Abstract
The size and arrangement of the obstacles and the presence of a source of heat (anthropogenic heat flux) are distinctive characteristics of an urban area. These two elements, together with the specific applications oriented to improve citizen’s comfort, determine the way urban heterogeneities are represented in mesoscale models. In this contribution two examples are presented. In the first a microscale fluid dynamics model is used to investigate the role of organized motions (dispersive fluxes) of a passive tracer emitted at the surface in a staggered and in an aligned array of cubes. The impact of the dispersive flux, that can reach 90 % of the total flux in the staggered array, is then assessed in a column model. The second example deals with the representation of anthropogenic heat fluxes and the estimation of thermal comfort by means of an urban canopy parameterization with a simple building energy model, implemented in a mesoscale model. The simulation of a typical summer day over the city of Madrid (Spain) shows that the anthropogenic heat fluxes have the largest impact on the air temperature in the eveningnight, and that the presence of the city prolongs to the late evening the period of thermal discomfort, compared with the rural areas surrounding the city. The paper is concluded by pointing out that future work must be devoted to deep on the relationship between the real morphology of a city and the simplified morphology adopted in the urban canopy parameterizations.
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Notes
With the term “mesoscale models” we refer to all the models that are not “building resolving”, e.g. with a resolution too coarse to explicitly resolve the buildings.
Passive tracer data are not available from the DNS, so a direct comparison is not possible.
References
United Nations, Department of Economic and Social Affairs, Population Division (2006) World Urbanization Prospects: the 2005 Revision. Working Paper No. ESA/P/WP/200.
Masson V (2000) A physicallybased scheme for the urban energy budget. Bound Layer Meteorol 94:357–397
Kusaka H, Kondo H, Kikegawa Y, Kimura F (2001) A simple singlelayer urban canopy model for atmospheric models: Comparison with multilayer and slab models. Bound Layer Meteorol 101:329–358
Martilli A, Clappier A, Rotach MW (2002) An urban surface exchange parameterization for mesoscale models. Bound Layer Meteorol 104:261–304
Coceal O, Belcher SE (2004) A canopy model of mean winds through urban areas. Q J R Meteorol Soc 130:1349–1372
Best MJ (2005) Representing urban areas within operational numerical weather prediction models. Bound Layer Meteorol 114:91–109
Dandou AM, Tombrou M, Soulakellis A, Bossioli E (2005) Development and evaluation of an urban parameterization scheme in the Penn State/NCAR Mesoscale model (MM5). J Geophys Res 110:D10102
Kanda M, Kawai T, Kanega M, Moriwaki R, Narita K, Hagishima A (2005) A simple energy balance model for regular building arrays. Bound Layer Meteorol 116:423–443
Kondo H, Genchi Y, Kikegawa Y, Ohashi Y, Yoshikado H, Komiyama H (2005) Development of a multilayer urban canopy model for the analysis of energy consumption in a big city: structure of the urban canopy model and its basic performance. Bound Layer Meteorol 116:395–421
Dupont S, Mestayer PG (2006) Parameterization of the urban energy budget with the Submesoscale Soil Model. J Appl Meteorol Climatol 45:1744–1765
Hamdi R, Masson V (2008) Inclusion of a drag approach in the Town Energy Balance (TEB) scheme: offline 1D evaluation in a street canyon. J Appl Meteorol Climatol 47:2627–2644
Lee SH, Park SU (2008) A vegetated urban canopy model for meteorological and environmental modelling. Bound Layer Meteorol 126:73–102
Oleson KW, Bonan GB, Feddema J, Vertenstein M, Grimmond CSB (2008) An urban parameterization for a global climate model. Part I: formulation and evaluation for two cities. J Appl Meteorol Climatol 47:1038–1060
Porson A, Clark PA, Harman IN, Best MJ, Belcher SE (2010) Implementation of a new urban energy budget scheme in the MetUM. Part I: description and idealized simulations. Q J R Meteorol Soc 136:1514–1529
Aoyagi T, Seino N (2011) A square prism urban canopy scheme for the NHM and its evaluation on summer conditions in the Tokyo Metropolitan area, Japan. J Appl Meteorol Climatol 50:1476–1496
Martilli A (2007) Current research and future challenges in urban mesoscale modelling. Int J Climatol 27:1909–1918
Loridan T, Grimmond CSB, GrossmanClarke S, Chen F, Tewari M, Manning K, Martilli A, Kusaka H, Best M (2010) Tradeoffs and responsiveness of the singlelayer urban canopy parametrization in WRF: an offline evaluation using the MOSCEM optimization algorithm and field observations. QJRMS 136:997–1019
Schubert S, GrossmanClarke S, Martilli A (2012) A doublecanyon radiation scheme for multilayer urban canopy models. Bound Layer Meteorol 145:439–468
Grimmond CSB, Oke TR (1999) Aerodynamic properties of urban areas derived from analysis of surface form. J Appl Meteorol 38:1262–1292
Di Sabatino S, Leo LS, Cataldo R, Ratti R, Britter RE (2010) Construction of digital elevation models for a Southern European City and a comparative morphological analysis with respect to Northern European and North American Cities. J Appl Meteorol Climatol 49:1377–1396
Kikegawa Y, Genchi Y, Yoshikado H, Kondo H (2003) Development of a numerical simulation system toward comprehensive assessments of urban warming countermeasures including their impacts upon the urban buildings energydemands. Appl Energy 76:449–466
Salamanca F, Krpo A, Martilli A, Clappier A (2010) 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
Bueno B, Pigeon G, Norford L, Zibouche K, Marchadier C (2012) Development and evaluation of a building energy model integrated in the TEB scheme. Geosci Model Dev 5:433–448
Martilli A (2009) On the derivation of input parameters for urban canopy models from urban morphological datasets. Bound Layer Meteorol 130:301–306
Rasheed A, Robinson D, Clappier A, Narayanan C, Lakehal D (2011) Representing complexities in urban geometry in mesoscale modeling. Int J Climatol 31:289–301
Leo LS, Buccolieri R, Di Sabatino S (2012) A novel approach for urban mean flow parameterisation. In: Proceedings of the 8th international conference on urban climates, UCD, Dublin Ireland, paper 374, 6th–10th August, 2012.
Santiago JL, Martilli A (2010) A dynamic urban canopy parameterization for mesoscale models based on CFDRANS microscale simulations. Bound Layer Meteorol 137:417–439
Krpo A, Salamanca F, Martilli A, Clappier A (2010) On the impact of anthropogenic heat fluxes on the urban boundary layer: a 2D numerical study. Bound Layer Meteorol 136:105–127
Salamanca A, Martilli A, Yague C (2012) A numerical study of the urban boundary layer over Madrid during the DESIREX (2008) campaign with WRF and an evaluation of simple mitigation strategies of the UHI. Int J Climatol 32:2372–2386
Martilli A, Santiago JL (2007) CFD simulation of airflow over a regular array of cubes. Part II: analysis of spatial average properties. Bound Layer Meteorol 122:635–654
Coceal O, Thomas TG, Castro IP, Belcher SE (2006) Mean flow and turbulence statistics over groups of urbanlike cubical obstacles. Bound Layer Meteorol 121:491–519
Dupont S, Otte T, Ching J (2004) Simulation of meteorological fields within and above urban and rural canopies with a mesoscale model (MM5). Bound Layer Meteorol 113:111–158
Heiple S, Sailor DJ (2008) Using building energy simulation and geospatial modelling techniques to determine high resolution building sector energy consumption profiles. Energy Build 40:1426–1436
Salamanca F, Martilli A (2010) A new building energy model coupled with an Urban Canopy Parameterization for urban climate simulations—Part II. Validation with one dimension offline simulations. Theor Appl Climatol 99:345–356
Salamanca F, Martilli A, Tewari M, Chen F (2010) A study of the urban boundary layer using different urban parameterizations and highresolution urban canopy parameters with WRF (The case of Houston). J Appl Meteorol Climatol 50:1107–1128
Belding HS, Hatch TF (1955) An index for evaluating heat stress in terms of resulting physiological strain. Heat Pip Air Cond 27(8):129
Oke TR (1987) Boundary layer climates, 2nd edn. Routledge, London, p 435
Fernández García F (2009) Ciudad y cambio climático: aspectos generales y aplicación al área metropolitana de Madrid. (in Spanish). Investigaciones Geográficas 49:173–195
Acknowledgments
Authors acknowledge Omduth Coceal for providing the DNS data for the validation of the RANS simulations. This study has been partially supported by the project “Modelización de la Influencia de la Vegetación Urbana en la Calidad del Aire y Confort Climático” (CGL201126173) funded by Spanish Ministry of Economy and Competitiveness and by the Project Supercomputation and EScience (SyeC) from the Spanish CONSOLIDER Programme.
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Appendices
Appendix 1
The column model used in this study solves the following equations, in addition to the conservation equation for the scalar (Eq. 7):
The first equation is the mean and spatially averaged conservation equation for the xcomponent of momentum, where the dispersive stress has been neglected. The first term on the right hand side, represents the gradient of the vertical turbulent flux of momentum (Reynolds stress), the second is the drag force, different than zero only within the canopy, and the third term \(\frac{u_\tau ^{2}}{4H}\) is added to represent a pressure gradient along the column to maintain the flow. In the simulations, \(u_\tau =1\,\hbox {m}/\hbox {s}\), and \(4H\) is the height of the domain.
The second equation is the conservation equation for the spatially averaged turbulent kinetic energy. The first term on the right hand side is the gradient of the vertical turbulent flux of TKE, the second is the gradient of the shear production, the third is the TKE production due to the drag force, and the 4th is the dissipation, modelled as \(\varepsilon =c_\varepsilon \frac{\left\langle {\overline{e}} \right\rangle ^{3/2}}{l_\varepsilon }\). The turbulent coefficient is computed as \(K_M =c_k l_k \sqrt{tke}\).
The length scales are based on the paper of [22],
where \(d_2 =\left( {1.\frac{a_1 }{a_2 }} \right) \frac{3}{2}H+\frac{a_1 }{a_2 }d\) is computed to ensure continuity in \(z=\frac{3}{2}H\).
The displacement height is computed as \(\frac{d}{H}=\lambda _p ^{0.13}\). The value of \(l_k \) is \(l_k =\frac{c_\mu }{c_\varepsilon c_k }l_\varepsilon \). The values of the numerical constants are as follows: \(c_\varepsilon =0.71,c_k =0.4,c_\mu =0.09,a_1 =2.19,a_2 =1.2\). The air density is assumed constant and equal to one. The model is run until steady state is reached (time derivative become zero).
Appendix 2
The mean radiant temperature for a person 1.80 m tall in the middle of the canyon is computed as follows:
where \(a_b\) is the absorption coefficient of the human body (taken as 0.7), \(\varepsilon _p\) is the emission coefficient of the human body (0.97), \(\sigma \) is the Stefan Boltzmann constant, \(R_{long}\) is the long wave contribution, and \(R^{*}_{short} \quad \) is the shortwave component.
The human body has been simplified by a vertical surface, 1.80 m height, infinite in the direction of the canyon, and equidistant from the two walls.
For the long wave contribution, we have, for a North–South oriented street canyon.
The meaning of the symbols is as follows:
 \(\varepsilon _{wall} \) :

is the emissivity of the wall (windows when the subscript is window)
 \(T^{wall}e_i ,T^{wall}w_i \) :

is the temperature of the east and west walls at the level \(i\) (of the windows when the superscript is window)
 \(pwin\) :

is the fraction of the wall occupied by the windows
 \(Rle^{wall}_i ,Rlw^{wall}_i \) :

is the long wave radiation reaching the east and west wall at the level \(i\)
 \(\Gamma _{i+1} \) :

is the probability to have a building at level i
 \(\Psi _i \) :

is the view factor from the wall at level i to the human body in the middle of the street (see below)
 \(Rl_{sky}\) :

is the long wave radiation from the sky to the human body in the middle of the street
 \(\Psi _{sky} \) :

is the view factor from the sky to the human body in the middle of the street
 \(\varepsilon _{street} \) :

is the emissivity of the street
 \(T^{street}\) :

is the temperature of the street
 \(Rl_{street} \) :

is the long wave radiation reaching the street
 \(\Psi _{street} \) :

is the view factor from the street to the human body
The short wave component is divided in direct and reflected, and treated as:
The reflected component is calculated using the view factors in a similar way as for the long wave radiation:
where \(Rse^{wall}_i ,Rsw^{wall}_i\) is the short wave radiations reaching the east and west wall at level i and \(Rs_{street}\) is the short wave radiation reaching the street.
For the direct short wave, the formula used is the following:
where \(R_{solar}\) is the solar radiation (in W/m\(^2\)) reaching an unobstructed horizontal surface, \(z_{man}\) is the height of the human body (1.80 m), and \(\gamma _{i+1}\) is the probability to have a building of height \(z_{i+1}\) (where \(z_{i+1}\) is the full height of the numerical level i+1— see more about the urban grid definition in [4]), and
For the physical meaning of x1 and x2, see Fig. A1 in [4]. This is valid for a canyon perpendicular to the sun direction. When it is not, it can be easily corrected (see again the technique used in [4]).
The values of fp are computed as:
and Zr solar zenith angle.
For the view factor calculation, the formulas used are the same as in [4], but with different parameters. In particular, from A15 of [4]:
from A16
and from A18
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Martilli, A., Santiago, J.L. & Salamanca, F. On the representation of urban heterogeneities in mesoscale models. Environ Fluid Mech 15, 305–328 (2015). https://doi.org/10.1007/s1065201393214
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DOI: https://doi.org/10.1007/s1065201393214