2.1. Top of Atmospheric Spectral Radiance
The first step of the algorithm is the input of Band 10. After inputting band 10, in the background, the tool uses formulas taken from the USGS web page for retrieving the top of atmospheric (TOA) spectral radiance ():where represents the band-specific multiplicative rescaling factor, is the Band 10 image, is the band-specific additive rescaling factor, and is the correction for Band 10 [6].
2.2. Conversion of Radiance to At-Sensor Temperature
After the digital numbers (DNs) are converted to reflection, the TIRS band data should be converted from spectral radiance to brightness temperature (BT) using the thermal constants provided in the metadata file. The following equation is used in the tool’s algorithm to convert reflectance to BT [7]:where and stand for the band-specific thermal conversion constants from the metadata.
For obtaining the results in Celsius, the radiant temperature is revised by adding the absolute zero (approx. −273.15°C) [8].
2.3. NDVI Method for Emissivity Correction
2.3.1. Calculating NDVI
Landsat visible and near-infrared bands were used for calculating the Normal Difference Vegetation Index (NDVI). The importance of estimating the NDVI is essential since the amount of vegetation present is an important factor and NDVI can be used to infer general vegetation condition [9]. The calculation of the NDVI is important because, afterward, the proportion of the vegetation () should be calculated, and they are highly related with the NDVI, and emissivity () should be calculated, which is related to the :where NIR represents the near-infrared band (Band 5) and represents the red band (Band 4).
2.3.2. Calculating the Proportion of Vegetation
is calculated according to (4). A method for calculating [4] suggests using the NDVI values for vegetation and soil ( and ) to apply in global conditions [10]:However, since the NDVI values differ for every area, the value for vegetated surfaces, 0.5, may be too low. Global values from NDVI can be calculated from at-surface reflectivities, but it would not be possible to establish global values in the case of an NDVI computed from TOA reflectivities, since and will depend on the atmospheric conditions [11].
2.3.3. Calculating Land Surface Emissivity
The land surface emissivity (LSE ()) must be known in order to estimate LST, since the LSE is a proportionality factor that scales blackbody radiance (Planck’s law) to predict emitted radiance, and it is the efficiency of transmitting thermal energy across the surface into the atmosphere [12]. The determination of the ground emissivity is calculated conditionally as suggested in [10]:where and are the vegetation and soil emissivities, respectively, and represents the surface roughness ( = 0 for homogenous and flat surfaces) taken as a constant value of 0.005 [13]. The condition can be represented with the following formula and the emissivity constant values shown in Table 1 [4]:When the NDVI is less than 0, it is classified as water, and the emissivity value of 0.991 is assigned. For NDVI values between 0 and 0.2, it is considered that the land is covered with soil, and the emissivity value of 0.996 is assigned. Values between 0.2 and 0.5 are considered mixtures of soil and vegetation cover and (6) is applied to retrieve the emissivity. In the last case, when the NDVI value is greater than 0.5, it is considered to be covered with vegetation, and the value of 0.973 is assigned.
The last step of retrieving the LST or the emissivity-corrected land surface temperature is computed as follows [14]:where is the LST in Celsius (°C, (2)), BT is at-sensor BT (°C), is the wavelength of emitted radiance (for which the peak response and the average of the limiting wavelength () [15] will be used), is the emissivity calculated in (6), andwhere is the Boltzmann constant (1.38 × 10−23 J/K), is Planck’s constant (6.626 × 10−34 J s), and is the velocity of light (2.998 × 108 m/s) [9].
Source :
Journal of Sensors Volume 2016 (2016), Article ID 1480307, 8 pages http://dx.doi.org/10.1155/2016/1480307
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