^{TM} model, presented here, however, does allow for long time integrations (needed for urban climate projections) at high spatial resolution of a few 100 m at modest computational cost.

**The surface module**

The surface module of the UrbClim^{TM} model comprises of an urbanized version of the LAICa "land surface interaction calculation" - scheme orginally by De Ridder and Schayes, (1997). The ‘urbanisation’ is accomplished in a rather simple way, by representing the urban surface as a rough impermeable slab, with appropriate values for the albedo, emissivity, thermal conductivity and volumetric heat capacity. The surface scheme includes a suitable parameterization of the inverse Stanton number kB^{-1} (De Ridder et al, 2012), being the logarithm of the ratio of aerodynamic and thermal roughness lengths. In contrast to homogenously vegetated surfaces, which contain porous-rough obstacles and are characterised by values of *kB*^{-1} ~ 2, urban areas, which are composed of bluff-rough obstacles, exhibit much larger values. The associated very low thermal roughness length values strongly inhibit the turbulent transfer of heat from the urban substrate to the atmosphere, so that a relatively large share of the available radiant surface energy flux is converted to storage heat rather than to turbulent sensible heating of the atmosphere, which, together with the typically high values of thermal inertia of urban materials, leads to the large storage heat flux values typically observed (or estimated as a residual of the surface energy balance) over urban areas.

Every surface grid cell is assumed to be composed of a mixture of vegetation, bare soil, and urban land cover, represented by their respective fractions *f _{v}*,

The output generated by the land surface scheme consists of the turbulent fluxes of sensible and latent heat, and momentum. These fluxes serve as lower boundary conditions for the atmospheric boundary layer model, which will be described next.

**The atmospheric module**

A full mesoscale model at kilometre-scale resolution is very costly in terms of the computational time required to perform a simulation. Therefore, we developed a very simple 3-D model of the lower atmosphere, comprising the atmospheric boundary layer and typically extending to a height of a few kilometres. This model is represented by conservation equations for horizontal momentum (considering zonal and meridional wind speed components *u* and *v*, respectively), potential temperature (*q*), specific humidity (*q*), and mass (involving the vertical wind speed component *w*). The pressure field however is not calculated internally, but prescribed from the large-scale host model from which our model receives its boundary conditions. Hence only the synoptic-scale pressure gradients are accounted for. By doing so we avoid the complexities associated with a full mesoscale meteorological model. More importantly, it allows the use of much longer time increments in the numerical solver, and a lower model top (since no absorbing layer is required to damp gravity waves), which makes the model much faster. On the downside, the UrbClim^{TM} model does not allow for local circulation patterns to develop.

The numerical solution of the atmospheric conservation equations is achieved using a finite difference scheme, based on an Arakawa C-grid discretisation. The advection terms are written in flux-conservative form and solved using the Walcek-scheme. Vertical diffusion is solved using the Crank-Nicolson algorithm. At the lower (surface) boundary, the momentum, heat, and moisture fluxes are specified as those generated by the land surface scheme described above. At the model top, which is taken at a few kilometres height, values interpolated from the large-scale driving model are imposed.

The specification, from the large-scale driving model, of the lateral and top boundary conditions, the synoptic-scale pressure gradient, and the downwelling radiation and precipitation fluxes, allows to account for the effect of synoptic weather on local climate, and defines the nesting of our urban boundary layer climate model within the large-scale host model.

More details about the UrbClim^{TM} model can be found in De Ridder et al, (2014).

The UrbClim^{TM} model has been validated in various cities using representative urban meteorological measurements. The figure shows a timeseries of the temperature difference between two urban stations in Antwerp (Lyceum and Borgerhout) and a rural station located at Vremde. The model is well able to capture the temporal dynamics of the UHI effect. Furthermore, a dedicated monitoring campaign during the summer of 2013 resulted in a satisfactory spatial validation of the average UHI intensity in different parts of the city of Antwerp.

The table below shows in addition a number of validation results obtained for different cities.

Ghent | Antwerp | Berlin | London | Bilbao | |
---|---|---|---|---|---|

RMSE (°C) | 1.0 | 1.0 | 0.9 | 1.2 | 1.0 |

Correlation | 0.68 | 0.70 | 0.71 | 0.62 | 0.70 |

The UrbClim^{TM} model has been deployed successfully to numerous cities around the world during various national and international projects. See the map above for an overview. Please check our project pages for more details on the different projects in which UrbClim^{TM} has been applied.

^{TM} allow to generate spatially explicit timeseries of hourly temperature and humidity maps from which a variety of indicators can be derived in postprocessing at the scale of a city neighbourhood. Such indicators can include the magnitude of the average urban heat island effect, the daily cycle of the effect or spatially explicit maps of heat stress indicators or heat wave days/intensity. The figure on the left for example indicates the number of heatwave days during the period 1985 - 2005 for the city of Antwerp according to the definition of the EuroHEAT project (D'Ippoliti et al, 2010).

- De Ridder, K., and G. Schayes, 1997. The IAGL Land Surface Model, J. Appl. Meteorol., 36, 167–182.
- De Ridder, K.; Bertrand, C.; Casanova, G.; Lefebvre, W. Exploring a new method for the retrieval of urban thermophysical properties using thermal infrared remote sensing and deterministic modeling. J. Geophys. Res. 2012, 117, 1–14.
- Demuzere, M.; De Ridder, K.; Van Lipzig, N. P. M. Modeling the energy balance in Marseille: Sensitivity to roughness length parameterizations and thermal admittance. J. Geophys. Res. 2008, 113, 1–19.
- De Ridder, K; Lauwaet D. and Maiheu B. UrbClim - a fast urban boundary layer climate model. Urban Climate, 12:21-48, June 2015.
- D’Ippoliti, D.; Michelozzi, P.; Marino, C.; de’Donato, F.; Menne, B.; Katsouyanni, K.; Kirchmayer, U.; Analitis, A.; Medina-Ramón, M.; Paldy, A.; et al. The impact of heat waves on mortality in 9 European cities: results from the EuroHEAT project. Environ. Health 2010, 9, 37.