*3.1. Satellite LST Retrieval Methods*

In this study, the following three commonly used methods for LST retrieval are examined: Radiative Transfer Equation (RTE) method, Single Channel Algorithm (SCA) [40], and Mono Window Algorithm (MWA) [39]. The input atmospheric parameters in the methods, such as downwelling radiance (L ↓ λ ), upwelling radiance (L ↑ λ ), and atmospheric transmittance (τ) were calculated using the Atmospheric Correction Parameter Calculator (ACPC) developed by National Aeronautics and Space Administration (NASA) of the US. ACPC uses the atmospheric profiles analyzed by the National Centers for Environmental Prediction (NCEP) as inputs to the radiative transfer codes for a given site and date to calculate the aforementioned atmospheric parameters [84,85].

#### 3.1.1. Brightness Temperature (Tb) Calculation

The brightness temperature of a target refers to the temperature of a blackbody emitting a similar quantity of radiation at a specific wavelength [86], and inverse solution of the Planck function is the way of calculating it. To obtain the brightness temperature image from TIR data, the first step is converting the Digital Number (DN) values to spectral radiance. This radiance conversion for Landsat 8 TIRs can be applied using Equation (1) [87]:

$$\mathbf{L}\_{\lambda}^{\text{sen}} = \mathbf{M}\_{\text{L}} \cdot \mathbf{Q}\_{\text{CAL}} + \mathbf{A}\_{\text{L}} \tag{1}$$

where L sen λ refers to the TOA spectral radiance in Watts/(m<sup>2</sup> ·srad·µm), QCAL is the calibrated and quantized standard product pixel values (DNs), A<sup>L</sup> is the additive rescaling factor of the corresponding band, and M<sup>L</sup> is the multiplicative rescaling factor of the corresponding band. A metadata file of the relevant Landsat 8 data contains the values of these parameters. The brightness temperature for Landsat 8 data can be calculated after radiance conversion using Equation (2):

$$\text{Tb} = \frac{\text{K}\_2}{\ln\left(\frac{\text{K}\_1}{\text{L}\_\lambda^{\text{SR}}} + 1\right)}\tag{2}$$

where Tb is the effective at-satellite brightness temperature in Kelvin, K<sup>1</sup> in Watts/(m<sup>2</sup> ·srad·µm) and K<sup>2</sup> in Kelvin refer to the calibration constants. K<sup>1</sup> and K<sup>2</sup> values for the Landsat 8 Band 10 are 774.89 (Watts/(m<sup>2</sup> ·srad·µm)) and 1321.08 K, respectively.

#### 3.1.2. Radiative Transfer Equation Method

The inverse solution of the radiative transfer equation (RTE) is a direct method for LST retrieval using a single TIR band. This inverse solution can be given by the following expressions:

$$\mathbf{L}\_{\lambda}^{\text{sen}} = [\varepsilon \mathbf{B}\_{\lambda}(\mathbf{T}\_{\text{s}}) + (1 - \varepsilon)\mathbf{L}\_{\lambda}^{\downarrow}]\pi + \mathbf{L}\_{\lambda}^{\uparrow} \tag{3}$$

where L sen λ (W·m−<sup>2</sup> ·sr−<sup>1</sup> ·µm−<sup>1</sup> ) represents the at-sensor spectral radiance of the corresponding TIR band, ε refers to the LSE, B<sup>λ</sup> in W·m−<sup>2</sup> ·sr−<sup>1</sup> ·µm−<sup>1</sup> is the blackbody radiance, Ts is the LST, L ↓ λ and L ↑ λ represent the downwelling and upwelling radiance, respectively, and τ is the atmospheric transmittance. B<sup>λ</sup> at a temperature of Ts is calculated by the inversion of the Equation (3):

$$\mathbf{B}\_{\lambda}(\mathbf{T}\_{\mathbf{s}}) = \frac{\mathbf{L}\_{\lambda}^{\mathrm{sen}} - \mathbf{L}\_{\lambda}^{\uparrow} - \tau (1 - \varepsilon) \mathbf{L}\_{\lambda}^{\downarrow}}{\tau \varepsilon} \tag{4}$$

and, eventually, Ts (LST) can be obtained from the inversion of Planck's law as in Equation (5):

$$\mathbf{T\_s} = \frac{\mathbf{K\_2}}{\ln\left(\frac{\mathbf{K\_1}}{\frac{\mathbf{I\_\lambda}^{\text{gen}} - \mathbf{L\_\lambda}^\dagger - \pi (1 - \epsilon)\mathbf{L\_\lambda}^\dagger}{\pi \epsilon}} + 1\right)}\tag{5}$$

where K<sup>1</sup> and K<sup>2</sup> refer to the calibration constants described in the previous section.

#### 3.1.3. Mono Window Algorithm

Qin et al. [39] developed the Mono Window Algorithm (MWA) for the Landsat TM data. Three essential variables, namely, LSE, effective mean atmospheric temperature, and atmospheric transmittance are required for LST retrieval using the MWA method. MWA-based LST can be retrieved by Equation (6):

$$\mathbf{T\_s} = \left\{ \mathbf{a} \cdot (\mathbf{1} - \mathbf{C} - \mathbf{D}) + \left[ \mathbf{b} \cdot (\mathbf{1} - \mathbf{C} - \mathbf{D}) + \mathbf{C} + \mathbf{D} \right] \cdot \mathbf{T} \mathbf{b} - \mathbf{D} \cdot \mathbf{T\_a} \right\} \div \mathbf{C} \tag{6}$$

where T<sup>a</sup> is the effective mean atmospheric temperature in Kelvin, a (−67.355351) and b (0.458606) are constants of the algorithm, C and D are the parameters of the algorithm calculated as C = ε × τ and D = (1 − τ)[1 + (1 − ε) × τ]. Table 2 provides empirical equations to estimate the T<sup>a</sup> through air temperature (To), since it is an essential parameter of MWA [39]. In this study, Ta values were computed for the mid-latitude summer region and To was obtained from the corresponding validation site.

**Table 2.** The linear equations for the calculation of the effective mean atmospheric temperature (Ta) from the near-surface air temperature (To) [39].


#### 3.1.4. Single-Channel Algorithm

Jiménez-Muñoz et al. [40] proposed a revised version of SCA for LST retrieval using Landsat TIR data. Concerning the SCA, Ts is obtained from Equation (7):

$$\mathbf{T\_s} = \sqrt{\frac{1}{\varepsilon}} (\psi\_1 \mathbf{L\_\lambda^{\text{sen}}} + \psi\_2) + \psi\_3 \Big| + \delta \tag{7}$$

where ψ<sup>1</sup> , ψ<sup>2</sup> , and ψ<sup>3</sup> refer to atmospheric functions defined as:

$$\boldsymbol{\Psi}\_{1} = \frac{1}{\pi} \; ; \; \boldsymbol{\Psi}\_{2} = -\mathbf{L}\_{\lambda}^{\downarrow} - \frac{\mathbf{L}\_{\lambda}^{\uparrow}}{\pi} \; ; \; \boldsymbol{\Psi}\_{3} = \mathbf{L}\_{\lambda}^{\downarrow} \tag{8}$$

Concerning the SCA method in this study, L ↑ λ , L ↓ λ , and τ obtained from NASA's ACPC were used for the computation of the ψ1, ψ2, and ψ3. On the other hand, the two parameters, γ and δ, are computed by:

$$\gamma \approx \frac{\text{Tb}^2}{\text{b}\_{\text{Y}}\text{L}\_{\text{sen}}} \tag{9}$$

$$\delta \approx \text{Tb} - \frac{\text{Tb}^2}{\text{b}\_{\text{\textdegree}}} \tag{10}$$

where bγ= c2/λ<sup>i</sup> and c<sup>2</sup> = 14,387.7 µm·K, and b<sup>γ</sup> is equal to 1320 K for Landsat 8 Band 10. λ<sup>i</sup> is the ith band's effective wavelength given by:

$$\lambda\_{\mathbf{i}} = \frac{\int\_{\lambda\_{1,\mathbf{i}}}^{\lambda\_{2,\mathbf{i}}} \lambda \mathbf{f}\_{\mathbf{i}}(\lambda) d\lambda}{\int\_{\lambda\_{1,\mathbf{i}}}^{\lambda\_{2,\mathbf{i}}} \mathbf{f}\_{\mathbf{i}}(\lambda) d\lambda} \tag{11}$$

where fi(λ) is ith band's spectral response function. λ1,i and λ2,i refer to the lower and upper boundary of f<sup>i</sup> (λ), respectively.

#### *3.2. NDVI-Based Land Surface Emissivity (LSE) Models*

Emissivity of a surface represents the ability of the surface to transform heat energy, relative to a black body, into radiant energy [88]. As presented in the above sections, LSE (ε) is a critical element for accurate TIR-based LST retrieval. Multi-channel Temperature/Emissivity Separation (TES), Physically Based Methods (PBMs), and Semi-Empirical Methods (SEMs) methods are three main types of space-based LSE estimation [31]. The NDVI-Based Emissivity Method (NBEM) [89,90] and Classification Based Emissivity Method (CBEM) [91,92] constitute the SEMs that are convenient for the Landsat-derived LSE. CBEM is not feasible because of the need of a priori information about the test site and in-situ emissivity of each class [93]. NDVI-based LSE models are practical and frequently used methods due to their easy application providing satisfactory results [88,94,95]. Li et al. [31] introduced a comprehensive research revealing limitations, advantages, and disadvantages of LSE models for satellite-derived LST. Moreover, Sekertekin and Bonafoni [34] provided an updated state-of-the-art table from Li et al. [31], presenting the used satellite missions with the corresponding LSE models. In this study, we examined the influence of six NDVI-based LSE models on the performance of three LST algorithms for both daytime and nighttime. To calculate NDVI from Landsat 8 data, firstly, DN values are converted to the TOA reflectance using the Equation (12) [87]. After applying reflectance (ρλ) conversion to the R and NIR bands, NDVI is obtained from Equation (13). Specifically:

$$\rho\_{\lambda} = \frac{\mathbf{M}\_{\text{p}} \cdot \mathbf{Q}\_{\text{CAL}} + \mathbf{A}\_{\text{p}}}{\sin \theta\_{\text{SE}}} \tag{12}$$

where QCAL is the calibrated and quantized standard product pixel values (DNs), A<sup>p</sup> is the additive rescaling factor of the corresponding band, Mp is the multiplicative rescaling factor of the corresponding band, and θSE represents the local sun elevation angle. The values of these parameters are obtained from the Metadata file of the relevant Landsat 8 data.

$$\text{NDVI} = \frac{\rho\_{\text{NIR}} - \rho\_{\text{R}}}{\rho\_{\text{NIR}} + \rho\_{\text{R}}} \tag{13}$$

where ρNIR refers to the reflectance image of the NIR band and ρ<sup>R</sup> is the reflectance image of the R band. In addition to NDVI, the Fractional Vegetation Cover (FVC or Pv), i.e., the proportion of vegetation, is another important factor for LSE estimation, and it is calculated from Equation (14) [96] as:

$$P\_{\rm v} = \left[\frac{\text{NDVI} - \text{NDVI}\_{\text{min}}}{\text{NDVI}\_{\text{max}} - \text{NDVI}\_{\text{min}}}\right]^2 \tag{14}$$

where NDVImin = 0.2 and NDVImax = 0.5 in a global context [93]. Table 3 presents the expressions of the six NDVI-based LSE models used in this work (hereafter referred to as LSE1, LSE2, . . . , LSE6). More details about these models can be found in the previous paper of the authors [34].


**Table 3.** The expressions of Normalized Difference Vegetation Index (NDVI)-based Land Surface Emissivity (LSE) models considered in this study.

dε = (1 − εs)εvF(1 − Pv): a term taking the cavity effect into account, which is based on the geometry of the surface. εs, ε<sup>v</sup> and F refer to soil emissivity, vegetation emissivity and geometrical shape factor (0.55), respectively. ρR: the reflectance image of R band; ρ<sup>j</sup> : the apparent reflectance in the OLI band j; a1i − a7i: the coefficients obtained from [98].

#### *3.3. In-Situ LST Estimation*

Station-based (in-situ or ground-based) LST measurements were obtained from four SURFRAD stations and five ARM SGP stations. As stated in Section 2.1, these stations do not measure LST directly; the upwelling and downwelling components of longwave radiation are considered for LST calculation regarding Stefan–Boltzmann law:

$$\text{LST} = \left[ \frac{\mathbf{F}\_{\lambda}^{\uparrow} - (\mathbf{1} - \varepsilon\_{\mathsf{b}}) \cdot \mathbf{F}\_{\lambda}^{\downarrow}}{\varepsilon\_{\mathsf{b}} \cdot \mathbf{\sigma}} \right]^{1/4} \tag{15}$$

where F ↓ λ and F ↑ λ in W/m<sup>2</sup> are the downwelling and upwelling thermal infrared irradiances, respectively, obtained simultaneously with satellite passages. σ is 5.670367 × 10−<sup>8</sup> W·m−<sup>2</sup> ·K−<sup>4</sup> that refers to the Stefan–Boltzmann constant. ε<sup>b</sup> is the broadband longwave surface emissivity that is not measured by the station instruments, thus [65,68] proposed the computation of the broadband emissivity by regression from narrowband emissivities of MODIS data, and many studies used these regression equations for acquiring the ε<sup>b</sup> [52,73,99]. The experimental results in [65,68] revealed that the longwave broadband emissivity can be used as a fixed value of 0.97, which was also considered in the studies of [74,100]. In this study, we assumed the broadband emissivity as 0.97, as well. This phenomenon only affects the accuracy of in-situ LST, not the satellite-based LST accuracy. Heidinger et al. [74] reported that a 0.01 error in broadband emissivity led to 0.25 K LST error in SURFRAD sites. Furthermore, Wang and Liang [65] showed that the LST accuracy of SURFRAD sites ranged from 0.1 K to 0.4 K due to the ±0.01 error in the broadband emissivity. This error is not negligible; however, it is not an overwhelming uncertainty source compared to the magnitude of the other uncertainties in LST retrieval [74]. Concerning this study, we also carried out the uncertainty analysis of broadband longwave surface emissivity and longwave radiation (the downwelling and upwelling components) on ground-based LST measurements in the next section.

#### *3.4. Sensitivity Analysis of In-Situ LST Measurements and LST Retrieval Methods*

Sensitivity analysis is an application of how the error of a model output (numerical, statistical, or otherwise) can be divided and allocated to different uncertainty sources in the model inputs [101]. It is difficult to determine the inputs of an algorithm, since these inputs unavoidably have initial errors affecting the accuracy of the LST retrieval methods [34,49]. To investigate the effect of input parameters' errors on LST retrievals from both satellites and stations, the following equation is utilized:

$$\delta \mathbf{T} = \mathbf{T\_s(x)} - \mathbf{T\_s(x + \delta x)}\tag{16}$$

where δT is the error on the LST; x represents one of the input parameters and δx is the potential error of this parameter; Ts(x + δx) and Ts(x) refer to the LST calculated for "x + δx" and "x", respectively. Some researchers reported the uncertainty of the input parameters on LST retrieval algorithms [49,102,103]. On the other hand, concerning the sensitivity analysis of in-situ LST measurements, [65,74] investigated the sensitivity of SURFRAD LST to broadband emissivity. In the previous paper of the authors [34], we already presented detailed sensitivity analysis for daytime LST retrieval considering MWA, SCA, and RTE. In this study, we mainly focused on the effect of LSE on LST retrieval methods for both daytime and nighttime LST retrievals, since we proposed using the daytime LSE images for nighttime LST retrieval. Furthermore, we also conducted a comprehensive sensitivity analysis for the in-situ LST measurements that is presented in Section 4.1.

#### *3.5. Temperature-Based (T-Based) Validation Method and Performance Metrics*

As stated in the introduction, the Radiance-based method (R-based), Temperature-based method (T-based), and cross-validation are the main techniques used to evaluate space-based LST [31,34]. The T-based technique, examined in this research, is a direct way of comparing the satellite-derived LST with in-situ LST simultaneous with satellite pass, and many researchers used this way to validate satellite-derived LSTs [48,52,62,104,105]. The major benefit of the T-based method is that it makes it possible to evaluate satellite sensor's radiometric quality and the efficiency of the LST algorithms based on emissivity and atmospheric parameters. On the other hand, the capability of the T-based technique depends mostly on the accuracy of the in-situ LST measurements and how well they represent the LST at the satellite pixel scale (land cover homogeneity of the study area) [31]. In this study, we considered both issues as we carried out the sensitivity analysis of the SURFRAD LST measurements and selected the validation sites whose footprint on Landsat 8 TIR pixel has homogeneous surface cover.

Satellite-derived LST and Station-based LST were analyzed considering the performance metrics such as Root Mean Square Error (RMSE), Standard Deviation (STD) of Error, and average Bias. The formulas of these metrics are given by:

$$\text{RMSE} = \sqrt{\frac{\sum \left[ \text{T}\_{\text{L8}} - \text{T}\_{\text{Station}} \right]^2}{\text{n}}} \tag{17}$$

$$\text{STD of Error} = \sqrt{\frac{\sum \left[ \text{T}\_{\text{Error}} - \overline{\text{T}\_{\text{Error}}} \right]^2}{\text{n}}} \tag{18}$$

$$\text{Bias} \, = \frac{\sum \left[ \mathbf{T}\_{\text{Station}} - \mathbf{T}\_{\text{L8}} \right]}{\mathbf{n}} \tag{19}$$

where TL8 and TStation are the Landsat 8-derived LST and Station-based LST, respectively, and n refers to the number of data. TError refers to the difference between Landsat 8-derived LST and Station-based LST, and TError is the mean value of these differences.

#### **4. Results**

To present the results of the LST retrieval methods for daytime and nighttime, 21 pairs of nighttime and daytime Landsat-8 data were utilized to obtain the daytime and nighttime LST images (see Appendix A). Specifically, concerning the daytime LST, 21 Landsat-8 images were used. On the other hand, 21 nighttime images, whose acquisition times are close to daytime data (the difference ranges from one day to four days), were utilized for the nighttime LST retrieval by using the corresponding 21 daytime reflective data for the NDVI-based LSE computation. We verified that rain and/or snow did not occur during these 1–4 days of difference. MWA, RTE, and SCA were performed for both daytime and nighttime LST estimation considering all datasets. The required input atmospheric parameters in the methods (τ, L ↑ λ , L ↓ λ ) were obtained from ACPC that considers the MODTRAN radiative transfer code, which uses NCEP-based atmospheric profiles as inputs. This section includes two sensitivity analyses: (i) Sensitivity of in-situ LST measurements and (ii) sensitivity of LST retrieval methods to LSE. Lastly, the accuracy assessment of the LST retrieval algorithms and LSE models for both daytime and nighttime at the nine SURFRAD and ARM stations is proposed.

#### *4.1. Sensitivity Results of In-Situ LST Measurements*

Concerning the in-situ LST measurements utilized in this work, the average upwelling and downwelling radiances, respectively, were calculated as 482.18 W/m<sup>2</sup> and 331.15 W/m<sup>2</sup> for daytime, and 388.16 W/m<sup>2</sup> and 326.68 W/m<sup>2</sup> for nighttime. In addition, as stated in the previous section, we used a fixed broadband emissivity value as 0.97. Thus, these values were considered in the sensitivity analysis of in-situ LST measurements. To carry out a sensitivity analysis of a method's output to an input parameter, the other input parameters are assumed to be fixed. For instance, to manage the sensitivity analysis of the downwelling radiance in the daytime (Figure 2a), the upwelling radiance and the broadband emissivity was fixed to 482.18 W/m<sup>2</sup> and 0.97, respectively. Then, the sensitivity of the downwelling radiance to in-situ LST accuracy was revealed by changing the downwelling radiance at 5 W/m<sup>2</sup> intervals (Figure 2a). The same procedure was applied to present the sensitivity results of the other parameters. As reported in Section 2.1, the two pyrgeometers have an accuracy of about 4.2 W/m<sup>2</sup> and a precision of around 1–2 W/m<sup>2</sup> . Considering the daytime sensitivity results, the following results were obtained: (i) ±5 W/m<sup>2</sup> error in downwelling and upwelling radiance led to ±0.024 K and ±0.8 K error in LST, respectively (Figure 2a,b) and (ii) 0.01 error in the broadband emissivity caused ±0.25 K error in LST (Figure 2c). On the other hand, nighttime sensitivity results showed that (i) ±5 W/m<sup>2</sup> error in downwelling and upwelling radiance led to ±0.029 K and ±0.95 K error in LST, respectively (Figure 2d,e) and (ii) 0.01 error in the broadband emissivity caused ±0.12 K error in LST. It is evident from Figure 2 that the uncertainty of the downwelling and upwelling radiance is almost identical in daytime and nighttime. However, the uncertainty of the broadband emissivity in the nighttime is half of the daytime.

**Figure 2.** Sensitivity results of in-situ Land Surface Temperature (LST) measurements to downwelling radiance, upwelling radiance, and broadband emissivity, respectively, for both daytime (**a**–**c**) and nighttime (**d**–**f**). LST error is computed as in Equation (16).

#### *4.2. Sensitivity Results of LST Retrieval Methods to LSE*

∙ − ∙ − ∙μ <sup>−</sup> ∙ − ∙ − ∙μ <sup>−</sup> In this sensitivity analysis, we mainly focused on the effect of LSE on LST retrieval methods for both daytime and nighttime LST retrievals, since we proposed using the daytime LSE images for nighttime LST calculation. A detailed uncertainty analysis of all parameters on LST retrieval methods (RTE, SCA, and MWA) for daytime can be found in the previous paper of the authors [34]. In the sensitivity analysis of daytime LST images, the following input parameters were utilized based on the current datasets: Air temperature, upwelling and downwelling radiances, atmospheric transmittance, and effective mean atmospheric temperature. Minimum, maximum, and mean near-surface air temperature values from ground stations and simultaneous with the satellite passages were 282.51 K, 302.41 K, and 295.95 K, respectively. Thus, the near-surface air temperature was assumed to be 295.95 K in the sensitivity analysis and, as a consequence, the effective mean atmospheric temperature was computed as 290.12 K. The atmospheric transmittance ranged from 0.63 to 0.94 with a mean value of 0.84, which was used in this analysis. Mean downwelling and upwelling radiances were observed as 2.06 W·m−<sup>2</sup> ·sr−<sup>1</sup> ·µm−<sup>1</sup> and 1.24 W·m−<sup>2</sup> ·sr−<sup>1</sup> ·µm−<sup>1</sup> , respectively, and these values were utilized in the sensitivity analyses. The brightness temperature range was assumed between 280 K and 310 K, because the brightness temperature computed from the daytime Landsat scenes ranged from 282.66 K to 314.84 K. The LSE value was fixed as 0.97.

Figure 3 illustrates the sensitivity results of the LST retrieval methods to LSE under a specific brightness temperature range of daytime. Figure 3a,c,e shows the variations in the error of the LST under different brightness temperatures for MWA, RTE, and SCA, respectively, when the LSE error is constant. These figures show that when the LSE error is constant for MWA and SCA, LST error increases with increasing brightness temperature. Instead, when the LSE error is constant for RTE, the LST error is stable with increasing brightness temperature. It is important to note that, since the LST error is computed as in Equation (16), an overestimation (underestimation) of the emissivity produces a positive (negative) value in the LST error. Figure 3b,d,f represents how LSE error impacts the LST error for the MWA, RTE, and SCA, respectively, under different brightness temperature conditions. The findings in these figures support the previous ones (Figure 3a,c,e) by showing that a constant LSE error produces LST error variations under different brightness temperature conditions for MWA and SCA, except for RTE. The intercomparison of the results proves that MWA is more sensitive to LSE error than RTE and SCA under increasing brightness temperatures, while RTE is the least sensitive one.

**Figure 3.** Sensitivity results of Mono Window Algorithm (MWA) (**a**,**b**), Radiative Transfer Equation (RTE) (**c**,**d**), and Single Channel Algorithm (SCA) (**e**,**f**) to LSE for daytime Landsat 8 images. LST error is computed as in Equation (16).

∙ − ∙ − ∙μ <sup>−</sup> ∙ − ∙ − ∙μ <sup>−</sup> In the sensitivity analysis of the nighttime LST images, minimum, maximum, and mean near-surface air temperature values from the ground stations were 271.65 K, 300.75 K, and 291.07 K, respectively. Considering the mean value (291.07 K), the effective mean atmospheric temperature was 285.60 K. The atmospheric transmittance varied between 0.51 to 0.96 with a mean value of 0.83, while mean upwelling and downwelling radiances were 1.37 W·m−<sup>2</sup> ·sr−<sup>1</sup> ·µm−<sup>1</sup> and 2.20 W·m−<sup>2</sup> ·sr−<sup>1</sup> ·µm−<sup>1</sup> . These mean values were utilized in the sensitivity analyses. A brightness temperature range from 270 K to 295 K was investigated since the brightness temperature computed from the nighttime Landsat scenes varied from 267.77 K to 297.22 K. LSE value equal to 0.97 was assumed.

Figure 4 depicts the sensitivity results of the LST retrieval methods to LSE under a specific brightness temperature range of nighttime. Figure 4a,c,e demonstrates the variations in the LST error under different brightness temperatures for MWA, RTE, and SCA, respectively, when the LSE error is constant. Moreover, Figure 4b,d,f represents how LSE error impacts the LST error for the MWA, RTE, and SCA, respectively, varying the brightness temperature values. The sensitivity analysis of nighttime data shows results with a trend similar to the daytime one; however, the variation in the LST error is smaller than daytime, also considering the lower brightness temperature values in the nighttime.

**Figure 4.** Sensitivity results of MWA (**a**,**b**), RTE (**c**,**d**), and SCA (**e**,**f**) to LSE for nighttime Landsat 8 images. LST error computed as in Equation (16).
