Evaluation of Urban LocalScale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas
Abstract
Nine methods to determine localscale aerodynamic roughness length \((z_{0})\) and zeroplane displacement \((z_{d})\) are compared at three sites (within 60 m of each other) in London, UK. Methods include three anemometric (singlelevel high frequency observations), six morphometric (surface geometry) and one referencebased approach (lookup tables). A footprint model is used with the morphometric methods in an iterative procedure. The results are insensitive to the initial \(z_{d}\) and \(z_{0}\) estimates. Across the three sites, \(z_{d}\) varies between 5 and 45 m depending upon the method used. Morphometric methods that incorporate roughnesselement height variability agree better with anemometric methods, indicating \(z_{d}\) is consistently greater than the local mean building height. Depending upon method and wind direction, \(z_{0}\) varies between 0.1 and 5 m with morphometric \(z_{0}\) consistently being 2–3 m larger than the anemometric \(z_{0}\). No morphometric method consistently resembles the anemometric methods. Windspeed profiles observed with Doppler lidar provide additional data with which to assess the methods. Locally determined roughness parameters are used to extrapolate windspeed profiles to a height roughly 200 m above the canopy. Windspeed profiles extrapolated based on morphometric methods that account for roughnesselement height variability are most similar to observations. The extent of the modelled source area for measurements varies by up to a factor of three, depending upon the morphometric method used to determine \(z_{d}\) and \(z_{0}\).
Keywords
Aerodynamic roughness length Anemometric methods Logarithmic windspeed profile Morphometric methods Source area Zeroplane displacement1 Introduction
The urban environment is arguably the most critical interface between humans and the atmosphere. Considerable progress has been made in understanding and modelling the urban environment across a broad spectrum of topics (e.g. Roth 2000; Arnfield 2003; Stewart 2011; Tominaga and Stathopoulos 2013). Wind speed is critical to the vertical and horizontal exchange of scalars and pollutants, and is important when considering, for example, the construction and insurance of buildings (Walker et al. 2016), pedestrian comfort (Stathopoulos 2006) and renewable energy (Drew et al. 2013). The world’s urban population is expected to increase to 66% by 2050 (UN 2014), and as cities grow outwards and more importantly upwards, larger populations become more exposed to urban wind regimes. Therefore, improved knowledge of urban flow effects is vital to the development of cities.
The prospect of an equilibrium boundarylayer windspeed profile, represented using just a few parameters, is appealing, especially above a rough urban surface with complex flow across numerous length and time scales (Britter and Hanna 2003). Several relationships to describe the spatially and temporallyaveraged windspeed profile above a surface exist, such as the powerlaw profile (Sedefian 1980), the logarithmic profile (Tennekes 1973) and profiles described by Deaves and Harris (1978), Emeis et al. (2007), Gryning et al. (2007) and Peña et al. (2010). A precursor to the use of each method is representation of the zeroplane displacement \((z_{d})\) and the aerodynamic roughness length \((z_{0})\).
Although the magnitude of both \(z_{d}\) and \(z_{0}\) is fundamentally related to surface morphology, assigning appropriate values remains challenging. This is particularly true in city centres, with pronounced variability in roughnesselement heights and density, creating unique, complex surface morphology. Individual tall buildings often rise above midrise buildings, whilst in the suburbs more homogeneous roughnesselement height and density are common.
The numerous methods used to determine \(z_{d}\) and \(z_{0}\) can be grouped into three classes: (i) referencebased, (ii) anemometric and (iii) morphometric. The referencebased method is the simplest, as a neighbourhood is compared to published tables or figures (e.g. Grimmond and Oke 1999; Wieringa et al. 2001; Stewart and Oke 2012) to determine appropriate values. Anemometric and morphometric methods both directly incorporate the unique surface morphology of an area and can account for variations in meteorological conditions (e.g. wind direction, wind speed or stability).
In the present study, highquality databases are used to compare methods to determine \(z_{d}\) and \(z_{0}\) in urban areas. For the study area (central London, UK) the methods employed are: referencebased using aerial photography, anemometric using single and multilevel observations and morphometric using digital elevation databases. Previous studies related to aerodynamic parameters relevant to London (Ratti et al. 2002, 2006; Padhra 2010; Drew et al. 2013; Kotthaus and Grimmond 2014b) have results that vary with the study area, method and gridded datasets (e.g. Evans 2009) used. Overall, the maximum \(z_{d}\) and \(z_{0}\) from these studies are 20 and 2 m, respectively. The objectives are a sitespecific evaluation of: (i) the intermethod variability in aerodynamic parameters, and (ii) the implications for modelling the spatially and temporallyaveraged windspeed profile.
The methodology to determine \(z_{d}\) and \(z_{0}\) through surface morphology is provided for use in the Urban Multiscale Environmental Predictor (UMEP, http://www.urbanclimate.net/umep/UMEP, Lindberg et al. 2016) for the open source geographical information software QGIS.
2 Background
2.1 The Urban Boundary Layer and Logarithmic Wind Law
The urban boundary layer is traditionally subdivided into distinct layers (Fernando 2010), which are determined by urban surface characteristics and mesoscale conditions (Barlow 2014). Surface roughness elements are located within the urban canopy layer (UCL) (Roth 2000; Oke 2007), which experiences highly variable flow as a consequence of the close proximity to roughness elements. The UCL is within the roughness sublayer (RSL) (Roth 2000), of depth \(H_{\textit{RSL}}\). The depth \(H_{\textit{RSL}}\) is typically 2–5 times the average roughnesselement height \((H_{\textit{av}})\) (Roth 2000; Barlow 2014), but can be considerably larger (e.g. Roth 2000, their Table 2), varying with the density (Raupach et al. 1991; Grimmond and Oke 1999; Roth 2000; Oke 2007; Barlow 2014), staggering (Cheng and Castro 2002) and height variability (Cheng and Castro 2002) of roughness elements, as well as meteorological conditions (Roth 2000). Idealized physical models (Cheng and Castro 2002; KastnerKlein and Rotach 2004; Xie et al. 2008), largeeddy simulations (LES) (Giometto et al. 2016) and observations in a dense urban setting (Grimmond et al. 2004) suggest the minimum \(H_{\textit{RSL}} =2H_{\textit{av}}\).
Between a height \(z= H_{\textit{RSL}}\) and approximately 10% of the boundarylayer depth is the inertial sublayer (ISL), though when there is considerable roughnesselement height variability the RSL encroaches upon the ISL (Cheng and Castro 2002; Cheng et al. 2007; Mohammad et al. 2015b) and an ISL may cease to exist (Rotach 1999). Within the ISL, the flow becomes free of the individual wakes and channelling associated with roughness elements, and the small variation of the turbulent fluxes of heat and momentum with height leads to the assumption of a constantflux layer. In addition, if the airflow is fully adapted to upwind roughness elements (i.e. disregarding an internal boundary layer) a horizontally homogeneous flow is observed (Barlow 2014) and it is therefore possible to determine a spatially and temporallyaveraged windspeed profile.
3 Determination of Aerodynamic Parameters in Urban Areas
3.1 ReferenceBased Methods
Referencebased approaches require comparison between site photography and firstorder height and/or density estimates to reference tables (e.g. Grimmond and Oke 1999; Wieringa et al. 2001). Wieringa’s (1993) comprehensive review of roughness length data provides tables for homogenous surfaces, whilst Grimmond and Oke (1999) focus upon urban areas, therefore the latter is used here.
3.2 Morphometric Methods
3.2.1 Relations Between Aerodynamic Parameters and RoughnessElement Geometry
Morphometricallydetermined aerodynamic parameters in urban areas traditionally consider three flow regimes—isolated, wake interference and skimming (Oke 1987). These are related to the plan area index (ratio of plan built area occupied by roughness elements \((A_{\mathrm{p}})\) to total area under consideration \((A_{T}){:}\,\lambda _{p}= A_\mathrm{p}/A_{T})\) and frontal area index (ratio of the windward facing area of roughness elements \((A_{\mathrm{f}})\) to \(A_{T}{:}\,\lambda _{f}= A_\mathrm{f}/A_{T}\)). As surface cover \((A_\mathrm{p})\) increases the magnitude of \(z_{d}\) scaled by \(H_{\textit{av}}\) is traditionally observed to produce a convex curve asymptotically increasing from zero to 1 (Fig. 1a). In contrast, the relation between \(\lambda _{f}\) and \(z_{0}/H_{\textit{av}}\) has a peak at \(\lambda _{f}\) between 0.1 and 0.4 depending on the method used to determine \(z_{0}\) (Fig. 1b). The maximum possible \(\lambda _{p}\) is unity, although \(\lambda _{f}\) can exceed this.
Staggered and nonuniformly oriented groups of roughness elements generate a larger drag force than regular arrays, causing a more pronounced peak in \(z_{0}\), as well as larger values of \(z_{d}\) (Macdonald 2000; Cheng et al. 2007; Hagishima et al. 2009; Zaki et al. 2011; Claus et al. 2012). Roughnesselement height variability also influences flow and turbulent characteristics, as the taller roughness elements generate a disproportionate amount of drag (Xie et al. 2008; Mohammad et al. 2015b). This suggests \(z_{d}\) can be greater than the average roughnesselement height (e.g. Jiang et al. 2008; Xie et al. 2008; Hagishima et al. 2009; Zaki et al. 2011; MillwardHopkins et al. 2011; Tanaka et al. 2011; Kanda et al. 2013), with a peak \(z_{0}\) up to five times greater and displaced to higher \(\lambda _{f}\) (Hagishima et al. 2009; Zaki et al. 2011). Roughnesselement staggering, orientation and most importantly height heterogeneity therefore need to be considered in morphometric calculations; especially in complex city centres, such as the current study site (Sect. 4.1).
3.2.2 MorphometricMethod Application in Urban Areas
Numerous morphometric methods exist (“Appendix”) and each method has its own assumptions and intended range of applicability. Newer methods have incorporated increasingly complex geometric features or theoretical ideas pertaining to the relation between aerodynamic parameters and surface morphology.
Morphometric methods assessed (rows) with their required geometric parameters (columns)
Abbreviation  \(H_{\textit{av}}\)  \(\lambda _{p}\)  \(\lambda _{f}\)  \(H_{\textit{max}}\)  \(\sigma _{H}\) 

Morphometric methods  
RT  \(\checkmark \)  
Rau  \(\checkmark \)  \(\checkmark \)  
Bot  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  
Mac  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  
Mho  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  
Kan  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \) 
The six morphometric methods are applied across a range of roughnesselement densities with homogeneous (Fig. 1a, b) and heterogeneous (Fig. 1c, d) height. Their comparison demonstrates that aerodynamic parameters determined using the RT, Rau, Bot and Mac methods are independent of the height array used. Hereafter, these methods are collectively referred to as \(\textit{RE}_{\textit{av}}\) (i.e. based upon average roughnesselement height). In contrast, obvious differences occur for aerodynamic parameters determined using the Mho and Kan methods because of their direct consideration of height heterogeneity. Hereafter, the Mho and Kan methods are collectively referred to as \(\textit{RE}_{\textit{var}}\) (i.e. they account for variable roughnesselement heights).
Across the six methods, \(z_{d}\) increases with \(H_{\textit{av}}\) and \(\lambda _{p}\) (\(\lambda _{f}\) for \(\textit{Rau}_{z_\mathrm{d}}\)). The Mho and Kan methods both resolve the more considerable drag that is exerted by groups of roughness elements with height heterogeneity, therefore \(\textit{Mho}_{z_\mathrm{d}}\) also increases with \(\sigma _{H}\) and \(\textit{Kan}_{z_{d}}\) increases with both \(\sigma _{H}\) and \(H_{\textit{max}}\). Results for \(\textit{Bot}_{z_{d}}\) and \(\textit{Mac}_{z_{d}}\) vary similarly with density \((\lambda _{p})\). The difference between \(\textit{Mac}_{z_{d}}\) for square or staggered arrays is negligible compared to intermethod variability (Fig. 1a, c). For the homogeneous array (Fig. 1a, b) both \(\textit{Kan}_{z_{d}}\) and \(\textit{Mho}_{z_{d}}\) (\(\textit{Mho}_{z_{d}}\) at \(\lambda _{p}<0.8\)) are larger than for the other morphometric methods. \(\textit{Kan}_{z_{d}}\) becomes larger than \(H_{\textit{av}}\) and \(\textit{Mho}_{z_{d}}\) levels off, implying both do not fulfil the requirement that \(z_\mathrm{d}/H_{\textit{av}}=1\) when \(\lambda _{p}=1\). Therefore, when \(\lambda _{p}>0.50\) the Kan and Mho methods may under and overestimate \(z_{d}\) for homogeneous arrays, respectively. As the methods were derived from datasets with 0.05 \(<\lambda _{p} <0.50\) this is beyond their limits, and is uncommon for real cities (e.g. Fig. 1).
When roughnesselement height heterogeneity is introduced (Fig. 1c, d), the \(\textit{RE}_{\textit{av}}\) method results are identical to the homogeneous case because \(H_{\textit{av}}\) is the only height attribute used. In fact, \(\textit{Kan}_{z_{d}}\) and \(\textit{Mho}_{z_{d}}\) increase by a factor of approximately two and are therefore consistently twice the values for the \(\textit{RE}_{\textit{av}}\) methods. The increase of \(\textit{Kan}_{z_{d}}\) and \(\textit{Mho}_{z_{d}}\) suggests \(z_{d}\) is larger than \(H_{\textit{av}}\) for most plan area densities. This is especially true for \(\textit{Kan}_{z_{d}}\), which scales with \(H_{\textit{max}}~\)(assumed 117 m) and increases with density to become over twice \(H_{\textit{av}}\).
3.3 Anemometric Methods
Anemometric methods used to calculate the (a) zeroplane displacement \((z_{d})\) and (b) aerodynamic roughness length \((z_{0})\) with their respective meteorological variables and required stability condition
Abbreviation  z  \(z_{d}\)  L  \(u_{*}\)  \(\bar{u}_\mathrm{z}\)  \(\sigma _\mathrm{w}\)  \(\sigma _\mathrm{u}\)  \(\sigma _{T}\)  \(T_{*}\)  Stability 

Anemometric methods  
(a) \(z_{d}\)  
TVM  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  Unstable  
WVM  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  Unstable  
(b) \(z_{0}\)  
EC  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  \(\checkmark \)  Neutral 
4 Methods
4.1 Site Description
4.2 Observations
The period analysed for aerodynamic parameter determination is 2014 for the KSSW site and 2011 for the KSS and KSK sites. During independent assessment of the methods (Sect. 6), an additional 2 months in 2010 are considered at the KSS site. Identical instrumentation is used at the KSS and KSSW sites, as the equipment was moved along the Strand building (Fig. 2c) in 2012 preventing temporal overlap across all sites. The periods analyzed allow for seasonal variability of meteorological conditions, whilst limiting surface cover changes (e.g. construction).
A sonic anemometer (CSAT3, Campbell Scientific, US) measured the threedimensional wind velocity and sonic temperature at a sampling frequency of 10 Hz at each site. The anemometers were supported by a single tube mast at the KSK site (Clark Masts CSQ T97/HP) and a triangular tower at the KSSW and KSS sites (Aluma T45H). Instrument orientation was southwesterly to minimize potential mastinduced distortion for the prevailing wind directions.
The sensor heights are at \(z=1.97H_{\textit{av}}\) (KSK), \(2.48H_{\textit{av}}\) (KSS) and \(2.55H_{\textit{av}}\) (KSSW) for \(H_{\textit{av}}\) in the surrounding area of 1km radius (Table 3). Although relative heights vary with direction and meteorological conditions (e.g. Sect. 7), measurements at the KSK site are closest to the top of the RSL and therefore more likely to be affected by roughnesselement wakes. In contrast the sensors at the KSS and KSSW sites are assumed to be at heights above the RSL. To evaluate this assumption, analysis of drag coefficient and turbulence intensities was undertaken around the sites to identify potential flow disturbance from nearby roughnesselement wakes (e.g. Barlow et al. 2009). The analysis at the KSK site reveals that flow from the northern sector is disturbed by the Strand building (Fig. 2c, as noted by Kotthaus and Grimmond 2014b). At the KSS site, disturbance of flow is aligned with a nearby rooftop microscale anthropogenic source of moisture and heat that has previously been shown to influence turbulent fluxes (Kotthaus and Grimmond 2012). At the KSSW site, potential disturbance is aligned with a tall slender structure protruding from the Strand building roof (Fig. 2c). Elsewhere, no disturbance is identified, indicating the measurements at the KSS and KSSW sites are predominantly clear of roughnesselement wakes and therefore above \(z=H_{\textit{RSL}}\).
Data are preprocessed following Kotthaus and Grimmond (2014a). Eddycovariance planar fit coordinate transformation is performed using ‘ECpack’ software (Van Dijk et al. 2004) and a yaw rotation provides wind speed aligned to the mean direction (Kaimal and Finnigan 1994). Humidity corrections are applied to the sonic temperature (Schotanus et al. 1983) and 30min flux calculations are used to capture both the high and low end of the energy spectrum. An Ogive test (Moncrieff et al. 2004) ensured that this was an appropriate time period.
Characteristics of the measurement sites within a 1km fetch: (a) sensor heights: metres above ground level, river position: bearing of the most northern point of the north bank, (b) geometric parameters and (c) surface cover
Site  WGS84: Lat (N), Lon (E)  Instrument  Sensor height (m a.g.l.)  Host roof height (m)  Observation period analysed  Potential flow disturbance (bearing \(^{\circ })\)  River position (bearing \(^{\circ })\)  

(a) Instrument locations  
KSSW  \(51^\circ 30^{\prime }42.48^{\prime \prime }\)–\(0^\circ 7^{\prime }0.192^{\prime \prime }\)  Halo Photonics Streamline pulsed Doppler lidar  –  35.6  1 Oct 2010–18 May 2011  –  097–212  
50.3  35.6  1 Jan 2014–31 Dec 2014  230–245  
KSS  \(51^\circ 30^{\prime }43.2^{\prime \prime }\)–\(0^\circ 6^{\prime }58.8594^{\prime \prime }\)  CSAT3 Campbell Scientific 3D sonic anemometer  48.9  35.6  1 Oct 2010–31 Dec 2011  045–090  095–215  
KSK  \(51^\circ 30^{\prime }41.04^{\prime \prime }\)–\(0^\circ 6^{\prime }57.9594^{\prime \prime }\)  38.8  30.2  1 Jan 2011–31 Dec 2011  270–045  092–223 
\(H_{\textit{av}}\) (m)  \(\lambda _{p}\)  \(H_{\textit{max}}\) (m)  \(\sigma _{H}\) (m)  Built  Paved  Grass  Trees and shrubs  Water 

(b) Geometric parameters  (c) Surface cover (%)  
19.74  0.41  116.72  10.83  40.7  40.3  6.8  1.00  11.2 
4.3 Determination of Aerodynamic Parameters
4.3.1 Flow Diagram Illustrating Framework of Analysis
At each of the measurement sites, local aerodynamic parameters are determined using the referencebased, morphometric and anemometric methods (Fig. 3) and evaluated (Sect. 5). Windspeed profiles are then extrapolated using the logarithmic wind law (Eq. 1) and aerodynamic parameters from each method for comparison to wind speeds observed aloft using Doppler lidar (Fig. 3, \(\hbox {L}_{\mathrm{1}}\)) (Sect. 6). An example of the impacts upon the source area for measurements is also shown (Sect. 7).
4.3.2 Anemometric Determination of Aerodynamic Parameters
To determine \(z_{d}\) with the temperature and velocity variance methods (Fig. 3, \(\hbox {A}_{\mathrm{3}})\), \(10^\circ \) directional sectors are used (\(000^{\circ }{}010^{\circ }\), etc) to provide sufficient observations whilst allowing for varying fetch. As the methods require unstable conditions (\(0.05 \le z'/L \le 6.2\), Roth 2000, where \(z' = zz_{d}\)), an a priori assumption of \(z_{d}\) is required (Fig. 3, \(\hbox {A}_{\mathrm{2}})\). The methods are applied by defining stability with several values of \(z_{d}\), ranging from zero to the measurement height in 5m increments, providing a range of solutions for each \(10^{\circ }\) sector. If the denominator in \(\phi _{T}\)\((T_{*})\) or \(\phi _\mathrm{w} (u_{*})\) (Eqs. 20, 21, respectively) approaches zero, periods are removed. The additional criteria of \(u_{*}>0.05\hbox { m s}^{1}\) and \(T_{*}<0.05\hbox { K}\) may remove difficulties encountered using the methods in previous studies (e.g. De Bruin and Verhoef 1999; Rooney 2001). The methods are applied using rural (\(C_{1}C_{4}\), Sect. 3.3) and urban (Roth 2000) constants, as well as those determined using nonlinear regression (Bates and Watts 1988) of Eqs. 20 and 21 to observations at each site. However, the two latter methods require an a priori assumption of \(z_{d}\) and therefore provide a solution that is similar to the initial \(z_{d}\), and not useful.
The \(z_{d}\) value from both the temperature and velocity variance methods for each \(10^{\circ }\) sector are used to determine neutral conditions \(z'/L\le 0.05\) (Fig. 3, \(\hbox {A}_{\mathrm{4}})\), and subsequently to calculate \(z_{0}\) (Fig. 3, \(\hbox {A}_{\mathrm{5}})\) using the EC method (Eq. 23).
4.3.3 Morphometric Determination of Aerodynamic Parameters
A 4m resolution surface elevation dataset (Lindberg and Grimmond 2011) is used to determine the geometric parameters required to apply the morphometric methods (Fig. 3, \(\hbox {M}_{{1}}\)). For each morphometric method an initial estimation of \(z_{d}\) and \(z_{0}\) is made for \(1^{\circ }\) sectors and a 1km fetch (\(\textit{Miz}_{d}\), \(\textit{Miz}_{0}\)) (Fig. 3, \(\hbox {M}_{{3}}\)). During this process, four annuli are used (0–250, 250–500, 500–750 and 750–1000 m; e.g. Fig. 2b for the KSSW site) to weight surface geometry (50.00, 31.25, 12.5 and 6.25%, respectively), based on Kotthaus and Grimmond’s (2014b) footprint climatology. The Kormann and Meixner (2001) analytical footprint model (Fig. 3, \(\hbox {M}_{{4}}\)) is then used to indicate the probable extent of the turbulent flux source area for each 30min period of meteorological observations. The footprint model requires the measurement height and the observed \(\sigma _{v}\) (standard deviation of the lateral velocity component), \(\textit{L},\,u_{*}\) and wind direction. It also requires \(z_{d}\) and \(z_{0}\), hence their initial estimation (\(\textit{Miz}_{d}\) and \(\textit{Miz}_{0}\)) that is averaged across \(\sigma _{v}\) for each period of observations (Kotthaus and Grimmond 2014b).
The 80% cumulative source area for each measurement (30min) is used to weight the fractional contribution of each grid square in the surface elevation database (Fig. 3, \(\hbox {M}_{\mathrm{5}}\)). A weighted geometry is then determined, allowing for source area specific aerodynamic parameters (\(\textit{Mz}_{d}\) and \(\textit{Mz}_{0}\)) to be calculated for each morphometric method (Fig. 3, \(\hbox {M}_{\mathrm{6}})\). The \(\textit{Mz}_{d}\) and \(\textit{Mz}_{0}\) values for each observation period are iteratively provided to the source area model until the mean absolute difference of the parameter between iterations is \(<5{\%}\) or four iterations are performed. The latter is deemed appropriate given computational requirements and the range of values across the methods (Sect. 5). The methodology implies that \(\textit{Mz}_{d}\) and \(\textit{Mz}_{0}\) vary for each 30min time period as a consequence of the varying source area. When the source area becomes so small that it covers only the nearest few roughness elements (e.g. during very unstable conditions or large \(z_{d}\)) a morphometrically determined \(z_{d}\) or \(z_{0}\) is inappropriate. Therefore, only source areas extending horizontally beyond 100 m from the measurement sensor are considered.
The initiallyestimated aerodynamic parameters (Fig. 3, step \(\hbox {M}_{{3}}\): \(\textit{Miz}_{d}\) and \(\textit{Miz}_{0}\)) were found to be independent of the solution, irrespective of source area model (Kormann and Meixner 2001; Kljun et al. 2015 models used). Thus, it is possible to omit steps \(\hbox {M}_{\mathrm{2}}\) and \(\hbox {M}_{\mathrm{3}}\) (Fig. 3) and initialize the model with any reasonable roughness parameters (e.g. open country: \(z_{0}= 0.03\,\hbox {m},\,z_{d}= 0.2\,\hbox {m}\)). Here, steps \(\hbox {M}_{{2}}\) and \(\hbox {M}_{{3}}\) are retained for completeness. In addition, the Kormann and Meixner (2001) model is used, as the Kljun et al. (2015) model requires specification of the boundarylayer height, which is not available for all observations.
5 Results
5.1 ZeroPlane Displacement \((z_{d})\)
5.1.1 \(z_{d}\) Determined by Anemometric Methods
The stages of the application of the temperature and velocity variance methods are demonstrated for the KSSW site in Fig. 4. The \(z_{d}\) values determined by each method are unbiased by the initial \(z_{d}\) used to define stability (Sect. 4.3.2), which causes <5m variability in any wind direction (indicated by the range in each method, Fig. 5). In addition, the impact of varying the empirical coefficients \(C_{1}C_{4}\) (Sect. 3.3.) (based on Sorbjan 1989 and Hsieh et al. 1996) is \(<5\,\hbox {m}\) in any \(10^{\circ }\) sector, and therefore generates similar uncertainty to that of the stability definition (Fig. 5a–c).
Toda and Sugita (2003) suggest application of both the temperature and velocity variance methods assist in the determination of \(z_{d}\). This is true at both the KSSW and KSK sites where \(z_{d}\) determined using each method varies by approximately 5 m for each \(10^{\circ }\) sector (Figs. 4f, 5a, c). In comparison, the method solutions at the KSS site consistently vary by \(>13\,\hbox {m}\) (Fig. 5b). The large variability at the KSS site is most likely associated with the nearby rooftop microscale anthropogenic sources of moisture and heat (Kotthaus and Grimmond 2012) influencing turbulent fluxes.
The \(z_{d}\) based on the temperature variance method is consistently larger than that for the velocity variance method (Fig. 5a–c). Previous studies found \(z_{d}\) may be larger than \(H_{\textit{av}}\) in urban areas using both the temperature (Grimmond et al. 1998, 2002; Feigenwinter et al. 1999; Kanda et al. 2002; Christen 2005; Chang and Huynh 2007; Tanaka et al. 2011) and velocity (Tsuang et al. 2003) variance approaches. Results at the KCL sites support this, as \(z_{d}\) is up to twice \(H_{\textit{av}}~(H_{\textit{av}}= 19.74\,\hbox {m}\), Table 3).
No obvious association is evident between the directional variability of \(z_{d}\) and surface characteristics. For the temperature variance method, \(z_{d}\) is similar for all directions at each site (Fig. 5a–c), varying by < 5 m. Whereas, the velocity variance method \(z_{d}\) varies by up to 10 m, possibly because of occasional flow interference from roughnesselement wakes. The parks (1–2 km upwind to the west) do not obviously influence \(z_{d}\), but considering the extent of the source area for the measurements (Sect. 7) this is expected. The River Thames (Fig. 5a–c, blue shading) and small parks (Fig. 2b) closer to the measurement sites also do not affect the \(z_{d}\) values. Following Jackson (1981), \(z_{d}\) is the centroid of the drag profile of the roughness elements. The lack of directional variability in anemometric \(z_\mathrm{d}\) indicates the surface drag is dominated by taller roughness elements (maximum building height is 40–60 m in all directions). This is consistent with the disproportionate amount of drag observed to be exerted by taller roughness elements in a heterogeneous mix (Xie et al. 2008; Mohammad et al. 2015b).
5.1.2 \(z_{d}\) Determined by Morphometric Methods
There is less intersite variability in \(z_{d}\) values determined using each morphometric method, compared to the anemometric methods (Fig. 5a–c). However, the range of values between morphometric methods (intrasite variability) is larger than for the anemometric methods. There is an obvious separation between the methods based upon uniform (RT, Bot, Rau, Mac: \(\textit{RE}_{\textit{av}})\) and heterogeneous (Kan and Mho: \(\textit{RE}_\mathrm{var})\) roughnesselement heights. Across the sites, the former range between 5 and 20 m, whereas the latter are between 25 and 40 m (or almost twice the \(\textit{RE}_{\textit{av}}\) methods). The river, between directions \(092^{\circ }{}223^{\circ }\) (site dependent, see Table 1), causes a reduction in average height and therefore also in \(z_{d}\) determined by the \(\textit{RE}_{\textit{av}}\) methods. In comparison, the \(\textit{RE}_{\textit{var}}\) methods are unresponsive because \(\sigma _{H}\) becomes larger in these directions. The variability between the morphometric methods therefore becomes at least a factor of four in directions where the river is located.
When the measurement footprint has higher urban densities (nonriver directions) \(z_{d}\) determined by the \(\textit{RE}_{\textit{av}}\) methods varies between 15 and 20 m across all three sites, with an approximate intermethod variability of \(\pm 5\,\hbox {m}\). This increases to \(\pm 10\,\hbox {m}\) when the river sector is included, with \(z_{d}\) values as low as 5 m at the KSK site. The variability of the \(\textit{RE}_{\textit{av}}\) methods in the river sector (Fig. 5a–c) is proportional to the extent of the source area that is occupied by the river, which reduces \(\lambda _{p}\). Between the methods, \(\textit{Bot}_{z_{d}}\) is consistently smallest and \(\textit{Mac}_{z_{d}}\) is the largest for more densely packed directions.
As expected from the sensitivity analysis (Fig. 1), \(\textit{Kan}_{z_{d}}\) is consistently up to 5 m larger than \(\textit{Mho}_{z_{d}}\) (Fig. 5a–c). Both methods indicate \(z_{d}\)\(\ge 1.5H_{\textit{av}}\) for the surrounding area—a value typically used to estimate the minimum RSL depth (Roth 2000). Such high \(z_{d}\) values support the contention that roughnesselement height variability is important when considering the determination of \(H_{\textit{RSL}}\), in addition to, for example, \(H_{\textit{av}}\) and roughnesselement spacing (Cheng and Castro 2002). An effective mean building height has been suggested as a more appropriate scaling parameter for \(H_{\textit{RSL}}\) that incorporates buildingheight variability (MillwardHopkins et al. 2011, their Eq. 21). It may also be possible to consider the influence of height variability on \(H_{\textit{RSL}}\) through directly considering \(\sigma _{H}\) or \(H_{\textit{max}}\) (e.g. \(H_{\textit{RSL}}= 2H_{\textit{av}}+\sigma _{H})\). At the KSK site, the \(z_{d}\) value determined by the \(\textit{RE}_{\textit{var}}\) methods is consistently of the order of the measurement height, or greater, suggesting that the flux footprint either cannot be calculated or is consistently smaller than 100 m in horizontal extent and therefore few values are reported here (Fig. 5c, f).
If the \(f_\mathrm{d}\) constant used in the RT method is doubled (Eq. 2), the predicted \(z_{d}\) value aligns reasonably well with the \(z_{d}\) value estimated by the \(\textit{RE}_{\textit{var}}\) methods (Fig. 5a–c, 2RT). This suggests that if limited geometric parameters are available (i.e. only \(H_{\textit{av}})\), the choice of \(2\textit{RT}_{z_{d}}\) may provide a useful proxy for \(z_{d}\) determined by the \(\textit{RE}_{\textit{var}}\) methods in a heterogeneous mix. Assessment of the geometric parameters for each morphometric method’s respective source area indicates the magnitude of \(z_{d}\) for all methods is fundamentally determined by the directional variability in \(\lambda _{p}\). This includes \(\textit{Mho}_{z_{d}}\) and \(\textit{Kan}_{z_{d}}\), both of which are more sensitive to variability in \(\lambda _{p}\), despite their direct incorporation of \(\sigma _{H}\) and/or \(H_{\textit{max}}\).
5.2 Aerodynamic Roughness Length \((z_{0})\)
5.2.1 \(z_{0}\) Determined by Anemometric Methods
The aerodynamic roughness length determined using the EC method is a function of both observations (i.e. \(\bar{u}_\mathrm{z}\) and \(u_{*}\) for each 30min observation) and the \(z_{d}\) determined using the temperature and velocity variance methods. Therefore, the consistently larger \(z_{d}\) determined using the temperature variance method (Fig. 5a–c) implies that the associated \(z_{0}\) is consistently lower than that of the velocity variance method. For each method, the interquartile range of \(z_{0}\) (Fig. 5d–f shading around lines) consistently falls within \(\pm 0.25\,\hbox {m}\) from the median for each \(10^{\circ }\) sector. In directions where turbulence data indicate disturbance (Sect. 4.2, Fig. 5, directions with red shading) there is an increase in \(z_{0}\) because of the increased friction velocity in the same direction.
In directions without the river, the median \(z_{0}\) varies between 0.25 and 3 m, tending towards the lower end of typical \(z_{0}\) values reported for cities (Grimmond and Oke 1999). This is likely because the dense packing of roughness elements (\(\lambda _{f}\) and \(\lambda _{p}\ge 0.5\)) creates a flow more characteristic of skimming than chaotic (e.g. Oke 1987).
When the flow is aligned with the river (Fig. 5d–f, between \(090^{\circ }{}120^{\circ }\) and \(190^{\circ }{}210^{\circ })\), \(z_{0}\) values become smallest at the KSSW and KSS sites (as low as 0.1 m) because of flow along the smoother more homogeneous surface. This reduction is not obvious at the KSK site because of its lower siting and associated smaller source area (i.e. these measurements tend not to be affected by the river) (Sect. 7). At the KSSW site a reduction in \(z_{0}\) to 0.25 m also occurs when the flow is aligned with the adjacent Strand street canyon (\(060^{\circ }\), Fig. 2), because of the reduction of drag as flow is channelled along the canyon. The effect of the channelling is not observed at the KSK site because of its lower and more southerly siting, nor at the KSS site because of the microscale anthropogenic heat and moisture source in the same direction (Sect. 4.2).
5.2.2 \(z_{0}\) Determined by Morphometric Methods
The morphometric methods (except for the Mho method) have relative peaks in \(z_{0}\) at the edges of the river sector (Fig. 5 blue shading) similar to where the anemometric \(z_{0}\) becomes lowest (Sect. 5.2.1). This is because, although the majority of a source area may lack roughness elements and be smooth, the morphometric methods are responsive to the geometry calculated within the source area, which according to the morphometric method formulations generates disrupted flow. The peaks in the morphometricallydetermined \(z_{0}\) occur when the source area falls upon both river and buildings causing \(\lambda _{f}\) to be close to \(\lambda _{{fcrit}}\) (Fig. 1). When most of the source area is river, \(\lambda _{f}\) becomes smallest \((\lambda _{f }=0.2)\). Here, the Mho method indicates the highest \(z_{0}\) because the maximum \(\textit{Mho}_{{z}_{0}}\) occurs at these smaller \(\lambda _\mathrm{f}\) values (Fig. 1).
All morphometric methods indicate increased roughness to the north of the sites, in response to increased roughnesselement height (\(H_{\textit{av}}\) up to 30 m). The variable surface morphology implies that intermethod variability is largest in these directions, varying between 1 and 4 m. In comparison, intermethod variability is least in the river sector (1.0–3.5 m), associated with the most consistent surface morphology. The directional variability of \(z_{0}\) is primarily a function of \(\lambda _{f}\) for all methods (except the RT method). The \(\lambda _{f}\) value varies between 0.2 and 0.8 with wind direction, and the greater sensitivity of \(\textit{Bot}_{{z}_{0}}\) and \(\textit{Mac}_{{z}_{0}}\) to \(\lambda _\mathrm{f}\) (Fig. 1), implies they vary most with direction. \(\textit{Bot}_{{z}_{0}}\) is consistently 2 m larger than all other morphometric methods because of its more pronounced peak of \(z_{0}\) (Fig. 1). In comparison, \(\textit{Mac}_{{z}_{0}}\) tends to be lowest, especially where there is a greater frontal area index of roughness elements (e.g. \(240^{\circ }300^{\circ }\) where \(\lambda _{f}\ge ~0.5\)) because of its comparatively steep reduction of \(z_{0}\) at higher \(\lambda _{f}\) (e.g. Fig. 1).
The inclusion of \(\textit{Mac}_{{z}_{0}}\) in \(\textit{Kan}_{z_{0}}\) means that they vary similarly with direction. However, \(\textit{Kan}_{z_{0}}\) tends to be 1–2 m larger than \(\textit{Mac}_{{z}_{0}}\) in directions with higher frontal area, as the former does not have the steep drop off found in \(\textit{Mac}_{{z}_{0}}\) at higher \(\lambda _{f}\) (e.g. \(240^{\circ }300^{\circ }\) at the KSSW and KSS sites). An increasingly smaller source area occurs as the \(\textit{RE}_{\textit{var}}\) method values of \(z_{d}\) become similar to the measurement height at the KSK site. This explains the spread and lack of calculated \(\textit{Kan}_{z_{0}}\) and \(\textit{Mho}_{z_{0}}\) here (Fig. 5f).
5.3 Comparison Between Anemometric and Morphometric Aerodynamic Parameters
Errors across the sites range between 2.25 and 31.4 m for zeroplane displacement and 1.25–2.7 m for roughness length (Fig. 6). For \(z_{d}\), similarity between the anemometric methods and the \(\textit{RE}_{\textit{var}}\) morphometric methods (Figs. 5, 6), suggests \(z_{d}>H_{\textit{av}}\) in the surrounding area (20 m, Table 3). Use of the Kan, Mho and 2RT methods results in the lowest \({{ RMSE}}_{z_{d}}\) across all observations (approximately 10 m), in comparison to the \(\textit{RE}_{\textit{av}}\) methods that have \({{ RMSE}}_{z_{d}}\)\(=25\,\hbox {m}\) (Fig. 6, large circles). The morphometricallydetermined \(z_{0}\) is consistently greater than the anemometric \(z_{0}\) (Fig. 5d–f), which is more obvious for the temperature variance method \(({\textit{RMSGE}}_{z_{0}}\) up to 2.70 m) than the wind variance method \(({\textit{RMSGE}}_{z_{0}}\) of up to 2 m) (Fig. 6). No individual morphometric method calculates \(z_{0}\) that is consistently similar to the anemometric methods, with \({\textit{RMSGE}}_{z_{0}}\) values for all observations ranging between 1.75 and 2 m (Fig. 6, circles). However, \(\textit{Bot}_{z_{0}}\) deviates the furthest from observations \(({\textit{RMSGE}}_{z_{0}}>2.2\,\hbox {m})\) given its considerably larger magnitude (Fig. 5d–f).
5.4 ReferenceBased Approach
Aerodynamic parameters from numerous field studies using observations and morphometric methods (the \(\textit{RE}_{\textit{av}}\) methods only) informed Grimmond and Oke’s (1999, their Table 6 and Fig. 7) synthesis, which is complemented with photography for application. Use of a referencebased approach to determine aerodynamic parameters at the KCL sites indicates only that \(z_{d}>7\,\hbox {m}\) and \(z_{0}>0.8\,\hbox {m}\) for all directions. This demonstrates the limitations of using referencebased approaches in complex urban areas, as they offer a broad range of values. In addition, the referencebased approach does not have sufficient detail to resolve the directional variability in \(z_{d}\) and \(z_{0}\) with local features, such as the channelling of wind flow along the River which lowered \(z_{0}\) determined from observations (Sect. 5.2.1). The variability in both land cover and roughnesselement height are only coarsely considered in reference classes. In addition, use of aerial photography remains subjective—for example ‘high’ and ‘highrise’ categories (Grimmond and Oke 1999 their Fig. 7) both occur in the vicinity of the KCL sites, so selection may be inconsistent.
6 Independent Method Assessment—WindSpeed Profile Extrapolation
Observations at a greater height have a larger source area. Identical fetch in any direction is rare in an urban area, therefore, it is likely that \(z_{d}\) and \(z_{0}\) should also adjust with source area. To constrain changes in \(z_{d}\) and \(z_{0}\) throughout the profile, as well as the likelihood of overlapping internal boundary layers from surface discontinuities (e.g. Garratt 1990), the analysis is undertaken for the most homogeneous fetch within 10 km of the KSSW site (Fig. 2). This is deemed to be the \(000^{\circ }{}045^{\circ }\) direction based upon 500m grid squares of average ground height and the \(H_{\textit{av}}\), \(H_{\textit{max}}\) and \(\sigma _{H}\) values of roughness elements from the surface elevation database (Lindberg and Grimmond 2011).
The mean observed wind speeds in each 30m gate are 10.4, 10.9 and \(11.4\hbox { m s}^{1}\) (lowest to highest, Fig. 7a). These are most similar to the greater wind speeds extrapolated using aerodynamic parameters from the Kan, Mho and temperature variance methods (Fig. 7a). Both \(z_{d}\) and \(z_{0}\) are free parameters in Eq. 25, therefore two different pairs of values can predict the same wind speed aloft. However, the comparatively lower \(z_{d}\) of the \(\textit{RE}_{\textit{av}}\) methods and lack of compensation for this in \(z_{0}\) means that their extrapolated wind speeds are less than those from both the \(\textit{RE}_{\textit{var}}\) methods and observations (Fig. 7).
The differences \((U_{\textit{diff}})\) between wind speeds extrapolated using the different methods and wind speeds observed by the lidar (for each of the 33 profiles compared) are summarized in Fig. 7b. Over 95% of observed wind speeds are underestimated by the \(\textit{RE}_{\textit{av}}\) methods, with median underestimation between 1.5 a and \(2.9\hbox { m s}^{1}\) (Fig. 7b). The higher extrapolated wind speeds using the \(\textit{RE}_{\textit{var}}\) methods have a median \(U_{\mathrm{diff}}<0.6\hbox { m s}^{1}\) for all three lidar gates, which is within 6% of the mean observed wind speed. In addition, wind speeds extrapolated using the \(\textit{RE}_{\textit{var}}\) methods most resemble the distribution of observed wind speeds, tending to evenly underestimate or overestimate observations (approximately 50% of cases respectively). The temperature variance method’s largest \(z_{d}\) and smallest \(z_{0}\) produce a consistent overestimate in the wind speed (75% of cases), however it still shows a median \(U_{\mathrm{diff}} <1.1\hbox { m s}^{1}\) for all gates (Fig. 7b).
7 SourceArea Modelling Using the Morphometric Methods
Site  Morphometric method  \(H_{\textit{av}}\) (m)  \(\lambda _{p}\)  \(\lambda _{f}\)  \(H_{\textit{max}}\) (m)  \(\sigma _{H}\) (m) 

(a) Geometric parameters: median (min, max)  
KSSW  Mho  23.01  0.42  0.49  52.11  9.50 
(9.80, 30.14)  (0.21,.90)  (0.12, 3.01)  (31.97, 184.73)  (4.71, 16.29)  
Mac  21.30  0.40  0.43  77.80  10.21  
(9.30. 29.93)  (0.16, 0.79)  (0.04, 2.71)  (32.64 , 184.73)  (4.53, 17.63)  
KSS  Mho  23.41  0.44  0.48  46.10  9.22 
(10.76, 30.74)  (0.25, 0.84)  (0.11, 2.80)  (34.42, 184.73)  (5.67, 13.96)  
KSK  Mho  23.38  0.55  0.63  39.51  8.48 
(18.38, 29.76)  (0.32, 0.99)  (0.19, 2.27)  (28.60, 184.73)  (3.66, 13.59) 
Site  Built  Paved  Grass  Trees and shrubs  Water  

(b) Surface Cover (%) for 80% source area  
KSSW  Mho  42  48  3  1  6 
Mac  40  39  4  3  14  
KSS  Mho  45  48  2  1  4 
KSK  Mho  57  42  1  0  0 
The surface characteristics weighted by the footprint climatology (Fig. 8, Table 4) are different to those of the unweighted surrounding 1km radius (Table 3). The similar measurement heights at the KSSW and KSS sites implies that their footprint climatology characteristics are similar. In comparison, the lower siting of the KSK site produces a smaller source area (Fig. 8d), which is predominantly built and paved, with only 0.7% water. A wide range of geometric parameters occur in the source areas (Table 4a), which modifies the ratio of the measurement height to roughnesselement heights. The median \(H_{\textit{av}}\) for all sites is approximately 23 m and roughnesselement height varies between 9.2 and 9.5 m (median \(\sigma _{H}\)). The smallest \(H_{\textit{av}}\) recorded is 10 m, in which case the measurement height \(=5H_{\textit{av}}\) and well above the RSL (Sect. 2.1). However, some source areas have \(H_{\textit{av}}= 30\,\hbox {m}\), in which case measurements are at \(z= 1.67H_{\textit{av}}\) and therefore more likely influenced by roughnesselement wakes.
The source areas modelled using the \(\textit{RE}_{\textit{av}}\) methods are larger than the \(\textit{RE}_{\textit{var}}\) methods because the greater zeroplane displacement of the latter leads to a smaller effective height of the measurements. For example, \(\textit{Mho}_{{z}_\mathrm{d}}\) is typically twice \(\textit{Mac}_{{z}_{d}}\) and a comparison of the source areas modelled at the KSSW site using each respective method demonstrates this difference (Fig. 8a, b). The upwind distance contributing to the 80% cumulative source area is consistently over three times further in all directions for the Mac method. This influences the surface characteristics that are determined for the source area. For example, the parks to the southwest of the sites (Sect. 4.1) are not within the Mho method source area, but fall within the 80% of the Mac method, explaining the larger proportion of vegetated land cover (grass and trees) using the latter (Table 4b). Geometric parameters are also influenced, which subsequently influence morphometricallydetermined aerodynamic parameters. For example, the larger source area modelled using aerodynamic parameters from the Mac method gives a relatively larger \(H_{\textit{max}}\), \(\sigma _{H},\lambda _{p},\lambda _{f}\) and lower \(H_{\textit{av}}\) than within the Mho method source area (Table 4a).
8 Conclusions
Morphometric and anemometric analysis of aerodynamic parameters for three adjacent sites in Central London give estimates of zeroplane displacement \((z_{d})\) between 5 and 45 m and aerodynamic roughness length \((z_{0})\) between 0.1 and 5 m. A sourcearea footprint model (Kormann and Meixner 2001) is used to apply the morphometric methods in an iterative procedure. Although a firstorder estimate of \(z_{d}\) and \(z_{\mathrm{0}}\) is required, the final \(z_{d}\) and \(z_{0}\) values are similar, independent of the initial estimation. This conclusion is true for another sourcearea model (Kljun et al. 2015), indicating that an iterative procedure removes the need for initial site specific values. This saves time and also ensures more appropriate values of the aerodynamic parameters and source area dimensions.
Two methods that rely on surfacelayer scaling during unstable conditions are used to determine \(z_{d}\) from observations (Rotach 1994; Toda and Sugita 2003). The methods, not obviously sensitive to the initial \(z_{d}\) used to define stability, agree that \(z_{d}\) is larger than the average roughnesselement height \((H_{\textit{av}})\) in the surrounding 1km fetch. Although this conclusion is supported by the literature, previously these values have been considered unreasonably large (Grimmond et al. 1998, 2002; Feigenwinter et al. 1999; Kanda et al. 2002; Tsuang et al. 2003; Christen 2005; Chang and Huynh 2007).
Morphometric methods to determine \(z_{d}\) can be split into two types based on the attributes of roughnesselement height used, i.e. the average height \((\textit{RE}_{\textit{av}})\) or the variability/ maximum height \((\textit{RE}_{\textit{var}})\). The zeroplane displacement determined by the \(\textit{RE}_{\textit{var}}\) methods is consistently larger than \(H_{\textit{av}}\) and twice the magnitude of that from the \(\textit{RE}_{\textit{av}}\) methods, which is approximately \(0.7H_{\textit{av}}\). A simple doubling of \(z_{d}\) determined by a ruleofthumb morphometric method that is based only upon average roughnesselement height, brought values more in line with the \(z_{d}\) values determined using the \(\textit{RE}_{\textit{var}}\) methods.
There is agreement between anemometric methods and the morphometric methods which consider height variability, that \(z_{d}\) is larger than \(H_{\textit{av}}\). This conclusion is supported by numerical and physical experiments (e.g. Jiang et al. 2008; Hagishima et al. 2009; Zaki et al. 2011; MillwardHopkins et al. 2011; Tanaka et al. 2011; Kanda et al. 2013) indicating the taller roughness elements in a heterogeneous mix exert a disproportionate amount of drag on the flow (Xie et al. 2008; Mohammad et al. 2015b) lifting the dragprofile centroid (Jackson 1981) above \(z=H_{\textit{av}}\). The results verify Kanda et al.’s (2013) proposition that the maximum height \((H_{\textit{max}})\) is a more suitable scaling parameter for \(z_{d}\) and the standard deviation of the roughnesselement height \((\sigma _{H})\) (also used by MillwardHopkins et al. 2011) is useful to parametrize roughnesselement height heterogeneity. This conclusion has implications for the interpretation of output from anemometers (and potentially other meteorological sensors) in the heterogeneous urban environment. Sensors may need to be located higher above roughness elements to provide a localscale (or neighbourhood), rather than microscale, measurement.
Morphometricbased \(z_{0}\) values are consistently larger than the anemometric \(z_{0}\) by 2–3 m. Although the two classes of morphometric methods (\(\textit{RE}_{\textit{av}}\) and \(\textit{RE}_{\textit{var}}\)) do not demonstrate an obvious difference, rootmeansquare error analysis demonstrates the \(\textit{RE}_{\textit{var}}\) methods are most similar to observations. Individual \(\textit{RE}_{\textit{av}}\) methods consistently result in the largest (Bottema and Mestayer 1998) and smallest (Macdonald et al. 1998) \(z_{0}\) values.
The ability of each method to correctly estimate wind speed with height is assessed using locally determined aerodynamic parameters and the logarithmic wind law. Wind speeds observed with Doppler lidar (up to 200 m above the canopy) are underestimated with the \(\textit{RE}_{\textit{av}}\) morphometric methods (median underestimation: \(1.52.9\hbox { m s}^{1}\) for average wind speeds: \(10.411.4\,\hbox {m s}^{1})\). Whereas, the larger \(z_{d}\) determined using the \(\textit{RE}_{\textit{var}}\) methods provides similar results to the observations (median differences \(<0.62\,\hbox {m s}^{1}\)), demonstrating the importance of considering roughnesselement height heterogeneity when estimating the windspeed profile.
The modelled eddycovariance source area is typically a third (or smaller) of the size when \(\textit{RE}_{\textit{var}}\) methods are used, as the effective measurement height (i.e. with \(z_{d}\) accounted for) tends to be half that of the \(\textit{RE}_{\textit{av}}\) methods. This has implications for landcover and geometric parameters determined for a source area and their subsequent uses.
The tools for morphometric determination of \(z_{d}\) and \(z_{0}\) (including the two footprint models used) are available in the Urban MultiScale Environmental Predictor (UMEP, http://www.urbanclimate.net/umep/UMEP, Lindberg et al. 2016), which is an extension to the open source geographical information software QGIS.
Acknowledgements
This work is funded by a NERC CASE studentship in partnership with Risk Management Solutions (NE/L00853X/1) and Newton Fund/Met Office CSSP China. Observations used in these analyses were funded from NERC ClearfLo (KCL and Reading), EUf7 BRIDGE, H2020 UrbanFluxes, EPSRC ACTUAL, KCL and University of Reading. The numerous people who maintain the daily operations, collection and processing of data for the London Urban Meteorological Observatory network (http://micromet.reading.ac.uk/) including Will Morrison and Kjell zum Berge are gratefully acknowledged, along with King’s College London for provision of the sites.
Funding information
Funder Name  Grant Number  Funding Note 

Natural Environment Research Council 

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