Wind direction and cool surface strategies on microscale urban heat island

Urban Climate 31 (2020) 100548

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Wind direction and cool surface strategies on microscale urban heat island

T

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Sushobhan Sen , Jeffery Roesler Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL 61801-2352, United States of America

ABS TRA CT

The Urban Heat Island (UHI) effect, defined as the temperature difference between urban and rural areas, is caused by the increased absorption and storage of solar energy by artificial surfaces as compared to natural vegetation. In addition to surface material, the urban form and wind direction also affect the UHI intensity. A model was developed to study the effect of various cool surface strategies on the microscale UHI intensity for hypothetical urban blocks in Chicago, USA. The statistically warmest hour of the year was analyzed for eight wind directions, whose probabilities were obtained from existing climatic data. Pavements, walls, and roofs with high albedo and high diffusivity had the lowest UHI intensity, approximately 0.05∘C above the mesoscale intensity, while those with low albedo and low diffusivity had the greatest increase of about 0.6∘C. The UHI intensity varied with spatial location within the urban area because of constricted airflow. The UHI intensity of an urban canyon averaged over the probability of wind blowing from different directions, was found to have a strong correlation (R = 0.94) with the probability that it is an interior canyon that experiences lower wind speed on account of turbulent dissipation.

1. Introduction The Urban Heat Island (UHI) effect leads to higher temperatures in cities as compared to adjoining rural areas. It has been observed in hundreds of cities across the world (Peng et al., 2011; Tran et al., 2006; Estoque et al., 2017; Zhou et al., 2015). The UHI can be examined in terms of the temperature difference between urban and rural areas (called the UHI intensity, ΔTur) at three levels: Surface UHI (SUHI), which is the difference between surface temperatures; Canopy Layer UHI (CLUHI), which is the difference between temperatures at about 2 m above the ground; and Boundary Layer UHI (BLUHI), which extends several kilometers above the ground. This paper focuses on the CLUHI, which Oke (Oke, 1976) showed depends on the local microscale features of the urban area, such as urban form and materials. The canopy layer is important for cities as it is where most human outdoor activity takes places. Oke (Oke, 1982) explained the UHI effect in terms of differences in heat fluxes between urban and rural areas, with urban areas typically absorbing and storing more sensible heat than rural areas. He further showed that the UHI intensity increases as the population of the city increases, while UHI intensity decreases as wind speed increases (Oke, 1973). These have been confirmed by more recent studies as well (Kotharkar and Surawar, 2015; Ward et al., 2016; Bokaie et al., 2016; Li et al., 2016; Wang et al., 2019). Kleerekoper et al. (Kleerekoper et al., 2012) listed seven features of urban areas that lead to a higher temperature in them. Two of these were the increased absorption and storage of solar radiation because of the widespread use of construction materials, and lower wind speed in urban canyons due to turbulent dissipation of the kinetic energy of wind. Through extensive data collection in Portland, USA, Hart and Sailor (Hart and Sailor, 2009) further showed that the UHI intensity varied within a city, depending on local Land Use/Land Cover (LULC) patterns, urban form, and materials. Levermore et al. (Levermore et al., 2018) concluded the increased used of construction materials was the main cause for the increasing UHI effect in Manchester, UK.

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Corresponding author. E-mail addresses: [email protected] (S. Sen), [email protected] (J. Roesler).

https://doi.org/10.1016/j.uclim.2019.100548 Received 19 April 2019; Received in revised form 8 October 2019; Accepted 24 October 2019 2212-0955/ © 2019 Elsevier B.V. All rights reserved.

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Pavements cover a significant fraction of urban areas. For example, a study in Sacramento, USA determined that roads, parking lots, and sidewalks cover between 29% to 68% of the plan surface area of different parts of the city (Akbari et al., 2003). Another study investigated the contribution of pavements to the UHI (Golden, 2006) in Phoenix, USA and found that pavements play a signficant role in influencing the surrounding air temperature, with both solar reflectance (albedo) and thermal properties affecting it. Several studies, summarized by Santamouris (Santamouris, 2013), Aleksandrowicz et al. (Aleksandrowicz et al., 2017), and Qin (Qin, 2015), have recommended the use of cool pavements, which have a higher albedo than typical pavements, to mitigate UHI intensity in cities. Others (Gui et al., 2007; Sen and Roesler, 2017a) have shown that increasing the thermal diffusivity of the pavement could also decrease the peak surface temperature by conducting heat away from the surface. This lowers surface temperatures, leading to a cooler air temperature and reducing the UHI intensity. Similarly, other studies have recommended the use of cool roofs and walls (Akbari and Kolokotsa, 2016; Razzaghmanesh et al., 2016; Taleghani, 2018; Morini et al., 2018) for mitigating UHI. In addition to wind speed and surface temperature, wind direction also affects UHI intensity in different parts of a city. Gedzelman et al. (SD Gedzelman et al., 2003) investigated the mesoscale UHI effect in New York City, USA and showed that the UHI intensity varies with season and direction of the wind, as wind coming from land tends to be warmer than that blowing from the sea. At a microscale, Nakamura and Oke (Nakamura and Oke, 1988) and Oke (Oke, 1988) showed that the direction of wind flow in a city establishes different currents within urban canyons, which leads to varying air temperatures. Golany (Golany, 1996) showed that the urban form can affect the distribution of wind speed and direction within a city and therefore, each city needs to be modeled to understand its unique microscale wind flow characteristics. Wong et al. (Wong et al., 2010) mapped ‘ventilation corridors' in the dense urban environment of Hong Kong and showed that such corridors, through which wind flows without obstruction, have a lower UHI intensity than more restricted parts of a city. Ren et al. (Ren et al., 2018) advocated designing urban ventilation corridors to mitigate the UHI through a case study in Chegdu, China. A previous study by the authors (Sen and Roesler, 2017b) showed for a given wind direction, the UHI intensity varies in different parts of an urban area, with areas in the path of the wind having a lower intensity because of advection of warmer air, and those perpendicular to the wind having a higher intensity because of low wind speed. Despite the effect of wind direction on the UHI intensity, no studies were found in the literature that have incorporated wind direction and effectiveness of cool surfaces (pavements, walls, and roofs). This study builds on previous studies by the authors (Sen and Roesler, 2017b; Sen and Roesler, 2017c) and proposes a method to evaluate the UHI mitigation obtained from cool surfaces, considering different wind directions and their corresponding probability. This will enable engineers and urban planners to direct resources for cool surfaces in those parts of cities where they have the highest potential for UHI reductions. 2. Study area and numerical model 2.1. Urban domain For this study, a hypothetical urban block consisting of a 3 × 3 array of buildings of a constant height and spacing was used based on a previous study (Sen and Roesler, 2017b). As shown in Fig. 1(a), the urban area consists of buildings with a square footprint of size W x W, where W is the width of the building. The buildings are separated by roads whose width is also W. This simple footprint was assumed for simplicity, as more complex building geometry would add to the number of factors to be considered. The top of the domain was assumed to be north for the analysis. Each building has a height H, as shown in the elevation view in Fig. 1(b). This hypothetical array of buildings with roads in between was the physical domain of interest. For computational modeling, the domain extended beyond the physical domain to a distance of 15H horizontally, and 5H vertically above the top of the buildings. These parameters for the size of the computational domain are based on best-practice guidelines for Computational Fluid Dynamics (CFD) modeling of the urban environment (Franke

Fig. 1. Hypothetical urban block showing (a) plan view with numbered urban canyons, (b) elevation view, and (c) plan view with wind directions. Coordinate system is also specified. 2

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et al., 2011), which prescribes the minimum distances for lateral boundaries as a function of H. Nakamura and Oke (Nakamura and Oke, 1988), as early as 1967, used the concept of an urban canyon to study the UHI phenomenon. An urban canyon is a configuration that consists of a road bounded by building walls on two sides and open to wind on other sides. The urban canyon is commonly used as a representative urban unit to study microscale UHI. As shown in Fig. 1(a), the domain considered in this study consisted of twelve canyons, numbered 1 to 12. Road intersections were not considered canyons because they were not bounded by adjacent walls. The aspect ratio of the canyons, H/W, was an independent parameter that was fixed at 1.0 throughout the study. 2.2. Meshing In order to determine the average air temperature at the canopy height (2 m) for each urban canyon, the airflow and temperature fields need to be solved numerically. The first step was to discretize the domain into a structured mesh. The following principles were used for the domain discretization to achieve acceptable results within the urban canyons while still limiting the computational cost: 1. A higher resolution was provided within each urban canyon as compared to other parts of the domain as the solution in the urban canyons was of primary interest, and gentler gradients are expected outside of it. 2. Boundary layer elements were provided along each of the surfaces (roads, walls, and roofs) in order to better resolve the boundary layer. The extrusion-exclusion meshing technique proposed by van Hooff and Blocken (Van Hooff and Blocken, 2010) was used, in which the 2D horizontal plane of the domain was first discretized with a structured mesh, and then the mesh was extruded to convert the structured 2D mesh into a structured 3D mesh. Finally, the parts of the mesh corresponding to the solid buildings were excluded from the final mesh, leaving only the mesh corresponding to the fluid domain with a high-quality mesh consisting of only hexahedral elements. The mesh was defined using the open-source meshing tool Gmsh (Geuzaine and Remacle, 2009). Three meshes were developed: a’Coarse’ mesh with about 720,000 elements, a ‘Medium’ mesh with about 1.4 million elements, and a’Fine’ mesh with about 2.6 million elements. Fig. 2 shows the parts of the ‘Medium’ mesh with roads, walls, and roofs. 2.3. Numerical model In order to determine canopy-level wind speed and air temperature, the steady-state incompressible Reynold's Average NavierStokes (RANS) equations, shown in Eqs. (1) and (2), were solved numerically. To account for buoyancy, the Boussinesq approximation was used in the form of the last term on the right in Eq. (2). Here, Ui is ith component of the RANS velocity (in ms−1), P the kinematic pressure (in m2s−2), ν the kinematic viscosity of air (assumed to be a constant value of 1.6 × 10−5 m2s−2 within the temperature range of the problem), νt is the turbulent viscosity that is calculated through a closure model, β is the coefficient of thermal expansion of air (assumed to be a constant value of 3.3 × 10−3/K within the temperature range of the problem), T is the RANS temperature (in K), Tref is a reference temperature that was set to the average of the far-field air temperature and the pavement surface temperature, and gi is the acceleration due to gravity (in ms−2).

∂Ui =0 ∂x i Uj

(1)

∂2Ui

∂Ui ∂P =− + (ν + νt ) − β (T − Tref ) gi ∂x i ∂x i ∂x j ∂x j

(2)

Fig. 2. Structured mesh created for the hypothetical urban block domain discretized into approximately 1.3 million elements. 3

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RANS temperature T was evaluated by solving the heat equation, shown in Eq. (3). Here, α = Pr /ν is the thermal diffusivity of air with Prandtl number Pr fixed at 0.7 within the temperature range of the problem, and αt = Prt/νt is the turbulent thermal diffusivity with turbulent Prandtl number Prt = 0.85. These Prandtl numbers were based on Ref (William Morrow Kays, 2012).

Uj

∂T ∂ 2T = (α + αt ) 2 ∂x i ∂x i

(3)

For closure, the turbulent viscosity νt was evaluated by solving for turbulent kinetic energy (TKE) k and rate of TKE dissipation ϵ using the realizable k − ϵ model developed by Shih et al. (Shih et al., 1995a), as shown in Eqs. (4) and (5) respectively. In these equations, ρ is the density of air at Tref, Pk and Pb are the rate of production of TKE due to velocity gradients and buoyancy respectively and S is the modulus of the strain rate tensor, all of which are calculated from the RANS velocity and temperature fields. C1, C2, C1ε, C3ε, σk and σε are model constants.

ρ

∂kUi ν ∂ 2k = ρ ⎛ν + t ⎞ 2 + Pk + Pb − ρϵ ∂x i σk ⎠ ∂x i ⎝

ρ

∂ϵUi ν ∂ 2ϵ ϵ2 ε = ρ ⎛ν + t ⎞ 2 + ρC1 S ϵ − ρC2 + C1ϵ C3ϵ Pb ∂x i σk ⎠ ∂x i k + νϵ k ⎝

⎜

⎟

⎜

(4)

⎟

(5)

Finally, the turbulent viscosity is evaluated as νt = Cμk /ϵ. Here, Cμ varies depending on the velocity, TKE, and rate of TKE dissipation fields so as to obtain a physically meaningful solution in regions of flow separation, as described in Ref (Shih et al., 1995b). In addition, the velocity near the wall was modeled using the standard wall function developed by Launder and Spalding (Launder and Spalding, 1983), as recommended by the best practice guidelines (Franke et al., 2011). This is shown in Eq. (6) in terms of non-dimensionalized velocity and distance from the walls u+ and y+ respectively, and is valid for y+ > 30. 2

u+ = 2.44 ln y+ + 5.2

(6)

The temperature profile near the wall was similarly modeled as per Jayatilleke (Jayatilleke, 1969) and shown in Eq. (7), where the P term defined in Eq. (8) represents enhanced resistance to heat transfer near the wall. This wall function is also valid for y+ > 30.

T + = Prt [2.44 ln y+ + 5.2 + P ]

⎛ Pr ⎞ P = 9.24 ⎡ ⎢ Prt ⎣⎝ ⎠ ⎜

⎟

0.75

(7)

−0.007 Pr Prt ⎤ ⎡ − 1⎤ ⎥ ⎣1 + 0.28e ⎦ ⎦

(8)

2.4. Model grid convergence and validation To check for grid convergence and to validate the model, data from the wind tunnel experiments by Uehara et al. (Uehara et al., 2000) was used for the proposed urban model. To match the experimental conditions, H was set to 100 mm while keeping the aspect ratio H/W = 1.0, and the wind speed profile at the inlet U(z) = U was assumed to be constant with height z and blowing from the west. The value of the inlet wind speed was selected to make the Reynold's Number Re = UH/ν = 3500 to match experimental gH (T − T ) conditions. The bulk Richardson number was set to Rb = T 0U2 s = −0.21, where Ts and T0 are the road surface temperature and 0 inlet air temperature, respectively (in K), to match experimental conditions. The inlet air temperature profile was assumed to be constant. The ground (including the road and the computational domain outside the main urban area), walls, and roofs were modeled as noslip walls with fixed temperature. As no wall or roof temperatures were prescribed in the wind tunnel study, they were fixed at inlet temperature T0 and only the road surface was heated to Ts. The lateral boundaries were modeled as no-slip walls with a fixed temperature equal to T0, the outlet as a pressure outlet, and the top of the domain as a symmetry boundary. Finally, the wall corresponding to the fetch of the flow was modeled with a aerodynamic roughness length z0 (defined by Raupach et al. (Raupach et al., 1991)) of 3.3 mm as measured by the experimental study. In addition to the wind tunnel study, the computational results were also compared to other numerical studies by Xie et al. (Xie et al., 2007) (Re = 3500, Rb = − 0.21) and Kim and Baik (Kim and Baik, 2001) (Re = 3500, Rb = − 0.27). Although these studies solved Eqs. (1)–(3) on different geometries and with different solvers than this study, they can be used to compare the results from this study to show an acceptable variation of numerical results from the experimental wind tunnel data. The numerical problem was solved using second-order finite volume discretization techniques and the SIMPLE algorithm for pressure-velocity coupling with appropriate relaxation factors. The wind tunnel problem was solved in parallel on a 16-core computer using the open-source Computational Fluid Dynamics (CFD) solver OpenFOAM version 5.0 (Weller et al., 1998). Iterations were performed until residuals fell below 10−3, except for P, where the residual was below 10−2. For convergence, the drag coefficient on the walls, roofs, and roads were compared at the end of the simulation for each of the three meshes developed. The relative absolute difference as well as a Grid Convergence Index (GCI) of the relatively finer mesh with respect to the relatively coarser mesh, as recommended by Roache (Roache, 1994), were calculated. The GCI is the error scaled to what it is expected to be if the mesh resolution was doubled with a second-order solver. GCI provides a uniform method to report 4

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Table 1 Grid convergence results for drag coefficient. Mesh case

Number of elements

Relative absolute difference (%)

GCI [fine] (%)

Coarse Medium Fine

723,128 1,383,624 2,608,396

– 4.66 1.54

– 25.82 8.79

errors. It was calculated for the relatively finer mesh using Eq. (9). Here, p is the order of convergence of the numerical solver (2 in this case), and r is the refinement ratio. For a 3D mesh, r = (N1/N2)1/3, where N1 and N2 are the number of elements in the relatively finer and coarser meshes respectively.

GCI =

3∣ϵ∣ rp − 1

(9)

The relative absolute difference and GCI are shown in Table 1. The relative absolute difference between the ‘Medium’ and’Coarse’ mesh was small (4.66%) but its GCI was somewhat high (25.82%). In comparison, the relative absolute difference and GCI between the’Fine’ and ‘Medium’ cases were small (1.54% and 8.79% respectively), indicating that the solution had converged satisfactorily with the ‘Medium’ mesh case. Therefore, for the rest of the study, the ‘Medium’ mesh consisting of 1.3 million cells was used to balance between accuracy and computational time. For validation, the temperature and x-component of wind speed (U1) profiles in the middle of canyon 7 in Fig. 1(a) was obtained for wind blowing from the west. This analysis location corresponds to the sensor placed in the interior canyon in the experimental study (Uehara et al., 2000) and similarly-located profiles in the numerical studies (Xie et al., 2007; Kim and Baik, 2001). The nondimensionalized temperature θ and x-component of wind speed profiles ϒ were obtained from the corresponding dimensional terms (T and U1) using Eqs. (10) and (11) respectively.

θ=

T − Ts T0 − Ts

(10)

Υ=

U1 U

(11)

The non-dimensional results from the model validation case are shown in Fig. 3 together with data from the wind tunnel and other

Fig. 3. Experimental (Uehara et al.) and numerical (this study, Kim & Baik and Xie et al.) validation results for non-dimensionalized (a) temperature and (b) x-component of wind speed. 5

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numerical studies. Except for very close to the road surface (z/H < 0.1), there is good agreement between all the results. Very close to the road surface, numerical results agree with each other but deviate from experimental ones. This is possibly because the heated road surface also heats the walls. Given the wall temperature was not measured in the experimental study, it was not considered in the numerical studies. Likewise, in the case of wind speed, the walls in the experimental urban model did have some roughness, which was not quantified and thus, the smooth walls were assumed in the numerical model. Overall, the Root Mean Squared Error (RMSE) between the wind tunnel data and the results from this study is less than 10% for both temperature and wind speed, which is an acceptable level of accuracy for this study. 3. Effect of cool surfaces 3.1. Meteorological parameters In this study, the UHI analysis was performed for the city of Chicago (USA). In a previous study (Sen and Roesler, 2017c), the authors showed that the Typical Meteorological Year (TMY) database could be used to determine the statistically warmest hour of the day so that the effectiveness of cool pavements could be analyzed. The TMY is a synthetic, hourly record of one year of meteorological conditions that are closest to the average meteorological conditions over a thirty-year period (1961–1990). In that study (Sen and Roesler, 2017c), it was shown that July 19 at 3:00 PM is the statistically warmest hour of the year in Chicago, with an air temperature Turban of 35∘C. The corresponding air temperature Trural from the TMY database of DuPage County, which is a suburban location about 60 km west of Chicago, was 31∘C and thus, the mesoscale UHI intensity was ΔTur, meso = Turban − Trural = 4∘C. The mesoscale intensity is the bulk temperature difference considering the urban and rural areas as a whole, without including the localized effects of specific urban form, surface materials, and wind direction. The microscale UHI intensity ΔTur, micro, which will be calculated in this study, was the difference between the average canopy-level air temperature in the urban area for each of the twelve canyons Tcanyon, and the rural air temperature Trural, as defined in Eq. (12). Unlike the mesoscale intensity, the microscale intensity includes localized effects and can be used to show the spatial distribution of the UHI.

ΔTur , micro = Tcanyon − Trural

(12)

In the algorithm used for developing the TMY database, wind speed is weakly weighed, while wind direction is not included in the algorithm at all (National Renewable Energy Lab, 2008). Thus, the wind directions provided in the TMY database are not statistically representative of the local climate, and an alternative source was used to obtain those statistics. Statistical information about wind speed and direction was obtained from climatic data at the Illinois State Water Survey (Illinois State Water Survey, 2019), where long-term measurements were taken at a height of 1.5 m. Fig. 4 shows the probability of wind blowing in Chicago from eight directions: north (N), east (E), south (S), west (W), northwest (NW), northeast (NE), southeast (SE), and southwest (SW), each of which is represented by its bearing angle (clockwise from north). These probabilities will be used later to determine the average UHI intensity in the canyons of the hypothetically analyzed domain shown in Fig. 1. The sum of the probabilities is approximately 0.95, with the remaining 0.05 corresponding to calm conditions, which were not considered in this study. The cumulative probability distribution of the wind speed is shown in Fig. 5. From this, the 20th percentile wind speed for Chicago was found to be about 2 ms−1, which is used in the numerical simulation as the inlet velocity at 1.5 m height. This wind speed represents a typical low value for the

Fig. 4. Probability of prevailing wind direction in Chicago. Wind directions are shown in terms of their bearing angles, so that north is 0∘, northeast is 45∘, etc. 6

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Fig. 5. Cumulative probability distribution of wind speed in Chicago.

area, which leads to a considerable UHI intensity as warm area is not quickly advected by cooler air. 3.2. Solution framework The framework for evaluating the effect of cool surfaces (with a particular focus on cool pavements) on the canopy-level air temperature in each of the twelve urban canyons is based on the uncoupled pavement-urban canyon model (Sen and Roesler, 2017c) shown schematically in Fig. 6. In the pre-processing step, the statistically warmest hour of the year is chosen from the TMY database for both Chicago as the city of interest and DuPage as the suburban area for comparison. Next, in the solver step, two separate models are run. First, a 1D numerical pavement heat transfer model called the Illinois Thermal Analysis Program (ILLITHERM) was run. This model calculates the temperature profile for a given pavement and meteorological conditions using an energy balance, as shown in Eq. (13). Here, G is the ground heat flux, S is the shortwave radiation absorbed by the pavement during the day (corrected for cloud cover and albedo), L is the difference between longwave radiation emitted by the pavement and that emitted by clouds that are absorbed by the pavements, and C is the convective heat flux which depends on the wind speed and pavement and air temperatures. This energy balance provides a boundary condition to numerically solve the Heat Equation (which depends on pavement thermal diffusivity) and calculate a surface temperature. Further details of the

Fig. 6. Framework for the numerical solution of the microscale UHI problem based on (Sen and Roesler, 2017c). 7

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model can be found in Ref (Sen and Roesler, 2017a). (13)

G+S+L+C=0

ILLITHERM was used with the TMY meteorological data as an input to evaluate the pavement surface temperature for the hour of analysis for each of the cool pavement strategies discussed in the next subsection. The same surface temperature was also applied to walls and roofs. Then, the wind speed, pressure, and temperature fields for the 3D urban domain were solved numerically for wind blowing either from the W or NW directions, shown in Fig. 1(c), with the solutions for the other directions obtained from symmetry. The ILLITHERM model calculated the road surface temperature using air temperature and wind speed from the TMY database and not the urban canyon model. This is why the current model is called uncoupled, as there is only a unidirectional flow of information from the pavement model to the urban canyon model. Previous studies, such as (Aliabadi et al., 2017; Yaghoobian et al., 2014; Allegrini et al., 2015; Allegrini and Carmeliet, 2017; Sen and Roesler, 2019a), used uncoupled models to decrease computational requirements while modeling the urban climate. However, as noted by Aliabadi et al. (Aliabadi et al., 2017), this can lead to an underestimation of air temperature by as much as 1∘C. Therefore, results from the present study using an uncoupled model are most likely an underestimation of the actual UHI intensity. Finally, in the post-processing step, the air temperature at canopy height (2 m) in each of the twelve urban canyons was extracted from the output of the urban canyon model. The difference between a particular urban canyon and the corresponding air temperature in the suburban area from the TMY database for DuPage is the microscale UHI intensity. These differences were evaluated for each of the 8 wind directions and 4 pavement strategies.

3.3. Cool pavement strategies Two cool pavement strategies discussed in the literature to mitigate UHI are increasing the thermal diffusivity (αp) and albedo (ρp) of the pavement surface layer. For this study, a two-level, two-factor analysis was used to consider four cool pavement strategies, as shown in Table 2. For each factor (thermal diffusivity and albedo), two levels were selected: a low value (designated L, with αp = 0.5 mm2s−1 and ρp = 0.10), and a high value (designated H, with αp = 1.0 mm2s−1 ρp = 0.50). These levels were based on typical values of these variables for pavements, as reported in literature such as Refs (Hui Li and Kendall, 2013; Sen and Roesler, 2016; Yang et al., 2016; Sen and Roesler, 2019b). The resultant factorial analysis had the following nomenclature: the first letter describing the thermal diffusivity level, and the second letter the albedo level. Thus, the four cool pavement strategies were designated LL, LH, HL, and HH. The surface temperatures calculated for these was then applied to walls and roofs as well, turning these into comprehensive strategies for cool surfaces. The low value of thermal diffusivity represents porous asphalt or concrete, while the high value represents more conventional asphalt or concrete pavements. The low value of albedo corresponds to a new asphalt pavement, while the high value corresponds to an asphalt pavement that has been treated with a reflective coating, or a concrete pavement that has been designed to have a high albedo. Using the TMY database for Chicago and the ILLITHERM model, the pavement surface temperature corresponding to the statistically warmest hour of the year for each of the four strategies was calculated using the pavement model. The results are shown in Table 3 with the highest surface temperature belonging to case LL, which has both a low thermal diffusivity and albedo. Higher surface temperatures will result when either or both of the following condition exists: the pavement surface absorbs more solar energy (lower albedo) and the pavement stores more energy near the surface (lower thermal diffusivity) as seen in the values in Table 3. In comparison, the case HH with high thermal diffusivity and high albedo has the lowest surface temperature as it absorbed less solar energy and also diffused that energy away from the surface faster. Case HL had higher surface temperature than LH signifying albedo during the day affects surface temperature more than the diffusivity level.

3.4. Urban canyon model For the urban canyon model, the building height H was set to 5.0 m (representing a two-story building) with aspect ratio H/ W = 1.0. The inlet velocity was not assumed constant but instead, an Atmospheric Boundary Layer (ABL) velocity inlet condition (Raupach et al., 1991) was used as shown in Eq. (14) and as recommended in best-practice guidelines (Franke et al., 2011). Here, u∗ is the friction velocity and κ = 0.41 is the von Karman constant. Table 2 Thermal diffusivity and albedo for the cool pavement strategies. Case

αp (mm2s−1)

ρp

LL LH HL HH

0.5 0.5 1.0 1.0

0.10 0.50 0.10 0.50

(Low) (Low) (High) (High)

8

(Low) (High) (Low) (High)

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Table 3 Surface temperature of pavement strategies.

U (z ) =

Case

Surface Temperature (∘C)

LL LH HL HH

41.85 36.53 40.42 35.45

u∗ ⎛ z + z 0 ⎞ ln κ ⎝ z0 ⎠ ⎜

⎟

(14)

As demonstrated by Oke (Oke, 1973), the UHI intensity varies inversely with approximately the square root of the wind speed. Therefore, a higher wind speed will decrease the UHI intensity. In order to model conditions with a significant UHI intensity, a reference wind speed of 2 ms−1 at a reference height of 1.5 m was used, which corresponds to the 20th percentile wind speed in Chicago as shown in Fig. 5. The W and NW wind directions were solved for each of the pavement cases, and the solution for the other wind directions was obtained from symmetry. The inlet profiles for k and ϵ as recommended for an ABL by (Franke et al., 2011) and based on the work of Raupach et al. (Raupach et al., 1991) are shown in Eqs. (15) and (16), respectively. These were implemented with the same reference wind speed and reference height.

k (z ) =

ϵ(z ) =

(u∗)2 Cμ U (z )

(15)

(u∗)3 κ (z + z 0 )

(16)

The aerodynamic roughness length z0 was set to 1.0 m based on the updated Davenport aerodynamic roughness length classification (Wieringa, 1992). This represents a surrounding landscape covered in irregularly spaced buildings of similar height, thus placing the urban domain with regularly-spaced roads and buildings of similar height and width. This approach allowed the surrounding landscape to be modeled without being explicitly resolved. The urban domain itself, consisting of the buildings and roads, were resolved explicitly and therefore no aerodynamic roughness length was applied within its boundaries. The inlet temperature profile was constant and equal to the TMY air temperature of 35∘C. This constant profile inlet is the most commonly-used boundary condition for stratified atmospheric boundary layer simulations in literature, as very few temperature profiles consistent with the ABL profiles for U, k, and ϵ have been proposed. This is why the condition was adopted for this study as well. Recently, Toparlar et al. (Toparlar et al., 2019) demonstrated that a constant temperature profile can lead to errors of about 4–12∘C very close to the ground (z/H < 0.05) and recommended a new inlet profile. However, at higher elevations, there was no significant error. Since 2 m air temperature is the primary variable of interest in the present study, which is significantly above the ground (z/H = 0.4), a constant temperature inlet profile is expected to be sufficiently accurate. The pavement surface temperatures calculated by the ILLITHERM model and shown in Table 3 were applied as fixed temperature boundary conditions for the roads as well as the building roofs and walls in the urban domain, so that the cool pavement cases apply to all the surfaces. In the rest of this study, ‘cool pavement cases' will be used interchangeably with ‘cool surface cases' to imply a comprehensive cooling strategy involving pavements, roofs, and walls. The same numerical schemes and convergence criteria as the validation case were applied to solve for the RANS wind speed and temperature fields. Other settings were kept the same as for the validation case.

3.5. Microscale UHI Intensity The microscale UHI intensity was determined for the hypothetical urban domain and each of pavement cases for all wind directions considered using Eq. (12). For each of the simulations, the non-dimensionalized distance from the wall y+ was greater than 30 (the average value was about 1500), indicating that the wall functions were properly applied. For the twelve canyons in the domain and the eight wind directions, the results are shown in Tables 4–7 for the pavement cases LL, LH, HL, and HH, respectively. Given the most prevalent wind direction is SW (see Fig. 4), the microscale UHI intensity in the twelve urban canyons is shown in Fig. 7(a)–(d) for the four pavement cases (LL, LH, HL, and HH) with respect to the SW wind direction. The UHI intensity correlated well with the surface temperatures. Case LL, which had the highest surface temperature, also had the highest UHI intensity as shown in Table 4 and Fig. 4(a). After the case LL, case HL had the second highest UHI intensity, followed by LH, and then HH. The UHI intensity varied between canyons, with canyons 4, 6, 7, and 9 (interior canyons) consistently having a higher intensity than the others across all wind directions. In addition for a single canyon, the UHI intensity also varied with the wind direction as seen in Tables 4–7. This is the same ranking as the surface temperatures. The results demonstrate that direction of the wind, spatial location of the canyon, urban form, and surface thermal/optical properties impact UHI intensity. 9

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Table 4 Microscale UHI intensity (in ∘C) for the twelve canyons and across the eight wind directions for the case LL (low diffusivity and albedo). Canyon

N

NE

E

SE

S

SW

W

NW

1 2 3 4 5 6 7 8 9 10 11 12

4.16 4.16 4.45 4.56 4.45 4.29 4.29 4.55 4.69 4.55 4.38 4.38

4.30 4.31 4.47 4.53 4.33 4.73 4.49 4.80 4.67 4.31 4.69 4.40

4.55 4.45 4.38 4.29 4.16 4.69 4.56 4.38 4.29 4.16 4.55 4.45

4.69 4.40 4.80 4.67 4.31 4.73 4.49 4.47 4.53 4.33 4.30 4.31

4.38 4.38 4.55 4.69 4.55 4.29 4.29 4.45 4.56 4.45 4.16 4.16

4.40 4.69 4.31 4.67 4.80 4.49 4.73 4.33 4.53 4.47 4.31 4.30

4.45 4.55 4.16 4.29 4.38 4.56 4.69 4.16 4.29 4.38 4.45 4.55

4.31 4.30 4.33 4.53 4.47 4.49 4.73 4.31 4.67 4.80 4.40 4.69

Table 5 Microscale UHI intensity (in ∘C) for the twelve canyons and across the eight wind directions for the case LH (low diffusivity and high albedo). Canyon

N

NE

E

SE

S

SW

W

NW

1 2 3 4 5 6 7 8 9 10 11 12

4.04 4.04 4.10 4.13 4.10 4.07 4.06 4.12 4.15 4.12 4.09 4.09

4.07 4.07 4.11 4.12 4.07 4.16 4.11 4.18 4.15 4.07 4.15 4.09

4.12 4.10 4.09 4.06 4.04 4.15 4.13 4.09 4.07 4.04 4.12 4.10

4.15 4.09 4.18 4.15 4.07 4.16 4.11 4.11 4.12 4.07 4.07 4.07

4.09 4.09 4.12 4.15 4.12 4.06 4.07 4.10 4.13 4.10 4.04 4.04

4.09 4.15 4.07 4.15 4.18 4.11 4.16 4.07 4.12 4.11 4.07 4.07

4.10 4.12 4.04 4.06 4.09 4.13 4.15 4.04 4.07 4.09 4.10 4.12

4.07 4.07 4.07 4.12 4.11 4.11 4.16 4.07 4.15 4.18 4.09 4.15

Table 6 Microscale UHI intensity (in ∘C) for the twelve canyons and across the eight wind directions for the case HL (high diffusivity and low albedo). Canyon

N

NE

E

SE

S

SW

W

NW

1 2 3 4 5 6 7 8 9 10 11 12

4.13 4.13 4.36 4.45 4.36 4.23 4.23 4.43 4.55 4.43 4.30 4.30

4.24 4.24 4.37 4.42 4.26 4.58 4.38 4.63 4.53 4.24 4.54 4.32

4.43 4.36 4.30 4.23 4.13 4.55 4.45 4.30 4.23 4.13 4.43 4.36

4.54 4.32 4.63 4.53 4.24 4.58 4.38 4.37 4.42 4.26 4.24 4.24

4.30 4.30 4.43 4.55 4.43 4.23 4.23 4.36 4.45 4.36 4.13 4.13

4.32 4.54 4.24 4.53 4.63 4.38 4.58 4.26 4.42 4.37 4.24 4.24

4.36 4.43 4.13 4.23 4.30 4.45 4.55 4.13 4.23 4.30 4.36 4.43

4.24 4.24 4.26 4.42 4.37 4.38 4.58 4.24 4.53 4.63 4.32 4.54

4. Urban form and cool surfaces 4.1. Interior score It is hypothesized that urban canyons that are directly in the wind path have a lower UHI intensity than those for which the wind is constrained by an upstream canyon or building. This is because the upstream canyons have a higher turbulent dissipation, which reduces the wind speed in them and thus increases the air temperature. In order to test this hypothesis, the concept of an interior canyon score is introduced. Canyons that are directly in the path of the wind are called boundary canyons, and those with an upstream canyon or building are called interior canyons. Whether a canyon in the domain is a boundary or an interior canyon depends on the direction the wind is blowing. Fig. 8(a) and (b) shows boundary and interior canyons for wind blowing from W and NW, respectively. For boundary canyons, an interior score of 0 was given, while for interior canyons, a value of 1 was assigned. Thus, for each of the eight wind directions, each of the twelve canyons were assigned an interior score.

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Table 7 Microscale UHI intensity (in ∘C) for the twelve canyons and across the eight wind directions for the case HH (high diffusivity and albedo). Canyon

N

NE

E

SE

S

SW

W

NW

1 2 3 4 5 6 7 8 9 10 11 12

4.01 4.01 4.03 4.04 4.03 4.02 4.02 4.04 4.05 4.04 4.03 4.03

4.02 4.02 4.03 4.03 4.02 4.05 4.03 4.05 4.04 4.02 4.05 4.03

4.04 4.03 4.03 4.02 4.01 4.05 4.04 4.03 4.02 4.01 4.04 4.03

4.05 4.03 4.05 4.04 4.02 4.05 4.03 4.03 4.03 4.02 4.02 4.02

4.03 4.03 4.04 4.05 4.04 4.02 4.02 4.03 4.04 4.03 4.01 4.01

4.03 4.05 4.02 4.04 4.05 4.03 4.05 4.02 4.03 4.03 4.02 4.02

4.03 4.04 4.01 4.02 4.03 4.04 4.05 4.01 4.02 4.03 4.03 4.04

4.02 4.02 4.02 4.03 4.03 4.03 4.05 4.02 4.04 4.05 4.03 4.05

Fig. 7. Microscale UHI intensity (in ∘C) for SW wind direction in each of the twelve canyons for case (a) LL (b) LH (c) HL and (d) HH.

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Fig. 8. Boundary and interior canyons with corresponding interior score for wind blowing from (a) west and (b) northwest directions.

Fig. 9. Urban canyons interior score based on wind direction and wind direction probability-weighted average interior score (on secondary axis).

The interior score for each canyon is shown in Fig. 9 in the form of a stacked bar chart. For a given canyon, some wind directions are not seen because the canyon is a boundary canyon for that direction and thus has a score of 0. A weighted average interior score is also shown, which is defined in the next sub-section.

4.2. Wind direction-weighted average For each wind direction i, blowing with a probability of pi shown in Fig. 4, the weighted average UHI Intensity of the kth urban canyon (ΔTur, k) was evaluated by weighting it with the probability of the direction of wind flow, as shown in Eq. (17), where ΔTur, k, i is the UHI intensity of the kth urban canyon for the ith wind direction.

∑ pi ΔTur , k, i ΔTur , k =

i

∑ pi

(17)

i

Similarly, the weighted average interior score of the kth urban canyon (Ik) could be obtained from the interior score of that urban canyon Ik, i for the ith wind direction as shown in Eq. (18). The weighted average interior score can be interpreted as the likelihood that the urban canyon is an interior canyon over all the possible wind directions. 12

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Fig. 10. Wind direction weighted average UHI intensity.

∑ pi Ik, i Ik =

i

∑ pi

(18)

i

The weighted average interior score is also shown in Fig. 9 on the secondary axis. For canyons 4, 6, 7, and 9, it was 1.0, indicating that for all wind directions, these canyons were always interior, which can also be seen in Fig. 1(a). The weighted average interior score of other canyons varied, with canyons 3, 8, 11, and 12 having a score of 0.5 or less, indicating that throughout the year they have a higher likelihood of being boundary canyons than interior canyons. The weighted average UHI intensity (ΔTur, k) is shown in Fig. 10. Once again, the wind direction weighted average UHI intensity was greatest for case LL and lowest for case HH. In terms of magnitude, the microscale UHI intensity was higher than the mesoscale value by up to 0.6∘C. The smallest increase in UHI intensity was less than 0.05∘C. Considering case LL across the twelve canyons, canyons 4 and 7 had the highest UHI intensity, while Canyons 1 and 11 had the lowest for case LL (see Fig. 10). The maximum spatial variation in the UHI intensity for the same pavement surface properties (case LL) was approximately 0.2∘C. A similar observation could be seen for the other pavement cases but to a lesser magnitude. Thus, for a fixed pavement case, the UHI intensity varies with the location of the canyon relative to the wind direction. The most significant factor in reducing the UHI intensity in this study was the choice of the cool surface strategy (HH or LH) as seen in Fig. 10. Case HH significantly decreased the UHI intensity across all the canyons to the extent that the effect of urban form and wind direction became negligible. While urban form led to a spatially-varying microscale UHI intensity in cases LL and HL, the case HH could almost completely eliminate the microscale UHI effect across all canyons. Finally, the wind direction weighted average UHI intensity was plotted against weighted average interior score in Fig. 11 for each of the twelve canyons. The Pearson correlation coefficient (R) between the average interior score and the average UHI intensity for each of the cool surface strategies was 0.94, indicating a strong linear correlation between the two variables. Thus, interior canyons have a higher UHI intensity with closely-spaced buildings in dense urban areas leading to potentially higher UHI than buildings in a more open space. 5. Conclusion Cool surfaces (pavements, roofs, and walls) are a promising method to mitigate the Urban Heat Island (UHI) in cities. The two most common strategies that have been reported in the literature are increasing the albedo to absorb less solar energy and, in the case of pavements, increase the thermal diffusivity to diffuse absorbed solar energy away from the surface. The microscale UHI intensity in urban areas are affected by the specific combination of these optical and thermal strategies, the urban form, and the direction from which the wind blows. No study to date has attempted to simultaneously quantify the microscale UHI effect for these three factors. An uncoupled pavement-urban canyon computational model was developed to determine the effectiveness of four cool surface strategies in a two-factor, two-level factorial design with high and low values of pavement thermal diffusivity and albedo. The same strategies were also applied to walls and roofs to come up with comprehensive cool surface strategies. In order to quantify the potential UHI impact of each of the cases, the statistically warmest hour of the year for Chicago, USA was obtained from the Typical Meteorological Year (TMY) database. The warmest hourly air temperature for a TMY in Chicago was 35∘C. The corresponding air temperature in the adjacent suburban area (DuPage county) was 31∘C, which gives a baseline, mesoscale UHI intensity of 4∘C. The microscale UHI for each surface strategy was determined for wind blowing from eight different directions, with the probability of each wind direction being obtained from existing climatic data. 13

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Fig. 11. Wind direction-weighted average UHI intensity as a function of wind direction-weighted average interior score for each canyon.

A 3D computational fluid dynamics model was used to analyze a hypothetical urban domain with a 3 × 3 array of buildings forming twelve urban canyons. To determine the average UHI intensity, the values obtained from the analysis for each canyon were averaged over the probability of the wind direction, for each of the four cool surface cases. Both wind direction and thermal/optical properties were found to affect the microscale UHI intensity in the canyons within the urban domain. Surfaces with low albedo (0.10 in this study) and low thermal diffusivity (0.5 mm2s−1 in this study) had the highest microscale UHI intensity as they absorbed more heat and retained them closer to the surface, which led to a higher surface temperature and in turn, a higher canopy level air temperature. The microscale UHI intensity was higher than the mesoscale value by as much as 0.6∘C. In addition, the microscale UHI varied by as much as 0.2∘C in different canyons for the same surface type, which was a result of the direction of the wind relative to the spatial location of the canyon. In contrast, surface with high albedo (0.50 here) and high thermal diffusivity (1.0 mm2s−1 here) absorbed less heat and diffused it away from the surface, leading to a lower surface temperature and canopy level air temperature and nearly eliminating the microscale UHI intensity. To study the correlation between the spatial position of a canyon and its average UHI intensity, each canyon was assigned an interior score. This was the probability of a canyon being shielded from direct wind flow by an upstream canyon or building. The weighted average interior score was then evaluated with the probability of wind direction as weights to create a measure of the probability of a canyon being shielded from upstream wind flow across all wind directions. The average UHI intensity of a canyon showed a strong correlation with its average interior score (Pearson's R = 0.94). Thus, dense urban areas with closely-spaced buildings have a higher UHI intensity, with cool surfaces being effective in reducing the intensity. Acknowledgments Funding for this study was provided by the US Department of Transportation (USDOT) through the University Transportation Center for Highway Pavement Preservation (UTCHPP) at Michigan State University with Contract Number DTR13-G-UTC44. I, the undersigned, hereby certify on behalf of the authors of the manuscript, ‘Wind direction and cool surface strategies on microscale urban heat island,’ that we have no conflict of interest to declare for the consideration of this manuscript for publication. Signed: Sushobhan Sen. References Akbari, Hashem, Kolokotsa, Dionysia, 2016. Three decades of urban heat islands and mitigation technologies research. Energy Build. 133, 834–842. Akbari, H., Shea Rose, L., Taha, H., 2003. Analyzing the land cover of an urban environment using high-resolution orthophotos. Landsc. Urban Plan. 63 (1), 1–14. Aleksandrowicz, O., Vuckovic, M., Kiesel, K., Mahdavi, A., 2017. Current trends in urban heat island mitigation research: observations based on a comprehensive research repository. Urban Clim. 21, 1–26. Aliabadi, A.A., Krayenhoff, E.S., Nazarian, N., Chew, L.W., Armstrong, P.R., Afshari, A., Norford, L.K., 2017. Effects of roof-edge roughness on air temperature and pollutant concentration in urban canyons. Bound.-Layer Meteorol. 164 (2), 249–279. Allegrini, J., Carmeliet, J., 2017. Coupled cfd and building energy simulations for studying the impacts of building height topology and buoyancy on local urban microclimates. Urban Clim. 21, 278–305. Allegrini, J., Dorer, V., Carmeliet, J., 2015. Coupled cfd, radiation and building energy model for studying heat fluxes in an urban environment with generic building configurations. Sustain. Cities Soc. 19, 385–394. Bokaie, M., Zarkesh, M.K., Arasteh, P.D., Hosseini, A., 2016. Assessment of urban heat island based on the relationship between land surface temperature and land use/ land cover in Tehran. Sustain. Cities Soc. 23, 94–104. Estoque, R.C., Murayama, Y., Myint, S.W., 2017. Effects of landscape composition and pattern on land surface temperature: an urban heat island study in the megacities of southeast asia. Sci. Total Environ. 577, 349–359.

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