# A new building energy model coupled with an urban canopy parameterization for urban climate simulations—part I. formulation, verification, and sensitivity analysis of the model

• Original Paper
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## Abstract

The generation of heat in buildings, and the way this heat is exchanged with the exterior, plays an important role in urban climate. To analyze the impact on urban climate of a change in the urban structure, it is necessary to build and use a model capable of accounting for all the urban heat fluxes. In this contribution, a new building energy model (BEM) is developed and implemented in an urban canopy parameterization (UCP) for mesoscale models. The new model accounts for: the diffusion of heat through walls, roofs, and floors; natural ventilation; the radiation exchanged between indoor surfaces; the generation of heat due to occupants and equipments; and the consumption of energy due to air conditioning systems. The behavior of BEM is compared to other models used in the thermal analysis of buildings (CBS-MASS, BLAST, and TARP) and with another box-building model. Eventually, a sensitivity analysis of different parameters, as well as a study of the impact of BEM on the UCP is carried out. The validations indicate that BEM provides good estimates of the physical behavior of buildings and it is a step towards a modeling tool that can be an important support to urban planners.

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## Notes

1. To solve numerically the equation, the wall is discretized in several layers of depth ∆x. Here and in Eq. 6 T wall represents the temperature of the layer close to the surface, while $$\left. {\frac{{\partial T_{\text{wall}} }}{{\partial x}}} \right|_{n - 1}$$represents the gradient between the layer close to the surface and the closest internal layer.

2. It must be remembered here that the ventilation has an impact not only on air temperature, but also on indoor air quality (for example, it helps to disperse pollutants emitted indoor). The optimal ventilation must then, takes into account both effects.

3. The convective heat coefficient h is used to estimate the sensible heat H exchanged between the external wall surface and the atmosphere, using the formula H = h (T aT wall), where T wall is the temperature of the external surface of the wall, and T a is the outdoor air temperature. H enters in the surface energy budget at the external surface and gives the b.c. for the heat diffusion equation in the wall.

## References

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## Acknowledgements

The authors wish to thank CIEMAT and LPAS-EPFL for the doctoral fellowships held by Francisco Salamanca and Andrea Krpo, respectively. We also thank Y. Kikegawa for providing important data for the validation. This work has been funded by the Ministry of Environment of Spain.

## Author information

Authors

### Corresponding author

Correspondence to Francisco Salamanca.

## Appendix

### Appendix

List of symbols

albwall,j :

albedo of the indoor surface of the wall j

A f :

floor area (m2)

$$A_i^{\text{wall}}$$ :

surface area of the wall i (m2)

$$A_j^{\text{wind}}$$ :

surface area of window in the wall j (m2)

C p :

specific heat of air (J K−1 kg−1)

h wall,i :

convective heat transfer coefficient between the indoor air and the wall i (WK−1 m−2)

h wind,j :

convective heat transfer coefficient between the indoor air and the window in the wall j (WK−1 m−2)

l :

latent heat of evaporation (J kg−1)

T a :

outdoor air temperature (K)

T r :

indoor air temperature (K)

T wall,i :

indoor surface temperature of the wall i (K)

T wind,j :

temperature of the window in the wall j (K)

P :

peak number of occupants per floor area (person m−2)

q E :

sensible heat gain from equipments per floor area (W m−2)

q hl :

latent heat generation from the occupants (W person−1)

q hs :

sensible heat generation from the occupants (W person−1)

q Va :

specific humidity of the outdoor air (kg kg−1)

q Vr :

specific humidity of the indoor air (kg kg−1)

Rl j :

Rs :

solar radiation energy crossing the windows received directly by the indoor walls (W m−2)

Rs j :

V a :

total ventilation rate (m3 s−1)

α wind, j :

% of window in the wall j

β :

thermal efficiency of the total heat exchanger, $$0 \le \beta \le 1$$

ε wall,j :

emissivity of the indoor surface of the wall j

ε wind :

emissivity of the windows

φ P :

ratio of hourly occupants to P, $$0 \le \phi_p \le 1$$

ρ :

air density (kg m−3)

σ :

Stefan-Boltzmann constant (W m−2 K−4)

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Salamanca, F., Krpo, A., Martilli, A. et al. A new building energy model coupled with an urban canopy parameterization for urban climate simulations—part I. formulation, verification, and sensitivity analysis of the model. Theor Appl Climatol 99, 331–344 (2010). https://doi.org/10.1007/s00704-009-0142-9