Following preprocessing, we calculated the Top-of-Atmosphere (TOA) radiance. This conversion endowed the dataset with radiometric precision, rendering it physically meaningful and amenable to temperature estimation.

TOA radiance, Lλ = ML x Qcal + AL-Qi (1)

• ML = Specific multiplicative scaling factor of each band. Value obtained from    the MTL metadata file under the name of "RADIANCE_MULT_BAND_X".

• Qcal = Is the band or the cut of it.

• AL = Value included in the MTL metadata "Radiance_Add_Band_X", where X    corresponds to the number of the band

The radiometric data was further transformed into degrees Kelvin (K), a vital conversion for accurate land surface temperature estimation. This transformation primed the dataset for precise temperature calculations.

BT = [K2/ In (K1/ Lλ + 1)] - 273.15 (2)

K1 and K2 = Conversion constants, included in the metadata (K1_CONSTANT_BAND_x and K2_CONSTANT_BAND_x) apply to each band, 10 and 11.

We computed the Normalized Difference Vegetation Index (NDVI), a pivotal step in assessing regional vegetation health and land use patterns. The NDVI values, ranging from -1 to 1, played a critical role in evaluating green cover within the study area.

NDVI = (Near infrared – Red)/ (Near infrared + Red) (3)

Building upon the derived NDVI values, we assessed the proportion of vegetation (PV), quantifying the extent of vegetative cover across the study area. This metric provided valuable insights for our land surface temperature assessment.

Pv = Square ((NDVI - NDVImin) / (NDVImax - NDVImin)) (4)

The determination of land surface emissivity values was a fundamental step, as these values significantly influenced temperature estimations. Emissivity values were based on surface properties and land cover types, ensuring the temperature estimates accurately reflected the region's unique characteristics.

e = m Pv + n (5)

• m = value of emissivity of vegetation, in this case 0.004 was used

• Pv = corresponds to the percentage of vegetation

• n = Soil emissivity value, in this case 0.986 was used

Therefore, LSE = 0.004 * Pv + 0.986 (7)

The pinnacle of our methodology was the estimation of land surface temperature (LST). This process involved the application of the Radiative Transfer Equation (RTE), which integrated brightness temperature, emissivity values, and atmospheric properties. The final output was a spatial distribution of LST values across Chikmagalur Taluk 4.

LST = BT / 1 + w (BT / p) * Ln (ε) (8)

• BT = Brightness temperature

• w = Length of the emitted radiation (band 10 or 11 as the case may be)

• p = Constant value obtained by the formula h * c / s that when substituting the values is 1.438 * 10^ -34Js and results in 14,380

• ε is LSE

Figure 3

Our meticulous geospatial analysis revealed a diverse pattern of LST changes in Chikmagalur Taluk. Notably, the eastern part of the Taluk exhibited localized decreases in temperature, while the hill regions in the west and central areas experienced significant temperature increases.

These temperature increases, particularly in the hill regions, corresponded with recent environmental incidents in Chikmagalur. Reports of deforestation, increased land clearing for agriculture, urban infrastructure projects, and a surge in tourism have raised concerns. These incidents may be contributing to localized urban heat island effects and the observed temperature changes. While our analysis doesn't establish causation, it underscores the need for further investigations to comprehensively understand these temperature variations and their potential implications for the region 5.

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