A seasonal relationship between land surface temperature and normalized difference bareness index

The present study analyzes the seasonal variability of the relationship between the land surface temperature (LST) and normalized difference bareness index (NDBaI) on different land use/land cover (LULC) in Raipur City, India by using sixty-five Landsat images of four seasons (pre-monsoon, monsoon, post-monsoon, and winter) of 1991-1992, 1995-1996, 1999-2000, 2004-2005, 2009-2010, 2014-2015, and 2018-2019. The results show that the post-monsoon season indicates the best correlation (0.59), followed by the monsoon (0.56), pre-monsoon (0.47), and winter (0.44) season. The water bodies reflect a strongly positive correlation in all the four seasons (0.65 in pre-monsoon, 0.51 in monsoon, 0.53 in post-monsoon, and 0.62 in winter). On green vegetation, this correlation is also strongly positive in monsoon (0.57), post-monsoon (0.62), and winter (0.55), whereas it is moderate positive in pre-monsoon (0.37) season. The built-up area and bare land build a moderate positive correlation in all the four seasons (0.35 in pre-monsoon, 0.43 in monsoon, 0.48 in postmonsoon, and 0.39 in winter). Among the four seasons, the post-monsoon season builds the best correlation for all LULC types, whereas the pre-monsoon season has the least correlation. This research work is beneficial for land use and environmental planning of any city under similar climatic conditions.


Introduction
Land surface temperature (LST) is a significant factor in analyzing the bio-geochemical functions of the land surface features (Tomlinson et al. 2011;Hao et al. 2016;Guha 2017). Green plants, wetlands, and water bodies generate low LST, whereas human settlement, and bare land surface produce high LST in the summer season of tropical areas (Chen et al. 2006;Guha et al. 2020). Thus, LST related studies are quite important in the ecological planning of the recent urban agglomerations . Normalized difference bareness index (NDBaI) is the most popular index for bare land extraction that is invariably used in LULC and LST related studies (Zhao and Chen 2005;Chen et al. 2006;Weng and Quattrochi 2006;Essa et al. 2012;Chen et al. 2013;Guha et al. 2019;Yuan et al. 2017).
Several research articles presented the LST-NDBaI relationship in different parts of the world. As-Syakur et al. (2012) investigates various bareness indices for bare land mapping in Denpasar of Bali, Indonesia. Ahmed (2013) used NDBaI along with other LULC indices to simulate the land surface changes and their impact on LST in Dhaka, Bangladesh. Sharma et al. (2013) examined the relationship between LST and NDBaI in Surat City of India. Guo et al. (2014)  The study will be a beneficial one ecological planning and management. The seasonal LST-NDBaI relationship means the relationship between LST and NDBaI in different seasons like pre-monsoon, monsoon, post-monsoon, and winter. It is determined by using a number of Landsat satellite data of these four aforesaid seasons from 1991-92 to 2018-19. The study tries to establish a long-term relationship between LST and NDBaI for various seasons and also on different types land use/land cover. No such type of study has been conducted on this city before the work. The study is beneficial for ecological planning because it focuses on the LST-NDBaI relationship on different LULC types.  Mapper Plus (ETM+) data, whereas band 10 for Landsat 8 Operational Land Imager (OLI)/ Thermal Infrared Sensors (TIRS) data]. The whole study was performed by using ArcGIS 9.3 software.

Study area and data
Landsat 8 TIRS dataset has two TIR bands (bands 10 and 11) in which band 11 has a larger calibration uncertainty. Thus, only TIR band 10 data (100 m resolution) has been recommended for the present study (Barsi et al. 2014). The TIR band of Landsat 5 TM data and Landsat 7 ETM+ data is band 6.
The TIR bands of each Landsat sensors have been resampled to 30 m x 30 m pixel size by the data provider (EROS) using the cubic convolution resampling method.

Retrieving LST from Landsat data
In this study, the mono-window algorithm was applied to retrieve LST from multi-temporal Landsat satellite sensors where three necessary parameters are ground emissivity, atmospheric transmittance, and effective mean atmospheric temperature (Qin et al. 2001;Weng et al. 2004;Wang et al. 2016;Sekertekin and Bonafoni 2020). At first, the original TIR bands (100 m resolution for Landsat 8 OLI/TIRS data, 120 m resolution for Landsat 5 TM data and 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. Radiance for TIR band of Landsat 5 TM data and Landsat 7 ETM+ data is obtained using equation where, is Top of Atmosphere (TOA) spectral radiance (Wm -2 sr -1 mm -1 ), is the quantized calibrated pixel value in DN, (Wm -2 sr -1 mm -1 ) is the spectral radiance scaled to , (Wm -2 sr -1 mm -1 ) is the spectral radiance scaled to , is the minimum where, is the TOA spectral radiance (Wm -2 sr -1 mm -1 ), is the band-specific multiplicative rescaling factor from the metadata, is the band-specific additive rescaling factor from the metadata, 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 data, the reflectance value is obtained from radiances using equation [3] (USGS): where, is unitless planetary reflectance, is the TOA spectral radiance (Wm -2 sr -1 µm -1 ), is Earth-Sun distance in astronomical units, is the mean solar exo-atmospheric spectral irradiances (Wm -2 µm -1 ) and is the solar zenith angle in degrees. values for each band of Landsat 5 and 7 data can be obtained from the handbooks of the related mission. and values can be attained from the metadata file.
For Landsat 8 data, reflectance conversion can be applied to DN values directly as in equation [4] (Zanter 2019): where, is the band-specific multiplicative rescaling factor from the metadata, is the bandspecific additive rescaling factor from the metadata, is the quantized and calibrated standard product pixel values (DN) and is the local sun elevation angle from the metadata file.
The land surface emissivity , is estimated from equation [6] using the NDVI Thresholds Method (Sobrino et al. 2001;.
where, is land surface emissivity, is vegetation emissivity, is soil emissivity, is fractional vegetation, is the effect of the geometrical distribution of the natural surfaces and internal reflections that can be expressed by equation [7]: where, is vegetation emissivity, is soil emissivity, is fractional vegetation, is a shape factor whose mean is 0.55, the value of may be 2% for mixed land surfaces (Sobrino et al. 2004).
The fractional vegetation , of each pixel, is determined from the NDVI using equation where, ( ) < 0.2 for bare soil; ( ) > 0.5 for vegetation; ( )0.2 <= < = 0.5 for mixed land with bare soil and vegetation (Sobrino et al. 2001; where, is the water vapour content (g/cm 2 ), 0 is the near-surface air temperature in Kelvin (K), is the relative humidity (%). These parameters of atmospheric profile are obtained from the where, is the total atmospheric transmittance, is the water vapour content (g/cm 2 ).
where, is the land surface emissivity, is the total atmospheric transmittance, and are internal parameters based on atmospheric transmittance and land surface emissivity, is the at-sensor brightness temperature, is the mean atmospheric temperature, 0 is the near-surface air temperature, is the land surface temperature, = −67.355351, = 0.458606.

Extraction of different types of LULC by using NDBaI
In this study, special emphasis has been given on NDBaI for determining the relationship with LST (Chen et al. 2006;Zhao and Chen 2005). NDBaI is determined by the short wave infrared (SWIR) and thermal infrared (TIR) bands. For, Landsat 5 TM and Landsat 7 ETM+ data, band 5 is used as the SWIR band and band 6 is used as TIR band, respectively. For Landsat 8 OLI and TIRS data, band 6 and band 10 are used as the TIR bands, respectively ( Table 2). The value of NDBaI is ranged between −1 and +1. Generally, the positive value of NDBaI indicates the bare land (

Characteristics of the spatial distribution of LST and NDBaI
There is a prominent seasonal variation of different periods that occurred in mean and standard deviation (STD) values of LST (Table 3) Table 3.   winter ( Figure 6) season. At the macro-level, the areas with high LST values show the urban heat island phenomenon. These areas have relatively high NDBaI values. At the micro-level, the high peaks of LST also presented the high peaks of NDBaI. The correlation coefficient values of Pearson's linear correlation between the LST and NDBaI are positive (for any year or season). The postmonsoon season has the best mean (mean value of 1991-92, 1995-96, 1999-00, 2004-05, 2009-10, 2014-15, and 2018-19) correlation coefficient value (0.59), followed by the monsoon (0.56), premonsoon (0.48), and winter (0.44) season. It is seen from Figure 3

Conclusion
The present study analyzed the temporal and seasonal relationship of LST and NDBaI in Raipur City, India using sixty-five Landsat data sets of four different seasons (pre-monsoon, monsoon, postmonsoon, and winter) for different years. The main expectation was the relationship should be positive between LST and NDBaI across seasons. Moreover, another expectation was that the strength of the relationship should tend to be weaker with time. Another one is that the relationship should be stronger in comparatively wet season. The results support the expectations.
In general, the results show that LST is positively related to NDBaI, irrespective of any season. In

Acknowledgment
The author is indebted to the United States Geological Survey (USGS).

Disclosure statement
No potential conflict of interest was reported by the author.