Tercera Etapa de Rediseño y Pruebas de funcionamiento

In this study, Landsat 4 and 5 (TM) and Landsat 8 datasets were employed to retrieve LST. A single thermal band of Landsat 4 and 5 (TM) and two thermal bands of Landsat 8 (bands 10 and 11) were used. Unfortunately, there were some artifacts (e.g., stray light) resulting from thermal energy that affected the data collected in the Landsat 8 TIRS bands. In particular, band 11 was substantially more contaminated than band 10 by stray light. Therefore, U.S. Geological Survey (USGS) have suggested that only band 10 should be used for LST retrieval (https://landsat.usgs.gov/using-usgs-landsat- 8-product).

Several algorithms have been proposed to retrieve LST from Landsat data. These algorithms may be roughly grouped into three categories: single-channel methods, multi-channel methods, and multi-angle methods (Li et al., 2013c). The most popular algorithms from the single-channel methods are the Mono-Window (MW) algorithm

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(Qin et al., 2001) and the generalised Single-Channel (SC) algorithm (Jiménez‐Muñoz & Sobrino, 2003). For the multi-channel methods, the most popular is the Split- Window (SW) algorithm (Becker & Li, 1990), and an algorithm proposed by Sobrino et al. (1996) has been preferred for the Multi-Angle (MA) method. Historical data from a TM sensor and a single band from TIRS-Landsat 8 (Band 10 only) were used in this work, and these were not suitable for the split-window and multi-angle methods, because their algorithms require two channels to retrieve LST (Jiménez‐Muñoz & Sobrino, 2003). Additionally, multi-angle methods can only be used for homogeneous areas (e.g., the sea surface or densely vegetated forest) but not for heterogeneous areas (Li et al., 2013c).

For the single-channel methods, the mono-window algorithm has been proposed to retrieve LST using two parameters, atmosphere transmittance and mean atmospheric temperature. Whereas, the generalised single-channel algorithm requires a distribution of both atmospheric temperature and water vapour content. Sobrino et al. (2004) proved that the single-channel algorithm provides better results than the mono-window algorithm, generating root mean square deviation values of 0.9 K and 2 K, respectively, when radio-sounding data is not used. These algorithms were also tested by Vlassova et al. (2014) who found that the root mean square deviation values were 1 °C and 2.3 °C for the single-channel algorithm and mono-window algorithm, respectively. The main disadvantage of these methods is that certain atmospheric parameters must be available.

In order to retrieve LST from historical Landsat datasets, there are often difficulties in obtaining in-situ atmospheric profile data during the satellite overpass. In this study, radiosonde data and atmospheric water vapour content were unavailable for the images used. Therefore, an image-based method (single-channel-based surface emissivity) was the only method that could be applied to retrieve LST from geometrically corrected Landsat data. Land surface emissivity (LSE), which is considered to be a modifying parameter for atmospheric correction methods and surface characterisation, has been proven to be related to the Normalised Difference Vegetation Index (NDVI) (Valor and Caselles, 1996). Therefore, land surface emissivity (LSE) computed from the NDVI, based on (Sobrino & Raissouni, 2000), was adopted as a parameter for atmospheric correction when retrieving LST in this study.

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Ding and Xu (2008) conducted a comparison among the image-based method, the mono-window algorithm and the generalised single-channel algorithm, over the city of Fuzhou, China. They found that the image-based method provided superior results than mono-window algorithm and single-channel algorithm. Furthermore, this method has proved to be straightforward and has been widely used in various settings (e.g., Weng & Yang, 2004; Xiao & Weng, 2007; Zhang et al., 2013a; Ayanlade & Jegede, 2015; Estoque & Murayama, 2017; Fathizad et al., 2017; Pal & Ziaul, 2017; Dai et al., 2018; Madanian et al., 2018; Silva et al., 2018; Xiao et al., 2018).

Thermal bands of Landsat data were used to retrieve LST. The thermal bands of Landsat 4 and 5 have a spatial resolution of 120 × 120 m and Landsat 8 has that of 100 × 100 m. These thermal bands had already been resampled to 30 × 30 m by USGS. A three-step process was used to calculate LST.

Step 1: Conversion of digital number (DN) values of Landsat thermal bands to top of atmosphere (TOA) spectral radiance using the Equation 4.3.

Lλ = ML × Qcal + AL (4.3)

Where:

Lλ = TOA spectral radiance

ML = Band specific multiplicative rescaling factor (radiance multi-

band x, where x is the band number)

AL = Band specific additive rescaling factor (radiance add band x,

where x is the band number)

Qcal = Quantized and calibrated standard product pixel values (DN)

Step 2: Conversion of spectral radiance to at-satellite brightness temperature (Tb) in Celsius (°C) using Planck's law, as in the Equation 4.4.

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65 Where:

Tb = Effective at-satellite temperature in Kelvin (K)

Lλ = TOA spectral radiance

K1 = First calibration constant

K2 = Second calibration constant

The thermal constants of band 6 (TM) and bands 10 and 11 (TIRS) are shown in Table 4.1 and are available in metadata for the images used (USGS, 2015b).

Table 4.1 K1 and K2 calibration constant values for thermal bands of Landsat data.

K1 (W m-2 sr-1 μm-1) K2 (Kelvin)

TM band 6 607.76 1260.56

TIRS band 10 774.89 1321.08

Step 3: Correction of Land Surface Temperature (LST): this step was used to retrieve land surface temperature (LST) from Tb imagery and atmospherically

corrected emissivity data using the Equation 4.5, developed by (Artis & Carnahan, 1982).

LST = Tb/ (1+ (λ×Tb/ρ) × Ln (ε)) (4.5) Where:

λ = Wavelength of emitted radiance (the peak response and the average of the limiting wavelengths (λ = 11.5 μm)

ρ = h c / σ (1.438 × 10-2 _mK)

h = Planck’s constant (6.26 × 10-34 Js)

c = the velocity of light (2.998 × 108 s-1)

σ = Stefan–Boltzmann’s constant (1.38 × 10-23 J K-1) ε = Surface emissivity

Surface emissivity (ε) was computed from NDVI using Equation (4.6) as suggested by Stathopoulou et al. (2007).

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ε = 0.017 Pv + 0.963 (4.6) Where: Pv = proportion of vegetation that was computed from the NDVI according to

Equation (4.7)

Pv = (NDVI - NDVImax)2/ (NDVImax - NDVImin)2 (4.7)

Where: NDVI = Normalised Difference Vegetation Index. The NDVI was computed from the red and NIR bands of Landsat data.