Improving models of urban greenspace: from vegetation surface cover to volumetric survey, using waveform laser scanning

Urban greenspace has a major impact on human health and quality of life, and thus the way in which such green infrastructure is constructed, managed and maintained is of critical importance. A range of studies have demonstrated the relationship between the areal coverage and distribution of vegetation and the provision of multiple urban ecosystem services. It is not known how sensitive findings are to the spatial resolution of the underlying data relative to the grain size of urban land cover heterogeneity. Moreover, little is known about the three‐dimensional (3D) structure of urban vegetation and delivery of services, and addressing such questions is limited by the availability of data describing canopy structure from the tree tops to the ground. Waveform airborne laser scanning (lidar) offers a new way of capturing 3D data describing vegetation structure. We generated voxels (volumetric pixels) from waveform lidar (1·5 m resolution), differentiated vegetation layers using height as a determinant, and computed statistics on surface cover, volume and volume density per stratum. We then used a range of widely available remote sensing products with varying spatial resolution (1 to 100 m) to map the same greenspace, and compared results to those from the waveform lidar survey. We focused on data from three urban zones in the UK with distinct patterns of vegetation cover. We found −3%, +7·5% and +26·1% differences in green surface cover compared with, respectively, town planning maps (<10 m resolution), national land cover maps (25 m) and European land cover maps (100 m). There were differences of −59·1%, +12·4% and −2·4% in tree cover compared with global (30 m resolution), European (25 m) and national (1 m) estimates. Waveform lidar captured sub‐canopy structure and detected empty spaces in the understorey which contributed a 16% bias in the total green volume derived from non‐waveform lidar observations. We conclude that waveform lidar has a key role to play in estimating important quantitative metrics of urban green infrastructure, which is important because urban greenspace is highly fragmented and shows high levels of spatial and volumetric heterogeneity.


Introduction
The last decade has seen an explosion of research interest in measuring and mapping the provision of ecosystem services within urban areas (including, but not limited to, carbon storage, noise reduction, air pollution reduction, pollination, biodiversity, and human health and well-being; Elmqvist et al. 2013;Gaston, Avila-Jim enez & Edmondson 2013;Haase et al. 2014;Derkzen, van Teeffelen & Verburg 2015). This has arisen for three reasons (Gaston, Avila-Jim enez & Edmondson 2013). First, whilst urban land cover remains relatively restricted at a global scale, it is the fastest growing land use, can be very extensive at a regional scale, and can thus account for the delivery of substantial proportions of regional ecosystem services . This significance can be enhanced because urbanization tends disproportionately to occur in areas that are relatively rich in many services (e.g. in areas at lower elevations, of greater natural primary production; McDonald, Marcotullio & Guneralp 2013). Second, particularly in regions that have otherwise extensively experienced alternative forms of intensive land use (e.g. intensive agriculture), cities and towns can have higher levels of some ecosystem services than are found elsewhere (e.g. carbon storage; Davies et al. 2011;Edmondson et al. 2012). Third, it has become increasingly clear that the local delivery of some ecosystem services, particularly those associated with human health and well-being, may be critical to redressing some of the challenges of urban living (Elmqvist et al. 2015;Sandifer, Sutton-Grier & Ward 2015).
Whatever the motivation, key to the measurement and mapping of the vast majority of ecosystem services within cities and towns is a detailed knowledge of the extent and structure of the *Correspondence author. E-mail: stefano@casalegno.net greenspaces within their bounds. It is well established that (i) the overall coverage of such greenspaces is often much greater than was long thought, particularly when both public and private (e.g. domestic gardens) spaces are accounted for (Gaston et al. 2005); and (ii) this overall coverage is almost invariably comprised of huge numbers of individual greenspace patches, with the small ones often contributing a substantial proportion of both the total number and the overall coverage, and hence of the benefits that greenspace provides (Cameron et al. 2012;Gaston, Avila-Jim enez & Edmondson 2013). The spatially variable structure and fragmentation makes the measurement and mapping of urban greenspaces particularly challenging, and even more so is the measurement and mapping of key land cover components within those fragmented, small spaces (e.g. tree cover, vegetation volume; Gaston, Avila-Jim enez & Edmondson 2013).
Most urban ecology research to date has used one of three methods for the two-dimensional characterization of urban greenspace: (i) analysis of historical town planning maps, inventories or cadastral plans; (ii) analysis of regional-extent satellite remote sensing data from one or more of a range of systems operating at different spatial resolutions; and (iii) analysis of fine-grained commercial satellite data (e.g. IKONOS) or airborne remote sensing data including airborne laser scanning (e.g. lidar) and aerial photography. These three approaches have various limitations. First, the fine-grained maps (i) usually focus on publicly maintained gardens and spaces, neglecting privately owned features, and whilst they can convey information about the historic layout of a town or city these data may rapidly lose their currency, therefore failing to capture information about the changing nature of the greenspace. Second, maps derived from freely available satellite remote sensing datasets (here we refer specifically to medium resolution data from systems such as Landsat which have a spatial resolution typically of between 25 and 30 m) are commonly used to produce land cover datasets (EEA 2006;Morton et al. 2011) of final resolution ranging from 25 to 1000 m, describing variables such as green cover or tree cover (Kempeneers et al. 2011;Hansen et al. 2013). The coarse spatial resolution of these data in comparison to the grain size of features and patterns in urban spaces inevitably results in mixed pixels and as a result reliance on such data means that smaller greenspace patches are frequently misclassified (Momeni, Aplin & Boyd 2016). Finer grained maps derived using what may be considered more 'scale appropriate' data (i.e. with spatial resolutions finer than 10 m) provide one solution to this problem (Pu 2011;Pu & Landry 2012;Jeanjean et al. 2015). However, to date these data have been exploited principally to assess the extent of greenspace rather than its structural composition, and to deliver two-dimensional data, or at best two-and-a-half dimensional data (e.g. in the case of a canopy height model derived from discrete return lidar; Sankey et al. 2013). Whilst it is possible to exploit discrete return lidar data to model 3D canopy characteristics, previous work has illustrated the lack of sub-canopy information in discrete return airborne lidar data (see figs 11 and 13 in Hancock et al. 2017). Neglecting to measure the threedimensional character of urban greenspace means that a critical component of its 'quality' is overlooked (Wang, Weinacker & Koch 2008).
Recent developments in laser scanning technology have made available new advanced systems that are capable of waveform scanning (Anderson et al. 2016). These waveform lidar systems offer a potential solution to the gap in urban greenspace volume data. Waveform lidar is different from traditional (i.e. 'discrete return') lidar in that it is capable of measuring the reflected laser intensity as a function of range (Mallet & Bretar 2009). This gives information on all objects visible to the airborne laser scanner (see Fig. 1), but requires signal processing to extract target properties. Once processed (a non-trivial task requiring system pulse and attenuation to be calibrated; Hancock et al. 2015Hancock et al. , 2017Anderson et al. 2016), the resulting waveform is made up of the distribution of objects within the footprint. The final product has great potential to detect fine-grained vegetation structure beneath complex canopies. The extra information contained within waveform lidar has been used to measure biomass (Drake et al. 2002), forest structure (Hyde et al. 2005), land cover (Reitberger, Krzystek & Stilla 2008), urban forest species, leaf area index and carbon storage (Alonzo et al. 2016), but there are currently only a few papers evidencing their application fully to characterise 3D urban vegetation structure (Mallet, Soergel & Bretar 2008;Guo et al. 2011;Yan, Shaker & El-Ashmawy 2015), and none that have specifically assessed within canopy variation and understory (Anderson et al. 2016). Hancock et al. (2017) provide a comprehensive review of literature describing the status quo of vegetation surveying using different laser scanning technologies and are the first to demonstrate an improvement over past studies in the 3D mapping of vegetation canopies using airborne waveform lidar, over large areas at fine scales (sub-2 m resolution).
The aims of this paper are threefold: 1. To identify differences between estimates of urban green surface cover derived from (i) a new waveform lidar voxel dataset (described fully in Hancock et al. 2017) and (ii) those from satellite data products. We aim to explore the extent to which small patches of greenspace and private garden space are neglected by the latter due to their coarser spatial resolution. In exploring these differences, it will then be possible to highlight biases in analyses of urban greenspace utilizing such satellite data products. 2. To quantify differences in estimates of urban tree cover derived from other remote sensing data products at a range of scales as compared to our own waveform lidar analysis. 3. To quantify surface and volumetric differences in urban greenspace derived from measurements of discrete canopy height maxima (e.g. such as would be achieved from discrete return lidar analysis) using waveform lidar and to apply the first validated volumetric model from waveform lidar data (described fully in Hancock et al. 2017) to generate estimates of vegetation structure per stratum with information on volume of vegetation density.

S T U D Y A R E A
This study was conducted in the 'Cranfield triangle', a region in southern England, U.K., comprising the three adjacent towns of Milton Keynes (52°02 0 N, 0°45 0 W), Luton (51°53 0 N, 0°25 0 W), and Bedford (N52°58 0 N, 0°28 0 W with population sizes and density of, respectively, c. 230 000 and 2500/km 2 ; c. 240 000 and 4800/km 2 ; c. 160 000 and 2200/km 2 (2011 Census, UK). Overall, the survey area encompassing all three towns occupied an area of 166 km 2 , and comprises a diverse array of urban forms, history, and management (Hebbert 2008). Milton Keynes is a 'new town' built in the 1960s with designed green corridors, a gridded road pattern and squared districts with planned greenspace. Bedford is a smaller county town arising from a medieval layout with much of the greenspace found along the banks of the Great Ouse River. Finally, Luton has large areas characterised by dense Victorian terraced houses (modest construction with very small, usually paved garden 'yards') alongside large industrial areas. These three towns thus represent an array of sizes, shapes, types and contexts of greenspace against which the objectives of the research could be tested.

R E M O T E S E N S I N G D A T A C A P T U R E
The Natural Environment Research Council Airborne Research and Survey Facility collected remote sensing data from a piloted Dornier 228 aircraft between June and September 2012 during four flights. The aircraft was flying at 1Á5 km altitude over Milton Keynes (achieving 7 footprints per m 2 ) and 2Á6 km altitude over Luton and Bedford (achieving 2 footprints per m 2 ) and carrying different sensors: a standard digital camera (Leica Camera AG, Wetzlar, Germany, model RCD105 CH39), an imaging spectrometer (Eagle) and a waveform-capable lidar instrument (Leica Camera AG, model ALS50-II). The maximum scan angle for the lidar sensor was 8°. The spectrometer covered the wavelength region from 407Á08 nm (blue) to 1007Á10 nm (near infrared) in 253 bands. The hyperspectral data from Eagle were provided at 2 m resolution, with the exception of a small area of Luton for which they were at 4 m spatial resolution due to flying height restrictions near a major commercial airport. The hyper-spectral data was examined for across-track angular effects, and none were found. The following sections of the manuscript detail the image processing approaches and data comparison exercises undertaken to address the major research questions.

Q U A N T I F I C A T I O N O F V E G E T A T I O N S U R F A C E , V O L U M E A N D V O L U M E D E N S I T Y I N V E R T I C A L S T R A T A
The first stage in processing the acquired remote sensing data was to produce a binary layer describing the distribution of green and nongreen spaces across the towns. For this purpose, the Eagle imaging spectrometer data were most useful because they could be processed at 2 m grid resolution to generate a simple Normalized Difference Vegetation Index (NDVI; Tucker 1979) for discriminating vegetated (NDVI ≥ 0Á2) from non-vegetated areas providing a binary map of greenspace distribution; the 0Á2 NDVI threshold was chosen following Liang (2004).
A ground DEM was generated with lastools (Isenburg 2011) and vegetation height determined. This was used for a more detailed classification of the type of vegetation stratum (grass, shrubs and trees) present within the regions classified above as being 'green'. Vegetation strata were classified using the NDVI dataset and the waveform lidar data where: Grass -NDVI ≥ 0Á2 and height < 0Á5 m; Shrubs: NDVI ≥ 0Á2 and height between 0Á5 and 4 m; Trees: NDVI ≥ 0Á2 and height > 4 m; All greencover: NDVI ≥ 0Á2 and height > 0; and Not Representation of presence-absence of vegetation cover layers according to discrete canopy height products (D in red) and full-waveform lidar products (W in black). The discrete canopy height representation detects canopy cover and is unable to detect understorey vegetation or grass covered by shrubs. We consider this model as a two and a half rather than a three-dimensional green cover characterization. green: NDVI < 0Á2. The height thresholds were chosen to make our classification scheme comparable with other datasets which define trees as being taller than 4 m (Kempeneers et al. 2011;Hansen et al. 2013). Subsequently, as an additional and necessary step, we computed a further tree layer which utilised a 3 m rather than 4 m threshold in vegetation height to allow a further comparison with another tree dataset (Bluesky 2015); note, this did not affect the shrub or grass layers because this enquiry related only to the tree canopy. The threshold of 0Á5 m distinguishing between grass and shrubs was chosen for two reasons -UK grasses in urban areas rarely exceed this height, and secondly this was the minimum available vertical grain size permitted by our voxel dataset. Using these thresholds, we processed waveform lidar to quantify the 2D surface cover of the stratum type.
The waveform lidar data were processed as described in Hancock et al. (2017) and the open-source code to perform the same processing is available from https://bitbucket.org/StevenHancock/voxelate. This allowed gap fraction estimates to be generated along each beam by denoising (Hancock et al. 2011), deconvolving (Hancock et al. 2008) and correcting for attenuation (Harding et al. 2001). Gap fractions for each beam were averaged into voxels of 1Á5 m by 1Á5 m (horizontal) by 50 cm (vertical) resolution.
We then used the voxel data and converted the signal into a binary dataset where the presence of a signal in the voxel was used to indicate the presence of vegetation. A threshold was applied to those data, using 1% within voxel cover as a minimum requirement for classifying a voxel as having vegetation presentthis was used to filter noise error (Hancock et al. 2015). Finally, we projected the 3D voxel presence of each stratum into its corresponding 2D surface projection on the ground and quantified the surface cover for each stratum individually. To provide a comparable dataset showing discrete canopy height maxima (such as might be used in a discrete return lidar dataset), we also computed the same surface projection on the ground using the uppermost altitudinal signal in the positive voxel layer, and assumed that all voxels below this point were positive (i.e. containing vegetation, as one would treat a discrete return lidar; Fig. 1). We refer to this as a discrete canopy height product in the text hereafter, although it is different from the same measurement that would be delivered by a discrete return algorithm applied independently. Note that we intentionally chose not to use the standard discrete return lidar product here because, as Anderson et al. (2016) report, such products show biases compared to waveform lidar and quantifying these biases is not the topic of this paper. We accept that this is a somewhat simplistic estimation of the true biases because it is possible, theoretically, to model sub-canopy vegetation from discrete return lidar data. However, the Leica ALS50-II data used in this study has been shown to be incapable of mapping understorey vegetation at fine resolution (Hancock et al. 2017), so we suggest that the resultant statistics that are calculated and reported later in the manuscript are likely to overestimate the biases. They should however provide an initial useful comparative insight into the two methodologies.
Finally, the quantification of vegetation volume per stratum was undertaken by accumulating the number of positive voxels from the discrete canopy height product and waveform lidar. To compute volume density, we accumulated voxel signals per stratum.

C O M P A R I S O N W I T H E X I S T I N G M E T H O D O L O G I E S
To allow comparison with published datasets describing urban greenspace, we computed statistics within administrative units (UK Census Area Statistic ward) and selected all ward units where at least 99% of their spatial extent was contained within the coverage of our waveform lidar survey flight zone (Fig. 2). Within these administrative units, we determined the surface coverage of vegetation (both green cover and tree cover) using the following datasets:

Green cover datasets
We used data from Richardson & Mitchell (2010) as green cover estimates for each ward administrative unit. These estimates (hereafter referred to as the 'town planning map' TPM6; the '6' in the notation refers to the nominal spatial resolution of the data as being 6 m) are based on high resolution Ordnance Survey MasterMap products which are the most comprehensive and updated vector datasets available for the UK. MasterMap data are provided at scales as fine as 1 : 1250 for most urban areas, hence the estimates from Richardson & Mitchell (2010) should include all vegetated areas larger than 5 m 2 in area, but critically for urban systems, this product excludes domestic gardens.
Two supplementary green cover estimates were calculated, using a 25 m resolution national land cover map for the UK (NLC25; Morton et al. 2011) and the 100 m resolution European land cover map (EULC100; EEA 2006). For both, we distinguished vegetated and nonvegetated features within layer classes, resampled data at 2 m resolution and summed surface cover to make them comparable with estimates from our other datasets.

Tree cover datasets
Tree cover estimates were derived from national, European and global datasets, respectively, we used the national tree map for the UK (Bluesky 2015) at 1 m resolution (NTM1); the European tree map (Kempeneers et al. 2011) at 25 m resolution (EUTM25); and the global tree map (Hansen et al. 2013) at 30 m resolution (GLTM30). The NTM1 is a commercial airborne remote sensing derived map while the latter two maps (EUTM25 and GLTM30) are derived from optical satellite measurements that are freely available. To integrate the GLTM30 in our comparison, we downloaded the cloud-free and normalized top of atmosphere reflectance multispectral imagery (bands 5, 4 and 3), computed NDVI and applied the same threshold of NDVI ≥ 0Á2 to distinguish the presence/absence of tree cover in grid pixels. For all three tree cover estimates, we resampled data at 2 m resolution to compare estimates with our data.

D E S C R I B I N G D I F F E R E N C E S B E T W E E N D I S C R E T E C A N O P Y H E I G H T P R O D U C T S A N D T H O S E D E R I V E D F R O M W A V E F O R M L I D A R
We compared 3D mapping from two airborne lidar products, a discrete canopy height product that estimated canopy greenspace volume, using spot-height canopy maxima and waveform lidar products describing the full 3D structural elements of the vegetation canopy from the top to the ground and its density (see Fig. 1). The discrete canopy height product used here assumed that all vegetation volume below the top canopy was full of vegetation, and did not quantify empty space, whilst the waveform lidar product enabled quantification of this.

G R E E N C O V E R S U R F A C E A R E A M A P P I N G
We found positive and negative biases between green covers according to the different datasets we compared to waveform lidar ( Table 1). The TPM6 overestimated greenspace (with the exception of for Luton) (Table 1 and Fig. 3) while the EULC100 and NLC25 underestimated greenspace in all three towns (Table 1 and Fig. 5). We expected underestimations of green cover from the TPM6 because these data are known to exclude private gardens and small green patches (<6 m 2 ), but instead we found positive biases of +6Á8% and +2Á3 for Milton Keynes and Bedford while Luton was less green (À2Á5%) according to this comparison (Table 1, Figs 3 and 5). The 25 m resolution NLC25 map showed differences of between À2Á4% (Milton Keynes), À8Á7% (Bedford) and À14Á6% (Luton) in green cover (Table 1, Figs 3 and 4) compared to our data from waveform lidar. The 100 m resolution EULC100 showed an even larger underestimation (À21Á9% Milton Keynes, À31Á5% Bedford and À29Á1% Luton) of green cover. In summary, we found overall underestimation biases in green cover increased as the spatial resolution of the land cover product was coarsened. Table 2 shows that of the three datasets compared, the strongest agreement was found between the 1 m NTM1 and our waveform lidar data, with differences of +2Á6% (Milton Keynes), 2Á2% (Luton) and +1Á9% (Bedford). A visual comparison of the products is shown in Fig. 4 for a section of the town of Luton, and a zoomed area with clear detail is shown in Fig. 5e-h. The EUTM25 data showed larger differences as compared to metrics derived from waveform lidar estimates of À9Á7% (Luton), +12Á0% (Bedford) and +14Á4% (Milton Keynes), with the greatest biases in the most tree covered town (Milton Keynes; Table 2). The EUTM25 was designed to capture large forest stands while omitting sparse trees and lines of trees. We found the greatest biases in tree cover estimates derived from the GLTM30, which we have shown to be poor in describing tree cover in the diverse and heterogeneous urban system (see Table 2, Figs 4 and 5). From this last comparison we found overestimations of +56Á5% (Bedford), +56Á8% (Luton) and +61Á5% (Milton Keynes) while using the GLTM30 as compared to our own analysis.

D M A P P I N G : O V E R A L L V O L U M E A N D V O L U M E D E N S I T Y O F V E G E T A T I O N
The waveform lidar capability allowed us to generate stratified results showing the distribution of grass, shrubs and trees, including those in the understorey in the three towns. These results show that Milton Keynes was the 'greenest' town in terms of tree volume, followed by Bedford and Luton (Table 3). This is not an unexpected result, because Milton Keynes was a designed new town with directed planting and planned urban greenspace, whilst Luton and Bedford show older urban forms with more dense housing and fewer parks.
The volume density of vegetation in trees (Table 4) was higher in Milton Keynes, while shrubs were similarly dense in Milton Keynes and Bedford and less dense in Luton. Grass volume density is higher in Bedford as compared to the other two towns (see Table 4). Fig. 2. Location of the overall study area within the UK (left) and details of the three towns considered (right). The black zones in the right panel define the flight missions on which the lidar data were collected; the areas coloured in white (Bedford), red (Milton Keynes) and yellow (Luton) define the ward administrative boundaries within the flight zones and considered here for data comparison. Our comparisons of vegetation volume reveal that if one relies on fine-grained discrete canopy height products (e.g. products derived from lidar DSMs) to describe the urban greenspace, one first overlooks the 'hidden' vegetation beneath the canopy object that shows its surface expression to the remote sensing instrument. In this way, the canopy top hides between 34Á0% (Bedford), 23Á2% (Milton Keynes) and 21Á3% (Luton) of shrubby vegetation and between 19Á5% (Bedford), 15Á4% (Luton) and 12Á0% (Milton Keynes) of grass vegetation (Table 5).
In using waveform lidar data, these components of greenspace are made visible. Secondly, if one relies on a discrete canopy height product and assumes that the entire volume from the measured canopy top to the ground is filled with vegetation, then there will be an overestimation in vegetation volume by up to 18Á5% (Table 3), because there are 'voids' in green volume beneath canopy tops that are not measurable from non-waveform systems.

Discussion
Urban greenspace mapping has been used in a broad range of contexts, including those of ecosystem services (Rudd, Vala & Schaefer 2002;Roe et al. 2013), microclimate (Ren, Ng & Katzschner 2011), atmospheric pollution (Jeanjean et al. 2015), climate change (Gaffin, Rosenzweig & Kong 2012),  sociology (Watkins et al. 2017), and politics (Heynen 2006). By way of example, there has been a great deal of research into the relationships between human health/well-being and the distribution of urban vegetation based on greenspace estimates derived from remotely sensed data of similar spatial resolutions to the satellite-derived datasets compared in this study (see Table 1 in Supporting Information for references), including (i) broad grain size land cover maps capable of detecting objects larger than 2 ha; (ii) land cover maps with a spatial resolution of 100 m; (iii) land cover maps with a spatial resolution of between 25 and 30 m; (iv) optical remote sensing products with a spatial resolution between 20 and 30 m; (v) land cover maps with a 10 m spatial resolution; and (vi) town planning maps which are able to detect vegetation at sub-10 m spatial resolution, but which omit private gardens. The work presented in this paper has demonstrated that in urban systems which have a highly heterogeneous land   cover distribution, including private gardens, these widely used medium spatial resolution products (20 m and coarser) deliver unreliable data with biases in green cover estimates ranging from +7Á5% to +26Á1% (Table 1), and in tree cover estimates ranging from +12Á4 up to À59Á1% (Table 2) when compared to our 1Á5 m waveform lidar derived dataset. Biases were reduced as the spatial resolution of the remote sensing product increased for both green cover and tree cover estimates (i.e. À3% comparing urban green cover waveform estimates with the TPM6; À2Á4% comparing tree cover waveform estimates with the national tree map). Mitchell, Astell-Burt & Richardson (2011, p. 11), evaluating three different greenspace indicators with varying spatial resolution, commented that indicators with different 'origins' (i.e. spatial resolution) showed 'considerable agreement on the amounts of greenspace they detected and in their association with mortality and morbidity'. However, critically, they explained that, 'these indicators did disagree in more socioeconomically deprived areas, and this is probably because such areas have fewer larger greenspaces'. Our work, using fine-grained data from three towns with varying spatial patterns, has highlighted the importance of considering the impact of the resolution of the imaging product on the quality of the inferences that can be determined. The discrepancies reported here between the waveform lidar data and, for example, CORINE landcover data as used by Mitchell, Astell-Burt & Richardson (2011), were as large as 31Á5% (Table 1 EULC100 in Bedford)so these heterogeneously distributed patches of private gardens and other greenspace are a major proportion of the overall urban green area which are not captured by coarse resolution products. This is particularly important when considering the multiple impacts on human health, for example, because nature close to home is visited more frequently and is most important in delivery of health benefits (Soga et al. 2015).
Whilst the grain size problem with mapping in urban systems is not a new finding (e.g. Aplin & Atkinson 2001;Grafius et al. 2016;Momeni, Aplin & Boyd 2016), and waveform lidar has been used recently to characterize urban vegetation at very fine spatial resolution (Alonzo et al. 2016), here we quantify the biases in comparison to medium and fine spatial resolution datasets. We advise that these biases are strongly dependent on the grain size and spatial distribution of greenspace features within the urban extent with biases up to 61Á5% if relying solely on GLTM30 data. In improving the grain of urban greenspace mapping, it will be possible to determine the impacts of urban greenspace distribution on a broad set of ecosystem services that humans benefit from.
Finally, our work has shown the importance of characterising urban greenspace not as a two-dimensional attribute but as the three-dimensional volume and its density. In using waveform lidar we have been the first to capture detail at high (<30 m) spatial resolution in the urban canopy structure, describing the complex understorey components, and quantifying the empty volumetric space within the canopy (i.e. 11Á4% to 18Á5% in Table 3). Even with recent developments in photogrammetric workflows, and widespread availability of aerial acquired stereo photography that can deliver sub-meter sampling of greencover, unlike waveform lidar, these technologies are not able to measure the sub-canopy structure. We have also reported on the density of vegetation in the urban volume which is impossible to achieve using any of the other datasets compared. This has shown that there are great differences in the density of vegetation in tree, shrub and grass strata across different urban forms (e.g. vegetation density is higher in trees for Milton Keynes, in shrubs for Bedford and in grass for Luton).
Potential adopters of our methodology will be faced with computational challenges in translating the waveform signal into voxel data due to the complex issues of multiple scattering and signal attenuation, to give just two examples. In this respect, we provide an open source code to process the voxel data, full details of which can be found in Hancock et al. (2017) and at https://bitbucket.org/StevenHancock/voxelate It is important to consider that waveform lidar has a high economic cost both in terms of acquisition and processing of data, and in storage of voxel layers which have high data volumes. However, waveform lidar is emerging as a new strand in geospatial surveying and with NASA's forthcoming Global Ecosystems Dynamics Investigation (GEDI) mission (due to be operational from the International Space Station in 2019) and the increasing number of lidar sensors being sold with this capability (Anderson et al. 2016), there is opportunity for its reproducibility in time and space.
Authors' contributions S.C. and K.A. conceived the ideas and designed methodology; S.C., K.A. and S.H. collected and analysed the data; S.C., K.A. and K.G. led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication. Values 9 100 accumulated voxels signals per surface area.