*4.4. Accuracy of LST Retrieval Algorithms and LSE Models for Nighttime*

In Figure 6, the accuracy assessment of the LST retrieval methods for nighttime Landsat 8 data is reported for the six NDVI-based LSE models. Considering all LST methods and LSE models for the nighttime, the RMSE values ranged from 0.94 K to 3.34 K. In the nighttime LST analysis, the SCA method with LSE5 presented the best results, with RMSE, STD of Error, and Bias equal to 0.94 K, 0.72 K, and 0.60 K, respectively. On the other hand, MWA and RTE also provided very high accuracy with the RMSE equal to 1.01 K and 0.95 K, respectively, when using with LSE5. In general, the nighttime results revealed that for all LSE models, except for LSE2, all LST retrieval methods provided good accuracies with the highest RMSE as 1.51 K. As a summary, Table 4 shows the best LST retrieval methods and LSE models for the proposed daytime and nighttime LST validation test at the nine SURFRAD and ARM stations.

**Table 4.** Validation test of Landsat 8 LST retrieval at the nine ground stations: The best LST methods and LSE models and accuracy results for daytime and nighttime LST.


Compared to the daytime, during nighttime all LST retrieval methods provided highly accurate results with the different LSE models. Moreover, the overestimation of daytime LST retrieval is no longer evident at night, and the bias is clearly reduced. The proposed test with ground measurements as reference suggests that the use of daytime NDVI-based LSE, whose acquisition is close to nighttime data (the difference ranges from one day to four days in this work), is an accurate solution for the nighttime LST retrieval from thermal band observations. We assumed that the LSE does not significantly change in a short time period if rain and/or snow does not occur: This weather condition was verified for the selected images.

**Figure 6.** Nighttime LST from Landsat 8, period 2013–2019 (see Appendix A): Accuracy assessment of MWA, RTE, and SCA retrieval methods with different LSE models at the nine SURFRAD and ARM stations.

### **5. Discussion**

Numerous factors affect the accuracy of the LST retrieval from satellite TIR data. Atmospheric profiles, sensor parameters (spectral range and viewing angle), and surface parameters (emissivity and geometry) are amongst the major factors. On the other hand, development of an LST retrieval method has its own error sources due to including some parameterization steps for the retrieval of coefficients and estimation of some initial parameters. Therefore, it is of great importance to conduct sensitivity/uncertainty analyses for a new method by considering all input parameters. Concerning the LST validation procedure in space sciences, two main error sources emerge from both ground-based LST and satellite-based LST. Examining the sensitivity analysis for ground-based LST measurements, it emerges that the reliability of the upwelling radiance measurements is a key factor for the overall accuracy of the LST computation. Then, the effect of LSE on satellite-based LST retrieval methods for both daytime and nighttime were investigated, since we proposed using the daytime LSE images for nighttime LST retrieval. The results showed that the LST sensitivity to LSE error is typically dependent on the brightness temperature values suggesting that areas and study periods with lower Tb could guarantee lower LST errors. Atmospheric parameters needed in the LST retrieval methods were obtained from the NASA's ACPC that is based on MODTRAN radiative transfer code. It is not possible to find in-situ (radiosonde data etc.) atmospheric profiles for any place and any time. Thus, even though this usage (a simulation of profile information on atmosphere with ACPC) affects the accuracy of the methods, it is clear from our results and literature that NASA's ACPC provides satisfactory and effective simulations.

Comparing the results obtained in this research with the ones of other similar studies would be helpful for the readers. The daytime LST results of this study were compatible with the results presented in our previous paper [34]. Yu et al. [51] investigated the daytime LST results from RTE and SCA methods using Landsat 8 data with LSE5. They determined the RMSE values for RTE and SCA as 0.9 K and 1.39 K, respectively. However, we obtained 2.71 K RMSE and 2.85 K RMSE for RTE and SCA, respectively, with the same LSE model. Wang et al. [105] revealed that the generalized SCA and Practical Single-Channel Algorithm (PSCA) presented 2.24 K and 1.77 K, respectively. We obtained 2.73 K RMSE with the SCA and same LSE model (LSE3). Sekertekin [47] obtained 3.12 K RMSE using RTE and LSE4, while it was 2.62 K RMSE in this test. Guo et al. [54] used SCA with daytime Landsat 8 data and obtained 2.74 K and 2.47 K RMSE before and after the stray light correction, respectively. In our study, SCA results ranged from 2.73 K to 2.85 K RMSE under different NDVI threshold-based LSE models. We also observed negative biases for the selected dataset, whereas Guo et al. [54] did not observe biases in their case study. These validation studies of Landsat 8-derived LST refer to the daytime data, and they suggest how the accuracies can differ in similar test sites if the number of scenes and their acquisition time change.

Validation studies were not previously published for nighttime LST from Landsat 8. This test shows that, compared to the daytime, the nighttime accuracy is better, the daytime LST overestimation is no longer present, and the bias is distinctly reduced. It is an interesting and beneficial result for the researchers thinking of using the nighttime LST data from Landsat-8. Further studies can be conducted in different land cover types including also urban areas to confirm the effectiveness of the nighttime LST results. However, it may be difficult to find reliable ground-based LST measurements for accuracy assessments in these different areas.

Satellite-based LST retrieval methods are generally developed considering different conditions and assumptions. Thus, no universal method is yet available to provide accurate LSTs from all satellite TIR data, and it cannot be said that one method is systematically superior to the others. Concerning the stationarity of the methods used in this study, since RTE and SCA are obtained by the radiative transfer equation solution, they are valid for each sensor and atmospheric condition. On the other hand, the MWA is linked to atmospheric parameters and fixed coefficients regardless of the sensor type. However, these coefficients could be refined for different sensors (with different bandwidths), and the results validated.

### **6. Conclusions**

In this study, three LST retrieval algorithms, namely, RTE, SCA, and MWA, were evaluated using daytime and nighttime Landsat 8 OLI/TIRS data. To the best of our knowledge, this is the first study proposing the retrieval and validation of nighttime LST from TIR data of Landsat 8, also with a performance comparison with respect to daytime LST retrieval. Since LSE is one of the most important factors affecting the accuracy of LST retrieval methods, the effects of six NDVI-based LSE models on satellite-based LST accuracy were also investigated.

Concerning nighttime LST retrievals, we proposed the combined use of daytime LSE and nighttime TIR data when the difference in acquisitions of both datasets are close (a few days) and unchanged weather condition is observed. Concerning the evaluation of the LST retrieval methods and LSE models under daytime and nighttime conditions, SURFRAD and ARM SGP sites were used to calculate in-situ LST simultaneous with TIR data acquisitions.

In addition to the accuracy evaluation of the LST methods, we conducted detailed sensitivity/uncertainty analyses for in-situ measurements and sensitivity of LST methods on LSE for both daytime and nighttime. Considering the daytime sensitivity results of in-situ measurements, we proved that ±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, and 0.01 error in the broadband emissivity caused ±0.25 K error in LST. On the other hand, concerning the nighttime sensitivity results of in-situ measurements, we observed ±5 W/m<sup>2</sup> error in downwelling and upwelling radiance caused ±0.029 K and ±0.95 K error in LST, respectively, and 0.01 error in the broadband emissivity provided ±0.12 K error in LST. The sensitivity results of in-situ LST measurements revealed that the uncertainty of the downwelling and upwelling radiance was almost identical in daytime and nighttime. Nevertheless, the uncertainty of the broadband emissivity in the nighttime was half of that in the daytime.

Then, we investigated the sensitivity of the LST methods to LSE for both daytime and nighttime LST retrievals. The sensitivity results indicated that when the LSE error was constant for MWA and SCA, the LST error increased with increasing brightness temperature. However, when the LSE error was constant for RTE, LST error was stable with increasing brightness temperature. On the other hand, the nighttime sensitivity analysis showed identical trends to daytime ones; however, the variation in the LST error was smaller than daytime mainly due to the lower brightness temperatures.

The accuracy results of the daytime Landsat 8 data at the nine ground stations showed that the MWA method with LSE4 and LSE6 presented the best results for the daytime. In general, for all the LSE models, except for the LSE2, the MWA indicated slightly better results than the RTE, and the RTE demonstrated slightly better results than the SCA for daytime LST retrievals. Considering the nighttime, the SCA method with LSE5 presented the best results. However, MWA and RTE provided very similar results with SCA. Compared to the daytime, all LST retrieval methods provided highly accurate results with the different LSE models in the nighttime. The systematic overestimation of daytime LST retrieval is no longer present at night, with an evident reduced bias. The validation test shows that the use of daytime NDVI-based LSE with reflective data close to nighttime thermal data is a reliable solution for the nighttime LST retrieval.

**Author Contributions:** Conceptualization, A.S.; methodology, A.S.; software, A.S.; validation, A.S.; writing—review and editing, A.S. and S.B.; supervision, A.S. and S.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors thank USGS for providing Landsat 8 satellite imagery free of charge. In addition, the authors thank NOAA for providing in-situ LST measurements publicly.

**Conflicts of Interest:** The authors declare no conflict of interest.
