The Vertical City Weather Generator (VCWG) is a computationally efficient urban microclimate model developed to predict temporal and vertical variation of potential temperature, wind speed, specific humidity, and turbulent kinetic energy. It is composed of various sub-models: a rural model, an urban vertical diffusion model, a radiation model, and a building energy model. Forced with weather data from a nearby rural site, the rural model is used to solve for the vertical profiles of potential temperature, specific humidity, and friction velocity at 10

Urban areas interact with the atmosphere through various exchange processes of heat, momentum, and mass, which substantially impact human comfort, air quality, and energy consumption. Such complex interactions are observable from the urban canopy layer (UCL) to a few hundred meters within the atmospheric boundary layer

Mesoscale models incorporating the urban climate were initially aimed to resolve weather features with grid resolutions of at best a few hundred meters horizontally and a few meters vertically, without the functionality to resolve micro-scale three-dimensional flows or to account for atmospheric interactions with specific urban elements such as roads, roofs, and walls

Urban microclimate models must account for a few unique features of the urban environment. Urban obstacles such as trees and buildings substantially contribute to changing flow and turbulence patterns in cities

Heat exchanges between indoor and outdoor environments significantly influence the urban microclimate. Various studies have attempted to parametrize heat sources and sinks caused by buildings such as heat fluxes due to infiltration, exfiltration, ventilation, walls, roofs, roads, windows, and building energy systems (e.g., condensers and exhaust stacks)

Urban vegetation can substantially reduce the adverse effects of UHI (

Numerous studies have focused on high-fidelity urban microclimate models with high spatiotemporal flow resolution, capturing important features of the urban microclimate with acceptable accuracy

In this study, we present a new urban microclimate model, called the Vertical City Weather Generator (VCWG), which attempts to overcome some of the limitations mentioned in the previous section. It resolves vertical profiles of climate variables, such as potential temperature, wind, specific humidity, and turbulent kinetic energy in relation to urban design parameters. VCWG also includes a building energy model. It allows parametric investigation of design options with urban climate control at multiple heights, particularly if multistory building design options are considered. This is a significant advantage over bulk flow (single-layer) models such as UWG, which only consider one point for flow dynamics inside a hypothetical canyon

The paper is structured as follows. Section ^{TM} Weather (EPW) dataset, the rural model (RM), the one-dimensional vertical diffusion model, the building energy model, and the radiation model. This section also describes the location and details of the BUBBLE field campaign used for model evaluation. Section

Figure

The sub-models are integrated to predict vertical variations of urban microclimate variables including potential temperature, wind speed, specific humidity, and turbulent kinetic energy as influenced by aerodynamic and thermal effects of urban elements including longwave and shortwave radiation exchanges, sensible heat fluxes released from urban elements, cooling effect of trees, and the induced drag by urban obstacles. The RM takes into account latitude, longitude, dry bulb temperature, relative humidity, dew point temperature and pressure at 2

The schematic of the Vertical City Weather Generator (VCWG).

Simplified urban area used in VCWG and corresponding layers of control volumes within and above the canyon. The height of the domain is 3 times the average building height. A leaf area density (LAD) (

Building energy and solar radiation simulations are typically carried out with standardized weather files. EPW files include recent weather data for 2100 locations and are saved in the standard EnergyPlus^{TM} format developed by the US Department of Energy (

In the rural model, the Monin–Obukhov similarity theory (MOST) is used to solve for the vertical profiles of potential temperature, specific humidity, and friction velocity at 10

In the dimensionless stability parameter

It has been observed that there is a monotonic reduction in friction velocity with increasing stratification

Friction velocity can be determined by integrating Eq. (

The potential temperature profiles are also obtained by integration of Eq. (

Given the similarity of heat and mass transfer (sensible and latent heat fluxes), the same universal dimensionless temperature gradient can be used for the universal dimensionless specific humidity gradient, i.e.,

Meteorological information obtained from a weather station, including direct and diffuse shortwave radiation, longwave radiation, temperature at 2

The rural model also outputs a horizontal pressure gradient based on the friction velocity calculation that is later used as a source term for the urban one-dimensional vertical diffusion momentum equation. The pressure gradient is parameterized as

After calculating potential temperature and specific humidity at the top of the domain by the rural model, these values can be applied as a fixed-value boundary condition at the top of the domain in the urban one-dimensional vertical diffusion model for the potential temperature and specific humidity transport equations.

Numerous studies have attempted to parameterize the interaction between urban elements and the atmosphere in terms of dynamical and thermal effects, from very simple models based on MOST

For the one-dimensional vertical diffusion model, any variable such as cross- and along-canyon wind velocities (

To calculate the vertical profile of potential temperature in the urban area, the energy transport equation can be derived as

In this study, the balance equation for convection, conduction, and radiation heat fluxes is applied to all building elements (walls, roof, floor, windows, ceiling, and internal mass) to calculate the indoor air temperature. Then, a sensible heat balance equation, between convective heat fluxes released from indoor surfaces and internal heat gains as well as sensible heat fluxes from the HVAC system and infiltration (or exfiltration), is solved to obtain the time evolution of indoor temperature as

A similar balance equation can be derived for latent heat to determine the time evolution of the indoor air specific humidity and the dehumidification load

The building energy model is a single-zone model with respect to both the indoor and outdoor (urban canopy) environments. That is, only a single temperature is assumed for indoor air, and only a single potential temperature is assumed for outdoor air by integrating the potential temperature profile over height from the street to roof levels. Further, all wall temperatures are assumed to be uniform with height.

In VCWG, there are two types of vegetation: ground vegetation cover and trees. The ground vegetation cover fraction is specified by

To evaluate the model, VCWG's predictions are compared to observations from the Basel UrBan Boundary Layer Experiment (BUBBLE)

In this section, first the VCWG model results are evaluated against microclimate field measurements. Next, the model performance is explored through various parametric simulations. A uniform Cartesian grid with 2

The results of the VCWG are compared to the measured data from the BUBBLE campaign. The input parameters representing the urban area are listed in Table

List of input parameters used in the VCWG for model evaluation; input variables are extracted from assumptions, datasets, and simulation codes available from

To compare VCWG results with measured meteorological variables from the BUBBLE campaign, the bias, root mean square error (RMSE), and coefficient of determination

Scatter plots of observed (BUBBLE) versus simulated (VCWG) values of potential temperature for different altitudes and months; each data point corresponds to a 1 h comparison between the model and observation.

Bias (

Figure

Comparison between the observed (BUBBLE) versus simulated (VCWG) values of potential temperature. The hourly means are shown, and nighttime is indicated by shaded regions. Solid line: model, dashed line: observation. Times are in local standard time (LST).

Figure

Scatter plots of observed (BUBBLE) versus simulated (VCWG) values of wind speed for different altitudes and months; each data point corresponds to a 1 h comparison between the model and observation.

Bias (

Figure

Scatter plots of observed (BUBBLE) versus simulated (VCWG) values of specific humidity for different altitudes and months; each data point corresponds to a 1 h comparison between the model and observation.

Bias (

Figure

Comparison between the observed (BUBBLE) versus simulated (VCWG) values of specific humidity. The hourly means are shown, and nighttime is indicated by shaded regions. Solid line: model, dashed line: observation. Times are in local standard time (LST).

To compare VCWG results with measured UHI (

Hourly mean and standard deviation (band) of UHI (

Bias (

In this section we explore the capability of the VCWG model to predict urban climate for investigations of the effects of building dimensions, urban vegetation, building energy configuration, radiation configuration, seasonal variations, and other climates. These results are reported in the Supplement in detail. Here only brief references to the analysis are made. Many explorations consider both nighttime and daytime urban microclimate. First, we investigate how the urban geometry, which is characterized by plan area density

The Vertical City Weather Generator (VCWG) is an urban microclimate model designed to calculate vertical profiles of meteorological variables including potential temperature, wind speed, specific humidity, and turbulent kinetic energy in an urban area. The VCWG is composed of four sub-models for ingestion of urban parameters and meteorological variables in a rural area (as input and boundary conditions) as well as prediction of the meteorological variables in a nearby urban area, the building energy performance variables, and the shortwave and longwave radiation transfer processes. VCWG combines elements of several previous models developed by

To evaluate VCWG, its predictions of potential temperature, wind speed, and specific humidity are compared to observations from the Basel UrBan Boundary Layer Experiment (BUBBLE) microclimate field campaign for 8 months from December 2001 to July 2002

This study shows that the urban microclimate model VCWG can successfully extend the spatial dimension of preexisting bulk flow (single-layer) urban microclimate models to one dimension in the vertical direction, while it also considers the relationship of the urban microclimate model to the rural meteorological measurements and the building energy conditions. The effect of the key urban elements such as building configuration, building energy systems (e.g., location of condensers and exhaust stacks), surface vegetation, and trees are considered, but there is still opportunity to improve VCWG further. The urban site is simplified as blocks of buildings with symmetric and regular dimensions, which can be more realistically represented if more considerations are taken into account regarding the nonuniform distribution of building dimensions. Also, the building energy model in VCWG is a single-zone model, assuming a uniform temperature with height in both indoor and outdoor environments. This limitation can be overcome by improving the radiation model, urban vertical diffusion model, and building energy model so that wall and indoor temperatures can vary with height, allowing the development of a multi-zone building energy model. In addition, horizontal advection from the rural area can be considered and parameterized in future work. Future studies can also focus on an improvement of the flow-field parameterization or include additional source and sink terms in the transport equations to model horizontal motions, eddies, and flow fluctuations in the urban area, which is realistically very three-dimensional and heterogeneous. Urban hydrology can be added to VCWG in the future to account for precipitation effects. At present, the developed VCWG model can account for the spatial variation of urban microclimate in a computationally efficient manner independent of an auxiliary mesoscale model. This advantage is really important for urban planners, architects, and consulting engineers for operationally fast VCWG simulations.

In Eq. (

The pressure and skin drags exerted on the flow in Eqs. (

The heat fluxes in Eq. (

A summary of details for the radiation model is provided here from

For net longwave radiation flux on each urban surface, the difference between the incoming and outgoing longwave radiation fluxes is considered. These fluxes depend on surface temperatures. Infinite reflections of longwave radiation within the urban canyon are considered. Again, no obstructions are considered for roofs; i.e., trees cannot be taller than buildings. The canyon air does not impact the radiation exchange. The energy associated with the longwave radiation exchange on each urban surface is conserved.

For the case of no trees, analytical view factors are calculated using standard equations

The VCWG v1.3.2 is developed at the Atmospheric Innovations Research (AIR) Laboratory at the University of Guelph:

The supplement related to this article is available online at:

MM wrote the paper with significant conceptual input from ESK and AAA as well as critical feedback from all co-authors. BB and LKN developed the base Urban Weather Generator (UWG) program in MATLAB. CM and SV translated UWG from MATLAB to Python. NN and ESK provided their code for the one-dimensional vertical diffusion model for the urban climate that was integrated into VCWG. MM and AAA developed the Vertical City Weather Generator (VCWG) program in Python by integrating various modeling components developed by BB, LKN, CM, SV, ESK, and NN. BD, AN, MKN, and MRN edited the paper.

The authors declare that they have no conflict of interest.

The computational platforms were set up with the assistance of Jeff Madge, Joel Best, and Matthew Kent at the University of Guelph. The authors thank Alberto Martilli at the Centre for Energy, Environment and Technology (CIEMAT) in Madrid, Spain, who developed and shared an earlier version of the one-dimensional vertical diffusion model for the urban climate. The authors thank Naika Meili at the Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland, who developed and shared an earlier version of the urban radiation model. The authors also thank Andreas Christen at the University of Freiburg (Environmental Meteorology), Freiburg, Germany, who provided the observation data from an extended period of the BUBBLE campaign.

This work was supported by the following: the University of Guelph through the International Graduate Tuition Scholarship (IGTS) for the lead author; the Accelerate program (460847) from Mathematics of Information Technology and Complex Systems (MITACS); the Discovery Grant program (401231) from the Natural Sciences and Engineering Research Council (NSERC) of Canada; the Government of Ontario through the Ontario Centres of Excellence (OCE) under the Alberta–Ontario Innovation Program (AOIP) (053450); and Emission Reduction Alberta (ERA) (053498). OCE is a member of the Ontario Network of Entrepreneurs (ONE).

This research has been supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada (grant no. 401231), the Government of Ontario (grant no. 053450), Emission Reduction Alberta (grant no. 053498), and the Accelerate program (460847) from Mathematics of Information Technology and Complex Systems (MITACS).

This paper was edited by Wolfgang Kurtz and reviewed by four anonymous referees.