- Email: [email protected]
Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment
Accepted Manuscript
Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment M.G. Giometto, A. Christen, P.E. Egli, M.F. Schmid, R.T. Tooke, N.C. Coops, M.B. Parlange PII: DOI: Reference:
S0309-1708(17)30648-6 10.1016/j.advwatres.2017.06.018 ADWR 2878
To appear in:
Advances in Water Resources
Received date: Revised date: Accepted date:
22 June 2016 14 June 2017 22 June 2017
Please cite this article as: M.G. Giometto, A. Christen, P.E. Egli, M.F. Schmid, R.T. Tooke, N.C. Coops, M.B. Parlange, Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment, Advances in Water Resources (2017), doi: 10.1016/j.advwatres.2017.06.018
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Highlights • LES and tower measurements are used to quantify effect of urban trees
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on flow • Roughness length and displacement height increase with increasing foliage density
• The ratio of turbulent to mean kinetic energy increases with increasing foliage
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• Dense trees reduce downward turbulent transport of high-momentum fluid.
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Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment
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M. G. Giomettoa,∗, A. Christenb , P. E. Eglic , M. F. Schmida , R. T. Tooked , N. C. Coopsd , M. B. Parlangea a Department
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of Civil Engineering, Faculty of Applied Science, University of British Columbia, Vancouver, BC, Canada b Geography / Atmospheric Science Program, University of British Columbia, Vancouver, BC, Canada c Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerland d Department of Forestry, University of British Columbia, Vancouver, BC, Canada
Abstract
Large-eddy simulations (LES) are used to gain insight into the effects of trees on turbulence, aerodynamic parameters, and momentum transfer rates
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characterizing the atmosphere within and above a real urban canopy. Several areas are considered that are part of a neighbourhood in the city of Vancouver, BC, Canada where a small fraction of trees are taller than buildings. In this
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area, eight years of continuous wind and turbulence measurements are available from a 30 m meteorological tower. Data from airborne light detection and
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ranging (LiDAR) are used to represent both buildings and vegetation at the LES resolution. In the LES algorithm, buildings are accounted through an immersed boundary method, whereas vegetation is parameterized via a location-
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specific leaf area density. LES are performed including and excluding vegetation from the considered urban areas, varying wind direction and leaf area density. Surface roughness lengths (z0 ) from both LES and tower measurements are
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sensitive to the 0 ≤ LAI/λbf < 3 parameter, where LAI is the leaf area index
and λbf is the frontal area fraction of buildings characterizing a given canopy. For instance, tower measurements predict a 19% seasonal increase in z0 , slightly ∗ Corresponding
author Email address: [email protected] (M. G. Giometto)
Preprint submitted to Advances in Water Resources
June 27, 2017
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lower than the 27% increase featured by LES for the most representative canopy (leaves-off LAI/λbf = 0.74, leaves-on LAI/λbf = 2.24). Removing vegetation from such a canopy would cause a dramatic drop of approximately 50% in z0
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when compared to the reference summer value. The momentum displacement height (d) from LES also consistently increases as LAI/λbf increases, due in
large part to the disproportionate amount of drag that the (few) relatively
taller trees exert on the flow. LES and measurements both predict an increase
in the ratio of turbulent to mean kinetic energy (TKE/MKE) at the tower sampling height going from winter to summer, and LES also show how including
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vegetation results in a more (positive) negatively skewed (horizontal) vertical
velocity distribution – reflecting a more intermittent velocity field which favors sweep motions when compared to ejections. Within the urban canopy, the effects of trees are twofold: on one hand, they act as a direct momentum sink for the mean flow; on the other, they reduce downward turbulent transport of high-momentum fluid, significantly reducing the wind intensity at the heights
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where people live and buildings consume energy.
Keywords: aerodynamic roughness, roughness sublayer, trees, turbulence,
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urban canopy, urban forest, vegetation, wind.
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1. Introduction
The physical structure of cities controls and modifies the exchange of momentum, heat, water, and air pollutants between the surface and the atmo-
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sphere. The three-dimensional form of cities is intrinsically spatially variable,
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and this influences the properties of wind, turbulence and turbulent exchange on
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street, neighbourhood and city scales (Belcher, 2005). Up to a height of several times the size of buildings – in the layer known as roughness sublayer (RSL) – flow statistics are strongly dependent on the actual shape and arrangement of buildings, and Monin-Obukhov similarity (MOS) scaling is generally inaccurate
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(Roth, 2000). Field experiments and numerical studies have shown that in the surface layer above the RSL – the inertial sublayer (ISL) – the air flow over
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cities (and complex surfaces in general) becomes statistically homogeneous, and the neutral flow is completely determined by the friction velocity u∗ , aerodynamic roughness length z0 and zero-plane displacement d, and is obeying MOS scaling for diabatic situations (Parlange and Brutsaert, 1989; Brutsaert et al.,
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1989; Parlange and Brutsaert, 1990; Brutsaert and Parlange., 1992; Katul and Parlange, 1992; Parlange et al., 1995; Feigenwinter et al., 1999; Bou-Zeid et al., 2004; Yang, 2016). Aerodynamic properties of cities control exchange rates of
momentum and scalars such as heat and humidity and therefore have impor20
tant implications for weather and hydrological modelling at urban and regional
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scales (Brutsaert, 1982).
The term “urban canopy” refers to the assemblage of buildings, built objects and vegetation that make up the three dimensional interface between the land surface and the atmosphere in cities. In many low- to medium-density urban 25
areas, vegetation, including tall trees, forms an important component of the urban canopy (Oke et al., 2017). Trees can significantly modify meteorological and
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hydrological processes in the RSL and also affect the flow in the ISL above (Oke, 1989). Furthermore, trees are an important design tool to manage building and
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street climates (e.g. Oke, 1988; Shashua-Bar and Hoffman, 2000; Johansson and Emmanuel, 2006; Bowler et al., 2010). At the coarser scales, urban vegetation is relevant for managing heat stress and air quality at neighborhood to city
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scales. For example, model simulations by Li and Bou-Zeid (2013) suggest that urban forestry is a critical tool to prevent exacerbated urban-rural temperature
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differences during heat waves. To ensure safety and health of urban dwellers, and to efficiently manage
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energy and water in urban systems, we need numerical models that represent
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weather, climate and hydrology under current conditions and future climate and planning scenarios (Chen et al., 2012). The presence of urban canopies on the atmosphere is generally represented in hydrology and mesoscale weather models
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using “urban land surface models” (ULSMs). ULSMs describe the energetics, hydrology and dynamics of the urban surface, by either implying certain bulk values or simulating the behaviour of different tiles such as roofs, walls, roads 4
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and urban vegetation. More complex ULSMs targeted to resolve the climate of the RSL and inside 45
the urban canopy are called urban canopy parameterizations (UCPs). UCPs
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represent the three-dimensional geometry of an urban surface, and account for interactions between tiles, the atmosphere, the building interior and subsurface, often applying a multi-layer approach (Masson, 2005).
Recent assessments of our capabilities to accurately reproduce land-atmosphere 50
exchange in urban environments using ULSMs have shown that the lack of, or a
crude and improper representation of urban vegetation, in particular the direct
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interaction of trees with buildings and vice versa, is a major weakness. The
international urban energy balance model comparison concluded that “taking vegetation cover into account (or not) significantly impacts model performance” 55
in particular related to energy partitioning and evapotranspiration (Grimmond et al., 2010).
Trees interact in a three-dimensional way with buildings radiatively (e.g. shading
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and radiation trapping), energetically (e.g. transpiration), and dynamically (e.g. wind sheltering). However, most of UCPs to date do not include trees as three dimensional objects. Recently, there have been efforts to represent the three-
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dimensional radiative and energetic effects in urban modelling systems (Lee and Park, 2008; Krayenhoff et al., 2014; Ryu et al., 2015; Lee et al., 2016).
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The dynamical impact of urban trees, however, is not included in operational ULSMs and UCPs.
The dynamical effect is not only referring to the sheltering effect and change
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of scaling parameters z0 and d, but also the fact that trees modify turbulence
and consequently turbulent length scales that affect transfer of scalars and dis-
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sipation rates in the RSL. Krayenhoff et al. (2015) use CFD simulations over generic urban geometries to inform parameterizations of the dynamical effect of
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urban trees for given densities and clumping. The influence of trees is also timedependent. Deciduous trees in mid- and high-latitude cities change their leaf area density (a in the following) with season. Although some ULSMs for hydrology applications prescribe changing leaf area densities over the year (e.g. J¨ arvi 5
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et al., 2011), no operational USLM considers the effect of seasonally changing a 75
on mean wind and turbulent exchange. The overall goal of this study is to assess the role of urban trees and changing
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leaf densities on the flow dynamics within and above a realistic urban canopy. This helps to inform the next-generation ULSMs when, where and how incorporating or not the effects of urban vegetation at the scale of neighbourhoods 80
or cities is appropriate and possible. The specific research questions are:
• To determine the effect of trees and changing leaf density on the aerody-
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namic roughness length and zero-plane displacement in the urban environment.
• To test the sensitivity of integral turbulence statistics in the ISL above the urban canopy to the characteristics of the urban vegetation.
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• To characterize the effect of trees and changing a on vertical transfer of
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momentum and mean kinetic energy in the urban RSL.
A combination of detailed large-eddy simulations (LES) and long-term mea-
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surements from a tower over an urban canopy in Vancouver, Canada, is used to answer these questions. A Digital Surface Model (DSM) derived from airborne Light Detection and Ranging (LiDAR) data is used to characterize the
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surface and represent both buildings and vegetation at high spatial resolution in the LES. The LES is run under the same forcing with the DSM including
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vegetation at various densities and once without vegetation (reference case). 95
The latter condition is of course not possible to reproduce on the tower measurements. Measurements from the tower are instead conditionally sampled
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discerning between leaves-on (Summer) and leaves-off (Winter) seasons to investigate the effect of varying leaf area density in the real atmosphere.
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To date, numerical simulations of the flow and turbulence over cities with
buildings resolved (as opposed to modelled) have primarily represented cities as idealized rectangular patches of different surface roughness and arrays of cubes or cuboids with varying spatial organization (Kanda et al., 2004; Kanda, 6
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2006; Xie and Castro, 2006; Coceal et al., 2007b; Xie et al., 2008; Inagaki et al., 2012; Anderson et al., 2015; Li et al., 2016b; Yang et al., 2016; Yang, 2016; 105
Sadique et al., 2016; Anderson, 2016; Zhu et al., 2016). In addition, several
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studies modelled the aerodynamic effect of urban trees using simple, generic street geometries to investigate the effect of trees on pollutant dispersion (Balcz´ o et al., 2009; Salim et al., 2011; Moonen et al., 2013; Gromke and Blocken, 2015;
Vranckx et al., 2015). Such idealized studies show consistently that trees reduce 110
the vertical exchange of scalars and deteriorate air quality when sources are below the canopy, a conclusion also supported by wind tunnel simulations (e.g.
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Gromke and Ruck, 2008).
With increasing parallel computing power and the availability of Digital Surface Models (DSMs) it is now feasible to simulate subsets of a real cities (e.g. 115
Xie and Castro, 2009; Kanda et al., 2013; Giometto et al., 2016; Hertwig et al., 2016a,b). However, to the best of our knowledge, no LES study in the literature has simulated a real urban neighborhood including the effect of individually
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resolved, clumped trees. In the absence of buildings, the effect of a plant canopy on airflow and turbulence and, inversely, the effect of flow on trees, has been studied using LES assuming uniform a distributions (e.g. Shaw and Schumann,
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1992a; Kanda and Hino, 1994; Dwyer et al., 1997; Finnigan et al., 2009a) and more recently with explicitly resolved plants and realistically clumped a (Yue
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et al., 2007; Huang et al., 2009; Bailey and Stoll, 2013; Patton et al., 2016). Likewise, observational studies in cities have provided limited insight on the role of urban trees. Most studies quantified turbulence generated within and
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above urban canopies using multiple measurements located at different heights on towers in the RSL and/or ISL (e.g. Rotach, 1993; Feigenwinter et al., 1999;
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Christen et al., 2007; Nelson et al., 2007; Christen et al., 2009; Ramamurthy and Pardyjak, 2011, 2015). However, observational studies with simultaneous
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measurements within and above urban canopies have targeted urban canopies without or with very limited trees, and no observational study has been able to isolate the effect of trees on mean wind and turbulence from the effect of buildings. 7
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Figure 1: Filled color contour of buildings and vegetation height (hb and hv respectively) in a 974 × 620 m2 area surrounding the 28.8 m “Vancouver-Sunset” meteorological tower in
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Vancouver, BC, Canada. Surface data are based on LiDAR measurements. Selected subsets for use in large-eddy simulation (LES) are highlighted (S1, S2, S3, and S4).
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2. Methods 135
2.1. Study area
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Figure 1 depicts a 974×620 m2 area in south central Vancouver, BC, Canada, centered on the micrometeorological research tower “Vancouver-Sunset” (Fluxnet ID “Ca-VSu”, 123.0784◦ W, 49.2261◦ N, 78 m a.s.l.). The area is characterized by a relatively homogeneous mix of streets and detached one to two storey 140
houses (12.8 Bldg. ha−1 ), and is representative of the majority of Vancouver’s neighbourhoods and North American cities (Local Climate Zone 6, according to
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Stewart and Oke (2012)). The area has been the focus of a number of observa-
tional campaigns related to flow and turbulence characteristics over suburban surfaces (Schmid et al., 1991; Roth and Oke, 1993; Roth, 1993; Roth and Oke, 145
1995; Grimmond et al., 1998; Grimmond and Oke, 2002)
Vegetation in the area (circle of 400 m radius around tower) has a density of 19.2 Stems ha−1 and comprises of about 23% evergreen trees and 77% deciduous
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trees (Liss et al., 2013). The large fraction of deciduous trees is resulting in a strong seasonal variation of the Leaf Area Index (LAI). Liss et al. (2013) estimates that the LAI of trees is 0.39 m2 m−2 in summer. The average tree
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height is estimated 8.4 m for broadleaf trees (n = 742) and 11.1 m (n = 223) for coniferous trees.
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The entire surface (S4) displayed in Fig. 1 and three smaller surfaces (S1, S2 and S3) comprised within S4 are selected for use in LES. The reason to 155
separately consider a number of sub-surfaces is to provide a broader range of
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realistic canopies, each characterized by its peculiar distribution of buildings and trees, to further support conclusions and to study the dependence of flow
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statistics on relevant surface parameters (such as LAI and the frontal-area index of buildings). For the considered wind approaching direction (see Sect. 2.4.2), all
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surfaces (S1, S2, S3 and S4) are mostly within the 70%, and entirely within the 80% long-term cumulative footprint of the tower. The 80% long-term cumulative footprint climatology covers an area of 1.04 km2 and is shown in Fig. 1 of
Crawford and Christen (2015a).
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2.2. Light detection and ranging data The detailed building heights and vegetation information used in the LES
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are derived from a LiDAR point cloud dataset, mapped to a two-dimensional
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horizontal Cartesian grid with stencil of 0.5 m in both directions. The LiDAR dataset was acquired in February 2014, during leaves-off conditions, which al-
lowed for good penetration of the laser through the vegetation canopies. Ex170
tracted buildings information comprise the building heights (hb ), function of the horizontal coordinates x and y, whereas vegetation elements are represented as a spatially distributed leaf area density (a) coefficient. The a coefficient has been
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computed as a function of the foliage probability distribution (Pf ) following Tooke et al. (2011):
a(x, λ, k) = − ln [1 − Pf (x, λ, k)] , 175
(1)
where the functions λ, k : (x, y) → R+ and where Pf is itself approximated as a two parameters Weibull distribution
k z (k−1) exp [−(z/λ)k ] . λ λ
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Pf =
(2)
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The λ(x, y) > 0 and k(x, y) > 0 are the scale and shape parameters, and are evaluated based on a non-linear fit to the LiDAR beam interception probability, representing probability of branches and evergreen foliage at a given height. A random spatial orientation of leaves was assumed. To calculate summer a, the
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overall LAI resulting from the LiDAR dataset has been rescaled to match the
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LAI = 0.39 value of Liss et al. (2013), representative of the area in the summer season.
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2.3. Tower-based turbulence measurements
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The 30 m triangular lattice tower that hosted turbulence instrumentation
is situated 5 m from the south-eastern corner of a power substation (Fig. 1). Continuous long-term measurements were made from 1 May, 2008 to 30 April, 2016 at a single height, using a CSAT-3 three-axis ultrasonic anemometerthermometer (Campbell Scientific, Logan, UT, USA) operated at 28.4 m above 10
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local ground facing an azimuth of 180◦ . Because the base of the tower is recessed by 4 m from the surrounding terrain, an effective measurement height of z=24.4 m is used for the measurements in further calculations (Crawford and Christen,
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2015b). Measured quantities include the instantaneous three components of the wind vector (u,v,w, all rotated into the mean wind using a double-rotation) sam195
pled at 60 Hz and stored at 20 Hz. Block averages over 30 min were calculated and filtered following the procedures outlined in Crawford et al. (2012).
Conditional sampling of the tower data has been performed, isolating 30 minute blocks with a neutral dynamic stability following the criteria of −0.075 < 200
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(z − d)/L < 0.075, where d is the zero-plane displacement (set to d = 5.46 m, see Sect. 4.2), and L is the Obukhov-Length measured on the tower as: L=
T u∗ κ g θ∗
(3)
where κ is the von K´ arm´ an constant (we assumed κ = 0.4), T the absolute 2
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temperature, u∗ the friction velocity calculated as u∗ = (u0 w0 + v 0 w0 )0.25 and
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θ∗ the temperature scale calculated as θ∗ = −w0 T 0 /u∗ . To ensure consistent wind direction over the 30 minute block, the RMSE of the cyclic wind direction (α) calculated for 6 subintervals of 5 minutes each, was set to not exceed 15◦ in
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each block. Only data with a wind speed of > 2 m s−1 and wind direction 150◦ ≤
α ≤ 300◦ was considered, hence approaching between SSE and WNW (excluding
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sectors where potential flow distortion is found by the instrumentation and the wake of a nearby school building). This resulted in 4700 datasets further considered (3.4% of the period of 8 years, or 3.2 months of data). To avoid effects
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of seasonally changing wind direction to affect results, conditional averages were formed as follows: Averages and statistics were calculated separately for 30◦
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wind direction sectors and each month of the year. To calculate summer values, conditional averages from all 30◦ sectors between 150◦ and 300◦ and all months
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between May and September were selected and equally weighted.
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2.4. Numerical algorithm The LES algorithm adopted in this study was originally developed in Albertson and Parlange (1999a,b) and updated to develop linear and non-linear
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LES closure models (Meneveau et al., 1996; Port´e-Agel et al., 2000; Bou-Zeid
et al., 2005; Lu and Port´e-Agel, 2010), wall models (Anderson and Meneveau,
2010, 2011; Anderson et al., 2012; Hultmark et al., 2013), and has been extensively used in wind energy applications (Calaf et al., 2010, 2011; Sharma et al., 2016), urban applications (Tseng et al., 2006; Bou-Zeid et al., 2009; Cheng and
Port´e-Agel, 2013, 2015; Anderson et al., 2015; Giometto et al., 2016) and in studies of flow over vegetation canopies (Chester and Meneveau, 2007; Chester
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et al., 2007; Yue et al., 2007, 2008; Bailey and Stoll, 2013).
It integrates the spatially filtered Navier-Stokes equations in their rotation form
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∂u ˜i ∂u ˜i ∂u ˜j ∂π ˜ ∂τij +u ˜j ( − )=− − + Fi + f˜ib + f˜iv ∂t ∂xj ∂xi ∂xi ∂xj ∂u ˜i = 0, ∂xi
(5)
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Ω × [0, T ] where Ω denotes a regular domain, T is the total integration
in 230
(4)
time, u ˜i are the space filtered velocity components in the x, y and z Cartesian coordinate directions, π ˜ is a modified filtered kinematic pressure (˜ π = +
1 ˜i u ˜i ), 2u
+
ρ is a reference constant density, τij denotes the subgrid-scale
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1 3 τii
1 ˜ ρp
(SGS) kinematic stress tensor, and Fi ≡ (u2∗ /Lz , 0, 0) is a constant kinematic pressure gradient forcing that is introduced to drive the flow in the x coordinate direction. In addition, f˜ib is an immersed-boundary method (IBM) forcing term
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that is used to impose the desired boundary condition at the building interface
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and in the below-interface locations (it has a finite value at and inside the buildings interface and is zero elsewhere), and f˜iv is a volumetric force that is introduced to account for drag from vegetation elements (see Sect. 2.4.1).
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The equations are solved on a regular domain Ω using a mixed pseudospec-
tral - finite differences algorithm (Orszag, 1969, 1970), time advancement is performed using an explicit second-order accurate Adam Bashforth scheme, and 12
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the pressure field is evaluated through a fractional step method (Chorin, 1968). A free-lid boundary condition is imposed at the top of the domain (H), periodic 245
boundary conditions apply in the horizontal directions, due to the pseudospec-
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tral approach, and zero velocity is enforced at Γb and below via the f˜ib forcing term (this approach is known in literature as the discrete forcing approach IBM
method (Mittal and Iaccarino, 2005)). In addition, tangential stresses are applied in a band centered around the buildings interface Γb via a logarithmic equi250
librium wall-law. Specifically, the band is defined as −1.1∆ ≤ Φ(x, y, z) ≤ 1.1∆, where Φ denotes the distance from Γb and ∆ = (∆x×∆y×∆z)1/3 , where ∆x, ∆y
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and ∆z are the grid stencils in the three coordinate directions. The wall-law reads τw = −
κ(k˜ ut k2 ) ln (1 + ∆/z0 )
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in
Γb × [0, T ] ,
(6)
where u ˜t = u ˜ − (˜ u · n)n is the tangential-to-surface velocity vector, n is the 255
surface normal vector, and z0 is the aerodynamic roughness length parameter.
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τw is the kinematic surface stress defined in the previously introduced band and 0 0 it corresponds to τ13 = τ31 in a local Cartesian coordinate system centered at
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the given collocation node and defined by e01 = u ˜ t /k˜ uk, e02 = (˜ ut × n)/k˜ uk,
e03 = n. After evaluation τw is rotated back in the {e1 , e2 , e3 } canonical co-
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ordinate system to provide τij at Γb . Gibbs oscillations that arise when IBM
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methods are implemented within spectral-like discretizations are here reduced via a Laplacian smoothing approach, as described in Chester et al. (2007). Al-
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ternative approaches to perform such a task have also been proposed recently (Fang et al., 2011; Li et al., 2016a) A dynamic Smagorinsky LES model with planar (x, y) averaged coefficient
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is adopted to evaluate τij from spatially-resolved quantities, thus closing the system of equations 4 and 5 in the bulk of the flow (Germano et al., 1991; Lilly, 1992). The dynamic model is based on the mixing length concept, and evaluates the SGS kinematic stresses as a function of the local resolved strain rate tensor: ˜ 2 S˜ij , τij = −2νt S˜ij = −2(cs,∆ ∆)2 kSk 13
(7)
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where cs,∆ is the Smagorinsky coefficient at grid scale ∆ (Scotti et al., 1993). Unlike the original Smagorinsky model (Smagorinsky, 1963), which requires an ad-hoc specification of cs,∆ , the dynamic model computes cs,∆ dynamically
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by taking advantage of information contained in the smallest resolved scales (the scales between ∆ and a test-filter scale e.g. 2∆). More sophisticated 275
Smagorinsky-type SGS models have been proposed during the past two decades,
see for instance the works of Meneveau et al. (1996); Port´e-Agel (2004); Bou-Zeid et al. (2005), and a plethora of other approaches exist to close the space-filtered
Navier-Stokes equations (Meneveau and Katz, 2000). However, when it comes
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to LES of flow over bluff elements such as urban canopies, pressure (or form)
drag is the main sink of momentum and SGS contributions are – on average – only a minor percentage of the overall momentum flux (see e.g., Giometto et al., 2016). Because of this, the velocity field is known to be poorly dependent on the specific SGS approach when compared to flow over streamlined elements, and simple and efficient closure models yield accurate results. Note that these conclusions do not apply to convective scalar transfer within these same envi-
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ronments, as scalar transfer occurs via molecular diffusion independently of the
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shape of the obstacles (see e.g., Li et al., 2016b). Note also that using Eq. 6 for the specification of surface stresses, in conjunction with Eq. 7, results in a system of equations that does not depend on the molecular viscosity parameter, hence guaranteeing scaling similarity of solutions (i.e., normalized solutions are
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independent of the imposed friction velocity or outer velocity U∞ ). A more de-
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tailed description of the LES algorithm and specifics on the IBM implementation can be found in Chester et al. (2007).
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2.4.1. Representation of vegetation in the LES
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The term f˜iv is included in the momentum conservation equation (Eq. 4) to
account for the kinematic drag from vegetation elements, and is defined as f˜iv (x, t) = −CV a ˜(x, λ, k)˜ ui k˜ uk2 ,
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(8)
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where CV is a constant sectional drag coefficient and a ˜ is the spatially-filtered (filter width = ∆) leaf area density, derived from high-resolution LiDAR measurements. CV = 0.2 is assumed, which is the optimized value determined by Katul and Albertson (1998) and used in Krayenhoff et al. (2015).
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Vegetation drag is set proportional to a velocity squared, in line with previous studies of flow over vegetation canopies (Shaw and Schumann, 1992b; Finni-
gan et al., 2009b). This implies that leaves elements are assumed to be in fully rough regime (i.e., the total drag from vegetation elements is form drag), which 305
is an acceptable approximation within the goal of the current study (Thom,
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1968; Brunet et al., 1994).
In addition, it is known that the turbulent wakes behind vegetation elements, resulting from the action of pressure and viscous drag on branches and leaves, yield a transfer of energy from the mean flow and from larger-scale turbulence 310
to smaller-scale turbulence, thus short circuiting the inertial energy cascade (e.g., Wilson, 1988; Poggi et al., 2004; Cava and Katul, 2008). Wake turbulence
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dissipates quickly, but it is a non-negligible contribution to the SGS kinetic energy budget (Shaw and Patton, 2003), and should therefore be accounted for
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in 1.5-order closure schemes, in which SGS TKE is predicted with a prognostic energy equation.
First-order algebraic LES closures – such as the dynamic Smagorinsky model
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used herein – are relatively simple and do not carry information on SGS energetics. As such, they are not amenable to modifications to account for the
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aforementioned effects induced by wake motions on SGS dynamics. This might 320
limit their applicability in flows over vegetation when the canopy occupies a significant fraction of the airspace, thus constantly sustaining small-scale wake
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turbulence and affecting SGS dissipation rates. However, the behavior of Smagorinsky models is expected to improve when
used in flows within explicitly resolved sparse canopies with sub-tree grid reso-
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lution as in the current settings. Under such conditions the energetic range of wake motions, which are about the size of full vegetation elements (Cava and Katul, 2008), is explicitly resolved by LES, whereas SGS wake turbulence is 15
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expected to survive over a limited portion of the overall airspace. This is due to the sparsity of trees and to the rapid dissipation rates of SGS wake energy, 330
which support the working conjecture that SGS wake energy can be neglected
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with little loss in accuracy in the predicted velocity field.
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2.4.2. Setup of LES simulations
Figure 2: Pseudocolor plot of the instantaneous streamwise velocity field corresponding to
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simulation S4SV W (see Table 1).
To quantify the effect of vegetation on mean flow and turbulence over and
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within the selected urban canopies (S1, S2, S3 and S4 in Fig. 1), three vegetative configurations are considered for each surface, namely
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335
• Urban surfaces with no vegetation (NV); • Urban surfaces with wintertime vegetation (WV); • Urban surfaces with summertime vegetation (SV).
Table 2 displays the overall LAI for the S1, S2, S3 and S4 canopies in the sum340
mertime, which are based on LiDAR data. The LiDAR-derived a ˜(x) has been 16
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rescaled so that for a 1 × 1 km2 surface centered around the measurement tower the LAI matches the one reported in Liss et al. (2013) for the same area. To simulate wintertime vegetative conditions the LAI value of each surface is reduced
345
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by an estimated factor of 3, based on separate LAI determined for broadleaf and coniferous trees in the study area by Liss et al. (2013), assuming broadleaf trees are all deciduous and considering the effect of trunks and branches to the total projected area in winter. Table 1 summarizes the setup of all simulations.
Table 1: Summary of simulation parameters. Surfaces correspond to those displayed in Fig. 1.
Lx , Ly , Lz and Nx , Ny , Nz denote the domain size and number of collocation nodes in the
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x, y, z coordinate directions, and α denotes the approaching wind direction (α = 180◦ → wind approaching from south, and α = 270◦ → wind approaching from west). Notation: S1α β, α = NV (no vegetation) or α = WV (winter vegetation) or α = SV (summer vegetation); β = W (wind from west) or β = S (wind from south).
Label
surface
Lx × Ly × Lz (m)
Nx × Ny × Nz
α (deg)
LAI
NV S1NV W , S1S
410 × 210 × 96
320 × 160 × 192
180, 270
0
S1WV S
S1
320 × 160 × 192
0.094
S1SV S
410 × 210 × 96
180, 270
S1SV W ,
S1
320 × 160 × 192
180, 270
0.282
NV S2NV W , S2S
410 × 210 × 96
S2
410 × 210 × 96
320 × 160 × 192
180, 270
0
S2
410 × 210 × 96
320 × 160 × 192
180, 270
0.082
S2
410 × 210 × 96
320 × 160 × 192
180, 270
0.246
S3
380 × 410 × 96
320 × 320 × 192
180, 270
0
S3
320 × 320 × 192
180, 270
0.152
SV S3SV W , S3S
380 × 410 × 96
S3
320 × 320 × 192
180, 270
0.458
NV S4NV W , S4S
380 × 410 × 96
S4
974 × 620 × 192
512 × 320 × 384
180, 270
0
S4
974 × 620 × 192
512 × 320 × 384
180, 270
0.117
S4
974 × 620 × 192
512 × 320 × 384
180, 270
0.351
S2WV S
S2SV W ,
S2SV S
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NV S3NV W , S3S
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S2WV W ,
S3WV S
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S3WV W ,
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S4WV W ,
S4WV S
SV S4SV W , S4S
M
S1
S1WV W ,
Two approaching wind directions are considered for each surface, namely
west and south, corresponding to situations excluding the sectors influenced by
350
sensor mounting and the unusually tall school-building to the East (see Fig. 1). The Cartesian reference system in each case is chosen so that the x axis points 17
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in the streamwise direction, and the y axis points in the spanwise direction (the reference system displayed in Fig. 1 corresponds to that used in simulations with west approaching wind angle). To evaluate z0 in equation 6 the approach of Giometto et al. (2016) is adopted, which results in z0 = ∆/15 for the considered
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355
runs. Simulations are initialized imposing a velocity field obtained from LES at
twice as coarse resolution for each case, corresponding to a condition of dynamic equilibrium of the system (Monin, 1977). LES are then run for an additional
T ≡ h/u∗ = 400 and temporal averaging is carried out over the last T = 150. This yields well converged statistics throughout the boundary layer.
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360
3. Averaging
The intrinsic double averaging (DA) approach is used herein (Nikora et al., 2007). Within the DA framework, a generic variable θ(x, y, z, t) can be decom-
(9)
and a fluctuation component (θ0 ≡ θ − hθi). Specifically, the intrinsic spatial
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365
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posed into a space and time average component Z Z Z Z 1 1 hθi(z) ≡ θ(r, τ )dV dτ , T T VF (z) VF (z)
averaging is here performed first, over horizontal slabs of total volume VF (z) = Lx × Ly × ∆z in the fluid domain only, and the time averaging is performed
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afterwards.
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4. Results and discussion Using data from the airborne LiDAR, from LES runs and from turbulence
370
instruments on the tower, we identify, isolate and discuss the importance of the
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urban tree canopy on flow and turbulence above and within the urban canopy. Section 4.1 summarizes the characteristics of the urban building and vege-
tation layers extracted from LiDAR. In section 4.2 we then present the effect
375
of trees on integral scaling parameters z0 and d. Next, we quantify turbulence characteristics and turbulent exchange in the ISL (Section 4.3) and provide a
18
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detailed analysis of the vertical exchange of momentum and energy in the RSL (Section 4.4).
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4.1. LiDAR derived characteristics of buildings and vegetation Relevant geometric statistics for the subsets S1, S2, S3 and S4 extracted from
380
the LiDAR point cloud are reported in Tab. 2. The range of plan area fractions of buildings (λbp ≡ Abp /A0 ) and frontal area fractions of buildings (λbf ≡ Abf /A0 )
in absence of vegetation, classify the selected surfaces as moderately dense with a wake-interference type flow regime (Oke, 1988; Britter and Hanna, 2003; Barlow,
2014). Here, Abp (m2 ) is the total plan area of buildings, Abf (m2 ) is the total
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385
frontal (silhouette) area of buildings, and A0 ≡ Lx × Ly (m2 ) is the total planar area of the considered subset. The tree canopy cover (plan area fraction of trees, λvp ≡ Avp /A0 ranges between 9 and 13%, and matches well the reported 11% for a
1.9 × 1.9 km box surrounding the tower (Kellett et al., 2013). λvp is substantially 390
lower that the average tree canopy cover for the City of Vancouver with 18%
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(City of Vancouver) and lower than the tree canopy coverage reported for US North-Western urban forests of 33% in (Nowak and Crane, 2002). The four
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considered surfaces S1, S2, S3 and S4 are relatively similar in terms of geometry of building and vegetation characteristics, S3 has a slightly higher amount of 395
taller trees and a higher LAI, whereas S2 is the most sparsely vegetated subset.
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As is typical of realistic urban canopies, and in contrast to uniform-height, synthetically-generated cube-array surfaces, the building plan and frontal area fractions are a function of z throughout the RSL. The vertical structure of
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the buildings plan and frontal area fractions, as well as the vegetation plan
400
area fraction and vertical profiles of the horizontally-averaged (fluid only) leaf
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area density (h˜ ai), important parameters from a aerodynamic perspective (Di
Sabatino et al., 2008), are shown in Fig. 3. Figure 4 depicts the probability density function (pdf ) of building and veg-
etation height for the S4 surface (qualitatively similar to those of the other
405
canopies, which are not shown). The building height distribution is characterized by three principal modes at z ≈ 1 m, z ≈ 3 m and z ≈ 6 m, corresponding 19
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Table 2: Relevant statistics of buildings and vegetation of the modeled urban canopy subsets in simulations S1, S2 and S3 and S4. S4 corresponds to the full surface displayed in Fig. 1. hb
and hv denote the height of an individual building or vegetation element (tree, bushes, etc.),
respectively. h ≡ mean (hb ) + σhb , where σhb is the standard deviation of buildings height. v b b λb p and λp are the plan area fraction of buildings and vegetation, respectively. λf,west , λf,south
denote the frontal area fraction of buildings with respect to west and south approaching wind
Unit
S1
S2
S3
S4
4.5
4.6
4.4
4.5
8.3
8.9
9.0
9.0∗
6.6
6.7
6.3
6.7
0.340
0.337
0.309
0.282
–
0.199
0.201
0.158
0.161
–
0.182
0.186
0.155
0.152
Buildings m
max (hb )
m
h
m
λbp
–
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λbf,south
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mean (hb )
λbf,west
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directions. LAI denotes the summer leaf area index of the canopy.
Vegetation
m
3.5
3.0
4.6
3.84
max (hv )
m
25.2
20.7
26.2
26.2
λvp
–
0.108
0.088
0.128
0.109
LAI
–
0.282
0.278
0.430
0.35
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mean (hv )
* the unusually tall school building has been artificially reduced to 9 m height,
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to homogenize the surface and reduce undesired propagation of wake motions from such a structure in the inlet boundary (due to the prescribed periodic boundary conditions).
20
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Figure 3: Top left: vertical structure of the building plan area fraction Ab p /AT . Top right: frontal area fraction dAf /dV as seen by west (black lines) and south (red lines) approaching wind. Bottom left: vertical structure of the vegetation plan area fraction Avp /AT . Bottom right: vertical structure of the horizontally averaged leaf area density h˜ ai(z) in the summer
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season. Different line-styles correspond to different subsets (see legend).
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to short surface elements (e.g., fences, landscaping), to one and to two storey houses, respectively. Conversely, the vegetation height distribution decreases rapidly from its surface value, indicative of a large number of small plants and shrubs.
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4.2. Vegetation effects on integral scaling parameters z0 and d in the ISL The aerodynamic roughness length (z0 ) and the zero-plane displacement (d)
are key parameters to properly simulate flow and turbulence over urban areas at city to regional scale in weather prediction, air quality dispersion, hydrology 21
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Figure 4: Binned p.d.f. of the roofs height (left) and of the vegetation height (right) for the
415
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S4 canopy (see Fig. 1).
and climate models (Stensrud, 2007). Current morphometric methods employed to estimate z0 and d from urban form do not consider urban vegetation at all (Grimmond et al., 1998), despite its ubiquity. To address this issue, the dependence of z0 and d on urban vegetation is explored in this section.
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Table 3 compares the LES modeled and corresponding tower measured d and z0 parameters. In both cases, values for each surface in different vegetation
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conditions are proposed (no vegetation, leaves-off and leaves-on). z0 is evaluated from the LES runs via logarithmic fit of the LES h˜ ui i(z) velocity in the range p −1 3 < z/h < 5, with fixed u∗ ≈ Lz kFi k = 1 (m s ), assuming κ = 0.4, and
425
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relating the displacement height d to the center of action of the drag force from buildings and vegetation (Jackson, 1981). The fitting interval was chosen based
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on the observed velocity profiles, which display a logarithmic behavior down to z − d ≈ h in most cases (see e.g. mean velocity profiles for cases over the S4 subset displayed in Fig. 5). Logarithmic velocity profiles well within the UCL
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(z ≤ max (hb , hv )) were previously reported in the wind tunnel measurements
430
of Cheng and Castro (2002) for flow over urban-like surfaces, in LES of flow over surface mounted cubes of variable height in Yang et al. (2016), and in LES over surface mounted rectangular prisms with high aspect ratio in Sadique et al. (2016). Unlike LES, direct tower measurements cannot be used to determine the
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Figure 5: Left: DA (intrinsic) streamwise LES velocity over the S4 canopy for west (black lines) and south (gray lines) wind approaching directions. Symbols: solid lines, no vegetation cases; dashed lines: winter vegetation cases; dot-dashed lines: summer vegetation cases. A reference logarithmic profile is shown in red. Center: % increase in z0 as a function of LAI/λb f. Right: % increase in d as a function of LAI/λb f.
435
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flow characteristics in complete absence of trees. However, tower measurements allow one to study the effect of varying LAI on mean wind and momentum
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transfer by conditionally sampling and comparing leaves-off (between November to February), and leaves-on season (between May to September). Using a SV WV SV fixed d/h = 0.81 (average over the S4WV W , S4W , S4S , S4S LES runs), z0 is
440
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calculated based on tower measurements for each block satisfying the (neutral) stability and wind-direction requirements, inverting the logarithmic wind profile
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equation, following Grimmond et al. (1998): ku z0 ≡ (z − d) exp , u∗
(10)
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with mean horizontal wind u and friction velocity u∗ directly measured by the eddy-covariance system (see Sect. 2). Note that since ln (zt ) ≈ ln (zt − d)
variations in d results in minor changes in the resulting z0 , hence the choice
445
of using a fixed d. This choice also ensures that the two approaches (LES and tower measurements) remain independent. Computing d as center of action of the surface drag forces predicts a signif23
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Table 3: Aerodynamic roughness lengths and displacement heights for the considered cases. For the LES runs the displacement height d is computed as center of action of the sum of drag forces from the building and vegetation canopies (hf˜ib i(z) and hf˜iv i(z) respectively), whereas z0 is obtain by linear fit of the LES h˜ ui i(z) velocity in the range 3 < z/h < 5. The
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displacement height for tower measurements is computed as average from the LES runs S4WV W , WV , S4SV and roughness lengths are evaluated as z ≡ (z − d) exp (−uκ/u ), where S4SV t ∗ 0 W , S4S S
zt denotes the measurements height and u and u∗ are the time-averaged velocity and frictionvelocity at the tower sampling location. Tower data from all wind sectors SE to NW have
been equally weighted into 15◦ bins to remove directional effects. Near-Neutral conditions (−0.075 < (z − d)/L < 0.075) and wind > 2 ms−1 , RMSE(α) < 15◦ , and 150◦ < α < 300◦ . Summer is day of year (DOY) 121 to 274. Winter is DOY 305 to 59.
Wind
No veg. d/h
West
0.54
S1
South
0.61
S2
West
0.54
S2
South
0.62
S3
West
S3
South
S4
d/h
z0 /h
d/h
z0 /h
0.056
0.77
0.078
0.89
0.094
0.041
0.84
0.069
0.89
0.087
0.055
0.66
0.069
0.69
0.075
0.044
0.73
0.056
0.77
0.068
0.049
0.97
0.096
1.06
0.130
0.53
0.083
1.01
0.088
1.11
0.124
West
0.48
0.056
0.75
0.086
0.84
0.106
South
0.52
0.048
0.79
0.077
0.88
0.102
150 < α < 300
—
—
0.81
0.119
0.81
0.142
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0.50
S4 Tower
Summer veg.
z0 /h
M
S1
Winter veg.
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Surface
icant increase in both d and z0 as a function of LAI/λbf , as displayed in Fig. 5
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and tabulated in Tab. 3, highlighting the important role of vegetation elements
450
in affecting the aerodynamics of the flow over the considered realistic urban
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settings.
LES runs predict variations of d from the leaves-off and leaves-on cases be-
tween +5% and +15%, due to significant contributions to the overall drag force that taller trees are exerting on the flow, despite their modest plan area fraction
455
Avp /AT (see Fig. 3). Corresponding variations in z0 are between +10% and +40%. It is also apparent that in complete absence of trees z0 would dramat-
24
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0.30
2.0
95% 75% Mean
1.5
0.20 0.15 0.10 615
660
1035
967
504
537
226
318
452
514 844
549
0.05 0.00
J
F
M
A
M
J
J
A
S
O
N
Month of the year
D
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1.0
50% 25% 5%
z0 (m)
z0 / hb
0.25
0.5 0.0
Leaves-on Transition
Leaves-off
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Figure 6: Aerodynamic roughness length (z0 ) measured on the tower at a height of zt = 24.4
m and sorted by month of the year (see Sect. 2.3 for additional details). The numbers under each category refer to the number of half hourly measurements represented in the statistics.
ically decrease, down to more than half of their reference summer values for the 2 / LAI/λbf / 3 cases. In complete absence of trees d is also significantly
M
reduced.
Specifically, z0 and d both display a sub-linear dependence on LAI/λbf , high-
460
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lighting how increasing LAI results in additional sheltering induced by vegetation on buildings and on other vegetation elements. Sheltering between roughness elements is known to be an important dynamical mechanism, responsible
465
PT
to reduce the overall drag that a surface exerts on the flow in the high λbf or LAI range (Macdonald et al., 1998; Raupach, 1992; Yang et al., 2016; Sadique et al., 2016). Conversely, the strong non-linear dependence of d on LAI/λbf can
d∼
LAIHv + λbf Hb , LAI + λbf
(11)
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be justified by considering that
where Hv and Hb are reference heights for the vegetation and buildings elements.
Equation 11 is a simplified version of the formula for the evaluation of the center
470
of action (barycenter) of buildings and vegetation forces (Jackson, 1981). Note that with opportunely chosen Hv and Hb , Eq. 11 well approximates the d dependence on LAI/λbf (not shown).
25
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Figure 6 shows z0 calculated from the tower-data following Eq. 10 for each month of the year. As the leaves emerge in March and April of each year, z0 475
increases to higher summer values, and then with senescence in October, z0
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drops. Overall, the conditionally sampling leaf-off and leaf-on periods on the tower we can identify a statistically significant (T-means test, p < 0.01) in-
crease by 19% from a mean normalized z0 /h = 0.119 (0.80 m) during leaves-off
to z0 /h = 0.142 (0.95 m) in the leaves-on season. LES determined z0 for the 480
full subset are 32% and 27% lower than the measured values on the tower, with
winter and summer vegetation, respectively. For subsets S1 and S3 which are
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most representative for the tower footprint, the LES are 36% and 11% lower than tower measurements in summer, and 38% and 23% lower in winter, re-
spectively. We relate such trends to the lack of information in the LiDAR data 485
(e.g., fences, chimneys, power lines) when compared to reality – resulting in an aerodynamically smoother urban canopy – and to the gentle orography that was removed in simulations to enable the use of periodic boundary conditions in the
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horizontal directions (x, y). Nevertheless, LES predictions fall in the interquartile range in all but two months (see Figure 6), validating both approaches and highlighting once more how vegetation effects on aerodynamic parameters can be significant.
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490
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4.3. Vegetation effects on integral turbulence statistics in the ISL Table 4 shows a comparison of dimensionless integral turbulence statistics evaluated at z = 24.4 m height between tower measurements and intrinsically DA LES over the S4 canopy. Note that DA LES statistics include dispersive
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contributions due to the chosen order of averaging operations (spatial averaging
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is performed first). Normalized streamwise and vertical velocity fluctuations (σu /u∗ , σw /u∗ ) and the turbulent momentum exchange efficiency (ruw , correlation coefficient between vertical wind and horizontal wind) indicate that tower
500
measurements are in the ISL irrespective of leaf situation, as they follow closely the neutral limits of the surface layer as predicted by MOS. No statistically significantly seasonal changes (T-means test, p < 0.01) is observed for such 26
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Table 4: Comparison of dimensionless integral turbulence statistics at z = 24.4 m height between tower measurements and DA LES. LES results are representative of flow over the S4 canopy, averaged over the west and south approaching wind directions and separated into “no vegetation”, “leaf-off” (winter) and “leaf-on” (summer) conditions. Tower-measured
refers to the surface layer neutral limits (Panofsky, 1984).
Tower
SL
Winter
Summer
No trees
Winter
Summer
σu /u∗
2.310
2.323
2.35
2.30
2.32
2.2
σw /u∗
1.206
1.209
1.16
1.17
1.175
1.25
ruw
-0.366
-0.365
-0.364
-0.372
-0.366
Skw
0.142
0.204
0.177
0.150
0.118
TKE / MKE
0.155
0.174
0.071
0.089
0.104
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Parameter
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quantities are separated into “leaf-off” and “leaf-on” conditions as described in Sect. 2.3. SL
-0.36
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quantities in measurements, and LES further support such a finding. Measurements predict a positive Skw , as is typical of surface layers (SLs), 505
which is observed in 90% and 87% of all cases in summer and winter, respec-
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tively, indicating the distribution is skewed to more positive values (updrafts less frequent but more intense). The skewness increases statistically significant
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(T-means test, p < 0.01) by 44% from a mean of 0.142 during leaf-off to a more skewed value of 0.204 in the leaf-on season (Tab.4). In contrast with mea510
surements, LES of flow over the S4 surface, averaged over the west and south
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approaching wind directions, predict a 15% and 33% decrease in Skw at z = 24.4 m from the no-vegetation to leaf-on and from the leaf-off to leaf-on cases, respectively. It should be noted that simulations over the S4 surface are characterized
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by a large max (hv , hb )/Lz ratio, which ensures that turbulence statistics (in-
515
cluding Skw ) up to z ≈ 5h are poorly dependent on the vertical extent of the computational domain (the sensitivity of flow statistics on Lz was tested using
half the current spatial resolution and is not shown). The most plausible reason for such a mismatch is hence the inability of LES to account for thermally
27
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95%
0.30
50% 25% 5%
0.25 0.20
Leaves-on
0.15 1035
615
0.10
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TKE / MKE
75% Mean
J
967
537
504
318
452
226
514 844
660
F
549
Transition
Leaves-off
M
A
M
J
J
A
Month of the year
S
O
N
D
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Figure 7: TKE to MKE ratio measured on the tower at a height of zt = 24.4 m and sorted
by month of the year (see Sect. 2.3 for additional details). The numbers under each category refer to the number of half hourly measurements represented in the statistics.
induced large-scale outer-layer structures, which are likely to influence Skw via 520
their interaction with the underlying canopy. The vertical structure of Skw from
quantity is provided.
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LES is described and commented in Sect. 4.4, where further insight on such a
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Figure 7 shows the ratio of turbulent to mean kinetic energy measured at 24.4 m. The ratio TKE / MKE increases statistically significant (T-means test, 525
p < 0.01) by about 12% from a mean of 0.155 during leaf-off to a value of 0.174
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in the leaf-on season (Tab.4). Again, clearly as leaves emerge in March and April, the ratio TKE/MKE increases and in fall drops again. This is explained
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by the increased roughness of the leaved canopy which converts more MKE and large-scale TKE to small-scale “wake” TKE. TKE/MKE increases in LES
530
from no-vegetation to leaf-on (summer) cases, and displays a 17% gain between
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the leaf-off and leaf-on season, in qualitative agreement with results from tower measurements. However, not surprisingly, LES predicts lower TKE/MKE ratios when compared to measurements. This can be again justified by the presence of outer layer flow structures that the LES does not include, which are an
535
important contribution to the overall TKE and are not affected by the local
28
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surface as shown in Roth and Oke (1995) for this site. A significantly larger computational domain would be required to account for such structures, which
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is beyond current computational capabilities. 4.4. Vegetation effects on momentum and energy transfer rates in the RSL The DA momentum equation reads
540
(12)
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1 d −Fx = [−ϕ(h˜ u0 w ˜ 0 i + hτxz i)] |{z} ϕ dz | {z } | {z } Forcing SGS Turbulent Z b 1 ˜ ˜ + (f + τ xj nj ) dΓ + hfxv i , |{z} Vf (z) Γb (z) x | {z } Vegetation Buildings
where (·) denotes temporal averaging, ni is the normal-to-interface (Γb ) vector pointing into the fluid domain, ϕ(z) ≡ (1−λbp ) and Vf ≡ ϕ(Lx ×Ly ×∆z ) are the area fraction of fluid and the volume of fluid at a given height (z), h˜ u0 w ˜0 i
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545
and hτxz i are the turbulent (including dispersive) and SGS kinematic stresses, b R 1 ˜ Vf (z) Γb (z) (f x +τ xj nj ) dΓ is the kinematic drag force that buildings are exerting
on the flow (sum of a normal and a deviatoric component), and hf˜xv i ≤ 0 is the
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kinematic drag force from trees.
Fig. 8 features selected components of the kinematic stress balance (Eq. 12). Profiles are qualitatively representative of the other LES runs. Below max hb , the largest contribution to the total canopy drag force is from
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550
buildings, and results in an approximately linear vertical momentum flux con-
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tribution, from the reference (negative) surface value to zero at z = max (hb ). Conversely, a significant portion of the vegetation drag force is exerted above
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555
max (hb ), resulting in a monotonic decrease of the corresponding momentum R hmax flux ( z v hf˜xv i dζ) at such heights, with direct impact on the turbulent flux
term h˜ u0 w ˜ 0 i, which experiences an equal decrease in magnitude (note that the to-
tal normalized momentum flux is the same among simulations). Throughout the runs, the downward flux of momentum from turbulent motions is decreased from the “no-vegetation” to the “leaves-on” cases within the UCL (z < max (hb , hv )).
29
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Figure 8: Vertical structure of the turbulent momentum flux (h˜ u0 w ˜ 0 i, black lines), total drag b R hmax 1 R ˜ b from buildings ( z (f + τ xj nj ) dΓdζ, gray lines), and from vegetation eleVf (ζ) Γb (ζ) x R max ments ( zhv hf˜xv i dζ, red lines). Profiles are representative of simulations over the S4 surface, west wind approaching angle. Different line styles denote different runs: S4NV W , solid lines; SV S4WV W , dashed lines; S4W , dot-dashed lines. SGS contributions are negligible throughout the
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boundary-layer and hence not shown. A smaller portion of the total domain height is shown.
uih˜ u0 w ˜ 0 i) 1 d(ϕh˜ , ϕ dz
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Figure 9: Turbulent transport of mean kinetic energy (Tt ≡
black lines),
production of MKE by the imposed pressure gradient (PΠ ≡ Fx h˜ ui, grey lines), and sink of
MKE from the work of vegetation drag (Pv ≡ hf˜xv ih˜ ui , red lines) for simulations over the S4 surface, west wind approaching angle. Different line styles denote different simulations: S4NV W ,
SV ∗ solid lines; S4WV W , dashed lines; S4W , dot-dashed lines. (·) is used to denote normalization
of each term by (u3∗ /h). A smaller portion of the total domain height is shown.
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To better quantify the impact of vegetation on the mean flow, Fig. 9 features
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the vertical structure of selected terms of the mean kinetic energy (MKE) budget equation. It is apparent how vegetation has a twofold effect on MKE in the
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considered urban canopies: on one hand, it is a direct sink of MKE via its work against the mean flow (Pv ), proportional to the LAI characterizing a given 565
canopy. On the other hand, its impact on h˜ u0 w ˜ 0 i and h˜ ui (via the work that
f˜iv performs against the mean flow) results in a significant decrease of MKE downward turbulent transport (Tt ) below max (hb ). At such heights where
people live and buildings consume energy, Tt is the major source of MKE (Tt LAI results in a substantial decrease of wind speed magnitudes.
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Fx h˜ ui > 0), and is thus no surprise that reductions in such a term with increasing
Figure 10: Vertical structure of the horizontal (left) and vertical (right) velocity skewness
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for LES cases over the S4 surface west (black lines) and south (red lines) approaching wind angles. Symbols: solid lines, no vegetation cases; dashed lines, leaves-off cases; dot-dashed
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lines, leaves-on cases.
Based on Fig. 10 it is clear how the upper RSL is dominated by ejections,
while the lower RSL and urban canopy layer show a dominance of sweeps in the turbulent momentum exchange, which is in agreement with several field studies within and/or above urban canopies (Rotach, 1993; Oikawa and Meng,
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1995; Christen et al., 2007). As vegetation is added Sku and Skw increase in 31
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Figure 11: Difference between the two-dimensional histogram of h˜ u0 w ˜ 0 i at z = hb for simu-
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WV NV SV lations S4NV ˜0 /u∗ and w ˜ 0 /u∗ sampled W , S4W (left) and S4W , S4W (right). Point clouds of u
in the plane z = hb have been uniformly binned in a two dimensional histogram for each simulation and the difference between the two dimensional histograms for the cases without and with vegetation are displayed. Red, white and black dots denote a decrease, no changes, and increase in the number of observations that fall within a given bin.
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magnitude within the UCL, highlighting a more intermittent turbulence field, which favors u ˜0 > 0 and w ˜ 0 < 0 fluctuations (i.e., sweep motions). The height of
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the crossover for Sku and Skw also increases with the addition of vegetation and with increasing LAI, highlighting how the presence of irregular sparse roughness 580
with irregular heights results in a thicker RSL. Note that even in the absence of
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vegetation, the height of the crossover at z/h = 1.38 is higher than the crossover of z/h = 1.25 observed in simulations over cubical obstacles of uniform height
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(Coceal et al., 2007a) but comparable to the crossover in neutral conditions at z/h = 1.5 over a denser urban canopy without significant trees (Christen et al.,
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2007).
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Figure 11 provides a qualitative description how turbulent fluctuations con-
tributing to h˜ u0 w ˜ 0 i at z = hb are modified by vegetation. The specific cases of flow over the S4 surfaces with wind approaching from west are considered WV SV (S4NV W , S4W and S4W ). As is apparent, including vegetation results in a pro-
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gressive damping of streamwise fluctuations u ˜0 (red areas) contributing to both quadrant 2 and quadrant 4 events, reducing the variance of the u ˜0 probability 32
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density function. This behavior is consistent among the considered cases. Note also how the sparse vegetation suppresses ejections more effectively than sweeps, in line with the observed increase in the Sku and Skw magnitude at hb (see Fig. 10). In an absolute frame, sparse vegetation thus tends to make the turbulent
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field more isotropic in the lower RSL. Accordingly, in addition to a direct fluid dynamical implication, including vegetation has potential benefits from an urban comfort perspective, as gusts affecting pedestrians, and dynamical pressure
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5. Summary and Conclusions
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variations that cause building energy losses are minimized (“sheltering effects”).
This research explored the role of trees over a realistic urban canopy using a combination of detailed LES, eight years of continuous measurements, and airborne LiDAR data to map and describe the detailed urban form and leaf area density. Unlike previous computational fluid dynamics simulations that investigated the effect of urban trees on pollutant dispersion in idealized streets,
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the current study focused on how trees and changing leaf area density affect the neighborhood-averaged flow and turbulence fields. A number of surfaces were
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considered, representative of a typical suburban area of Vancouver, Canada, where a small fraction of trees are taller than buildings. LES and tower measurements showed that aerodynamic roughness lengths
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(z0 ) are sensitive to variations in the 0 ≤ LAI/λbf < 3 parameter for each of the considered canopies. Specifically, z0 increments were characterized by a
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sub-liner dependence on LAI/λbf for each of the considered canopies, indicative of additional sheltering occurring between vegetation elements as well as be-
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tween vegetation and buildings as LAI increases. z0 from LES fell within the
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interquartile range of corresponding values from tower measurements, but mean z0 values were underpredicted by approximately 30% in the LES runs over the S4 surface (the most representative of what the tower sees). Such a behavior is mostly due to lack of information in the LiDAR measurements when compared
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to real settings (power lines, chimneys, fences) and to the gentle orography that
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was not considered in simulations. Specifically, the aerodynamic roughness determined from tower measurements was seasonally changing with a statistically significant 19% increase from leaf-off season (z0 /h = 0.119) to the leaf-on season
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(z0 /h = 0.142). Similarly, LES results over the S4 subset averaged over south and west wind approaching directions found a seasonal change in z0 with an
increase by 27% from the winter (LAI/λbf = 0.74, z0 /h = 0.081) to the summer
season (LAI/λbf = 2.24, z0 /h = 0.104). LES also showed that in the absence
of vegetation z0 would experience a significant decrease, down to over 50% its reference summer value in most cases.
The zero-plane displacement d, computed as center of action of the total
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surface drag from LES, was found to also increase as a function of the LAI/λbf parameter, mostly due to the disproportionate amount of drag that the (few) relatively taller trees exert on the flow.
Integral statistics σu /u∗ , σw /u∗ and ruw at the measurement height of the 635
tower (z/h = 3.75, where h ≡ mean(hb ) + σhb ) were not subject to any seasonal
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change (evidence provided by both measurements and LES). They followed predicted surface layer values in summer and winter, hence at such a height and
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above, we can expect a well-developed ISL in which the neutral limits of MOS are fulfilled. Statistically significant increases between leaf-off and leaf-on cases 640
were found at z/h = 3.75 in the ratio of TKE to MKE (+12% in measurements,
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+17% in LES over the S4 canopy averaged between west and south wind approaching direction), but the magnitude from LES were over 50% smaller than
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the corresponding measured quantity. Furthermore, LES and tower measurements predicted a positive vertical velocity skewness (Skw > 0) at the tower
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sampling location, as is typical of atmospheric surface layers where ejections of
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low momentum fluid are the main contribution to the total momentum flux. However, tower data were characterized by an increase in Skw from winter to
summer, whereas LES data predicted a decrease in such a quantity in that same period. The most plausible reason for such a mismatch in both TKE/MKE and
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in Skw is the inability of LES to account for thermally induced large-scale outer-layer structures, which are likely to influence such flow statistics via their 34
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interaction with the underlying canopy. The analysis of the vertical transfer of momentum in the LES showed how trees exert a significant portion of the total drag in both the winter and the summer season, thus reducing pressure loads on buildings. In most cases, the
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total drag from vegetation elements during the summer season was even larger than that of buildings. In addition, as vegetation is added Sku and Skw increase in magnitude within the UCL, highlighting a more intermittent turbulence field
favoring sweep motions, and resulting in higher locations in sign crossover for 660
both statistics. From the quadrant analysis that was performed at z = hb , it is
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also apparent that including vegetation results in a progressive damping in the magnitude of streamwise fluctuations u0 , thus reducing extreme wind events in the UCL, with potential benefits from an urban comfort perspective.
Lastly, the analysis of selected mean kinetic energy budget terms in the LES 665
showed that urban trees influence the flow in the RSL twofold: on one hand, trees are a direct sink of MKE via the work of their drag force against the
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mean flow; on the other hand, they reduce downward turbulent transport of high momentum fluid from higher atmospheric layers. Given that most of the
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MKE in the lower RSL is generated by downward transport from large organized turbulent motions, it is apparent how the specific shape, clumping and density of urban vegetation controls flow at the height where people live in a city, hence
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suggesting the need for careful landscape architecture design strategies. With more than 50% of the global population now living in cities (United
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Nations, 2014), the atmosphere which the majority of us experiences is not a 675
classical surface layer, but the roughness sublayer embedded within and above urban canopies. In many cities of the world, trees are important elements of the
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urban form, and also a design tool to mitigate adverse effects on pedestrians, provide shelter and shade, mitigate heat stress, and conserve energy in buildings. However, trees also affect the dispersion of air pollutants emitted at ground level
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negatively (e.g. Salmond et al., 2013). Our current ability to incorporate the effect of trees in ULSMs is limited, but the current study shows that the role of trees and their seasonally changing leaf area density (a) in cities has a crucial 35
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effect on both, turbulence and flow in the ISL above vegetated cities and flow an turbulence in the urban roughness sublayer, including at street level and 685
these effects should be considered in next-generation ULSMs. This may help in
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future to make improved predictions that benefit the management of air quality, heat stress and generally assist the planning of energy efficient and intelligently designed cities.
Acknowledgements
This research was funded by the Swiss National Science Foundation (SNSF-
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200021-134892), the Competence Center for Environmental Sustainability (CCESSwissEx) of the ETH domain, the NSERC Discovery Grant program (Parlange, Christen). Selected instrumentation was supported by the Canada Foundation for Innovation (Grant 33600). Numerical simulations were supported by a grant 695
from the Swiss National Supercomputing Centre (CSCS) under project ID s633.
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We are grateful to the peer reviewers whose comments helped to improve the overall quality of the manuscript.
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Appendix A. Grid resolution requirements To assess the resolution requirements for the LES runs the subset S1 is selected with west wind approaching direction and summer vegetation conditions
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(similar to case S1SV W ). Four different resolutions are considered, as indicated
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in Fig. 12, and quantities such as the mean turbulent kinetic energy (TKE ≡ (1/2)h˜ u0i u ˜0i i) and the mean rate of TKE shear production (Ps ≡ h˜ u0 w ˜ 0 i(dh˜ ui/dz)) are inter-compared. The second quantity is often used as indicator of the quality of a numerical solution, as it encodes information on both mean flow and tur-
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bulence. The grid stencil in the vertical direction (∆z = 0.5 m) is not modified across the considered runs and only the horizontal grid stencils are varied, from a maximum of ∆x ≈ ∆y = 3.14 (m) to a minimum of ∆x ≈ ∆y = 1.04 (m).
Varying only the horizontal grid stencil is justified considering that the vertical 710
resolution is much higher than the horizontal across the various cases. Note 36
Figure 12: (1/2)h˜ u0 u ˜0 i)
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Comparison of time- and space-averaged turbulent kinetic energy (TKE ≡
(left plot) and TKE production rate (Ps ≡ h˜ u0 w ˜ 0 i(dh˜ ui/dz)) (right plot) for
case S1SV W (see Table 1 for details) at different spatial resolutions.
that the coarser among the considered horizontal grid stencils is approximately
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60% larger than that used in the runs over the S4 surface (see Table 1), the second coarser resolution case (Nx × Ny × Nz = 192 × 96 × 168) corresponds to approximately 10% stencil increased when compared to that used in the S4 runs, and the second finer resolution (Nx × Ny × Nz = 320 × 160 × 168) corresponds
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to that used in all the other runs (flow over the S1, S2, and S3 cases).
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TKE and Ps profiles convergenge as the grid stencil is refined. Assuming the finer resolution as reference, largest departures in the TKE magnitude occur in the near surface region for the coarsest run, and at z/h ≈ 2 for the other cases. Large errors in max (Ps ) are also localized in the near surface region
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for the coarsest case, whereas the remaining runs are well converged as such a location, and greatest departures occur near max (Ps ). The latter height is
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where thin shear layers separate from buildings. Such flow features are regions of strong TKE production where small and highly energetic motions set tough
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requirements in terms of grid resolution. The grid convergence study indicates that the chosen resolution for the runs over the S1, S2, and S3 surfaces is fine enough to correctly capture the TKE and max (Ps ) profiles within the RSL. The
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resolution chosen for the S4 runs is slightly larger, and the current convergence tests shows that local variations in the TKE and in Ps with respect to the exact 730
value are bounded to a maximum of 16% and 8% respectively. Such modest
and validate the quality of the proposed LES results.
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Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment M.G. Giometto, A. Christen, P.E. Egli, M.F. Schmid, R.T. Tooke, N.C. Coops, M.B. Parlange PII: DOI: Reference:
S0309-1708(17)30648-6 10.1016/j.advwatres.2017.06.018 ADWR 2878
To appear in:
Advances in Water Resources
Received date: Revised date: Accepted date:
22 June 2016 14 June 2017 22 June 2017
Please cite this article as: M.G. Giometto, A. Christen, P.E. Egli, M.F. Schmid, R.T. Tooke, N.C. Coops, M.B. Parlange, Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment, Advances in Water Resources (2017), doi: 10.1016/j.advwatres.2017.06.018
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Highlights • LES and tower measurements are used to quantify effect of urban trees
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on flow • Roughness length and displacement height increase with increasing foliage density
• The ratio of turbulent to mean kinetic energy increases with increasing foliage
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• Dense trees reduce downward turbulent transport of high-momentum fluid.
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Effects of trees on mean wind, turbulence and momentum exchange within and above a real urban environment
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M. G. Giomettoa,∗, A. Christenb , P. E. Eglic , M. F. Schmida , R. T. Tooked , N. C. Coopsd , M. B. Parlangea a Department
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of Civil Engineering, Faculty of Applied Science, University of British Columbia, Vancouver, BC, Canada b Geography / Atmospheric Science Program, University of British Columbia, Vancouver, BC, Canada c Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerland d Department of Forestry, University of British Columbia, Vancouver, BC, Canada
Abstract
Large-eddy simulations (LES) are used to gain insight into the effects of trees on turbulence, aerodynamic parameters, and momentum transfer rates
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characterizing the atmosphere within and above a real urban canopy. Several areas are considered that are part of a neighbourhood in the city of Vancouver, BC, Canada where a small fraction of trees are taller than buildings. In this
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area, eight years of continuous wind and turbulence measurements are available from a 30 m meteorological tower. Data from airborne light detection and
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ranging (LiDAR) are used to represent both buildings and vegetation at the LES resolution. In the LES algorithm, buildings are accounted through an immersed boundary method, whereas vegetation is parameterized via a location-
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specific leaf area density. LES are performed including and excluding vegetation from the considered urban areas, varying wind direction and leaf area density. Surface roughness lengths (z0 ) from both LES and tower measurements are
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sensitive to the 0 ≤ LAI/λbf < 3 parameter, where LAI is the leaf area index
and λbf is the frontal area fraction of buildings characterizing a given canopy. For instance, tower measurements predict a 19% seasonal increase in z0 , slightly ∗ Corresponding
author Email address: [email protected] (M. G. Giometto)
Preprint submitted to Advances in Water Resources
June 27, 2017
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lower than the 27% increase featured by LES for the most representative canopy (leaves-off LAI/λbf = 0.74, leaves-on LAI/λbf = 2.24). Removing vegetation from such a canopy would cause a dramatic drop of approximately 50% in z0
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when compared to the reference summer value. The momentum displacement height (d) from LES also consistently increases as LAI/λbf increases, due in
large part to the disproportionate amount of drag that the (few) relatively
taller trees exert on the flow. LES and measurements both predict an increase
in the ratio of turbulent to mean kinetic energy (TKE/MKE) at the tower sampling height going from winter to summer, and LES also show how including
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vegetation results in a more (positive) negatively skewed (horizontal) vertical
velocity distribution – reflecting a more intermittent velocity field which favors sweep motions when compared to ejections. Within the urban canopy, the effects of trees are twofold: on one hand, they act as a direct momentum sink for the mean flow; on the other, they reduce downward turbulent transport of high-momentum fluid, significantly reducing the wind intensity at the heights
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where people live and buildings consume energy.
Keywords: aerodynamic roughness, roughness sublayer, trees, turbulence,
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urban canopy, urban forest, vegetation, wind.
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1. Introduction
The physical structure of cities controls and modifies the exchange of momentum, heat, water, and air pollutants between the surface and the atmo-
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sphere. The three-dimensional form of cities is intrinsically spatially variable,
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and this influences the properties of wind, turbulence and turbulent exchange on
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street, neighbourhood and city scales (Belcher, 2005). Up to a height of several times the size of buildings – in the layer known as roughness sublayer (RSL) – flow statistics are strongly dependent on the actual shape and arrangement of buildings, and Monin-Obukhov similarity (MOS) scaling is generally inaccurate
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(Roth, 2000). Field experiments and numerical studies have shown that in the surface layer above the RSL – the inertial sublayer (ISL) – the air flow over
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cities (and complex surfaces in general) becomes statistically homogeneous, and the neutral flow is completely determined by the friction velocity u∗ , aerodynamic roughness length z0 and zero-plane displacement d, and is obeying MOS scaling for diabatic situations (Parlange and Brutsaert, 1989; Brutsaert et al.,
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1989; Parlange and Brutsaert, 1990; Brutsaert and Parlange., 1992; Katul and Parlange, 1992; Parlange et al., 1995; Feigenwinter et al., 1999; Bou-Zeid et al., 2004; Yang, 2016). Aerodynamic properties of cities control exchange rates of
momentum and scalars such as heat and humidity and therefore have impor20
tant implications for weather and hydrological modelling at urban and regional
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scales (Brutsaert, 1982).
The term “urban canopy” refers to the assemblage of buildings, built objects and vegetation that make up the three dimensional interface between the land surface and the atmosphere in cities. In many low- to medium-density urban 25
areas, vegetation, including tall trees, forms an important component of the urban canopy (Oke et al., 2017). Trees can significantly modify meteorological and
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hydrological processes in the RSL and also affect the flow in the ISL above (Oke, 1989). Furthermore, trees are an important design tool to manage building and
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street climates (e.g. Oke, 1988; Shashua-Bar and Hoffman, 2000; Johansson and Emmanuel, 2006; Bowler et al., 2010). At the coarser scales, urban vegetation is relevant for managing heat stress and air quality at neighborhood to city
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scales. For example, model simulations by Li and Bou-Zeid (2013) suggest that urban forestry is a critical tool to prevent exacerbated urban-rural temperature
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differences during heat waves. To ensure safety and health of urban dwellers, and to efficiently manage
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energy and water in urban systems, we need numerical models that represent
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weather, climate and hydrology under current conditions and future climate and planning scenarios (Chen et al., 2012). The presence of urban canopies on the atmosphere is generally represented in hydrology and mesoscale weather models
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using “urban land surface models” (ULSMs). ULSMs describe the energetics, hydrology and dynamics of the urban surface, by either implying certain bulk values or simulating the behaviour of different tiles such as roofs, walls, roads 4
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and urban vegetation. More complex ULSMs targeted to resolve the climate of the RSL and inside 45
the urban canopy are called urban canopy parameterizations (UCPs). UCPs
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represent the three-dimensional geometry of an urban surface, and account for interactions between tiles, the atmosphere, the building interior and subsurface, often applying a multi-layer approach (Masson, 2005).
Recent assessments of our capabilities to accurately reproduce land-atmosphere 50
exchange in urban environments using ULSMs have shown that the lack of, or a
crude and improper representation of urban vegetation, in particular the direct
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interaction of trees with buildings and vice versa, is a major weakness. The
international urban energy balance model comparison concluded that “taking vegetation cover into account (or not) significantly impacts model performance” 55
in particular related to energy partitioning and evapotranspiration (Grimmond et al., 2010).
Trees interact in a three-dimensional way with buildings radiatively (e.g. shading
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and radiation trapping), energetically (e.g. transpiration), and dynamically (e.g. wind sheltering). However, most of UCPs to date do not include trees as three dimensional objects. Recently, there have been efforts to represent the three-
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dimensional radiative and energetic effects in urban modelling systems (Lee and Park, 2008; Krayenhoff et al., 2014; Ryu et al., 2015; Lee et al., 2016).
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The dynamical impact of urban trees, however, is not included in operational ULSMs and UCPs.
The dynamical effect is not only referring to the sheltering effect and change
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of scaling parameters z0 and d, but also the fact that trees modify turbulence
and consequently turbulent length scales that affect transfer of scalars and dis-
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sipation rates in the RSL. Krayenhoff et al. (2015) use CFD simulations over generic urban geometries to inform parameterizations of the dynamical effect of
70
urban trees for given densities and clumping. The influence of trees is also timedependent. Deciduous trees in mid- and high-latitude cities change their leaf area density (a in the following) with season. Although some ULSMs for hydrology applications prescribe changing leaf area densities over the year (e.g. J¨ arvi 5
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et al., 2011), no operational USLM considers the effect of seasonally changing a 75
on mean wind and turbulent exchange. The overall goal of this study is to assess the role of urban trees and changing
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leaf densities on the flow dynamics within and above a realistic urban canopy. This helps to inform the next-generation ULSMs when, where and how incorporating or not the effects of urban vegetation at the scale of neighbourhoods 80
or cities is appropriate and possible. The specific research questions are:
• To determine the effect of trees and changing leaf density on the aerody-
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namic roughness length and zero-plane displacement in the urban environment.
• To test the sensitivity of integral turbulence statistics in the ISL above the urban canopy to the characteristics of the urban vegetation.
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• To characterize the effect of trees and changing a on vertical transfer of
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momentum and mean kinetic energy in the urban RSL.
A combination of detailed large-eddy simulations (LES) and long-term mea-
90
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surements from a tower over an urban canopy in Vancouver, Canada, is used to answer these questions. A Digital Surface Model (DSM) derived from airborne Light Detection and Ranging (LiDAR) data is used to characterize the
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surface and represent both buildings and vegetation at high spatial resolution in the LES. The LES is run under the same forcing with the DSM including
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vegetation at various densities and once without vegetation (reference case). 95
The latter condition is of course not possible to reproduce on the tower measurements. Measurements from the tower are instead conditionally sampled
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discerning between leaves-on (Summer) and leaves-off (Winter) seasons to investigate the effect of varying leaf area density in the real atmosphere.
100
To date, numerical simulations of the flow and turbulence over cities with
buildings resolved (as opposed to modelled) have primarily represented cities as idealized rectangular patches of different surface roughness and arrays of cubes or cuboids with varying spatial organization (Kanda et al., 2004; Kanda, 6
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2006; Xie and Castro, 2006; Coceal et al., 2007b; Xie et al., 2008; Inagaki et al., 2012; Anderson et al., 2015; Li et al., 2016b; Yang et al., 2016; Yang, 2016; 105
Sadique et al., 2016; Anderson, 2016; Zhu et al., 2016). In addition, several
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studies modelled the aerodynamic effect of urban trees using simple, generic street geometries to investigate the effect of trees on pollutant dispersion (Balcz´ o et al., 2009; Salim et al., 2011; Moonen et al., 2013; Gromke and Blocken, 2015;
Vranckx et al., 2015). Such idealized studies show consistently that trees reduce 110
the vertical exchange of scalars and deteriorate air quality when sources are below the canopy, a conclusion also supported by wind tunnel simulations (e.g.
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Gromke and Ruck, 2008).
With increasing parallel computing power and the availability of Digital Surface Models (DSMs) it is now feasible to simulate subsets of a real cities (e.g. 115
Xie and Castro, 2009; Kanda et al., 2013; Giometto et al., 2016; Hertwig et al., 2016a,b). However, to the best of our knowledge, no LES study in the literature has simulated a real urban neighborhood including the effect of individually
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resolved, clumped trees. In the absence of buildings, the effect of a plant canopy on airflow and turbulence and, inversely, the effect of flow on trees, has been studied using LES assuming uniform a distributions (e.g. Shaw and Schumann,
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1992a; Kanda and Hino, 1994; Dwyer et al., 1997; Finnigan et al., 2009a) and more recently with explicitly resolved plants and realistically clumped a (Yue
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et al., 2007; Huang et al., 2009; Bailey and Stoll, 2013; Patton et al., 2016). Likewise, observational studies in cities have provided limited insight on the role of urban trees. Most studies quantified turbulence generated within and
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125
above urban canopies using multiple measurements located at different heights on towers in the RSL and/or ISL (e.g. Rotach, 1993; Feigenwinter et al., 1999;
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Christen et al., 2007; Nelson et al., 2007; Christen et al., 2009; Ramamurthy and Pardyjak, 2011, 2015). However, observational studies with simultaneous
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measurements within and above urban canopies have targeted urban canopies without or with very limited trees, and no observational study has been able to isolate the effect of trees on mean wind and turbulence from the effect of buildings. 7
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Figure 1: Filled color contour of buildings and vegetation height (hb and hv respectively) in a 974 × 620 m2 area surrounding the 28.8 m “Vancouver-Sunset” meteorological tower in
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Vancouver, BC, Canada. Surface data are based on LiDAR measurements. Selected subsets for use in large-eddy simulation (LES) are highlighted (S1, S2, S3, and S4).
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2. Methods 135
2.1. Study area
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Figure 1 depicts a 974×620 m2 area in south central Vancouver, BC, Canada, centered on the micrometeorological research tower “Vancouver-Sunset” (Fluxnet ID “Ca-VSu”, 123.0784◦ W, 49.2261◦ N, 78 m a.s.l.). The area is characterized by a relatively homogeneous mix of streets and detached one to two storey 140
houses (12.8 Bldg. ha−1 ), and is representative of the majority of Vancouver’s neighbourhoods and North American cities (Local Climate Zone 6, according to
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Stewart and Oke (2012)). The area has been the focus of a number of observa-
tional campaigns related to flow and turbulence characteristics over suburban surfaces (Schmid et al., 1991; Roth and Oke, 1993; Roth, 1993; Roth and Oke, 145
1995; Grimmond et al., 1998; Grimmond and Oke, 2002)
Vegetation in the area (circle of 400 m radius around tower) has a density of 19.2 Stems ha−1 and comprises of about 23% evergreen trees and 77% deciduous
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trees (Liss et al., 2013). The large fraction of deciduous trees is resulting in a strong seasonal variation of the Leaf Area Index (LAI). Liss et al. (2013) estimates that the LAI of trees is 0.39 m2 m−2 in summer. The average tree
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height is estimated 8.4 m for broadleaf trees (n = 742) and 11.1 m (n = 223) for coniferous trees.
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The entire surface (S4) displayed in Fig. 1 and three smaller surfaces (S1, S2 and S3) comprised within S4 are selected for use in LES. The reason to 155
separately consider a number of sub-surfaces is to provide a broader range of
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realistic canopies, each characterized by its peculiar distribution of buildings and trees, to further support conclusions and to study the dependence of flow
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statistics on relevant surface parameters (such as LAI and the frontal-area index of buildings). For the considered wind approaching direction (see Sect. 2.4.2), all
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surfaces (S1, S2, S3 and S4) are mostly within the 70%, and entirely within the 80% long-term cumulative footprint of the tower. The 80% long-term cumulative footprint climatology covers an area of 1.04 km2 and is shown in Fig. 1 of
Crawford and Christen (2015a).
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2.2. Light detection and ranging data The detailed building heights and vegetation information used in the LES
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are derived from a LiDAR point cloud dataset, mapped to a two-dimensional
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horizontal Cartesian grid with stencil of 0.5 m in both directions. The LiDAR dataset was acquired in February 2014, during leaves-off conditions, which al-
lowed for good penetration of the laser through the vegetation canopies. Ex170
tracted buildings information comprise the building heights (hb ), function of the horizontal coordinates x and y, whereas vegetation elements are represented as a spatially distributed leaf area density (a) coefficient. The a coefficient has been
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computed as a function of the foliage probability distribution (Pf ) following Tooke et al. (2011):
a(x, λ, k) = − ln [1 − Pf (x, λ, k)] , 175
(1)
where the functions λ, k : (x, y) → R+ and where Pf is itself approximated as a two parameters Weibull distribution
k z (k−1) exp [−(z/λ)k ] . λ λ
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Pf =
(2)
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The λ(x, y) > 0 and k(x, y) > 0 are the scale and shape parameters, and are evaluated based on a non-linear fit to the LiDAR beam interception probability, representing probability of branches and evergreen foliage at a given height. A random spatial orientation of leaves was assumed. To calculate summer a, the
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overall LAI resulting from the LiDAR dataset has been rescaled to match the
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LAI = 0.39 value of Liss et al. (2013), representative of the area in the summer season.
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2.3. Tower-based turbulence measurements
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The 30 m triangular lattice tower that hosted turbulence instrumentation
is situated 5 m from the south-eastern corner of a power substation (Fig. 1). Continuous long-term measurements were made from 1 May, 2008 to 30 April, 2016 at a single height, using a CSAT-3 three-axis ultrasonic anemometerthermometer (Campbell Scientific, Logan, UT, USA) operated at 28.4 m above 10
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local ground facing an azimuth of 180◦ . Because the base of the tower is recessed by 4 m from the surrounding terrain, an effective measurement height of z=24.4 m is used for the measurements in further calculations (Crawford and Christen,
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2015b). Measured quantities include the instantaneous three components of the wind vector (u,v,w, all rotated into the mean wind using a double-rotation) sam195
pled at 60 Hz and stored at 20 Hz. Block averages over 30 min were calculated and filtered following the procedures outlined in Crawford et al. (2012).
Conditional sampling of the tower data has been performed, isolating 30 minute blocks with a neutral dynamic stability following the criteria of −0.075 < 200
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(z − d)/L < 0.075, where d is the zero-plane displacement (set to d = 5.46 m, see Sect. 4.2), and L is the Obukhov-Length measured on the tower as: L=
T u∗ κ g θ∗
(3)
where κ is the von K´ arm´ an constant (we assumed κ = 0.4), T the absolute 2
2
temperature, u∗ the friction velocity calculated as u∗ = (u0 w0 + v 0 w0 )0.25 and
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θ∗ the temperature scale calculated as θ∗ = −w0 T 0 /u∗ . To ensure consistent wind direction over the 30 minute block, the RMSE of the cyclic wind direction (α) calculated for 6 subintervals of 5 minutes each, was set to not exceed 15◦ in
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each block. Only data with a wind speed of > 2 m s−1 and wind direction 150◦ ≤
α ≤ 300◦ was considered, hence approaching between SSE and WNW (excluding
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sectors where potential flow distortion is found by the instrumentation and the wake of a nearby school building). This resulted in 4700 datasets further considered (3.4% of the period of 8 years, or 3.2 months of data). To avoid effects
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of seasonally changing wind direction to affect results, conditional averages were formed as follows: Averages and statistics were calculated separately for 30◦
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wind direction sectors and each month of the year. To calculate summer values, conditional averages from all 30◦ sectors between 150◦ and 300◦ and all months
215
between May and September were selected and equally weighted.
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2.4. Numerical algorithm The LES algorithm adopted in this study was originally developed in Albertson and Parlange (1999a,b) and updated to develop linear and non-linear
220
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LES closure models (Meneveau et al., 1996; Port´e-Agel et al., 2000; Bou-Zeid
et al., 2005; Lu and Port´e-Agel, 2010), wall models (Anderson and Meneveau,
2010, 2011; Anderson et al., 2012; Hultmark et al., 2013), and has been extensively used in wind energy applications (Calaf et al., 2010, 2011; Sharma et al., 2016), urban applications (Tseng et al., 2006; Bou-Zeid et al., 2009; Cheng and
Port´e-Agel, 2013, 2015; Anderson et al., 2015; Giometto et al., 2016) and in studies of flow over vegetation canopies (Chester and Meneveau, 2007; Chester
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225
et al., 2007; Yue et al., 2007, 2008; Bailey and Stoll, 2013).
It integrates the spatially filtered Navier-Stokes equations in their rotation form
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∂u ˜i ∂u ˜i ∂u ˜j ∂π ˜ ∂τij +u ˜j ( − )=− − + Fi + f˜ib + f˜iv ∂t ∂xj ∂xi ∂xi ∂xj ∂u ˜i = 0, ∂xi
(5)
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Ω × [0, T ] where Ω denotes a regular domain, T is the total integration
in 230
(4)
time, u ˜i are the space filtered velocity components in the x, y and z Cartesian coordinate directions, π ˜ is a modified filtered kinematic pressure (˜ π = +
1 ˜i u ˜i ), 2u
+
ρ is a reference constant density, τij denotes the subgrid-scale
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1 3 τii
1 ˜ ρp
(SGS) kinematic stress tensor, and Fi ≡ (u2∗ /Lz , 0, 0) is a constant kinematic pressure gradient forcing that is introduced to drive the flow in the x coordinate direction. In addition, f˜ib is an immersed-boundary method (IBM) forcing term
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that is used to impose the desired boundary condition at the building interface
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and in the below-interface locations (it has a finite value at and inside the buildings interface and is zero elsewhere), and f˜iv is a volumetric force that is introduced to account for drag from vegetation elements (see Sect. 2.4.1).
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The equations are solved on a regular domain Ω using a mixed pseudospec-
tral - finite differences algorithm (Orszag, 1969, 1970), time advancement is performed using an explicit second-order accurate Adam Bashforth scheme, and 12
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the pressure field is evaluated through a fractional step method (Chorin, 1968). A free-lid boundary condition is imposed at the top of the domain (H), periodic 245
boundary conditions apply in the horizontal directions, due to the pseudospec-
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tral approach, and zero velocity is enforced at Γb and below via the f˜ib forcing term (this approach is known in literature as the discrete forcing approach IBM
method (Mittal and Iaccarino, 2005)). In addition, tangential stresses are applied in a band centered around the buildings interface Γb via a logarithmic equi250
librium wall-law. Specifically, the band is defined as −1.1∆ ≤ Φ(x, y, z) ≤ 1.1∆, where Φ denotes the distance from Γb and ∆ = (∆x×∆y×∆z)1/3 , where ∆x, ∆y
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and ∆z are the grid stencils in the three coordinate directions. The wall-law reads τw = −
κ(k˜ ut k2 ) ln (1 + ∆/z0 )
2
in
Γb × [0, T ] ,
(6)
where u ˜t = u ˜ − (˜ u · n)n is the tangential-to-surface velocity vector, n is the 255
surface normal vector, and z0 is the aerodynamic roughness length parameter.
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τw is the kinematic surface stress defined in the previously introduced band and 0 0 it corresponds to τ13 = τ31 in a local Cartesian coordinate system centered at
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the given collocation node and defined by e01 = u ˜ t /k˜ uk, e02 = (˜ ut × n)/k˜ uk,
e03 = n. After evaluation τw is rotated back in the {e1 , e2 , e3 } canonical co-
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ordinate system to provide τij at Γb . Gibbs oscillations that arise when IBM
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methods are implemented within spectral-like discretizations are here reduced via a Laplacian smoothing approach, as described in Chester et al. (2007). Al-
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ternative approaches to perform such a task have also been proposed recently (Fang et al., 2011; Li et al., 2016a) A dynamic Smagorinsky LES model with planar (x, y) averaged coefficient
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is adopted to evaluate τij from spatially-resolved quantities, thus closing the system of equations 4 and 5 in the bulk of the flow (Germano et al., 1991; Lilly, 1992). The dynamic model is based on the mixing length concept, and evaluates the SGS kinematic stresses as a function of the local resolved strain rate tensor: ˜ 2 S˜ij , τij = −2νt S˜ij = −2(cs,∆ ∆)2 kSk 13
(7)
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270
where cs,∆ is the Smagorinsky coefficient at grid scale ∆ (Scotti et al., 1993). Unlike the original Smagorinsky model (Smagorinsky, 1963), which requires an ad-hoc specification of cs,∆ , the dynamic model computes cs,∆ dynamically
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by taking advantage of information contained in the smallest resolved scales (the scales between ∆ and a test-filter scale e.g. 2∆). More sophisticated 275
Smagorinsky-type SGS models have been proposed during the past two decades,
see for instance the works of Meneveau et al. (1996); Port´e-Agel (2004); Bou-Zeid et al. (2005), and a plethora of other approaches exist to close the space-filtered
Navier-Stokes equations (Meneveau and Katz, 2000). However, when it comes
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to LES of flow over bluff elements such as urban canopies, pressure (or form)
drag is the main sink of momentum and SGS contributions are – on average – only a minor percentage of the overall momentum flux (see e.g., Giometto et al., 2016). Because of this, the velocity field is known to be poorly dependent on the specific SGS approach when compared to flow over streamlined elements, and simple and efficient closure models yield accurate results. Note that these conclusions do not apply to convective scalar transfer within these same envi-
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ronments, as scalar transfer occurs via molecular diffusion independently of the
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shape of the obstacles (see e.g., Li et al., 2016b). Note also that using Eq. 6 for the specification of surface stresses, in conjunction with Eq. 7, results in a system of equations that does not depend on the molecular viscosity parameter, hence guaranteeing scaling similarity of solutions (i.e., normalized solutions are
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independent of the imposed friction velocity or outer velocity U∞ ). A more de-
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tailed description of the LES algorithm and specifics on the IBM implementation can be found in Chester et al. (2007).
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2.4.1. Representation of vegetation in the LES
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The term f˜iv is included in the momentum conservation equation (Eq. 4) to
account for the kinematic drag from vegetation elements, and is defined as f˜iv (x, t) = −CV a ˜(x, λ, k)˜ ui k˜ uk2 ,
14
(8)
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where CV is a constant sectional drag coefficient and a ˜ is the spatially-filtered (filter width = ∆) leaf area density, derived from high-resolution LiDAR measurements. CV = 0.2 is assumed, which is the optimized value determined by Katul and Albertson (1998) and used in Krayenhoff et al. (2015).
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Vegetation drag is set proportional to a velocity squared, in line with previous studies of flow over vegetation canopies (Shaw and Schumann, 1992b; Finni-
gan et al., 2009b). This implies that leaves elements are assumed to be in fully rough regime (i.e., the total drag from vegetation elements is form drag), which 305
is an acceptable approximation within the goal of the current study (Thom,
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1968; Brunet et al., 1994).
In addition, it is known that the turbulent wakes behind vegetation elements, resulting from the action of pressure and viscous drag on branches and leaves, yield a transfer of energy from the mean flow and from larger-scale turbulence 310
to smaller-scale turbulence, thus short circuiting the inertial energy cascade (e.g., Wilson, 1988; Poggi et al., 2004; Cava and Katul, 2008). Wake turbulence
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dissipates quickly, but it is a non-negligible contribution to the SGS kinetic energy budget (Shaw and Patton, 2003), and should therefore be accounted for
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in 1.5-order closure schemes, in which SGS TKE is predicted with a prognostic energy equation.
First-order algebraic LES closures – such as the dynamic Smagorinsky model
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used herein – are relatively simple and do not carry information on SGS energetics. As such, they are not amenable to modifications to account for the
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aforementioned effects induced by wake motions on SGS dynamics. This might 320
limit their applicability in flows over vegetation when the canopy occupies a significant fraction of the airspace, thus constantly sustaining small-scale wake
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turbulence and affecting SGS dissipation rates. However, the behavior of Smagorinsky models is expected to improve when
used in flows within explicitly resolved sparse canopies with sub-tree grid reso-
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lution as in the current settings. Under such conditions the energetic range of wake motions, which are about the size of full vegetation elements (Cava and Katul, 2008), is explicitly resolved by LES, whereas SGS wake turbulence is 15
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expected to survive over a limited portion of the overall airspace. This is due to the sparsity of trees and to the rapid dissipation rates of SGS wake energy, 330
which support the working conjecture that SGS wake energy can be neglected
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with little loss in accuracy in the predicted velocity field.
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2.4.2. Setup of LES simulations
Figure 2: Pseudocolor plot of the instantaneous streamwise velocity field corresponding to
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simulation S4SV W (see Table 1).
To quantify the effect of vegetation on mean flow and turbulence over and
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within the selected urban canopies (S1, S2, S3 and S4 in Fig. 1), three vegetative configurations are considered for each surface, namely
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• Urban surfaces with no vegetation (NV); • Urban surfaces with wintertime vegetation (WV); • Urban surfaces with summertime vegetation (SV).
Table 2 displays the overall LAI for the S1, S2, S3 and S4 canopies in the sum340
mertime, which are based on LiDAR data. The LiDAR-derived a ˜(x) has been 16
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rescaled so that for a 1 × 1 km2 surface centered around the measurement tower the LAI matches the one reported in Liss et al. (2013) for the same area. To simulate wintertime vegetative conditions the LAI value of each surface is reduced
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by an estimated factor of 3, based on separate LAI determined for broadleaf and coniferous trees in the study area by Liss et al. (2013), assuming broadleaf trees are all deciduous and considering the effect of trunks and branches to the total projected area in winter. Table 1 summarizes the setup of all simulations.
Table 1: Summary of simulation parameters. Surfaces correspond to those displayed in Fig. 1.
Lx , Ly , Lz and Nx , Ny , Nz denote the domain size and number of collocation nodes in the
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x, y, z coordinate directions, and α denotes the approaching wind direction (α = 180◦ → wind approaching from south, and α = 270◦ → wind approaching from west). Notation: S1α β, α = NV (no vegetation) or α = WV (winter vegetation) or α = SV (summer vegetation); β = W (wind from west) or β = S (wind from south).
Label
surface
Lx × Ly × Lz (m)
Nx × Ny × Nz
α (deg)
LAI
NV S1NV W , S1S
410 × 210 × 96
320 × 160 × 192
180, 270
0
S1WV S
S1
320 × 160 × 192
0.094
S1SV S
410 × 210 × 96
180, 270
S1SV W ,
S1
320 × 160 × 192
180, 270
0.282
NV S2NV W , S2S
410 × 210 × 96
S2
410 × 210 × 96
320 × 160 × 192
180, 270
0
S2
410 × 210 × 96
320 × 160 × 192
180, 270
0.082
S2
410 × 210 × 96
320 × 160 × 192
180, 270
0.246
S3
380 × 410 × 96
320 × 320 × 192
180, 270
0
S3
320 × 320 × 192
180, 270
0.152
SV S3SV W , S3S
380 × 410 × 96
S3
320 × 320 × 192
180, 270
0.458
NV S4NV W , S4S
380 × 410 × 96
S4
974 × 620 × 192
512 × 320 × 384
180, 270
0
S4
974 × 620 × 192
512 × 320 × 384
180, 270
0.117
S4
974 × 620 × 192
512 × 320 × 384
180, 270
0.351
S2WV S
S2SV W ,
S2SV S
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NV S3NV W , S3S
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S2WV W ,
S3WV S
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S3WV W ,
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S4WV W ,
S4WV S
SV S4SV W , S4S
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S1
S1WV W ,
Two approaching wind directions are considered for each surface, namely
west and south, corresponding to situations excluding the sectors influenced by
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sensor mounting and the unusually tall school-building to the East (see Fig. 1). The Cartesian reference system in each case is chosen so that the x axis points 17
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in the streamwise direction, and the y axis points in the spanwise direction (the reference system displayed in Fig. 1 corresponds to that used in simulations with west approaching wind angle). To evaluate z0 in equation 6 the approach of Giometto et al. (2016) is adopted, which results in z0 = ∆/15 for the considered
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runs. Simulations are initialized imposing a velocity field obtained from LES at
twice as coarse resolution for each case, corresponding to a condition of dynamic equilibrium of the system (Monin, 1977). LES are then run for an additional
T ≡ h/u∗ = 400 and temporal averaging is carried out over the last T = 150. This yields well converged statistics throughout the boundary layer.
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3. Averaging
The intrinsic double averaging (DA) approach is used herein (Nikora et al., 2007). Within the DA framework, a generic variable θ(x, y, z, t) can be decom-
(9)
and a fluctuation component (θ0 ≡ θ − hθi). Specifically, the intrinsic spatial
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posed into a space and time average component Z Z Z Z 1 1 hθi(z) ≡ θ(r, τ )dV dτ , T T VF (z) VF (z)
averaging is here performed first, over horizontal slabs of total volume VF (z) = Lx × Ly × ∆z in the fluid domain only, and the time averaging is performed
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afterwards.
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4. Results and discussion Using data from the airborne LiDAR, from LES runs and from turbulence
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instruments on the tower, we identify, isolate and discuss the importance of the
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urban tree canopy on flow and turbulence above and within the urban canopy. Section 4.1 summarizes the characteristics of the urban building and vege-
tation layers extracted from LiDAR. In section 4.2 we then present the effect
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of trees on integral scaling parameters z0 and d. Next, we quantify turbulence characteristics and turbulent exchange in the ISL (Section 4.3) and provide a
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detailed analysis of the vertical exchange of momentum and energy in the RSL (Section 4.4).
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4.1. LiDAR derived characteristics of buildings and vegetation Relevant geometric statistics for the subsets S1, S2, S3 and S4 extracted from
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the LiDAR point cloud are reported in Tab. 2. The range of plan area fractions of buildings (λbp ≡ Abp /A0 ) and frontal area fractions of buildings (λbf ≡ Abf /A0 )
in absence of vegetation, classify the selected surfaces as moderately dense with a wake-interference type flow regime (Oke, 1988; Britter and Hanna, 2003; Barlow,
2014). Here, Abp (m2 ) is the total plan area of buildings, Abf (m2 ) is the total
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frontal (silhouette) area of buildings, and A0 ≡ Lx × Ly (m2 ) is the total planar area of the considered subset. The tree canopy cover (plan area fraction of trees, λvp ≡ Avp /A0 ranges between 9 and 13%, and matches well the reported 11% for a
1.9 × 1.9 km box surrounding the tower (Kellett et al., 2013). λvp is substantially 390
lower that the average tree canopy cover for the City of Vancouver with 18%
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(City of Vancouver) and lower than the tree canopy coverage reported for US North-Western urban forests of 33% in (Nowak and Crane, 2002). The four
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considered surfaces S1, S2, S3 and S4 are relatively similar in terms of geometry of building and vegetation characteristics, S3 has a slightly higher amount of 395
taller trees and a higher LAI, whereas S2 is the most sparsely vegetated subset.
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As is typical of realistic urban canopies, and in contrast to uniform-height, synthetically-generated cube-array surfaces, the building plan and frontal area fractions are a function of z throughout the RSL. The vertical structure of
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the buildings plan and frontal area fractions, as well as the vegetation plan
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area fraction and vertical profiles of the horizontally-averaged (fluid only) leaf
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area density (h˜ ai), important parameters from a aerodynamic perspective (Di
Sabatino et al., 2008), are shown in Fig. 3. Figure 4 depicts the probability density function (pdf ) of building and veg-
etation height for the S4 surface (qualitatively similar to those of the other
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canopies, which are not shown). The building height distribution is characterized by three principal modes at z ≈ 1 m, z ≈ 3 m and z ≈ 6 m, corresponding 19
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Table 2: Relevant statistics of buildings and vegetation of the modeled urban canopy subsets in simulations S1, S2 and S3 and S4. S4 corresponds to the full surface displayed in Fig. 1. hb
and hv denote the height of an individual building or vegetation element (tree, bushes, etc.),
respectively. h ≡ mean (hb ) + σhb , where σhb is the standard deviation of buildings height. v b b λb p and λp are the plan area fraction of buildings and vegetation, respectively. λf,west , λf,south
denote the frontal area fraction of buildings with respect to west and south approaching wind
Unit
S1
S2
S3
S4
4.5
4.6
4.4
4.5
8.3
8.9
9.0
9.0∗
6.6
6.7
6.3
6.7
0.340
0.337
0.309
0.282
–
0.199
0.201
0.158
0.161
–
0.182
0.186
0.155
0.152
Buildings m
max (hb )
m
h
m
λbp
–
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λbf,south
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mean (hb )
λbf,west
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directions. LAI denotes the summer leaf area index of the canopy.
Vegetation
m
3.5
3.0
4.6
3.84
max (hv )
m
25.2
20.7
26.2
26.2
λvp
–
0.108
0.088
0.128
0.109
LAI
–
0.282
0.278
0.430
0.35
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mean (hv )
* the unusually tall school building has been artificially reduced to 9 m height,
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to homogenize the surface and reduce undesired propagation of wake motions from such a structure in the inlet boundary (due to the prescribed periodic boundary conditions).
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Figure 3: Top left: vertical structure of the building plan area fraction Ab p /AT . Top right: frontal area fraction dAf /dV as seen by west (black lines) and south (red lines) approaching wind. Bottom left: vertical structure of the vegetation plan area fraction Avp /AT . Bottom right: vertical structure of the horizontally averaged leaf area density h˜ ai(z) in the summer
PT
season. Different line-styles correspond to different subsets (see legend).
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to short surface elements (e.g., fences, landscaping), to one and to two storey houses, respectively. Conversely, the vegetation height distribution decreases rapidly from its surface value, indicative of a large number of small plants and shrubs.
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4.2. Vegetation effects on integral scaling parameters z0 and d in the ISL The aerodynamic roughness length (z0 ) and the zero-plane displacement (d)
are key parameters to properly simulate flow and turbulence over urban areas at city to regional scale in weather prediction, air quality dispersion, hydrology 21
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Figure 4: Binned p.d.f. of the roofs height (left) and of the vegetation height (right) for the
415
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S4 canopy (see Fig. 1).
and climate models (Stensrud, 2007). Current morphometric methods employed to estimate z0 and d from urban form do not consider urban vegetation at all (Grimmond et al., 1998), despite its ubiquity. To address this issue, the dependence of z0 and d on urban vegetation is explored in this section.
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Table 3 compares the LES modeled and corresponding tower measured d and z0 parameters. In both cases, values for each surface in different vegetation
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conditions are proposed (no vegetation, leaves-off and leaves-on). z0 is evaluated from the LES runs via logarithmic fit of the LES h˜ ui i(z) velocity in the range p −1 3 < z/h < 5, with fixed u∗ ≈ Lz kFi k = 1 (m s ), assuming κ = 0.4, and
425
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relating the displacement height d to the center of action of the drag force from buildings and vegetation (Jackson, 1981). The fitting interval was chosen based
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on the observed velocity profiles, which display a logarithmic behavior down to z − d ≈ h in most cases (see e.g. mean velocity profiles for cases over the S4 subset displayed in Fig. 5). Logarithmic velocity profiles well within the UCL
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(z ≤ max (hb , hv )) were previously reported in the wind tunnel measurements
430
of Cheng and Castro (2002) for flow over urban-like surfaces, in LES of flow over surface mounted cubes of variable height in Yang et al. (2016), and in LES over surface mounted rectangular prisms with high aspect ratio in Sadique et al. (2016). Unlike LES, direct tower measurements cannot be used to determine the
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Figure 5: Left: DA (intrinsic) streamwise LES velocity over the S4 canopy for west (black lines) and south (gray lines) wind approaching directions. Symbols: solid lines, no vegetation cases; dashed lines: winter vegetation cases; dot-dashed lines: summer vegetation cases. A reference logarithmic profile is shown in red. Center: % increase in z0 as a function of LAI/λb f. Right: % increase in d as a function of LAI/λb f.
435
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flow characteristics in complete absence of trees. However, tower measurements allow one to study the effect of varying LAI on mean wind and momentum
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transfer by conditionally sampling and comparing leaves-off (between November to February), and leaves-on season (between May to September). Using a SV WV SV fixed d/h = 0.81 (average over the S4WV W , S4W , S4S , S4S LES runs), z0 is
440
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calculated based on tower measurements for each block satisfying the (neutral) stability and wind-direction requirements, inverting the logarithmic wind profile
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equation, following Grimmond et al. (1998): ku z0 ≡ (z − d) exp , u∗
(10)
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with mean horizontal wind u and friction velocity u∗ directly measured by the eddy-covariance system (see Sect. 2). Note that since ln (zt ) ≈ ln (zt − d)
variations in d results in minor changes in the resulting z0 , hence the choice
445
of using a fixed d. This choice also ensures that the two approaches (LES and tower measurements) remain independent. Computing d as center of action of the surface drag forces predicts a signif23
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Table 3: Aerodynamic roughness lengths and displacement heights for the considered cases. For the LES runs the displacement height d is computed as center of action of the sum of drag forces from the building and vegetation canopies (hf˜ib i(z) and hf˜iv i(z) respectively), whereas z0 is obtain by linear fit of the LES h˜ ui i(z) velocity in the range 3 < z/h < 5. The
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displacement height for tower measurements is computed as average from the LES runs S4WV W , WV , S4SV and roughness lengths are evaluated as z ≡ (z − d) exp (−uκ/u ), where S4SV t ∗ 0 W , S4S S
zt denotes the measurements height and u and u∗ are the time-averaged velocity and frictionvelocity at the tower sampling location. Tower data from all wind sectors SE to NW have
been equally weighted into 15◦ bins to remove directional effects. Near-Neutral conditions (−0.075 < (z − d)/L < 0.075) and wind > 2 ms−1 , RMSE(α) < 15◦ , and 150◦ < α < 300◦ . Summer is day of year (DOY) 121 to 274. Winter is DOY 305 to 59.
Wind
No veg. d/h
West
0.54
S1
South
0.61
S2
West
0.54
S2
South
0.62
S3
West
S3
South
S4
d/h
z0 /h
d/h
z0 /h
0.056
0.77
0.078
0.89
0.094
0.041
0.84
0.069
0.89
0.087
0.055
0.66
0.069
0.69
0.075
0.044
0.73
0.056
0.77
0.068
0.049
0.97
0.096
1.06
0.130
0.53
0.083
1.01
0.088
1.11
0.124
West
0.48
0.056
0.75
0.086
0.84
0.106
South
0.52
0.048
0.79
0.077
0.88
0.102
150 < α < 300
—
—
0.81
0.119
0.81
0.142
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0.50
S4 Tower
Summer veg.
z0 /h
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S1
Winter veg.
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Surface
icant increase in both d and z0 as a function of LAI/λbf , as displayed in Fig. 5
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and tabulated in Tab. 3, highlighting the important role of vegetation elements
450
in affecting the aerodynamics of the flow over the considered realistic urban
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settings.
LES runs predict variations of d from the leaves-off and leaves-on cases be-
tween +5% and +15%, due to significant contributions to the overall drag force that taller trees are exerting on the flow, despite their modest plan area fraction
455
Avp /AT (see Fig. 3). Corresponding variations in z0 are between +10% and +40%. It is also apparent that in complete absence of trees z0 would dramat-
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0.30
2.0
95% 75% Mean
1.5
0.20 0.15 0.10 615
660
1035
967
504
537
226
318
452
514 844
549
0.05 0.00
J
F
M
A
M
J
J
A
S
O
N
Month of the year
D
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1.0
50% 25% 5%
z0 (m)
z0 / hb
0.25
0.5 0.0
Leaves-on Transition
Leaves-off
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Figure 6: Aerodynamic roughness length (z0 ) measured on the tower at a height of zt = 24.4
m and sorted by month of the year (see Sect. 2.3 for additional details). The numbers under each category refer to the number of half hourly measurements represented in the statistics.
ically decrease, down to more than half of their reference summer values for the 2 / LAI/λbf / 3 cases. In complete absence of trees d is also significantly
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reduced.
Specifically, z0 and d both display a sub-linear dependence on LAI/λbf , high-
460
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lighting how increasing LAI results in additional sheltering induced by vegetation on buildings and on other vegetation elements. Sheltering between roughness elements is known to be an important dynamical mechanism, responsible
465
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to reduce the overall drag that a surface exerts on the flow in the high λbf or LAI range (Macdonald et al., 1998; Raupach, 1992; Yang et al., 2016; Sadique et al., 2016). Conversely, the strong non-linear dependence of d on LAI/λbf can
d∼
LAIHv + λbf Hb , LAI + λbf
(11)
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be justified by considering that
where Hv and Hb are reference heights for the vegetation and buildings elements.
Equation 11 is a simplified version of the formula for the evaluation of the center
470
of action (barycenter) of buildings and vegetation forces (Jackson, 1981). Note that with opportunely chosen Hv and Hb , Eq. 11 well approximates the d dependence on LAI/λbf (not shown).
25
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Figure 6 shows z0 calculated from the tower-data following Eq. 10 for each month of the year. As the leaves emerge in March and April of each year, z0 475
increases to higher summer values, and then with senescence in October, z0
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drops. Overall, the conditionally sampling leaf-off and leaf-on periods on the tower we can identify a statistically significant (T-means test, p < 0.01) in-
crease by 19% from a mean normalized z0 /h = 0.119 (0.80 m) during leaves-off
to z0 /h = 0.142 (0.95 m) in the leaves-on season. LES determined z0 for the 480
full subset are 32% and 27% lower than the measured values on the tower, with
winter and summer vegetation, respectively. For subsets S1 and S3 which are
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most representative for the tower footprint, the LES are 36% and 11% lower than tower measurements in summer, and 38% and 23% lower in winter, re-
spectively. We relate such trends to the lack of information in the LiDAR data 485
(e.g., fences, chimneys, power lines) when compared to reality – resulting in an aerodynamically smoother urban canopy – and to the gentle orography that was removed in simulations to enable the use of periodic boundary conditions in the
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horizontal directions (x, y). Nevertheless, LES predictions fall in the interquartile range in all but two months (see Figure 6), validating both approaches and highlighting once more how vegetation effects on aerodynamic parameters can be significant.
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4.3. Vegetation effects on integral turbulence statistics in the ISL Table 4 shows a comparison of dimensionless integral turbulence statistics evaluated at z = 24.4 m height between tower measurements and intrinsically DA LES over the S4 canopy. Note that DA LES statistics include dispersive
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contributions due to the chosen order of averaging operations (spatial averaging
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is performed first). Normalized streamwise and vertical velocity fluctuations (σu /u∗ , σw /u∗ ) and the turbulent momentum exchange efficiency (ruw , correlation coefficient between vertical wind and horizontal wind) indicate that tower
500
measurements are in the ISL irrespective of leaf situation, as they follow closely the neutral limits of the surface layer as predicted by MOS. No statistically significantly seasonal changes (T-means test, p < 0.01) is observed for such 26
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Table 4: Comparison of dimensionless integral turbulence statistics at z = 24.4 m height between tower measurements and DA LES. LES results are representative of flow over the S4 canopy, averaged over the west and south approaching wind directions and separated into “no vegetation”, “leaf-off” (winter) and “leaf-on” (summer) conditions. Tower-measured
refers to the surface layer neutral limits (Panofsky, 1984).
Tower
SL
Winter
Summer
No trees
Winter
Summer
σu /u∗
2.310
2.323
2.35
2.30
2.32
2.2
σw /u∗
1.206
1.209
1.16
1.17
1.175
1.25
ruw
-0.366
-0.365
-0.364
-0.372
-0.366
Skw
0.142
0.204
0.177
0.150
0.118
TKE / MKE
0.155
0.174
0.071
0.089
0.104
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Parameter
LES
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quantities are separated into “leaf-off” and “leaf-on” conditions as described in Sect. 2.3. SL
-0.36
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quantities in measurements, and LES further support such a finding. Measurements predict a positive Skw , as is typical of surface layers (SLs), 505
which is observed in 90% and 87% of all cases in summer and winter, respec-
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tively, indicating the distribution is skewed to more positive values (updrafts less frequent but more intense). The skewness increases statistically significant
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(T-means test, p < 0.01) by 44% from a mean of 0.142 during leaf-off to a more skewed value of 0.204 in the leaf-on season (Tab.4). In contrast with mea510
surements, LES of flow over the S4 surface, averaged over the west and south
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approaching wind directions, predict a 15% and 33% decrease in Skw at z = 24.4 m from the no-vegetation to leaf-on and from the leaf-off to leaf-on cases, respectively. It should be noted that simulations over the S4 surface are characterized
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by a large max (hv , hb )/Lz ratio, which ensures that turbulence statistics (in-
515
cluding Skw ) up to z ≈ 5h are poorly dependent on the vertical extent of the computational domain (the sensitivity of flow statistics on Lz was tested using
half the current spatial resolution and is not shown). The most plausible reason for such a mismatch is hence the inability of LES to account for thermally
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95%
0.30
50% 25% 5%
0.25 0.20
Leaves-on
0.15 1035
615
0.10
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TKE / MKE
75% Mean
J
967
537
504
318
452
226
514 844
660
F
549
Transition
Leaves-off
M
A
M
J
J
A
Month of the year
S
O
N
D
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Figure 7: TKE to MKE ratio measured on the tower at a height of zt = 24.4 m and sorted
by month of the year (see Sect. 2.3 for additional details). The numbers under each category refer to the number of half hourly measurements represented in the statistics.
induced large-scale outer-layer structures, which are likely to influence Skw via 520
their interaction with the underlying canopy. The vertical structure of Skw from
quantity is provided.
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LES is described and commented in Sect. 4.4, where further insight on such a
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Figure 7 shows the ratio of turbulent to mean kinetic energy measured at 24.4 m. The ratio TKE / MKE increases statistically significant (T-means test, 525
p < 0.01) by about 12% from a mean of 0.155 during leaf-off to a value of 0.174
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in the leaf-on season (Tab.4). Again, clearly as leaves emerge in March and April, the ratio TKE/MKE increases and in fall drops again. This is explained
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by the increased roughness of the leaved canopy which converts more MKE and large-scale TKE to small-scale “wake” TKE. TKE/MKE increases in LES
530
from no-vegetation to leaf-on (summer) cases, and displays a 17% gain between
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the leaf-off and leaf-on season, in qualitative agreement with results from tower measurements. However, not surprisingly, LES predicts lower TKE/MKE ratios when compared to measurements. This can be again justified by the presence of outer layer flow structures that the LES does not include, which are an
535
important contribution to the overall TKE and are not affected by the local
28
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surface as shown in Roth and Oke (1995) for this site. A significantly larger computational domain would be required to account for such structures, which
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is beyond current computational capabilities. 4.4. Vegetation effects on momentum and energy transfer rates in the RSL The DA momentum equation reads
540
(12)
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1 d −Fx = [−ϕ(h˜ u0 w ˜ 0 i + hτxz i)] |{z} ϕ dz | {z } | {z } Forcing SGS Turbulent Z b 1 ˜ ˜ + (f + τ xj nj ) dΓ + hfxv i , |{z} Vf (z) Γb (z) x | {z } Vegetation Buildings
where (·) denotes temporal averaging, ni is the normal-to-interface (Γb ) vector pointing into the fluid domain, ϕ(z) ≡ (1−λbp ) and Vf ≡ ϕ(Lx ×Ly ×∆z ) are the area fraction of fluid and the volume of fluid at a given height (z), h˜ u0 w ˜0 i
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545
and hτxz i are the turbulent (including dispersive) and SGS kinematic stresses, b R 1 ˜ Vf (z) Γb (z) (f x +τ xj nj ) dΓ is the kinematic drag force that buildings are exerting
on the flow (sum of a normal and a deviatoric component), and hf˜xv i ≤ 0 is the
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kinematic drag force from trees.
Fig. 8 features selected components of the kinematic stress balance (Eq. 12). Profiles are qualitatively representative of the other LES runs. Below max hb , the largest contribution to the total canopy drag force is from
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550
buildings, and results in an approximately linear vertical momentum flux con-
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tribution, from the reference (negative) surface value to zero at z = max (hb ). Conversely, a significant portion of the vegetation drag force is exerted above
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555
max (hb ), resulting in a monotonic decrease of the corresponding momentum R hmax flux ( z v hf˜xv i dζ) at such heights, with direct impact on the turbulent flux
term h˜ u0 w ˜ 0 i, which experiences an equal decrease in magnitude (note that the to-
tal normalized momentum flux is the same among simulations). Throughout the runs, the downward flux of momentum from turbulent motions is decreased from the “no-vegetation” to the “leaves-on” cases within the UCL (z < max (hb , hv )).
29
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Figure 8: Vertical structure of the turbulent momentum flux (h˜ u0 w ˜ 0 i, black lines), total drag b R hmax 1 R ˜ b from buildings ( z (f + τ xj nj ) dΓdζ, gray lines), and from vegetation eleVf (ζ) Γb (ζ) x R max ments ( zhv hf˜xv i dζ, red lines). Profiles are representative of simulations over the S4 surface, west wind approaching angle. Different line styles denote different runs: S4NV W , solid lines; SV S4WV W , dashed lines; S4W , dot-dashed lines. SGS contributions are negligible throughout the
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boundary-layer and hence not shown. A smaller portion of the total domain height is shown.
uih˜ u0 w ˜ 0 i) 1 d(ϕh˜ , ϕ dz
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Figure 9: Turbulent transport of mean kinetic energy (Tt ≡
black lines),
production of MKE by the imposed pressure gradient (PΠ ≡ Fx h˜ ui, grey lines), and sink of
MKE from the work of vegetation drag (Pv ≡ hf˜xv ih˜ ui , red lines) for simulations over the S4 surface, west wind approaching angle. Different line styles denote different simulations: S4NV W ,
SV ∗ solid lines; S4WV W , dashed lines; S4W , dot-dashed lines. (·) is used to denote normalization
of each term by (u3∗ /h). A smaller portion of the total domain height is shown.
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To better quantify the impact of vegetation on the mean flow, Fig. 9 features
560
the vertical structure of selected terms of the mean kinetic energy (MKE) budget equation. It is apparent how vegetation has a twofold effect on MKE in the
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considered urban canopies: on one hand, it is a direct sink of MKE via its work against the mean flow (Pv ), proportional to the LAI characterizing a given 565
canopy. On the other hand, its impact on h˜ u0 w ˜ 0 i and h˜ ui (via the work that
f˜iv performs against the mean flow) results in a significant decrease of MKE downward turbulent transport (Tt ) below max (hb ). At such heights where
people live and buildings consume energy, Tt is the major source of MKE (Tt LAI results in a substantial decrease of wind speed magnitudes.
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570
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Fx h˜ ui > 0), and is thus no surprise that reductions in such a term with increasing
Figure 10: Vertical structure of the horizontal (left) and vertical (right) velocity skewness
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for LES cases over the S4 surface west (black lines) and south (red lines) approaching wind angles. Symbols: solid lines, no vegetation cases; dashed lines, leaves-off cases; dot-dashed
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lines, leaves-on cases.
Based on Fig. 10 it is clear how the upper RSL is dominated by ejections,
while the lower RSL and urban canopy layer show a dominance of sweeps in the turbulent momentum exchange, which is in agreement with several field studies within and/or above urban canopies (Rotach, 1993; Oikawa and Meng,
575
1995; Christen et al., 2007). As vegetation is added Sku and Skw increase in 31
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Figure 11: Difference between the two-dimensional histogram of h˜ u0 w ˜ 0 i at z = hb for simu-
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WV NV SV lations S4NV ˜0 /u∗ and w ˜ 0 /u∗ sampled W , S4W (left) and S4W , S4W (right). Point clouds of u
in the plane z = hb have been uniformly binned in a two dimensional histogram for each simulation and the difference between the two dimensional histograms for the cases without and with vegetation are displayed. Red, white and black dots denote a decrease, no changes, and increase in the number of observations that fall within a given bin.
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magnitude within the UCL, highlighting a more intermittent turbulence field, which favors u ˜0 > 0 and w ˜ 0 < 0 fluctuations (i.e., sweep motions). The height of
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the crossover for Sku and Skw also increases with the addition of vegetation and with increasing LAI, highlighting how the presence of irregular sparse roughness 580
with irregular heights results in a thicker RSL. Note that even in the absence of
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vegetation, the height of the crossover at z/h = 1.38 is higher than the crossover of z/h = 1.25 observed in simulations over cubical obstacles of uniform height
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(Coceal et al., 2007a) but comparable to the crossover in neutral conditions at z/h = 1.5 over a denser urban canopy without significant trees (Christen et al.,
585
2007).
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Figure 11 provides a qualitative description how turbulent fluctuations con-
tributing to h˜ u0 w ˜ 0 i at z = hb are modified by vegetation. The specific cases of flow over the S4 surfaces with wind approaching from west are considered WV SV (S4NV W , S4W and S4W ). As is apparent, including vegetation results in a pro-
590
gressive damping of streamwise fluctuations u ˜0 (red areas) contributing to both quadrant 2 and quadrant 4 events, reducing the variance of the u ˜0 probability 32
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density function. This behavior is consistent among the considered cases. Note also how the sparse vegetation suppresses ejections more effectively than sweeps, in line with the observed increase in the Sku and Skw magnitude at hb (see Fig. 10). In an absolute frame, sparse vegetation thus tends to make the turbulent
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595
field more isotropic in the lower RSL. Accordingly, in addition to a direct fluid dynamical implication, including vegetation has potential benefits from an urban comfort perspective, as gusts affecting pedestrians, and dynamical pressure
600
5. Summary and Conclusions
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variations that cause building energy losses are minimized (“sheltering effects”).
This research explored the role of trees over a realistic urban canopy using a combination of detailed LES, eight years of continuous measurements, and airborne LiDAR data to map and describe the detailed urban form and leaf area density. Unlike previous computational fluid dynamics simulations that investigated the effect of urban trees on pollutant dispersion in idealized streets,
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605
the current study focused on how trees and changing leaf area density affect the neighborhood-averaged flow and turbulence fields. A number of surfaces were
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considered, representative of a typical suburban area of Vancouver, Canada, where a small fraction of trees are taller than buildings. LES and tower measurements showed that aerodynamic roughness lengths
610
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(z0 ) are sensitive to variations in the 0 ≤ LAI/λbf < 3 parameter for each of the considered canopies. Specifically, z0 increments were characterized by a
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sub-liner dependence on LAI/λbf for each of the considered canopies, indicative of additional sheltering occurring between vegetation elements as well as be-
615
tween vegetation and buildings as LAI increases. z0 from LES fell within the
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interquartile range of corresponding values from tower measurements, but mean z0 values were underpredicted by approximately 30% in the LES runs over the S4 surface (the most representative of what the tower sees). Such a behavior is mostly due to lack of information in the LiDAR measurements when compared
620
to real settings (power lines, chimneys, fences) and to the gentle orography that
33
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was not considered in simulations. Specifically, the aerodynamic roughness determined from tower measurements was seasonally changing with a statistically significant 19% increase from leaf-off season (z0 /h = 0.119) to the leaf-on season
625
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(z0 /h = 0.142). Similarly, LES results over the S4 subset averaged over south and west wind approaching directions found a seasonal change in z0 with an
increase by 27% from the winter (LAI/λbf = 0.74, z0 /h = 0.081) to the summer
season (LAI/λbf = 2.24, z0 /h = 0.104). LES also showed that in the absence
of vegetation z0 would experience a significant decrease, down to over 50% its reference summer value in most cases.
The zero-plane displacement d, computed as center of action of the total
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630
surface drag from LES, was found to also increase as a function of the LAI/λbf parameter, mostly due to the disproportionate amount of drag that the (few) relatively taller trees exert on the flow.
Integral statistics σu /u∗ , σw /u∗ and ruw at the measurement height of the 635
tower (z/h = 3.75, where h ≡ mean(hb ) + σhb ) were not subject to any seasonal
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change (evidence provided by both measurements and LES). They followed predicted surface layer values in summer and winter, hence at such a height and
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above, we can expect a well-developed ISL in which the neutral limits of MOS are fulfilled. Statistically significant increases between leaf-off and leaf-on cases 640
were found at z/h = 3.75 in the ratio of TKE to MKE (+12% in measurements,
PT
+17% in LES over the S4 canopy averaged between west and south wind approaching direction), but the magnitude from LES were over 50% smaller than
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the corresponding measured quantity. Furthermore, LES and tower measurements predicted a positive vertical velocity skewness (Skw > 0) at the tower
645
sampling location, as is typical of atmospheric surface layers where ejections of
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low momentum fluid are the main contribution to the total momentum flux. However, tower data were characterized by an increase in Skw from winter to
summer, whereas LES data predicted a decrease in such a quantity in that same period. The most plausible reason for such a mismatch in both TKE/MKE and
650
in Skw is the inability of LES to account for thermally induced large-scale outer-layer structures, which are likely to influence such flow statistics via their 34
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interaction with the underlying canopy. The analysis of the vertical transfer of momentum in the LES showed how trees exert a significant portion of the total drag in both the winter and the summer season, thus reducing pressure loads on buildings. In most cases, the
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655
total drag from vegetation elements during the summer season was even larger than that of buildings. In addition, as vegetation is added Sku and Skw increase in magnitude within the UCL, highlighting a more intermittent turbulence field
favoring sweep motions, and resulting in higher locations in sign crossover for 660
both statistics. From the quadrant analysis that was performed at z = hb , it is
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also apparent that including vegetation results in a progressive damping in the magnitude of streamwise fluctuations u0 , thus reducing extreme wind events in the UCL, with potential benefits from an urban comfort perspective.
Lastly, the analysis of selected mean kinetic energy budget terms in the LES 665
showed that urban trees influence the flow in the RSL twofold: on one hand, trees are a direct sink of MKE via the work of their drag force against the
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mean flow; on the other hand, they reduce downward turbulent transport of high momentum fluid from higher atmospheric layers. Given that most of the
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MKE in the lower RSL is generated by downward transport from large organized turbulent motions, it is apparent how the specific shape, clumping and density of urban vegetation controls flow at the height where people live in a city, hence
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suggesting the need for careful landscape architecture design strategies. With more than 50% of the global population now living in cities (United
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Nations, 2014), the atmosphere which the majority of us experiences is not a 675
classical surface layer, but the roughness sublayer embedded within and above urban canopies. In many cities of the world, trees are important elements of the
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urban form, and also a design tool to mitigate adverse effects on pedestrians, provide shelter and shade, mitigate heat stress, and conserve energy in buildings. However, trees also affect the dispersion of air pollutants emitted at ground level
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negatively (e.g. Salmond et al., 2013). Our current ability to incorporate the effect of trees in ULSMs is limited, but the current study shows that the role of trees and their seasonally changing leaf area density (a) in cities has a crucial 35
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effect on both, turbulence and flow in the ISL above vegetated cities and flow an turbulence in the urban roughness sublayer, including at street level and 685
these effects should be considered in next-generation ULSMs. This may help in
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future to make improved predictions that benefit the management of air quality, heat stress and generally assist the planning of energy efficient and intelligently designed cities.
Acknowledgements
This research was funded by the Swiss National Science Foundation (SNSF-
690
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200021-134892), the Competence Center for Environmental Sustainability (CCESSwissEx) of the ETH domain, the NSERC Discovery Grant program (Parlange, Christen). Selected instrumentation was supported by the Canada Foundation for Innovation (Grant 33600). Numerical simulations were supported by a grant 695
from the Swiss National Supercomputing Centre (CSCS) under project ID s633.
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We are grateful to the peer reviewers whose comments helped to improve the overall quality of the manuscript.
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Appendix A. Grid resolution requirements To assess the resolution requirements for the LES runs the subset S1 is selected with west wind approaching direction and summer vegetation conditions
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(similar to case S1SV W ). Four different resolutions are considered, as indicated
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in Fig. 12, and quantities such as the mean turbulent kinetic energy (TKE ≡ (1/2)h˜ u0i u ˜0i i) and the mean rate of TKE shear production (Ps ≡ h˜ u0 w ˜ 0 i(dh˜ ui/dz)) are inter-compared. The second quantity is often used as indicator of the quality of a numerical solution, as it encodes information on both mean flow and tur-
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bulence. The grid stencil in the vertical direction (∆z = 0.5 m) is not modified across the considered runs and only the horizontal grid stencils are varied, from a maximum of ∆x ≈ ∆y = 3.14 (m) to a minimum of ∆x ≈ ∆y = 1.04 (m).
Varying only the horizontal grid stencil is justified considering that the vertical 710
resolution is much higher than the horizontal across the various cases. Note 36
Figure 12: (1/2)h˜ u0 u ˜0 i)
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Comparison of time- and space-averaged turbulent kinetic energy (TKE ≡
(left plot) and TKE production rate (Ps ≡ h˜ u0 w ˜ 0 i(dh˜ ui/dz)) (right plot) for
case S1SV W (see Table 1 for details) at different spatial resolutions.
that the coarser among the considered horizontal grid stencils is approximately
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60% larger than that used in the runs over the S4 surface (see Table 1), the second coarser resolution case (Nx × Ny × Nz = 192 × 96 × 168) corresponds to approximately 10% stencil increased when compared to that used in the S4 runs, and the second finer resolution (Nx × Ny × Nz = 320 × 160 × 168) corresponds
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to that used in all the other runs (flow over the S1, S2, and S3 cases).
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TKE and Ps profiles convergenge as the grid stencil is refined. Assuming the finer resolution as reference, largest departures in the TKE magnitude occur in the near surface region for the coarsest run, and at z/h ≈ 2 for the other cases. Large errors in max (Ps ) are also localized in the near surface region
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for the coarsest case, whereas the remaining runs are well converged as such a location, and greatest departures occur near max (Ps ). The latter height is
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where thin shear layers separate from buildings. Such flow features are regions of strong TKE production where small and highly energetic motions set tough
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requirements in terms of grid resolution. The grid convergence study indicates that the chosen resolution for the runs over the S1, S2, and S3 surfaces is fine enough to correctly capture the TKE and max (Ps ) profiles within the RSL. The
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resolution chosen for the S4 runs is slightly larger, and the current convergence tests shows that local variations in the TKE and in Ps with respect to the exact 730
value are bounded to a maximum of 16% and 8% respectively. Such modest
and validate the quality of the proposed LES results.
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