sustainability

Article A Quantitative Study of Geometric Characteristics of Urban Space Based on the Correlation with Microclimate

Huimin Ji, Yunlong Peng and Wowo Ding * School of and Urban Planning, Nanjing University, Nanjing 210093, China; [email protected] (H.J.); [email protected] (Y.P.) * Correspondence: [email protected]

 Received: 5 August 2019; Accepted: 7 September 2019; Published: 11 September 2019 

Abstract: With the sustainability of contemporary cities gaining more and more attention, interest in the correlation between urban geometry and urban microclimate is increasing. On this basis, this paper aims to investigate the quantification of geometric characteristics of urban space. Based on a combination of easily accessible software packages, a quantitative method composed of spatial partition, spatial characteristic indices (area, shape, and openness), and a spatial classification chart is proposed for the study of the correlation between urban spatial geometry and urban microclimate. Two blocks with different spatial geometric characteristics of the Xinjiekou central area in Nanjing are selected as the cases to verify the operability and effectiveness of this method. The results reveal that complex real urban space can be quantitatively described and classified by this spatial quantification method. In addition, a possible correlation between urban spatial geometry and urban wind environment is demonstrated by using the method, which may also be applicable to the correlation study between urban spatial geometry and other environmental issues.

Keywords: built environment; urban space; geometric characteristics; quantitative approach; urban microclimate

1. Introduction Due to rapid urbanization in China, the spatial scale, construction capacity and building density of many cities have increased rapidly [1]. This dramatic transformation has improved the living standards of residents to a certain extent, but also increased the environmental burden, leading to increasingly serious urban environmental problems, such as air pollution, the heat island effect and ventilation problems [2,3]. Since urban microclimate affects human comfort and health, evaluating the effects of urban geometry on urban microclimate in urban planning and architectural has become a significant issue for sustainable urban development [4]. The association between urban geometry and urban microclimate is widely considered to be the beginning of Oke [5]. Oke associates the aspect ratio (H/W) of the ideal street canyon with the airflow pattern inside and draws the interior of the canyon with different aspect ratios. There are several different forms of airflow, i.e., the isolated roughness flow regime (H/W < 0.3), the wake interference flow regime (0.3 < H/W < 0.67), the skimming flow regime with one main vortex (0.67 < H/W < 1.67), and multi-vortex flow regime (H/W > 1.67). Moreover, some correlated research has focused on urban-like configurations, and the plan area ratio (λp) and height variation (σH), which can represent the density and complexity, have also been added [6–9]. On the basis of urban-like geometry, some scholars have abstracted the model into a more representative real city and added more morphological parameters to investigate the relationship between morphology and microclimate. Through fixing the floor area ratio in urban planning and changing the building coverage, Peng conducted over 100

Sustainability 2019, 11, 4951; doi:10.3390/su11184951 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 4951 2 of 13 ideal urban plot configurations to investigate the relationship between the coverage changes and the local ventilation efficiency [10]. You studied the relationship between the length of the building, the distance between the buildings within residential community and the ventilation performance of the local space [11]. The quantitative description of urban space has been investigated by many researchers. Space syntax, proposed by Bill Hillier, is a theory and method to study space organization by quantifying spatial structure [12–15]. It pays attention to the relationship between human society and urban space, not to the geometry and actual size of urban space. As an analysis software of space syntax, DepthmapX divides the space into equal grids and calculates the connectivity, step depth, and integration of these regions. Based on the concept of ‘isovist’ and ‘convex space’, many analysis tools used to quantify the spatial characteristics have been developed [16]. In the initial analysis of isovist, Benedikt divided the space into a series of continuous grids, obtained the corresponding isovist shapes from the central points of each grid, and identified six geometric parameters—area, perimeter, occlusivity, variance, skewness, and circularity—to analyze the geometric characteristics of these shapes [17]. Batty proposed a usable computational method to measure isovist fields and explained how to visualize their spatial characteristics using maps and frequency distributions [18,19]. Ratti developed a method for quantifying the geometric characteristics of urban texture by using the raster-based model to evaluate the urban environment [20]. Despite numerous studies, there is a lack of an effective link between urban geometry and the quality of urban microclimate, which is partly attributed to the difficulty in quantitatively describing the complex real urban space [20]. Current quantitative research on urban space usually divides complex urban space into a series of small grids, and then quantify the spatial characteristics from each grid, ignoring the overall geometric characteristics of urban space. Geometric indices, such as spatial width and the aspect ratio, which are widely associated with the quality of microclimate, have limitations and are more suitable for ideal models or extreme urban space cases. Although some studies have attempted to correlate morphological parameters of real cities with microclimates, complex spatial features are still difficult to use with effective morphological parameters, and these real urban spaces are still idealized and use traditional morphological parameters [21–24]. The main purpose of this study is to investigate a quantitative method of spatial geometric characteristics that can be directly related to urban microclimate. For simplicity, as the basic unit of urban space, block space is focused on. In Section2, blocks in the Xinjiekou central area in Nanjing, a typical rapidly urbanizing area in china, are selected as the study cases. Subsequently, the quantitative method of spatial geometric characteristics is described, including the spatial identification and partition, the quantification of spatial characteristic indices (area, shape, and openness), and the spatial classification based on the indices. A possible correlation method between spatial characteristic indices and the microclimate evaluation index is also proposed in this section. In Section3, the case in Nanjing is used to verify the feasibility of the quantitative method and the possible correlation between the spatial characteristic indices and the microclimatic evaluation index. The spatial morphological classification chart based on the spatial characteristic indices and wind velocity distribution map is presented. Finally, we systematically discuss the effectiveness, limitations and future prospects of this quantitative method of the geometric characteristics of urban space.

2. Materials and Methods

2.1. Study Area As the core area with dense buildings, overlapping functions, concentrated population and frequent outdoor public activities, the urban central area has a more significant impact on urban microclimate, and more prominent microclimate problems [25]. The Xinjiekou central area in Nanjing, a typical rapidly urbanizing area in China, has a variety of building types, including large commercial complexes, residential buildings and office buildings, which results in a complex urban spatial form. Sustainability 2019, 11, 4951 3 of 13

Sustainability 2019, 11, x FOR PEER REVIEW 3 of 13 The environmental and spatial conditions of this area have been studied by researchers in many Sustainability 2019, 11, x FOR PEER REVIEW 3 of 13 fieldsof urban from form the [25–27]. simulation Therefore, of the urban the study wind cases and thermalselected environment in this study to are the two quantification blocks (block of A urban and form [25–27]. Therefore, the study cases selected in this study are two blocks (block A and B) with B) ofwith urban different form [25–27]. spatial Therefore,geometric thecharacteristics study cases locatedselected inin thethis Xinjiekou study are centraltwo blocks area (block (Figure A and1). diffB)erent with spatial different geometric spatial geometric characteristics characteristics located inlocated the Xinjiekou in the Xinjiekou central central area (Figure area (Figure1). 1).

FigureFigure 1. 1. The The location location ofof thethe study area in in Nanjing. Nanjing. Source: Source: Google Google Earth. Earth.

2.2.2.2. Method Method

2.2.1.2.2.1. The The Identification Identification Identification and and Partition Partition ofof Urban Urban Space TheThe premise premise of of quantifying quantifying spatialspatial geometricgeometric featurfeatur featureseses isis to to identify identify and and divide divide the the continuous continuous space.space. To To thisthis this end,end, end, wewe we proposepropose propose a a methoda method method for forfor identifying identifying and andand partitioning partitioning partitioning the the the complex complex complex spacesspaces spaces basedbased based on theonon connectivitythe the connectivity connectivity graph graph andgraph Peponis’ andand Peponis’Peponis’ theory of theory surface ofof partition, surfacesurface which partition,partition, proposes which which that proposes theproposes discontinuity that that the the of discontinuity of spatial information is caused by the discontinuity of the spatial boundary, such as spatialdiscontinuity information of spatial is caused information by the discontinuity is caused by of the the discontinuity spatial boundary, of the such spatial as building boundary, corners such [28 as]. building corners [28]. The connectivity graph can be generated by DepthmapX, which is a space Thebuilding connectivity corners graph[28]. The can connectivity be generated graph by DepthmapX, can be generated which isby a spaceDepthmapX, syntax analysiswhich is software a space syntax analysis software that can calculate the connectivity of the space by dividing the space into thatsyntax can analysis calculate software the connectivity that can ofcalculate the space the by connectivity dividing the of space the intospace small by dividing grids [29 ].the Connectivity space into small grids [29]. Connectivity actually calculates the number of other points located in each grid’s actuallysmall grids calculates [29]. Connectivity the number actually of other pointscalculates located the innumber each grid’s of other center points that located a particular in each point grid’s can seecenter within that its a line particular of sight, point which can can see be within applied its toline quantify of sight, the which spatial can visibility be applied to distinguishto quantify urbanthe centerspatial that visibility a particular to distinguish point can urban see withinspace [30]. its liTakingne of sight,the ideal which spatial can model be applied shown to in quantify Figure 2a the space [30]. Taking the ideal spatial model shown in Figure2a as an example, the spatial partition spatialas an visibility example, tothe distinguish spatial partition urban methodspace [30]. is de Takingmonstrated. the ideal Firstly, spatial conn modelect the shown building in cornersFigure 2a method is demonstrated. Firstly, connect the building corners outside the space to define the scope of as outsidean example, the space the tospatial define partition the scope method of the whole is de monstrated.space (Figure Firstly, 2b). Secondly, connect connect the building the building corners the whole space (Figure2b). Secondly, connect the building corners of the whole space (Figure2c). outsidecorners the of space the whole to define space the (Figure scope 2c).of the Finally, whole according space (Figure to the 2b). connectivity Secondly, graph connect generated the building by Finally, according to the connectivity graph generated by DepthmapX (Figure2d), select the spatial cornersDepthmapX of the (Figurewhole 2d),space select (Figure the spatial 2c). Finally, partition according lines (Figure to the 2e). connectivity graph generated by partitionDepthmapX lines (Figure (Figure 2d),2e). select the spatial partition lines (Figure 2e).

Figure 2. The spatial partition method: (a) the ideal spatial model; (b) connect the building corners outside the space to define the scope of the whole space; (c) connect the building corners of all space; Figure 2. The spatial partition method: ( aa)) the ideal spatial model; ( b) connect the buildingbuilding corners (d) generate the connectivity graph by using DepthmapX; (e) select the spatial partition lines. outside the space to define define the scope of the whole space; ( c) connect the building building corners corners of of all all space; space; (d) generate the connectivity graphgraph byby usingusing DepthmapX;DepthmapX; ((ee)) selectselect thethe spatialspatial partitionpartition lines.lines. 2.2.2. The Definition and Quantification of Spatial Characteristic Indices

2.2.2. The Definition and Quantification of Spatial Characteristic Indices

Sustainability 2019, 11, 4951 4 of 13 Sustainability 2019, 11, x FOR PEER REVIEW 4 of 13 SustainabilitySustainability 2019 2019, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 44 of of 13 13 2.2.2. The Definition and Quantification of Spatial Characteristic Indices Measurable spatial characteristic indices are very important for understanding and shaping the MeasurableMeasurable spatial spatial characteristic characteristic indices indices are are ve veryry important important for for understanding understanding and and shaping shaping the the urbanMeasurable spatial spatialenvironment characteristic and application indices are to verythe ur importantban design for process understanding [31]. There and are shaping various theindices urbanurban spatial spatial environment environment and and application application to to the the ur urbanban design design process process [31]. [31]. There There are are various various indices indices urbanthat spatial can be environment used to measure and application the urban to spatial the urban characteristics process [31]. There because are variousof the complexity. indices thatthat can can be be used used to to measure measure the the urban urban spatial spatial ge geometricometric characteristics characteristics because because of of the the complexity. complexity. thatFor can urban be used activities, to measure the area the of urban open spatialspace determin geometrices the characteristics function and because carrying of capacity the complexity. of the space, ForFor urban urban activities, activities, the the area area of of open open space space determin determineses the the function function and and carrying carrying capacity capacity of of the the space, space, For urbanand affects activities, the thephysical area of environment open space determines of the sp theace, function which andare carryingall important capacity factors of the for space, urban andand affectsaffects thethe physicalphysical environmentenvironment ofof thethe spspace,ace, whichwhich areare allall importantimportant factorsfactors forfor urbanurban andsustainable affects the physical development environment [32]. On of the the space, condition which of are the all importantsame area, factors the shape for urban of the sustainable space often sustainablesustainable developmentdevelopment [32].[32]. OnOn thethe conditioncondition ofof thethe samesame area,area, thethe shapeshape ofof thethe spacespace oftenoften developmentdetermines [32 whether]. On the a conditionspace is wide of the and same spacious, area, the or shapelong and of thenarrow space [33]. often Even determines if the area whether and shape determinesdetermines whether whether a a space space is is wide wide and and spacious, spacious, or or long long and and narrow narrow [33]. [33]. Even Even if if the the area area and and shape shape a spaceof the is space wide andare the spacious, same, the or longenclosure and narrowdegree of [33 the]. Evenspace ifcan the also area determine and shape the of nature the space of activities are ofof the the space space are are the the same, same, the the enclosure enclosure degree degree of of the the space space can can also also determine determine the the nature nature of of activities activities the same,and change the enclosure the wind degree and sunshine of the space environment can also determine of the space. the Because nature of the activities area, shape, and change and enclosure the andand change change the the wind wind and and sunshine sunshine environment environment of of the the space. space. Because Because the the area, area, shape, shape, and and enclosure enclosure winddegree and sunshine of space environment can distinguish of the different space. types Because of thespace area, and shape, can be and understood enclosure degreeby urban of spacedesigners degreedegree of of space space can can distinguish distinguish different different types types of of space space and and can can be be understood understood by by urban urban designers can distinguishand architects diff toerent design types corresponding of space and canurban be understoodspaces, these by geometric urban designers characteristics and architects of space to are andand architectsarchitects toto designdesign correspondingcorresponding urbanurban spaces,spaces, thesethese geometricgeometric characteristicscharacteristics ofof spacespace areare designfurther corresponding defined as spatial urban spaces,characteristic these geometricindices, including characteristics area, shape, of space andare openness further (Table defined 1). as furtherfurther defined defined as as spatial spatial characteristic characteristic indices, indices, including including area, area, shape, shape, and and openness openness (Table (Table 1). 1). spatial characteristic indices, including area, shape, and openness (Table1). Table 1. The spatial characteristic indices and the corresponding schematic diagram. TableTable 1. 1. The The spatial spatial characteristic characteristic indices indices and and the the corresponding corresponding schematic schematic diagram. diagram. Table 1. The spatial characteristic indices and the corresponding schematic diagram. Spatial SpatialSpatial Spatial Characteristic Area Shape Openness CharacteristicCharacteristic AreaAreaArea ShapeShape Openness OpennessOpenness IndicesIndices IndicesIndices

Schematic SchematicSchematicSchematic diagram diagram diagramdiagram

Area is the size of the divided space. Shape is similar to elongation and can be measured by the AreaAreaArea is the is is the the size size size of of theof the the divided divided divided space. space. space. Shape Shape Shape is is is similar similar similar toto to elongationelongation elongation andand and can can be be measured measured by byby the the ratio of the average horizontal distance to the maximum horizontal distance from the center of space theratio ratioratio of of the the average average horizontal horizontal horizontal distance distance distance to to to the the the maximum maximum maximum horizontal horizontal horizontal distance distance distance from from from the the the center center center of of space ofspace to the boundary of space [33]. Openness is related to the number and size of openings in the space. spacetoto the tothe the boundary boundary boundary of of space ofspace space [33]. [33]. [33 Openness Openness]. Openness is is related related is related to to the tothe thenumber number number and and and size size size of of openings ofopenings openings in in the the in thespace. space. On the basis of their respective calculation methods, in order to use computer programming to space.OnOn On thethe the basisbasis basis ofof of theirtheir their respectiverespective respective calculation calculation meth methods,methods,ods, ininin order orderorder to toto use useuse computer cocomputermputer programming programmingprogramming to toto improve the computation efficiency, this study develops a new method of spatial data acquisition improveimproveimprove the computationthethe computation computation efficiency, efficiency, efficiency, this studythis this study study develops develops develops a new a methoda new new method method of spatial of of spatial dataspatial acquisition data data acquisition acquisition and and proposes the calculation method for spatial characteristic indices based on the collected data. proposesandand proposes proposes the calculation the the calculation calculation method method formethod spatial for for characteristicspatial spatial ch characteristicaracteristic indices basedindices indices on based based the collected on on the the collected collected data. data. data. Figure3a illustrates a spatial plane graph and the isovist from point O. An isovist can be considered as the area that is not in the shadows cast from a point light source [18]. The point O shows the observer’s location and the grey area shows the area visible from the location. Based on the concept of isovist, a spatial data acquisition method is developed. First, the buildings are scanned counterclockwise from the X-axis around point O and the horizontal distance from point O to the buildings is recorded every 1◦, which is called ri (Figure3a). Second, the corresponding point-based spatial data graph is created based on the horizontal distance and scanning angle (Figure3b). When the measuring point is at the centroid of space, the spatial characteristic indices can be calculated by analyzing the numerical changes of the point-based spatial data graph. Through analysis, a Python script is developed to calculate the spatial characteristic indices (see the Supplementary Material: Script S1). The mathematical development of the indices is shown below.

Figure 3. The spatial plane graph and the point-based spatial data graph: (a) scanning of the buildings FigureFigure 3. 3. The The spatial spatial plane plane graph graph and and the the point-based point-based spatial spatial data data graph: graph: ( a(a) )scanning scanning of of the the buildings buildings counterclockwise from the X-axis around point O and recording of the horizontal distance from point counterclockwisecounterclockwise from from the the X X-axis-axis around around point point O O and and recording recording of of the the horizontal horizontal distance distance from from point point O to the building every 1°, which is called ri; (b) of the corresponding point-based spatial O to the building every 1°, which is called ri; (b) illustration of the corresponding point-based spatial O to the building every 1°, which is called ri; (b) illustration of the corresponding point-based spatial data graph. datadata graph. graph.

Sustainability 2019, 11, x FOR PEER REVIEW 4 of 13

Measurable spatial characteristic indices are very important for understanding and shaping the urban spatial environment and application to the process [31]. There are various indices that can be used to measure the urban spatial geometric characteristics because of the complexity. For urban activities, the area of open space determines the function and carrying capacity of the space, and affects the physical environment of the space, which are all important factors for urban sustainable development [32]. On the condition of the same area, the shape of the space often determines whether a space is wide and spacious, or long and narrow [33]. Even if the area and shape of the space are the same, the enclosure degree of the space can also determine the nature of activities and change the wind and sunshine environment of the space. Because the area, shape, and enclosure degree of space can distinguish different types of space and can be understood by urban designers and architects to design corresponding urban spaces, these geometric characteristics of space are further defined as spatial characteristic indices, including area, shape, and openness (Table 1).

Table 1. The spatial characteristic indices and the corresponding schematic diagram.

Spatial Characteristic Area Shape Openness Indices Sustainability 2019, 11, x FOR PEER REVIEW 5 of 13

Figure 3a illustrates a spatial plane graph and the isovist from point O. An isovist can be consideredSchematic as the area that is not in the shadows cast from a point light source [18]. The point O shows thediagram observer’s location and the grey area shows the area visible from the location. Based on the concept of isovist, a spatial data acquisition method is developed. First, the buildings are scanned counterclockwise from the X-axis around point O and the horizontal distance from point O to the buildings is recorded every 1°, which is called ri (Figure 3a). Second, the corresponding point-based spatial data graph is created based on the horizontal distance and scanning angle (Figure 3b). When the measuringArea is the point size ofis atthe the divided centroid space. of space, Shape the is similarspatial characteristicto elongation indicesand can can be measuredbe calculated by theby analyzingratio of the the average numerical horizontal changes distance of the topoint-based the maximum spatial horizontal data graph. distance Through from analysis,the center a of Python space scriptto the isboundary developed of spaceto calculate [33]. Openness the spatial is relatedcharacteristic to the numberindices (seeand sizethe Supplementaryof openings in theMaterial: space. ScriptOn the S1). basis The of mathematical their respective development calculation of themeth indicesods, in is ordershown to below. use co mputer programming to improveSustainabilityArea the measures2019 computation, 11, 4951 the size efficiency, of space, thiswhich study is the develops basic characteristic a new method of open of spatial space data(Figure acquisition 4a).5 The of 13 equationand proposes used theis as calculation follows: method for spatial characteristic indices based on the collected data. ° Area = ∑ [m2] (1) where ri (1 ≤ i ≤ 360) represents the horizontal distance from a measuring point to the spatial boundary composed of the building walls and spatial partition lines. Shape measures the narrowness of urban space, which can be used to distinguish short and wide spaces from long and thin spaces. Figure 4b illustrates that as the shape becomes longer and narrower, the ratio of maximum horizontal distance to average horizontal distance increases. Therefore, the equation used is as follows:

𝑟 Shape = [−] (2) 𝑟 where rave and rmax are the average horizontal distance and maximum horizontal distance from a measuring point to the spatial boundary composed of the building walls and spatial partition line.

The shape value ranges from 0 to 1. The larger the value is, the wider the space is. The smaller the valueFigure is, the 3. narrower TheThe spatial spatial the plane plane space graph graph is. and and the the point-based point-based spatial data graph: ( (aa)) scanning scanning of of the the buildings buildings Opennesscounterclockwise is related from to the the X-axis number around and point size O ofand th recording recordinge openings of the in urbanhorizontal horizontal space. distance distance The fromequation from point point used is as follows:O to the building every 1 °◦,, which which is called ri;;( (bb)) illustration illustration of of the the corresponding corresponding point-based spatial data graph. 𝑁 × 𝐴 Openness = [−] (3) Area measures the size of space, which360° is the basic characteristic of open space (Figure4a). whereThe equation NO is the used number is as follows:of openings in the space around the measuring point, and AO is the angle of openings in the space around the measuring point. As shown in Figure 4c, openings in space have a X riri+1 sin 1◦ h i direct relationship with the changeArea of= horizontal distance in mthe2 point-based spatial data graph.(1) 2 Therefore, a Python script is developed to calculate NO and AO by analyzing the change of horizontal distancewhere ri (1(see ithe360) Supplementary represents the Material: horizontal Script distance S1). The from larger a measuring the value point is, the to more the spatial open boundarythe space ≤ ≤ is.composed The smaller of the the building value is, walls the more and spatialclosed partitionthe spacelines. is.

FigureFigure 4. TheThe spaces spaces with with different different geometric characteri characteristicsstics shown shown in in a a spatial spatial plane plane graph graph and and the the correspondingcorresponding point-basedpoint-based spatialspatial data data graph: graph: ( a()a the) the spaces spaces of of di ffdifferenterent areas areas with with the the same same shape shape and openness; (b) the spaces of different shapes with the same area and openness; (c) the space with two openings, which are marked in red.

Shape measures the narrowness of urban space, which can be used to distinguish short and wide spaces from long and thin spaces. Figure4b illustrates that as the shape becomes longer and narrower, the ratio of maximum horizontal distance to average horizontal distance increases. Therefore, the equation used is as follows: r Shape = ave [ ] (2) rmax0 − where rave and rmax are the average horizontal distance and maximum horizontal distance from a measuring point to the spatial boundary composed of the building walls and spatial partition line. The shape value ranges from 0 to 1. The larger the value is, the wider the space is. The smaller the value is, the narrower the space is. Sustainability 2019, 11, 4951 6 of 13

Openness is related to the number and size of the openings in urban space. The equation used is as follows: No Ao Openness = × [ ] (3) 360◦ − where NO is the number of openings in the space around the measuring point, and AO is the angle of openings in the space around the measuring point. As shown in Figure4c, openings in space have

Sustainabilitya direct relationship 2019, 11, x FOR with PEER the REVIEW change of horizontal distance in the point-based spatial data graph.6 of 13 Therefore, a Python script is developed to calculate NO and AO by analyzing the change of horizontal distanceand openness; (see the Supplementary (b) the spaces of Material:different shapes Script wi S1).th the The same larger area the and value openness; is, the (c more) the space open with thespace is. Thetwo smaller openings, the which value are is, marked the more in red. closed the space is.

2.2.3.2.2.3. Spatial Spatial Classification Classification Method Method Based Based on on Spatial Spatial Characteristic Characteristic Indices Indices TheThe spatial spatial morphological classificationclassification chartchart withwith area, area, shape, shape, and and openness openness as as axes axes is is proposed proposed to toclassify classify urban urban space space with with different different geometric geometric characteristics. characteristics. Figure 5Figurea shows 5a three shows groups three of groups controlled of controlledtrials with ditrialsfferent with spatial different geometric spatial characteristics: geometric keepingcharacteristics: the other keeping two spatial the characteristic other two spatial indices characteristicunchanged, the indices area of unchanged, a1 to a4 gradually the area increases, of a1 to the a4 shapegradually of b1 increases, to b4 gradually the shape decreases, of b1 and to theb4 graduallyopenness ofdecreases, c1 to c4 graduallyand the increases.openness Figureof c1 5tob showsc4 gradually the distribution increases. of Figure a1 to c4 5b on shows the spatial the distributionmorphological of classificationa1 to c4 on the chart. spatial Different morphological spatial forms classification present diff erentchart. aggregation Different spatial conditions forms on presentthe spatial different classification aggregation chart. Byconditions analyzing on the the distribution spatial classification of density, urbanchart. spaceBy analyzing with different the distributiongeometric characteristics of density, urban can bespace classified. with different geometric characteristics can be classified.

FigureFigure 5. 5. ControlledControlled experiments experiments with with different different spatial spatial geometric geometric characteristics: characteristics: ( (aa)) keeping keeping the the other other twotwo spatial spatial characteristic characteristic indices unchanged,unchanged, thethe areaarea of of a1 a1 to to a4 a4 gradually gradually increases, increases, shape shape of of b1 b1 to to b4 b4gradually gradually decreases, decreases, and and openness openness of c1 of to c1 c4 to gradually c4 gradually increases; increases; (b) the (b distribution) the distribution of a1 toof c4a1 on to thec4 onspatial the spatial morphological morphological classification classification chart. chart.

2.2.4.2.2.4. The The Correlation Correlation Method Method of of Spatial Spatial Characteristic Characteristic Indices Indices and and Microclimate Microclimate Evaluation Evaluation Index Index InIn order order to to verify verify the the feasibility feasibility of of the the correlation correlation study study between between the the above above spatial spatial quantitative quantitative methodmethod and urban spatialspatial microclimate,microclimate, computational computational fluid fluid dynamics dynamics (CFD) (CFD) was was used used to simulateto simulate the thewind wind field field of pedestrianof pedestrian height height (h (h= 1.5= 1.5 m) m) in in the the block. block. TheThe standardstandard k-k-εε model of the 3-D 3-D steady steady ReynoldsReynolds Average Average Navier-Stokes Navier-Stokes (RANS) (RANS) approach approach was was employed employed for for the the nume numericalrical simulation simulation [34]. [34]. TheThe summersummer typical typical inflow inflow wind inwind Nanjing in wasNanjing taken aswas the inflowtaken windas the speed inflow (https: //windweatherspark. speed (https://weatherspark.com/y/132872/Average-Weathercom/y/132872/Average-Weather-in-Nanjing-China-Year-Round-in-Nanjing-China-Year-Round).). A validation study against A validation the wind studytunnel against experiment the wind has been tunnel performed experiment in a previous has been study performed [11]. In in order a previous to better study verify [11]. the applicabilityIn order to betterof the verify correlation the applicability study between of the space correlation and local study ventilation, between the space spatial and wind local velocityventilation, ratio the (VR) spatial was wind velocity ratio (VR) was employed as a quantitative evaluation index in this study. By comparing the three spatial characteristic indices (area, shape and openness) with VR, it can provide ideas for the study of the correlation between urban spatial geometry and urban microclimate. The equation of VR is as follows: 𝑈 VR = [−] (4) 𝑈 Here, VR donates the spatial velocity ratio, U is the specified velocity at a pedestrian (h = 1.5 m), and U0 is the reference velocity in the far upstream free flow.

Sustainability 2019, 11, 4951 7 of 13 employed as a quantitative evaluation index in this study. By comparing the three spatial characteristic indices (area, shape and openness) with VR, it can provide ideas for the study of the correlation between urban spatial geometry and urban microclimate. The equation of VR is as follows:

U VR = [ ] (4) U0 −

Here, VR donates the spatial velocity ratio, U is the specified velocity at a pedestrian level (h = 1.5 m), Sustainabilityand U0 is the 2019 reference, 11, x FOR velocity PEER REVIEW in the far upstream free flow. 7 of 13

3. Results Results and and Analysis Analysis 3.1. Spatial Partition and Spatial Data Collection 3.1. Spatial Partition and Spatial Data Collection According to the spatial partition method mentioned above, the space in block A and B is identified According to the spatial partition method mentioned above, the space in block A and B is and divided (Figure6a). As verification, the spatial partition is compared with the connectivity graph identified and divided (Figure 6a). As verification, the spatial partition is compared with the generated by DepthmapX (Figure6b). The subspaces of block A and B are numbered, and there connectivity graph generated by DepthmapX (Figure 6b). The subspaces of block A and B are are 36 subspaces from A0 to A35 in block A and 17 subspaces from B0 to B16 in block B (Figure6c). numbered, and there are 36 subspaces from A0 to A35 in block A and 17 subspaces from B0 to B16 in The measuring points are set in the centroid of these subspaces to collect information on the space block B (Figure 6c). The measuring points are set in the centroid of these subspaces to collect (Figure6d). information on the space (Figure 6d).

Figure 6. The partition, connectivity connectivity graph, graph, numbers numbers an andd measuring measuring points points of of the the space space in in block A and B: ( a) spatial partition; ( b) superposed spatial partition lines on the connectivity graph based on DepthmapX; ( cc)) 36 36 subspaces subspaces from from A0 A0 to to A35 A35 in in block block A A an andd 17 17 subspaces subspaces from from B0 B0 to to B16 B16 in in block block B; B; (d) the measuring points placed in the centroid ofof thethe subspaces.subspaces.

3.2. Spatial Data Processing and Analysis The spatial data processing flow is as follows. Firstly, the grasshopper program in Rhino software is used to collect the spatial data around the measuring points. Second, the python script is run with the collected spatial data to calculate the spatial characteristic indices. Finally, the values of these spatial characteristic indices are employed to quantify and classify the geometric characteristics of the block spaces. Figure 7 shows the calculation results of the spatial characteristic indices of the blocks (the values of the spatial characteristic indices can be seen in the Supplementary Material: Table S2). It can be found that the range of area is from 25 m2 to 13,394 m2, the range of shape is from 0.04 to 0.99, and the range of openness is from 0.03 to 2.01. The numerical differences between different spaces are obvious. Moreover, by comparing the values of the spatial characteristic indices (area, shape, and openness), different spatial geometrical characteristics can be distinguished. Take the index values of

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3.2. Spatial Data Processing and Analysis The spatial data processing flow is as follows. Firstly, the grasshopper program in Rhino software is used to collect the spatial data around the measuring points. Second, the python script is run with the collected spatial data to calculate the spatial characteristic indices. Finally, the values of these spatial characteristic indices are employed to quantify and classify the geometric characteristics of the block spaces. Figure7 shows the calculation results of the spatial characteristic indices of the blocks (the values of the spatial characteristic indices can be seen in the Supplementary Material: Table S2). It can be found that the range of area is from 25 m2 to 13,394 m2, the range of shape is from 0.04 to 0.99, and the range of openness is from 0.03 to 2.01. The numerical differences between different spaces are obvious.

Moreover,Sustainability 2019 by comparing, 11, x FOR PEER the REVIEW values of the spatial characteristic indices (area, shape, and openness),8 of 13 different spatial geometrical characteristics can be distinguished. Take the index values of spaces in blockspaces A in and block block A and B as block an example, B as an example, where the wher rede frame the red in frame Figure in7 shows Figure four7 shows di ff erentfour different types of spacestypes of (space spaces A4, A6,(space A23, A4, and A6, B14) A23, in the and blocks B14) with in distinctlythe blocks diff erentwith spatialdistinctly characteristic different indices:spatial characteristic indices: The space with a small area, large shape, and large openness is a small, open and spacious space • • (suchThe space as space with A4); a small area, large shape, and large openness is a small, open and spacious space The(such space as space with A4); a small area, small shape, and small openness is a small, closed and narrow space • • (suchThe space as space with A6); a small area, small shape, and small openness is a small, closed and narrow space The(such space as space with A6); a large area, small shape, and small openness is a large, closed and narrow space • • (suchThe space as space with A23); a large area, small shape, and small openness is a large, closed and narrow space The(such space as space with A23); a large area, large shape, and large openness is a large, open and spacious space • (suchThe space as space with B14). a large area, large shape, and large openness is a large, open and spacious space (such as space B14).

Figure 7. The spatial characteristic indices charts and four types of spaces in block A and B: space A4, A6, A23, and B14.

3.3. Urban Spatial Classification with Di erent Geometric Characteristics 3.3. Urban Spatial Classification with Differentff Geometric Characteristics According toto thethe statisticsstatistics of of the the spatial spatial characteristic characteristic indices indices (area, (area, shape, shape, and and openness) openness) and and the distributionthe distribution of the of statisticsthe statistics on the on spatial the spatial morphological morphological classification classification chart, chart, the spaces the spaces in two in blocks two ofblocks the Xinjiekou of the Xinjiekou central areacentral can area be generally can be generall classifiedy classified into five categories into five categories as shown below as shown (Figure below8a). (Figure 8a). • Type 1 (large open spacious space) with a large area, shape, and openness (marked in red); • Type 2 (large closed narrow space) with a large area and small shape and openness (marked in green); • Type 3 (small closed narrow space) with a small area, shape, and openness (marked in blue); • Type 4 (large open narrow space) with a large area and openness and small shape (marked in light purple); • Type 5 (small open spacious space) with a small area and large shape and openness (marked in yellow). Figure 8b illustrates the spatial distribution of these five spatial types on the map to intuitively reveal the difference of the spaces, which is also validation of the above classification methods.

Sustainability 2019, 11, 4951 9 of 13

Type 1 (large open spacious space) with a large area, shape, and openness (marked in red); • Type 2 (large closed narrow space) with a large area and small shape and openness (marked • in green); Type 3 (small closed narrow space) with a small area, shape, and openness (marked in blue); • Type 4 (large open narrow space) with a large area and openness and small shape (marked in • light purple); Type 5 (small open spacious space) with a small area and large shape and openness (marked • in yellow). Sustainability 2019, 11, x FOR PEER REVIEW 9 of 13

(a)

(b)

Figure 8. Spatial morphological classificationclassification chart chart and and the the corresponding corresponding spatial spatial distribution distribution map: map: (a) (Typea) Type 1 is 1 a is large a large open open spacious spacious space, space, Type Type 2 is a 2 large is a large closed closed narrow narrow space, space, Type 3Type is a small3 is a closedsmall closednarrow narrow space, Typespace, 4 Type is a large 4 is a open large narrow open narrow space, andspace, Type and 5 Type is a small 5 is a open small spacious open spacious space; (space;b) the (spatialb) the spatial distribution distribution of the five of the spatial five spatial types on types the map.on the map.

3.4. ComparisonFigure8b illustrates of the Spatial the Average spatial distributionWind Velocity of Ratio these and five Spatial spatial Characteristic types on the Indices map to intuitively reveal the difference of the spaces, which is also validation of the above classification methods. We performed a simulation of the wind flow field of pedestrian height in block B according to the method mentioned in Section 2. The simulation results are shown in Figure 9a. In order to further compare them with the spatial geometry, the spatial partition lines are superposed on the wind velocity distribution (Figure 9b), and the spatial average wind velocity ratio of each subspace is calculated based on the spatial partition (statistics can be seen in the Supplementary Material: Table S3). According to the numbers of subspaces in block B, the calculated spatial average wind velocity ratio can be compared with the spatial characteristic indices of different subspaces to analyze the changing trend of its value (Figure 10). The bar chart with different colors represents the different spatial characteristic indices, and the line chart represents the spatial average wind velocity ratio. Complex and real urban space can be quantified into three spatial characteristic indices, which can be combined as different aspects of the whole space to compare with spatial average wind velocity ratio comprehensively.

Sustainability 2019, 11, 4951 10 of 13

3.4. Comparison of the Spatial Average Wind Velocity Ratio and Spatial Characteristic Indices We performed a simulation of the wind flow field of pedestrian height in block B according to the method mentioned in Section2. The simulation results are shown in Figure9a. In order to further compare them with the spatial geometry, the spatial partition lines are superposed on the wind velocity distribution (Figure9b), and the spatial average wind velocity ratio of each subspace is calculated basedSustainability on the 2019 spatial, 11, x FOR partition PEER REVIEW (statistics can be seen in the Supplementary Material: Table S3). 10 of 13

Sustainability 2019, 11, x FOR PEER REVIEW 10 of 13

Figure 9. ((aa)) The The wind velocity at a pedestrian leve levell (h = 1.51.5 m) in block B of summer; (b) spatial partition lines superposed on the wind velocity distribution.distribution.

According to the numbers of subspaces in block B, the calculated spatial average wind velocity ratio can be compared with the spatial characteristic indices of different subspaces to analyze the changing trend of its value (Figure 10). The bar chart with different colors represents the different spatial characteristic indices, and the line chart represents the spatial average wind velocity ratio.

Complex and real urban space can be quantified into three spatial characteristic indices, which can be combinedFigure 9. as(a) diThefferent wind aspectsvelocity ofat thea pedestrian whole space level to(h compare= 1.5 m) in with block spatial B of summer; average ( windb) spatial velocity ratiopartition comprehensively. lines superposed on the wind velocity distribution.

Figure 10. A line chart with statistics of the spatial average wind velocity ratio and a bar chart with spatial characteristic indices (area, shape, and openness) of subspaces in block B.

4. Discussion By comparing the spatial average wind velocity ratio of each subspace with the spatial characteristic indices of the area, shape, and openness of each subspace, the relationship between the wind environment and the spatial geometric characteristics could be inferred. It could be generally inferredFigure that 10. the A linearea chart and withopenness statistics are ofrelated the spatial to th average e wind environment,wind veloci velocityty ratio but theand shapea bar chartis not. with Taking spacespatial B0 and characteristic space B1 as indices examples, (area, the shape, area and and openness) openness ofof subspacessubspacesof space B0 inin blockareblock larger B.B. than space B1, while the shape of space B0 and space B1 is similar, and the average wind velocity ratio of space B0 is larger 4. Discussion 4.than Discussion space B1. However, this relationship between area and openness and the wind environment is not absolute.By comparing For example, the spatial space average B14 wind has the velocity largest ratio area of eachand subspaceopenness within all the subspaces spatial characteristic of block B, By comparing the spatial average wind velocity ratio of each subspace with the spatial indiceswhile the of spatial the area, average shape, wind and velocity openness ratio of is eachnot the subspace, largest. This the relationshipphenomenon between may be caused the wind by characteristic indices of the area, shape, and openness of each subspace, the relationship between the environmentthe surrounding and space the spatial environment geometric or characteristicsother spatial characteristics could be inferred. of the It space. could be generally inferred wind environment and the spatial geometric characteristics could be inferred. It could be generally It is worth noting that the north side of space B14 is another block, which is separated with block inferred that the area and openness are related to the wind environment, but the shape is not. Taking B by a street. At the beginning of the quantitative study of urban space, block space, as the basic unit space B0 and space B1 as examples, the area and openness of space B0 are larger than space B1, while of urban space, is taken as the research object. While the space outside the blocks, which is usually the shape of space B0 and space B1 is similar, and the average wind velocity ratio of space B0 is larger the street space between the blocks, is not taken into account. This space may have an impact on the than space B1. However, this relationship between area and openness and the wind environment is microclimate inside the block, especially the wind environment. Therefore, the spatial partition not absolute. For example, space B14 has the largest area and openness in all subspaces of block B, method may need to be optimized according to different researching purposes and spatial conditions. while the spatial average wind velocity ratio is not the largest. This phenomenon may be caused by the surrounding space environment or other spatial characteristics of the space. 5. Conclusions It is worth noting that the north side of space B14 is another block, which is separated with block B by a street. At the beginning of the quantitative study of urban space, block space, as the basic unit of urban space, is taken as the research object. While the space outside the blocks, which is usually the street space between the blocks, is not taken into account. This space may have an impact on the microclimate inside the block, especially the wind environment. Therefore, the spatial partition method may need to be optimized according to different researching purposes and spatial conditions.

5. Conclusions

Sustainability 2019, 11, 4951 11 of 13 that the area and openness are related to the wind environment, but the shape is not. Taking space B0 and space B1 as examples, the area and openness of space B0 are larger than space B1, while the shape of space B0 and space B1 is similar, and the average wind velocity ratio of space B0 is larger than space B1. However, this relationship between area and openness and the wind environment is not absolute. For example, space B14 has the largest area and openness in all subspaces of block B, while the spatial average wind velocity ratio is not the largest. This phenomenon may be caused by the surrounding space environment or other spatial characteristics of the space. It is worth noting that the north side of space B14 is another block, which is separated with block B by a street. At the beginning of the quantitative study of urban space, block space, as the basic unit of urban space, is taken as the research object. While the space outside the blocks, which is usually the street space between the blocks, is not taken into account. This space may have an impact on the microclimate inside the block, especially the wind environment. Therefore, the spatial partition method may need to be optimized according to different researching purposes and spatial conditions.

5. Conclusions We proposed a new quantitative method of spatial geometric characteristics, including spatial partition, spatial characteristic indices (area, shape, and openness), and spatial classification, to provide ideas for the study of the correlation between urban spatial geometry and urban microclimate. The spatial partition and quantification methods proposed in this paper make the quantified spatial objects clearer, so as to make the objects of correlation study clearer. For urban planners and building designers, the specific urban space can be designed and improved according to the results of the relationship between the spatial geometry and the wind environment. Three spatial characteristic indices, including area, shape, and openness, can effectively describe the complex urban space to a certain extent. In addition to area and shape, which are recognized as the basic spatial characteristic indices, openness is a very important index for describing the spatial form, which is usually calculated by obtaining the ratio of the spatial entity boundary perimeter to total spatial perimeter. In fact, the openness of space is not only related to the length of spatial openings, but also to the number and distribution of these openings. Therefore, this research optimizes the calculation method of openness and makes it more pertinent. In this study, the quantification of urban geometry focuses on the spatial plane geometry. However, for the wind environment, height is also an important morphological index. Therefore, how to incorporate height into the current quantitative methods and the relationship between all these indices may need further study. Taking two blocks in the Xinjiekou central area in Nanjing as an example, the spatial average wind speed ratio and the spatial characteristic indices are compared and analyzed, and the effectiveness and practicability of the correlation research between the wind environment and urban spatial geometry have been verified. In the correlation research with the wind environment, the shape has little correlation, and the area and openness are correlated with the wind environment to some extent, but the correlation is not absolute. Further analysis is needed in combination with the specific space and its surrounding spatial environment. When the area, shape and openness are not correlated with the wind environment, other spatial characteristic indices may be needed. It is worth noting that when the shape is the same, if the direction of the shape and wind is different, although the visual perception of space is the same, the wind environment is different. Therefore, it is necessary to discuss the direction of shape in a future correlation study on spatial geometrical configurations and the wind environment. In addition, it is found that there may not be a unique spatial partition, which depends on different environmental issues. For example, when associated with the wind environment, the spatial partition can take into account the space outside the block. The spatial partition method will be further discussed for different microclimate problems in future research.

Supplementary Materials: The following are available online at http://www.mdpi.com/2071-1050/11/18/4951/s1, Script S1. Python Script of Spatial Characteristic Indices; Table S2. Statistics of the Spatial Characteristic Indices of Subspaces in Block A and B. Table S3. Statistics of Spatial Average Wind Velocity Ratio of Subspaces in Block B. Sustainability 2019, 11, 4951 12 of 13

Author Contributions: H.J. constructed the method, analyzed the data, and wrote and revised the manuscript. Y.P. performed the numerical simulation, improved the figures and revised the manuscript. W.D. designed the analytical framework and revised the manuscript. All authors read and approved the final manuscript. Funding: This research was supported by National Natural Science Foundation of China (No. 51538005). Acknowledgments: The authors would like to thank the MDPI English editing service for carefully checking the English writing of the manuscript. A warm acknowledgment is given to Juan Li for comments and suggestions. Conflicts of Interest: The authors declare no conflict of interest.

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