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Ecological Indicators

journal homepage: www.elsevier.com/locate/ecolind

Thermal impacts of greenery, water, and impervious structures in Beijing’sOlympic area: A spatial regression approach

Zhaoxin Daia,b, Jean-Michel Guldmannc,⁎, Yunfeng Hua,⁎

a State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, University of ChineseAcademy of Sciences, No. 11A Datun Road, Chaoyang District, 100101 Beijing, Chinab Chinese Academy of Surveying and Mapping, 28 Lianhuachi West Road, Haidian District, 100830 Beijing, Chinac Department of City and Regional Planning, The Ohio State University, 275 West Woodruff Avenue, Columbus, OH 43210, USA

A R T I C L E I N F O

Keywords:Urban heat islandLand usesTreesGrassSpatial autocorrelation

A B S T R A C T

This paper explores the urban land-use determinants of the urban heat island (UHI) in Beijing’s Olympic Area,using different statistical models, land surface temperatures (LST) derived from Landsat 8 remote sensing, andland-use data derived from 1-m high-resolution imagery. Data are captured over grids of different sizes. Spatialregressions are necessary to capture neighboring effects, particularly when the grid unit is small. Grass, trees,water bodies, and shades have all significant and negative effects on LST, whereas buildings, roads and otherimpervious surfaces have all significant and positive effects. The results also point to significant nonlinear andinteraction effects of grass, trees and water, particularly when the grid cell size is small (60m-90m). Trees arefound to be the most important predictor of LST. When the grids are smaller than 180m, the indirect impacts arelarger than the direct ones, whereas, the opposite takes place for larger grids. Because of their strong perfor-mance (R2 ranging from 0.839 to 0.970), the models can be used for predicting the impacts of land-use changeson the UHI and as tools for urban planning. Finally, extensive uncertainty and sensitivity analyses show that themodels are very reliable in terms of both input data accuracy and estimated coefficients precision.

1. Introduction

Rapid urbanization has led to the transformation of natural land-scapes, such as vegetation cover, water bodies, and agrarian lands, intourban buildings and impervious surfaces. This transformation has re-duced vegetation evapotranspiration and increased solar radiation ab-sorption by impervious materials, leading to the urban heat island(UHI), with higher air and surface temperatures in urban areas ascompared to suburban and rural areas. A precise understanding andmodeling of the urban factors that influence temperature is thereforeimportant for mitigating the UHI (Buyantuyev and Wu, 2012).

Making use of very precise land-use data derived from high-re-solution satellite images for the Olympic Area of Beijing, this paper (1)investigates the spatial relationship between land surface temperature(LST) and the land-use pattern, (2) specifies statistical regressionmodels accounting for spatial neighborhood effects, (3) assesses howthese effects vary across different grid scales, and (4) explores nonlinearand interaction effects among water bodies, grass, trees, buildingshades, building footprints, impervious surfaces, roads, and bare lands.A hierarchy of grids, with cell sizes ranging from 30m to 600m, is used

to integrated all the data.The paper is organized as follows. Section 2 presents a review of the

relevant literature. Section 3 introduces the study area and datasources. The regression methodology is described in Section 4. Section 5presents and analyzes the regression results, with a focus on nonlineareffects and direct and indirect spatial impacts. Section 6 consists inuncertainty and sensitivity analyses of the estimated models. Section 7further discusses the findings. Section 8 summarizes the results andoutlines areas for further research.

2. Literature review

The UHI can be analyzed with both air and surface temperatures.However, due to the sparse and irregular distribution of weather sta-tions, the UHI has been predominantly analyzed with land surfacetemperatures (LST) derived from thermal infrared remote-sensing sa-tellite imagery (Sheng et al., 2017). The spatial pattern of LST providesa record of the radiation energy emitted from the ground surface.

The relationship between LST and land-use/land-cover (LULC)patterns has been the object of recent research (Tran et al., 2017; Wu

https://doi.org/10.1016/j.ecolind.2018.09.041Received 25 February 2018; Received in revised form 24 July 2018; Accepted 21 September 2018

⁎ Corresponding authors.E-mail addresses: daizx@lreis.ac.cn (Z. Dai), guldmann.1@osu.edu (J.-M. Guldmann), huyf@lreis.ac.cn (Y. Hu).

Ecological Indicators 97 (2019) 77–88

1470-160X/ © 2018 Elsevier Ltd. All rights reserved.

T

et al., 2014). Several studies show that impervious construction in-creases the UHI (Peng et al., 2016). Estoque et al. (2017) find a strongcorrelation between LST and the density of impervious surface (posi-tive), green space (negative), and the size, shape complexity, and ag-gregation of patches along the urban–rural gradient of several cities,using linear regression analysis. Zhao et al. (2016) find that the UHIspatiotemporal changes are consistent with urban land expansion.Berger et al. (2017) point to a high correlation between remotely-sensed urban site characteristics and LST. Chun and Guldmann (2014)report that larger building roof-top areas increase LST, and a largerNDVI decreases it. Song et al. (2014) find that spatial resolutions of660m and 720m are best for measuring the relationships betweenlandscape composition and LST.

Another important consideration is the relationship between theUHI and green land uses. Urban green spaces, such as trees and grass,can significantly reduce the UHI and modify the urban microclimate(Al-Gretawee, 2016). Armson et al. (2012) report that both trees andgrass can reduce regional and local temperatures. Li et al. (2013) showthat the spatial pattern of greenspace, both in composition and con-figuration, affects LST. Kong et al. (2014) find that the urban cool islandis affected by the areas of forested vegetation and their spatial ar-rangement. Al-Gretawee (2016) reports that parks have a significantcooling effect up to a distance of 860m from their boundaries. Zhouet al. (2017) show that the relationship between the spatial config-uration of trees and LST varies across different cities with differentclimatic conditions. Feyisa et al. (2014) show that the cooling effects ofgreen spaces are closely related to their species, canopy cover, andsizes.

The shortcomings of existing UHI research are as follows. First, itrarely focuses on the impacts of building shades. Middel et al. (2014)show that building shades may lead to a significant decrease in surfacetemperature, especially in the case of artificial surfaces. Second, in-vestigations of greenspace cooling effects have mostly used NDVI orvegetation cover, thus combining all greenery, with little researchdistinguishing vegetation by type (Myint et al., 2015; Tayyebi andJenerette, 2016; Zhou et al., 2011). Third, most studies have usedconventional regression analysis, without considering spatial auto-correlation (Chun and Guldmann, 2014; Song et al., 2014; Zhou et al.,2017), leading to possible estimation biases. Finally, all impacts havebeen assumed linear, thus ignoring possible nonlinear and interactioneffects (Tran et al., 2017). The present study addresses all these issues.

3. Study area and data sources

3.1. Study area

The focus of this research is the Olympic Area, located in the northof Beijing, across the fourth and fifth ring roads, with a surface of67.40 km2 (Fig. 1). It includes three zones: the Olympic core area, theOlympic central area, and the Olympic functional area. It is the world’slargest comprehensive Olympic culture exhibition area, with the goal ofintegrating culture, residence, sports, exhibition, tourism, business andother functions. The reason for choosing this area is that it is differentfrom most urban areas, including not only a variety of urban buildingsand impervious areas, but also many urban greenspaces, such as theOlympic Green Park. This diversity and the availability of very detailedremote-sensing land-use imagery made this area a compelling choicefor UHI analysis.

3.2. Data sources

3.2.1. Land surface temperaturesA Landsat 8 Thermal Infrared Sensor (TIRS) image was acquired

from the United States Geological Survey (USGS) for May 18, 2015, atapproximately 10:52 am (Beijing time). There are three reasons for thischoice. First, the UHI and its negative effects are strongest in spring and

summer. Understanding the UHI at such time is therefore very im-portant. Second, vegetation is in bloom from May to September, whenits effect on the UHI is very significant. Third, Landsat 8 images are notavailable every day, and clouds may render them unusable. Severalclear images in the spring/summer of 2015 were compared, leading tothe May 18 image.

The Image-Based Method (IBM) is used to compute land surfacetemperatures (Li et al., 2011). The IBM is relatively straightforward andhighly accurate (Zhao et al., 2016). The band 11 of the TIRS image wasused, and all the bands were resampled with a pixel size of 30m. Thedigital numbers (DNs) of the thermal infrared band are first convertedto radiation. The standard Landsat 8 products provided by the USGSEROS Center consist of quantized and calibrated DNs representingmultispectral image data acquired by both the Operational Land Imager(OLI) and the TIRS. These products are delivered in 16-bit unsignedinteger format, and TIRS band data are rescaled to the Top of Atmo-sphere (TOA) reflectance and/or radiance, using radiometric rescalingcoefficients provided in the product metadata file (MTL), with:

= ∗ +λL ML DN AL (1)

where λL is the TOA spectral radiance (W· − −m ·sr2 1· −μm 1), ML the re-scaled gain (value= 3.342*10-4), and AL the rescaled bias(value= 0.1). OLI band data can also be converted to TOA planetaryreflectance using reflectance rescaling coefficients provided in the MTL:

= ∗ +ρλ ρ ρ θ(M DN A )/sin( SE) (2)

where ρλ is the TOA planetary reflectance, ρM the rescaled gain(value= 2.0*10−5), ρA the rescaled bias (value=−0.1), and θSE thescene center sun elevation angle.

After calculating the NDVI and vegetation fraction (Fv), the landsurface emissivity ε is calculated using the method of decomposition ofmixed pixels based on NDVI. Then, the radiation luminance is con-verted to at-satellite brightness temperature T:

=+( )

T K2

ln 1λK1L (3)

where K1= 480.89 (W· − −m ·sr2 1· −μm 1) and K2=1201.14 K.Finally, T is corrected for the variable emissivity (ε) of different

landscapes, and the resulting land surface temperature (LST) is com-puted (Artis and Carnahan, 1982):

=+ ( ) ε

LST T

1 lnλρT

(4)

In Eq. (4), λ is the wavelength at the center of the thermal infraredband (12.0 μm for Landsat 8 TIRS band 11), ρ= hc/δ=1.438× 10−2 mK, and ε is the land surface emissivity.

Based on the above steps, the LST map was retrieved (Fig. 2),showing that LST varies between 20 °C and 37 °C.

3.2.2. Land-use classificationTwo Gaofen-2 (GF2) high-resolution remote-sensing images, ac-

quired on August 27, 2016, at 11:30 am (Beijing time), have been usedto extract land-use information. GF2 is the first civil optical satellite,with a resolution superior to 1m, developed independently in China.GF2 was launched on August 19, 2014. GF2 imagery consists of fourmultispectral bands (4m resolution) and a panchromatic band (1mresolution). After ortho-rectification, the multispectral bands and pan-chromatic band are fused, producing a four-band pan-sharpened mul-tispectral image with 1-m resolution. Through a series of mosaic andatmospheric corrections, computer-aided visual interpretation, errorchecking and field validation (Liu et al., 2003), a map with eight land-use classes, including water bodies, grass, trees, building shades,building footprints, impervious surfaces, roads, and bare land, is pro-duced, as illustrated in Fig. 3.

In the Olympic Area, trees account for the largest land-use

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proportion (25.11%), followed by grass (21.59%), buildings (18.18%),roads (16.94%) and impervious surfaces (6.96%). Building shades ac-count for 7.43%, and water and bare land for 2.39% and 1.40%, re-spectively.

4. Statistical modeling methodology

The relationship between LST and the land-use pattern is analyzedseparately over thirteen different grids: 30m, 60m, 90m, 120m,150m, 180m, 240m, 300m, 360m, 420m, 480m, 540m, and 600m.

The smallest cell size (30m) is the spatial resolution of the satellitederived land-use and LST information. The land-use data make up ahigh-resolution vector coverage, which is then converted to a 30m cellraster coverage. The data are then summed up to generate the data forlarger grid cells. In all grids, the land-use data are normalized to sum upto one. However, LST is averaged out to larger grid cells. In order todetermine the best UHI estimation method, ordinary least squares(OLS) multiple linear regression and spatial regression are both used.

The OLS regression model is the most commonly used statisticalanalysis method, with:

= +Xβ εLST (5)

where LST is the vector of the dependent variable, X a matrix of mindependent variables, β a vector of regression coefficients, and ε avector of normal and independent random errors with constant var-iance. The Moran I test can be used to assess whether there is spatialautocorrelation among the error terms of the OLS model. If so, thenspatial regression models are more appropriate to analyze the re-lationship between LST and X. Three spatial regression models areconsidered: the spatial lag model (SLM), the spatial error model (SEM),and the general spatial model (GSM).

The formulation of the SLM, where the spatial autocorrelation takesplace among the dependent variables, is:

= + +ρ Xβ εLST WLST (6)

where W is a row-sum standardized spatial weight matrix, WLST thevector of spatially lagged dependent variables, and ρ the spatial lagfactor, a measure of the spatial autocorrelation. The matrix W is ofdimensions N*N, where N is the number of observations. Each elementwij of W measures the spatial connectivity between cells i and j. Formore details on W, see LeSage and Pace (2009).

The formulation of the SEM, where only the error terms are spatiallyautocorrelated and λ is a measure of this spatial autocorrelation, is:

= +XβLST u (7)

= +λ δu Wu (8)

The formulation of the GSM, which combines the features of theSLM and SEM, is:

Fig. 1. Beijing metropolitan region: Panel A shows the location of Beijing in China; Panel B presents Beijing’s boundaries, ring-roads, and the Olympic Area; Panel Cshows the three zones of the Olympic Area.

Fig. 2. Spatial distribution of Land Surface Temperature (LST) in the OlympicArea on May 18, 2015.

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= + +ρ XβLST W LST u1 (9)

= +λ δu W u2 (10)

where W1 and W2 are two possibly different spatial weight matrices. Todetermine which model is the most suitable, several criteria, such as theR2, the Akaike Information Criterion (AIC), and the Lagrange Multiplier(LM) test, can be used (Chun and Guldmann, 2014).

The effects of the independent variables in a spatial regressionmodel that involves the lag of the dependent variable LST are morecomplex than those in an OLS model, where the partial derivative ofLST with regard to an independent variable is the proper measure ofthis effect, and is simply the corresponding regression coefficient. TheOLS derivative can be incorporated into the calculation of the elasticity(∂

∂/LST

xLST

x ) to explore the rate of change of LST for a 1% change in x.However, this approach is not valid when the dependent variable isspatially autocorrelated. LeSage and Pace (2009) propose a method tointerpret the coefficients in models with a spatial lag term. Each in-dependent variable has direct, indirect, and total impacts, which aremeasured using the matrix (I-ρW)-1. The direct impact is related to theimpact of the variables within the spatial unit (cell) itself, while theindirect impact represents the effects of the variables in neighboringcells, as defined by the spatial matrix W. The total impact is the sum ofthe direct and indirect impacts.

In order to clarify the mathematical formulation of the impacts,consider the following formulation of the GSM obtained by combiningEqs. (9) and (10):

= − + − −− − −ρ β ρ λ δLST [I W ] X [I W ] [I W ]11

11

21 (11)

The matrix of the partial derivatives of LST with respect to the kthexplanatory variables of X is:

∂

∂⋯

∂

∂= − −

x xρW β[ LST LST ] [I ]

1k Nk1

1k (12)

The diagonal elements of (12) represent the direct effects, while theoff-diagonal elements represent the spillover or indirect effects. Theaverage direct effect is then computed as:

∑=∂

∂= ∙ −

=

−β

ρADE 1N

LSTx N

t ([I W ] )γki 1

Ni

ik

k1

1

(13)

where tγ(o) is the trace operator. The average total effect is computedas:

∑ ∑=∂

∂= ∙ −

= =

−β

ρATE 1N

LSTx N

I [I W ] Iki 1

N

j 1

Ni

jk

k 'N 1

1N

(14)

where IN is the unit column vector of dimension N, and I'N its transpose.

The average indirect effect is then:

=ANE ATE -ADEk k k (15)

5. Results

5.1. Descriptive statistics for LST

Table 1 presents descriptive statistics for LST across the various landuses in the study area. Impervious surfaces are characterized by thehighest mean temperature (30.35 °C), followed by buildings (30.08 °C).The lowest mean temperature characterizes water bodies (25.40 °C),followed by trees (27.48 °C). The temperature for grass (28.49 °C) ishigher than for trees. Building shades, as expected, exhibit lower tem-peratures than the buildings themselves (29.38 °C). Roads and barelands are characterized by intermediate temperature levels (29.59 °Cand 29.88 °C, respectively). These statistics illustrate the well-knownfact that replacing natural landscapes (water bodies or vegetation) withbuilt-up areas increases LST. The LST standard deviation of bare land ishighest (2.06 °C), which may be due to different surface characteristics

Fig. 3. Spatial distribution of land uses in the Olympic Area.

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(e.g., unmanaged soils, mine land, or construction sites). Water alsodisplays a larger standard deviation (1.99 °C), which may be due tovariations in water bodies (rivers, lakes, fishing ponds, and city moats).The lowest standard deviation characterizes building shades, due totheir homogenous characteristics.

5.2. Explaining LST with OLS linear regression and SLM

The OLS linear regression model explains LST as a function of theproportions of the 8 land uses, with:

= + + + + + + + +a a a a a a a a aLST W G T SH BU IS R BL0 1 2 3 4 5 6 7 8

(16)

where W is the land proportion of water bodies, G the proportion ofgrass, T the proportion of trees, SH the proportion of building shades,BU the proportion of buildings, IS the proportion of impervious sur-faces, R the proportion of roads, and BL the proportion of bare lands.

Table 2 presents the R2 and Moran I tests for the OLS linear re-gressions. To avoid perfect multi-collinearity (sum of proportions= 1),bare land was removed from the set of independent variables. In ad-dition, impervious surfaces and roads were combined into a unique“impervious surface” variable. The smaller the grid, the smaller the R2.Its value increases by more than 0.35 when shifting from 30m to600m, because (1) LST has a wider range in smaller than in larger cells,and therefore LST variations may be more difficult to capture precisely,and (2) spatial autocorrelation is likely to be stronger in smaller gridsbecause of closer cell proximity. Almost all the coefficients are sig-nificant at the 1% level, with signs consistent with earlier research:negative for grass, tree, water and shade, and positive for building andimpervious surface. Table 2 also shows that the Moran-I values aresignificant in all grids, pointing to spatial autocorrelation (SA) in theOLS error term.

In order to eliminate SA, the SLM model is next estimated. Thespatial lag matrix W is defined as a 1st-order spatial contiguity matrix.The coefficients of all the independent variables have the same signsand levels of significance as in the OLS case. The lag factor ρ is alwayshighly significant and positive, which confirms the high level of SA forLST, with value decreasing from 0.979 to 0.402 when the grid shiftsfrom 30m to 600m, suggesting that the smaller the distance betweenadjacent cells, the stronger their mutual influences (Chun andGuldmann, 2014). The R2 decreases from 0.982 for the 30m grid to0.829 for the 600m grid. This suggests that the SLM model is moreappropriate for smaller grids. Table 2 also includes the log-likelihoodand Akaike information criterion (AIC) for each SLM model. The AICmay be useful for comparing the SLM and GSM models. The lower theAIC, the better the model.

The differences in R2 between the SLM and OLS models becomesmaller when the grid becomes larger, further suggesting that SA isstronger with smaller grids, but less of a problem with larger ones. Thevalues of the SLM coefficients are smaller than the OLS ones in smallergrids, which is consistent with SA effects. Hence, not accounting for SAin small grids may lead to misleading parameter estimates. The LM testsfor the SLM indicate SA still remains significant in all grids. The generalspatial model (GSM) is then used to further to reduce this SA.

5.3. General spatial model in the linear case

Because of the size of the model (W matrixsize= 73,151×73,151), the GSM could not be estimated for the 30mgrid with available Matlab software. Hence, Table 3 presents results forgrids of size 60m and larger. The 1st-order spatial lag matrix W is usedfor both the lagged LST and the lagged error term. The lag coefficients ρand λ are positive and significant at the 1% level in all grids, withvalues decreasing with increasing grid size.

The signs and significance levels of the GSM variables are similar tothe SLM ones. The effects of water, grass, trees and shades are all al-ways negative, and the effect of buildings and impervious surfaces arealways positive. The R2 decreases from 0.967 (60m) to 0.837 (600m),with values similar to those of the SLM, and this is also the case for theAIC. The spatial lag factor ρ is smaller in the GSM than in the SLM, andthe uniformly high significance of the error lag λ suggest that the GSMcapture SA better than the SLM.

Fig. 4 shows a scatterplot of the coefficient estimates for each in-dependent variable across the grids. The general trends are for thepositive coefficients to increase and negative ones to decrease (or in-crease in absolute terms). The reason for these trends may be twofold:(1) a given proportion (%) of a cell represents more land in a large cellthan in a smaller one, and a large area of a given land use may have a

Table 1Descriptive statistics for LST by land use.

Land-use type LST (°C)

Mean Minimum Maximum Standard deviation

Water Bodies 25.40 20.16 32.25 1.99Grass 28.49 21.77 35.71 1.86Trees 27.48 21.29 34.88 1.82Building Shades 29.38 22.74 36.27 1.60Building 30.08 23.09 37.33 1.76Impervious Surfaces 30.35 23.40 36.55 1.75Roads 29.59 22.29 37.31 1.78Bare land 29.88 23.99 33.72 2.06

Table 2OLS and SLM model summary at multiple grid scales.

Variable OLS SLM

N R2 Moran-I R2 ρ Log-likelihood AIC LM-test

30m 73,151 0.432 0.785** 0.982 0.979 −11,551 23,11860m 18,063 0.523 0.701** 0.961 0.943 −5545 11,080 3723.0**

90m 7976 0.578 0.645** 0.931 0.878 −4379 8768 1429.5**

120m 4498 0.620 0.610** 0.905 0.813 −2997 6010 715.6**

150m 2906 0.652 0.574** 0.883 0.752 −2142 4305 449.5**

180m 2018 0.666 0.531** 0.868 0.710 −1570 3170 262.9**

240m 1129 0.695 0.463** 0.846 0.636 −897 1818 135.4**

300m 735 0.701 0.389** 0.823 0.588 −607 1250 51.9**

360m 504 0.720 0.330** 0.817 0.537 −407 846 20.0**

420m 373 0.747 0.302** 0.818 0.486 −294 604 21.1**

480m 286 0.764 0.246** 0.820 0.428 −210 446 9.0**

540m 220 0.778 0.233** 0.824 0.400 −158 335 7.6**

600m 181 0.788 0.208** 0.829 0.402 −116 254 5.3*

** P < 0.01.* P < 0.05; N=number of observations.

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stronger impact on LST; (2) the strong SA for smaller cells is partiallyinternalized within larger cells, and the larger coefficients reflect thecapture of these SA effects.

5.4. General spatial model in the nonlinear case

The GSM model presented in the previous section assumes that theeffects on LST of all the independent variables are all linear. However, itis quite possible that there are nonlinear and interaction effects amongthese variables. To test for such effects, the squares of each of the sixvariables and all their possible cross-products were initially added tothe original variables, and the expanded GSM model was estimated.However, the only significant additional variables turned out to be thesquare of water (W2), the square of grass (G2), the square of trees (T2),the product of grass and water (GW), the product of grass and tree (GT),and the product of water and tree (WT).

The results are presented in Table 4. All insignificant variables havebeen deleted. The cross product GW and WT are significant for the 60mand 90m grids only. The cross-product GT is significant up to the 300mgrid but not beyond. These results suggest that these interactions canonly be captured in smaller cells, where the adjacency between grass,trees and water is measured more precisely, whereas it may be lost inlarger cells. It is also noticeable that the nonlinear effects of individualvariables turned out to be insignificant in some cases: (a) grass for the180m, 240m, 300m, and 480m grids; (b) trees for the 600m grid; (c)water for the 60m, 120m, 180m, and 600m grids. In all these cases,the strong linear and negative effects of these variables remain. Finally,notice that the linear component of grass turns out insignificant in thecells of the 360m, 420m, 540m, and 600m grids, but the nonlinear

component remains highly significant and negative.In order to further explore the above nonlinearities and interaction

effects, the focus below is on the GSM for the 90m grid, where all thecoefficients are significant at the 1% level. In order to analyze theseeffects, consider the non-lagged component of the GSM, as presented inEq. (17):

= − ∗ − ∗ − ∗ − ∗ + ∗

+ ∗ + ∗ + ∗ + ∗ + ∗

+ ∗ + ∗

F 7.435 3.369 W 2.691 G 3.042 T 1.622 SH 0.761 BU0.476 IS 1.523 G 0.869 W 1.565 T 1.065 GW2.773 GT 1.090 WT

2 2 2

(17)

In order to further analyze the nonlinearities and interactions re-lated to grass, trees and water, the following functions are then ex-tracted from Eq. (17), involving the grass, tree and water variables:

= ∗ − ∗ + ∗ + ∗F 1.523 G 2.691 G 1.065 GW 2.773 GTgrass2 (18)

= ∗ − ∗ + ∗ + ∗F 1.565 T 3.042 T 1.090 WT 2.773 GTtree2 (19)

= ∗ − ∗ + ∗ + ∗F 0.869 W 3.369 W 1.065 GW 1.090 WTwater2 (20)

These three functions are graphed on Fig. 5. These graphs show thatthe negative effect of each variable (grass, tree, water) increases, asexpected, with an increasing proportion of the variable, but at a de-creasing rate, and that the form of the curve depends upon the pro-portion of the other two variables. For instance, in the case of grass(Fig. 5.a), when tree=water= 0.2, the value of grass may range from0 to 0.6, whereas this limit is 0.8 when tree=water= 0.1. Clearly, theeffect of any given variable depends on the mix of the other two vari-ables. Both grass and trees display fairly distinct curves. However, inthe case of water (Fig. 5c), differences are less noticeable, and all thecurves are more closely bunched together.

5.5. Direct, indirect and total impacts

The average direct, indirect, and total impact elasticities in the caseof the nonlinear GSM estimates are presented in Table 5. The resultsshow that the indirect impacts are larger than the direct ones when thegrids are smaller than 180m, whereas the opposite applies to gridslarger than 180m. This result confirms that indirect impacts from ad-jacent cells should not be ignored in the case of smaller grids.

Water bodies have negative direct and indirect impacts in all gridsand are effective in mitigating the UHI. Increasing by 1% the area ofwater bodies will lead to LST decreases in between 0.144% and 0.372%.Grass has negative direct and indirect impacts in all grids. Increasing by1% the area of grass leads to LST decreases between 0.440% and1.423%, with a declining trend when the grid shifts from 60m to600m. Trees have also negative direct and indirect impacts in all grids.Increasing by 1% the area of trees leads to LST decreases between

Table 3GSM regression estimates in the linear case.

Grid Variables

Constant W G T SH BU IS ρ λ R2 Log-likelihood

60m 4.078 −1.275** −0.822** −0.889** −0.401** 0.355** 0.156** 0.871** 0.592** 0.967 −4398.5390m 7.742 −2.721** −1.326** −1.568** −1.659** 0.784** 0.428** 0.753** 0.611** 0.941 −3907.43120m 11.202 −4.446** −1.936** −2.353** −3.254** 0.958** 0.513** 0.648** 0.608** 0.919 −2736.43150m 13.859 −5.382** −2.070** −2.684** −4.041** 1.424** 1.073** 0.555** 0.638** 0.903 −1955.78180m 15.509 −5.734** −2.229** −2.740** −4.580** 1.934** 1.424** 0.495** 0.638** 0.889 −1443.25240m 17.927 −7.231** −2.819** −3.209** −6.377** 2.184** 1.660** 0.422** 0.628** 0.873 −833.40300m 19.494 −7.172** −2.447** −2.776** −5.407** 3.366** 2.618** 0.343** 0.631** 0.851 −564.70360m 18.890 −8.774** −2.360** −2.911** −6.546** 3.635** 2.073** 0.371** 0.463** 0.830 −393.14420m 22.606 −9.951** −3.154** −4.181** −7.263** 3.206** 1.699** 0.268** 0.515** 0.831 −282.76480m 23.160 −9.676** −2.731** −3.652** −6.372** 3.740** 2.619** 0.227** 0.518** 0.836 −201.08540m 24.660 −9.668** −2.803** −3.909** −7.163** 4.871** 2.053** 0.178* 0.417** 0.822 −155.09600m 23.988 −12.339** −2.217** −3.593** −6.009** 4.007** 2.542** 0.194* 0.476** 0.837 −111.63

** P < 0.01.* P < 0.05.

Fig. 4. Coefficients of the independent variables across grids.

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1.047% and 2.097%, with also a declining trend when the grid shiftsfrom 60m to 600m. This is the highest elasticity range, which confirmsthat trees play a more important role than any other land use. Buildingshades, in contrast to building themselves, have always negative directand indirect impacts, helping to mitigate the UHI. An increase of 1% inbuilding shade area leads to LST decreases between 0.239% and0.791%. Building footprints have positive effects on LST across all grids.Increasing by 1% the footprint of buildings leads to LST increases be-tween 0.499% and 1.086%, with an increasing trend when the gridshifts from 60m to 600m. Finally, impervious surfaces, which includeboth impervious open areas and roads, have positive direct and indirectimpacts in all grids. On average, increasing by 1% the area of im-pervious surfaces leads to LST increases between 0.107% and 0.281%.

6. Uncertainty and sensitivity analyses

Any model is an attempt to explain and replicate reality by focusingon the most important determinative factors. Therefore, any model ischaracterized by some uncertainty because of the factors that are notaccounted for. In the case of the regression models presented earlier,this uncertainty is subsumed in the error term, and the R2 coefficient ofdetermination is a measure of the overall fit. As the results in Table 4indicate, the R2 varies between 0.838 and 0.970, implying that themodels explain between 83.8% and 97.0% of the variations of LST, thedependent variable. Therefore, some uncertainties do remain, whichare more fully explored in this section.

First, the data used to estimate the models may be characterized bymeasurement errors, and measurement accuracy for both LST and theland-use variables are assessed in Section 6.1. Second, the regressioncoefficients are inherently random variables. Their estimated values arebased on the sample used, and may therefore differ from the true(unknown) population coefficients. Section 6.2 assesses the impacts onthe computed LST values of having regression coefficients vary alongtheir probability distribution curves. Finally, Section 6.3 consists in astandard model validation, wherein the model is estimated on a subsetof the Olympic Area, and the resulting model is used to estimate LST inthe remaining area. The estimated and actual values are then com-pared.

6.1. Data accuracy

6.1.1. Land surface temperature (LST)While the method for computing LST (Section 3.2.1) is widely used

and has been shown by Zhao et al. (2016) to be highly accurate, it is notpossible to compare past Landsat-retrieved LST values with actualground temperature measurements as the latter cannot be made ret-roactively. As an alternative, LST is compared to measured air tem-perature AT. It is well known that AT and LST are closely related, withLST higher than AT at any given location. For instance, Li et al. (2017)show that the time series of average annual LST and AT data over2001–2015 in Fujian Province, China, are highly correlated, with LSTexceeding AT by around 2 °C on average. Mutiibwa et al. (2015) reporta correlation of R2=0.90 with Nevada data, and an average LST/ATratio of 1.35.

The AT observed at 18 meteorological stations in Beijing is com-pared with the average retrieved LST calculated over the 25 (5*5) 30mraster cells centered at each station. The AT acquisition time is 11:00am on May 18, 2016. The weather on this day was very similar to theweather on May18, 2015, the time of LST retrieval, thus supporting acomparative statistical analysis of the two sets of temperatures. A re-gression analysis is applied to the relationship between LST and AT. Thebest results are obtained with a log–log model (linear in logarithms),with a high R2=0.8372, as illustrated on Fig. 6. The mean difference(LST-AT) is 4.62 °C, confirming that LST is higher than AT. The dottedline on Fig. 6 corresponds to LST equal to AT. These results suggest thatLandsat-derived LST values are accurate measures of actual ground-level temperatures.

6.1.2. Land usesIn order to evaluate the accuracy of the land-use classification

(Section 3.2.3), a random sample of 150 points check is conducted,using a Google map for ground truthing.

The resulting comparison is summarized by the confusion matrix inTable 6, where each row represents the actual land-use distribution. Forinstance, the first row (Grass) indicates that, out of 34 points classifiedas Grass, 33 are actually grass, and 1 is actually a tree, with a ProducerAccuracy of 97.06%. The overall accuracy is 91.33%. Water and shadepoints are perfectly identified, while grass and trees have very highaccuracy rates (95%–97%). The identifications of buildings, roads,impervious areas, and bare lands are slightly less accurate (75%–83%),in large part due to internal misclassification within this group of land

Table 4GSM regression estimates in the nonlinear case.

Variables Grid

60m 90m 120m 150m 180m 240m 300m 360m 420m 480m 540m 600m

Constant 4.116** 7.435** 11.053** 13.913** 15.786** 18.203** 19.773** 18.663** 23.133** 23.486** 25.126** 23.894**

W −1.300** −3.369** −4.195** −5.953** −5.534** −8.426** −8.536** −12.858** −12.053** −13.701** −12.694** −12.078**

G −1.979** −2.691** −3.479** −3.691** −2.468** −2.774** −3.017** – – −2.658** – –T −2.342** −3.042** −3.920** −4.396** −4.143** −3.818** −5.395** −3.911** −5.105** −4.537** −5.144** −3.493**

SH −0.398** −1.622** −3.164** −4.019** −4.647** −6.410** −5.712** −6.961** −7.424** −6.473** −7.342** −5.868**

BU 0.336** 0.761** 0.924** 1.381** 1.940** 2.180** 3.353** 3.507** 3.563** 3.692** 5.172** 4.089**

IS 0.187** 0.476** 0.571** 1.077** 1.433** 1.675** 2.640** 1.876** 1.953** 2.734** 2.261** 2.394**

G2 1.258** 1.523** 1.725** 1.721** – – – −3.992** −4.935** – −4.974** −4.175**

W2 – 0.869** – 1.689** – 3.082* 4.960* 17.996** 8.626** 17.967* 14.702* –T2 1.523** 1.565** 1.657** 1.811** 1.621** 0.909** 3.187** 1.649** 2.134** 1.691 2.502** –GT 2.443** 2.773** 2.780** 3.260** 1.721** – 3.463** – – – – –GW 0.495** 1.065** – – – – – – – – – –WT 0.734** 1.090** – – – – – – – – – –ρ 0.875** 0.770** 0.661** 0.563** 0.490** 0.414** 0.344** 0.378** 0.235** 0.245** 0.152** 0.189*

λ 0.585** 0.602** 0.601** 0.633** 0.640** 0.623** 0.651** 0.483** 0.603** 0.561** 0.571** 0.505**

R2 0.970** 0.944** 0.922** 0.906** 0.891** 0.874** 0.858** 0.841** 0.843** 0.846** 0.838** 0.841**

Log−likelihood −3697.51 −3724.71 −2657.71 −1909.55 −1429.87 −827.51 −550.34 −378.77 −273.21 −194.30 −148.38 −110.1

** P < 0.01* P < 0.05

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uses. However, overall the results suggest a very good accuracy in theidentification of the land-use data.

6.2. Regression coefficients variability

Any of the regression models (Section 5) relates the output LST,measured over a specific geographical area unit, to inputs that include(1) six land-use variables (water, grass, tree, shade, building, im-pervious surface), and (2) their associated regression coefficients. The90m cell nonlinear GSM model is selected for further analysis. It is themost complete and complex model, with a high R2= 0.944 and 14estimated coefficients, including the spatial lag and the nonlinear ones.This model is represented, in reduced form, by Eq. (21) where the errorterm δ is assumed equal to zero:

= − − ∗ − ∗ − ∗ − ∗

+ ∗ + ∗ + ∗ + ∗ + ∗

+ ∗ + ∗ + ∗

−LST [I 0.770W ] [7.435 3.369 W 2.691 G 3.042 T 1.623 SH

0.761 BU 0.477 IS 1.523 G 0.869 W 1.565 T1.065 GW 2.773 GT 1.090 WT]

11

2 2 2

(21)

Local and/or global methods can be used to analyze the sensitivityof the output to variations in the inputs. Local methods involve varyingeach input separately while keeping all the other inputs constant,measuring the output variations one-factor-at-a-time. Global methodsassess the impact on the output of varying all the inputs at the sametime. An example of such methods is the Global Sensitivity andUncertainty Analysis (GSUA), as applied by Convertino et al. (2014) tothe MaxEnt habitat suitability simulation model. In this model, theinputs include various land covers, such as estuarine beach and saltmarsh, and various model parameters. All these inputs are assignedlikely probability distributions (discrete, uniform, etc.). Future landcovers may vary, depending upon climate change and sea-level rise.Using the Sobol computational scheme (Sobol, 1993), the variance ofthe output (habitat suitability) is computed as the sum of the inputvariances. A basic GSUA requirement is that the inputs be (1) char-acterized by probability distributions, and (2) independent of eachother.

Can the GSUA method be applied to the LST regression models?Urban land uses are the product of active and directed human design(urban planning), and not the results of random processes. For thesevariables, the only possible source of uncertainty is measurement erroror misclassification, which has been shown to be quite small (Section6.1.2). In addition, these variables are not independent of each other.The land use in a given cell is related to the land uses in neighboringcells because of physical interconnections (for instance, a building ex-tending over several cells cannot be modified into alternative land usesin some of the cells). In contrast, statistical theory indicates that theregression coefficients are inherently random. However, they are notindependent of each other, as their variance–covariance matrix is neverpurely diagonal. Hence, GSUA premises are not satisfied. As an alter-native, a local sensitivity approach is implemented to analyze the im-pacts of varying the regression coefficients.

The GSM coefficients are characterized by t-statistics that essentiallyfollow normal distributions because of the large number of observa-tions. The z-probabilities associated with these t-statistics are all <10−6, except for W2 (0.06), GW (0.07), and WT (0.05). Hence, the nullhypothesis that these coefficients are not significantly different fromzero can be rejected with at least a 7% confidence level. However, thecoefficients may follow normal distributions centered on their esti-mated values. Let X be one of the estimated coefficients, and t its t-statistics. Its standard deviation is then: σ=X/t. The following coeffi-cient values are next considered: X-2σ, X-σ, X, X+σ, X+ 2σ. Equation(21) is used to compute LST for each of these 5 values separately.Summary statistics (mean, minimum, maximum, standard deviation)are computed over the 7,976 LST values in each case, and are reportedin Table 7.

The results in Table 7 point to very small variations, particularly inthe case of the mean LST, which varies at most by about half a degreeCelsius. For instance, it varies between 28.793 and 28.879 in the case ofWater. Note also that, in the cases of the variables Water, W2, GW, andWT, the maximum values are essentially constant. This is so because themaximum cell, located in the western part of the Olympic Area, is faraway from any water. Therefore, changing the water-related coeffi-cients has no impact because the spatial effect of water at other loca-tions is too small to be numerically noticeable. As expected, the resultsin the X column are the same across all coefficients, as they apply to theestimated coefficients. They are left in the table to facilitate compar-isons. In summary, varying the regression coefficients along theirprobability distribution curves has little effect on the temperatureoutput. This result is, of course, due to the high statistical precision ofthe estimates.

Fig. 5. Nonlinear effects for the 90m grid: (a) grass, (b) trees, (c) water.

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6.3. Model validation

In the case of historical time-series data over T periods, it is commonto estimate a model over the first (T-n) periods, use the estimated modelto predict values for the variable of interest over the last n periods, andthen compare predicted and actual (historically known) values for va-lidation purposes. However, because the present data are cross-

sectional, the validation approach involves separating the wholeOlympic Area into training and testing areas, as mapped on Fig. 7. Thetraining area includes 6343 30m cells, and the testing area 1633 suchcells.

The model estimated over the training area is:

= − − ∗ − ∗ − ∗ − ∗

+ ∗ + ∗ + ∗ + ∗ + ∗

+ ∗ + ∗ + ∗

−LST [I 0.756W ] [7.665 3.461 W 2.485 G 2.750 T 1.447 SH

0.989 BU 0.629 IS 1.376 G 0.829 W 1.327 T0.240 GW 2.468 GT 1.455 WT]

11

2 2 2

(22)

All the coefficients are significant at the 1% level, except for W2,GW, and WT (5%), with R2=0.946. Eq. (22) can be directly comparedto Eq. (21). Except for the variable GW, all the corresponding coeffi-cients are very similar in both equations.

Let LSTa be the Landsat-retrieved LST value of a given cell in thetesting area, and LSTc the value computed with Eq. (22). The ratioR= LSTc/LSTa is a measure of the deviation between these two values.The mean value of R is 1.064, and its range is [0.92–1.26]. Additionalpercentile values are presented in Table 8. While the model slightlyoverestimates LST in the testing area, the mean overestimation is only6.4%. These results suggest that the model is quite robust and can beused for prediction and impact analysis purposes.

7. Discussion

Building shades turn out to have significant negative effects on LST,a finding consistent with Middel et al. (2014). As the absolute values ofthe shade coefficient increases with grid size, one can conclude thatlarger concentrations of building shades generated by clusters of large

Table 5Average direct, indirect and total impact elasticities with nonlinear GSM estimates.

Grid Effect Land Use

Water Grass Tree Shade Building Impervious Surface

60m Direct −0.031 −0.232 −0.342 −0.039 0.081 0.018Indirect −0.161 −1.192 −1.755 −0.200 0.418 0.090Total −0.191 −1.423 −2.097 −0.239 0.499 0.107

90m Direct −0.079 −0.337 −0.488 −0.142 0.165 0.040Indirect −0.209 −0.895 −1.294 −0.376 0.439 0.107Total −0.288 −1.232 −1.782 −0.517 0.604 0.148

120m Direct −0.109 −0.490 −0.696 −0.258 0.189 0.046Indirect −0.181 −0.811 −1.152 −0.428 0.313 0.075Total −0.290 −1.301 −1.847 −0.686 0.502 0.121

150m Direct −0.148 −0.493 −0.749 −0.315 0.270 0.081Indirect −0.167 −0.559 −0.848 −0.357 0.305 0.092Total −0.315 −1.052 −1.597 −0.672 0.575 0.173

180m Direct −0.136 −0.460 −0.775 −0.354 0.370 0.106Indirect −0.117 −0.397 −0.668 −0.305 0.319 0.091Total −0.253 −0.857 −1.444 −0.659 0.689 0.197

240m Direct −0.165 −0.611 −0.864 −0.480 0.409 0.121Indirect −0.107 −0.396 −0.560 −0.311 0.265 0.078Total −0.271 −1.006 −1.424 −0.791 0.674 0.199

300m Direct −0.143 −0.467 −0.778 −0.424 0.614 0.183Indirect −0.076 −0.249 −0.416 −0.227 0.328 0.098Total −0.219 −0.717 −1.194 −0.651 0.942 0.281

360m Direct −0.095 −0.362 −0.780 −0.516 0.651 0.135Indirect −0.053 −0.202 −0.435 −0.288 0.363 0.075Total −0.148 −0.565 −1.215 −0.803 1.014 0.210

420m Direct −0.183 −0.431 −1.000 −0.542 0.639 0.132Indirect −0.059 −0.140 −0.324 −0.176 0.207 0.043Total −0.243 −0.571 −1.324 −0.718 0.847 0.175

480m Direct −0.290 −0.558 −0.913 −0.468 0.658 0.189Indirect −0.083 −0.159 −0.260 −0.133 0.187 0.054Total −0.372 −0.716 −1.172 −0.601 0.846 0.243

540m Direct −0.123 −0.434 −0.971 −0.524 0.925 0.158Indirect −0.021 −0.076 −0.169 −0.091 0.161 0.028Total −0.144 −0.510 −1.141 −0.616 1.086 0.186

600m Direct −0.284 −0.360 −0.852 −0.418 0.725 0.163Indirect −0.063 −0.080 −0.189 −0.093 0.161 0.036Total −0.347 −0.440 −1.041 −0.511 0.885 0.199

Fig. 6. Relationship between LST and AT.

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buildings have increasing negative effects on LST, as compared to thecase of smaller and dispersed buildings. It is, however, important toremember that shades vary with the position of the sun in the sky, asmeasured by the altitude and azimuth angles. At the time of the land-use data capture (August 27, 11:30 am), the altitude was 59.13°, veryclose to the maximum of 59.95° on that day. It is also notable that thealtitude of the sun at the time of LST capture (May 18, 10:52 am) was63.40°, or 7% above 59.13°, implying slightly larger shades than onAugust 27. As a result, the shade coefficient may slightly underestimatethe effect of a unit shade area, and should be viewed as a conservativeestimate.

Impervious surfaces, including both open impervious spaces androads, increase surface temperatures, but less so than buildings, parti-cularly in larger grids. This is probably related to the fact that a more

Table 6Confusion matrix.

Class Grass Tree Building Road Bare land Impervious Water Shade Total PA

Grass 33 1 0 0 0 0 0 0 34 97.06%Tree 2 38 0 0 0 0 0 0 40 95.00%Building 1 1 26 2 0 1 0 0 31 83.90%Road 0 0 1 15 0 1 0 1 18 83.33%Bare land 1 0 0 0 5 0 0 0 6 83.33%Impervious 1 0 0 0 0 3 0 0 4 75.00%Water 0 0 0 0 0 0 4 0 4 100.00%Shade 0 0 0 0 0 0 0 13 13 100.00%Total 38 40 27 17 5 5 4 14 150UA 86.84% 95.00% 96.30% 88.24% 100.00% 60.00% 100.00% 92.86% 91.33%

Note: Row distributions represent actual land uses; column distributions represent classified land uses; PA is the Producer Accuracy; UA is the User Accuracy.

Table 7Impacts of regression coefficients variability on LST values.

Variables Effect X - 2σ X – σ X X + σ X+2σ

Water Mean 28.743 28.789 28.836 28.882 28.928Minimum 20.231 21.561 22.893 24.133 24.957Maximum 34.487 34.488 34.488 34.488 34.488Std. Dev. 1.912 1.850 1.791 1.738 1.689

Grass Mean 28.598 28.717 28.836 28.955 29.074Minimum 22.839 22.866 22.893 22.920 22.947Maximum 34.475 34.482 34.488 34.494 34.501Std. Dev. 1.826 1.807 1.791 1.779 1.771

Tree Mean 28.558 28.697 28.836 28.975 29.114Minimum 22.594 22.767 22.893 23.019 23.144Maximum 34.471 34.480 34.488 34.498 34.511Std. Dev. 1.974 1.881 1.791 1.705 1.624

Shade Mean 28.764 28.800 28.836 28.871 28.907Minimum 22.892 22.893 22.893 22.893 22.893Maximum 34.457 34.472 34.488 34.508 34.527Std. Dev. 1.766 1.778 1.791 1.805 1.819

Building Mean 28.692 28.764 28.836 28.907 28.979Minimum 22.888 22.890 22.893 22.895 22.898Maximum 34.041 34.264 34.488 34.723 34.958Std. Dev. 1.719 1.755 1.791 1.828 1.865

Impervious Mean 28.654 28.745 28.836 28.927 29.017Minimum 22.859 22.876 22.893 22.909 22.926Maximum 34.233 34.360 34.488 34.628 34.769Std. Dev. 1.722 1.756 1.791 1.827 1.863

G2 Mean 28.736 28.786 28.836 28.886 28.936Minimum 22.873 22.883 22.893 22.902 22.912Maximum 34.484 34.486 34.488 34.490 34.492Std. Dev. 1.820 1.805 1.791 1.779 1.768

W2 Mean 28.793 28.814 28.835 28.857 28.879Minimum 20.391 21.641 22.893 23.853 24.343Maximum 34.488 34.488 34.488 34.488 34.488Std. Dev. 1.856 1.823 1.791 1.762 1.735

T2 Mean 28.696 28.766 28.836 28.906 28.975Minimum 22.754 22.823 22.893 22.962 23.031Maximum 34.480 34.484 34.488 34.493 34.499Std. Dev. 1.906 1.848 1.791 1.737 1.684

GT Mean 28.793 28.815 28.836 28.857 28.878Minimum 22.864 22.879 22.893 22.907 22.921Maximum 34.485 34.487 34.488 34.489 34.490Std. Dev. 1.822 1.806 1.791 1.776 1.762

GW Mean 28.816 28.826 28.836 28.846 28.856Minimum 22.866 22.879 22.893 22.906 22.919Maximum 34.487 34.488 34.488 34.488 34.487Std. Dev. 1.811 1.801 1.791 1.782 1.773

WT Mean 28.806 28.821 28.836 28.851 28.866Minimum 22.560 22.755 22.893 22.998 23.103Maximum 34.487 34.488 34.488 34.488 34.487Std. Dev. 1.831 1.811 1.791 1.772 1.753

ρ Mean 28.538 28.686 28.836 28.987 29.140Minimum 22.645 22.768 22.893 23.019 23.146Maximum 34.139 34.313 34.488 34.665 34.844Std. Dev. 1.776 1.784 1.791 1.799 1.806

Fig. 7. Spatial distribution of training and testing areas.

Table 8Descriptive statistics for the ratio R= computed LST/Landsat-retrieved LST.

Percentiles

1% 10% 25% 75% 90% 99%

R 0.991 0.940 1.036 1.102 1.131 1.185

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visible open sky enhances air circulation, which can better dissipateurban heat. This result is consistent with previous research on the effectof the Sky View Factor (SVF). Indeed, urban areas with low SVF in-crease absorption of solar radiation onto surfaces, decrease terrestrialradiation emissions, reduce wind flows, and decrease total heat trans-port, which all directly lead to increases in LST (Chun and Guldmann,2014). Open spaces are characterized by SVF=1, whereas buildingclusters have smaller SVF values. Larger grids mean larger areas of openspaces, with faster and stronger winds and increased heat transport.

The average direct, indirect and total impacts were calculated forthe different land uses, and elasticities were reported instead of deri-vatives, because elasticities provide a better basis for comparing effects.The results indicate that trees play a more important role than all theother land uses, followed by grass (Armson et al., 2012; Edmondsonet al., 2016). This is consistent with previous studies. For instance,Myint et al. (2015) report that a tree canopy is more effective than grassfor LST cooling, for two reasons. First, evapotranspiration is the mainmechanism by which urban greenspaces reduce surface temperatures.However, in contrast to trees which have “Tridimensional Green Bio-mass (TGB)”, grass generates less evapotranspiration, and therefore isless effective for cooling. In addition, trees can also provide shades,which, like building shades, have significant negative effects on LST.

The nonlinearities and interaction effects uncovered, particularly insmaller grids, suggest that the mixture of land uses can modify theimpacts of a given land use on LST. This interaction is strongest fortrees, which may due to the aforementioned fact that trees play a moreimportant role than all other land uses.

The strong performance of the models, with R2 ranging from 0.839to 0.970 across the various grids (30m to 600m), makes them potentialtools for assessing the thermal changes resulting from planned land-usechanges, such as erecting new buildings over green spaces, constructingnew roads, developing artificial water bodies, or converting impervioussurfaces back to grass and/or trees. The thermal implications of theshadows cast by these new buildings can also be assessed. Thus, thesemodels can be part of the toolkit of urban planners dealing with dif-ferent scenarios of urban expansion or redevelopment and their effectson the UHI. In order to illustrate this process, consider the 90m GSM(Table 4), under the assumption of an average error term δ=0, asrepresented by Eq. (21) in Section 6.2. Any land-use scenario could beexpressed by assigning specific values to the variables {W, G, T, SH, BU,IS} for each 90m cell of the study area. The resulting expected LSTvalue for each 90m cell could then be calculated with Eq. (21). Theuncertainty and sensitivity analyses carried out in Section 6 show thatthe GSM models are based on accurate data and are very reliable interms of coefficients precision. Hence, decision-makers should be con-fident in using them for management and planning purposes.

One caveat is that land-use impacts on the UHI were analyzed at onemoment in time. It is known that the relationship between land usesand LST varies seasonally (Chun and Guldmann, 2018). However, theUHI and its negative effects are strongest in the spring and summer,hence the focus on the May timeline. While the study area is char-acterized by a very diversified land-use structure, it may also be arguedthat the land use/LST relationship could be different under differentclimatic conditions. Therefore, an important thrust for future researchcould be to extend the analysis to other sites under different climatesand at different times of year. Such extensions were beyond the scope ofthe present research.

8. Conclusions

Understanding the relationship between land uses and land surfacetemperatures (LST) is crucial for mitigating the UHI. Previous researchhas focused on this relationship at larger scales, focusing on broad land-use categories, and has usually implemented conventional regressionmodels or general correlation analyses to assess these relationships,without considering spatial autocorrelations. Using finer analytical

scales, detailed and accurate land-use data, and appropriate spatialregression models is important for UHI research and provides a betterbasis for urban planning.

The above issues have motivated this research, which has developeda detailed land-use inventory for the Olympic Area of Beijing, distin-guishing buildings, impervious areas, building shades, water bodies,bare lands, and different vegetation types (grass and trees). This arrayof land uses is larger and more precise than in earlier studies. Thequantitative relationships between LST and these land uses are exploredwith different statistical regression methods over several grids. Theconclusions are as follows:

(1) LST is highest at buildings, followed by impervious surfaces, barelands, roads, building shades, grass and trees. The lowest meantemperature occurs in water bodies. LST patterns depend on thearea proportions of the various land uses. It is notable that, unlikethe positive impacts of buildings, building shades have significantnegative effects on LST.

(2) Spatial autocorrelation (SA) impacts the relationship between LSTand the independent variables, particularly at finer analyticalscales. The Spatial Lag Model (SLM) was found to be more effectivethan the OLS regression model, particularly in smaller grids.However, because the SLM still had SA among its residuals, theGeneral Spatial Model (GSM), which accounts for spatial auto-correlation in both the dependent variable (LST) and the error term,was finally selected for estimation.

(3) The effects of water bodies on LST change the most, and increase atan increasing rate with increasing grid size, while the effects ofimpervious surfaces change the least, possibly because larger gridsmay include larger open areas with a more visible open sky thatenhances air circulation.

(4) The indirect impacts are larger than the direct ones when the gridcells are smaller than 180m. The opposite effect holds for grid cellslarger than 180m, suggesting that impacts from adjacent cells in-crease with smaller cells. Trees are the most important predictor ofLST, playing a more important role than the other landscape com-ponents.

(5) LST depends in a nonlinear way on grass, tree and water. Addingsquares terms and product terms yields better models. The magni-tude of the effect of either grass or trees or water depends upon themix of the other two components.

(6) Uncertainty and sensitivity analyses show that (a) the input data(LST and land uses) are very accurate, and (b) the estimated LSTvaries very little when varying the regression coefficients alongtheir probability distribution curves, due to their high statisticalprecision.

(7) A validation analysis further confirms that the models can be usesfor prediction and planning purposes.

This research has enhanced our understanding of the effects of theurban landscape on the UHI. However, this research has also limita-tions. For instance, the range of grid sizes was [30m - 600m], andsmaller and larger grids could also be considered. The spatial ar-rangements and configurations of the various land uses might also haveeffects on the UHI, beyond the simple land proportions, and could becaptured with landscape ecology metrics. Finally, the results obtainedin the specific case of Beijing’s Olympic Area and at one moment intime, should be confirmed or qualified by conducting similar analyseswith similarly detailed land-use data for other urban sites and differenttimes of year.

Acknowledgment

The authors are grateful for the financial support of the NationalKey Research and Development Program of China (2016YFB0501502,2016YFC0503701) and the Key Project of High Resolution Earth

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Observation System (00-Y30B14-9001-14/16).

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