Possible high COVID-19 airborne infection risk in deep and poorly ventilated 2D street canyons

Despite the widespread assumption that outdoor environments provide sufficient ventilation and dilution capacity to mitigate the risk of COVID-19 infection, there is little understanding of airborne infection risk in outdoor urban areas with poor ventilation. To address this gap, we propose a modified Wells-Riley model based on the purging flow rate (QPFR), by using computational fluid dynamics (CFD) simulations. The model quantifies the outdoor risk in 2D street canyons with different approaching wind speeds, urban heating patterns and aspect ratios (building height to street width). We show that urban morphology plays a critical role in controlling airborne infectious disease transmission in outdoor environments, especially under calm winds; with deep street canyons (aspect ratio > 3) having a similar infection risk as typical indoor environments. While ground and leeward wall heating could reduce the risk, windward heating (e.g., windward wall ~10 K warmer than the ambient air) can increase the infection risk by up to 75%. Our research highlights the importance of considering outdoor infection risk and the critical role of urban morphology in mitigating airborne infection risk. By identifying and addressing these risks, we can inform measures that may enhance public health and safety, particularly in densely populated urban environments.


Introduction
The coronavirus disease (COVID-19) pandemic caused by the SARS-CoV-2 virus has threatened lives and livelihoods globally.As of February 6th, 2023, the World Health Organization reported over 750 million confirmed cases globally, along with more than 6.8 million associated fatalities (WHO 2023).In terms of disease transmission, scientific evidence suggests the airborne transmission route plays a significant role in the spread of COVID-19 (Cheng et al. 2022), and the current understanding of the COVID-19 pandemic suggests that indoor spaces with poor ventilation, such as in religious events, restaurants, and public transport (James et al. 2020;Li et al. 2021;Cheng et al. 2022), are the main contributors to virus transmission.
There is a general consensus in the literature that airborne transmission risk in outdoor places is low primarily due to sufficient ventilation, adequate physical distancing between people and limited exposure time (cf.indoor environments) (Bulfone et al. 2021).However, outdoor locations are affected by transient atmospheric conditions of variables (e.g., wind speed, temperature and relative humidity), which are known to play an essential role in airborne transmission risk (Bourouiba 2020).The effectiveness of ventilation in reducing the concentration of airborne particles and the associated infection risk depends on various factors, including wind and buoyancy-driven ventilation (Mei and Yuan 2022).The ventilation rate and pattern, however, are not uniform among outdoor locations due to the complex and diverse urban morphologies that  5)-( 8) N number of data points [-], Eqs. ( 12)-( 13) nMAE normalised mean absolute error [-], Eq. ( 14) nMBE normalised mean bias error [-], Eq. ( 16) nMSE normalised mean squared error [-], Eq. ( 15) O i observed wind tunnel values [-], Eqs. ( 12)-( 16) P pressure [Pa], Eq. (2) P i simulations predicted values [-], Eqs. ( 12)-( 16) P indoor indoor infection risk [%], Eq. ( 9) P outdoor outdoor infection risk [%], Eq. ( 10 exist in different regions (Qin et al. 2020;Xiong and Chen 2022).As a result, the infection risk associated with outdoor spaces remains largely unknown, particularly in densely populated urban environments where high-rise buildings can significantly reduce wind dilution capacity (Chen et al. 2021).
While outdoor infectious transmission is considered generally low-risk, some studies suggest possible COVID-19 transmission at outdoor locations (e.g., jogging tracks, parks, and construction sites) (Leclerc et al. 2020;Qian et al. 2021).Although the exact infection location is inconclusive, outdoor places are expected to be open with greater wind speeds than indoors.However, urban canyons with buildings on both sides of a street are both common (Nicholson 1975) and known to have high concentrations of airborne material linked to the sources, airflow and dispersion patterns inside (Wang et al. 2011;Fan et al. 2022;Zheng et al. 2022).As canyons have different street widths and building heights, many combinations occur creating complex, flow and dispersion patterns within (Li et al. 2006;Tominaga and Stathopoulos 2013).Understanding how such complex urban flows could impact infectious disease transmission is still limited.
Recent studies focus on droplet transmission dynamics inside a 2D street canyon under different wind speed and relative humidity conditions, but quantitative assessment of the associated risk is not provided (Fan et al. 2022).Within street canyon recirculation patterns are influenced by the approach wind speed and people's thermal plumes.These are believed to be crucial factors for droplet dispersion inside the canyon, but the impact of building height to street width ratio (aspect ratio) has not been examined (Yang et al. 2021a).Solar radiation heating of building walls and ground heating can significantly impact ventilation and recirculation within street canyons (Yang et al. 2021b), but has not been addressed in studies (Fan et al. 2022).
Currently, no research explores the relationship between urban morphology and infection risk.This is needed to inform the development of infection-resilient urban design and planning strategies.To fill this gap, our study combines the Wells-Riley model and computational fluid dynamics (CFD) simulations to evaluate the risk of outdoor airborne infections within 2D urban street canyons.We propose a model to provide an understanding of airborne infection risk patterns across varying aspect ratios, wind velocity and urban heating.To provide context, we compare our findings to typical indoor environments, where there is an established understanding of the relationship between ventilation and airborne transmission risk.

Governing equations for CFD simulations
The airflow within the 2D street canyon is characterized as non-isothermal, and the associated buoyancy effects resulting from wall/ground heating are taken into account.The time-averaged quantities are computed using the Reynolds-averaged Navier-Stokes equations (RANS) with the RNG k-ε turbulence model.The commercial CFD software Ansys Fluent v18.1 is employed in this work (Ansys 2017).
The velocity, concentration and thermal fields are described by the mass continuity, momentum, scalar, and energy equations (Ansys 2017): where the overbars (  ) denote the average and primes ( ¢  ) represent the unresolved turbulence quantities.The Reynolds stress tensor ij uu ¢¢ is modelled based on the Boussinesq hypothesis as a function of the mean velocity gradients and closure is obtained by the RNG k-ε turbulence model, which provides equations for the turbulent kinetic energy k and turbulent kinetic energy dissipation rate ε (Ansys 2017): where the model parameters are , and u 2 and u 1 are the parallel and perpendicular velocity components related to the gravitational vector, respectively (Ansys 2017).The turbulent kinetic energy production due and the generation of turbulence by buoyancy is , where Pr t is the turbulent Prandtl number for energy.
The second-order upwind scheme is employed to solve all variables and pressure and velocity equations are coupled by using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) scheme for coupling pressure and velocity.The under-relaxation factors for the pressure term, momentum term, k, ε and energy terms are 0.3, 0.7, 0.8, 0.8 and 1, respectively.Convergence is considered to be achieved for residuals under 10 −8 for all variables.

Computational domain and boundary conditions
This study models a 2D domain with a single street canyon oriented perpendicular to the approaching wind direction, and it is located within an urban boundary layer (Figure 1(a)).We select a 2D street canyon as it represents a worst-case scenario in the context of canyon ventilation (Chen et al. 2021) and can be found widely in most European cities. Full-scale dimensions are used with street width W = 10 m that remains constant for all simulations.However, the building height (H) changes, and the aspect ratio is therefore modified to represent different cases.The model domain width is of 3W and the height of 5W + H (see Figure 1(a)), which satisfies the best practice requirements in urban wind CFD simulation (Tominaga et al. 2008).
The 2D computational domain is discretized into rectangular cells inside the canyon and above the building top, as shown in Figure 1(b).A constant square grid size of 0.1 m × 0.1 m is used inside the canyon, while the grid size increases with an expansion rate of 1.02 above the canyon.
The enhanced wall function is employed to model the buoyancy effects caused by wall heating, as described in previous studies (Lin et al. 2016;Yang et al. 2021c).The first cell is placed at a distance of 1 mm from the wall to ensure that the viscous sublayer is properly modelled, with a dimensionless wall distance y + < 5.At the domain inlet, the velocity profile from a wind tunnel model (Allegrini et al. 2013) is used, with u ref set at the domain top (y = 5W + H).Arbitrary initial conditions for turbulent kinetic energy (TKE) and TKE dissipation rate are set assuming 10% intensity and a turbulent length scale of 1 m.The canyon ground, walls and roofs are defined with no-slip condition (stationary wall) and zero normal gradient is imposed at the top and outlet (outflow) (Figure 1(a)).Heated facets are given a constant temperature, which is higher than the non-heated facets (e.g., roof) set as adiabatic.

Infection risk model
The Wells-Riley model is used to quantify airborne infection, where quanta account for the number of infectious airborne particles needed to infect a person (Wells 1934).The inhalation of a quantum corresponds to a probability of infection of 63% (1 − 1/e) and the quantum generation rate is a combination of pathogen infectivity and the infectious source strength in the outbreak.The model (Eq.( 9)) considers transmission only through airborne infectious particles and assumes a spatially and temporally uniform distribution of pathogen-laden aerosols in the indoor space: indoor 1e x p where P indoor is the indoor infection risk, I is the number of infectors [person], p is the pulmonary ventilation rate [m 3 s −1 ], q is the quanta generation rate [quanta (s person) −1 ], t is the exposure time interval [s], Q is the room ventilation rate with clean air [m 3 s −1 ].The model, first used to understand a measles outbreak (Riley et al. 1978), is now widely used for airborne infection risk assessment (Andrews et al. 2013;Zhang et al. 2018;Kurnitski et al. 2021;Wang et al. 2022).
Indoor infection risk has been calculated for many typical scenarios e.g., educational settings, retail stores, offices and restaurants (Shen et al. 2021).A minimum air ventilation rate (Q min ) can be determined based on floor (ground) area and location (indoor) occupancy, following the ASHRAE 62.1 standard (ASHRAE 2007), which represents the minimum ventilation rate required to maintain good indoor air quality.The ventilation rate factor γ is calculated as Q/Q min to determine the ventilation efficiency from the minimum ventilation required for each space, and it could vary in our calculations (see Figure 9).Table 1 summarises the input parameters used in the indoor scenarios risk assessment., where the latter is held constant (W = 10 m).The boundary conditions for the inlet (blue line), top (yellow) and outlet (red), with prescribed uniform tracer emission rate (Sc) at pedestrian level (blue area).Within the canyon, there is (b) a constant grid size (0.1 m), above there is an expansion rate of 1.02, and near-wall refinement with y + < 5 (dashed red box).The reference height (at uref) is for both windspeed and the ambient air temperature from which the ΔT values are assigned Tabl e 1 Dimensions for typical indoor spaces (Shen et al. 2021) used with Eq. ( 9) to assess the indoor infection risk (Pindoor) Here, we modify the Wells-Riley model (Eq.( 9)) to assess outdoor infection risk in street canyons, by using a purging flow rate (Q PFR ) to represent ventilation in the urban environment: Although many indices exist to quantify urban ventilation and pollutant dilution capacity (Peng et al. 2020), Q PFR can assess dilution capacity and pollutants removal for a whole area (Hang et al. 2015).The index gives the effective ventilation rate and is independent of the tracer emission rate and can be determined by Eq. ( 11) (Bady et al. 2008 where S c is tracer emission rate [kg (m 3 s) −1 ], V is the volume [m 3 ] into which the tracer gas is homogeneously emitted, and <> c is the spatial and temporal mean concentration [kg m −3 ] in volume V (see list of symbols for notations used in this study).Here, in our CFD set-up, we use a tracer gas (carbon monoxide, CO) emitted uniformly within the pedestrian space (y = 0 → 2 m, Figure 1), with S c set to 10 −7 kg (m 3 s) −1 to ensure little disturbance to the flow (Hang et al. 2015).The use of Q PFR [m 3 s −1 ] as a ventilation index is reasonable since Wells-Riley equations assume well-mixed air and a steady-state infectious particle concentration which is determined by ventilation rate.Larger Q PFR values indicate more effective ventilation and lower infectious aerosol concentration in the pedestrian zone.
The approaching air (at u ref ) temperature is kept constant at 293.15 K and the non-heated facets have a zero-heat flux.Temperature differences of 9-14 K have been observed in street canyons in the summertime in both France (Idczak et al. 2007) and Greece (Santamouris et al. 1999), and have been used as maximum values in previous 2D CFD modelling studies (Hang et al. 2020;Yang et al. 2021c).The parameters used in the different simulation cases (for each AR) are listed in Table 2, including u ref and ΔT alongside the respective total grid cells.

Results and discussion
3.1 Grid sensitivity and numerical model evaluation  turbulent kinetic energy (TKE) for the current simulation using medium grid and wind tunnel observations (Allegrini et al. 2013) in the centre of the canyon (inset) for a street canyon with AR = 1 (Ding et al. 2019;Fan et al. 2022).The discrepancy is probably due to RANS's turbulent viscosity tendency to overpredict the mean and underpredict the fluctuations and its poorer ability to predict separated shear flows (cf.high-order models) (Blocken 2018).
In addition to the qualitative analysis based on Figure 4, the accuracy of the simulation results is quantitatively estimated using common metrics used in similar CFD studies (Schatzmann et al. 2010;Hood et al. 2021;Zhang et al. 2022).
(1) Factor-of-2 of observations (FAC2):  () where N is the number of data points and W a (= 0.05) is the allowed absolute deviation, P the mean of the simulation's values, O is the mean of the wind tunnel observations (Allegrini et al. 2013) and i the individual values.Table 3 presents the calculated values of evaluation metrics for velocity (u) and turbulent kinetic energy (TKE) alongside the acceptable criteria.This study adopts the following criteria: FAC2 > 0.5, nMSE <1.5, and R > 0.8 as recommended by previous studies (Chang and Hanna 2004;Moonen and Allegrini 2015).The normalized mean squared error (nMSE) is 0.148 for velocity with little underestimation (nMBE < 0.200) in the vertical region of 0.2 < y/H < 0.4. the nMSE = 1.409 for turbulent kinetic energy, which is slightly below the acceptable criteria (nMSE < 1.5), but still consistent with other similar CFD studies (Di Sabatino et al. 2011).These combined metrics provide further confidence

Impact of street canyon aspect ratio and approaching wind speed
The impact of aspect ratio (AR) on the purging flow rate (Q PFR ) and the resultant infection risk is investigated while keeping a constant wind speed at the top of the canyon (e.  infection risk (P outdoor ).The risk decreases consistently with increasing u ref (Figures 5(a)-(c)), indicating an approximately 10-fold decrease in the Q PFR inside the canyon for most cases from u ref = 4 m s −1 to 0.5 m s −1 (e.g., Q PFR decreases from 0.465 m s −1 to 0.045 m s −1 for AR = 1).This decrease in the Q PFR may be accentuated for deeper canyons (AR > 3) due to the formation of multiple vortex patterns inside the canyon (Figure 5(f)) and can reach 20-fold for AR = 4. Table 4 shows Q PFR and P outdoor simulated for different aspect ratios (AR) and approaching wind speeds (u ref ) for the isothermal case.

Impact of individual facet heating
In non-isothermal conditions, the local buoyancy as well as the approaching wind speed magnitude have an impact on the airflow inside a street canyon.For a street canyon with AR = 1 and u ref = 2 m s −1 , we consider three different heated facets: ground, leeward and windward wall.Figure 6 shows that there is a gradual increase in Q PFR as the buoyancy increases for the heated ground and leeward cases, indicating an improvement in the canyon ventilation (cf.isothermal case) leading to reduced infection risk.The infection risk reduction can be up to 27.4% and 24.1%, for a temperature difference of 10 K between approaching airflow and ground and leeward walls, respectively.These heating patterns accelerate vortex rotation via buoyancy-assisted wind-driven flow (Cai 2012;Mei and Yuan 2022).Whereas the vortex rotation is suppressed due to the thermally driven flow opposing the downwash flow from the canyon top generated from the windward wall heating (Buccolieri et al. 2022), potentially leading to poorer in-canyon ventilation and higher infection risk (i.e., 0.5% for windward heating and 10 K temperature difference).
Tabl e 4 QPFR and Poutdoor for street canyons with different aspect ratios (AR) and approaching wind speeds (uref) for the isothermal case  For a canyon with AR = 1 and a u ref = 2 m s −1 , increasing the temperature of the ground and leeward facets (from 2 to 10 K) results in a slightly stronger inner recirculation (Figure 7).Similarly, when the windward wall is heated by 5 K (cf.approaching airflow temperature) the buoyancy force is insufficient to disrupt the predominant skimming flow, leading to a slightly lower Q PFR (cf.0 K case).However, the upward buoyancy force predominates (cf.downward airflow) when the windward wall temperature difference is ΔT = 10 K (Lin et al. 2016), disrupting the usual canyon vortex (Figure 7(i)) and decreasing Q PFR considerably.Although there is little change in outdoor risk for heated windward case ΔT from 0 to 5 K, the infection risk increases by 75% inside the canyon when ΔT =10 K (Figure 6).
There is a more noticeable reduction in the infection risk for all heated facets for a canyon with AR = 5 and a u ref = Fig.7 Flow field and streamlines for a street canyon with AR = 1 and approaching wind speed of 2 m s −1 with different heated facets (a-c) ground, (d-f) leeward and (g-i) windward, with temperature differences higher than the approaching airflow temperature of (a, d, g) 2 K, (b, e, h) 5 K and (c, f, i) 10 K 2 m s −1 (Figure 8(a), cf.canyon with AR = 1, Figure 6).The reduction in risk is due to the increased relative buoyancy force, which offsets the weakened airflow near the ground.Increasing the facet's temperature from 0 to 2 K compared to the airflow temperature leads to a stronger inner recirculation and lower infection risk.When the ground is heated with a temperature difference of ΔT = 10 K, a multi-vortex flow structure is formed inside the canyon (Figure 8(b)), which traps aerosol particles near the ground and decreases the removal capacity.As a result, the infection risk is greater when the ground is heated (cf.heated leeward and windward facets).Although street canyons with AR = 5 have a higher infection risk than with AR = 1, the latter is very common in cities (Nicholson 1975) and windward wall heating can increase infection risk for pedestrians walking in these areas, which is relevant to public health considerations.

Comparison to indoor risk
For the infection risk in indoor spaces, we evaluated five different indoor spaces with varying levels of ventilation rate factor (γ = Q/Q min ) ranging from poorly ventilated (γ = 0.5) to well-ventilated (γ = 2).Our results indicate that dormitory rooms have the highest risks, while auditoriums and approaching wind speed of 2 m s −1 (a) with four temperature differences (ΔT = 0, 2, 5, and 10 K, colours).The plots below are the flow field and streamlines for (b) ground, (c) leeward and (d) windward, with temperature differences higher than the approaching airflow temperature of 10 K have the lowest risks with P indoor = 21.46% and 0.05%, respectively, when γ = 1 (Figure 9).This difference can be mainly attributed to the variations in floor area and volume of the indoor spaces (see Table 1).Although auditoriums may have more occupants than other indoor spaces, they also present higher maximum ventilation rates, which leads to lower risks in these locations.
When considering outdoor cases, Figure 9 shows that the infection risk can be as high as 30.6% for a street canyon with AR = 5 when the approaching wind speed (u ref ) is 0.5 m s −1 .This risk level is comparable to dormitory rooms with very poor ventilation.For AR = 4, the risk is 11.46%, which is similar to the risk levels found in typical indoor locations such as open offices or fast-food restaurants (Figure 9).Therefore, our results demonstrate that deep canyons may pose a significant risk to individuals engaging in outdoor activities, especially on calm wind days, and can be comparable to typical indoor spaces in terms of infection risk.However, the outdoor risk decreases considerably for lower aspect ratios, reaching 2.65% for a street canyon with AR = 3 with approaching wind speed equal to 0.5 m s −1 (see Table 4).These results have important implications for public health and urban planning and suggest the need for effective measures to mitigate the risk of airborne transmission in outdoor settings.

Limitations of this study
We follow best practices for CFD simulations and for methodological assumptions but limitations still could affect the results:  Two-dimensional (2D) modelling can accurately represent street canyon airflow and aerosol dispersion features if the approaching wind speed is perpendicular to the street axis (Zheng et al. 2021).This situation typically has the poorest dispersion because the ventilation capacity increases with oblique wind directions (Zhang et al. 2016;Jon et al. 2023).It is important to consider worst-case scenarios in risk assessments.However, 2D simulations will not capture the 3D wind field, such as lateral wind circulation around a 3D urban structure (Mei et al. 2019).Hence, it is recommended future studies include 3D simulations with different wind directions. This study has focused on ventilation as a means of controlling and removing infectious particles from outdoor environments.However, it is worth noting that other processes can also contribute to the removal of these particles, including droplet deposition on surfaces such as the ground and building walls, ultraviolet (UV) radiation and precipitation (Jones et al. 2021;He et al. 2022).
Further studies should assess the individual importance of these processes. Whilst we analyse the impact of the bulk ventilation capacity on the infection risk, other in-canopy elements, such as traffic, can affect the flow and dispersion patterns of infectious particles, and hence, the interpersonal transmission.This effect can be especially pronounced at low wind speeds when car movement can create a piston effect (Zheng and Yang 2022). The Wells-Riley model is widely used for estimating the risk of airborne infectious disease transmission.However, this model assumes well-mixed conditions, which may not accurately reflect the complex and dynamic airflow patterns that occur in outdoor environments.While acknowledging this limitation, the Wells-Riley model can still provide valuable insights and contribute to the understanding of infectious disease transmission in urban environments.

Conclusions
In this study, the outdoor risk of airborne infection is investigated by using the Wells-Riley model and CFD simulations of 2D urban street canyons under various conditions of aspect ratios, wind velocities and urban heating patterns.The results we report contradict the general view that outdoor spaces are safer zones compared to indoors with plentiful ventilation and dilution capacity.Although shallow street canyons may not represent a high outdoor infection risk, deep and poorly ventilated street canyons could pose a high COVID-19 infection risk.Street canyons with AR > 3 have a similar COVID-19 infection risk as that in poorly ventilated indoor spaces.The infection risk can be reduced through local heating of ground and leeward walls, which improves in-canyon ventilation.However, the infection risk may increase by 75% when the windward wall is heated up to 10 K compared to ambient air.In these cases, passive ventilation enhancers, such as void decks (Chew and Norford 2018), could be an effective method to mitigate flow stagnation near the ground within deep canyons and potentially reduce the risk.
This study focuses on the often-overlooked outdoor infection risk.We highlight the critical need for a comprehensive understanding of factors influencing the transmission of airborne infectious diseases in urban environments.Our findings demonstrate outdoor infection risk should not be overlooked, and that urban morphology is a significant factor in the control and mitigation of outdoor airborne infectious disease transmission.Prediction of outdoor environments infection risk can inform decisionmaking and promote public health and safety.Public health officials, event planners, employers, city planners, and individuals can use our proposed model to assess disease transmission risk and take appropriate measures to protect the community.Further research and development of this tool are warranted to enhance our understanding of outdoor environment infectious disease transmission and to improve our ability to prevent and control disease outbreaks.

Fig. 1
Fig.1Model simulation setup uses a (a) 2D street canyon (e.g., shown AR = 1.5) with domain size specified by height (H) and width (W), where the latter is held constant (W = 10 m).The boundary conditions for the inlet (blue line), top (yellow) and outlet (red), with prescribed uniform tracer emission rate (Sc) at pedestrian level (blue area).Within the canyon, there is (b) a constant grid size (0.1 m), above there is an expansion rate of 1.02, and near-wall refinement with y + < 5 (dashed red box).The reference height (at uref) is for both windspeed and the ambient air temperature from which the ΔT values are assigned

Fig. 2
Fig. 2 Three non-isothermal cases prescribed by temperature differences (ΔT) between the facet and ambient air at uref (held constant at 293.15 K): (a) ground (b) windward wall and (c) leeward wall

Figure 3
Figure3shows the grid sensitivity tests undertaken for three grid sizes namely coarse (W/50), medium (W/100) and fine (W/160).The grid sensitivity is assessed by comparing the vertical profile of normalized velocity along two locations at x = 0.33W and 0.66W away from the leeward wall.Qualitative analysis suggests a medium grid size of 0.1 m provides greater computational efficiency (cf.fine grid) without losing accuracy, and higher accuracy results (cf.coarse grid), and is therefore chosen for all the CFD simulations.Comparison of CFD simulations and wind tunnel measurements of normalized velocity u and TKE profiles along the canyon centreline(Allegrini et al. 2013) have good agreement (Figure Notably, for the u profiles between y = 0.2H to 0.8H (Figure 4(a)), but the model underestimates for y < 0.2H and slightly overestimates for y > 0.8H.The simulated TKE profile for y < 0.4H more evidently underestimates (Figure 4(b)), but beyond that, there is good agreement with experimental data.The result is consistent with prior street canyon ventilation CFD studies

Fig. 4
Fig.4Vertical profiles of (a) normalized velocity (u) and (b) turbulent kinetic energy (TKE) for the current simulation using medium grid and wind tunnel observations(Allegrini et al. 2013) in the centre of the canyon (inset) for a street canyon with AR = 1 Pearson correlation coefficient (R): Normalised mean bias error (nMBE):

Tabl e 3
Assessment metrics for velocity (u) and turbulent kinetic energy (TKE) with their ideal values and acceptable criterion g., u ref = 0.5 m s −1 , Figure 5(a)).Deeper canyons, which have larger AR or taller buildings (Figures 5(e)-(f)), experience slower wind speeds near the ground due to the above canyon flow taking longer to reach the ground.This reduces both dilution rates and the removal capacity of infectious aerosols.Overall, the Q PFR decreases with the increase of AR, but the outdoor infection risk increases sharply for street canyons with AR ≥ 3, indicating significantly lower near-ground ventilation capacity in deeper canyons compared to shallower canyons (Figures5(a)-(c)).The risk can be relatively low (< 5%) for street canyons with AR < 4, suggesting a similar single vortex pattern (Figures5(d)-(e), cf.Figure5(f)) inside the canyon promoting similar dilution capacity.However, the risk can be as high as 30% inside deeper canyons with AR = 5 under low wind speeds (u ref = 0.5 m s −1 ), suggesting that deeper canyons are more vulnerable to outdoor infection risk.The approaching wind speed (u ref ) has a significant impact on both the purging flow rate (Q PFR ) and the outdoor

Fig. 8
Fig. 8 QPFR (lines) and Poutdoor (bars) for street canyon with AR = 5 and approaching wind speed of 2 m s −1 (a) with four temperature differences (ΔT = 0, 2, 5, and 10 K, colours).The plots below are the flow field and streamlines for (b) ground, (c) leeward and (d) windward, with temperature differences higher than the approaching airflow temperature of 10 K

Fig. 9
Fig.9Infection risk for indoor (dashed black, see Table1for parameters) and outdoor street canyons with different AR under isothermal flow (colour) Table 1 for parameters) and outdoor street canyons with different AR under isothermal flow (colour)