A Predictive Model for Steady State Ozone Concentration at an Urban-Coastal Site

Ground level ozone (O3) plays an important role in controlling the oxidation budget in the boundary layer and thus affects the environment and causes severe health disorders. Ozone gas, being one of the well-known greenhouse gases, although present in small quantities, contributes to global warming. In this study, we present a predictive model for the steady-state ozone concentrations during daytime (13:00–17:00) and nighttime (01:00–05:00) at an urban coastal site. The model is based on a modified approach of the null cycle of O3 and NOx and was evaluated against a one-year data-base of O3 and nitrogen oxides (NO and NO2) measured at an urban coastal site in Jeddah, on the west coast of Saudi Arabia. The model for daytime concentrations was found to be linearly dependent on the concentration ratio of NO2 to NO whereas that for the nighttime period was suggested to be inversely proportional to NO2 concentrations. Knowing that reactions involved in tropospheric O3 formation are very complex, this proposed model provides reasonable predictions for the daytime and nighttime concentrations. Since the current description of the model is solely based on the null cycle of O3 and NOx, other precursors could be considered in future development of this model. This study will serve as basis for future studies that might introduce informing strategies to control ground level O3 concentrations, as well as its precursors’ emissions.


Introduction
Tropospheric ozone (O 3 ) is known for causing severe health effects and having environmental impacts [1,2]. Among other photochemical oxidants, O 3 is one of the widely studied subjects worldwide under the category of air pollution. Besides that, O 3 is a key precursor of hydroxyl radicals (OH), which control the oxidizing power of the lower atmosphere and by that alters its chemical properties [3].
Ground level O 3 formation depends on photochemistry, meteorological conditions, and air mass transport [4][5][6][7]. For instance, O 3 is found to peak during the summer time accompanying high temperatures and long daytime hours and thus seems to be correlated with solar radiation intensity [8][9][10][11][12][13]. In urban environments, the diurnal cycle of O 3 consists of nighttime low concentrations and daytime high concentrations, which may last for several hours (Figure 1). This high O 3 concentration during the daytime is mainly attributed to photochemical reactions mainly within the NO x -O 3 cycle. The low O 3 concentrations during nighttime are the result of the pause in ozone production, due to the absence of photochemical reactions. Eventually, the O 3 is recycled through chemical reactions or is lost by deposition [14]. It is interesting that the daytime steady-state O 3 concentration on weekends is higher than that on workdays. The latter can be attributed to higher traffic on workdays than on weekends, releasing more NO x , which in turn uses up the daytime available ozone, leaving behind a lower concertation of steady state ozone on workdays. The aforementioned assumptions are discussed in more detail in the following sections. Being the major source of daytime ground level O 3 , we believe that the NO x -O 3 null cycle, can be applied to predict the steady-state daytime O 3 concentrations in urban areas. temperatures and long daytime hours and thus seems to be correlated with solar radiation intensity [8][9][10][11][12][13]. In urban environments, the diurnal cycle of O3 consists of nighttime low concentrations and daytime high concentrations, which may last for several hours (Figure 1). This high O3 concentration during the daytime is mainly attributed to photochemical reactions mainly within the NOx-O3 cycle. The low O3 concentrations during nighttime are the result of the pause in ozone production, due to the absence of photochemical reactions. Eventually, the O3 is recycled through chemical reactions or is lost by deposition [14]. It is interesting that the daytime steady-state O3 concentration on weekends is higher than that on workdays. The latter can be attributed to higher traffic on workdays than on weekends, releasing more NOx, which in turn uses up the daytime available ozone, leaving behind a lower concertation of steady state ozone on workdays. The aforementioned assumptions are discussed in more detail in the following sections. Being the major source of daytime ground level O3, we believe that the NOx-O3 null cycle, can be applied to predict the steady-state daytime O3 concentrations in urban areas. The momentary change rate of O3 concentrations can be described by its sources and sinks involved in atmosphere [15,16]. For instance, in urban environments, O3 is formed through a series of daytime reactions that involve NOx (NO and NO2), which are of anthropogenic origin. Other sources of O3 include volatile organic compounds (VOCs) and carbon monoxide (CO) [17]. The priority of the reactions depends on the concentrations of NOx and VOCs, as well as the ratio of the two (NOx/VOC) [18]. Accordingly, two regimes for O3 formation have been proposed. The first one is the NOx-sensitive regime in which the increase in NOx concentration causes an increase in O3 concentration and the formation of O3 is mainly independent of the VOCs concentration. The second one is the VOC-sensitive regime in which the O3 formation is solely dependent on the VOCs concentration [19,20]. Therefore, the prevailing regime is specific to the dominant environmental conditions.
In the urban atmosphere, NO and NO2 are emitted from anthropogenic activities, including combustion processes (e.g., traffic and industrial activities). Their daily patterns (Figures 2 and 3) are, therefore, controlled by these emissions [21][22][23]. Since NO is a primary pollutant and acts to form NO2 upon a series of reactions [24], the NO2 morning peak appears one hour later than the NO peak. The NOx concentrations vary between morning and evening and the change is attributed to many factors. First, during the early hours of daytime, high traffic emissions are accumulated in the atmosphere when the photo-chemically produced O3 concentrations are still low; O3 acts as a sink for both NO and NO2. Concurrent with sunrise, these pollutants are consumed with daytime produced O3 and are subject to thermal turbulence, due to higher temperature resulting in their dilution, dispersion within expansion in the boundary layer and eventually a drop in their concentrations [25,26]. On the other hand, along with sunset NO and NO2 encounter lower temperature, less boundary layer mixing and low dispersion leading to an increase in their concentrations. The momentary change rate of O 3 concentrations can be described by its sources and sinks involved in atmosphere [15,16]. For instance, in urban environments, O 3 is formed through a series of daytime reactions that involve NO x (NO and NO 2 ), which are of anthropogenic origin. Other sources of O 3 include volatile organic compounds (VOCs) and carbon monoxide (CO) [17]. The priority of the reactions depends on the concentrations of NO x and VOCs, as well as the ratio of the two (NO x /VOC) [18]. Accordingly, two regimes for O 3 formation have been proposed. The first one is the NO x -sensitive regime in which the increase in NO x concentration causes an increase in O 3 concentration and the formation of O 3 is mainly independent of the VOCs concentration. The second one is the VOC-sensitive regime in which the O 3 formation is solely dependent on the VOCs concentration [19,20]. Therefore, the prevailing regime is specific to the dominant environmental conditions.
In the urban atmosphere, NO and NO 2 are emitted from anthropogenic activities, including combustion processes (e.g., traffic and industrial activities). Their daily patterns (Figures 2 and 3) are, therefore, controlled by these emissions [21][22][23]. Since NO is a primary pollutant and acts to form NO 2 upon a series of reactions [24], the NO 2 morning peak appears one hour later than the NO peak. The NO x concentrations vary between morning and evening and the change is attributed to many factors. First, during the early hours of daytime, high traffic emissions are accumulated in the atmosphere when the photo-chemically produced O 3 concentrations are still low; O 3 acts as a sink for both NO and NO 2 . Concurrent with sunrise, these pollutants are consumed with daytime produced O 3 and are subject to thermal turbulence, due to higher temperature resulting in their dilution, dispersion within expansion in the boundary layer and eventually a drop in their concentrations [25,26]. On the other hand, along with sunset NO and NO 2 encounter lower temperature, less boundary layer mixing and low dispersion leading to an increase in their concentrations.  The characteristics and patterns of ground level O3 have been the subject of many studies worldwide [27]. Specifically, the chemical coupling between O3 and its precursors (NO and NO2) was investigated thoroughly in urban environments [19,22,[28][29][30][31]. However, very few studies considered modelling of ground level O3 [32][33][34][35]. In fact, O3 is involved in many chemical reactions that sometimes make its prediction very difficult. In this study, we present a simple statistical predictive model to calculate the steady-state daytime and nighttime O3 concentrations at an urban coastal site. For the purpose of model evaluation, we utilized a one-year data-base of ozone (O3) and nitrogen oxides (NO and NO2) measured in Jeddah, which is located on the western part of Saudi Arabia [36]. Our model could be modified to evaluate ozone in other urban environments with similar diurnal patterns.

Simple Statistical Predictive Model
In the troposphere, ozone (O3) and nitrogen oxides (NOx) undergo a well-known null cycle in which each gaseous species maintains a steady-state concentration [37]; i.e., balanced production and loss rates balance each other (Figures 1-3). As postulated in the introduction, the daytime steadystate O3 concentration is higher than that during the nighttime steady-state concentrations. Furthermore, the chemical reactions involved with the O3 are different during both periods. Therefore, we postulate the simple predictive model for two time periods: Daytime and nighttime.  The characteristics and patterns of ground level O3 have been the subject of many studies worldwide [27]. Specifically, the chemical coupling between O3 and its precursors (NO and NO2) was investigated thoroughly in urban environments [19,22,[28][29][30][31]. However, very few studies considered modelling of ground level O3 [32][33][34][35]. In fact, O3 is involved in many chemical reactions that sometimes make its prediction very difficult. In this study, we present a simple statistical predictive model to calculate the steady-state daytime and nighttime O3 concentrations at an urban coastal site. For the purpose of model evaluation, we utilized a one-year data-base of ozone (O3) and nitrogen oxides (NO and NO2) measured in Jeddah, which is located on the western part of Saudi Arabia [36]. Our model could be modified to evaluate ozone in other urban environments with similar diurnal patterns.

Simple Statistical Predictive Model
In the troposphere, ozone (O3) and nitrogen oxides (NOx) undergo a well-known null cycle in which each gaseous species maintains a steady-state concentration [37]; i.e., balanced production and loss rates balance each other (Figures 1-3). As postulated in the introduction, the daytime steadystate O3 concentration is higher than that during the nighttime steady-state concentrations. Furthermore, the chemical reactions involved with the O3 are different during both periods. Therefore, we postulate the simple predictive model for two time periods: Daytime and nighttime. The characteristics and patterns of ground level O 3 have been the subject of many studies worldwide [27]. Specifically, the chemical coupling between O 3 and its precursors (NO and NO 2 ) was investigated thoroughly in urban environments [19,22,[28][29][30][31]. However, very few studies considered modelling of ground level O 3 [32][33][34][35]. In fact, O 3 is involved in many chemical reactions that sometimes make its prediction very difficult. In this study, we present a simple statistical predictive model to calculate the steady-state daytime and nighttime O 3 concentrations at an urban coastal site. For the purpose of model evaluation, we utilized a one-year data-base of ozone (O 3 ) and nitrogen oxides (NO and NO 2 ) measured in Jeddah, which is located on the western part of Saudi Arabia [36]. Our model could be modified to evaluate ozone in other urban environments with similar diurnal patterns.

Simple Statistical Predictive Model
In the troposphere, ozone (O 3 ) and nitrogen oxides (NO x ) undergo a well-known null cycle in which each gaseous species maintains a steady-state concentration [37]; i.e., balanced production and loss rates balance each other (Figures 1-3). As postulated in the introduction, the daytime steady-state O 3 concentration is higher than that during the nighttime steady-state concentrations. Furthermore, the chemical reactions involved with the O 3 are different during both periods. Therefore, we postulate the simple predictive model for two time periods: Daytime and nighttime.

Daytime Steady-State O 3 Concentrations Prediction
Under atmospheric conditions and in the presence of solar radiation (λ < 424 nm), the O 3 -NO x null cycle includes three successive reactions [37]: where M is an inert ground state (either N 2 or O 2 ) that acts as a surface for the reaction to take place and M* is the excited state of the molecule, hv is the energy of the solar radiation photons that induces photochemical oxidation, O is known to be highly reactive and disappears as soon as it is generated. Here, the concentration of O 2 is assumed to be constant.
Under steady-state conditions, the null cycle has the steady-state formula, where J NO2 is the rate coefficient of NO 2 photolysis, k 3 is the reaction rate coefficient of O 3 and NO. It is well known that the k 3 is temperature dependent [38]; k 3 = 3.23 exp(−1430/T) in units of ppb −1 min −1 . However, the seasonal temperature variation is few degrees; and therefore, we do not expect k 3 to have a considerable variation throughout the year in Jeddah. Re-arrangement of Equation (2) yields a simple equation to predict the concentration of O 3 from the ratio of NO 2 to NO concentrations during daytime, where αis a constant equivalent to J NO2 /k 3 and δ 1 (ppb)is also constant related to the background O 3 concentrations (e.g., migrates from the stratosphere to the troposphere, long-range transport, product of other reactions). During daytime steady-state, using Equation (1): Upon rearranging we get Equation (2). We then compute a linear regression of [O 3 ] vs. [NO 2 /NO] of measured data. We, thus, are able to derive the constants for the model as y = ax + b (Equation (3)), where a is a constant equivalent to J NO2 /k 3 and b is also constant related to the background O 3 concentrations.

Nighttime Steady-State O 3 Concentrations Prediction
During night-time hours, O 3 is mainly consumed through its reaction with NO 2 , Applying reaction rate kinetics and rearrangement of the Equation (4) yields a simple equation to predict the nighttime O 3 based on the concentration of its major nighttime sink compound NO 2 , where β(ppb 2 ) is a constant equivalent to the reaction rate of O 3 with NO 2 and δ 2 (ppb) is again a constant related to the background O 3 concentrations during the night. During nighttime, Equation (4) steady state conditions are: Upon rearranging we get Equations (6) and (7). We then compute a linear regression of [O 3 ] vs. [NO 2 ] of measured data. We, thus, are able to derive the constants for the model as y = ax + b (Equation (3)), where a is a constant equivalent to k (reaction rate of O 3 with NO 2 ) and b is again a constant related to the background O 3 concentrations.

Data-Base
In this study, we utilized a one-year data-base of O 3 and NO x concentrations measured at an urban site in Jeddah, Saudi Arabia between 1 January and 31 December 2012 [36]. The data-base is utilized to only evaluate the above described simple predictive model for steady-state O 3 concentrations. The measurement was conducted at the King Abdul-Aziz University (KAU) campus, which is surrounded by major roads and a highway. Jeddah itself is situated on the west coast of Saudi Arabia and is considered the largest sea port on the Red Sea. Potential sources of air pollution in the city are mainly vehicle emissions (1.4 million vehicles; [39]) and industrial (oil refinery, desalination plant, power generation plant, and manufacturing industry). A lot of these emissions act as O 3 precursors; under favored meteorological conditions and abundance of solar radiation, which are available in Jeddah.

Overview of the Daily Patterns
The O 3 concentrations showed a clear daily pattern with high concentrations during the daytime, which was as high as 39 ppb and 47 ppb on workdays (Saturday-Wednesday) and weekends (Friday), respectively ( Figure 1). The nighttime (before 05:00) concentrations were between 7.5 ppb and 13.2 ppb. As mentioned before in the introduction section, higher O 3 concentrations on weekends daytime are not only attributed to the NO x cycle, but also possibly due to differences in the concentrations of other precursors (e.g., CO and VOC). The presence of VOCs changes the path of O 3 formation by altering the NO x cycle mechanism through reactions of hydroxyl radicals, which in turn oxidize NO without the use of O 3 . The latter, along with the photolysis of NO 2 , leads to accumulation of O 3 during the daytime on weekends. Furthermore, when NO x concentrations are high, the reaction of NO 2 and OH to give HNO 3 is favored [17], which reduces the NO 2 concentrations available for photolysis. In turn, this leads to low photolysis rate J NO2 during the weekends.

(represented by the concentrations ratio [O 3 ][NO]/[NO 2 ]
) is characterized by a double peak (before noon and in the afternoon). The nighttime value varied between 0.5 and 1 ppb. The daytime value was as high as 5 ppb on weekends and as high as 8 on workdays ( Figure 4). As claimed before, k 3 does not have significant differences throughout the year in Jeddah; and thus, the daily pattern, shown in Figure 4, should represent the daily pattern of J NO2 . In general, J NO2 is the rate of photolysis of NO 2 and it seems to be lower on weekends than on workdays. In general, it has been well known that photolysis occurs more rapidly during lower PM (particulate matter) concentrations; This is mainly observed during the weekends [31,40].

Prediction of Steady-State O3 Concentration
As shown in Figures 1-3, regarding the daily pattern of O3 and NOx, the steady-state conditions are met during 13:00-17:00 (referred to as daytime steady-state period) and 01:00-05:00 (referred to as nighttime steady-state period). We considered the 30-minutes average of the data-base and selected these time periods separately to apply the simple predictive model, which is a linear regression model. We applied the fitting to the whole data set. The nighttime period for all weekdays was considered as one period whereas the daytime period was considered separately for workdays (Saturday-Wednesday) and weekends (Friday).
The O3 concentration prediction for the daytime period according to Equation ( (8) The predicted O3 concentrations based on these equations are shown and compared to the measured ones in Figure 6. Note that the regression model parameters were obtained based on the 30-minutes average of the O3 and NOx data-base. In addition, the model predictions were also based on the 30-minutes average of the concentrations and Figure 6 is based on averaging the results to obtain the daily patterns.

Prediction of Steady-State O3 Concentration
As shown in Figures 1-3, regarding the daily pattern of O3 and NOx, the steady-state conditions are met during 13:00-17:00 (referred to as daytime steady-state period) and 01:00-05:00 (referred to as nighttime steady-state period). We considered the 30-minutes average of the data-base and selected these time periods separately to apply the simple predictive model, which is a linear regression model. We applied the fitting to the whole data set. The nighttime period for all weekdays was considered as one period whereas the daytime period was considered separately for workdays (Saturday-Wednesday) and weekends (Friday).
The O3 concentration prediction for the daytime period according to Equation (3) is best represented by: The predicted O3 concentrations based on these equations are shown and compared to the measured ones in Figure 6. Note that the regression model parameters were obtained based on the 30-minutes average of the O3 and NOx data-base. In addition, the model predictions were also based on the 30-minutes average of the concentrations and Figure 6 is based on averaging the results to obtain the daily patterns.

Prediction of Steady-State O 3 Concentration
As shown in Figures 1-3, regarding the daily pattern of O 3 and NO x , the steady-state conditions are met during 13:00-17:00 (referred to as daytime steady-state period) and 01:00-05:00 (referred to as nighttime steady-state period). We considered the 30-minutes average of the data-base and selected these time periods separately to apply the simple predictive model, which is a linear regression model. We applied the fitting to the whole data set. The nighttime period for all weekdays was considered as one period whereas the daytime period was considered separately for workdays (Saturday-Wednesday) and weekends (Friday).
The O 3 concentration prediction for the daytime period according to Equation (3) is best represented by: NO + 29.35 Workdays R 2 = 0.37 0.50 NO + 35.47 Weekends R 2 = 0.31 (8) The predicted O 3 concentrations based on these equations are shown and compared to the measured ones in Figure 6. Note that the regression model parameters were obtained based on the 30-minutes average of the O 3 and NO x data-base. In addition, the model predictions were also based on the 30-minutes average of the concentrations and Figure 6 is based on averaging the results to obtain the daily patterns. Based on Equation (6), the α constant, which is supposed to be equivalent to JNO2/k3, is found to be 1.09 ppb and 0.50 ppb for workdays and weekends daytime, respectively. The δ constant, which is related to the background ozone concentrations, is 29.35 ppb and 35.47 ppb for workdays and weekends, respectively. The theoretical value of JNO2/k3 calculated from the kinetics of the daytime reactions involved in O3 formation at steady-state are presented by the function is found to be 8.7 ppb. This can be easily verified for JNO2 provided by ACOM online database (http://cprm.acom.ucar.edu/Models/TUV/Interactive_TUV/) and substituting k3 as proposed with Equation (2).
This means that α value is different than the ideal one represented by JNO2/k3. Note that the kinetic model represents the ideal case, when the concentration of O3 depends solely on the NOx-O3 cycle with no contribution from additional sources or the involvement of other precursors in the O3 formation processes. Additionally, the ideal case occurs in full solar exposure, without factors leading to solar radiation attenuation, including daytime PM and cloudiness. Also note that the additional parameter δ1 can be thought of as a parameter that accounts for other processes contributing to the O3 formation in Jeddah. Interestingly, the value of δ1 is higher on weekends than on workdays. Other parameters which contribute to δ1 include long range transport of O3, as well as stratospheretroposphere O3 migration. The latter is aided by the high temperature in Jeddah which enables this irreversible phenomenon to occur by increasing boundary layer height favoring proper mixing [41].
The O3 concentration prediction for the nighttime period according to Equation (5) is best represented by, 267.01 1. 16 0.58 (9) The predicted O3 concentrations are also shown and compared to the measured ones in Figure  6. Again, the regression model parameters were obtained based on the 30-minutes average of the O3 and NOx data-base.
This equation is based on the fact that NO2 acts as a major sink for the night-time O3 [24]. Here the parameter β can be thought of as the reaction rate of O3 with NO2. In our analysis, β is rather similar for all days of the week and its value is about 267 ppb 2 . The second parameter δ2 has a value of 1.16 ppb. The theoretical value for the reaction rate of O3 with NO2 during nighttime is about 1250 ppb 2 [42][43][44]. Again, the deviations between β and the reaction rate of O3 with NO2 during nighttime can be explained by the occurrence of additional sinks of ozone, including surface reactions of particulate matter and deposition [24]. Based on Equation (6), the α constant, which is supposed to be equivalent to J NO2 /k 3 , is found to be 1.09 ppb and 0.50 ppb for workdays and weekends daytime, respectively. The δ constant, which is related to the background ozone concentrations, is 29.35 ppb and 35.47 ppb for workdays and weekends, respectively. The theoretical value of J NO2 /k 3 calculated from the kinetics of the daytime reactions involved in O 3 formation at steady-state are presented by the function is found to be 8.7 ppb. This can be easily verified for J NO2 provided by ACOM online database (http://cprm.acom.ucar.edu/ Models/TUV/Interactive_TUV/) and substituting k 3 as proposed with Equation (2).
This means that α value is different than the ideal one represented by J NO2 /k 3 . Note that the kinetic model represents the ideal case, when the concentration of O 3 depends solely on the NO x -O 3 cycle with no contribution from additional sources or the involvement of other precursors in the O 3 formation processes. Additionally, the ideal case occurs in full solar exposure, without factors leading to solar radiation attenuation, including daytime PM and cloudiness. Also note that the additional parameter δ 1 can be thought of as a parameter that accounts for other processes contributing to the O 3 formation in Jeddah. Interestingly, the value of δ 1 is higher on weekends than on workdays. Other parameters which contribute to δ 1 include long range transport of O 3 , as well as stratosphere-troposphere O 3 migration. The latter is aided by the high temperature in Jeddah which enables this irreversible phenomenon to occur by increasing boundary layer height favoring proper mixing [41].
The O 3 concentration prediction for the nighttime period according to Equation (5) is best represented by, The predicted O 3 concentrations are also shown and compared to the measured ones in Figure 6. Again, the regression model parameters were obtained based on the 30-minutes average of the O 3 and NO x data-base.
This equation is based on the fact that NO 2 acts as a major sink for the night-time O 3 [24]. Here the parameter β can be thought of as the reaction rate of O 3 with NO 2 . In our analysis, β is rather similar for all days of the week and its value is about 267 ppb 2 . The second parameter δ 2 has a value of 1.16 ppb. The theoretical value for the reaction rate of O 3 with NO 2 during nighttime is about 1250 ppb 2 [42][43][44]. Again, the deviations between β and the reaction rate of O 3 with NO 2 during nighttime can be explained by the occurrence of additional sinks of ozone, including surface reactions of particulate matter and deposition [24].

Conclusions
In this study, we suggested a simple statistical predictive model to calculate the steady-state daytime and nighttime O 3 concentrations at an urban coastal site. This model was formulated based on a modified approach of the null cycle of O 3 and NO x . The model evaluation was performed by utilizing a one-year data-base of ozone (O 3 ) and nitrogen oxides (NO and NO 2 ) measured in Jeddah, which is located on the west coast of Saudi Arabia. The steady-state conditions for O 3 and NO x at this site were observed during daytime (13:00-17:00) and nighttime (01:00-05:00).
The simple model for daytime concentrations was proposed to be linearly dependent on the concentration ratio of NO 2 to NO whereas that for the nighttime period it was suggested to be inversely proportional to NO 2 concentrations. Since the daytime O 3 concentrations on workdays (Saturday-Wednesday) were lower than those on weekends (Friday), two separate formulas were suggested for the daytime concentration predictions. Recalling the complex reactions involved in tropospheric O 3 formation, this proposed simple model provided reasonable predictions for the daytime and nighttime concentrations. Since the current description of the model is solely based on null cycle of O 3 and NO x , other precursors should be considered in future development of this simple model.
Our study could be applied to several urban environments with similar emission patterns, as well as fill the gaps in O 3 data when no measurements were collected. Our study could also serve as basis for future studies for enforcing strategies to control ground level O 3 concentrations, as well as its precursors' emissions in polluted environments.