3.1.

Image Preprocessing

Landsat 5 TM images of May 23, 2010 were used in this research. Image bands through 1 to 5 and 7 have a spatial resolution of 30 m, and the thermal infrared band has a spatial resolution of 120 m. We also employed some auxiliary data such as land use map and meteorological data. Data preprocessing was mainly carried out in ENVI 4.3. First, the raw images were geo-referenced to a common universal transverse mercator projection coordinate system based on the SPOT reference images and the 1:25,000 scale topographic maps, and were resampled using the nearest neighbor algorithm with a pixel size of $30\times 30\mathrm{m}$ for all bands, including the thermal band. The root mean square error of rectification was $<0.5\text{pixels}$ in this study. Then, the surface reflectivities of six optical bands of the raw images were obtained after radiometric calibration and atmospheric correction by the ENVI FLAASH tool.

3.2.

Derivation of NDVI, NDBI, and NDWI and Land Use Classification

The normalized indices NDVI, NDBI, and NDWI were used to characterize the land cover types and quantify the relationships between land cover type and UHI effect. NDVI is widely used because of its advantages, such as lower influence of atmospheric variations, greater sensitivity to chlorophyll, and reduction of noise by normalization. NDVI is expressed as follows:²⁷

The NDBI index was introduced by Zha to analyze increments of reflectance on TM bands 4 and 5 for images of urbanized and barren land areas,²⁸ which can reflect the building information more accurately. The NDBI index is described as

NDWI is a normalized difference water index, also called leaf area water-absent index, which implies the water content within the vegetation. The NDWI index is described as^29,30

Among the above three equations, $\rho$ represents the reflectivity, DN represents the digital number. Subscript $R$, NIR, and MIR represents red band, near-infrared band, and middle infrared band, respectively. For Landsat TM image, $R$, NIR, and MIR represents band 3, band 4, and band 5, respectively.

According to the SPOT images and background information of the study area, there are eight land use types in this area, namely farmland, woodland, grassland, residential land, commercial land, traffic land, bare land, and water. From a pixel scale, the earth surface is generally regarded to be composed of three types, namely natural surface, urban, and water.³¹ As the spectral features of woodland, grassland, and farmland are similar, these types belong to the natural surface; the spectral features of residential land, commercial land, traffic, and bare land are similar, these four types belong to urban.

We established the classification model in the study area using the decision tree classification tool of ENVI. The classification model is described as

3.3.

Derivation of Land Surface Temperature

The TM thermal infrared band (10.4 to 12.5 μm) data were utilized to derive the LST. First, the DN is converted to top-of-atmospheric (TOA) radiance measured by the instrument.

Next, the TOA radiance is converted to surface-leaving radiance by removing the effects of the atmosphere.³²

Three atmospheric parameters, namely $\tau$, $L_{\text{upper}}$, and $L_{\text{down}}$, are inversed by the atmospheric correction tool developed by Barsi et al.,³² which is available at the NASA website ( http://atmcorr.gsfc.nasa.gov).

Moreover, the $\epsilon$ in Eq. (5), namely the surface emissivity, was estimated according to the classification result and NDVI. The surface emissivity from satellite pixel scale is calculated by following equation:³³

In Eq. (7), ${\mathrm{NDVI}}_V$ and ${\mathrm{NDVI}}_S$ represent the NDVI value of vegetation and bare land, respectively.

Finally, the surface radiance is converted to LST using the Landsat specific estimate of the Planck curve, expressed as

In Eq. (8), LST is the surface temperature in Kelvin ($K$), for Landsat 5 TM images, $K1=607.76$ (${\mathrm{Wm}}^{-2}{\mathrm{sr}}^{-1}{\mu \text{m}}^{-1}$) and $K2=1260.56\mathrm{K}$.

3.4.

Relationships Between LST and Driving Factors at Different Spatial Scales

This section mainly analyzes the relationships between LST and NDVI, NDBI, NDWI, and the changing trends of these relationships at different spatial scales. The main ideas are as follows:

First, the LST, NDVI, and NDBI at different spatial scales are obtained by aggregation processing, and the expressions are shown below:

In Eq. (9), $X(k,l)$ represents the original pixel value, $X(i,j)$ represents the aggregated pixel value, $X$ represents LST, NDVI, NDBI, $S$ is the aggregated area, and $M$ is the number of pixels of aggregated area.

Then, the regression models of LST and NDVI, NDBI, NDWI are built by the least-squares method at different spatial scales, and the relationships between spatial scale and the fitting accuracy of the regression models are further analyzed.

4.1.

Experimental Results

The NDVI, NDBI, NDWI, and the land use classification result of the study area are shown in Fig. 2.

Fig. 2

The NDVI, NDBI, NDWI, and classification result of the study area.

Then the atmospheric upwelling radiance, atmospheric downwelling radiance, and the atmospheric transmittance of the study area of May 23, 2010, were obtained from NSAS website, which were $2.35,3.73{\mathrm{Wm}}^{-2}{\mathrm{sr}}^{-1}{\mu \text{m}}^{-1}$, and 0.7, respectively. Also, the LST of the study area was inversed as shown in Fig. 3.

Fig. 3

The land surface temperature of the study area (°C).

The surface temperatures of urban areas are mainly distributed in 30 to 49°C, the average temperature is 35.6°C; the surface temperature of rural areas are mainly distributed in 22 to 32°C, the average temperature is 26.8°C; and the water temperature is distributed in 17 to 23°C, the average temperature is 18.5°C.

4.2.

Spatial Distribution of Surface UHIs

Heat island intensity was defined as the average temperature difference between urban and rural. The average temperature of urban area and rural area was 37.6°C and 27.9°C, respectively. So, the heat island intensity of the study area was 9.7°C, and the heat island effects were obvious.

Simultaneously, we used the thermal field variance index to analyze the heat island effects’ spatial distribution of the study area quantitatively. Also, the thermal field variance index (HI) is defined as follows:³⁴

The thermal field variance index was graded into four degrees in this paper: $\mathrm{HI}\le 0.0$ represented no heat island effect; $0.0<\mathrm{HI}\le 0.1$ represented weak heat island effect; $0.1<\mathrm{HI}\le 0.3$ represented stronger heat island effect; and $\mathrm{HI}>0.3$ represented strongest heat island effect. The spatial distribution of heat island of the study area was shown in Fig. 4.

Fig. 4

The spatial distribution of surface heat island of the study area.

From Fig. 4, we can find the spatial distribution patterns of UHI of the study area are as follows: (1) UHIs are distributed approximately along northeast and southwest directions. (2) The UHI centers are located in the industrial park in the Dadukou district and the railway station in the JiangBei district, and other high energy consumed and densely populated areas, where UHI intensity is about between 5 and 10°C. (3) The heat island effects of the densely built areas such as the Yuzhong district are not obvious, mainly because of the effect of the Yangtze River and the Jialing River.

4.3.

Relationships Between LST and Impact Factors at Different Spatial Scales

The surface temperature is mainly affected by the land use types and is also controlled by the various land cover parameters. The indexes NDVI, NDBI, and NDWI are the three main influencing factors. In this paper, we selected the three index factors to analyze how they affect the surface temperature and the spatial scale effects.

First, the 30-m LST, NDVI, NDBI, and NDWI images were aggregated to the resolutions of 60, 120, 240, 480, 960, and 1200 m. Due to the limited space, we only gave the aggregated results of LST, as shown in Fig. 5. With the increase of spatial scale, images became fuzzy. Especially after spatial scale was increased to 960 m, the overall contour of LST almost vanished.

Fig. 5

The surface temperature of study area at different spatial scales: (a) 30 m, (b) 120 m, (c) 240 m, (d) 480 m, (e) 960 m, and (f) 1200 m.

Figures 6Fig. 7–8 are the scatter plots of LST and NDVI, NDBI, NDWI at different spatial scales, respectively. Then, the regression models between LST and NDVI, NDBI, NDWI at different spatial scales were constructed. As the variation of water temperature is relatively small and the relationships between LST and NDVI, NDBI and NDWI are special, the water pixels were masked from the samples. All of the regression models are significant at 0.05 level.

Fig. 6

The scatter figure of the LST and NDVI at different spatial scales: (a) 30 m, (b) 120 m, (c) 240 m, (d) 480 m, (e) 960 m, and (f) 1200 m.

Fig. 7

The scatter figure of the LST and NDBI at different spatial scales: (a) 30 m, (b) 120 m, (c) 240 m, (d) 480 m, (e) 960 m, and (f) 1200 m.

Fig. 8

The scatter figure of the LST and NDWI at different spatial scales: (a) 30 m, (b) 120 m, (c) 240 m, (d) 480 m, (e) 960 m, and (f) 1200 m.

It is apparent from Fig. 6 that with the increase of spatial scale, the distribution range between LST and NDVI continuously decreases. The distribution range of LST changes from 16 to 51°C (30 m) to 25 to 35°C (1200 m) while the distribution range of NDVI changes from $-0.3$ to 0.9 (30 m) to about 0.2 to 0.7 (1200 m). At all these spatial scales, LST tends to negatively correlate with NDVI, which proves consistent with many previous research results.^13–17,25 Due to NDVI, standing for normalized differential vegetation index, the more the numerical value is, the higher the vegetation coverage degree is, the lower the LST is in corresponding regions. The regression coefficient (RC) ranges from the values of $-5.75$ (30 m) to $-7.60$ (120 m), $-8.77$ (240 m), $-9.89$ (480 m), $-11.23$ (960 m), and $-11.28$ (1200 m). The above result indicates that at the spatial scale of 30 m, when NDVI increases 0.1, LST will fall 0.58°C; as the spatial scale increases to 1200 m, when NDVI increases 0.1, LST will fall 1.13°C. With the increase of spatial scale, the effect by NDVI to decrease LST is growing.

It can also be found from Fig. 6 that the fitting determination coefficients ($R^2$) of the regression model of LST and NDVI reveal a continual increase from the values of 0.23 (30 m) to 0.31 (120 m), 0.38 (240 m), 0.45 (480 m), 0.54 (960 m), and 0.57 (1200 m), which is inconsistent with that of Ref. 25 which states that the $R^2$ of linear regression model between NDVI and LST at different spatial scales gradually begins to augment when resolution reaches 30 m, maximum when resolution reaches 120 m, then gradually falls. After numerous attempts and trials, similar results have not been found yet. What caused different results needs further research. The standard deviation (SD) reveals a continual decrease from the values of 2.47°C (30 m) to 2.23°C (120 m), 1.95°C (240 m), 1.59°C (480 m), 1.24°C (960 m), and 1.09°C (1200 m). The above results show that the degree of correlation between the LST and the NDVI increases as the pixels in the original NDVI and LST images were averaged to the desired resolution level.

It can be found from Fig. 7 that the LST is positively correlated with NDBI at all spatial scales, which conforms to many previous research results.^16,17,18 It results from that NDBI as normalized differential building index, the bigger the NDBI value is, the higher the building coverage degree is, the higher the LST is. The RC increases from the values of 17.96 (30 m) to 31.68 (1200 m). The result shows that at the spatial scale of 30 m, as NDBI increases 0.1, LST will heighten 1.80°C; when the spatial scale rises to 1200 m, as NDBI increases 0.1, LST will heighten 3.17°C. With the increase of spatial scale, the effect by NDBI to enhance LST grows. Under the circumstance of same spatial scale, the effect by NDBI to enhance LST is greater than that by NDVI to decrease LST.

From Fig. 7, the $R^2$ reveals a continual increase from the values of 0.34 (30 m) to 0.49 (120 m), 0.56 (240 m), 0.62 (480 m), 0.67 (960 m), and 0.70 (1200 m), and the SD reveals a continual decrease from the values of 2.29°C (30 m) to 1.93°C (120 m), 1.63°C (240 m), 1.32°C (480 m), 1.03°C (960 m), and 0.92°C (1200 m). The above results clearly show that the relevance between LST and NDBI increases with the increase of spatial aggregation scale.

Figure 8 throws light on the result that with the incessant increase of aggregation scale, the distribution range of NDWI is on the incessant decrease from $-0.4$ to 0.6 (30 m) to 0.0 to 0.5 (1200 m). Meanwhile, very like NDVI, NDWI is negatively correlated with LST at all spatial scales with its RC falling from $-13.2$ (30 m) to $-25.8$ (1200 m) at intervals. This illustrates that at the spatial scale of 30 m, as NDWI increases 0.1, LST will fall 1.32°C; at the spatial scale of 1200 m, as NDWI increases 0.1, LST will fall 2.58°C. Another discovery is that at the same spatial scale, the effect by NDWI to decrease LST is greater than that by NDVI, but is less than that by NDBI to enhance LST. Moreover, the regression model of NDWI and LST is similar with that of NDBI and LST in fitting accuracy, with $R^2$ increasing from 0.31 (30 m) to 0.68 (1200 m), SD decreasing from 2.34°C (30 m) to 0.94°C (1200 m). The result makes clear that the relevance between LST and NDWI is mounting up with the increase of space aggregation scale.

In order to further study the quantitative relation between fitting accuracy (including $R^2$ and SD) and spatial scale in the respective regression models made up of LST with NDVI, NDBI, and NDWI, we constructed regression models and two scatter charts, one of which is $R^2$ and spatial scale, and the other is SD and spatial scale, as is seen from Fig. 9 and the following equations:

Fig. 9

The relationships between spatial scale and the fitting accuracies of the regression models.

In Eqs. (11) and (12), $R_{T-\mathrm{NDVI}}^2$, $R_{T-\mathrm{NDBI}}^2$, and $R_{T-\mathrm{NDWI}}^2$ represent the $R^2$ of the regression models of LST and NDVI, NDBI, NDWI, respectively; ${\mathrm{SD}}_{T-\mathrm{NDVI}}$, ${\mathrm{SD}}_{T-\mathrm{NDBI}}$, and ${\mathrm{SD}}_{T-\mathrm{NDWI}}$ represent the SD of the regression models of LST and NDVI, NDBI, NDWI, respectively; and $x$ represents the spatial scale.

From Fig. 9 and Eqs. (11) and (12), $R^2$ in the regression models made up of LST with NDVI, NDBI, and NDWI keep increasing with the increase of spatial scale, which reveals that there is apparent positive logarithmic function relation between $R^2$ and spatial scale, and fitting degrees of all these three logarithmic models are relatively high, with $R^2$ reaching 0.975, 0.995, and 0.997, respectively. On the contrary, the SD values of the regression models of LST with NDVI, NDBI, and NDWI keep decreasing with the increase of spatial scale, which represents distinct negative logarithm function relation between SD and spatial scale, with $R^2$ of three logarithmic models 0.987, 0.984, and 0.951, respectively. The reason why we made such change is maybe that we adopt the method to acquire a mean value resulting in the resolution change from high to low, and the fitting accuracies of the regression models of LST with NDVI, NDBI, and NDWI continue to rise.