Development of a two-box model

Figure 4.9 Spatial variations of intensities of segregation (in percentage) between (a) O₃ and NO; (b) OH and VOCs.

4.3.5 Development of a two-box model

The preliminary results from the LES model show the formation of two primary counter-rotating vortices (Figure 3.6) and the associated spatial variation of air pollution (Figure 4.1) in the deep street canyon (AR=2), providing the motivation to develop an alternative simplified two-box model. The averaged pollutant concentration in the lower box could be up to about 2 times than that in the upper box, which reflects the potential segregation effect by the counter-rotating vortices. In order to capture this significant concentration contrast, the deep street canyon is divided into two boxes with the corresponding vortex inside each box (Figure 3.6 and Figure 4.10) by using a plane at the level of z /H  (where  is the box height ratio determined by the flow structure with the street canyon;

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here  0.25). It is assumed that each vortex has sufficient intensity for the chemical species to be well-mixed within the corresponding box (Murena et al., 2011). The mass transfer between two adjacent boxes is expressed by the introduction of an ‘exchange velocity’. A one-box chemistry model has been previously adopted by Liu and Leung (2008) to study reactive pollutant dispersion in street canyons (AR=0.5, 1, 2), using the values of exchange velocities derived from LESs for different ARs. Because they treated the whole canyon as one well-mixed box for all ARs, their model was unable to reproduce the substantial contrasts of pollutant concentration between the lower and upper canyon as shown in Figure 4.1. In this study, a more complex box model (i.e. a two-box model) is adopted. The mathematical description of the two-box model (Figure 4.10) is as follows:

Figure 4.10 Sketch of the two-box model framework. C_i,L and C_i,U are the concentrations of i^th species in the lower and upper boxes, respectively; H_L^and H_U are the height of the lower and upper boxes, respectively; w_t,L is the exchange velocity between the lower and upper boxes, and w_t,U ^{is the} exchange velocity between the upper box and the overlying background atmosphere; and E_i,L ^{is the} emission rates of i^th species.

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Exchange velocities implemented into the two-box model are determined from the current

LES model by calculating the ventilation of a passive scalar, i.e.

U the flux between the upper box and the overlying background atmosphere and ‘ps’ denotes the passive scalar. The resulting values applied into the two-box model are 0.018 m s^-1 for

L

wt_, and 0.014 m s^-1 for w_t,U.

Figure 4.11 shows the time evolution of the volume averaged mixing ratios of NO, NO2, O₃, NO_x, O_x , OH and HO₂ calculated by the LES-chemistry model and the two-box model, respectively. Volume- and time-averaged (over the period of 180-240 min) mixing ratios

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in the lower and upper boxes derived from the LES-chemistry model and the two-box model are also listed in Table 4.2. In Figure 4.11, it is interesting that there are apparent fluctuations in the mixing ratios of chemical species (especially for NO and NO₂) inherent in the LES approach due to dynamically-driven variability of large scale eddies and unsteady ventilation caused by the two primary vortices in the canyon. It is observed that there are rapid changes in mixing ratios when the emissions are released into the street canyon at 30 min. Compared with the LES-chemistry model over the period of 180-240 min, the two-box model underestimates NO levels by about 5.25 % and 5.8 % for the lower and upper boxes respectively, but overestimates NO2 levels by about 8.47 % and 5.94 % for the lower and upper boxes respectively. Levels of O₃ derived from the two-box model are about 1.97 % and 1.83 % lower for the lower and upper boxes respectively than those derived from the LES-chemistry model. These differences are small, suggesting that the two-box approach performs pretty well compared with the “ture” LES-chemistry model. These results also indicate that segregation effects caused by incomplete mixing (i.e.

spatial inhomogeneity represented by the LES-chemistry model) reduce the conversion rate of NO to NO₂ through chemistry (dominated by NO and O₃ titration with an additional pathway through VOCs chemistry), which is consistent with negative values of intensities of segregation between NO and O₃, and between OH and VOCs (shown in Table 4.1). It is also observed that NO2/NO ratios in the two-box model are generally higher than those in the LES-chemistry model, i.e. about 14.47 % for the lower box and about 12.50 % for the upper box. Therefore, there are higher levels of O₃ and NO, but lower levels of NO₂ in the LES-chemistry model than those in the two-box model for both lower and upper boxes.

The LES-chemistry model has slightly higher levels of NO_x (about 1.59 % for the lower box and 1.69 % for the upper box) compared with the two-box model, which suggests that

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segregation effects slightly reduce the NOx loss rate to other species (e.g. HNO3 and HONO). This is also consistent with negative values of intensities of segregation between OH and NO₂, and between OH and NO (shown in Table 4.1). Lower levels of O_x are observed in the LES-chemistry model compared with the two-box model, i.e. about 7.89 % for the lower box and 5.15 % for the upper box. This indicates that segregation effects generally reduce the rate of oxidation chemistry for both the lower and upper boxes. It is observed that the two-box model slightly underestimates levels of both OH and HO2

(generally around 1%) compared with the LES-chemistry model. This may be explained as levels of OH and HO2 are rather lower within street canyons and their reactions with other chemical species are very fast. Segregation effects can reduce the rate for some of these chemical reactions, but increase the rate for others of these chemical reactions (indicated in Table 4.1). The total segregation effect may be slightly balanced by each other. In terms of general performance, the two-box model generally matches the LES approach in the mixing ratios for both the lower and upper boxes.

Table 4.2 Volume- and time-averaged (over the period of 180-240 min) mixing ratios in the lower and upper boxes derived from the LES-chemistry model (LES-RCS) and the two-box model (BOX-RCS), respectively.

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Figure 4.11 Time evolution of the volume averaged mixing ratios of (a) NO, (b) NO₂, (c) O₃, (d) NO_x and O_x, (e) OH and (f) HO₂ derived from the LES-chemistry model (LES-RCS) and the two-box model (BOX-RCS), respectively. ‘L’ represents the lower box while ‘U’ represents the upper box.

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