UHSM

The Urban Heat Storage Model (UHSM) enhances the Oke's urban energy balance equation and it was developed by Bonacquisti et al. (2006) [119]. The model is founded on four-equation energy balance at the ground level and building level, namely:


It involves three simulation sections, i.e., atmospheric layer (maximum height above building heights) and building and ground levels. The aforementioned equations formulate a system of linearized algebraic equations to relate four major unknown variables, i.e., building surface temperature, ground surface temperature, air temperature, and relative humidity. Ground and building aerodynamic roughness are evaluated as function of drag coefficients of soil and of wind speed in the canopy layer. Wind deceleration within the urban canopy was evaluated as a function of buildings' density, drag coefficients, and wind speeds within the atmospheric layer section. Anthropogenic heat is also taken into account, using expressions representing heat releases by buildings (produced mainly by electricity and fuel consumption), by transportation (vehicles exhausts), and by human metabolic rates. The equations are spatially discretized in the domain (sub-domains) and based on the heat storage within the urban canopy an iterative solution procedure is followed towards the calculation of the unknown variables in each sub-domain.

The main data used as inputs in the model are the thermo-physical and optical properties of urban surfaces as well as atmospheric parameters. The main output of the tool is the spatial distribution (in hourly basis) of ground and building surface temperature, air temperature and relative humidity, the mean surface temperature, and mean temperature at the pedestrian level height. The tool was applied by Bonacquisti et al. [119] in the case of Rome, Italy, and air temperature was used as a validation parameter, i.e., it was compared with in situ temperature observations. Using this tool, the same authors concluded UHI intensities (temperature increase compared to rural areas) of 2 ◦C and 5 ◦C, for winter and summer, respectively.

### TEB

The Town Energy Budget (TEB) tool [120] was developed in the Centre National de Recherches Météorologiques, Toulouse, France, and it was presented by Masson [121]. The TEB tool is canyon-based but generalized to capture large horizontal scales. Due to the complex shape of the cityscape, the urban energy budget is divided into three parts, i.e., for roofs, walls, and roads. The model simulates turbulent fluxes into the atmosphere at the surface of the meso-scale atmospheric model covered by buildings, roads, or any other artificial material. Heat fluxes are computed for each land type by the appropriate scheme, and then they are averaged in the atmospheric model grid mesh, with respect to the proportion occupied by each type. The fluxes calculated are Latent and sensible heat fluxes, upward radiative fluxes, and component momentum fluxes.

Cityscape geometry is normally represented by buildings that have the same dimensions. Buildings are located along identical roads, the lengths of which are considered far greater than their widths. Finally, any road orientation is possible, all existing with the same probability, and this hypothesis allows the computation of averaged imposition parameters for road and wall surfaces. In order to treat the conduction fluxes through solid surfaces, TEB discretizes each surface type into several layers. The equations applied to represent temperature evolution in these layers are based on energy budget considerations and several prognostic equations for the surface layers of roofs, walls, and roads emerge. The set of equations describing heat transfer mechanisms and turbulent fluxes is similar to that of the UHSM tool. The main difference is that the surface layer is represented by the Monin–Obukhov equations. Its latest version includes a Building Energy Model

(BEM) suite mainly for thermal loads' predictions. Ren et al. [122] integrated TEB into a climate change air quality model and demonstrated improvement of predictions of NOx, PM2.5, and ground-level O3 in four major north American Cities. The tool was used by Reder et al. [123] towards the suggestion of climate resilience strategies and measures by means of UHI mitigation. As documented by Pigeon et al. [124], the software, enhanced with the BEM suite, allows reliable predictions of buildings' heating and cooling demands in comparison with the more detailed model, EnergyPlus, for various building types. Lately, and in view of recent trends referring to assessments of future climate change impacts on the development of energy policies, TEB has gained interest in the prediction of impacts of climate change scenarios on UHI and urban energy performance [125–127].
