The neighbourhood-scale ADMS-Urban climate model calculates local perturbations to vertical profiles of temperature and humidity, representative of rural conditions upwind of the modelled urban area, in response to spatially varying surface parameters. These upwind profiles are calculated from near-surface meteorological measurements recorded outside the modelled urban area, ideally coinciding with air advecting towards the urban centre (i.e. upwind), and depend on the planetary boundary layer height (PBLH), surface roughness length (z0) and the stability parameter PBLH/LMO. LMO is the Monin–Obukhov length, a measure of the relative importance of mechanical turbulence and buoyancy (Hood et al., 2018; CERC, 2020). Calculation of the local perturbations to these vertical profiles arises from surface thermal and morphological parameters modifying heat and moisture processes, allowing a 3-D temperature and humidity field to be modelled across the domain.

The temperature and humidity perturbations are calculated by solving a coupled system of equations that govern heat and moisture processes at the ground (Carruthers and Weng, 1992; Raupach et al., 1992). The conservation of heat's boundary conditions are dependent on moisture via the latent heat flux, and evaporative processes are temperature dependent. The equations account for the spatial variation of surface heat fluxes, moisture, mean airflow and vertical turbulent diffusion (CERC, 2018). Heat fluxes are governed by variations in net radiation (Q∗) and storage heat, airflow and turbulent diffusion are controlled by variations in surface roughness (z0), and the moisture terms depend on the surface's resistance to evaporation, which accounts for both surface wetness and sub-surface moisture, with water surfaces having near-zero surface resistance to evaporation (Table 1).

Upwind Q∗ is determined from near-surface hourly meteorological measurements representative of conditions upwind of the model domain, following Eq. (1) (Holstag and van Ulden, 1983): 1Q∗=1-rK+-5.67×10-8T4+5.31×10-13T6+60CL81.12, where the first term represents the incoming SW radiation (K+) absorbed by the surface, which is dependent on the upwind surface albedo (r) defined around the edge of the modelled urban area. The second term in Eq. (1) accounts for the LW radiation released by the surface, a function of the upwind near-surface air temperature, T, and the downwelling LW radiation from the gaseous atmosphere and cloud cover (CL) are given by the third and fourth terms, respectively (Holstag and van Ulden, 1983).

The upwind storage heat flux (G) is calculated as a function of Q∗ according to Eq. (2) (Camuffo and Bernardi, 1982): 2G=a1dQ∗dt+a2Q∗+a3, where a1 (h), a2, and a3 (W m-2) are coefficients that depend on the land cover and surface moisture (Grimmond et al., 1991; Grimmond and Oke, 1999) and vary sinusoidally throughout the year (Keogh et al., 2012; Sun et al., 2017). For this application, the coefficients selected correspond to a hybrid of urban and rural surface properties (Grimmond and Oke, 1999) that allow for both the influence of urban materials on heat exchanges as well as the advection of nighttime stable atmospheric conditions from the rural to urban areas, with an annual mean of a1=0.7 h, a2=0.3 and a3=-7.5 W m-2 (CERC, 2018). These values represent the high proportion of Q∗ absorbed into the ground during the day in urban areas and re-released overnight, respectively, with the asymmetry relating to the urban fabric absorbing more heat in the early part of the day and the model requirement that the upwind PBLH corresponds to stable conditions at night. In reality, in urban areas, the nocturnal release of stored heat is often sufficient to produce an upward convective heat flux and hence maintain an unstable PBL (Oke et al., 1999); in ADMS-Urban, this is modelled via perturbations to the upwind conditions. The model accounts for the diurnal variation of ground heat storage and release by summing the daytime storage heat flux and releasing it linearly throughout the evening.

The magnitude of Q∗-G determines the amount of energy available for partitioning between the latent (LE) and sensible heat fluxes (H). Local perturbations (Δ) to the upwind surface heat fluxes are calculated based on relative differences between upwind surface parameters defined around the edge of the modelled urban area and the spatially varying surface characteristics defined across the model domain, according to the surface energy balance equation: 3ΔQ∗-ΔG-ΔLE=ΔH.

The model requires the following surface parameters (Table 1): thermal admittance (J K-1 m-2 s-1/2), surface resistance to evaporation (s m-1), albedo, surface roughness length (z0) (m) and normalised building volume (NBV) (m). NBV is defined as the volume of buildings within a grid cell per grid cell area and provides a measure of the density of buildings across the domain. Local ΔQ∗ values depend on the urban–upwind differences in albedo and NBV. ΔG is based on spatial differences in the surface's thermal properties (thermal admittance). Perturbations to energy lost through evaporation at the surface (ΔLE) depend on locally varying surface resistance to evaporation, air temperature and surface moisture content. ΔH represents spatially varying rates at which heat energy is transferred from the surface to the atmosphere by convection. Local perturbations to the upwind temperature profile due to surface characteristics depend on the cumulative effect of ΔH and the local surface roughness length (z0) accounting for the impact of building morphology on advection and turbulent diffusion and hence heat transfer processes.

Simulations are performed for the winter (10 November–10 December 2016) and summer (17 May–21 June 2017) APHH-China measurement campaigns (Shi et al., 2019). These are periods of interest given the expected impact of the urban canopy layer UHI on air pollution dispersion.

For this study, a single set of meteorological measurements, representing upwind conditions, are used to drive the model. Near-surface air temperature and relative humidity (∼ 8 m a.g.l. and ∼ 50 m a.s.l.) recorded at the rural APHH-China field campaign site (Han, 2019) in Xibaidian village, Pinggu (40.17∘ N, 117.05∘ E) (hereafter, the rural site), are used along with wind speed, wind direction and cloud cover data from the Beijing Capital International Airport Meteorology Observatory. Pinggu is located ∼ 60 km north-east of the urban APHH-China field site at IAP (39.97∘ N, 116.37∘ E) (hereafter the urban site). The World Meteorological Organization (WMO) Beijing Capital International Airport Meteorology Observatory (https://ncdc.noaa.gov/, last access: 19 May 2020) is situated approximately halfway between the two sites, inside the Sixth Ring Road (Fig. 1). Measurements of wind speed and direction from the airport site are used as the “rural”, or upwind data, instead of those from the rural site, as it is subject to WMO quality assurance and is likely to be less influenced by local frictional effects of neighbouring small buildings and vegetation, compared to the rural site, due its more exposed location. Upwind vertical wind speed profiles are perturbed locally in the model, impacting heat advection, following modifications to PBL stability due to spatially varying heat fluxes and surface roughness.

Incorporating near-surface air temperature measurements from a single rural meteorological station is a limitation of this study. Ideally, we would use several rural meteorological sites distributed around the model domain, selecting the air temperature measurement from the site coinciding with upwind conditions; an upwind measurement is desirable so that the air temperature sensor is not strongly influenced by the advection of urban heat. Air temperatures measured at the airport site were not deemed appropriate for this study given that the local environment is likely heavily affected by the warming effects of surrounding urban surface thermal properties and nearby AHEs. For this study, the only accessible upwind air temperature measurement data were from the rural field campaign site at Pinggu. However, during the winter period, the predominant wind direction was from the north-east, situating the model domain downwind of the rural site. During the summer period, winds from the north and east are the most prevalent; however, a growing frequency of south-westerly winds is also observed. Therefore, summer air temperatures measured at the rural site may be influenced at times by heat advection from urban Beijing.

At the urban site, a ceilometer gathered attenuated backscatter that were analysed with the CABAM algorithm (Kotthaus and Grimmond, 2018) to provide the mixing-layer height, the atmosphere's lowest layer in contact with Earth's surface resulting from turbulent exchange (Shi et al., 2019; Hertwig et al., 2020). This was assumed to equate to the PBLH.

Near-surface air temperatures are modelled across the area contained within Beijing's Sixth Ring Road (Fig. 1); the resolution of the model calculation grid is ∼ 105 m. Thermal and morphological properties covering the modelled urban area and surrounding suburban regions are derived from OpenStreetMap (OSM) data (https://openstreetmap.org/, last access: 9 March 2020) and LCZs mapped by the World Urban Database and Access Portal Tools (WUDAPT) project (http://www.wudapt.org/cities/in-asia/, last access: 19 May 2020). The function and plan area of specific buildings, green spaces and waterways are obtained from OSM (Fig. 2). Table A1 provides a full list of the OSM land use types and the thermal admittance, surface resistance to evaporation and albedo values assigned to each, based on data reported in the literature (Oke, 1982; Cox et al., 1999; Hamilton et al., 2014; CERC, 2018; K. Wang et al., 2019).

OSM land use information is overlaid onto Beijing's LCZ classes, which are mapped at 100 m resolution (Fig. 2). The methodology for generating LCZ maps for specific cities is well-documented (Stewart and Oke, 2012; Bechtel et al., 2015; Ching et al., 2018). For Beijing, there are nine urban and six rural LCZ types (Fig. 2; Table 1). The surface parameters assigned to each LCZ (Table 1) are based on ranges of values suggested by Stewart and Oke (2012), derived from previous urban climate observational and numerical modelling studies. Following Ching et al. (2018), thermal admittance values are assigned by selecting the midpoints of the Stewart and Oke (2012) ranges. Estimates of surface resistance to evaporation are not provided with the LCZ data; therefore, we use literature-reported values (Oke, 1982; Cox et al., 1999; Hamilton et al., 2014; CERC, 2018). A surface resistance to evaporation of 200 s m-1 is widely deemed in the literature to characterise urban surfaces, and thus we assign it to LCZs described by Stewart and Oke (2012) as consisting entirely of impervious materials (LCZ 1–3, 8 and 10). However, to account for the high density of green spaces and prevalence of road wetting for cleaning purposes across urban Beijing noted by Dou et al. (2019), we lower the surface resistance to evaporation given to LCZs described by Stewart and Oke (2012) as consisting of abundant pervious land cover (e.g. plants and trees) (LCZ 4–6 and 9) to 150 s m-1; this value is an approximate midpoint between the surface resistance to evaporation values given to green spaces and urban surfaces (Tables A1 and 1). Given the strong influence on daytime air temperatures of surface resistance to evaporation, this adjustment is made to ensure sufficient spatial heterogeneity in modelled air temperature is captured across central urban areas. The albedo values selected for each LCZ are the lower bounds of Stewart and Oke's (2012) ranges, closely matching the literature-reported albedo values used for the OSM data. Surface roughness lengths (z0) correspond with the Davenport classes Davenport et al. (2020) assigned to each LCZ by Stewart and Oke (2012). The NBV are calculated as the product of the midpoints of Stewart and Oke's (2012) ranges for roughness element height and building surface fraction.

A spatially weighted mean of the surface parameters is calculated at 100 m resolution (Fig. 3), matching the resolutions of the LCZ data and the model calculation grid (∼ 105 m). Surface characteristics at the upwind meteorological site are represented by a 1 km border extending around the perimeter of each thermal and morphological surface parameter map in Fig. 3. Differences between upwind surface parameters and those within the model domain are used to calculate the urban temperature perturbations (Sect. 2.1). The surface information defined between the Sixth Ring Road and the 1 km upwind border (Fig. 3), covering suburban areas, is required in the model to prevent erroneous simulated temperatures associated with a sharp transition between urban and rural surface parameters. Upwind parameters (Table 1) were derived from Stewart and Oke's (2012) ranges for LCZ 9 based on its definition as a “natural setting with sparsely arranged buildings and abundant pervious land cover”, closely matching the environment at the rural site in Pinggu (Shi et al., 2019). Stewart and Oke's (2012) LCZ 9 parameter values were modified to those given in Table 1 following model sensitivity tests, with thermal admittance most notably reduced to 600 J K-1 m-2 s-1/2, accounting for the large increment of heat stored in Beijing's urban fabric relative to neighbouring rural areas. Altitude effects on temperature are accounted for with the use of terrain elevation data (Fig. 3f) (https://www.usgs.gov/land-resources/eros/coastal-changes-and-impacts/gmted2010, last access: 1 April 2020). Urban Beijing is situated on a plain at an altitude of ∼ 50 m, but mountainous terrain lies to the north and west of the city across the rural areas (Fig. 3f).

The anthropogenic heat flux is not included in Eq. (3) and needs to be accounted for. The main sources include power, industry, transportation, residential and commercial building use, and human metabolism (Sailor, 2011; Lu et al., 2016; Yu et al., 2018). Our values are based on a mean summer AHE value estimated by Dou et al. (2019) at IAP using the Large scale Urban Consumption of Energy model (LUCY) (Lindberg et al., 2013). Their daily mean aggregate summer AHE (48.1 W m-2) is derived from national- and provincial-level energy consumption data and spatial proxy information (population density, gross domestic product and vehicle ownership rates) (Dou et al., 2019), a methodology also applied to other worldwide megacities, such as London (Gabey et al., 2019) and Shanghai (Ao et al., 2018). For this study, we generate a 3 km resolution grid (Fig. 4) of aggregate AHEs, representing the sum of all AHE source sectors. First, the IAP value for summer (mean for June, July and August) is scaled to represent an annual mean AHE value based on literature-reported monthly scaling factors (Fig. 5) (Lu et al., 2016). This annual mean AHE for IAP is distributed spatially through further scaling by the magnitudes of AHE estimated for each LCZ class by Stewart and Oke (2012) relative to the AHE value for LCZ 1 (IAP is situated in LCZ 1), according to Eq. (4): 4AHEi=XiX1×YJJAMSFJJA, where AHEi is the annual mean AHE value for LCZi (i=11–15 for LCZ A, B, D, E and G, respectively). Xi and X1 represent the AHE value estimated by Stewart and Oke (2012) for LCZi and 1 (midpoint of range), respectively. YJJA is the summer (June, July and August) mean AHE calculated for IAP by Dou et al. (2019), and MSFJJA gives the mean scaling factor for summer months (Fig. 5). A spatially weighted mean of the LCZ-specific AHEs is calculated at 3 km resolution (Fig. 4).

Single diurnal and monthly profiles are applied to the AHEs based on the profiles estimated by Lu et al. (2016). Lu et al. (2016) derived annual sectoral AHE totals for all provinces and municipalities in China from the officially published energy consumption statistics, obtained from a variety of sources (e.g. China Energy Statistical Yearbook). Weighted means of the diurnal and monthly temporal profiles for each sector, from Lu et al. (2016), are determined in relative proportion to the total annual sectoral AHEs estimated for the Beijing municipality. The nocturnal contribution from transportation is increased, following Biggart et al. (2020), to account for the influx of heavy-duty diesel trucks (HDDTs) into urban Beijing after the daytime ban (06:00–23:00) within the Fourth Ring Road (Zhang et al., 2019). We assume approximate direct proportionality between air pollutant emissions (Biggart et al., 2020) and AHEs from HDDTs and increase the nocturnal transportation sector AHE component, estimated by Lu et al. (2016), by ∼ a factor of 2.

The resulting monthly and diurnal aggregate AHE profiles (Fig. 5) have winter and summer peaks primarily caused by elevated heating and cooling activities, respectively, in residential and commercial buildings (Ichinose et al., 1999). Emissions are assumed to be proportional to electricity and heating fuel consumption (Lu et al., 2016). Elevated daytime AHEs with late morning and early evening peaks are predominantly from the combination of daytime commercial building thermal regulation and residential cooking and heating, with a smaller contribution from rush-hour-related traffic volume maxima (Lee et al., 2009; Ao et al., 2018).

AHEs are modelled as individual plumes with the ADMS-Urban air quality model (Owen et al., 2000; CERC, 2018) and build upon the local temperature perturbations caused by spatially varying surface characteristics (Sect. 2.1). All AHEs are assumed to be released into the atmosphere and then dispersed assuming quasi-Gaussian distributions driven by the upwind meteorological variables, the PBLH and the PBLH/LMO stability parameter. The accumulation of dispersed plumes of anthropogenic heat gives an energy density field (CT), in units of J m-3, which is converted to a local air temperature increment (ΔT) in the model according to 5ΔT=CTρcp, where ρ (1.225 kg m-3) and cp (1012 kJ kg-1 K-1) are standard values for the density and specific heat capacity of air at 15 ∘C (CERC, 2018).

The magnitude and temporal variability of Beijing's winter and summer canopy layer UHI are evaluated using hourly near-surface air temperature measurements. Unlike city-scale urban climate modelling studies, which commonly compare regional-scale climate model output with the nearest meteorological measurement station to a model grid box (Chen et al., 2016, 2018; Fallmann et al., 2016), ADMS-Urban can simulate air temperatures at specific locations corresponding to the exact coordinates of measurement sites. We compare UHIIs modelled at the urban site at IAP, for the winter and summer periods, with measured UHIIs, calculated as the difference between near-surface air temperatures observed at the urban and rural sites. Air temperatures at the urban site are recorded at ∼ 8 m a.g.l. and ∼ 50 m a.s.l., matching the measurement height and terrain elevation of the temperature sensor at the rural site (Sect. 2.2). The following statistical performance measures are used for model evaluation: 6root-mean-square  errorRMSE:=1n∑i=1n(Oi-Mi)2;7fractional  biasFb:=M‾-O‾0.5(O‾+M‾);8Pearson's  correlation  coefficientR:=1n-1∑i=1nMi-M‾σMOi-O‾σO; where n denotes the total number of matching hourly modelled (M) and observed (O) UHIIs, M‾ and O‾ indicate mean modelled and observed UHIIs, respectively, and σ is the standard deviation.

Further measured–modelled air temperature comparisons are not possible due to a lack of access to other near-surface air temperature observations. However, satellite-derived LSTs are readily available for the Beijing area and, although the ADMS-Urban model does not calculate LST, the correlation between neighbourhood-scale spatial variations of modelled near-surface air temperature and satellite-derived LST provides a useful comparison for model evaluation. This technique was also adopted by K. Wang et al. (2019) for high-resolution UHI simulations across Kuala Lumpur using ADMS-Urban to assist in the evaluation of modelled near-surface air temperature spatial patterns. Landsat 8 Operational Land Imager (OLI)/Thermal Infrared Sensor (TIRS) thermal band TIRS-1 data (https://www.usgs.gov/land-resources/nli/landsat, last access: 1 April 2020) are acquired at 100 m resolution, matching the modelled spatial resolution. LSTs are retrieved using the single-channel algorithm developed by Jiménez-Muñoz et al. (2009). We focus on the summer for this analysis given the stronger incoming SW, compared to winter, and hence the expected more a direct relationship between LSTs and near-surface air temperatures (K. Wang et al., 2019), with near-surface air temperatures strongly influenced by the upwards flux of heat from the surface. Landsat 8 LSTs are available for 23 May 2017 at 10:53 LT (local time), a time with minimal cloud cover, and are compared with near-surface air temperatures simulated on the same day at 11:00 LT, with both sampled on the same 100 m resolution grid. LSTs are compared with simulations that exclude AHEs for the following reasons: (i) previous studies have reported difficulties in determining the impact of AHEs on LSTs (Kato and Yamaguchi, 2005; Wang et al., 2017), and (ii) micro-scale advection of heat released by nearby surfaces is known to uncouple LSTs and air temperatures (Roth et al., 1989; Voogt and Oke, 1998); thus, we expect the release of anthropogenic heat to have a similarly strong influence on near-surface air temperatures and further contribute to differences with spatial LST variability.

We perform simulations with four distinct model configurations, each involving different surface property or AHE scenarios (Table 2). The experiments are designed to identify how the modelled UHII can be optimised to best represent the observations by use of appropriate input parameters, thus providing insight into the key processes driving Beijing's UHI in winter and summer. The base case uses the initial surface parameters and AHEs (Sect. 2.3 and 2.4). Gabey et al. (2019) showed that the top-down approach for estimating AHEs, as used for the AHEs adopted for this study, tends to underestimate hotspots associated with dense inner-city road networks and compact building developments. Therefore, base case AHE values are increased by 50 % in the AHE50 case (Table 2). Given the unexpectedly high latent heat flux values measured previously at the IAP site (Dou et al., 2019), the surface resistance to evaporation values are reduced to 150 s m-1 in LCZ categories 1–3, 8 and 10 (Table 1), as well as for all urban OSM land use types (Table A1) for the Evp150 case (Table 2). This matches the surface resistance to evaporation assigned to the upwind domain. The noAHE case is designed to isolate the contribution to Beijing's UHI from land surface characteristics alone, and thus AHEs are excluded.

The winter and summer period mean observed canopy layer UHIIs (IAP-Pinggu) are 3.1 and 1.8 ∘C, respectively. These values are similar to those derived previously from a dense network of ground measurements in Beijing (Yang et al., 2013; Wang et al., 2017). Yang et al. (2013) reported winter and summer averages across central Beijing (within the Fourth Ring Road) of 2.4 and 1.5 ∘C, respectively. Base case simulated UHIIs are underestimated for both periods compared to the measurements, with the winter values less than half the observed UHIIs (RMSE = 2.90 and Fb = -0.76; Table 3). The summer underestimation is lower; however, the RMSE is proportionally higher (Table 3).

The UHI is known to have distinct diurnal characteristics (Oke et al., 2017), and thus analysis of the model's ability to simulate the diurnal UHII variation can inform on the daily varying contributions to urban climate perturbations from surface energy balance changes, AHEs and background meteorology. Measured UHIIs in winter and summer peak during the evening at ∼ 4.5 ∘C (Fig. 6). However, other studies have found Beijing's canopy layer UHII maximum to be up to a factor of 2 greater in winter compared to summer months (Liu et al., 2007; Wang et al., 2017). They attributed this to stronger winter AHEs from elevated energy consumption for building heating systems (Lu et al., 2016), which readily accumulate in Beijing's frequently stable and shallow winter nocturnal boundary layer (Zhang et al., 2016), and more efficient nocturnal cooling in rural areas under frequent strong winter temperature inversions (Yang et al., 2013). Summertime nocturnal UHIIs are influenced more by the delayed release of heat stored within the urban fabric throughout the day (Oke et al., 1999; Wang et al., 2013), with a smaller proportion attributed to AHEs from residential air conditioning units (Zhao et al., 2018).

Simulated evening UHII maxima are underestimated compared to measurements for all scenarios, with base case values ∼ 2.5 ∘C lower than measurements from 19:00 to 06:00 LT in winter and ∼ 2 ∘C lower between 21:00 and 04:00 LT in summer (Fig. 6). However, previous studies of Beijing's evening canopy layer UHI in summer measured at different central urban meteorological sites have reported mean values between 2 and 3 ∘C (Yang et al., 2013; Wang et al., 2017; Jiang et al., 2019), agreeing closely with our simulated results (Table 4; Fig. 6b). This suggests that Beijing's canopy layer UHI exhibits strong spatial variability and that our local site characteristics at IAP may be incorrect.

Increasing AHEs by 50 % reduces nocturnal measured–modelled discrepancies in winter by ∼ 0.7 ∘C (Table 4; Fig. 6a). However, a substantial model underestimation persists (∼ 2 ∘C), with nighttime RMSE and fractional bias values of 3.11 ∘C and -0.58, respectively (Table 4). These low simulated nocturnal UHIIs are likely related to the use of coarse-resolution (3 km) aggregate AHEs that fail to resolve strong, local emission sources around the urban site at IAP. The IAP temperature sensor is located ∼ 110 m south of a busy road (Biggart et al., 2020) and is surrounded by high-rise buildings (Fig. 1), both of which are likely strong sources of anthropogenic heat, with nearby buildings also hindering the dispersion of heat at night. Two of the four urban meteorological stations in Beijing used by Wang et al. (2017) are situated in green belts or parks, and thus they are likely to be less influenced by major local sources of AHEs, which may account for the lower nocturnal UHIIs observed there relative to IAP. Additionally, Cao et al. (2016) found a strong correlation between high concentrations of particulate matter over urban areas and the nocturnal UHI for several megacities in China due to enhanced atmospheric absorption and re-emission of LW radiation back to the surface, reducing the evening cooling rate. The ADMS-Urban radiation model does not account for nocturnal warming effects from haze pollution, which has been shown to change surface energy and water partitioning in Beijing (Kokkonen et al., 2019).

Summer UHII underestimations at night, relative to measurements, are similarly reduced by ∼ 0.6 ∘C with increased AHEs (Table 4; Fig. 6b), reflected by a fractional bias improvement from -0.61 to -0.4 (Table 4). The remaining measured–modelled discrepancy is likely related to the model's determination of nocturnal ground heat flux, with the restriction that modelled upwind PBL conditions remain stable at night (CERC, 2018). However, the evening release of stored heat in other dry, densely built megacities in summer, such as Mexico City (Oke et al., 1999), has been found to be of sufficient magnitude to maintain an upward flux of convective heat throughout the evening, therefore prolonging the warming of near-surface air.

The lowest measured urban–rural near-surface air temperature differential occurs between 13:00 and 14:00 LT in both the winter and summer periods (Fig. 6). In summer, the observed mean UHII minimum is negative (-1.1 ∘C). Daytime UHIIs are largely controlled by the balance between (i) the urban–rural evapotranspiration differences based on vegetation amounts and irrigation behaviour in both areas (Oke et al., 1982; Grimmond et al., 1993; Estoque et al., 2017; He et al., 2020) and by (ii) the large storage heat fluxes associated with the building volumes and impervious materials of high thermal conductivity and heat capacity in urban areas (Anandakumar, 1999; Grimmond and Oke, 1999; Oke et al., 1999). Dry or limited vegetation will increase the UHII, but urban structures and materials can both shade and enhance storage heat fluxes, leading to delayed turbulent heat fluxes and decreasing the urban near-surface temperatures. Negative afternoon UHIIs previously observed in Beijing (Wang et al., 2017) were ascribed to a substantial discrepancy between urban and rural measurement heights, but this is not a factor here (Sect. 2.2 and 2.5).

Modelled daytime UHIIs with elevated AHEs exceed the observed values (∼ 0.3 ∘C in winter and ∼ 0.9 ∘C in summer, Table 4; Fig. 6). However, previously observed daytime UHIIs in central Beijing at multiple meteorological stations (Yang et al., 2013; Jiang et al., 2019) are of similar magnitude to the AHE50 case values. The model's inability to replicate the negative daytime UHIIs observed at the urban site may be due to an underestimation of afternoon storage heat flux or possibly that there are nearby fine-scale green spaces, unresolved in the land cover data implemented for this study, that increase evaporative cooling at IAP and limit its representativeness of the central Beijing region.

Model predictions of summer afternoon UHIIs are improved when urban surface resistance to evaporation is reduced from 200 to 150 s m-1 (Evp150 case), with cooler urban air temperatures simulated as the latent heat flux (Eq. 3) is increased (R=0.52; Fb = -0.17; Table 4). High moisture availability in central Beijing (i.e. low Bowen ratio, where Bowen ratio = sensible heat flux/latent heat flux)  and specifically at IAP, has previously been observed (Dou et al., 2019) and is thought to be related to extensive use of water for road cleaning and for irrigating the high density of greenbelts in urban Beijing. Smaller decreases in simulated daytime temperature in winter, after increasing urban moisture levels, are due to weak levels of incoming SW radiation. Negligible differences (< 0.2 ∘C) occur in modelled winter UHIIs between AHE50 and Evp150 cases, in contrast with substantial reductions to all values (0.5–1.5 ∘C) in summer (Fig. 7). Furthermore, the simulated diurnal temperature range in summer without AHEs (noAHE case) is 3 times higher than in winter (∼ 2.5 ∘C) (Fig. 6), driven by much stronger incoming SW radiation, which enhances the urban–rural differences between available energy partitioning and therefore impacts all of the surface energy balance fluxes (Eq. 3).

Differences between UHIIs simulated with and without AHEs (both cases with high urban moisture levels) quantify the diurnally averaged and hourly AHE contributions to the UHI in winter and summer (Figs. 6 and 7). These results suggest that Beijing's urban warming in winter is dominated by AHEs, with a small contribution from surface radiative effects alone between -0.5 and +0.1 ∘C. In summer, AHEs increase the modelled UHII by ∼ 60 %–80 % throughout the day (Fig. 6), peaking at 84 % at 20:00 LT, associated with heat released from residential cooling systems and rush hour traffic (Fig. 5) accumulating in a stabilising evening PBL (Shi et al., 2019; Hertwig et al., 2020). Wang et al. (2013) simulated a similar daily maximum AHE contribution to the UHI in Beijing of 75 %. Excluding AHEs causes winter and summer UHII biases to grow (RMSE of 4.05 and 3.07, respectively), whereas the temporal variations become more similar (R=0.62 and 0.76 in winter and summer, respectively; Table 3), reflected by the increased linearity between observed and noAHE modelled UHIIs in Fig. 7. Substantially larger error bars associated with both simulations that include AHEs are related to increased measured–modelled differences caused by simulated and real-world PBL dynamics differences and subsequent impacts on modelled heat dispersion.

Quantifying the relative importance of urbanisation-induced surface energy balance changes, including AHEs, is useful for urban planners. Most notably, our results suggest that strategies aimed at reducing the daytime storage heat flux would help to decrease nighttime UHIIs in summer by reducing nocturnal heat release, hence lowering the cooling energy demand at night and therefore the contribution from AHEs to urban warming.

Maps of near-surface air temperature provide information on the location and physical characteristics of the warmest urban microclimates that may pose the biggest health risk to residents during extreme heat events. Urban cool islands (higher rural versus urban temperatures) associated with waterways and green spaces (K. Wang et al., 2019) can also be identified.

Neighbourhood-scale resolution (∼ 100 m) maps of simulated air temperature (2.5 m a.g.l.) across urban Beijing on 23 May 2017 at 11:00 LT are compared with Landsat 8 LSTs (Sect. 2.5) in Fig. 8. Due to the infrequency of Landsat 8 satellite image availability (every 16 d), we are unable to test how variable the spatial correlation between LSTs and modelled near-surface air temperatures is with time. However, the comparison for this single hour during the summer period provides a useful guide for assessing the general model performance in capturing urban Beijing's neighbourhood-scale air temperature patterns using a hybrid of LCZ and OSM land cover data. Near-surface temperatures are modelled with base and Evp150 case surface resistance to evaporation values (AHEs excluded) to test the representativeness of the enhanced urban moisture scenario for the full model domain.

Generally, the range of LSTs far exceeds that of near-surface air temperatures across urban areas. Large differences in thermal properties between impervious surfaces and the atmosphere and different heating mechanisms cause LSTs to heat more rapidly in response to the absorption at the surface of strong incident SW radiation in summer, whereas the atmosphere heats by convection (Anandakumar, 1999). Differences between LSTs and air temperatures vary diurnally, with the Landsat overpass time (11:00 LT) coinciding with an atmospheric urban cool island in summer (Fig. 6b) but also a growing surface urban heat island that peaks in the early afternoon (Meng et al., 2018; Li et al., 2020). Furthermore, air temperatures within the urban canopy are impacted by all of the energy exchange processes, including micro-scale advection of heat from nearby surfaces with varying moisture content, thermal properties and aerodynamic roughness, and thus they can become uncoupled from the LSTs (Voogt and Oke, 2003). These inherent differences between the two variables limit direct comparisons and thus the strength of the correlation to be expected; however, the relative spatial patterns are of interest.

The LSTs range between 16 and 47 ∘C within the domain (Fig. 8). They generally peak within the Fifth Ring Road and decrease with distance from the urban centre as the amount of green space increases (Estoque et al., 2017). Small areas of high LSTs in suburban zones between the Fifth Ring Road and Sixth Ring Road to the NW and SE (Fig. 8d) are reflective of the suburban expansion during the last decade observed by Liu et al. (2020). The modelled near-surface air temperatures at 11:00 LT range between 15 and 27 ∘C within the Sixth Ring Road (Fig. 8a and b). This spatial variation is greater during the early evening hours (not shown), when the canopy layer UHI peaks (Fig. 6b) with more clearly defined near-surface temperature hotspots.

Correlation between the spatial variation of LSTs and simulated near-surface air temperature improves when using the base case surface resistance to evaporation values (R=0.58) relative to the high urban moisture case (R=0.52; Fig. 9). This is caused by modelled air temperature increases within the Fifth Ring Road of 2 to 3 ∘C (Fig. 8c) as a result of reduced daytime evaporative cooling. Near-surface air temperatures simulated with high urban moisture do not have the same general decrease with distance from the urban centre as seen in the LSTs (Fig. 8) because the spatial variability in the surface resistance to evaporation has been removed. This is reflected in Fig. 9b, with no relationship between the highest LSTs and Evp150 case simulated air temperatures. Equal urban and upwind surface resistance to evaporation values (150 s m-1) lead to simulated central urban air temperatures that are mainly controlled by the much greater thermal admittance values across the modelling domain versus the upwind domain. This lowers central urban near-surface air temperatures at 11:00 LT relative to suburban regions between the Fifth Ring Road and Sixth Ring Road that have lower thermal admittances (Fig. 2), producing a homogeneous urban near-surface air temperature distribution (Fig. 8b). This is a further indication that local surface radiative cooling, likely due to nearby green spaces, differentiates the urban site from the mean conditions across the central Beijing region. Worse spatial correlation with LSTs but better agreement with near-surface air temperature measurements with increased urban moisture also reflects expected differences between LSTs and near-surface air temperatures. Micro-scale advection and turbulent diffusion within the urban canopy can mix warmer and cooler pockets of air, reducing the coupling between LSTs and air temperatures (Roth et al., 1989).

The lowest LSTs and modelled air temperatures correlate most strongly (Fig. 9), corresponding with green spaces, waterways (Fig. 2) and areas of high elevation (Fig. 3). The model's ability to capture these fine-scale urban cool islands, such as Qianhai Lake near the centre of Beijing (Fig. 2), in addition to the general urban temperature pattern, highlights the successful implementation for this study of the LCZ and OSM data.

Large-scale urban developments strongly impact local air temperatures, following the replacement of vegetative surfaces with expanses of concrete and asphalt, and therefore affect the thermal comfort, cooling and heating energy demand, and air quality across neighbouring residential areas (Hamilton et al., 2014). In this section, we investigate the extent to which simulated spatial temperature patterns near the Beijing Capital International Airport vary throughout the day due to different surface characteristics. Figure 10 shows a satellite image of the airport and its surroundings,, alongside maps (100 m resolution) of the surface properties that have the greatest influence on modelled near-surface air temperatures (CERC, 2018).

Figure 11 presents modelled local temperature perturbations (excluding AHEs) relative to upwind values, across the region displayed in Fig. 10, at four different times of the day on 23 May 2017. At 05:00 LT, prior to sunrise and in the absence of incoming SW radiation, modelled near-surface air temperatures at the airport are minimally affected by the underlying impervious surface (Fig. 11a). Cool regions adjacent to the Wenyu River, running SE to NW (Fig. 10) with UHIIs of ∼ -2 to -3 ∘C, are related to green spaces with both low thermal admittance and surface resistance to evaporation.

At 14:00 LT, when the mean canopy layer UHII at the urban site peaks (Fig. 6b), a clear spatial temperature pattern has developed (Fig. 11b). Modelled UHIIs at the airport site rise to ∼ 6–8 ∘C, caused by the high resistance to evaporation (200 s m-1) and low albedo (0.08) of the airport runways (Table A1). The low albedo surface absorbs more of the strong daytime incoming SW radiation, with a greater proportion of the net radiation partitioned to the upwards convective flux of sensible heat due to the low surface moisture content. The fine-scale structure of the Wenyu River is clearly defined at 14:00 LT as the water's near-zero resistance to evaporation cools near-surface temperatures relative to the neighbouring vegetation.

After sunset, at 19:00 LT, UHIIs to the north and west of the airport peak at ∼ 7–9 ∘C, matching air temperatures at the airport (Fig. 11c). The higher thermal admittance of these areas relative to the airport causes the release of greater amounts of stored heat in the early evening. Dispersion of this upwelling ground heat flux is inhibited by a stabilising nocturnal PBL, creating a positive temperature increment to the north of ∼ 2 ∘C relative to the cooling airport region at 23:00 LT (Fig. 11d).

Figure 12a shows the land cover at the residential and forest sites marked in Figs. 10 and 11. The sites are only ∼ 1 km apart, on opposite sides of the Wenyu River, but experience their own distinct microclimates driven by the underlying land surface characteristics. This is quantified in Fig. 12b by the mean summer diurnal modelled near-surface air temperature differences between the airport site and both the residential and forest sites.

After sunrise, the temperature difference (ΔT) between the airport and both the residential and forest site increases (Fig. 12b). ΔT rises more sharply at the forest site, due to its lower surface resistance to evaporation and therefore stronger evaporative cooling than in the residential area and peaks at 14:00 LT when the airport is ∼ 3 and ∼ 5 ∘C warmer than the residential and forest sites, respectively (Fig. 12b). In the evening, after sunset, ΔT decreases to ∼ 0.25 and ∼ 0.5 ∘C at the residential and forest sites (Fig. 12b), respectively, as spatial temperature variations due to surface characteristics reach a minimum (Fig. 11d). These negligible modelled nocturnal temperature differences (excluding AHEs) again highlight the dominant contribution from AHEs to UHIIs at night (Fig. 6).

Synergies between extreme heat events and UHIIs in Beijing are well documented (Li et al., 2015; Chen et al., 2018; Jiang et al., 2019; He et al., 2020). Two heatwave periods during the summer are identified from (a) 18 to 21 May and (b) 14 to 20 June (Fig. 13), with heatwave events defined here as 3 or more consecutive days with a daily maximum temperature (Tmax) at the urban site reaching at least 35 ∘C, following the Chinese Meteorology Administration heatwave definition (Tan et al., 2007; Jiang et al., 2019). In Fig. 13, red-shaded regions mark hours with higher urban than rural temperatures and highlight the build-up of heat in urban Beijing during the evening. Blue-shaded regions mark hours with higher rural than urban temperatures and emphasise the negative summer daytime UHI (Fig. 6b).

Mean measured and modelled (Evp150 case) daytime (10:00 to 16:00 LT) and nighttime (22:00 to 04:00 LT) UHIIs for heatwave and non-heatwave days are presented in Fig. 14. Day and night hours are defined based on previous UHI heatwave studies (Wang et al., 2017; Jiang et al., 2019).

At night, the mean measured UHII is 5.3 ∘C on heatwave days, 1.1 ∘C higher than on non-heatwave days. Previous nocturnal UHII increments of similar magnitude during heatwaves in Beijing (Jiang et al., 2019) have been attributed to greater daytime storage heat flux from stronger SW and LW radiation and therefore a more prolonged period of evening heat release warming the near-surface (Li et al., 2015). Warmer nights lead to increased residential AHEs from air conditioning units, further strengthening the UHII (Zhao et al., 2018).

Modelled UHIIs are underestimated by 31 % compared to measurements during non-heatwave nights. However, this increases to 56 % during heatwave nights and further suggests that the model-calculated evening stored heat release is too low (Sect. 3.1). Elevated daytime storage heat flux during heatwaves increases the model's underestimation of ground heat release at night, hence the measured–modelled evening UHII discrepancy grows (Fig. 14). Furthermore, the model does not account for the day-to-day accumulation of stored heat during a heatwave period, only the diurnal variation, therefore the model's underestimation of evening heat release grows incrementally throughout a heatwave. The use of the same diurnal AHE profile for all days also likely contributes, with the proportion of AHEs released at night expected to increase as cooling energy demand at night grows during heatwaves (Sailor and Vasireddy, 2006).

During the day, the mean measured UHII is -1.34 ∘C on heatwave days, compared to -0.57 ∘C on non-heatwave days (Fig. 14). This is contrary to previous measurements of Beijing's daytime UHII during extreme heat events, which have shown an increase relative to normal days (Li et al., 2015; He et al., 2020) explained by (a) greater urban-rural evapotranspiration and sensible heat flux differences, (b) stable synoptic conditions associated with heatwaves reducing mixing between urban and rural air, and (c) elevated AHEs (Li and Bou-Zeid, 2013; Li et al., 2015; He et al., 2020). Therefore, the daytime heatwave UHII decrease observed at the urban site is likely another example of the impact of local site characteristics (e.g. nearby vegetation) on air temperatures at IAP. Overall, extreme temperature events clearly worsen measured–modelled UHII comparisons in summer, and model performance is substantially better under non-heatwave conditions.