A long-term monthly analytical study on the relationship of LST with normalized difference spectral indices

ABSTRACT This study analyzes the long-term monthly variation of land surface temperature (LST) and its relationship with normalized difference spectral indices in the Raipur City of India using one hundred and 23 Landsat images from 1988 to 2020. In specific, the normalized difference vegetation index (NDVI), normalized difference water index (NDWI), normalized difference built-up index (NDBI), and normalized difference bareness index (NDBaI) were used to show the relationship between LST and land surface materials. In terms of LST, the warmest month is April (38.49°C) and the coldest month is January (23.04°C). The standard deviation in LST is noticed as 1.1022°C throughout the period. The growth pattern of LST is increasing in the earlier stage while it is steady and decreasing in the later stage. The linear regression method is used to correlate LST with the spectral indices. The mean regression coefficients for LST-NDVI is −0.42, LST-NDBI are 0.68, LST-NDWI is 0.27, and LST-NDBaI is 0.32. It indicates that the high ratio of green vegetation and water bodies resist the raise of LST, whereas the bare rock surface and built-up land accelerate the LST. The value of the spectral indices and LST varies with the change of month due to the physical change of the land surface materials. Hence, the study will be an effective one for the town and country planners for their future estimation of land conversion.


Introduction
Urbanization accelerates the ecological stress by warming the local or global cities for a large extent Fu & Weng, 2016;Grimm et al., 2008;Liu et al., 2018;Peng et al., 2018a). Presently, many urban areas are suffering with a huge land conversion and resultant new heat zones (Huang et al., 2009;Patz et al., 2005;Zhou et al., 2019). Remote sensing techniques are significantly effective in detecting the land use/ land cover (LULC) change and its consequences (Guha et al., 2018). Apart from the conventional LULC classification algorithms, some spectral indices are used in detecting specific land features. Recently, thermal infrared (TIR) bands are used by generating some indices for different types of LULC extraction (Kalnay & Cai, 2003;Peng et al., 2018b; X-L. Chen et al., 2006). These remote sensing indices are used significantly in various application fields like rocks and mineral mapping, forest mapping, agricultural monitoring, LULC mapping, hazard mapping, urban heat island mapping, and monitoring (Berger et al., 2017;Chen et al., 2006;Du et al., 2016;He et al., 2019;Peng et al., 2016).
Land surface temperature (LST) retrieved from various remotely-sensed data is widely used in the detection of urban heat island and ecological comfort zone (Fu & Weng, 2015;Hao et al., 2016;Tomlinson et al., 2011;Tran et al., 2017;Weng, 2009). LST can be changed significantly in a vast homogeneous land surface or even inside a relatively small heterogeneous urban area (Hou et al., 2010; X-L. Chen et al., 2006). Different types of LULC response differently in TIR band and consequently LST largely varies in an urban environment Ghobadi et al., 2014;Li et al., 2016;Shigeto, 1994;Stroppiana et al., 2014;Yue et al., 2007). The LULC types are mainly changed by land conversion process. Thus, time is an important factor in LST monitoring. These spatial and temporal data of LST is also varied with the seasonal changes as sun elevation and sun azimuth are changed with seasons. Hence, the seasonal variation of LST is quite important in any LULC related study.
Most popular index for vegetation is normalized difference vegetation index (NDVI) that is invariably used in LST-related studies from the very beginning (Tucker, 1979;Smith & Choudhury, 1990;Hope & McDowell, 1992;Julien, ;Yuan et al., 2017). NDVI is directly used in the determination of land surface emissivity and thus is a significant factor for LST estimation (Carlson & Ripley, 1997;Sobrino et al., 2004). Generally, the nature of LST-NDVI relationship in a region is negative and is controlled by a number of factors, such as, dry or wet vegetation, greenness of vegetation, air pollution, moisture content in air, heterogeneous man-made materials, dry or wet soil, etc. (Ghobadi et al., 2014;Qu et al., 2014;Zhou et al., 2011). In mixed urban land, high LST is related to low vegetal covered area (Voogt & Oke, 2003). NDVI depends on the method that computes LST (e.g., NDVI threshold method) (Goward et al., 2002) and many studies based on the LST-NDVI correlation (Gutman & Ignatov, 1998;Weng et al., 2004) are available to explore the pattern of LST. There are so many valuable research articles found on LST-NDVI relationships were conducted mainly in the Indian and Chinese landscape (Guha et al., 2020;Gui et al., 2019;Kikon et al., 2016;Kumar & Shekhar, 2015;Qu et al., 2020;Yuan et al., 2020). Normalized difference water index (NDWI) is the most popular index for extraction of water bodies and it is considerably used in LULC and LST related studies (Essa et al., 2012;McFeeters, 1996; X-L. Chen et al., 2006;Yuan et al., 2017). Generally, the nature of LST-NDWI relationship in an urban area is insignificant which is controlled by several factors, such as humidity, vegetation, wetland, bare land, air pollution, rock surface, dry or wet soil, heterogeneous man-made materials, etc. (Ghobadi et al., 2014;McFeeters, 1996McFeeters, , 2013. Normalized difference built-up index (NDBI) is the most popular built-up index which is invariably used in LST-related studies (Chen et al., 2013;Yuan et al., 2017;Zha et al., 2003). Generally, the nature of LST-NDBI relationship in a region is positive and is controlled by several factors, such as humidity, vegetation, air pollution, rock surface, dry or wet soil, heterogeneous man-made materials, etc. (Ghobadi et al., 2014). Normalized difference bareness index (NDBaI) is the most popular index for bare land extraction that is invariably used in LULC and LST-related studies as it builds a positive relationship in tropical environment (Essa et al., 2012;L Chen et al., 2013;X-L. Chen et al., 2006;Weng & Quattrochi, 2006;Yuan et al., 2017;Zhao & Chen, 2005). Moreover, the dependence on LST of different land covers and the relation of LST with different indices has also been discussed together in some previous works (Bala et al., 2020(Bala et al., , 2021.
However, these abovementioned research works mostly performed on temporal or seasonal analysis of the relationship. Number of research works conducted on monthly analysis of LST-spectral indices relationship is rare in any physical environment. Hence, it is a necessary task to build month-wise LST-spectral indices correlation for the sustainable development of town and country planning as the values of the LST and spectral indices change with the change of months due to the different climatic and biophysical factors. The study was conducted on Raipur City of India as it is a smart growing city with a moderate climatic condition. However, the strength of the LST-spectral indices relationship can change temporally, seasonally, and spatially. The relationship is changed with time as the land surface materials change with time. The relationship also depends on the LULC types as vegetation, soil, water, or built-up area change the values of spectral indices as well as LST. Different seasons also play a significant role in the LST-spectral indices relationship as the growth of vegetation and increase of LST primarily depend on seasonal change. However, no specific conclusion can be drawn on LST-spectral indices relationship for a small number of remotely-sensed data. Thus, longterm Landsat data sets are necessary to obtain a reliable result on this relationship. The present study analyzes the nature, strength, and trend of the effect of LST on NDVI, NDWI, NDBI, and NDBaI.

Study area and data
Raipur City is located in between 21°11ʹ22"N to 21° 20ʹ02"N and 81°32ʹ20"E to 81°41ʹ50"E ( Figure 1). Figure 1(a) presents the outline map of India where Chhattisgarh State is located in the middle part (Source: Survey of India). (Figure 1(b)) presents the outline map of Chhattisgarh State with districts (Source: Survey of India). (Figure 1(c)) represents the false colour composite (FCC) image of Raipur City from recent Landsat data. (Figure 1(d)) indicates the contour map of Raipur (Date: 11 October 2011) of Raipur City (Source: USGS). The total area covers around 165 km 2 . The southern part of the city is covered by dense forests. The Mahanadi River flows along the western side of the city. The elevation is higher in the middle part of the city compared to the outer part. The climate of the city is considered as dry and wet savannah climate (source: India Meteorological Department (IMD)). Four types of seasons are observed in Raipur, i.e., monsoon (June-September), pre-monsoon (March-May), postmonsoon (October-November), and winter (December-February). The mean annual temperature ranges from 12°C (December) to 42°C (May). The temperature often rises above 45°C in April and May. November to April remains almost dry (average rainfall <50 mm) compared to the June to September (average rainfall >200 mm). The study area is also characterized by tropical mixed deciduous vegetation and mixed red soil. The city has a widely diverse population that migrated from the different parts of the country. The city is considered as one of the fastest-growing smart cities in India.
A total of 123 cloud-free (<10% cloud coverage) Landsat TM, ETM+, and OLI/TIRS data from 1988 to 2020 were freely downloaded from the USGS Data Centre to conduct the whole study (https://www.earth explorer.usgs.gov). These satellite images were taken between 10th and 25th day of each and every month to obtain the minimum range of deviation in LST values. Moreover, only a single image can obtain between 10th and 25th day of any month due to the 16 days temporal resolution of Landsat satellite sensors. These satellite images have been radiomerically and geometrically corrected. All the TIR bands of OLI/TIRS, TM, and ETM+ data were resampled to 30 m resolution by USGS data centre using cubic convolution resampling method.

LST estimation from Landsat satellite sensors
Many LST retrieval methods are applicable for different satellite sensors. The mono-window algorithm (García-Santos et al., 2018;Gui et al., 2019;Qin et al., 2001;Sekertekin and Bonafoni, 2020;Yang et al., 2014), single-channel algorithm (Jiménez-Muñoz and Sobrino, 2003;Jiménez-Muñoz et al., 2009;Coll et al., 2010;Chatterjee et al., 2017), splitwindow algorithm (McMillin, 1975;Price, 1984;Becker and Li, 1990), and radiative transfer equation (C Qu et al., 2014) are the main well-known LST retrieval algorithms using Landsat thermal bands (Weng, 2001;Weng et al., 2004;Zhang et al., 2016). Despite giving a good result, the radiative transfer algorithm cannot be applicable without in situ parameters of atmospheric profile at the satellite pass. The actual measurement with infrared thermometer has not been applied to verify the results of the study due to some unavoidable circumstances. Although the split-window algorithm gives the accurate result, it was not used in the study as only band 10 of Landsat 8 OLI/TIRS data was selected for LST generation due to its better calibration (Barsi et al., 2014). The monowindow algorithm and single-channel algorithm also provide good results. In this study, the mono-window algorithm was applied to retrieve LST from multitemporal Landsat satellite images. Ground emissivity, atmospheric transmittance, and effective mean atmospheric temperature -these three parameters are needed to derive the LST using the mono-window algorithm. At first, the original TIR bands (100 m resolution for Landsat 8 OLI/TIRS data, 120 m resolution for Landsat 5 TM data, and 60 m resolution for Landsat 7 ETM+ data) were resampled into 30 m by USGS data centre for further application.
The TIR pixel values are firstly converted into radiance from digital number (DN) values. Band 10 of Landsat 8 data was used as TIR band for its better calibration (Barsi et al., 2014). Radiance for TIR bands of Landsat 5 TM data and Landsat 7 ETM+ data are obtained using Eq. (1) (USGS): where L λ is Top of Atmosphere (TOA) spectral radiance (Wm −2 sr −1 mm −1 ), Q CAL is the quantized calibrated pixel value in DN, L MINλ (Wm −2 sr −1 mm −1 ) is the spectral radiance scaled to QCAL MIN , L MAXλ (Wm −2 sr −1 mm −1 ) is the spectral radiance scaled to QCAL MAX , QCAL MIN is the minimum quantized calibrated pixel value in DN and QCAL MAX is the maximum quantized calibrated pixel value in DN. L MINλ , L MAXλ , QCAL MIN , and QCAL MAX values are obtained from the metadata file of Landsat 5 TM data and Landsat 7 ETM+ data. Radiance for Landsat 8 TIR band is obtained from Eq. (2) (Zanter, 2019): where L λ is the TOA spectral radiance (Wm −2 sr −1 mm −1 ), M L is the band-specific multiplicative rescaling factor from the metadata, A L is the bandspecific additive rescaling factor from the metadata, Q CAL is the quantized and calibrated standard product pixel values (DN). All of these variables can be retrieved from the metadata file of Landsat 8 data.
For Landsat 5 and Landsat 7 data, the reflectance value is obtained from radiances using Eq. (3) (USGS): where ρ λ is unitless planetary reflectance, L λ is the TOA spectral radiance (Wm −2 sr −1 µm −1 ), dis Earth-Sun distance in astronomical units, ESUN λ is the mean solar exo-atmospheric spectral irradiances (Wm −2 µm −1 ) and θ s is the solar zenith angle in degrees. ESUN λ values for each band of Landsat 5 and Landsat 7 data can be obtained from the handbooks of the related mission. θ s and dvalues can be attained from the metadata file.
For Landsat 8 data, reflectance conversion can be applied to DN values directly as in Eq. (4) (Zanter, 2019): where M ρ is the band-specific multiplicative rescaling factor from the metadata, A ρ is the band-specific additive rescaling factor from the metadata, Q CAL is the quantized and calibrated standard product pixel values (DN) and θ SE is the local sun elevation angle from the metadata file. Eq. (5) is used to convert the spectral radiance to atsensor brightness temperature (Wukelic et al., 1989; X-L. Chen et al., 2006): where T b is the brightness temperature in Kelvin (K), L λ is the spectral radiance in Wm −2 sr −1 mm −1 ; K 2 and K 1 are calibration constants. For Landsat 8 data, K 1 is 774.89, K 2 is 1321.08 (Wm −2 sr −1 mm −1 ). For Landsat 7 data, K 1 is 666.09, K 2 is 1282.71 (Wm −2 sr −1 mm −1 ). For Landsat 5 data, K 1 is 607.76, K 2 is 1260.56 (Wm −2 sr −1 mm −1 ). The land surface emissivityε, is estimated from Eq. (6) using the NDVI Thresholds Method (Sobrino et al., 2004(Sobrino et al., , 2001. where, ε is land surface emissivity, ε v is vegetation emissivity, ε s is soil emissivity, Fvis fractional vegetation, dεis the effect of the geometrical distribution of the natural surfaces and internal reflections that can be expressed by Eq. (7): where ε v is vegetation emissivity, ε s is soil emissivity, Fvis fractional vegetation, Fis a shape factor whose mean is 0.55, the value of dεmaybe 2% for mixed land surfaces (Sobrino et al., 2004). The fractional vegetationF v , of each pixel, is determined from the NDVI using Eq. (8) (Carlson & Ripley, 1997): where ðaÞNDVI < 0:2 for bare soil; ðbÞNDVI > 0:5 for vegetation; ðcÞ0:2 < ¼ NDVI < ¼ 0:5 for mixed land with bare soil and vegetation (Sobrino et al., 2004(Sobrino et al., , 2001. Finally, the land surface emissivity ε can be expressed by Eq. (9): where ε is land surface emissivity, Fvis fractional vegetation.
Water vapour content is estimated by Eq. (10) (X-L. Chen et al., 2006;Yang & Qiu, 1996): 17:27�ðT 0 À 273:15Þ 237:3þðT 0 À 273:15Þ where wis the water vapour content (g/cm 2 ), T 0 is the near-surface air temperature in Kelvin (K), RH is the relative humidity (%). These parameters of atmospheric profile are obtained from the Meteorological Centre, Raipur (http://www.imdraipur.gov.in). Atmospheric transmittance is determined for Raipur City using Eq. (11) and Table 2 (Qin et al., 2001;Sun et al., 2010): where τis the total atmospheric transmittance, wis the water vapour content (g/cm 2 ). Raipur City is located in the tropical region. Thus, Eq. (12) is applied to compute the effective mean atmospheric transmittance of Raipur (Qin et al., 2001;Sun et al., 2010): LST is retrieved from Landsat 5 TM and Landsat 8 OLI/TIRS satellite data by using Eq. (13-15) (Qin et al., 2001): where εis the land surface emissivity, τis the total atmospheric transmittance, C and D are internal parameters based on atmospheric transmittance and land surface emissivity, T b is the at-sensor brightness temperature, T a is the mean atmospheric temperature, T 0 is the near-surface air temperature, T s is the LST, a ¼ À 67:355351, b ¼ 0:458606.

Determination of NDVI, NDWI, NDBI, and NDBaI
In this study, special emphasis was given on NDVI (Ke et al., 2015;Purevdorj et al., 1998;Tucker, 1979), NDWI (McFeeters, 1996(McFeeters, , 2013, NDBI (Zha et al., 2003), and NDBaI (Zhao & Chen, 2005) for determining the relationship with LST. NDVI is a vegetation index used in LULC-related study and the determination of fractional vegetation. NDWI is a water index used to distinguish the water bodies from the wetland and moist soil. NDBI is a built-up index used in detecting the built-up areas and it is frequently used by the urban geographers in land use study. NDBaI is a bareness index used to differentiate the bare lands from semi-bare lands and other LULC types. The band combinations of these spectral indices were given in Table 1. The value of any normalized difference spectral index is ranged between −1 and +1. Various types of LULC can be estimated by using the threshold limits of these normalized difference spectral indices (Table 1). Generally, in the tropical city, the positive value of NDVI, NDWI, NDBI, and NDBaI indicates the vegetation surface, water surface, built-up surface, and bare land surface, respectively (X-L. Chen et al., 2006).   ( Figure (2-11)) show the spatial distribution maps of Raipur City in different months from 1988 to 2020. It is seen from (Figure (2-11)) that >90% area of the city was above 32°C mean LST in March-May of 1992, 2001, 2008, 2013). In June and September, 2005 have mean LST values more than the earlier or later years ( Figure (5-6)). The scenario was completely different in October to February ( Figure  (7-11)), where <10% area of the city was above 32° C LST. April (38.49°C mean LST), May (36.65°C mean LST), June (34.56°C mean LST), and March (31.80° C mean LST) -these four months have an average value of >30°C mean LST throughout the entire period of study. February (27.86°C mean LST), October (27.23°C mean LST), September (27.18°C mean LST), and November (25.83°C mean LST) -these four months have an average value of 25-28°C mean LST throughout the entire time. Only December (23.76°C mean LST) and January (23.04°C mean LST) months have an average value of <24°C mean LST for the entire period. The average value of the highest and the lowest mean LST from 1988 to 2020 is observed in April and January, respectively. The northwest and southeast parts of the study area exhibit high LST. These parts also have a low percentage of urban vegetation and a high percentage of built-up area and bare land. It shows that the proportion of vegetation was reduced significantly with time. Figure 12 shows the line graph of LST in different months from 1988 to 2019. October, November, and December present almost similar pattern of LST distribution. January and February show almost similar trend in their LST graph. A similarity also has been seen in the mean LST graph of March, April, and May.

Monthly variation in LST distribution
The LST graph of June shows a negative trend, while September shows a positive trend. Figure 13 shows the mean monthly variation of LST (°C) during the study. The mean LST graph is sharply rising from January to April. After that, the graph is gently falling from April to June. A sharp fall is also noticed from June to September. One fact should be remembered that there was no data available for July and August; otherwise the falling trend might be gentle. From September to December the LST graph falls continuously.   months have a moderate to weak positive correlation. A weak positive correlation is found in April (0.29), December (0.28), June (0.22), and May (0.21) months. Thus, the pre-monsoon and winter months indicate low correlation compared to the monsoon and postmonsoon months. Figure 14 shows the line graphs for monthly variation of LST-spectral indices relationships. The LST-NDVI correlation is always negative, whereas the LST-NDBI correlation and the LST-NDBaI correlation are always positive. From 1988 to 2000 a slightly falling trend is observed for LST-NDBI and LST-NDBaI correlation. The trend of LST-NDWI correlation is slightly rising or neutral. There is also no such variation in LST-NDVI correlation and the trend is almost neutral. LST-spectral indices build a stronger correlation between March and November. Figure 15 presents a comparison between LST and four aforesaid spectral indices. Average correlation coefficient was used to compare the monthly assessment of these relationships. LST builds the least correlation with NDVI, NDBI, and NDWI from November to February. Pre-monsoon months have the least correlation between LST and NDBaI as the dry soil and open land absorbs a lot of heat in the summer months. Humidity accelerates the strength of the correlation while dry weather reduces the correlation coefficient values.

Monthly analysis on LST-spectral indices relationship
This LST-NDVI correlation tends to be more negative with the increase of surface moisture (Lambin & Ehrlich, 1996; Moran et al., 1994;Sandholt et al., 2002). In high latitudes, positive LST-NDVI relationships have been observed (Karnieli et al., 2010) as the heat capacity of vegetation and water is more than the bare rock surface. Sun and Kafatos (2007) stated that the LST-NDVI correlation was positive in the winter season as vegetation retains temperature in winter; while it was negative in the summer season because presence of vegetation helps in cooling in summer. Yue et al. (2007) showed that the LST-NDVI relationship in Shanghai City, China was negative and was different in different LULC types. Liang et al. (2012) presented similar types of negative NDVI-LST correlation. This relationship was also negative in Mashhad, Iran (Gorgani et al., 2013). The relationship was strong negative in Berlin City for any season (Marzban et al., 2018). The present study also found the negative LST-NDVI correlation for all the months (average correlation coefficient value is −0.42 from 1988 to 2020). The value of the correlation coefficient is inversely related to the surface moisture content, i.e., the negativity of the relationship increases with the increase of surface moisture content.
The LST-NDBI correlation found in the present study is strong positive for each and every month.
The strongest correlation was noticed in October (0.80) and September (0.76), whereas the least correlation was found in December (0.52) and January (0.61). Moist climate intensifies the strength of the correlation. The result of this study is comparable with the other LST-NDBI related studies conducted in the other cities. LST and NDBI built a strong correlation in Fuzhou City of China (Zhang et al., 2009). L Chen et al. (2013) established a strong positive correlation between LST and NDBI in Wuhan City, China (0.639, 0.717, 0.807, and 0.762 in spring, summer, autumn, and winter, respectively). A strong positive LST-NDBI correlation was also observed in Kunming of China (Chen & Zhang, 2017). A strong positive correlation between LST and NDBI was noticed in Vila Velha, ES, Brazil (Dos Santos et al., 2017). In Melbourne City of Australia, LST and NDBI built a moderate to strong positive correlation (Jamei et al., 2019). Balew and Korme (2020) noticed a positive correlation in Bahir Dar City of Ethiopia. Using a long term Landsat series data in Chattogram Metropolitan Area of Bangladesh, Roy et al. (2020) showed that NDBI is positively correlated to LST. Son et al. (2020) showed that the LST-NDBI relationship was also strong positive (0.85) in San Salvador City of El Salvador in last 30 years. These        aforesaid examples of LST-NDBI positive correlations are simply based on the fact that the building and road construction materials like rock, cement, brick, concrete, tar, sand, stone chips, etc. produce high LST values. This result is very much similar to the result of the present study (mean correlation coefficients between LST and NDBI is 0.68 during the entire period).
The result is quite authentic with respect to the other LST-NDWI related studies in recent years. A study performed in Shenzhen City of China showed a significant negative LST-NDWI correlation on the water bodies (X-L. Chen et al., 2006). LST and NDWI built a negative correlation in desert landscape in Kuwait (Uddin et al., 2010). In Nanchang City of China, LST and NDWI develop a negative correlation on the water bodies . In Asansol-Durgapur Development Region of India, a negative LST-NDWI correlation was found in the water bodies (Choudhury et al., 2019). Das (Choudhury et al., 2019) presented a dynamic negative LST-NDWI correlation in the dry bare land of Northwest India and the surrounding places of Pakistan, where different types of rock compositions influence the values of LST and NDWI. LST and NDWI built a negative linear correlation in Banda Aceh City of Indonesia in the last 30 years (Achmad & Zainuddin, 2019). An insignificant correlation was found in Wuhan City of China. The current analysis showed an insignificant and weak positive correlation (average value of 0.27 for all the months during the study period) between LST and NDWI. These results are based on the fact that LST reduces significantly in water bodies or wetland, but other surface materials have an insignificant relationship because different materials have different water or moisture content ratio.
The LST-NDBaI correlation is positive, irrespective of any season. The post-monsoon season reveals the best correlation among all the four seasons. The present study indicates that LST builds a stable strong to a moderate positive correlation with NDBaI in Raipur City, India from 1988 to 2020. Essa et al. (2012) presented a moderate positive LST-NDBaI correlation (0.39) in Greater Dublin region, Ireland. The LST and NDBaI have built a weak negative correlation (−0.11) in Guangzhou, China (Guo et al., 2015) as the bare earth surface was less. Sharma and Joshi (2016) showed the moderate positive nature of LSI-NDBaI correlation in the National Capital Region of India. A weak positive correlation between LST and NDBaI was presented in London (0.086) and Baghdad (0.469) by Ali et al. (2017). Chen and Zhang (2017) noticed the strong positive nature of the correlation coefficient of the LST-NDBaI relationship in a study performed in Kunming, China due to the presence of high bare land ratio. This correlation was weak positive (0.06) in Harare Metropolitan City, Zimbabwe (Mushore et al., 2017). This relationship was also positive (0.458) in Kolkata Metropolitan Area, India (Nimish et al., 2020). The present study shows that the average correlation coefficient between LST and NDBaI for all the months from 1988 to 2020 is moderate positive (0.32). LST will obviously be increased if the ratio of the bare rock surface, sand, or dry soil is high. However, in many modern cities, percentage of barren land is low that promotes a moderate positive LST-NDBaI relationship. From the above examples, it is clear that the relationship between LST and the four spectral indices is consistent and reliable with respect to the other previous similar types of research works. The study reflects the relationship between LST and normalized difference spectral indices to take new action in environmental planning and management of any city. The area has a positive correlation promotes the LST whereas the area with a negative correlation reduces the LST. Hence, the environmental planners should take special attention in conversion of the barren or fallow lands into vegetation, water bodies, and wetland to control the rising trend of LST. In this way, the fallow or barren lands can be converted into parks, wetlands, or artificial water bodies. Forest or dense vegetation must be protected and social forestry can be introduced at a large scale. Most of the industrial and commercial activities must be restrained in particular areas located far away from the dense residential places. A specific area of the city should be allotted as wasteland. Thus, the correlation between LST and the spectral indices significantly determines the vulnerable area of the city and the ecological health of the city could be improved by converting these vulnerable places into vegetation and water bodies.

Conclusion
The present study estimates the monthly variation of LST distribution in Raipur City, India using 123 Landsat images from 1988 to 2020. April May, June, and March present higher LST value than the rest of the months. The present study also assesses the monthly correlation of LST and spectral indices in Raipur City. The results show that LST is inversely related to NDVI, and positively related to NDBI and NDBaI, irrespective of any month. NDWI does not generate significant correlation with LST. LST builds strong to moderate correlation with NDVI, NDBI, and NDWI between March and November, whereas it is found weak negative in the winter months (December to February). For LST-NDBaI correlation, the strength is reduced in the summer and winter months. The growth of vegetation depends on the climatic component and soil condition those are largely changed in different months. The LST is directly controlled by the ratio of green vegetation in a city. The value of the spectral indices and LST varies with the change of month. Thus, the study is useful for the environmentalist and urban planner for the future ecological planning.
There is obviously some limitations and future scope of the present study. First, LST can be derived by using other algorithms or from other satellite sensors to compare with the present result. Downscaling technique can be applied to get the LST with high pixel values. Secondly, the in situ measurement can be used to validate the result significantly. Third, some new spectral indices can be used for different land surface features to compare the result with the existing indices. Fourth, some other robust statistical techniques and diagrams can be applied to present these relationships. Finally, the entire method may be applied in other study areas with different climatic and physiographic regions.