The Air-temperature Response to Green/blue-infrastructure Evaluation Tool (TARGET v1.0): an efficient and user-friendly model of city cooling

The adverse impacts of urban heat and global climate change are leading policymakers to consider green and blue infrastructure (GBI) for heat mitigation benefits. Though many models exist to evaluate the cooling impacts of GBI, their complexity and computational demand leaves most of them largely inaccessible to those without specialist expertise and computing facilities. Here a new model called The Air-temperature Response to Green/blue-infrastructure Evaluation Tool (TARGET) is presented. TARGET is designed to be efficient and easy to use, with fewer user-defined parameters and less model input data required than other urban climate models. TARGET can be used to model average street-level air temperature at canyon-to-block scales (e.g. 100 m resolution), meaning it can be used to assess temperature impacts of suburb-to-city-scale GBI proposals. The model aims to balance realistic representation of physical processes and computation efficiency. An evaluation against two different datasets shows that TARGET can reproduce the magnitude and patterns of both air temperature and surface temperature within suburban environments. To demonstrate the utility of the model for planners and policymakers, the results from two precinct-scale heat mitigation scenarios are presented. TARGET is available to the public, and ongoing development, including a graphical user interface, is planned for future work.

1 Introduction

Policymakers and decision makers are increasingly aware of the cooling potential of green and blue infrastructure (GBI). Recent examples of this include the Australian Federal Government's 20 Millon Trees Program (Commonwealth of Australia, 2017) and Singapore Green Plan (Singapore Ministry of Environment and Water Resources, 2006). Governments and urban planners wish to evaluate the cooling effects of design and planning options. Urban climate models are becoming more complex, allowing more complete representation of urban physics. However, the complexity of urban climate models renders them inaccessible to consultants (Elasson, 2000), who typically work for designers and planners. Commonly used urban climate models, such as the Weather Research and Forecasting (WRF) model (Skamarock et al., 2008) and ENVI-met (Bruse, 1999), require trained research scientists and significant computational resources to run. As a result, consultants usually provide generic and unsubstantiated estimates of cooling magnitudes. Consequently, there is a need for simple, computationally efficient, and scientifically defensible urban climate models that can be used by consultants to provide reliable estimates of cooling to governmental planners and policymakers.

There are a number of existing micro-to-local-scale urban models capable of modelling GBI. The most complex models are primarily based on computational fluid dynamics (CFD) techniques. These include ENVI-met, hand-coded CFD models (such as OpenFOAM; OpenFOAM, 2011; or STAR-CD; CD-adapco, 2011) and other CFD-based approaches (Bailey et al., 2014, 2016; Kunz et al., 2000; Schlünzen et al., 2011; Yamada and Koike, 2011; Bruse, 1999). ENVI-met is the most commonly used urban microclimate model. However, numerous ENVI-met studies have reported concerns with model accuracy, particularly for representation of vegetation (Ali-Toudert and Mayer, 2006; Krüger et al., 2011; Acero and Herranz-Pascual, 2015; Spangenberg et al., 2008). In addition, the complexity of configuration and computational intensity of all CFD-based models (i.e. 24 h of simulation requiring 24 h of computation time) puts their usage out of the reach of non-specialized users.

A second group of commonly used models, such as SOLWEIG (Lindberg et al., 2008) and RayMan (Matzarakis et al., 2007, 2010), focus on radiation fluxes in urban areas. These models have been used to assess GBI cooling, especially tree shading. However, the limitations of these models may not allow a complete assessment of GBI cooling because the effects of evapotranspiration are neglected. The Temperatures of Urban Facets in 3-D (TUF-3D) model (Krayenhoff and Voogt, 2007) and a vegetated derivative (VTUF-3D) (Nice et al., 2018) provide a precise representation of urban canyon physical processes. However, TUF-3D and VTUF-3D require a high level of computer power, modelling experience, and parameter set-up.

The canyon air temperature (CAT) model (Erell and Williamson, 2006) shows potential as a computationally efficient model that calculates air temperatures using urban building and vegetation geometry and moisture availability. However, the lack of surface temperature prediction makes it difficult to derive human thermal comfort indexes. The Town Energy Balance (TEB) model (Masson, 2000) has emerged as a popular urban area parameterization scheme. The TEB-Veg (Lemonsu et al., 2012; Redon et al., 2017) variation includes urban vegetation and provides functionality to assess cooling impacts of GBI. However, the TEB-Veg model configuration and application requires a level of modelling skill normally outside the capability of environmental consultants.

While not an air temperature model, the Local-Scale Urban Meteorological Parameterization Scheme (LUMPS) (Grimmond and Oke, 2002) has been widely used to assess the impacts of GBI on surface energy balance (SEB). The Surface Urban Energy and Water Balance Scheme (SUEWS) (Järvi et al., 2011), a superset of LUMPS with added urban water balance functionality, provides a means to assess vegetation (and associated soil) transpiration impacts at local scales. SUEWS shows good performance in SEB evaluations for Vancouver and Los Angeles (Järvi et al., 2011), Helsinki (Järvi et al., 2014), and Singapore (Demuzere et al., 2017). Due to the success and simplicity of LUMPS, we use it as a key component of the model presented here.

The lack of an efficient yet accessible tool for assessing GBI is identified as a research gap. Here we introduce and evaluate a new model called The Air-temperature Response to Green/blue-infrastructure Evaluation Tool (TARGET). TARGET is a simple modelling tool that calculates surface temperature and street-level (below roof height) air temperature in urban areas. TARGET is designed to make quick and accurate assessments of urban temperatures and GBI cooling impacts with minimal input data requirements. TARGET calculates the average air temperature at street level in urban areas but does not represent micro-scale variations of radiation exchange or wind flow at the human scale. The model is designed to be used at the urban canyon to block scales (100–500 m). We recommend a minimum spatial resolution of 100 m for air temperature simulations and 30 m for surface temperature. It can be used to assess the canyon-averaged impacts of street-scale interventions or larger-scale suburban greening projects. TARGET is a climate-service-oriented tool that provides a first-order approximation of the impacts of GBI on surface temperature and street-level air temperature to provide scientific guidance to practitioners during the planning process. The computational efficiency of the model is such that a user (with 1–2 h of training) can calculate in minutes the 100 m horizontal resolution cooling effects, on a normal desktop computer, across an entire suburb/local government area or neighbourhood.

The main aims of this paper are the following: (1) to provide a technical description of TARGET, (2) to provide detailed evaluation of model performance, and (3) to provide proof of concept and illustrate how the model can be operationalized by consultants and practitioners.

2 Model description

2.1 Model overview

As outlined in Fig. 1, TARGET treats each model grid point as an idealized urban canyon with roofs, walls, and ground-level facets. Roof width (W_roof), building height (H), tree width (W_tree), and street width (W) are used to define the geometry of the canyon. The thermal and radiative characteristics of roofs and walls are considered to be uniform. At street level, the surfaces can be defined as concrete, asphalt, grass, irrigated grass, and water. Trees are represented at roof height, and the surfaces beneath trees are considered to be representative of the ground-level surfaces. To represent the first-order shading impacts of trees, we effectively represent the tree canopy as part of the urban canyon. As shown in Fig. 1, the width of the canyon (and therefore the amount of radiation that enters and leaves the canyon) is modulated by the planar area of trees. The simple method implies that none of the radiation effectively “intercepted” by trees enters the canyon. The area underneath trees (not shown in planar land cover maps) is added to the model to represent the additional thermal mass. This simple approach allows for a first-order representation of two major process associated with trees: solar shading and longwave trapping.

Additionally, water bodies are treated separate to all other surfaces using an independent module. More details about the model process are shown in Fig. 2. For each grid point, the average surface characteristics are used to calculate an aggregated surface temperature (T_surf). T_surf is converted to an average canopy layer air temperature (T_ac) using an estimated canopy wind speed (U_can) and above-canopy air temperature (T_b). A uniform T_b for all grid points is diagnosed for each time step using reference meteorological variables.

Figure 1 Schematic of TARGET urban canyon set-up. T_ac is the canopy layer air temperature, and T_b is the above-canopy air temperature, which is a uniform value across the whole domain. W_roof is the roof width, W_tree is the tree width, W is canyon width, and $W*=W-W_{\mathrm{tree}}$. The surface beneath trees is assumed to be representative of canyon ground-level surfaces.

Figure 2 Overview of approach used in TARGET. T_ac is street-level (urban canopy layer) air temperature (^∘C), T_b is the air temperature above the urban canopy layer (^∘C), T_surf,i is the surface temperature for surface type i, K↓ is incoming shortwave radiation (W m⁻²), L↓ is incoming longwave radiation (W m⁻²), T_a is reference air temperature (^∘C), R_n is net radiation (W m⁻²), RH is relative humidity (%), F_i is the fraction of land cover type i (%), Q_H,i is the sensible heat flux for surface i from LUMPS (W m⁻²), Q_G,i is the storage heat flux for surface type i from LUMPS (W m⁻²), U_z is the reference wind speed (m s⁻¹), H is the average building height (m), W is the average street width (m), r_s is the resistance from the surface to the canopy (s m⁻¹), and r_a is the resistance from urban canopy to the atmosphere (s m⁻¹). $T_{\mathrm{b}}^{\ast }$ is a homogeneous value for the whole domain, which is diagnosed through the processes laid out in Sect. 2.7.

2.2 Input data requirements

2.2.1 Land cover

TARGET uses simple data inputs that are intended to be easily accessible. The model requires the user to define the plan area of buildings (A_roof), concrete (A_conc), asphalt (A_asph), grass (A_gras), irrigated grass (A_igrs), tree (A_tree), and water (A_watr). These land cover categories are self-explanatory and describe most of the surfaces present in urban areas. Local governments often have geographical information system (GIS) datasets of land cover and/or land use that can be used for land cover input data. Further, we intend to develop a graphical user interface (GUI) that allows users to easily input land cover datasets and define the model domain. This feature will allow users to convert and upload GIS data (e.g. shape and raster files) directly into the model. The W_roof, W_tree, W, W*, and wall area (A_wall) are calculated from plan area land cover inputs. However, average building height (m) must be user-defined or set to a domain average value. If detailed land cover data are not available, input data can be defined from existing land-use lookup tables or from databases such as the World Urban Database and Portal Tool (WUDAPT) (Mills et al., 2015; Ching et al., 2018). See Wouters et al. (2016) for an example of how the WUDAPT data could be integrated.

2.2.2 Meteorological data

TARGET requires reference meteorological data to drive the model and calculate street-level air temperature. The following meteorological variables are required: incoming shortwave (solar) radiation (K↓), incoming longwave (terrestrial) radiation (L↓), relative humidity (RH), reference wind speed (typically at 10 m) (U_z), and air temperature (T_a). The user must define the height above ground of reference U_z and T_a. Meteorological data should be representative of a nearby airport or an open site with minimal buildings. At a minimum, reference meteorological data should conform to World Meteorological Organization guidelines (Oke, 2007).

2.3 Radiation calculation

The net radiation of the ith surface type (R_n,i) is calculated using the following:

$$\begin{array}{}\text{(1)}& R_{{\mathrm{n}}_{,}i}=\left(K\downarrow (\mathrm{1}-{\mathit{\alpha }}_i)+{\mathit{ϵ}}_i\left(L\downarrow -\mathit{\sigma }{T}_{\mathrm{surf},i,[t-\mathrm{2}]}^{\mathrm{4}}\right)\right){\mathrm{SVF}}_i,\end{array}$$

where α_i is surface albedo, ϵ_i is surface emissivity, and σ is the Stefan–Boltzmann constant ($\mathrm{5.67}\times {\mathrm{10}}^{-\mathrm{8}}$ W m⁻² K⁻⁴). The α_i and ϵ_i values are predefined for each surface (see Table 1). The right-hand side of the equation accounts for net longwave radiation. The modelled $T_{\mathrm{surf},i,[t-\mathrm{2}]}$ from two time steps (t) previously is used to calculate L↑. This is necessary to avoid circular logic in model calculations; modelled $T_{\mathrm{surf},i,[t-\mathrm{2}]}$ is calculated using the storage heat flux (Q_G,i), which takes R_n from the previous time step. The time lag does not significantly affect calculations when a 30 min time step is used. The average sky view factor (SVF_i) is included to broadly represent the interception of incoming and outgoing short- and longwave radiation by buildings and trees on the radiation balance. Addition of SVF restricts the net radiation exchange of each facet to its total view factor occupied by sky. It assumes that walls and ground surfaces have similar longwave emission relative to the sky and that the solar radiation receipt can be approximated by SVF, on average. This simplification means that the model makes no distinction between lit and unlit buildings walls and roads. SVF_i for ground-level, wall, and roof facets is defined as (Sparrow and Cess, 1978)

$$\begin{array}{}\text{(2)}& {\displaystyle }& {\displaystyle }{\mathrm{SVF}}_{\mathrm{ground}}={\left[\mathrm{1}+{\left({\displaystyle \frac{H}{W*}}\right)}^{\mathrm{2}}\right]}^{\frac{\mathrm{1}}{\mathrm{2}}}-{\displaystyle \frac{H}{W*}};\text{(3)}& {\displaystyle }& {\displaystyle }{\mathrm{SVF}}_{\mathrm{wall}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\left(\mathrm{1}+{\displaystyle \frac{W*}{H}}-{\left[\mathrm{1}+{\left({\displaystyle \frac{W*}{H}}\right)}^{\mathrm{2}}\right]}^{\frac{\mathrm{1}}{\mathrm{2}}}\right);\text{(4)}& {\displaystyle }& {\displaystyle }{\mathrm{SVF}}_{\mathrm{roof}}=\mathrm{1}.\end{array}$$

The R_n,i is then used to calculate a Q_G,i for each surface type.

Table 1 Parameter set-up for all TARGET simulations in this article.

¹ Oke (1987). ² Stewart et al. (2014). ³ Järvi et al. (2014). ⁴ Narita et al. (1984). ⁵ Asaeda and Ca (1993). ⁶ Grimmond et al. (1993). ⁷ Doll et al. (1985).
α is the surface albedo, ϵ is the surface emissivity, C is the volumetric heat capacity (J m⁻³ K⁻¹) (×10⁶), κ is the thermal diffusivity (m² s⁻¹) ($\times {\mathrm{10}}^{-\mathrm{6}}$), T_m is the average soil (ground) temperature (^∘C), α_pm is the LUMPS empirical parameter (alpha parameter), relating to surface moisture, β is the LUMPS empirical parameter (beta parameter), and T_m bracketed values are used in Mawson Lakes suburb simulations, derived from 1-month spin-up.
^a Soil layer beneath water layer. ^b The traditional force–restore method is not well suited to urban surfaces (e.g. roof and walls) — we use an artificially low thermal diffusivity to represent a thin layer. This is discussed further in Sect. 2.5. ^c Roof and wall layers are represented by the same model parameters. n/a: not applicable.

2.4 Storage heat flux (Q_G) calculation

The storage heat flux (Q_G,i) for the ith land cover class is calculated using an adapted version of the objective hysteresis model (OHM) (Grimmond and Oke, 2002):

$$\begin{array}{}\text{(5)}& Q_{G,i}=R_{\mathrm{n},i}{a}_{\mathrm{1},i}+\left({\displaystyle \frac{\partial R_{\mathrm{n},i}}{\partial t}}\right)a_{\mathrm{2},i}+a_{\mathrm{3},i},\end{array}$$

where $\frac{\partial R_{\mathrm{n},i}}{\partial t}=\mathrm{0.5}(R_{\mathrm{n},i,(t-\mathrm{1})}-R_{\mathrm{n},i,(t+\mathrm{1})})$ and the three a coefficients are defined using cited values for each surface (see Table 1). The a coefficients capture the hysteresis pattern commonly observed between the R_n and Q_G,i in urban areas. See Grimmond and Oke (1999) for a full description of the OHM and the role of the a parameters in Q_G,i calculations. The Q_G,i is then used to calculate the T_surf for each land cover type using the “force–restore” method.

2.5 Surface temperature calculation (force–restore)

The force–restore method is an efficient method for calculating surface temperature (Bhumralkar, 1975; Deardorff, 1978) and is an alternative to multilayer conduction approaches used in other climate models. The force–restore method is used to ensure that the model remains computationally efficient. The ground layer is conceptually divided into two layers with uniform vertical temperature: a thin surface layer and a deep soil layer. The forcing term, which is driven by Q_G,i, heats the surface layer. The restore term, driven by deep soil temperature, dampens the forcing term. The change in surface temperature T_surf for surface i, with respect to time (t), is calculated as (Jacobs et al., 2000)

$$\begin{array}{}\text{(6)}& {\displaystyle \frac{\partial T_{\mathrm{surf},i}}{\partial t}}={\displaystyle \frac{Q_{G,i}}{C_{i}D}}-{\displaystyle \frac{\mathrm{2}\mathit{\pi }}{\mathit{\tau }}}(T_{\mathrm{surf},i,[t-\mathrm{1}]}-T_{\mathrm{m},i,[t-\mathrm{1}]}),\end{array}$$

where C_i is the volumetric heat capacity (J m⁻³ K⁻¹), τ is the period (86 400 s), D is the damping depth of the diurnal temperature wave $D=\mathrm{2}\mathit{\kappa }/\mathit{\omega }\mathrm{0.5}$, $\mathit{\omega }=\mathrm{2}\mathit{\pi }/\mathit{\tau }$, and κ represents thermal diffusivity. The average soil (ground) temperature (^∘C) (T_m) is calculated using

$$\begin{array}{}\text{(7)}& {\displaystyle \frac{\partial T_{\mathrm{m},i}}{\partial t}}={\displaystyle \frac{\mathrm{\Delta }{Q}_{G,i}}{C_i{D}_y}},\end{array}$$

where $D_y=D\sqrt{\mathrm{365}}$, the damping depth for the annual temperature cycle (m).

The force–restore method, which assumes two layers each of uniform temperature, cannot be applied to more complex surfaces such as water, trees, walls, or roofs. For roofs we set C at a realistic value and use κ as a tuning parameter to represent layers of thermally active mass characteristic of most building roofs, which are often thinner than ground-level surfaces. This approach produces accurate T_surf,roof results (see Sect. 3.2), but ongoing work is needed to represent roofs in a physically realistic and efficient manner. For simplicity, the wall surfaces are assumed to have the same thermal properties as roofs. For trees, we assume that T_surf,tree is equal to T_a (see Fig. B3 for justification), and a simple water body model is used to calculate T_surf,watr.

2.6 Simple water body model

The water model is used for modelling small inland water bodies, such as lakes and wetlands. Our analysis suggests that the OHM–force–restore method cannot be used to reliably reproduce water surface temperatures. We tested the OHM modifications and parameters used by Ward et al. (2016) and found substantial over-predictions of surface water temperature (over 10 ^∘C) during the day. As such, we developed a simple water body model to stand in for the OHM–force–restore method. The water model in TARGET is based on a single water layer, overlaying a soil layer. Essentially, the force–restore surface temperature model is implemented and is overlain by a homogeneous mixed water layer (i.e. neglecting thermal stratification) representing a water body of depth d_watr (m). The model is designed to apply to water bodies of 0.1–1.0 m depths. The water model is based on the pan evaporation model of Molina Martínez et al. (2006), which closely follows that of the lake model of Jacobs et al. (1998). The water body model also determines the surface energy balance of the water surface. The energy balance model for the water layer is given by Molina Martínez et al. (2006):

$$\begin{array}{}\text{(8)}& S_{\mathrm{ab}}+L_{\mathrm{n}}+Q_{H,\mathrm{watr}}-Q_{E,\mathrm{watr}}-Q_{G,\mathrm{watr}}-\mathrm{\Delta }{Q}_{S,\mathrm{watr}}=\mathrm{0},\end{array}$$

where S_ab is absorbed shortwave radiation (W m⁻²), L_n is the net longwave radiation (W m⁻²), Q_G,watr is the convective heat flux at the bottom of the water layer and into the soil below (W m⁻²), and ΔQ_S,watr is the change in heat storage of the water layer (W m⁻²). Solar radiation penetrates the water surface and is absorbed as described by Beer's law (Molina Martínez et al., 2006):

$$\begin{array}{}\text{(9)}& S_{\mathrm{ab}}=K_{\mathrm{n}}\left[{\mathit{\beta }}_k+(\mathrm{1}-{\mathit{\beta }}_k)(\mathrm{1}-e^{-\mathit{\eta }})\right],\end{array}$$

where K_n is the net shortwave radiation (W m⁻²), β_k is the amount of shortwave radiation immediately absorbed by the water layer (set to 0.45) (Molina Martínez et al., 2006), and η is the extinction coefficient. Here, η is calculated according to Subin et al. (2012), for the water layer with depth d_watr (m):

$$\begin{array}{}\text{(10)}& \mathit{\eta }=\mathrm{1.1925}{d}_{\mathrm{watr}}^{-\mathrm{0.424}}.\end{array}$$

A correction factor for the solar path length zenith angle is often applied to Eq. (9) (Molina Martínez et al., 2006), but this is omitted from TARGET to reduce complexity.

The Q_G,watr into the soil at the base of the water layer is given by Molina Martínez et al. (2006):

$$\begin{array}{}\text{(11)}& Q_{G,\mathrm{watr}}=-C_{\mathrm{watr}}{\mathit{\kappa }}_{\mathrm{watr}}{\displaystyle \frac{\mathrm{\Delta }T}{\mathrm{\Delta }{d}_{\mathrm{watr}}}},\end{array}$$

where C_watr is the volumetric heat capacity of water (4.18×10⁶ J m⁻³ K⁻¹), κ_watr is the eddy diffusivity of water (m² s⁻¹), and the change in depth is Δd_watr=d_watr (the depth of the water layer). κ_watr is a complex function accounting for thermal stratification of water and surface friction velocity. To reduce complexity, and assuming a mixed homogeneous water layer, a constant κ_watr is selected based on shallow lakes reported in Salas De León et al. (2016). The change in temperature ΔT (^∘C) is the difference between the water temperature T_surf,watr (^∘C) and the soil temperature beneath the water layer T_soil (^∘C). T_soil is calculated using the force–restore model, where Q_G,watr is equivalent to Q_G,i in Eq. (6):

$$\begin{array}{ll}{\displaystyle \frac{\mathrm{d}{T}_{\mathrm{soil}}}{\mathrm{d}t}}=& {\displaystyle }{\displaystyle \frac{\left(Q_{G,\mathrm{watr}}+\left(K_{\mathrm{n}}-S_{\mathrm{ab}}\right)\right)}{C_{\mathrm{watr}}D}}\\ \text{(12)}& {\displaystyle }& {\displaystyle }-{\displaystyle \frac{\mathrm{2}\mathit{\pi }}{\mathit{\tau }}}\left(T_{\mathrm{soil},[t-\mathrm{1}]}-T_{\mathrm{m},[t-\mathrm{1}]}\right).\end{array}$$

To represent the radiation that is not absorbed by the water but is absorbed by the underlying soil layer, K_n−S_ab is added to Q_G,watr.

The latent heat flux (Q_E,watr) (W m⁻²) is given by Arya (2001):

$$\begin{array}{}\text{(13)}& Q_{E,\mathrm{watr}}=\mathit{\rho }v{L}_{\mathrm{v}}{h}_{\mathrm{v}}{U}_z\left(q_{\mathrm{s}}-q_{\mathrm{a}}\right),\end{array}$$

where ρv is the density of moist air (kg m⁻³), L_v is the latent heat of vaporization (i.e. 2.43 MJ kg⁻¹), h_v is the bulk transfer coefficient for moisture $(\mathrm{1.4}\times {\mathrm{10}}^{-\mathrm{3}})$ (Hicks, 1972; Jones et al., 2005), U_z is the reference wind speed, q_s is the saturated specific humidity at T_surf,watr, and q_a is the specific humidity of the air for the given T_a.

The sensible heat flux above the water surface is given by Molina Martínez et al. (2006):

$$\begin{array}{}\text{(14)}& Q_{H,\mathrm{watr}}={\mathit{\rho }}_{\mathrm{a}}{C}_p{h}_{\mathrm{c}}{U}_z\left(T_{\mathrm{a}}-T_{\mathrm{surf},\mathrm{watr}}\right),\end{array}$$

where ρ_a is the density of dry air (=1.2 kg m⁻³), C_p the specific heat of air (1013 J kg⁻¹ K⁻¹), and h_c the bulk transfer coefficient for heat (h_c=h_v).

Returning to Eq. (9), net long wave radiation $L_{\mathrm{n}}=R_{\mathrm{n}}-K_{\mathrm{n}}$, leaving ΔQ_S,watr from the energy balance equation, which is defined as (Molina Martínez et al., 2006)

$$\begin{array}{}\text{(15)}& \mathrm{\Delta }{Q}_{S,\mathrm{watr}}=C_{\mathrm{watr}}{d}_{\mathrm{watr}}{\displaystyle \frac{\mathrm{\Delta }{T}_{\mathrm{surf},\mathrm{watr}}}{\mathrm{\Delta }t}},\end{array}$$

where Δt is change in time (s), and C_watr is the volumetric heat capacity of water (J m⁻² K⁻¹). Solving for ΔT_surf,watr and adding the change in temperature to the previous time step ($T_{\mathrm{surf},\mathrm{watr}[\mathrm{t}+\mathrm{1}]}=T_{\mathrm{surf},\mathrm{watr},\left[\mathrm{t}\right]}+\mathrm{\Delta }{T}_{\mathrm{surf},\mathrm{watr}}$) gives the new water layer temperature.

2.7 Calculation of urban canopy layer air temperature (T_ac)

To calculate T_ac we first calculate a domain T_b for each time step. Assuming air temperature at 3 times the building height (3H) is consistent between the neighbourhood of interest and the reference weather station location, we extrapolate reference air temperature at measurement height to 3H assuming a constant flux layer and using a bulk Richardson-number-based approximation (Mascart et al., 1995). Through this simple calculation we define a domain constant T_b with the basic representation of atmospheric stability in TARGET.

The canyon air temperature is then calculated using a modified version of the canopy air temperature equation from the Community Land Model Urban (CLMU) (Oleson et al., 2010):

$$\begin{array}{}\text{(16)}& T_{\mathrm{ac}}={\displaystyle \frac{\sum _i^{\mathrm{7}}\left(T_{\mathrm{surf},i}{c}_{\mathrm{s}}{F}_i\right)+\left[\frac{T_{\mathrm{surf},\mathrm{roof}}}{\left(\frac{\mathrm{1}}{c_{\mathrm{s}}}+\frac{\mathrm{1}}{c_{\mathrm{a}}}\right)}{F}_{\mathrm{roof}}\right]+\left(T_{\mathrm{b}}{c}_{\mathrm{a}}W\right)}{\sum _i^{\mathrm{7}}\left(c_{\mathrm{s}}{F}_i\right)+\left[\frac{F_{\mathrm{roof}}}{\left(\frac{\mathrm{1}}{c_{\mathrm{s}}}+\frac{\mathrm{1}}{c_{\mathrm{a}}}\right)}\right]+\left(c_{\mathrm{a}}W\right)}},\end{array}$$

where F_i and T_surf,i are the 2-D fractional coverage and surface temperature of surface i in the canyon, c_s is the conductance from the surface to the urban canopy layer (m s⁻¹), and c_a is the conductance from the urban canopy to the above-canopy surface layer (m s⁻¹). In Eq. (16) we assume roofs are connected to the canyon via two resistances in series, thus representing the additional impediment to the transfer of heat from a rooftop into the canyon. We hypothesize that the heat transfer from roofs to the canyon air can be approximated by two resistances in series (the canyon-to-atmosphere resistance, c_a, and surface-to-canyon resistance, c_s). The logic here is that resistance to heat transfer from the roof surface to the canyon should be greater than c_a or c_s independently. Through sensitivity testing we are able to demonstrate that this assumption improves predicted canyon air temperature. The c_a is calculated following Masson (2000) and using the stability coefficients from Mascart et al. (1995). The c_s term is from Masson (2000):

$$\begin{array}{}\text{(17)}& r_{\mathrm{s}}={\displaystyle \frac{{\mathit{\rho }}_{\mathrm{a}}{C}_p}{\mathrm{11.8}+\mathrm{4.2}{U}_{\mathrm{can}}}},\end{array}$$

where $c_{\mathrm{s}}=\frac{\mathrm{1}}{r_{\mathrm{s}}}$ and U_can is the wind speed in the canyon (m s⁻¹) (Kusaka et al., 2001):

$$\begin{array}{}\text{(18)}& U_{\mathrm{can}}=U_{\mathrm{top}}\exp \left(-\mathrm{0.386}{\displaystyle \frac{H}{W}}\right),\end{array}$$

where U_top is the wind speed at the top of the canyon (m s⁻¹). U_top is estimated at 3H based on the observed wind speed at a nearby observational site (ideally an airport) using a logarithmic relationship. Airports are relatively devoid of roughness elements, and wind speed is typically measured at 10 m above the surface. As such, the assumption of a logarithmic profile through the roughness sublayer (Masson, 2000) is imposed.

3 Methods and data

3.1 Overview

As part of the model evaluation, we conduct a range of simulations that test model performance for both T_surf and T_ac. These validation experiments are focused on clear sky summertime conditions. Clear sky is chosen because the local cooling effects of GBI are most notable during these conditions. First, we test the model's ability to simulate T_surf for each land cover type that can be prescribed in TARGET (i.e. dry grass, asphalt etc.), using ground-based observations of T_surf (Sect. 3.2). These simulations by land cover type provide a detailed assessment of model parameters and the underlying energy balance dynamics and resulting T_surf for each land cover class. Second, we conduct suburb-scale simulations of Mawson Lakes, Adelaide, for which we have high-resolution remotely sensed T_surf observations and in situ T_ac data (Sect. 3.3). The suburb-scale simulations reflect the way the model is intended to be used by practitioners.

3.2 Land cover simulations

To test model performance at simulating T_surf of different land cover classes and perform sensitivity analysis on a number of model parameters, we use ground-based observations of T_surf from the Melbourne metropolitan area. Coutts et al. (2016) deployed infrared temperature sensors (SI-121, Apogee), during February 2012 (5 min averages), across a range of land cover types including asphalt, concrete, grass, irrigated grass, steel roof, and water. Infrared sensors were mounted above the aforementioned surface types installed at heights of approximately 1.5–2 m. The conditions during this period represented near-typical summertime conditions in Melbourne, including a number of days (15, 24, and 25 February) when air temperature exceeded 30 ^∘C (see Fig. B1). These hotter days were characterized by northerly winds, which bring hot and dry air from Australia's interior and often result in heatwave conditions in Melbourne. Additionally, there was at least one cloudy day when incoming shortwave radiation (K↓) dropped significantly and a negligible amount of rainfall occurred (17 February). To compare the Coutts et al. (2016) observations with TARGET we run the model for each surface type (i.e. 100 % grass or roof etc.) with radiation forcing data from the Melbourne Airport weather station during the time period in question. The T_b calculation is not needed since we only calculated T_surf for this part of the model evaluation. The 30 min output from TARGET is compared with T_surf observations, and statistics are calculated.

Figure 3 Mawson Lakes suburb with weather station locations. The numbers indicate individual weather stations, while the colour coding specifies groups of sites with statistically similar thermal characteristics. The names of each cluster indicate the average land surface characteristics: urban sites with nearby water (TA-1_[Urb+Wtr]), mixed land use with nearby water (TA-2_[Mxd+Wtr]), urban mid-rise-type sites (TA-3_[Urb+Mid]), urban residential sites (TA-4_[Urb+Res]), natural grass-dominated sites (TA-5_[Nat+Grs]), and a single outlier site (TA-6_[outlier]) (Broadbent et al., 2018b).

3.3 Suburb-scale simulations (Mawson Lakes)

In addition to the land cover category testing, we also conduct suburb-scale simulations of T_surf and T_ac for Mawson Lakes, Adelaide (Fig. 3). The suburb-scale simulations use observational data from the Mawson Lakes field campaign, conducted during 13–18 February 2011, which represented average summertime conditions in Adelaide (Broadbent et al., 2018b). For these simulations, the model is run on 30 m (T_surf) and 100 m (T_ac) grids over the Mawson Lakes suburb for the period 13–18 February (Fig. B2). Remotely sensed land cover data from the campaign are used to define land cover, and building morphology is defined using lidar data (see Broadbent et al., 2018b). The Mawson Lakes simulations use the same parameter set-up as above (summarized in Table 1) and are forced with meteorological data from the Kent Town Bureau of Meteorology (ID 023090) weather station. Modelled T_surf is validated using observed remotely sensed T_surf (night – 15 February and day – 16 February), which is resampled to 30 m resolution (Broadbent et al., 2018b). To validate T_ac, we use data from 27 automatic weather stations (AWSs) that were also deployed during the Mawson Lakes field campaign (see Fig. 3 for AWS locations).

4 Model evaluation results and discussion

4.1 Land cover simulations

The surface temperature for each land cover class is simulated for a 14-day period during February 2012. The results show that modelled surface temperature for all three impervious surfaces (concrete, asphalt, and roof) is reasonably well predicted, with a mean bias error (MBE) of 0.88, −0.22, and −1.16 ^∘C, respectively (Fig. 4a–f). The root mean square error (RMSE) values for impervious surfaces are around 3.5–4 ^∘C. These RMSE values represent about 15 % of diurnal T_surf variation, which implies good model skill given the simplicity of the approach.

Figure 4 Observed vs. modelled (a, b) T_surf,conc, (c, d) T_surf,asph, (e, f) T_surf,roof, (g, h) T_surf,watr, (i, j) T_surf,irgs, and (k, l) T_surf,gras. All time series plots are for the period 11–25 February. Note that the water site only had observational data for the period 11–21 February due to instrument failure; r² is the correlation coefficient, RMSE is the root mean square error, MBE is the mean bias error, and MAE is the mean absolute error.

The night of the 16 February is not well captured at the concrete and asphalt sites. The T_surf,conc and T_surf,asph are under-predicted (up to 5 ^∘C cooler than observations) on the night of 16 February, which may have been caused by warm air advection. The TARGET approach cannot account for the effects of warm air advection on surface temperature, as there is no feedback between T_ac and T_surf. Despite this limitation, the broad timing and magnitude of heating and cooling are well captured for all three impervious land cover types.

Model performance for T_surf,watr had a low MBE of 0.91 ^∘C, but the r² value of 0.76 suggests the model captured diurnal T_surf,watr variation less accurately than other surfaces (Fig. 4g–h). In particular, daily maximum T_surf,watr values are under-predicted on hotter days (e.g. 14 February). TARGET uses a different module for water bodies (see Sect. 2.6). This simple module treats water as a single layer overlying soil. Despite the under-prediction on 14 February, the simple water body model can reproduce T_surf,watr to an acceptable standard.

Modelled T_surf,irgs had a MBE (−1.56 ^∘C) comparable to that of impervious surfaces (Fig. 4i–j). However, the RMSE for irrigated grass (3.69 ^∘C) represents approximately 20 % of diurnal T_surf,igrs variation, suggesting model error is slightly higher than for the impervious surfaces. Generally T_surf,igrs is slightly over-predicted at night and under-predicted at the daily maxima. This skewing of the scatter plot suggests that thermal inertia is too high in the model. Overall, the model is skillful enough to capture the timing and amplitude of T_surf,igrs.

Dry grass had a small MBE (0.06 ^∘C) but the largest RMSE of the surfaces tested (4.38 ^∘C). However, this RMSE only equated to approximately 10 %–15 % of diurnal T_surf,gras variability (Fig. 4k–l) as dry grass had the largest amplitude of surface temperature variability. Dry grass exhibited the same skewing in the scatter plot as irrigated grass, with a general over-prediction of night-time temperatures and under-prediction of daytime maxima.

Figure 5 Mawson Lakes observed (a, d) T_surf and modelled (b, e) T_surf for day (a–c) and night (d–e). Areas where land cover is categorized as “other” are not simulated. Note that T_surf here does not include T_surf,wall for comparison with horizontally averaged aerial imagery observations.

4.2 Suburb-scale simulations (Mawson Lakes)

4.2.1 Surface temperature

In addition to the land cover simulations, we conduct suburb-scale modelling of the Mawson Lakes site. These simulations reveal how the TARGET model can be operationalized by practitioners who want to assess the cooling benefits of blue infrastructure or greening initiatives. Suburb-scale simulations are conducted using the same parameters as above (Table 1). We run the model at 30 m spatial resolution for T_surf simulations and 100 m for simulations of T_ac. Figure 5 shows the predicted T_surf for the Mawson Lakes domain plotted against observed T_surf. The Mawson Lakes simulations revealed the initial conditions of the T_m parameter (which represents the average temperature in the ground layer) are important for good model performance. A spin-up period (1 month) had to be used to obtain initial T_m values for each surface type. This can be quickly and easily achieved by running the force–restore module for a single point for each surface type. A future version of the model will automatically spin up initial T_m values. The model output also shows that some of the input land cover is poorly categorized, resulting in the population of grid points in which modelled T_surf is over-predicted. Additionally, errors in the observed T_surf caused by heterogeneity of roof emissivity also contribute to apparent inaccuracies of modelled T_surf. In general, the daytime T_surf is slightly over-predicted, and the complexity of spatial variability is not fully captured. However, this is a positive result given that only eight land cover classes are represented in the model. Overall, the daytime T_surf is well predicted, with the range and magnitude of T_surf captured by the model.

The results suggest that night-time T_surf is under-predicted by model. The range of modelled nocturnal T_surf variability (8 ^∘C) is much smaller than observed variability (18 ^∘C). This under-prediction of variability could reflect the fact that some processes that dictate the rate of nocturnal cooling are not fully accounted for in this approach. Nevertheless, the general spatial patterns of T_surf are captured well. Further, given that the range of T_surf is smaller at night, this under-prediction is of minimal consequence for modelled T_ac. The nocturnal T_surf of impervious surfaces is also under-predicted in the land cover simulations (i.e. Sect. 4.1) under warm advection conditions. Although warm advection conditions were not observed during the Mawson Lakes campaign, it is worthwhile further investigating this phenomenon in future work to negate its effect and improve nocturnal T_surf accuracy.

Figure 6 Spatial map of modelled T_ac (30 m) for (a) day (15:00) and (b) night (03:00) in the Mawson Lakes domain. Points with F_roof>0.75 are excluded.

4.2.2 Air temperature

Spatial plots of modelled 03:00 and 15:00 T_ac are shown in Fig. 6. The modelled air temperatures are biased towards warmer air temperature in urban areas and cooler air temperature in rural areas. These biases are partly driven by the lack of advection in the model. Without atmospheric mixing, the local impacts of pervious and impervious surfaces are exaggerated, causing an additional cooling and warming effect in rural and urban areas, respectively However, the general patterns of T_ac are reasonable and as expected. We also extract modelled T_ac from the grid points where the 27 AWSs are located (grid points were centred at the AWS) for a 2-day period (15–16 February 2011) (Fig. 7). The T_ac is generally well predicted (Fig. 7), with a RMSE of 2.0 ^∘C. These results have about the same accuracy as simulations, from the same site, conducted using a more sophisticated and computationally expensive urban climate model called SURFEX (Broadbent et al., 2018a). Although a simple model, TARGET appears to be as accurate as more complex models. Additionally, TARGET does not require the user to provide above-canyon forcing data (e.g. T_b), which are needed for other models and are not easily obtained. TARGET tends to over-predict average T_ac at all urban sites (Fig. 8). Residential sites (TA-4_[Urb+Res] cluster [red]) are too warm during the day. This over-prediction is likely due to the uniform wall and roof thermal parameters used, which are not representative of residential areas. Further, the lack of horizontal mixing may have exacerbated warmer temperatures in these areas. By contrast, the TA-5_[Nat+Grs] cluster is too cool at night. The model predicts the formation of a stable layer with cool air trapped near the surface. Overall, the diurnal range and average T_ac are well captured by the model.

Figure 7 Modelled T_ac vs. observed T_ac for Mawson Lakes weather stations (15–16 February 2011, 30 min data). The numbers and colours correspond to individual stations and clusters shown in Fig. 3.

Figure 8 Box plot of modelled T_ac (grey) vs. observed T_ac (black) for Mawson Lakes, with average, min, and max T_ac shown. Box plots are generated from 30 min data from the period 15–16 February 2011. The numbers and colours (x axis) correspond to individual stations and clusters in Fig. 3.

Finally, there is some hysteresis in Fig. 6, indicating that modelled T_ac is slightly out of sync with observed T_ac. This could be due to the approach used to diagnose T_b, which assumes a constant Ri in the surface layer and therefore heats up too quickly during the morning. Improvement in the T_b term is an area for future model development. However, we believe it is important that TARGET calculates T_b, as this makes the model much more accessible to non-expert users. Given the simplicity and computational efficiency of the model approaches used, TARGET shows good skill for predicting urban T_ac. Overall, the air temperature evaluation shows we can have confidence in the accuracy of the model and its potential to be used by practitioners.

5 Heat mitigation scenarios

To demonstrate how TARGET can be used by practitioners to predict GBI cooling impacts, two simple heat mitigation scenarios are presented: (1) a doubling of existing tree cover (“2×TREE”) (Fig. 9) and (2) all dry grass converted to irrigated grass (“IRRIGATION”) (Fig. 10). The 2×TREE scenario assumes a maximum tree coverage of 75 %. The results presented here represent the local maximum cooling potential of GBI. In reality, the cooling local magnitude will be decreased by advection, which TARGET does not represent.

Figure 9 The ΔT_ac (^∘C) for IRRIGATION − BASE at (a) 15:00 and (b) 03:00 for the Mawson Lakes domain.

Figure 10 The ΔT_ac (^∘C) for 2×TREE − BASE at (a) 15:00 and (b) 03:00 for the Mawson Lakes domain.

Table 2 Summary of domain average cooling impacts (^∘C) for GBI heat mitigation scenarios.

The 2×TREE scenario shows maximum cooling of 3.0 ^∘C during the day and a smaller effect (<0.25 ^∘C) at night (Fig. 9). The IRRIGATION scenarios suggests that increasing irrigation can have a small warming effect (<0.75 ^∘C) at night and cooling of up to 1.75 ^∘C at 15:00 (Fig. 10). The amount of land cover change differs in each scenario. As such, we calculate the cooling sensitivity (γ) as

$$\begin{array}{}\text{(19)}& \mathit{\gamma }=\left({\displaystyle \frac{\mathrm{\Delta }{T}_{\mathrm{ac}}}{\mathrm{\Delta }\mathrm{LC}}}\right)\times \mathrm{0.10},\end{array}$$

where ΔLC is the average land cover change (fraction) (Table 2); this metric demonstrates the average ΔT_ac per 10 % surface change. Model results suggest that trees are about 2.5 times more effective at providing cooling at 15:00 (Table 2). The results for both heat mitigation simulations are within the expected magnitudes based on previous heat mitigation modelling studies (Grossman-Clarke et al., 2010; Middel et al., 2015; Daniel et al., 2016; Broadbent et al., 2018a). These simulations demonstrate that TARGET not only reproduces observations accurately but can be used with confidence to efficiently assess the efficacy of heat mitigation measures.

6 Limitations of the model

As discussed above, TARGET aims to be a simple and accessible urban climate model that provides scientifically defensible and accurate urban temperature predictions. To achieve simplicity, the model necessarily makes some assumptions and omissions that users should be aware of. TARGET is primarily intended to model urban temperatures during clear sky conditions. The model does not simulate rainfall and therefore should not be used for periods containing significant precipitation. Further, the model can be used to simulate street-level air temperature and surface temperature for days to weeks (i.e. a heatwave) but has not been tested or validated for longer-scale simulations (i.e. months to years).

For computational efficiency, the model assumes no horizontal advection inside or above the urban canopy layer. In general, advection reduces the local impacts (i.e. cooling directly adjacent the cooling intervention) of GBI due to atmospheric mixing, and therefore we expect TARGET to provide estimates of near-maximum cooling benefits. In reality, cooling effects will be diminished by advection, especially during the day and during high wind conditions.

As mentioned, the force–restore method is used for roof and wall surfaces with an artificially reduced κ value. Although this approach generally performed well, it is our intention to develop and integrate a more realistic formula for modelling roof and wall Q_G,i. A conduction model, although more computationally expensive, would allow more flexibility as different types of roof (which do vary significantly) could be represented. Furthermore, wall surfaces are treated the same as roofs in TARGET, which is unrealistic. The improved representation of walls and roofs is a key area for future model development.

In addition, the Q_G,i (hence the heat transfer to the urban canopy atmosphere, as the residual) is parameterized according to R_n and the building parameters. This means that the dependency on the other atmospheric conditions, such as air temperature, wind speed, and humidity, is neglected in TARGET. However, given that the OHM (used to calculate Q_G,i) was developed based on observational data collected during summertime clear sky conditions, we are confident that TARGET will provide reasonable results during summer. Ongoing testing is needed to ascertain the limitations of the use of the OHM in TARGET.

The Q_G,i calculation for water sources used a different method to other surfaces (see Sect. 2.6). Further, a resistance formulation is used to calculate the Q_H,i over water bodies (see Eq. 14), whereas Q_H,i for the non-water surfaces is calculated as a residual (and not temperature- and wind-speed-dependent). These different model formulations for water may lead to artificial non-physical discrepancies. However, testing does not reveal any unexpected behaviour. As TARGET is a climate-service-oriented tool, we think that good model performance is more important than the consistency of physics schemes used.

7 Conclusions and future work

This paper has presented TARGET, a simple and user-friendly urban climate model that is designed to be accessible to urban planners and policymakers. The model contains a number of key limitations that are outlined above. However, despite these caveats, rigorous testing suggests TARGET shows excellent potential for modelling the cooling effects of GBI projects. We believe this novel model is well balanced between complexity and accuracy. The computational efficiency of the model and the reduced amount of input data required ensure that non-skilled users can use the model to ascertain reliable urban cooling estimates. Ongoing work will be done to improve TARGET, including the creation of a GUI, the addition of human thermal comfort indices, and the improvements to model physics outlined above.

Appendix A: List of symbols

a1	Objective hysteresis model (OHM) parameter
a2	Objective hysteresis model (OHM) parameter
a3	Objective hysteresis model (OHM) parameter
Aasph	land cover asphalt plan area (m2)
Aconc	land cover concrete plan area (m2)
Agras	land cover grass plan area (m2)
Aigrs	land cover irrigated grass plan area (m2)
Atree	land cover tree plan area (m2)
Aroof	land cover building plan area (m2)
Awall	land cover wall plan area (m2)
Awatr	land cover water plan area (m2)
Cwatr	volumetric heat capacity of water (J m−2 K−1)
ca	conductance from the urban canopy to the above-canopy surface layer (m s−1)
cs	conductance from the surface to the urban canopy layer (m s−1)
Cwatr	volumetric heat capacity of water (4.18×106 J m−3 K−1)
Cp	specific heat of air (1013 J kg−1 K−1)
dwatr	depth of water body (m)
Dy	damping depth for the annual temperature cycle (m)
η	extinction coefficient
Fi	fraction of land cover type i (%)
H	average building height (m)
hc	bulk transfer coefficient for heat (hc=hv)
hv	bulk transfer coefficient for moisture ($=\mathrm{1.4}\times {\mathrm{10}}^{-\mathrm{3}}$)
Kn	net shortwave radiation (W m−2)
K↓	incoming shortwave radiation (W m−2)
Ln	net longwave radiation (W m−2)
L↓	incoming longwave radiation (W m−2)
L↑	outgoing longwave radiation (W m−2)
Lv	latent heat of vaporization (=2.43 MJ kg−1)
QE,watr	latent heat flux for water surface (W m−2)
QG,i	storage heat flux for surface type i from LUMPS (W m−2)
QG,watr	convective heat flux at the bottom of the water layer (and into the soil below) (W m−2)
QH,i	sensible heat flux for surface i from LUMPS (W m−2)
QH,watr	sensible heat flux for water surface (W m−2)
ra	resistance from the urban canopy to the atmosphere (s m−1)
RH	relative humidity (%)
Ri	Richardson number
Rn	net radiation (W m−2)
Sab	absorbed shortwave radiation (W m−2)
SVF	sky view factor
rs	resistance from the surface to the canopy (s m−1)
Ta	reference air temperature (∘C)
TARGET	CRC for Water Sensitive Cities microclimate Toolkit model
Tac	street-level (urban canopy layer) air temperature (∘C)
Tb	air temperature above the urban canopy layer (∘C)
Tm	average soil (ground) temperature (∘C)
Thigh	upper-level temperature for Richardson number calculation (∘C)
Tlow	lower-level temperature for Richardson number calculation (∘C)
Tsoil	soil temperature (∘C)
Tsurf	surface temperature from the force–restore model (∘C)

Ucan	wind speed in canyon (m s−1)
Utop	wind speed at the top of the canyon (m s−1)
Uz	reference wind speed (m s−1)
W	average street width (m)
W*	average street width minus tree width (m)
Wtree	tree width (m)
Wroof	roof width (m)
α	surface albedo
αpm	LUMPS empirical parameter (alpha parameter), relating to surface moisture
β	LUMPS empirical parameter (beta parameter)
βk	amount of shortwave radiation immediately absorbed by the water layer (set to 0.45)
ΔQS,watr	change in heat storage of the water layer (W m−2)
ϵ	surface emissivity
κ	thermal diffusivity (m2 s−1)
κwatr	eddy diffusivity of water (m2 s−1)
λC	plan area ground-level surfaces (m2)
ρa	density of dry air (i.e. 1.2 kg m−3)
ρv	density of moist air (kg m−3)
σ	Stefan–Boltzmann constant ($\mathrm{5.67}\times {\mathrm{10}}^{-\mathrm{8}}$ W m−2 K−4)

Appendix B

B1 Meteorological conditions during validation periods

As outlined in Sect. 3, we conduct model validation experiments during two different periods. A summary of the meteorological conditions for land cover (Melbourne; Fig. B1) and suburb-scale (Mawson Lakes; Fig. B2) simulations are provided in the figures below.

Figure B1 Meteorological conditions during the land cover validation period. Data source: Melbourne Airport Bureau of Meteorology (ID 086282) weather station.

Figure B2 Meteorological condition during the Mawson Lakes field campaign. Data source: Bureau of Meteorology Parafield Airport (ID: 023013) and Kent Town (ID: 94675) weather stations, Adelaide.

Figure B3 Observed air temperature vs. observed tree T_surf.

B2 Tree surface temperature

To assess T_tree we obtain observational data from a tree experiment completed in Melbourne, which included T_surf observations of the tree canopy (collected during February 2014). We also obtain Bureau of Meteorology meteorological forcing data for the 2014 case study period. This period (not shown) was very similar to the February 2012 period (Fig. B1) used above. The tree data confirm that T_a is an excellent predictor of T_tree.