.2 have substant ia l ly less due to miss ing ai r temperature data). The interpolated values are only representat ive of the univar iate ozone t ime series and are not indicative of overal l sys tem structure; thus, interpolated values which do not include covariance interactions should not be used in mul t ivar iate t ime series analys is . A n excellent presentat ion of methods for the interpolation of mul t ivar iate miss ing data m a y be found in L i t t le and Rub in (1987). 2.3 A n A R I M A A n n u a l M o d e l The time series method of Box and Jenk ins (1976) may be used to develop a purely stochastic annual model: an Auto-Regressive Integrated Mov ing Average ( A R I M A ) model. G iven an or iginal series X^, the general form of the model is represented by w t - ^ w ^ - ... - c i , p w t . p = a t - - ... - dq^t.q (2-4) where w^. is the differenced original series, 23 w t = V Xt . (2.5) The backward difference operator, V , is defined as V * t = Xt - Xt-1 . <2-6> which m a y be repeated d t imes. The differencing operator is essential ly a high pass filter; ampl i tude spectra for f irst- and second-order differencing are presented in F igure 2.4. A n annoy ing property of the differencing f i l ter is its "noise ampl i f icat ion" noted by Bennett (1974). A l though in practice d rare ly exceeds two (Box and Jenk ins , 1976), the magni f icat ion of high frequency components may sti l l be consequential. The autoregressive (<t>) and moving average (d) model parameters are determined either by m a x i m u m likelihood or least-squares est imat ion. The a^. terms are " random shocks" or residuals (with mean value of zero) which incorporate the effects of a l l the factors other than past t ime series values which act to influence ozone concentrations. Inspection of the autocorrelat ion function for the ozone series suggested that the most appropriate model (i.e., the one w i th re lat ively smal l white noise var iance and a smal l number of parameters) is an A R I M A ( 1,1,0) model, us ing the notation of Box and Jenk ins (1976). The notation ARIMA(p ,d ,q ) refers to the number of autoregressive parameters, p, moving average parameters, q, as wel l as the number of differencing operations performed, d. In addition, var ious versions of 2.4 were tried to f ind a model which accurately describes annual var iab i l i ty whi le mainta in ing some degree of pars imony; however, w i th increasingly complex models, very sma l l decreases in residual var iance resulted. A n ARIMA(1 ,1 ,0 ) model has the fo rm w t - <$> w M = a t ; which when transformed to the or iginal series becomes (2.7) AMPLITUDE SPECTRA FOR DIFFERENCING FILTERS Figure 2.4 Amplitude spectra for differencing filters 25 (Z t - * M ) - 4>(Xt.! - X t. 2) = ^ . (2.8) Estimated values of model parameters for stations T9 and T i l are given in Table 2.3. All estimates of have a standard error of approximately 0.08. The ability of the ARIMA( 1,1,0) model to forecast daily ozone maxima using the mean value of <f> from Table 2.3 is discussed in Section 2.5. Table 2.3 Parameter Estimates for ARIMA(1,1,0) Model (May-September) 1978 1979 1980 1981 1982 1983 1984 1985 Mean T9: -.197 -.310 -.322 -.257 -.282 -.163 -.318 -.241 -.261 (24.6)a (29.1) (29.2) (33.2) (23.0) (24.5) (18.1) (20.3) (25.3) T i l : -.245 -.318 -.270 -.156 -.338 -.094 -.326 -.203 -.244 (16.2) (15.6) (16.2) (11.3) (18.2) (14.5) (15.0) (15.3) (15.3) a) numbers in parentheses are standard deviations of the a^ . series 2.4 A Temperature and Persistence Based Annual Model (TEMPER) The two annual models previously developed were variations of the "pure time series" approach; i.e., a univariate series is decomposed into various elements. In this section, a model which relates daily maximum ozone to an "external" variable, daily maximum air temperature, as well as to previous ozone values is developed. Pearson product-moment correlation coefficients for daily maximum ozone and daily maximum air temperature for station T9 were previously presented by year in Table 2.2. Although the correlation coefficient over the entire period of record for T9 is r = .652 (for T i l , r = .502), it is evident from the annual variation of the correlation coefficients that some form of non-stationarity of relationship is present, possibly due to the confounding effects of other variables (e.g., synoptic meteorological conditions, changes in pollutant emissions, etc.). However, of all meteorological variables, air temperature is generally agreed to have the strongest correlation with ozone concentrations for two reasons: (1) air temperature is an 26 excellent indicator of envi ronmental conditions conducive to ozone production and accumulat ion, i.e., anticyclonic conditions w i th their associated clear skies and l ight winds; and (2) the rate "constants" of photochemical reactions are highly temperature dependent ( O E C D , 1979). D u r i n g the months of M a y to September, ozone concentrations may be considered sufficiently s tat ionary for the purposes of developing a forecast model. The model proposed s imp ly relates dai ly m a x i m u m ozone concentration to dai ly m a x i m u m air temperature and the previous day 's dai ly m a x i m u m ozone concentration: Xt = b Q • . + b x T t + b2Xt_1 (2.9) Coefficients f rom an ordinary least-square regression are presented in Table 2.4. The dai ly m a x i m u m ai r temperature data used are taken f rom one-hour average air temperature values at station T 9 f rom 1982 to 1985 since temperature data was not available a t stat ion T 9 prior to 1982. If used operat ional ly in a forecasting mode, Equat ion 2.9 requires accurate forecasts of dai ly m a x i m u m temperature. The only forecast ver i f icat ion performed in the lower F r a s e r Va l l ey occurs at Vancouver Internat ional A i rpo r t where forecasts for the months of June to Augus t of 1986 had a mean absolute error of 1.27 degrees Celsius (Hammond, 1987). Far ther in land, temperature f luctuations are l ike ly to be more severe; nonetheless, dai ly m a x i m u m air temperature forecast errors of one degree result in ozone concentration forecast errors of only 2.5 ppb at station T 9 and 1.1 ppb at station T i l - these errors are smal l enough to war rant us ing forecast air temperature values. The abi l i ty of the T E M P E R model to forecast dai ly ozone m a x i m a is discussed in Section 2.5. 27 Table 2.4 Parameter Estimates for TEMPER Station T9: 16.32 (3.7) a 2.482 (0.19) .3085 (0.04) T i l : 1.506 (2.8) 1.145 (0.14) .4326 (0.04) a) numbers in parentheses are standard deviations of est imates 2.5 Forecasts Using Annual Models Previous sections have described three models of the temporal var iab i l i ty of ozone; however, no attempt has been made to compare and contrast the relat ive abi l i ty of each model to forecast dai ly m a x i m u m ozone concentrations. In this section, the forecast performance of each model w i l l be evaluated v ia the statistics recommended by Wi l lmot t (1984) arid Wi l lmot t et al. (1985) using ozone da ta f rom the year 1986: data not used i n model development. In addit ion, a l l models wi l l be compared w i th a "pure persistence" model (i.e., the next value in the series is forecast to be the same as the current one). To forecast dai ly m a x i m u m ozone concentrations w i th the D/S and A R I M A models, the random te rm, a t , is s imply set equal to its expected value, zero. Forecasts using the T E M P E R model employed actual not forecast dai ly max imum a i r temperature values. To test the sensit iv i ty of T E M P E R to air temperature forecast errors, a series of normal ly distr ibuted random numbers (with mean of 0.0 and standard deviat ion of 2.0) was added to observed temperatures. The ai r temperatures containing this random error were then used i n T E M P E R to forecast dai ly m a x i m u m ozone concentrations. 28 2.5.1 Model Evaluation Statistics Scatterplots of observed versus model-forecast dai ly m a x i m u m ozone concentrations are presented in Figure 2.5 a) to e) and F igure 2.6 a) to e). A l though model evaluat ion statist ics are shown on each scatterplot, they are summar ized in Table 2.5 for comparat ive purposes. A s one examines Table 2.5, a few st r ik ing aspects appear. F i r s t , the pure persistence model certainly performed as wel l as either the D /S model or the A R I M A model at stations T 9 and T i l . Second, for a l l models, the slope and intercept of an ordinary least-squares regression of observed on predicted values indicates that low concentrations are being over-predicted and high concentrations are being under-predicted - apparent ly, none of the models is sufficiently dynamic to capture the rap id changes in the ozone t ime series. Th i rd , the random noise added to the dai ly m a x i m u m air temperature data appears not to have affected the forecast performance of the T E M P E R model. To gain an understanding of why the A R I M A and persistence models performed s imi lar ly , it is useful to v iew the two models as f i l ters ~ the original t ime series is t ransformed into an uncor rec ted white noise sequence. The pure persistence model t ransforms t ime series in exact ly the same w a y as the first-order differencing filter described in Section 2.3 while the A R I M A ( 1 , 1 , 0 ) model is s imply an opt imal ly chosen (in this case v ia M a x i m u m Likel ihood Est imat ion) weighted average of the ozone series. Compar ison of the amplitude spectrum of the A R I M A and persistence filters (Figure 2.7) reveals the reason for their s imi lar forecasting abi l i ty - their f i l ter ing characterist ics are near ly identical (as one might also surmise f rom the magnitude of the A R I M A coefficients). The widespread use of the Box-Jenk ins method in the environmental sciences (see Bennett, 1979; or McLeod et al. 1977) results f rom its abi l i ty to forecast state variables whi le main ta in ing model simpl ic i ty -- for forecasting purposes, the models presented here have 29 F igure 2.5 Scatterplots of observed vs. predicted dai ly m a x i m u m ozone concentrations for annual models at stat ion T 9 : M a y to September, 1986. a) Determinist ic/Stochast ic model 30 F igure 2.5 b) A R T M A ( 1,1.0) model DAILY MAX OZONE AT T9 USING ARIMA( 1,1,0): SUMMER 1986 40.0 60.0 80.0 100.0 OBSERVED CONCENTRATION (PPB) 31 Figure 2.5 c) TEMPER model DAILY MAX OZONE AT T9 USING T E M P E R : SUMMER 1986 MAE = 1 2 . 3 1 : 1 / RMSE = 15 .6 RMSEs = 10 .8 RMSEu = 1 1 . 2 Regress ion Line Intercept = 2 2 . 7 Slope = 0 .636 d = 0 .832 + / + + + + ++ • -+ ++ + + ++ ++ Y +/ + + ++ + + + + + •£ y / + ++++ + + /+ + / + + + + / + ++ / OBS MEAN = 4 1 . 3 PRED MEAN = 4 9 . 0 OBS ST DEV = 2 1 . 1 PRED ST DEV = 1 7 . 5 9J •—o o -i cr° | _ 0 O z UJ (_) z • o <->„ cc o si 0.0 20.0 40.0 60.0 80.0 OBSERVED CONCENTRATION 120.0 140.0 /3 32 Figure 2.5 d) TEMPER model with random error in air temperature series DAILY MAX OZONE AT T9 USING TEMPER (W/ERROR): SUMMER 1986 40.0 60.0 80.0 100.0 OBSERVED C0NCENTRRTI0N (PPB) 33 Figure 2.5 e) Pu re persistence 34 Figure 2.6 Scatterplots of observed vs . predicted dai ly m a x i m u m ozone concentrations for annua l models at station T i l : M a y to September, 1986. a) Determinist ic/Stochast ic model DAILY MAX OZONE AT T11 USING D/S MODEL: SUMMER 1986 MAE = 9.8 1 : 1 / o RMSE = = 13.6 o o _ RMSEs = 11.3 RMSEu = 7.6 Regression Line Intercept = 26 0 Slope = 0.328 o d = 0. 686 o_ CO 5 o_ z o / + * 3NCENTRRT 60.0 i i / + 3NCENTRRT 60.0 i i + y + + + + + (_) i— COO + +fc +v + X + + + + + + LU or o LL-CS + + \ + + + o _ rsi OBS MEAN = 41.3 PRED MEAN =39.6 OBS ST DEV =16.6 o o i 1 I I I I PRED ST DEV =9.4 i i t 0.0 20.0 40.0 60.0 80.0 100.0 OBSERVED CONCENTRATION (PPB) 35 Figure 2.6 b) ARTMA( 1,1,0) model DAILY MAX OZONE AT T11 USING ARIMA(UO): SUMMER 1986 0.0 20.0 40.0 60.0 80.0 100.0 OBSERVED CONCENTRATION (PPB) 36 Figure 2.6 c) TEMPER model 37 Figure 2.6 d) T E M P E R model w i th random error in a i r temperature series DAILY MAX OZONE AT T11 USING TEMPER (W/ERROR): SUMMER 1986 OBSERVED CONCENTRATION IPPB) Figure 2.6 e) Pure persistence 38 DAILY MAX OZONE AT T11 USING PERSISTENCE: SUMMER 1986 0.0 20.0 40.0 60.0 80.0 100.0 OBSERVED CONCENTRATION (PPB) 39 T a b l e 2.5 M o d e l E v a l u a t i o n S t a t i s t i c s f o r A n n u a l M o d e l s  a) S ta t i on T 9 M o d e l a (1) (2) (3) (4) (5) Observed M e a n -- 41.3 --Observed Standard Deviat ion - 21.1 --Predicted M e a n 42.7 41.7 49.0 48.1 41.9 Predicted Standard Deviat ion 11.4 19.3 17.5 18.3 21.0 Regression L ine Intercept 29.7 21.0 22.7 21.9 18.7 Slope .313 .500 .636 .632 .560 M e a n Absolute E r ro r 13.2 13.6 12.3 12.9 13.2 Root M e a n Square E r ro r 17.3 19.3 15.6 16.2 19.7 Systemat ic Component 14.5 10.5 10.8 10.2 9.3 Unsystemat ic Component 9.3 16.2 11.2 12.6 17.4 Index of Agreement .678 .733 .832 .821 .743 b) S t a t i o n T i l M o d e l (1) (2) (3) (4) (5) Observed M e a n -- 41.3 -Observed Standard Deviat ion - 16.6 --Predicted M e a n 39.6 41.5 43.6 43.0 41.5 Predicted Standard Deviat ion 9.40 15.2 11.3 11.6 16.5 Regression L ine Intercept 26.0 21.5 23.8 23.3 17.9 Slope .328 .484 .480 .476 .570 M e a n Absolute E r ro r 9.8 10.7 9.3 9.7 10.4 Root M e a n Square E r ro r 13.6 15.5 12.0 12.2 15.3 Systemat ic Component 11.3 8.5 8.9 8.8 7.1 Unsystemat ic Component 7.6 12.9 8.1 8.5 13.5 Index of Agreement .686 .722 .798 .792 .752 a) (1) D /S , (2) A R I M A , (3) T E M P E R , (4) T E M P E R wi th error, (5) Persistence. AMPLITUDE SPECTRA OF VARIOUS FILTERS J i i i i i i i i i 0 20 40 60 80 100 120 140 160 180 LINEAR FREQUENCY (CYCLES PER YEAR) Figure 2.7 Ampl i tude spectra of persistence and A R I M A ( 1,1,0) models as filters 41 only one parameter (4>) to est imate; however, the performance of identif ied models should a lways be compared wi th that of a persistence model. A l though none of the models performs exceptional ly wel l , the T E M P E R model appears to be superior to the others regardless of random forecast errors in dai ly m a x i m u m air temperatures. T E M P E R clear ly forecasts wel l on days wi th extreme dai ly m a x i m u m ozone concentrations ~ an important prerequisite for a n operat ional ly used forecast model. The D/S model contains the most l inear systemat ic error , as evidenced by the systemat ic component of the Root M e a n Square E r ro r ( R M S E s ) ; therefore, i t is l ike ly that appropriate modifications (e.g., relate the "whi tened" series, a^., to a "whi tened" a i r temperature series) may improve its forecasting abi l i ty. However , its determin ism, represented by the second-order polynomial , is somewhat arb i t rary - the ampl i tude and t iming of the seasonal max imum in the ozone time series varies considerably f rom year to year . C lear ly , a static polynomial cannot accurately describe extreme inter-annual var iabi l i ty . T E M P E R ' S determinism m a y prove arb i t rary as wel l ; but p resuming that data f rom subsequent years are used for parameter est imat ion, forecasts should remain reasonably accurate. Un l i ke the D/S and T E M P E R models, the A R I M A and persistence models do not contain any determinist ic components. This is a clear advantage when deal ing wi th a seemingly stochastic system such as the photochemical one. A s stated above, there are great differences f rom year to year in the magnitude and t iming of the seasonal m a x i m u m (see F igure 2.1). In addit ion, extremely rap id transit ions f rom high to low ozone concentrations occur f rom day to day. These changes wh ich , to a great extent, appear to be random are most appropriately modeled by a stochastic process unless specific causes for the var iat ions are found. T E M P E R has explained a large proportion of the var iat ion in dai ly m a x i m u m ozone concentrations; hence, g iven reasonable forecasts for dai ly max imum air temperature, it is suggested that T E M P E R be used for forecasts of dai ly 42 maximum ozone concentrations in the lower Fraser Valley. The best "rule of thumb" (and certainly the simplest) forecast appears to be persistence. 2.5.2 Time of Daily Maximum Ozone Concentrations Although much has been said about the magnitude of the daily maximum one-hour average ozone concentration, the time that this value occurs has been ignored, A histogram of the hour of occurrence of the daily maximum ozone concentration is presented in Figure 2.8. Early afternoon is obviously the most common time for the daily maximum; however, it is also apparent that peak concentrations generally occur a few hours later at station T i l than at station T9, illustrating the importance of medium-range transport in the lower Fraser Valley. 200 UJ o 2 UJ CH cc o o o u . o >-o I D o UJ cr 150 STATION T9 STATION T11 100 50 0 r - i co _1_ X 0 500 1000 1500 HOUR OF OCCURRENCE (PST) 2000 Figure 2.8 Hour of occurrence of daily maximum ozone: May-Sep, 1978-1985 44 Chapter 3  Models of Diurnal Variability 3.1 Introduction Al though ozone air qual i ty is often stated in terms of the dai ly m a x i m u m one-hour average concentrat ion, the d iurnal behavior of concentrations w i l l often determine the sever i ty of adverse effects. If a pol lutant reaches elevated concentrations for only a brief t ime, the potential for damage is much lower than i f concentrations remain high for extended periods through the day (U .S . E P A , 1976). The potential integrated effect of elevated concentrations can only be est imated by examin ing d iurna l behavior. The d iurnal var iat ion of ozone in the polluted troposphere typical ly follows a sinusoidal pat tern, reaching a max imum in the ear ly afternoon and dropping to low levels short ly after sunset (see F igure 3.1; note the higher levels dur ing the night at station T i l , presumably due to lack of local emissions of N O ) . However , l ike the annua l var ia t ion, very little research has attempted to describe and model the dynamics of the d iurnal dependence. Benar ie (1980) states, "The d iurnal and annua l var iat ion of pol lutant concentrations tend to interfere w i th each other. Fo r this reason, d iurnal var iat ion is usual ly studied on the basis of observations taken at the same hour of the day averaged over 1 month or over identical months of several yea rs . " This sort of stat ic, descriptive approach does not reveal information pert inent to short- term forecasting — one must incorporate informat ion regarding the current state of the atmosphere (i.e., recent emissions and the potential for photochemical production and accumulation). Th is chapter attempts to uti l ize the persistent nature of ozone episodes as wel l as relationships wi th precursor pol lutants in order to model the d iurnal cycle. Two models of the d iurnal var iabi l i ty of ozone wi l l be presented - their comparat ive abi l i ty to forecast ozone throughout the day is discussed in the f inal section. MEAN VALUES OF OZONE THROUGH THE DAY: MAY-SEP 1978-1985 40 co CL o rr o O o UJ O M o 30 20 10 Or STATION T9 STATION T11 500 1000 1500 TIME OF DAY 2000 Figure 3.1 Mean values of ozone throughout the day at stations T9 and T i l : May to September, 1978-1985 46 3.2 An Exponentially-Weighted Persistence-Oriented Model (Daily Model 1) Often when strong cyclical behavior exists in a time series, a researcher will attempt to decompose the series into sinusoids (or polynomials) in order to remove periodic trends. However, the dynamic nature of hourly ozone concentrations does not present a system which is amenable to such a static analysis —. both the amplitude and the shape of the diurnal curve change dramatically from day to day. Since ozone time series contain a great amount of serial correlation, an alternative method is to remove periodicity by subtracting a weighted moving average of previous days' ozone concentrations at a given hour, h, from that day's concentration at the same hour: n et = *t,h - i i ? i wi xt-i,h ]. (3.i) The residual series, et, may then be related to deviations of early morning values (at time h*) from previous days' early morning values: n T e t = a h + bh[ X t j h * - i t - ! W i X H h * ] (3.2) For both stations T9 and T i l , a h was negligibly small (for T9, max|ah| = 0.72; for T i l , max|ajj| =0.22); therefore, when 3.1 and 3.2 are combined, n n *t,h = C iSl wi*t-i,h ] + V *t,h* - i ? i wi*t-i,h* 3 (3.3) Hence, the pollutant concentration at a given hour is separated in two components: the first term on the right side of 3.3 is representative of conditions at hour 'h' over the past few days while the second term indicates how today's values differ from previous days' values. The selection process regarding the most appropriate time for h* must consider both forecasting and practical requirements. It is necessary to compromise between (1) choosing a value of h* which is too early to aid forecasts and (2) having a forecast too late 47 in the day. F o r station T 9 , models employing both h* = 0800 P S T (Dai ly Model la ) and h* = 0900 P S T (Dai ly Mode l lb) were developed; whi le for station T i l , only h* = 0900 P S T was used ~ earl ier hours resulted in unstable parameter est imates for b n . The exponential ly-weighted moving average terms used are w^ = (4/7, 2/7, 1/7) as specified by Bennett (1981). Ord inary least-squares estimates of b n are presented in Table 3.1. The abil i ty of Da i l y Mode l 1 to forecast ozone concentrations is discussed in Section 3.4. T a b l e 3.1 P a r a m e t e r E s t i m a t e s o f b n f o r D a i l y M o d e l 1 H o u r T9(h» = 0800) T 9 ( h a ! = 0900) T l l ( h * = 0900) 0900: .898 (3.3 x 1 0 _ 2 ) a 1000: .817 (5.0 x 1 0 - 2 ) .947 (3.0 x 1 0 - 2 ) .863 (2.0 x 10" 2 ) 1100: .823 (6.5 x 10" 2 ) .910 (4.2 x 10" 2 ) .733 (5.8 x 1 0 - 2 ) 1200: .760 (7.4 x 1 0 ' 2 ) .836 (5.1 x 10* 2 ) .577 (4.3 x 10" 2 ) 1300: .655 (7.7 x 10" 2 ) .774 (5.5 x 10" 2 ) .478 (5.2 x 10. 2 ) 1400: .594 (7.9 x 10* 2 ) .736 (5.9 x 10" 2 ) .370 (5.8 x 10 ' 2 ) 1500: .514 (7.8 x 1 0 - 2 ) .644 (6.2 x 1 0 - 2 ) .301 (6.0 x 1 0 - 2 ) 1600: .445 (7.3 x 10" 2 ) .574 (5.9 x 10" 2 ) .315 (6.4 x 1 0 - 2 ) 1700: .382 (7.1 x l O " 2 ) .420 (5.8 x 10" 2 ) .289 (6.4 x 10" 2 ) 1800: .344 (6.2 x 1 0 ' 2 ) .340 (5.1 x 10" 2 ) .271 (5.6 x 10" 2 ) a) numbers in parentheses are standard errors of est imates 3.3 R e l a t i o n s h i p s B e t w e e n O z o n e a n d O t h e r V a r i a b l e s Another method for developing a model of the d iurnal var iabi l i ty of ozone is to relate ozone concentrations throughout the day to past values of other var iables ~ for forecasting purposes, one must use lagged relat ionships. The use of previous days ' values is l ikely to be less effective given the t imescale of photochemical reactions ( « 2-5 hours); therefore, exploratory analys is was used to find relationships wi th ear ly morn ing values. 48 3.3.1 Variable Selection A s discussed in Chapters 1 and 2, extreme ozone concentrations occur when slack pressure gradients are present and dispersion is l imited. Hence, in summer , concentrations of most pollutants (even those which destroy ozone) are l ikely to be high (relative to their mean value) when ozone concentrations are high. F o r this reason, it is necessary to choose predictor var iables which are str ict ly related to photochemical act iv i ty. Section 1.1 described the photochemistry of ozone, i l lustrat ing the importance of both nitrogen dioxide ( N 0 2 ) and nitr ic oxide (NO). N O is a p r imary pol lutant (i.e., it is emitted directly into the atmosphere) while N 0 2 is a product of photochemical act iv i ty. Hence, to forecast ozone concentrations, var iabi l i ty in concentrations of N 0 2 is much more meaningfu l than that in concentrations of N O - var iabi l i ty of N O is more closely related to strength of emissions than to atmospheric conditions. A i r temperature is also an extremely important indicator of ozone var iabi l i ty , as pointed out in Section 2.4. Both photochemical act iv i ty and the environmental conditions conducive to ozone accumulat ion have strong positive correlations wi th a i r temperature. Ord inary correlation coefficients of ear ly morn ing N 0 2 concentrations, a i r temperature, and ozone concentrations are presented in Table 3.2. A l l correlat ion coefficients were calculated from samples of wel l over 100 observations; therefore, the standard error of al l coefficients was much below 0.1. Scatterplots of al l combinations of var iables were inspected in order to detect the presence of non-l inear relat ionships; none were found. The temperature and N 0 2 data used are f rom station T 9 since N 0 2 data collected at station T i l showed no correlation w i th ozone concentrations at T i l . Concentrat ions of N 0 2 at T i l are general ly quite low (< 20 ppb) throughout the day. Temperature data f rom the ls t -order weather station at Abbotsford A i rpor t (the same location as stat ion T i l ) could have been used; however, GVRD personnel (i.e., those who would be responsible for mak ing forecasts) have easier access to data at station T 9 . Fur thermore, on a regional 49 Table 3.2 Ordinary Correlation Coefficients for Ozone, Air Temperature, and  Nitrogen Dioxide a) Station T9 O3(0800) Temperature(0800) NO2(0800) O3(0900) .904 .387 .139 O3(1000) .804 .429 .361 o3(noo) .736 .401 .404 O3(1200) .691 .432 .428 O3(1300) .663 .461 .417 O3(1400) .633 .433 .378 O3(1500) .638 .383 .365 O3(1600) .636 .364 .376 O3(1700) .657 .343 .370 O3U8OO) : .662 .361 .325 NO2(0800) : .044 .169 1.000 Temp(0800) : .303 1.000 .169 b) Station T i l O3(0800) Temperature(0800) NO2(0800) O3@T9(0800) O3(0900) .886 .155 .036 .659 Og(lOOO) .727 .175 .108 .704 O3(1100) .590 .323 .238 .682 O3(1200) .449 .376 .271 .654 O3(1300) .402 .385 .301 .623 O3(1400) .332 .353 .305 .561 O3(1500) .324 .311 .310 .515 O3(1600) .329 .291 .334 .538 O3(1700) .334 .201 .296 .533 O3(1800) .464 .293 .266 .603 NO2(0800) .007 .169 1.000 .044 Temp(0800) .303 1.000 .169 .303 O3@T9(0800) : .626 .303 .044 1.000 50 scale, a i r temperature is strongly spat ia l ly correlated; therefore, the use of temperature data f rom T 9 was deemed appropriate. It is interest ing to note that ultra-violet radiat ion data collected at station T 9 had a very smal l correlat ion (r < 0.2) w i th ozone concentrations at T 9 . M u n n (1975) has shown that the strength of solar radiat ion input across Canada is not a l imi t ing factor in photochemical reactions dur ing the summer. Fo r compar ison, at the summer solstice, Vancouver receives 22.4 x 1 0 ^ ^ photons (cm 2 sec)"^ of photolytic insolat ion (290-420 n m , uncorrected for albedo or elevation) whi le Los Angeles receives 23.7 x 1 0 1 5 photons ( cm 2 sec ) " 1 (Leighton, 1961). 3.3.2 D a i l y M o d e l 2 E x a m i n i n g Table 3.2a, for stat ion T 9 , ozone concentrations at 0800 hours should be an excellent predictor of ozone concentrations later in the day. E a r l y morn ing ai r temperature values and N 0 2 concentrations have high correlations as wel l ; however, when mult iple regression analyses were performed, the magnitude of the standard errors of the ai r temperature coefficients was prohibit ively high. Fur thermore, excluding temperature f rom the analys is did not "s igni f icant ly" effect the outcome of the mult iple regression. This is l ikely due to the col l ineari ty between a i r temperature at 0800 hours and ozone concentrations at 0800 hours (r = 0.303). Hence, for station T 9 , only ozone concentrations at 0800 and N 0 2 concentrations at 0800 were used to develop a forecasting model. F o r station T i l , ear ly morning ozone concentrations at both T 9 and T i l have extremely strong correlations w i th ozone concentrations throughout the day (see Table 3.2b). Bo th ai r temperature values and N 0 2 concentrations have weaker correlations wi th ozone concentrations at T i l than at station T 9 ; air temperature regression coefficients again had unacceptably high standard errors. Table 3.3 summar izes the variables used 51 for forecasting and their ordinary least-squares regression coefficients. The abi l i ty of Da i l y Model 2 to forecast ozone concentrations is discussed in the fol lowing section. 3.4 Evaluation of Daily Model Forecasts The model evaluat ion statistics suggested by Wi l lmot t (1984) and Wi l lmot t et al. (1985) are used to compare the relat ive ut i l i ty of the developed dai ly models. D a t a used for evaluat ion are f rom 1986 and were not used in the development of the models. Selected evaluat ion statist ics are presented i n Table 3.4 where a l l models are again compared w i th a pure persistence model. Fo r a dai ly model , a persistence forecast is s imply defined as the ozone concentration 24 hours previous. Scatterplots of observed and model-forecast ozone concentrations as wel l as the ful l a r ray of model evaluat ion statistics are presented in the Appendix . Table 3.3 Regression Equations for Daily Model 2 a) Station T9 Time Regression Equation 0900: 4.44 (.91)a + 1.08 (.05) 0 3 b 1000: -1.51 (2.1) + 1.12 (.07) 0 3 + .727 (.09) N0 2 1100: 2.06 (2.7) + 1.18 (.09) 0 3 + .918 (.12) N0 2 1200: 2.05 (2.8) + 1.18 (.09) 0 3 + 1.03 (.13) N0 2 1300: 9.05 (2.9) + .976 (.09) 0 3 + .936 (.13) N0 2 1400: 13.5 (3.4) + .957 (.11) 0 3 + .817 (.15) N0 2 1500: 15.2 (3.4) + .931 (.11) 0 3 .743 (.15) N0 2 1600: 14.7 (3.4) + .902 (.11) 0 3 + .738 (.15) N0 2 52 Table 3.3a (continued) 1700: 12.0 (3.1) + .923 (.10) Og + .734 (.14) N 0 2 1800: 9.06 (2.9) + .882 (.09) Og + .726 (.13) N 0 2 a) numbers in parentheses are standard errors of estimates b) all variables are hourly values at 0800 hours b) Station T i l Time Regression Equation 0900: 5.61 (.77)a + .890 (.04) O g @ T l l b 1000: 13.2 (1.8) + .603 (.07) Og@T9 + .161 (.08) N 0 2 c 1100: 15.4 (2.0) + .642 (.06) Og@T9 + .309 (.09) N 0 2 1200: 17.9 (2.3) + .686 (.07) 0 3@T9 + .394 (.11) N 0 2 1300: 19.3 (2.5) + .727 (.08) 0 3@T9 + .511 (.12) N 0 2 1400: 22.6 (2.9) + .696 (.09) 0 3@T9 + .537 (.13) N 0 2 1500: 25.0 (2.9) + .629 (.09) 0 3@T9 + .527 (.14) N 0 2 1600: 24.8 (2.8) + .649 (.09) 0 3@T9 + .527 (.13) N 0 2 1700: 26.5 (2.6) + .597 (.09) Og@T9 + .365 (.12) N 0 2 1800: 23.9 (2.4) + .631 (.08) Og@T9 + .335 (.11) N 0 2 a) numbers in parentheses are standard errors of estimates b) all variables are hourly values at 0800 hours c) all NO 2 data is from station T9 53 Table 3.4 Selected Evaluation Statistics for Daily Models (1986)  a) Station T9 0900: Model O P s o S P M A E d (la) 17.0 17.1 13.7 12.5 6.3 .876 (lb) — — - — ~ ~ (2) 17.0 17.4 13.7 12.4 4.8 .914 Persistence 17.0 17.4 13.7 13.7 9.8 .692 1000: Model O P s o S P M A E d (la) 22.2 22.4 15.7 14.2 9.3 .801 (lb) 22.2 22.3 15.7 15.2 5.7 .926 (2) 22.2 25.1 15.7 16.2 8.6 .858 Persistence 22.2 22.8 15.7 15.7 11.2 .726 1100: Model O P s o S P M A E d da) 25.8 26.3 17.5 15.0 10.6 .745 (lb) 25.8 26.2 17.5 15.9 8.5 .856 (2) 25.8 30.4 17.5 17.9 10.1 .842 Persistence 25.8 26.6 17.5 17.6 13.3 .667 1200: Model O P so S P M A E d (la) 29.1 29.8 19.7 15.9 11.4 .755 (lb) 29.1 29.6 19.7 16.8 9.7 .845 (2) 29.1 34.7 19.7 18.9 10.8 .863 Persistence 29.1 30.2 19.7 19.8 14.3 .678 1300: Model O P s o S P M A E d (la) 32.2 32.7 17.6 15.6 10.6 .808 (lb) 32.2 32.6 17.6 16.6 9.0 .866 (2) 32.2 37.7 17.6 16.4 9.8 .860 Persistence 32.2 33.0 17.6 17.9 12.2 .748 54 Table 3.4a (continued) 1400: Model O P s o S P M A E d (la) 35.3 35.9 18.5 16.3 11.5 .787 (lb) 35.3 35.7 18.5 17.4 11.1 .821 < 2 > 35.3 39.9 18,5 15.4 10.5 .832 Persistence 35.3 36.2 18.5 18.8 13.0 .745 1500: Model O P s o 8 P M A E d (la) 36.2 37.1 18.4 15.7 12.5 .745 (lb) 36.2 37.0 18.4 16.4 11.4 .788 (2) 36.2 40.2 18.4 14.8 10.6 .818 Persistence 36.2 37.2 18.4 19.0 14.1 .692 1600: Model O P s o S P M A E d (la) 34.5 35.9 16.6 14.2 12.0 .732 (lb) 34.5 35.7 16.6 15.1 11.3 .769 (2) 34.5 39.7 16.6 14.8 10.8 .788 Persistence 34.5 36.1 16.6 16.9 13.5 .684 1700: Model O P s o S P M A E d (la) 30.7 31.2 14.7 12.0 11.3 .684 (lb) 30.7 31.2 14.7 12.4 10.9 .721 (2) 30.7 36.4 14.7 14.3 10.7 .733 Persistence 30.7 31.4 14.7 14.7 12.6 .657 1800: Model O P s o S P M A E d (la) 26.5 26.7 13.3 11.0 10.2 .692 (lb) 26.5 26.7 13.3 11.1 9.4 .733 (2) 26.5 32.8 13.3 13.8 11.1 .678 Persistence 26.5 26.9 13.3 13.3 11.4 .671 55 Table 3.4 (continued)  b) Station T i l 0900: Model O P s 0 s p M A E d (1) (2) 17.4 17.6 8.5 7.2 2.9 .940 Persistence 17.4 1TA 8J5 JU5 5S .800 1000: Model O P sQ s p M A E d (1) 21.6 21.6 9.0 8.7 3.0 .943 (2) 21.6 23.6 9.0 7.5 5.2 .838 Persistence 21.6 2L7 9.0 9.3 (U) .793 1100: Model O P sQ s p M A E d (1) 25.5 25.6 10.8 9.4 4.9 .877 (2) 25.5 28.9 10.8 8.9 6.0 .858 Persistence 25.5 25.7 10J3 KL8 6.5 .800 1200: Model O P sG s p M A E d (1) 31.0 30.9 13.8 11.5 7.4 .813 (2) 31.0 34.6 13.8 10.2 7.3 .843 Persistence 31.0 3_L1 13J5 13JJ 814 .780 1300: Model O P sQ s p M A E d (1) 33.2 33.2 14.1 12.2 8.7 .773 (2) 33.2 37.5 14.1 11.1 8.1 .836 Persistence 33.2 33JJ l j k l 14J5 915 .753 1400: Model O P sQ s p M A E d (1) 35.2 36.0 14.6 12.6 9.3 .748 (2) 35.2 - 40.8 14.6 10.8 8.8 .813 Persistence 35.2 36.1 14.6 15.2 10.4 .738 56 Table 3.4b (continued) 1500: Model O P sQ s p M A E d (1) 37.5 38.2 15.7 13.5 10.3 .739 (2) 37.5 42.2 15.7 10.0 9.1 .784 Persistence 37.5 38L2 15/7 16^2 10J) .750 1600: Model O T sG s p M A E d (1) 37.9 37.8 16.5 14.1 11.2 .694 (2) 37.9 42.4 16.5 10.4 9.9 .757 Persistence 37.9 37.9 16.5 16.8 11.4 .720 1700: Model O P sQ s p M A E d (1) 36.7 36.5 16.2 13.5 11.5 .648 (2) 36.7 40.5 16.2 8.7 10.4 .676 Persistence 36.7 36.6 16.2 16J5 12J2 .667 1800: Model O P" s 0 s p M A E d (1) 33.1 33.1 14.2 11.5 10.2 .647 (2) 33.1 37.8 14.2 8.8 9.9 .659 Persistence 33.1 33.2 14.2 14.2 11.3 .640 57 There are a number of points regarding the forecast abi l i ty of each model which are evident f rom Table 3.4: - A l l models have smal ler average forecast error (i.e., M A E ) throughout the day than the persistence model. - The use of Model 2 general ly results in good forecasts although the observed means and standard deviations are poorly reproduced. - Fo r station T 9 , using h * = 0900 rather than h * = 0800 in Mode l 1 results in much better forecasts throughout the day. - Fo r station T i l , late in the afternoon, a persistence forecast performs near ly as wel l as either Model 1 or Model 2. To summar ize , both Models 1 and 2 produce forecasts which are superior (at least for the summer of 1986) to those of a persistence model. Model 2 is clearly the more determinist ic of the two models since it relates var iab i l i ty in ozone concentrations to that in NO2 concentrations; hence, its future use wi l l require cont inual re-estimation of system parameters. Conversely, Model 1 is much more adaptive since a large portion of its forecast var iabi l i ty is s imply determined by a weighted average of past values. Al though the forecasting abi l i ty of Model 1 may be marg ina l ly inferior to that of Model 2 at cr i t ical t imes of the day (i.e., late afternoon), f rom an intuit ive standpoint Mode l 1 may be viewed as the more " robust" of the two models. Regard ing the use of Model 1 at station T 9 , there is an obvious trade-off between the two values of h * employed. The persons responsible for mak ing forecasts must decide which is more desirable: less accurate forecasts performed ear ly in the day (h* = 0800) or more accurate forecasts performed later in the day (h* = 0900). 58 Chapter 4  Conclusions and Recommendations 4.1 Introduction The previous two chapters have presented several models which m a y be used to describe the temporal var iabi l i ty of ozone concentrations or to forecast short-term ozone var iat ions. The forecasting abil i ty of each model has been stat ist ical ly evaluated us ing a set of data which was not used in model development. The intent of this chapter is to summar ize the relat ive ut i l i ty of the var ious types of models w i th part icular regard to operational signif icance. In addit ion, comments pert inent to future investigations of pol lutant var iab i l i ty in the lower F rase r Va l l ey wi l l be made. 4.2 Investigative Summary and Conclusions The appropriateness of any model is determined by the purpose for its use. Regard ing pol lutant forecast models, i t is f i rst necessary to decide which is needed: (1) a probabil ist ic forecast (i.e., the probabil i ty of exceeding a given concentration level under specified circumstances) or (2) a quantitat ive forecast over a designated t ime period. Fo r a probabil ist ic forecast, one may simply consult ord inary histograms of past concentration levels. A more sophisticated (and more accurate - see Horowi tz and Baraka t , 1979) approach is that described in Section 2.2.1, i.e., to simulate frequency distributions ut i l iz ing information derived f rom histor ical ozone var iabi l i ty . The incorporation of elements concerning the var iabi l i ty of the photochemical system into a probabilistic forecast model is certainly an improvement over disregarding the inherent seasonali ty and autocorrelation in ozone time series. Regarding quanti tat ive forecasts of ozone concentrations over specific time periods, the models developed here may be divided into two distinct categories: (1) those models which 59 forecast the dai ly m a x i m u m one-hour average ozone concentration (see Chapter 2) and (2) those which forecast the d iurnal behavior of one-hour average ozone concentrations (see Chapter 3). The Canad ian Nat iona l A i r Qual i ty Objectives are stated in terms of one-hour average concentrations; however, the value commonly quoted for any given day is the dai ly max imum. Therefore, it is essential to be able to accurately forecast this value. F o r these purposes, the temperature and persistence based model ( T E M P E R ) provides the best forecasts although pure persistence works near ly as wel l (see Chapter 2 for detailed comparison of annual models). Nonetheless, forecasts of the dai ly m a x i m u m value do little to reveal information which is important for both public heal th policy and emissions control policy. The dai ly models provide a means of est imat ing the potential integrated effect of ozone concentrations throughout the day since the longer a pol lutant remains at dangerously h igh levels, the greater the potential impact on biological organisms. Regard ing the control of emissions, there is st i l l some uncertainty concerning the relat ionship between the emission of p r imary pollutants and the production of photochemical pol lutants (OECD,1979 ) ; however, an accurate dai ly model (i.e., Da i l y Mode l 1 or Da i l y Mode l 2) is capable of reveal ing informat ion relevant to the appropriate t iming of emissions control. 4.3 Recommendations for Future Work Al though a number of reasonably accurate forecast models have been developed, there are a number of analyses which m a y st i l l be performed wi th the data used here. In the future, stat ist ical methods may be used to attempt the fol lowing: - Ana lyze data strati f ied by weather conditions such as wind direction, cloud cover, precipitat ion, etc. - Examine case studies to reveal the dynamics of extreme pollutant episodes. - Incorporate t ime-var iant parameter est imat ion into var ious models. 60 - Determine the nature of secular trends in ozone concentrations throughout the lower F r a s e r Va l ley (see Chock et al., 1982; K u m a r and Chock, 1984). - Exam ine specific relat ionships between emissions and pol lutants (e.g., ratios of nitrogen oxides to non-methane hydrocarbons (see O E C D , 1979), effect of changes in certain pollutants at different locations, etc.). - A n a l y z e the spatial var iabi l i ty of ozone concentrations across the lower F r a s e r Va l ley in order to (1) forecast pollutant concentrations (see Bennett , 1979) and (2) detect spat ia l redundancy or inadequacy in the observation network (see Box and T iao, 1977; Bu r t , 1986). The analyses performed in this thesis are s imply a f irst attempt to describe and model the temporal var iab i l i ty of ozone concentrations in the lower F rase r Va l l ey . The approach used was purely stat ist ical although physica l principles were often used as a guide to explain sys tem var iabi l i ty . The accuracy of most of the developed models is acceptable; however, it is believed that the l imits of the "pure time ser ies" method (i.e., mathemat ica l decomposition of the time series) have been approached wi th these data. In the future, investigations us ing these data should attempt to answer specific questions regarding the physica l mechanisms governing photochemical act iv i ty. 61 References Bates, D. V., G. M . Be l l , C. D. B u r n h a m , M . H a z u c h a , J . M a n t h a , L . D. Pengel ly, and F . S i l ve rman, 1972: Short- term effects of ozone on the lung. Journal of Applied Physiology, 32: 176-181. Benar ie , M . M . 1980. 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Journal of Geophysical Research, 90, C5 :8995-9005. 64 Appendix Scatterplots and Summary Statistics for Evaluation of Daily Models 0900 OZONE FORECAST FOR T9 USING DAILY MODEL 1o: 1986 WOO OZONE FORECAST FOR T9 USING DAILY MODEL 1o: 1986 Figure A l Scatterplots of observed vs. predicted ozone concentrations for Daily Model l a at station T9: May-September, 1986 a), b) Forecasts for 0900,1000 1K)0 OZONE FORECAST FOR T9 USING DAILY MODEL la: 1986 1200 OZONE FORECAST FOR T9 USING DAILY MODEL 1a: 1986 Figure A l c), d) Forecasts for 1100,1200 1300 OZONE FORECAST FOR T9 USING DAILY MODEL 1a: 1986 MOO OZONE FORECAST FOR T9 USING DAILY MODEL 1a: 1986 Figure A l e), f) Forecasts for 1300,1400 1500 OZONE FORECAST FOR T9 USING DAILY MODEL 1a: 1986 1600 OZONE FORECAST FOR T9 USING DAILY MODEL 1a: 1986 Figure A l g), h) Forecasts for 1500,1600 1700 OZONE FORECAST FOR T9 USING DAILY MODEL 1o: 1986 1800 OZONE FORECAST FOR T9 USING DAILY MODEL 1o: 1986 Figure A l i), j) Forecasts for 1700,1800 1000 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 1100 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 Figure A2 Scatterplots of observed vs. predicted ozone concentrations for Daily Model lb at station T9: May-September, 1986 a), b) Forecasts for 1000,1100 1200 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 1300 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 Figure A2 c), d) Forecasts for 1200,1300 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 1500 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 Figure A2 e), f) Forecasts for 1400,1500 1600 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 1700 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 Figure A2 g), h) Forecasts for 1600,1700 1700 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 1800 OZONE FORECAST FOR T9 USING DAILY MODEL 1b: 1986 Figure A2 i), j) Forecasts for 1700,1800 0900 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 1000 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 Scatterplots of observed vs. predicted ozone concentrations for Daily Model 2 at station T9: May-September, 1986 a), b) Forecasts for 0900,1000 1100 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 1200 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 Figure A3 c), d) Forecasts for 1100,1200 1300 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 1400 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 Figure A3 e), f) Forecasts for 1300,1400 1500 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 1600 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 Figure A3 g), h) Forecasts for 1500,1600 1700 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 i 1 1 1 r — i r 0.0 20.0 4Q.Q n n OBSERVED CONCEN I-a UJp 1800 OZONE FORECAST FOR T9 USING DAILY MODEL 2: 1986 MAE - 11.1 t i y RMSE - 14.6 RMSEs - 8.6 RMSEu - U.7 Regression Line Intercept - 18.1 Slope - 0.555 d 0.678 + > + / . * ** y * X t*.* + + OBS MEAN - 26.3 PRED MEAN -32.8 OBS ST DEV - 13.3 1 1 1 1 1 1 1 r PRED ST DEV -13.8 CTPB1 o.o 20.0 r?B%ERVETf ffQNCEN?R'r5TI0N WA) 120.0 140.0 Figure A3 i), j) Forecasts for 1700,1800 0900 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 1000 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 o Figure A4 Scatterplots of observed vs. predicted ozone concentrations for pure persistence at station T9: May-September, 1986 a), b) Forecasts for 0900,1000 1100 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 1200 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 Figure A 4 c), d) Forecasts for 1100,1200 1300 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 U00 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 Figure A4 e), f) Forecasts for 1300,1400 1500 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 1600 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 Figure A4 g), h) Forecasts for 1500,1600 1700 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 1800 OZONE FORECAST FOR T9 USING PERSISTENCE : 1986 Figure A4 i), j) Forecasts for 1700,1800 1000 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 1100 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 Figure A5 Scatterplots of observed vs. predicted ozone concentrations for Daily Model 1 at station T i l : May-September, 1986 a), b) Forecasts for 1000,1100 1200 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 1300 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 Figure A5 c), d) Forecasts for 1200,1300 1400 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 1500 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 Figure A5 e), f) Forecasts for 1400,1500 1600 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 1700 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 Figure A5 g), h) Forecasts for 1600,1700 1700 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 1800 OZONE FORECAST FOR T11 USING DAILY MODEL 1: 1986 oo V£> Figure A5 i), j) Forecasts for 1700,1800 0900 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 1000 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 Figure A6 Scatterplots of observed vs. predicted ozone concentrations for Daily Model 2 at station T i l : May-September, 1986 a), b) Forecasts for 0900,1000 1100 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 1200 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 Figure A6 c), d) Forecasts for 1100,1200 1300 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 1400 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 U3 Figure A6 e), f) Forecasts for 1300,1400 1500 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 1600 OZONE FORECAST FOR T11 USING DAILY MOOEL 2: 1986 U3 Figure A6 g), h) Forecasts for 1500,1600 1700 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 1800 OZONE FORECAST FOR T11 USING DAILY MODEL 2: 1986 U 3 -t-Figure A 6 i), j) Forecasts for 1700^ 1800 0900 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 1000 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 Figure A7 Scatterplots of observed vs. predicted ozone concentrations for pure persistence at station T i l : May-September, 1986 a), b) Forecasts for 0900,1000 1100 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 1200 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 Figure A7 c), d) Forecasts for 1100,1200 1300 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 1400 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 Figure A7 e), f) Forecasts for 1300,1400 1500 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 1600 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 Figure A7 g), h) Forecasts for 1500,1600 1700 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 1800 OZONE FORECAST FOR T11 USING PERSISTENCE : 1986 Figure A7 i), j) Forecasts for 1700,1800 

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