1 Introduction

Land surface temperature (LST) is considered as an important parameter in analysing the exchange of composed material, energy balance and biophysical and chemical processes of the land surface (Tomlinson et al. 2011; Hao et al. 2016). LST of the different surface area is different due to surface reflectance and roughness of different land use/land cover (LULC) types (Hou et al. 2010). Recently, due to rapid urbanization, the characteristics of land surface types are being changed (Li et al. 2017). The presence of natural vegetation influenced a lot in the distribution of LST (Yuan 2017). Normalized difference vegetation index (NDVI) is a vegetation index which is generally used in LST-related study (Smith and Choudhury 1990; Hope and McDowell 1992; Julien et al. 2006). The LST–NDVI relationship is controlled by a number of factors like dense vegetation, sand dunes, water bodies, dry soil, exposed rock surface, wetland, building materials, etc., and hence, it is too complex in nature (Zhou et al. 2011; Ghobadi et al. 2014; Qu et al. 2014).

Currently, most of the research scholars applied thermal infrared remote sensing to build the relationship between LST and NDVI (Ghobadi et al. 2014; Stroppiana et al. 2014; Li et al. 2016; Wen et al. 2017). Most of the earlier LST–NDVI relationship-related studies were conducted on big cities, e.g., Tokyo (Shigeto 1994), Shanghai (Yue et al. 2006), Melbourne (Jamei et al. 2015), Bangkok (Estoque et al. 2017), Shiraz (Fatemi and Narangifard 2019), Rome (Bonafoni 2015), Chongqing (Luo and Li 2014), Shijiazhuang (Liu et al. 2014), Beijing, and Islamabad (Naeem et al. 2018). A spatial and temporal analysis of LST–NDVI relationship for in Monte Hermoso, Argentina was performed for urban planning (Ferrelli et al. 2018). Only a few studies have been conducted about the seasonal relationship between LST and NDVI in a tropical Indian city.

Generally, the spatial and temporal resolution of satellite sensor should follow the nature of surface configurations (Zhang et al. 2015). In any urban area, the high value of land surface temperature (LST) is generated mostly in the area with lower vegetation intensity (Voogt and Oke 2003). Therefore, most of the thermal remote sensing methods used the normalized difference vegetation index (NDVI) as the significant indicator of LST (Goward et al. 2002), and a number of studies based on the relationships of LST with NDVI were used to explore the pattern of LST (Gutman and Ignatov 1998; Weng et al. 2004; Guha et al. 2017, 2018, 2019; Govil et al. 2019). Fractal technique (De Cola 1989; Emerson et al. 1999; Lam 1990; Lam and Quattrochi 1992; Lam and De Cola 1993; Lam et al. 2002; Qiu et al. 1999; Weng 2003) has also been applied in determining the LST–NDVI relationship (Weng et al. 2004).

Some recent research works based on spatial–temporal relationship of LST–NDVI in tropical Indian cities have also been performed successfully, e.g., Ahmedabad (Mathew et al. 2018), Jaipur (Mathew et al. 2017), Kalaburagi (Kumar and Shekhar 2015), Noida (Kikon et al. 2016), and Lucknow (Singh et al. 2017). A number of new research works were performed on the LST–NDVI relationships in multidimensional approach (Hassan et al. 2007; Li and Yu 2008; Zhang and Wang 2008; Rozenstein et al. 2014; Slawsky et al. 2015; Hao et al. 2019; Liu and Weng 2018; Mohammad et al. 2019; Nowicki et al. 2019; Qi et al. 2019; Shi et al. 2019; Sun et al. 2019). It is a necessary task to assess the time series of LST–NDVI relationship in different LST and NDVI zones for a tropical city which has not been well addressed in the earlier studies. Generally, low NDVI region indicates high LST values and vice versa. It is also very important to know the change of LST with the change of NDVI. Generally, negative NDVI shows water bodies; positive NDVI up to 0.2 shows bare land and built-up areas; NDVI with more than 0.2 shows vegetation; and higher NDVI stands for the healthier vegetation with high chlorophyll content (Chen et al. 2006; Guha et al. 2017). To reveal the characteristics of spatiotemporal variation of LST–NDVI relationship in a tropical city, we selected Raipur City of India as the city is an excellent example of mixed landscape. We determined the LST–NDVI relationship under different ranges of LST and NDVI from various types of Landsat sensor products of pre-monsoon season for 2002, 2006, 2010, 2014, and 2018 as the landscape has been changed a lot during this time frame. These results can be useful for future environmental planning and sustainable development as Raipur is considered as a smart city and also one of the fastest growing cities in country. Importance of green areas, water bodies, and wetland has been increased for the city planners in a very short time span. The main aims of the study are (1) to determine the spatiotemporal variation of LST–NDVI relationship for the whole of the city, the area above mean LST, the area below mean LST; and (2) to explore the spatiotemporal variation of LST–NDVI relationship under different ranges of NDVI values.

2 Study area and data

Raipur City of Chhattisgarh State of India was selected as the study area for the entire research work. The total study area extends between 21° 11′ 22″ N to 21° 20′ 02″ N and 81° 32′ 20″ E to 81° 41′ 50″ E with a moderate range of elevation of 219 m to 322 m (Fig. 1). The study area is considered as tropical wet (Savannah) type of climate. The mean annual temperature of Raipur City is approximately 27 °C. According to the India Meteorological Department, there are four seasons are observed in Raipur, i.e. pre-monsoon (March–June), monsoon (July–September), post-monsoon (October–November), and winter (December–February). The pre-monsoon or summer months are usually hot and remain almost dry. The temperature often rises above 45 °C in April and May. The pre-monsoon season was selected for the present study for examining the nature of LST due to its severe intensity. July, August, and September months are considered under monsoon or rainy season. October and November months are often considered as the post-monsoon season, characterized by a pleasant climatic condition with comparatively low temperature and high to the moderate moisture content in the air. The presence of high density of green vegetation really adds an extra flavour in Raipur during the monsoon and the post-monsoon seasons. Winter months (December to February) experience a cool and dry climate. The study area is also characterized by tropical mixed deciduous vegetation and mixed red soil. According to the 2011 census, Raipur City had a total population of 1,010,087, with a sex ratio of 945 females per 1000 males and with a literacy rate of 86.45%.

Fig. 1
figure 1

Location of the study area

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In the present study, the main data sets are time series of Landsat images taken by the Landsat 5 Thematic Mapper (TM), Landsat 7 Enhanced Thematic Mapper Plus (ETM +), and Landsat 8 Operational Land Imager (OLI)/Thermal Infrared Sensor (TIRS) sensors, and have been obtained from the United States Geological Survey website (https://earthexplorer.usgs.gov). A total of fifteen Landsat images have been taken in the Landsat series as shown in Table 1. The Landsat sensor overpasses the Raipur City between approximately 04:25 and 04:56 GMT, which is 09:55 to 10:26 AM local time. This is known to be an opportunity for collecting images with maximum illumination, especially in LST studies. Satellite images have been obtained with 4-year intervals, and within the pre-monsoon season to avoid phenological variations. The interval period of four years (2002, 2006, 2010, 2014 and 2018) has been taken in the present research work so that we can compare the results to see the temporal changes in LST and NDVI. The software used to conduct image processing included ERDAS Imagine 9.1 and ArcGIS 9.3. MS-Excel 2007 has been used for conducting the statistical analysis. Pre-processing of Landsat images is necessary as it has a great impact on the results of the analysis. Usually, it is not necessary to conduct a geometric correction for Landsat level 1 products, as they are registered and ortho-rectified through a systematic process. The main correction needed is therefore a radiometric correction. The radiometric correction eliminates errors that affect the brightness values of the pixels. These errors are mainly due to the detection errors in the sensor system and environmental attenuation errors. The original image sizes are larger than the study area, and hence, after pre-processing they are edited using a shapefile of Raipur City. LST has been retrieved through thermal infrared bands of Landsat data sets (band 6 for Landsat 5 and Landsat 7 data, whereas band 10 and 11 for Landsat 8 data). Red, near-infrared, and thermal infrared bands are used in generating NDVI and LST.

Table 1 Specification of multi-date Landsat satellite sensors
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3 Methodology

3.1 Retrieving LST from Landsat data

In this study, the mono-window algorithm has been applied to retrieve LST from multi-temporal Landsat satellite images (Qin et al. 2001; Guha et al. 2017, 2018, 2019). Ground emissivity, atmospheric transmittance, and effective mean atmospheric temperature—these three parameters—are needed to derive the LST using mono-window algorithm. After determining the mean LST, the study has been performed into the whole of the city, the area above mean LST, and the area below mean LST.

At first, the original TIR band of Landsat sensor has been resampled into 30 m for further application. The entire procedure included the following equations:

$$L_{\lambda } = {\text{RadianceMultiBand}} \times {\text{DN}} + {\text{RadianceAddBand}}$$
(1)

where \(L_{\lambda }\) is spectral radiance (Wm−2 sr−1 mm−1).

$$T_{{\text{b}}} = \frac{{K_{2} }}{{\ln \left( {\frac{{K_{1} }}{{L_{\lambda } }} + 1} \right)}}$$
(2)

where Tb is the at-sensor brightness temperature (Kelvin); K2 and K1 are calibration constants. Here, K1 is 774.89 (Wm−2 sr−1 mm−1); K2 is 1321.08 (Wm−2 sr−1 mm−1) for Landsat 8 data. For Landsat 7 data, K1 is 666.09 (Wm-2sr-1mm-1); K2 is 1282.71 (Wm-2sr-1mm-1). For Landsat 5 data, K1 is 607.76 (Wm-2sr-1mm-1); K2 is 1260.56 (Wm-2sr-1mm-1).

$$F_{{\text{v}}} = \left( {\frac{{{\text{NDVI}} - {\text{NDVI}}_{\hbox{min} } }}{{{\text{NDVI}}_{\hbox{max} } - {\text{NDVI}}_{\hbox{min} } }}} \right)^{2}$$
(3)

where \({\text{NDVI}}_{\hbox{min} }\) is the minimum value (0.2) of NDVI for bare soil pixel and \({\text{NDVI}}_{\hbox{max} }\) is the maximum value (0.5) of NDVI for healthy vegetation pixel.

\(d\varepsilon\) is the geometric distribution effect for the natural surface and internal reflection. The value of \(d\varepsilon\) may be 2% for mixed and elevated land surfaces.

$$d\varepsilon = (1 - \varepsilon_{{\text{s}}} )(1 - F_{{\text{v}}} )F\varepsilon_{{\text{v}}}$$
(4)

where \(\varepsilon_{{\text{s}}}\) is soil emissivity; Fv is fractional vegetation; F is a shape factor (0.55); \(\varepsilon_{{\text{v}}}\) is vegetation emissivity.

$$\varepsilon = \varepsilon_{{\text{v}}} F_{{\text{v}}} + \varepsilon_{{\text{s}}} (1 - F_{{\text{v}}} ) + d\varepsilon$$
(5)

where \(\varepsilon\) is land surface emissivity. The value of \(\varepsilon\) is determined by the following equation:

$$\varepsilon = 0.004 \times F_{{\text{v}}} + 0.986$$
(6)

Water vapour content is determined by the following equation:

$$w = 0.0981 \times \left[ {10 \times 0.6108 \times \exp \left( {\frac{{17.27 \times (T_{0} - 273.15)}}{{237.3 + (T_{0} - 273.15)}}} \right) \times {\text{RH}}} \right] + 0.1697$$
(7)

where w is water vapour content (g/cm2); T0 is near-surface air temperature (Kelvin); RH is relative humidity (%). These parameters of atmospheric profile were the average values of 14 stations around Raipur which were obtained from the Meteorological Centre, Raipur and the Regional Meteorological Centre, Nagpur.

$$\tau = 1.031412 - 0.11536w$$
(8)

where \(\tau\) is the total atmospheric transmittance.

Raipur city is located in the tropical region. Thus, the following equations were applied to compute the effective mean atmospheric transmittance of Raipur:

$$T_{{\text{a}}} = 17.9769 + 0.91715T_{0}$$
(9)
$$T_{{\text{s}}} = \frac{{\left[ {a\left( {1 - C - D} \right) + \left( {b\left( {1 - C - D} \right) + C + D} \right)T_{{\text{b}}} - DT_{{\text{a}}} } \right]}}{C}$$
(10)
$$C = \varepsilon \tau$$
(11)
$$D = \left( {1 - \tau } \right)\left[ {1 + \left( {1 - \varepsilon } \right)\tau } \right]$$
(12)

where Ta is mean atmospheric temperature; Ts is land surface temperature; \(a = - 67.355351\), \(b = 0.458606\).

3.2 Generation of NDVI

In the earlier studies, various land surface biophysical parameters were applied to specify different types of land surface features (Bonafoni 2015; Luo and Li 2014; Liu et al. 2014; Guha et al. 2017, 2018, 2019). In this study, special emphasis has been given on NDVI for determining the relationship with LST. NDVI is generally used as a vegetation index which can also be used for extracting other LULC types (Purevdorj et al. 1998; Ke et al. 2015). In this study, NDVI has been determined using the red and near-infrared bands of Landsat sensors (Table 2). The NDVI values are further divided into some parts of a range of 0.1 NDVI value. Finally, the LST–NDVI relationship is examined under these ranges of NDVI values.

Table 2 Description of normalized difference vegetation index (NDVI)
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3.3 Preparation of LULC map

The LULC maps for the five selected years—2002, 2006, 2010, 2014, and 2018—have been prepared using the threshold limits of NDVI (Chen et al. 2006). The area with NDVI values of more than 0.2 indicated vegetation while less than 0 values of NDVI reflected water bodies. The intermediate values were used for the extraction of the built-up area and bare land. But these threshold values may differ due to atmospheric condition. An ISODATA classifier with the unsupervised clustering method and the maximum likelihood classification has also been applied to verify the output. The values of kappa coefficient and overall accuracy have been calculated as 0.87 and 91.62, respectively. Some small water bodies have been found in the central and the southern sections of the study area during the entire time span. In 2002, most of the areas were covered by green vegetation, whereas the built-up areas and bare lands have been found mainly in the central and north-western parts of the Raipur City. The portion of the built-up areas and bare lands has been expanded along the north-western border from 2002 to 2010. From 2006 to 2014, the percentage of urban vegetation was declined because of the conversion into built-up areas. From 2014 to 2018, green areas have been reduced significantly. Only some parts of east and south-west of the city are covered by green vegetation. Rest of the areas of the city has been converted into bare land and built-up area (Fig. 2).

Fig. 2
figure 2

LULC maps of Raipur City: a 2002, b 2006, c 2010, d 2014, and e 2018

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4 Results and discussion

4.1 Spatiotemporal variations of LST distribution

The retrieved LST maps using the pre-monsoon multi-temporal Landsat data sets have been shown in Fig. 3. The average aggregated LST values of 2002, 2006, 2010, 2014, and 2018 have been generated (Table 3). Figure 4 shows the mean LST values for 2002, 2006, 2010, 2014, and 2018. The annual average minimum LST ranges from 22.08 °C in 2002 to 33.98 °C in 2018. The annual average maximum LST ranges between 36.56 °C in 2002 and 50.40 °C in 2018. The annual average mean LST value has been increased from 31.91 °C (2002) to 43.53 °C (2018). The high LST values are found in the north-western and south-eastern parts of the city. This portion of the area is characterized by open bare land. The central part of the study area presents the low LST zones where a high concentration of urban vegetation and water bodies are observed.

Fig. 3
figure 3

Spatiotemporal distribution of LST (°C): a, b 2002, c, d 2006, e–g 2010, h–k 2014, and l–o 2018

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Table 3 Spatiotemporal variations of LST (°C) distribution (2002–2018)
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Fig. 4
figure 4

Mean LST (°C) values: a 2002, b 2006, c 2010, d 2014, and e 2018

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4.2 Validation of Landsat data derived LST with respect to the corresponding MODIS data derived LST

Before performing any kind of application, validation of derived LST is necessary with in situ measurement or with any other satellite sensor (Guha et al. 2019). In the present study, MODIS Terra data sets have been applied for the validation of LST values as a reference image. Landsat and modis sensor cannot overpass at same time for the same study area. Thus, MOD11A1 data (1000 m spatial resolution) of the following specific dates (Table 4) have been taken for the validation of estimated LST.

Table 4 Validation of Landsat data retrieved LST with MODIS data retrieved LST
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No such information has been obtained about the precipitation or atmospheric disturbances in the acquisition date of Landsat and MODIS sensors. For MODIS data, the spatial resolution of retrieved LST is 1000 m, whereas for Landsat 5, Landsat 7, and Landsat 8 data the resolutions of LST image are 120 m, 120 m, and 100 m, respectively. A little difference has been found between the LST retrieved from Landsat data sets and the corresponding MODIS data sets for the following reasons: (a) 30 min intervals between the Landsat sensors and MODIS sensors, (b) content of water vapour, and (c) resampling technique (Guha et al. 2019). In spite of not performing any upscaling or downscaling procedure, a significant correlation has been found between the mean derived LST from Landsat data sets and MODIS data sets (Table 4).

4.3 Spatiotemporal variation in the distribution of NDVI

NDVI images have been generated using the red and near-infrared bands of Landsat sensors, and the mean values of NDVI for particular years have been generated separately (Table 5). Figure 5 presents the NDVI values for fifteen pre-monsoon images. Figure 6 shows the mean NDVI values for 2002, 2006, 2010, 2014, and 2018. The high NDVI values have been found in the south-western and north-eastern parts of the city where vegetation is abundant and LST values are comparatively less. The maximum values of average annual NDVI (bold values in Table 5) have been decreased from 2002 to 2018 (0.56 in 2002, 0.52 in 2006, 0.50 in 2010, 0.48 in 2014, and 0.44 in 2014). It indicates that the proportion of vegetation of the city area has been reduced gradually with time. Figures 3, 4, 5, and 6 show that the LST and NDVI exhibit opposite spatial distribution patterns. At the macro level, the areas with high LST values show the urban heat island phenomenon. These areas have relatively low NDVI values. At the micro level, the high peaks of LST present a low valley of NDVI.

Table 5 Spatiotemporal variation of NDVI distribution for whole of the city (2002–2018)
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Fig. 5
figure 5

Spatiotemporal distribution of NDVI: a, b 2002, c, d 2006, e–g 2010, h–k 2014, and l–o 2018

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Fig. 6
figure 6

Mean NDVI values: a 2002, b 2006, c 2010, d 2014, and e 2018

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4.4 Distribution of LST for the area above mean LST, and for the area below mean LST

Figure 7 indicates a steady picture of the spatial distribution of LST values for the area above mean LST, and for the area below mean LST using fifteen multi-date images from 2002 to 2018. The high LST zones or area above mean LST are presented as red colour shades, whereas the low LST zones or the area below mean LST are presented as green colour shades. The central and southern parts of Raipur City are characterized by low LST values (area below mean LST), whereas the northern, western, and south-eastern parts reflect high LST zones (area above mean LST). The high LST zones are surrounded by built-up area and bare earth surface, whereas the low LST zones are developed mainly by the concentration of water bodies and dense vegetal cover.

Fig. 7
figure 7

The area above mean LST (red colour) and the area below mean LST (green colour): a, b 2002, c, d 2006, e–g 2010, h–k 2014, and l–o 2018

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4.5 LST–NDVI relationship for the whole area of the city, the area above mean LST, and the area below mean LST

Generally, LST presents a negative relationship with NDVI. This specific pattern of the relationship between LST and NDVI has been noticed throughout the whole study area (Table 6). It is clear that NDVI is strong to moderate related to LST for the whole of the study area. The relationship is strong negative in 2002, 2006, and 2010 (bold values in Table 6), whereas it is moderate negative in 2014 and 2018. There has been no such particular pattern seen in NDVI–LST relationship for the area above mean LST. It shows a moderate relationship throughout the entire time. This relationship has also been found moderate for the area below mean LST. It indicates the fact that small area reduces the strength of LST–NDVI relationship due to the presence of heterogeneity in landscape. The large area always enhances the scope of building a strong LST–NDVI relationship in urban area.

Table 6 Spatiotemporal variation of LST–NDVI relationship (2002–2018)
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Figures 8 and 9 present the mean temporal variation and year-wise analysis of LST–NDVI relationship for the study area, respectively. Figure 8 shows a strong negative relationship for whole area which has been decreased through time. In the area above mean LST and in the area below mean LST, these relationships are moderate negative without showing a specific increasing or decreasing trend. Figure 9 shows a smooth and steady decreasing rate on the negative relationship for the whole area from 2002 to 2018. The range of the correlation coefficient of LST–NDVI relationship for area above mean LST (−0.29 to −0.40) is narrower than the area below mean LST (−0.18 to −0.49).

Fig. 8
figure 8

Temporal status of LST–NDVI relationship

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Fig. 9
figure 9

Year-wise analysis of LST–NDVI relationship

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4.6 LST–NDVI relationship under different ranges of NDVI

LST–NDVI relationship varies with the various ranges of NDVI (Fig. 10). Under various range of NDVI, the values of LST are different. Table 7 presents the variation of LST–NDVI relationship where bold values show the correlation coefficient value of less than −0.20. Under the positive values of NDVI, the relationship is totally negative. Up to the NDVI value of 0.4, the correlation coefficient values are strong to moderate negative. This is mainly the region of green vegetation. Beyond the NDVI value of 0.4, the relationship is weak. We cannot predict any strong decision on LST–NDVI relationship where the NDVI values are negative (less than 0). Under these ranges of NDVI value, the relationship is weak and non-reliable. Generally, negative NDVI indicates the presence of water bodies or wetland. Hence, it can be said that in water bodies or wetland, the LST–NDVI relationship is non-consistent. Even in most of the cases, the relationship is positive in nature. It can be concluded that under the positive NDVI values, the range of the LST–NDVI relationship is narrow, whereas it is wide under the negative NDVI values.

Fig. 10
figure 10

LST–NDVI relationship under various ranges of NDVI

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Table 7 LST–NDVI relationship under different ranges of NDVI (2002–2018)
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5 Conclusion

In this paper, fifteen cloud-free pre-monsoon data from different Landsat sensors from 2002 (two), 2006 (two), 2010 (three), 2014 (four), and 2018 (four) have been used to investigate the relationship between LST and NDVI for the whole area of Raipur City, the area above mean LST, and the area below mean LST. The LST has been retrieved from Landsat data sets using the mono-window algorithm. The LST derived from Landsat data sets are strongly validated with MODIS Terra data sets. The results have also been applied on the different ranges of NDVI values. The results show that mean LST of the study area has been increased at a very significant rate (11.62 °C increase between 2002 and 2018). The rise of LST is mainly for the conversion of land and also for the climate change to some extent in the unchanged land area. Generally, LST is negatively related to NDVI for the whole of the study area. The relationship is weaker under the area above mean LST and the area below mean LST. It indicates that the small mixed lands are not suitable for strong LST–NDVI relationship. The results also indicate that under the positive NDVI values, the LST–NDVI relationship is strong to moderate negative, whereas it is positive and non-consistent under the negative values of NDVI. The city should be properly planned so that the NDVI values can be increased. It means the percentage of urban green bodies must be higher compared to the concrete materials. Otherwise, the city will be suffered from the gradual thermal stress. The results also show that the relationship is stronger in the earlier times compared to the recent times. It indicates the increase in built-up area as man-made materials enhance the reliability of LST–NDVI relationship.

The result of the present study is too significant in future town planning as most of the converted lands are built-up area or bare land which are responsible for high LST. For better sustainability, a large amount of urban plantation is needed along the road side and residential area. The present water bodies and green areas inside the city boundary must be preserved for providing a better life. Major commercial or industrial activities should be moved into the outskirts of the city to reduce the air and water pollution. The green building materials like earthen materials, wood, bamboo, natural clay, earth bags, natural fibre, etc., should be used in the construction of new buildings or apartments.