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

Abstract

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 NO_x 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 NO_x, 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.

1. Introduction

Tropospheric ozone (O₃) is known for causing severe health effects and having environmental impacts [1,2]. Among other photochemical oxidants, O₃ is one of the widely studied subjects worldwide under the category of air pollution. Besides that, O₃ 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 O₃ formation depends on photochemistry, meteorological conditions, and air mass transport [4,5,6,7]. For instance, O₃ 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 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 NO_x–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 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 O₃, we believe that the NO_x–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 NO_x (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 NO_x and VOCs, as well as the ratio of the two (NO_x/VOC) [18]. Accordingly, two regimes for O₃ 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 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 (Figure 2 and Figure 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 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 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 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.

2. Materials and Methods

2.1. Simple Statistical Predictive Model

In the troposphere, ozone (O₃) 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 (Figure 1, Figure 2 and Figure 3). As postulated in the introduction, the daytime steady-state 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.

2.2. Daytime Steady-State O₃ Concentrations Prediction

Under atmospheric conditions and in the presence of solar radiation (λ < 424 nm), the O₃–NO_x null cycle includes three successive reactions [37]:

$$\begin{gathered} N{O}_2+hv\to NO+O, \\ O+O_2+M\to O_3+M^{*}, \\ {O}_3+NO\to N{O}_2+O_2, \end{gathered}$$

(1)

where M is an inert ground state (either N₂ or O₂) 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 O₂ is assumed to be constant.

Under steady-state conditions, the null cycle has the steady-state formula,

$$\frac{J_{N{O}_2}}{k_3}=\frac{\left[NO\right]\left[O_3\right]}{\left[N{O}_2\right]} ,$$

(2)

where J_NO2 is the rate coefficient of NO₂ photolysis, k₃ is the reaction rate coefficient of O₃ and NO. It is well known that the k₃ is temperature dependent [38]; k₃ = 3.23 exp(−1430/T) in units of ppb⁻¹min⁻¹. However, the seasonal temperature variation is few degrees; and therefore, we do not expect k₃ to have a considerable variation throughout the year in Jeddah.

Re-arrangement of Equation (2) yields a simple equation to predict the concentration of O₃ from the ratio of NO₂ to NO concentrations during daytime,

$$\left[O_3\right]= \alpha \frac{\left[N{O}_2\right]}{\left[NO\right]}+ {\delta }_1,$$

(3)

where αis a constant equivalent to J_NO2/k₃ and δ₁(ppb)is also constant related to the background O₃ concentrations (e.g., migrates from the stratosphere to the troposphere, long-range transport, product of other reactions).

During daytime steady-state, using Equation (1):

$$\frac{d\left[N{O}_2\right]}{dt}=-J_{N{O}_2}\left[N{O}_2\right]+k_3\left[O_3\right]\left[NO\right]=0,$$

(4)

Upon rearranging we get Equation (2). We then compute a linear regression of [O₃] vs. [NO₂/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/k₃ and b is also constant related to the background O₃ concentrations.

2.3. Nighttime Steady-State O₃ Concentrations Prediction

During night-time hours, O₃ is mainly consumed through its reaction with NO₂,

$$O_3+N{O}_2\to N{O}_3+O_2,$$

(5)

Applying reaction rate kinetics and rearrangement of the Equation (4) yields a simple equation to predict the nighttime O₃ based on the concentration of its major nighttime sink compound NO₂,

$$\left[O_3\right]=\beta \frac{1}{\left[N{O}_2\right]}- {\delta }_2,$$

(6)

where β(ppb²) is a constant equivalent to the reaction rate of O₃ with NO₂ and δ₂(ppb) is again a constant related to the background O₃ concentrations during the night.

During nighttime, Equation (4) steady state conditions are:

$$\frac{d\left[O_3\right]}{dt}=k_{\left(N{O}_2,O_3\right)}\left[O_3\right]\left[N{O}_2\right]=0,$$

(7)

Upon rearranging we get Equations (6) and (7). We then compute a linear regression of [O₃] vs. [NO₂] 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 O₃ with NO₂) and b is again a constant related to the background O₃ concentrations.

2.4. Data-Base

In this study, we utilized a one-year data-base of O₃ 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 O₃ 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 O₃ precursors; under favored meteorological conditions and abundance of solar radiation, which are available in Jeddah.

3. Results

3.1. Overview of the Daily Patterns

The O₃ 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 O₃ 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 O₃ formation by altering the NO_x cycle mechanism through reactions of hydroxyl radicals, which in turn oxidize NO without the use of O₃. The latter, along with the photolysis of NO₂, leads to accumulation of O₃ during the daytime on weekends. Furthermore, when NO_x concentrations are high, the reaction of NO₂ and OH to give HNO₃ is favored [17], which reduces the NO₂ concentrations available for photolysis. In turn, this leads to low photolysis rate J_NO2 during the weekends.

Recalling Equation (2), the daily pattern of J_NO2/k₃ (represented by the concentrations ratio [O₃][NO]/[NO₂]) 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, k₃ 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 NO₂ 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]. The reason could be also referred to the change of both the [NO]/[NO₂] ratio and the O₃ concentration (‘weekend effect’). As shown in Figure 5, the daytime value of [NO]/[NO₂] is higher on workdays than on weekends.

3.2. Prediction of Steady-State O₃ Concentration

As shown in Figure 1, Figure 2 and Figure 3, regarding the daily pattern of O₃ 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 O₃ concentration prediction for the daytime period according to Equation (3) is best represented by:

$${\left[O_3\right]}_{\mathrm{daytime}}=\{\begin{array}{cc}1.09\frac{\left[N{O}_2\right]}{NO}+29.35& Workdays \left(R^2=0.37\right) \\ 0.50\frac{\left[N{O}_2\right]}{NO}+35.47& Weekends \left(R^2=0.31\right)\end{array}$$

(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 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 J_NO2/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 J_NO2/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 J_NO2 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 J_NO2/k₃. Note that the kinetic model represents the ideal case, when the concentration of O₃ depends solely on the NO_x–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 stratosphere-troposphere 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,

$${\left[O_3\right]}_{nighttime}=\frac{267.01}{\left[N{O}_2\right]}+1.16 All days\left(R^2=0.58\right)$$

(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 NO_x 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 ppb². 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 ppb² [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].

4. Conclusions

In this study, we suggested a simple statistical predictive model to calculate the steady-state daytime and nighttime O₃ concentrations at an urban coastal site. This model was formulated based on a modified approach of the null cycle of O₃ and NO_x. The model evaluation was performed by utilizing a one-year data-base of ozone (O₃) and nitrogen oxides (NO and NO₂) measured in Jeddah, which is located on the west coast of Saudi Arabia. The steady-state conditions for O₃ 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 NO₂ to NO whereas that for the nighttime period it was suggested to be inversely proportional to NO₂ concentrations. Since the daytime O₃ 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 O₃ 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 O₃ 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 O₃ data when no measurements were collected. Our study could also serve as basis for future studies for enforcing strategies to control ground level O₃ concentrations, as well as its precursors’ emissions in polluted environments.