**1. Introduction**

Land surface temperature (LST) is a key parameter in the studies of land surface progress, such as the surface energy budget, surface moisture budget, and urban ecology, which is important to nature and human health [1–6]. Remote sensing is an effective way to retrieve LST at the regional and even global scales [7–9]. Many satellites carry thermal infrared (TIR) sensors, such as Terra/advanced spaceborne thermal emission and reflection radiometer (ASTER), NOAA/advanced very high resolution radiometer (AVHRR), Terra and Aqua/moderate resolution imaging spectroradiometer (MODIS), Landsat 5/thematic mapper (TM), Landsat 7/enhanced thematic mapper plus (ETM+), Landsat 8/thermal infrared sensor (TIRS), and Sentinel-3/sea and land surface temperature radiometer (SLSTR). Landsat 8/TIRS is an important part of the Landsat program for monitoring surface energy and temperature. However, it was discovered to have a considerable stray light problem, which resulted in an absolute radiometric calibration error to the TIRS images [10,11]. The inaccurate radiometric calibration of TIRS, especially the excessive error in Band 11, made it difficult to apply the conventional split-window algorithms on retrieving LST from the two TIR bands of TIRS. Therefore, the data

provider, United States Geological Survey (USGS), recommends the users to develop a single-channel algorithm for LST retrieval. However, several studies still proposed different split-window algorithms for this sensor [12–14]. In certain validation cases, the LST retrieval accuracy from the split-window algorithms was found to be better than that of the single-channel algorithm [15]. As a result, those reports have made the readers and users puzzled in choosing retrieval algorithms.

A new stray light correction algorithm proposed by Montanaro et al. [16] demonstrates great potential toward removing most stray light effects from TIRS images. The algorithm has also been refined and implemented operationally into the Landsat Product Generation System from early 2017 [17]. Gerace and Montanaro [17] selected 20 scenes (almost offshore water scenes) acquired from TIRS and MODIS onboard the Terra satellite to verify Landsat 8 brightness temperature before and after the stray light correction. They found that the absolute radiometric error of TIRS images was reduced to approximately 0.5% in Bands 10 and 11 on average [17]. This correction should benefit the LST retrieval from TIRS images. Although García-Santos et al. [18] have compared three methods for estimating LST from Landsat 8/TIRS images after the stray light correction with 21 observations, further validation in other regions is necessary for the assessment of LST retrieval accuracy after the correction. Moreover, the comparison of LST retrieval accuracy before and after the correction has not been validated using ground-measured data. Hence, the correction influence on the LST retrieval accuracy in practice remains unknown and thus requires further investigation.

With the above motivations, this study aims to clarify the following two questions: (1) Has the LST retrieval accuracy improved after the stray light correction? (2) Which algorithm (the split-window or the single-channel algorithm) is better for LST retrieval from TIRS images after the stray light correction? To answer the above questions, this paper tries to evaluate the accuracy of the LST retrieved from Landsat 8 TIRS images before and after the stray light correction by using different published two-channel split-window and single-channel algorithms. As a result, the remainder of this paper is organized as follows: Section 2 briefly presents the principles of different split-window algorithms and the single-channel algorithm; Section 3 introduces the involved Landsat 8 images and ground-measured LST and their processing; Section 4 focuses on the band radiance and LST evaluation results to answer the above-mentioned two questions; Sections 5 and 6 provide the discussion and conclusions, respectively.

#### **2. Landsat 8 LST Retrieval Algorithms**

Five representative LST retrieval algorithms were selected for evaluation, including three two-channel split-window algorithms and one single-channel algorithm with Bands 10 and 11, respectively. These algorithms have been applied to different TIR sensors and always have been used as the reference algorithms for a new algorithm or as the state-of-art algorithms for LST validation [15,18–20]. Therefore, it is proper and valid to adopt these algorithms for validation in this research. Among the above algorithms, the generalized split-window algorithm was originally developed as the standard algorithm to estimate LST from MODIS TIR images and then refined in 2014 by adding a quadratic term [21]. The new version was confirmed to perform better than its previous version. Du et al. [14] applied this algorithm to conduct the LST retrieval from Landsat 8 TIRS images, and Gerace and Montanaro [17] used their algorithm to check the LST variation before and after the stray light correction. On the basis of the work of Qin et al. [22], a linear split-window algorithm for TIR images was proposed by Rozenstein et al. [13] to retrieve LST from Landsat 8/TIRS and had good performance. The split-window algorithm proposed by Jiménez-Muñoz et al. [12] was inherited from the mathematical form proposed by Sobrino et al. [23] first and modified by Sobrino and Raissouni [24], which has been developed to retrieve LST for several TIR sensors, such as AVHRR and ATSR2 [25]. The single-channel algorithm developed by Jiménez-Muñoz et al. [12] was applied to Landsat 5/TM and Landsat 7/ETM+ with a single TIR band [26,27]. Moreover, USGS recommended users to retrieve LST from Landsat 8 images with single-channel algorithm because of the serious stray light problem in

Band 11. Therefore, this algorithm was also analyzed in this study. The details of the above algorithms are presented in the following part.
