Numerical study of the urban geometrical representation impact in a surface energy budget model

Antonio Cantelli; Paolo Monti; Giovanni Leuzzi

doi:10.1007/s10652-013-9309-0

Environmental Fluid Mechanics

April 2015, Volume 15, Issue 2, pp 251–273 | Cite as

Numerical study of the urban geometrical representation impact in a surface energy budget model

Authors
Authors and affiliations

Antonio Cantelli
Paolo MontiEmail author
Giovanni Leuzzi

Original Article

First Online: 01 September 2013

Received: 27 February 2013

Accepted: 22 August 2013

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4 Citations

Abstract

The aim of this work is to investigate how both the orientation of the urban canyon and the modeling of the edge effects (i.e. urban canyons of finite length) are important in the numerical simulation of the surface energy budget in urban areas. Starting from the town energy balance scheme, two models of increasing complexity of the canyon geometry are developed. A sensitivity analysis of the role played by the chosen hypothesis and parameterizations is performed by coupling the canyon schemes with the numerical weather prediction model RAMS. The results suggest that a detailed description of the urban geometry could produce non-negligible differences of the energy balances and of the temperature fields with respect to what occurs using simpler schematizations, in particular during the summer.

Keywords

TEB Building Urban canyon Urban heat island Energy balance Meteorological models

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Supplementary material

10652_2013_9309_MOESM1_ESM.docx (42 kb)

Supplementary material 1 (docx 42 KB)

Appendices

Appendix 1

In the four-facet scheme, the reflection coefficients of the solar radiation undergo changes due to the modeling of both walls. Using the same notation adopted by [6], the component of the reflected solar radiation is:

$$\begin{aligned} \hbox {R}_{\mathrm{i}} ( 0)=\alpha _{\mathrm{i}} ( {\hbox {S}_{\mathrm{dir}} +\hbox {S}_{\mathrm{dif}} }), \qquad \hbox {i}~=~2, 3, 4 \end{aligned}$$

The reflected solar radiations for the road and the walls after n reflections are

$$\begin{aligned} \hbox {R}_3 ( {\hbox {n}+1})=\frac{\alpha _3 }{2}( {1-\psi _3 })(\hbox {R}_2 ( \hbox {n})+\hbox {R}_4 ( \hbox {n})) \end{aligned}$$

$$\begin{aligned} \hbox {R}_\mathrm{i} ( {\hbox {n}+1})=\alpha _{\mathrm{i}} \psi _{\mathrm{i}} \hbox {R}_3 ( \hbox {n})+\alpha _{\mathrm{i}} (1-2\psi _{\mathrm{i}} )\hbox {R}_{\mathrm{j}} ( \hbox {n}),\quad \hbox {i},\hbox {j}=2, 4\; \hbox {j}\ne \hbox {i} \end{aligned}$$

The sum of the n contributions for the different surfaces gives:

$$\begin{aligned} \mathop \sum \limits _{\hbox {k}=0}^n \hbox {R}_3 ( \hbox {k})=\frac{\alpha _3 }{2}( {1-\psi _3 })\left[ {\mathop \sum \limits _{\hbox {k}=0}^{\hbox {n}-1} \hbox {R}_2 ( \hbox {k})+\mathop \sum \limits _{\hbox {k}=0}^{\hbox {n}-1} \hbox {R}_4 ( \hbox {k})} \right] +\hbox {R}_3 ( 0) \end{aligned}$$

$$\begin{aligned} \mathop \sum \limits _{\hbox {k}=0}^{\mathrm{n}} \hbox {R}_{\mathrm{i}} ( \hbox {k})=\alpha _{\mathrm{i}} \psi _{\mathrm{i}} \mathop \sum \limits _{\hbox {k}=0}^{\hbox {n}-1} \hbox {R}_3 ( \hbox {k})+\alpha _{\mathrm{i}} (1-2\psi _{\mathrm{i}} )\mathop \sum \limits _{\mathrm{k}=0}^{\hbox {n}-1} \hbox {R}_{\mathrm{j}} ( \hbox {k})+\hbox {R}_{\mathrm{i}} ( 0),\quad \hbox {i},\hbox {j}=2, 4\; \hbox {j}\ne \hbox {i} \end{aligned}$$

Solving the geometric system above for an infinite number of reflections, one obtains [29]:

$$\begin{aligned} \mathop \sum \limits _{\mathrm{k}=0}^\infty \hbox {R}_3 ( \hbox {k})=\hbox {M}_3 =\frac{\hbox {a}\left[ {\hbox {R}_2 ( 0)( {\Xi _3 +\Theta _3 })+\hbox {R}_3 ( 0)( {\chi +\Upsilon _3 +\Pi _3 })+\hbox {R}_4 ( 0)(\Psi _3 +\Lambda _3 )} \right] }{\chi } \end{aligned}$$

$$\begin{aligned} \mathop \sum \limits _{\mathrm{k}=0}^\infty \hbox {R}_{\mathrm{i}} ( \hbox {k})=\hbox {M}_{\mathrm{i}} =\frac{\left[ {\hbox {R}_2 ( 0)( {\Xi _{\mathrm{i}} +\Theta _{\mathrm{i}} })+\hbox {R}_3 ( 0)( {\Upsilon _{\mathrm{i}} +\Pi _{\mathrm{i}} })+\hbox {R}_4 ( 0)(\Psi _{\mathrm{i}} +\Lambda _{\mathrm{i}} )} \right] }{\chi }, \quad \hbox {i}=2, 4 \end{aligned}$$

where

$$\begin{aligned} \chi =1-\left( \frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}}\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}}\right) . \end{aligned}$$

$$\begin{aligned} \hbox {a}=\frac{\alpha _3 }{2}(1-\psi _3 )\quad \hbox {b}=\alpha _2 \psi _2 \quad \hbox {c}=\alpha _2 (1-2\psi _2 )\quad \hbox {d}=\alpha _4 \psi _4 \end{aligned}$$

$$\begin{aligned} \hbox {e}=\alpha _4 (1-2\psi _4 )\quad \gamma =1-\frac{\alpha _3 }{2}( {1-\psi _3 })( {\alpha _2 \psi _2 -\alpha _4 \psi _4 })= 1-\hbox {a}(\hbox {b}-\hbox {d}) \end{aligned}$$

$$\begin{aligned} \Theta _{\mathrm{i}} =\left\{ {{\begin{array}{lll} {\frac{\gamma +\hbox {ab}}{\gamma -\hbox {abe}}}, &{}\hbox {i}=2 \\ {\frac{\gamma +\hbox {ab}}{\gamma -\hbox {abe}}\left( {1+\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}}}\right) ,}&{} \hbox {i}=3 \\ {\frac{\gamma +\hbox {ab}}{\gamma -\hbox {abe}}\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}}}, &{}\hbox {i}=4 \\ \end{array} }} \right. \, \Lambda _{\mathrm{i}} =\left\{ {{\begin{array}{lll} {\frac{\hbox {ab}}{\gamma -\mathrm{abe}},}&{} \hbox {i}=2 \\ {\frac{\hbox {ab}}{\gamma -\hbox {abe}}\left( {1+\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}}}\right) ,} &{}\hbox {i}=3 \\ \frac{\hbox {ab}}{\gamma -\hbox {abe}}\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}},&{} i=4 \\ \end{array} }} \right. \end{aligned}$$

$$\begin{aligned} \Xi _\mathrm{i} =\left\{ {{\begin{array}{lll} {\frac{\hbox {ad}}{\gamma -\hbox {acd}}\frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}},}&{} \hbox {i}=2 \\ {\frac{\hbox {ad}}{\gamma -\hbox {acd}}\left( {1+\frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}}}\right) ,}&{}\hbox {i}=3\\ {\frac{\hbox {ad}}{\gamma -\hbox {acd}},} &{}\hbox {i}=4 \\ \end{array} }} \right. \,\Pi _{\mathrm{i}} =\left\{ {{\begin{array}{lll} {\frac{\hbox {b}}{\gamma -\hbox {abe}},}&{}\hbox {i}=2 \\ {\frac{\hbox {b}}{\gamma -\hbox {abe}}\left( 1+\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}}\right) ,}&{} \hbox {i}=3 \\ {\frac{\hbox {b}}{\gamma -\hbox {abe}}\frac{\gamma \hbox {e}+\hbox {ade}}{\gamma -\hbox {acd}},}&{} \hbox {i}=4 \\ \end{array} }} \right. \end{aligned}$$

$$\begin{aligned} \Upsilon _{i} =\left\{ {{\begin{array}{lll} {\frac{\hbox {d}}{\gamma -\hbox {acd}}\frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}},} &{}\hbox {i}=2 \\ {\frac{\hbox {d}}{\gamma -\hbox {acd}}\left( {1+\frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}}}\right) ,} &{}\hbox {i}=3 \\ {\frac{\hbox {d}}{\gamma -\hbox {acd}},}&{} \hbox {i}=4 \\ \end{array} }} \right. \,\Psi _{\mathrm{i}} =\left\{ {{\begin{array}{lll} {\frac{\gamma +\hbox {ad}}{\gamma -\hbox {acd}}\frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}},} &{}\hbox {i}=2 \\ {\frac{\gamma +\hbox {ad}}{\gamma -\hbox {acd}}\left( {1+\frac{\gamma \hbox {c}+\hbox {abc}}{\gamma -\hbox {abe}}}\right) ,}&{} \hbox {i}=3\\ {\frac{\gamma +\hbox {ad}}{\gamma -\hbox {acd}}, }&{}\hbox {i}=4 \\ \end{array} }} \right. \end{aligned}$$

Appendix 2

The analytical expression of C has been obtained by the polynomial interpolation of the original law reported in [39], viz.:

$$\begin{aligned} \hbox {C}=\hbox {a} \ln \left( {\frac{\hbox {z}_0 }{\delta _0 }}\right) +\hbox {b} \ln \left( {\frac{\hbox {z}_0 }{\delta _0 }}\right) ^2+\hbox {c} \ln \left( {\frac{\hbox {z}_0 }{\delta _0 }}\right) ^{-1}+\hbox {d} \ln \left( {\frac{\hbox {z}_0 }{\delta _0 }}\right) ^{-2}+\hbox {e} \end{aligned}$$

where a $=$ 0.01643, b $=$ 4.399e$-$4, c $=$ $-1$.741, d $=$ $-0$.1722 and e $=$ 0.4128.

Appendix 3

In comparing the results obtained using the three UC schemes, the different geometry characterizing L2 with respect to the other two schemes should be born in mind. In fact, the presence of the crossroads modeled in L2 results in a greater extension of the road surface with respect to L1 and L0. Therefore, despite the aspect ratio is the same for the three schemes, a condition of non-comparability occurs. It is therefore of primary importance to set the condition of geometric equivalence:

$$\begin{aligned} \lambda _{\mathrm{p}}^{\mathrm{L}0} =\lambda _{\mathrm{p}}^{\mathrm{L}1} =\lambda _{\mathrm{p}}^{\mathrm{L}2} =\lambda _{\mathrm{p}} \end{aligned}$$

(47)

where $\lambda _{\mathrm{p}} =\hbox {A}_{\mathrm{b}} /( {\hbox {A}_{\mathrm{b}} +\hbox {A}_{\mathrm{r}} })$, while $\hbox {A}_{\mathrm{b}} $ and $\hbox {A}_{\mathrm{r}} $ are the roof top and the street surfaces, respectively. By setting a reference value of $\lambda _{\mathrm{p}}$, using the simplified version of L2 (see Sect. 3.3) and the assumption of square buildings of side L, Eq. (47) yields:

$$\begin{aligned} \lambda _{\mathrm{p}}^{\mathrm{L}2} =\lambda _{\mathrm{p}} =\frac{\hbox {L}^2}{\hbox {L}^2+\hbox {W}^2} \end{aligned}$$

(48)

Equation (48) can be rewritten as:

$$\begin{aligned} \hbox {L}^2( {1-\lambda _{\mathrm{p}} })-2\hbox {w}\lambda _{\mathrm{p}} \hbox {L}-\lambda _{\mathrm{p}} \hbox {W}^2=0 \end{aligned}$$

(49)

which has two distinct solutions:

$$\begin{aligned} L=W\left[ {\frac{\lambda _\mathrm{p} }{1-\lambda _\mathrm{p} }\pm \frac{\root \of {\lambda _\mathrm{p} }}{1-\lambda _\mathrm{p} }} \right] \end{aligned}$$

Since only the positive solution gives L$>$0 for $\lambda _{\mathrm{p}} \in ]0,1[$, one has:

$$\begin{aligned} \hbox {L}=\hbox {W}\left( {-1+\frac{1}{\sqrt{\lambda _{\mathrm{p}} } }}\right) ^{-1} \end{aligned}$$

(50)

which coincides with Eq. (46). This makes it possible to define the size of the building, so that, for a given road width W, the value of $\lambda _{\mathrm{p}} $ is retained.

References

1.
Fernando HJS, Zajic D, Di Sabatino S, Dimitrova R, Hedquist B, Dallman A (2010) Flow, turbulence, and pollutant dispersion in urban atmospheres. Phys Fluids 22:051301CrossRefGoogle Scholar
2.
Monti P, Leuzzi G (2005) A numerical study of mesoscale airflow and dispersion over coastal complex terrain. Int J Environ Pollut 25:239–250CrossRefGoogle Scholar
3.
Pelliccioni A, Monti P, Gariazzo C, Leuzzi G (2012) Some characteristics of the urban boundary layer above Rome, Italy, and applicability of Monin–Obukhov similarity. Environ Fluid Mech 12:405–428CrossRefGoogle Scholar
4.
Di Sabatino S, Leo LS, Cataldo R, Ratti C, Britter RE (2010) Construction of digital elevations models for a southern European city and a comparative morphological analysis with respect to northern European and north American cities. J Appl Meteorol Climatol 49:1377–1396CrossRefGoogle Scholar
5.
Masson V (2006) Urban surface modeling and the meso-scale impact of cities. Theor Appl Climatol 84(1):35–45CrossRefGoogle Scholar
6.
Masson V (2000) A physically-based scheme for the urban energy budget in atmospheric models. Boundary-Layer Meteorol 94:357–397CrossRefGoogle Scholar
7.
Kusaka H, Kondo H, Kikegawa Y, Kimura F (2001) A simple single-layer urban canopy model for atmospheric models: comparison with multi-layer and slab models. Boundary-Layer Meteorol 101:329–358CrossRefGoogle Scholar
8.
Dupont S, Mestayer G (2006) Parameterization of the urban budget with the submesoscale soil model. J Appl Meteorol Climatol 45:1744–1765CrossRefGoogle Scholar
9.
Lee S-H, Park S-U (2008) A vegetated urban canopy model for meteorological and environmental modeling. Boundary-Layer Meteorol 126:73–102CrossRefGoogle Scholar
10.
Ryu YH, Baik JJ, Lee SH (2011) A new single-layer urban canopy model for use in mesoscale atmospheric models. J Appl Meteorol Climatol 50(1773):1794Google Scholar
11.
Ca VT, Asaeda T, Ashie Y (1999) Development of a numerical model for the evaluation of the urban thermal environment. J Wind Eng Ind Aerodyn 81:181–196CrossRefGoogle Scholar
12.
Martilli A, Clappier A, Rotach MW (2002) An urban surface exchange parameterisation for mesoscale models. Boundary-Layer Meteorol 104:261–304CrossRefGoogle Scholar
13.
Otte TL, Lacser A, Dupont S, Ching JKS (2004) Implementation of an urban canopy parameterization in a mesoscale meteorological model. J Appl Meteorol 43:1648–1665CrossRefGoogle Scholar
14.
Kondo H, Genchi Y, Kikegawa Y, Ohashi Y, Yoshikado H, Komiyama H (2005) Development of a multi-layer urban canopy model for the analysis of energy consumption in a big city: structure of the urban canopy model and its basic performance. Boundary-Layer Meteorol 116:395–421CrossRefGoogle Scholar
15.
Schubert S, Grossman-Clarke S, Martilli A (2012) A double-canyon radiation scheme for multi-layer urban canopy models. Boundary-Layer Meteorol 145:439–468CrossRefGoogle Scholar
16.
Miao S, Li P, Wang X (2009) Building morphological characteristics and their effect on the wind in Beijing. Adv Atmos Sci 26:1115–1124CrossRefGoogle Scholar
17.
Chen F, Pielke RA Sr, Mitchell K (2001) Development and application of land-surface models for mesoscale atmospheric models: Problems and promises. In: Land-surface hydrology, meteorology, and climate: observation and modeling water science and application, vol 3. American Geophysical Union, Washington, DC, pp 107–135Google Scholar
18.
Holt T (2007) Urban canopy modeling of the New York City metropolitan area: a comparison and validation of single- and multilayer parameterizations. Mon Weather Rev 135:1906–1930CrossRefGoogle Scholar
19.
Masson V, Grimmond CSB, Oke TR (2002) Evaluation of the Town Energy Balance (TEB) scheme with direct measurements from dry districts in two cities. J Appl Meteorol 41:1011–1026CrossRefGoogle Scholar
20.
Lemonsu A, Grimmond CSB, Masson V (2004) Modelling the surface energy balance of the core of an old Mediterranean city: Marseille. J Appl Meteorol 43:312–27CrossRefGoogle Scholar
21.
Lemonsu A, Belair S, Mailhot J, Leroier S (2010) Evaluation of the Town Energy Balance model in cold and snowy conditions during the Montreal Urban Snow Experiment 2005. J Appl Meteorol Climatol 49:346–362CrossRefGoogle Scholar
22.
Freitas ED, Rozoff CM, Cotton WR, Dias PLS (2007) Interactions of an urban heat island and sea-breeze circulations during winter over the metropolitan area of São Paulo, Brazil. Boundary-Layer Meteorol 122:43–65CrossRefGoogle Scholar
23.
Rozoff CM, Cotton WR, Adegoke JO (2003) Simulation of St. Louis, Missouri, land use impacts on thunderstorms. J Appl Meteorol 42(6):716–738CrossRefGoogle Scholar
24.
Lei M, Niyogi D, Kishtawal C, Pielke RA, Beltrán-Przekurat A, Nobis TE, Vaidya SS (2008) Effect of explicit urban land surface representation on the simulation of the 26 July 2005 heavy rain event over Mumbai, India. Atmos Chem Phys Discuss 8:8773–8816CrossRefGoogle Scholar
25.
Cantelli A, Monti P, Leuzzi G (2011) An investigation of the urban heat island of Rome through a canyon-based subgrid scheme. Int J Environ Pollut 47(Nos 1/2/3/4):239–247Google Scholar
26.
Porson A, Harman IN, Bohnenstengel SI, Belcher SE (2009) How many facets are needed to represent the surface energy balance of an urban area? Boundary-Layer Meteorol 132(1):107–128Google Scholar
27.
Amicarelli A, Leuzzi G, Monti P, Thomson DJ (2011) LAGFLUM, a stationary 3D Lagrangian stochastic numerical micromixing model for concentration fluctuations: validation in canopy turbulence, on the MUST wind tunnel experiment. Int J Environ Pollut 47 (Nos 1/2/3/4):317–325Google Scholar
28.
Leuzzi G, Amicarelli A, Monti P, Thomson DJ (2012) A 3D Lagrangian micromixing dispersion model LAGFLUM and its validation with a wind tunnel experiment. Atmos Environ 54:117–126CrossRefGoogle Scholar
29.
Cantelli A (2012) Analisi dell’impatto della disomogeneità del tessuto urbano, sulla modellazione dell’isola urbana di calore, mediante uno schema parametrico di sottogriglia. PhD Thesis, Biblioteca Nazionale Centrale di Firenze, Archivio Regionale del LazioGoogle Scholar
30.
Roth M (2000) Review of atmospheric turbulence over cities. Q J R Meteorol Soc 126(564):941–990CrossRefGoogle Scholar
31.
Rotach MW (2001) Simulation of urban-scale dispersion using a Lagrangian stochastic dispersion model. Boundary-Layer Meteorol 99(3):379–410CrossRefGoogle Scholar
32.
Kastner-Klein P, Rotach MW (2004) Mean flow and turbulence characteristics in an urban roughness sublayer. Boundary-Layer Meteorol 111:55–84CrossRefGoogle Scholar
33.
Dyer AJ (1974) A review of flux-profile relationships. Boundary-Layer Meteorol 7:363–372CrossRefGoogle Scholar
34.
De Ridder KK (2010) Bulk transfer relations for the roughness sublayer. Boundary-Layer Meteorol 134:257–267CrossRefGoogle Scholar
35.
Garratt JR (1994) The atmospheric boundary layer. Cambridge University Press, CambridgeGoogle Scholar
36.
Mölder M, Grelle A, Lindroth A, Halldin S (1999) Flux-profile relationships over a boreal forest-roughness sublayer corrections. Agric For Meteorol 98:645–658CrossRefGoogle Scholar
37.
Yang K, Tamai N, Koike T (2001) Analytical solution of surface layer similarity equation. J Appl Meteorol 40(9):1647–1653CrossRefGoogle Scholar
38.
Harman IN, Barlow JF, Belcher SE (2004) Scalar fluxes from urban street canyons part II: model. Boundary-Layer Meteorol 113:387–410CrossRefGoogle Scholar
39.
Soulhac L, Perkins RJ, Salizzoni P (2008) Flow in a street canyon for any external wind direction. Boundary-Layer Meteorol 126(3):365–388CrossRefGoogle Scholar
40.
Oke TR (1987) Boundary layer climates. Routledge, LondonGoogle Scholar
41.
Johnson GT, Watson ID (1984) The determination of view-factors in urban canyons. J Appl Meteorol 23:329–335CrossRefGoogle Scholar
42.
Steyn DG, Lyons TJ (1985) Comments on the determination of view factors in urban canyons. J Clim Appl Meteorol 24(4):383–385CrossRefGoogle Scholar
43.
Cotton WR, Pielke RA Sr et al (2003) RAMS 2001: current status and future directions. Meteorol Atmos Phys 82:5–29CrossRefGoogle Scholar
44.
Walko RL, Band LE, Baron J, Kittel TGF, Lammers R, Lee TJ, Ojima D, Pielke RA Sr, Taylor C, Tague C et al (2000) Coupled atmosphere-biophysics-hydrology models for environmental modeling. J Appl Meteorol 39(6):931–944CrossRefGoogle Scholar
45.
Ratti C, Baker N, Steemers K (2005) Energy consumption and urban texture. Energy Build 37(7):762–776CrossRefGoogle Scholar
46.
Bonacquisti V, Casale GR, Palmieri S, Siani AM (2006) A canopy layer model and its application to Rome. Sci Total Environ 364:1–13CrossRefGoogle Scholar
47.
Piringer M, Joffre S, Baklanov A, Christen A, Deserti M, De Ridder K, Emeis S, Mestayer P, Tombrou M, Middleton D et al (2007) The surface energy balance and the mixing height in urban areas—activities and recommendations of cost-action 715. Boundary-Layer Meteorol 124(1):3–24CrossRefGoogle Scholar
48.
Grimmond CSB, Oke TR (1999) Aerodynamic properties of urban areas derived from analysis of surface form. J Appl Meteorol 38:1262–1292CrossRefGoogle Scholar

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Authors and Affiliations

Antonio Cantelli
- 1
Paolo Monti
- 1
Email author
Giovanni Leuzzi
- 1

1.Department of Civil and Environmental Engineering“Sapienza” Università di RomaRomeItaly

Numerical study of the urban geometrical representation impact in a surface energy budget model

Abstract

Keywords

Supplementary material

References

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