Advancing of Land Surface Temperature Retrieval Using Extreme Learning Machine and Spatio-Temporal Adaptive Data Fusion Algorithm

As a critical variable to characterize the biophysical processes in ecological environment, and as a key indicator in the surface energy balance, evapotranspiration and urban heat islands, Land Surface Temperature (LST) retrieved from Thermal Infra-Red (TIR) images at both high temporal and spatial resolution is in urgent need. However, due to the limitations of the existing satellite sensors, there is no earth observation which can obtain TIR at detailed spatialand temporal-resolution simultaneously. Thus, several attempts of image fusion by blending the TIR data from high temporal resolution sensor with data from high spatial resolution sensor have been studied. This paper presents a novel data fusion method by integrating image fusion and spatio-temporal fusion techniques, for deriving LST datasets at 30 m spatial resolution from daily MODIS image and Landsat ETM+ images. The Landsat ETM+ TIR data were firstly enhanced based on extreme learning machine (ELM) algorithm using neural network regression model, from 60 m to 30 m resolution. Then, the MODIS LST and enhanced Landsat ETM+ TIR data were fused by Spatio-temporal Adaptive Data Fusion Algorithm for Temperature mapping (SADFAT) in order to derive high resolution synthetic data. The synthetic images were evaluated for both OPEN ACCESS Remote Sens. 2015, 7 4425 testing and simulated satellite images. The average difference (AD) and absolute average difference (AAD) are smaller than 1.7 K, where the correlation coefficient (CC) and root-mean-square error (RMSE) are 0.755 and 1.824, respectively, showing that the proposed method enhances the spatial resolution of the predicted LST images and preserves the spectral information at the same time.


Introduction
In order to monitor the rapid and continual changes of the global environment, Land Surface Temperature (LST), as the prime and basic physical parameter of the earth's surface, has been studied for over a decade.LST plays a key role in modeling the surface energy balance [1,2] and has a significant impact on analyzing the heat-related issues such as soil moisture [3,4], evapotranspiration [5][6][7], and urban heat islands [8,9].Compared with traditional methods using data from weather stations, remote sensing satellite images provide a more effective and efficient method to estimate LST and offer a synoptic view of the study area.However, due to the limitations on both spatial and temporal resolution of the existing satellite sensors, there is no earth observation which can obtain Thermal Infra-Red images (TIR) at detailed spatial-and temporal-resolution simultaneously.
Currently, the applications of thermal infrared remote sensing in urban environment studies require heat-related information at high spatial resolution, as well as high temporal resolution [7].However, in order to collect more reflected and emitted signal from the earth, large spatial coverage, e.g., lower spatial resolution from the earth observation is required.For instance, several sensors such as Landsat Thematic Mapper (TM)/Enhanced TM Plus (ETM+)/Operational Land Imager (OLI) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), obtain TIR data between 60 m and 120 m [10][11][12][13] and they are always used for regional and global LST studies [14,15].In addition, the platforms with a minimum 16-day revisit cycle may prohibit its application.The revisit cycle for a particular area may be extended due to the poor atmospheric conditions, such as cloud and haze [16].Particularly in cloud-prone environments, e.g., Hong Kong and the Pearl River Delta region, the poor atmospheric conditions result in a very low probability of obtain cloud-free Landsat imagery (e.g., 10% in a year with cloud cover below 10%) [17].
On the contrary, other sensors, such as Advanced Very High Resolution Radiometer (AVHRR), and MODerate resolution Imaging Spectroradiometer (MODIS), provide a daily revisit cycle, but at a coarser spatial resolution ranging from 250-1000 m, which may not be able to detect the high level of detailed information and seriously impede their potential applications [18,19].As a consequence, it is necessary to develop a new image fusion method that can integrate complementary characteristics from multi-sensors, in order to generate synthetic LST data with high spatial and temporal resolution.
There are some previous studies of remote sensing data fusion methods using multiple optical sensors [20][21][22].Considering different characteristics between the TIR band and the visible bands, traditional image fusion models, such as the widely used Principle Component Analysis (PCA) based fusion methods [23,24], Intensity-Hue-Saturation (HIS) transformation method [25,26] and wavelet-based image fusion methods [27,28], are more concentrating on the visual effects of the fused images, which may not be useful for quantitative remote sensing applications.Hence, some downscaling approaches have been developed for TIR images.A generalized theoretical framework with semi-empirical regression and modulation integration techniques was constructed by Zhan et al. [29] and they evaluated all three fusion data including digital number, radiance and land surface temperature.Rodriguez-Galiano et al. [30] applied the Downscaling CoKriging (DCK) method to obtain high spatial resolution LST images using the same scene data at a coarser resolution and the Normalized Difference Vegetation Index (NDVI).The downscaled TIR band was also used to improve the land cover classification accuracy and derive evapotranspiration images of surface energy balance model in a large heterogeneous landscape [31][32][33].
However, this study is not only aiming on downscaling the TIR images to retrieve higher details of spatial information, but also on fusing high spatial and high temporal data from multi-sensors, e.g., blending high spatial resolution Landsat data and high temporal MODIS data, in order to generate synthetic LST maps.A spatial and temporal data fusion model named the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) [34] was firstly developed to predict daily surface reflectance at a Landsat 30 m spatial resolution using one or more pairs of Landsat and MODIS images on the same day, and one MODIS image on the predicted day, based on the weighted average approach.The STARFM algorithm has been widely used to provide information for monitoring the seasonal changes in vegetation cover and large changes in land use [34].The performance of STARFM is highly dependent on the characteristic of the landscape patch size.In order to overcome the shortcomings of STARFM, Zhu et al. [35] proposed an Enhance STARFM model to improve the accuracy of the predicted image.Compared to STARFM, ESTARFM results preserve more spatial details on finer resolution images, especially for heterogeneous land covers.Hilker et al. [36] also designed a new fusion approach named Spatial and Temporal Adaptive Algorithm for mapping Reflectance Change (STAARCH) for distinguishing and recording the changes of reflectances in both MODIS and Landsat data.Among the above approaches, only STAARH considers the change in land cover types, but it can only be used for predicting the changes in forest [36].A semi-physical fusion approach employs the MODIS BRDF/Albedo land surface characterization product and Landsat ETM+ data to predict ETM+ reflectance, and the method can also be used for ETM+ cloud/cloud shadow, SLC-off gap filling, and relative radiometric normalization [37].Through an unmixing-based spatial and temporal fusion model, Zurita Milla et al. [38] integrated Landsat TM and MERIS data, however, the results were highly dependent on the quality of the land cover map generated from Landsat images.In addition, a robust SParse representation-based SpatioTemporal reflectance Fusion Model (SPSTFM) has been developed to predict high spatial resolution surface reflectance through data blending with low spatial resolution data.Results show that the SPSTFM is able to capture the changes of surface reflectances in both the changes of phenology and land-cover types [39,40].These methods were designed for data fusion of surface reflectance rather than for TIR data.Huang et al. [41] developed a spatiotemporal image fusion model based on bilateral filtering to derive high resolution LST images.This model works in a densely time-series LST data for urban heat island monitoring.Weng et al. [42] proposed a new data fusion model named Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT) to predict synthetic thermal radiance and LST images at both high temporal and spatial resolution by blending daily MODIS and periodic Landsat datasets.The prediction accuracy of SADFAT, as measured by the mean absolute difference, ranged from 1.25 K to 2 K. SADFAT was developed for predicting Landsat-like thermal radiance and LST data based on the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) which also considers annual temperature cycle (ATC) and urban thermal landscape heterogeneity [42].
In this paper, in order to generate synthetic high spatial resolution LST images from available satellite-borne sensors, a thermal sharpening method based on extreme learning machine (ELM) algorithm for neural network regression model was firstly adopted, in order to enhance the 60 m Landsat ETM+ TIR band to 30 m resolution.Then, the MODIS LST and enhanced Landsat ETM+ TIR data were blended through Spatio-temporal Adaptive Data Fusion Algorithm for Temperature mapping (SADFAT) (followed by the algorithm developed by Weng et al. [42]) to generate synthetic LST data at 30 m resolution.

Extreme Learning Machine (ELM) Algorithm
For pattern recognition and image classification, traditional image fusion methods focus on the enhancement of visual effects, including color and texture enhancement; however, for quantitative remote sensing applications and thermal infrared image analysis, the preservation of spectral brightness values is a higher priority.In this paper, an extreme learning machine (ELM) algorithm [43,44] was selected to obtain the internal physical regression relationship between the 60 m Landsat ETM+ TIR image and corresponding 30 m multispectral bands (including visible, near and shortwave infrared bands).
Extreme Learning Machine (ELM) proposed by Huang et al. [45] is designed for single-hidden layer feed-forward neural networks (SLFNs) that can adjust the input weights and determine the output weights analytically.Due to the random determination of the input weights and hidden biases, ELM requires numerous of hidden neurons.In practice, the number of hidden neurons should be larger than the number of the variables in dataset, since the useless neurons from the hidden layer will be pruned automatically.
Figure 1 shows the structure of single hidden layer feed forward neural network based on ELM using the activation function,     Structure of the single hidden layer feed forward neural network using Extreme Learning Machine (ELM).
The output weight β for a training set ,

Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT)
The Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT), developed by Weng et al. [42], was used to predict synthetic Landsat-like thermal radiance and LST images in this paper.In the algorithm, the MODIS radiance images were first resampled to the same spatial resolution (e.g., 30 m) of Landsat ETM+ images, and M is denoted as the MODIS pixel while L is denoted as the Landsat pixel.In urban areas, most of the pixels from MODIS images covered more than one land cover type, and these were named mixed pixels.Therefore, the linear spectral mixture analysis (LSMA) algorithm was employed to define the radiance of a mixed pixel.In order to correlate the Landsat radiance with the MODIS radiance, it is assumed that each L pixel is deemed as pure pixel and can be considered as an end-member of a M pixel; as a result, the radiance of the M pixel can be defined as: where R denotes the radiance at the satellite sensor, N is the pixel number of Landsat within a MODIS pixel and li denotes the fraction of each Landsat pixel, (x, y) represents a given location, t is the acquisition date, and k1, k2 are the coefficients for the relative adjustment for the Landsat and MODIS radiance pixels [42].Therefore, if there are two pairs of Landsat ETM+ and MODIS image acquired at t1 and t2, respectively, Equation (2) indicates that the ratio of the radiance change of jth L pixel to the radiance of corresponding M pixel is constant for a certain L pixel can be quantified as below: where hj is denoted as the conversion coefficient for the purpose of consistency, ω reflects the phase shift of a pixel and is related with the thermal characteristics of land cover, and it is a constant if the land surface materials does not change in the period of observation [42].Thus, if there is a pair of L and M radiance images at t0 and an M radiance image at tp, the L radiance image at tp can be predicted by the following equation: By adding information from neighbouring spectral similar pixels, a moving window would be used to calculate the radiance of the central pixel [34].Therefore, supposing s is the moving window size, the predicted L pixel radiance can be rewritten as: where Wi represents the weight of a neighboring similar pixel, and N is the number of the spectral similar pixel.In this paper, after predicting the radiance image using SADFAT method, enhanced Landsat ETM+ TIR data with both high spatial and temporal resolution would be converted to LST using the generalized single channel method [46].More details of SADFAT can be referred to Weng et al. [42].

Implementation of the Proposed Data Fusion Model
Figure 2 presents a flowchart of the proposed fusion model.The implementation consists of two steps to produce synthetic spatial resolution LST maps using Landsat ETM+ and MODIS LST images.In the first step, a thermal sharpening method using ELM algorithm was selected to improve the Landsat ETM+ TIR 60 m resolution image to 30 m resolution.The multispectral and TIR digital number (DN) values were first converted to the radiance values using metadata, and these could ensure the two satellite images have a strong intrinsic correlation of the same land surface types.Then, the hidden layer output matrix, i.e., internal physical regression relationship between the 60 m spatial resolution of Landsat ETM+ TIR band and corresponding six 30 m resolution multispectral bands, was ascertained through the ELM algorithm where the hidden neurons were set to 1000.Finally, the enhanced 30 m resolution Landsat TIR data were computed using the weight vector obtained by neural network regression model.
In the second step, the MODIS LST and enhanced Landsat ETM+ TIR data were blended using SADFAT algorithm [42] to generate a final synthetic LST data at 30 m resolution.The algorithm requires at least two pairs of Landsat and MODIS images acquired at the same date and a set of MODIS images on the desired prediction dates.Before implementing the SADFAT algorithm [42], MODIS LST images should be converted to radiances at the Landsat ETM+ effective thermal wavelength and all the images including enhanced Landsat ETM+ TIR and the converted MODIS radiance images should be geo-registered to the same coordinate system and atmospherically calibrated to the surface radiance.The inputs of this step are two pairs of L and M images at t1 and t2 and one M image at the prediction date tp.
The details of data processing are described as below: (i) Two L images were used to search for the spectrally similar pixels using the method described by Gao et al. [34] that define a difference threshold between the central pixel and the neighbouring pixels in a moving window.(ii) The combined weight and conversion coefficient for each similar pixel were computed.Here, a similar pixel with higher thermal similarity and shorter distance to the central pixel would yield a higher weight and the conversion coefficients were decided by the regression analysis of the similar pixels [35].(iii) Equation ( 5) was employed to compute the desired predicted image at tp. Considering the temporal weights of the two images given by the temporal changes in coarser radiance images, an accurate radiance image can be computed by using the weighted combination of the two predicted radiance images as follows: P are the predicted radiance image using L image at t1 and t2 as the base image, respectively, in which the temporal weight Tk can be calculated as: 1 ( ( , , , ) ( , , , )) 1 ( ( , , , ) ( , , , )) where M(x, y ,t , B) is the resampled radiance at time t of band B.
(iv) Finally, the LST images can be derived using the generalized single channel method.

Study Area
A study area of 12 km × 12 km, part of Guangzhou, China, was selected (see Figure 3).The study area consists of various landscapes, including water, impervious surface, bare soil, vegetation, etc., and possesses a subtropical climate with moist summers and dry winters.
Three Landsat ETM+ images covering the study area (path/row: 122/44) were obtained from the United States Geological Survey (USGS) website.These datasets were acquired on 20 October, 7 December and 23 December 2013, and they are the L1G level product and are geographically corrected.
The corresponding daily MODIS LST (MOD11A1), reflectance data (MOD09GA) and water vapour content data (MOD05_L2) were downloaded through the Atmosphere Archive and Distribution System website.The MODIS LST (MOD11A1) products were derived from the generalized splitwindow LST algorithm and the uncertainty of the MODIS-LST production algorithm is around 1 °C in the range of −10 °C to 50 °C, for the surfaces with known emissivities [47].

Experiment Results
In this study, the developed fusion methodology was applied to three pairs of Landsat ETM+ and MODIS images both in testing and simulated experiments (Figure 4).Two pairs of the MODIS and Landsat images, acquired on 20 October and 23 December 2013, respectively, were used as base images input to the fusion model, while the remaining images acquired on 7 December 2013, was used to validate the accuracy of prediction.For the testing experiment, the original multispectral images and TIR image of Landsat ETM+ were downscaled to 120 m using the pixel averaging method, then the ELM algorithm was employed to enhance the spatial resolution of the degraded TIR image from 120 m to 60 m, and the original TIR image at 60 m was used as the referenced data for validation.The correlation coefficient (CC), root-mean-square error (RMSE), average difference (AD) and absolute average difference (AAD) were selected as indicators to evaluate the accuracy of thermal spatial sharpening of Landsat TIR images using ELM algorithm and to validate the synthetic LST.For the simulated experiments, since there is no reference to TIR images at 30 m resolution, the reliability of ELM and SADFAT was validated only through visual effects.Figures 5 and 6 showed the thermal spatial sharpening results (lower row) of all the testing and simulated Landsat radiance images (middle row) using the extreme learning machine (ELM) algorithm for the neural network regression model.Comparing the spatial sharpened images in both testing and simulated experiments, it can be observed that the sharpened images have more spatial details, such as roads, textural information of forest, urban streets and edges of rivers.Additionally, CC, RMSE, AD, AAD were computed between the sharpened and original radiance images at both 60 m resolution (Table 1).The RMSEs between the sharpened and original radiance images are 0.0844, 0.0891, and 0.0909, and the CC values are 0.8788, 0.8251, and 0.8017 on different dates, respectively.AD values on 20 October and 7 December 2013 are negative values showing that the predictions overestimate the TIR data slightly.Although some details may be lost during the ELM spatial enhancement, the low RMSEs and the strong CCs indicate that the ELM can preserve much of the physical TIR information in the original input TIR images for quantitative remote sensing applications.In the second step of the proposed fusion model, considering the characteristics of complex surface in this study area, the size of the searching window was set to three MODIS pixels and there are five land cover types in the SADFAT.To ensure the accuracy of searching similar pixels and obtain the NDVI values at the prediction date for LST retrieval, the reflectance values of both Band 3 and Band 4 combined with the thermal radiance information from Band 6 of Landsat ETM+ and its corresponding bands of MODIS at t1 and t2 were input into the SADFAT fusion model developed by Weng et al. [42].Figures 7 and 8 showed the results of predicted images at 60 m and 30 m on 7 December 2013, respectively.For both the testing and simulated experiments, the predicted LST images (Figure 7b and Figure 8b) are visually similar to the original Landsat LST images (Figure 7c and Figure 8c), but they provide higher spatial details in terms of thermal information.Figure 9 displays the scatter plots between the predicted and observed LSTs for testing experiment on 7 December 2013.It shows a strong agreement between predicted and observed LSTs in testing experiment.Nevertheless, there are slight differences in some pixels between the predicted and observed LSTs, owing to the limitation of SADFAT that may not be suitable for the changes in land cover and other surface conditions during the prediction period [42].Table 2 shows the results of CC, RMSE, AD and AAD between the predicted and observed LSTs for the testing experiment at 60 m.The values of AD and AAD are smaller than 2.0 K whereas the CC values are larger than 0.75 suggesting significant consistency.

Discussion
The proposed fusion model employs ELM to enhance the spatial resolution of TIR data before using the spatial-temporal fusion algorithm.As shown in Figures 5 and 6, the sharpened images of both testing and simulated experiments have more spatial details compared with original Landsat TIR images.As shown in Figure 7b and Figure 8b, it can be observed that the predicted LST images provide higher spatial details in terms of thermal information than the original Landsat LST images (Figure 7c and Figure 8c) in both the testing and simulated experiments.In Figure 9, the scatter plot of the testing experiment shows a strong relationship between predicted and original LSTs at 60 m.In addition, small values of AD and AAD (Table 2) (less than 1.7 K) and high values of CC (larger than 0.75) are observed.These results show that our proposed method can enhance the spatial resolution of the predicted LST image and also preserve the spectral information simultaneously.
However, there are still some limitations/errors in the proposed method, including: (i) the thermal spatial sharpening ELM algorithm is highly time-consuming; (ii) some important information in the original TIR images may be lost during the ELM spatial enhancement; (iii) the proposed fusion method cannot predict the changes in LST that are not presented on the MODIS and/or Landsat images, especially in the missing pixels caused by cloud contamination [42]; (iv) the proposed fusion method requires at least two input pairs of fine and coarse resolution images, in the same season or under similar atmospheric conditions; (v) the number of land cover types and the size of a moving window should be determined by searching similar pixels in SADFAT, which may limit the automated process.Thus, more research on the following issues will be conducted in the near future: (i) by improving the fusion accuracy and efficiency of ELM simultaneously, and (ii) developing a more advanced fusion method for generating synthetic LST images to resolve the limitations of seasonal changes and different atmospheric conditions.

Conclusion
In this paper, a novel data fusion method by integrating a thermal spatial sharpening algorithm with spatial-temporal fusion to generate synthetic LST datasets at both high spatial and temporal revolution was developed.The performance of this method was tested using Landsat ETM+ and MODIS images both in testing and simulated experiments.At first, the extreme learning machine algorithm was selected to enhance the spatial resolution of the Landsat ETM+ TIR data.Then, the MODIS LST and enhanced Landsat ETM+ TIR data were fused using SADFAT developed by Weng et al. [42] to derive high temporal resolution synthetic data.The proposed image fusion method provides an alternative to generate the synthetic high resolution image for remote sensing applications from multi-source satellite data.Compared with the traditional spatio-temporal adaptive data fusion algorithm, the synthetic LST images derived in this study can depict more spatial details.The generated synthetic LST product can be used for monitoring the variation of land surface temperature in urban heat island studies.Further research on other sensors such as Landsat TIRS, HJ-1B satellite will be conducted.
, the standard SLFNs equipped with N  hidden neurons and activation function can be mathematically expressed as: where , And H represents the hidden layer output matrix of the neural network; i b is the threshold of the ith hidden neuron; , , , w w w  w  denotes the weight vector connecting the ith hidden neuron and the input neurons; stands for the weight vector connecting the ith hidden neuron and the output neurons.

Appendix B. Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT)
The Spatio-Temporal Adaptive Data Fusion Algorithm for Temperature Mapping (SADFAT), developed by Weng et al. [42], was used in this study to predict synthetic thermal radiance and LST images in the second step.Below is a brief description of the algorithm: If there are two pairs of Landsat ETM+ and MODIS image acquired at t1 and t2, respectively, the changes of radiance of a M pixel between t1 and t2 can be computed as: where R denotes the radiance at the satellite sensor, N is the pixel number of Landsat within a MODIS pixel and i l denotes the fraction of each Landsat pixel, t is the acquisition date, and 1 k is the coefficient for the relative adjustment for the Landsat and MODIS radiance pixels.Considering the seasonal change of LST based on ATC, and through the Planck's law, the radiance change of an L pixel from 1 t to 2 t can be expressed as: where a is the angular frequency, ω is the phase shift, or heat lag, d is the amplitude of the radiance variation, D is the constant, and e is the mean acquisition date, By combining Equation (9) with Equation (10), the Equation (11) indicates that the ratio of the radiance change of jth L pixel to the radiance of the corresponding M pixel is constant for a certain L pixel, which can be quantified as below:     where i W represents the weight of a neighbouring similar pixel, and N is the number of the spectral similar pixel.In this paper, after predicting the radiance image using SADFAT method (Weng et al. [42]), enhanced Landsat ETM+ TIR data with both high spatial and temporal resolution would be converted to LST using the generalized single channel method [46].The following equations are the implementation procedures of the generalized single channel method for ETM+ TIR data.
  where  is the water vapour content, which can be obtained from the water vapour content product (MOD05_L2).
activation function   g x and hidden neuron N  can be calculated according to the following steps: (i) Allocate the input weight i w and bias , 1,2, , Compute the hidden layer output matrix H . (iii) Use the equation 1   β H Tto calculate the output weight matrix β .

Figure 2 .
Figure 2. Flowchart of the proposed fusion model for predicting synthetic LST image at 30 m resolution.

Figure 3 .
Figure 3. Location of the study area.

Figure 4 .
Figure 4.The flowchart of the testing and simulated experiment.

Figure 5 .
Figure 5. Thermal spatial sharpening results of testing experiments via ELM algorithm.False colour images of downscaled Landsat ETM+ multispectral data at 60 m (upper row), downscaled TIR images at 120 m (middle row) and sharpened TIR images at 60 m (lower row).The original TIR images at 60 m refer to the middle row in Figure 6.From left to right, they were acquired on 20 October, 7 December and 23 December 2013.

Figure 6 .
Figure 6.Thermal spatial sharpening results of simulated experiments using ELM algorithm.False colour images of observed Landsat ETM+ multispectral data at 30 m (upper row), TIR images at 60 m (middle row) and Enhanced TIR images at 30 m (lower row).From left to right, they were acquired on 20 October, 7 December and 23 December 2013.

Figure 7 .
Figure 7. SADFAT result in the testing experiment.(a) MODIS LST images resampled from 1 km to 60 m; (b) SADFAT-derived image at 60 m; (c) original Landsat ETM+ LST image at 60 m spatial on 7 December 2013.

Figure 9 .
Figure 9. Scatter plots between the predicted and original LSTs at 60 m of the testing experiment on 7 December 2013.x-axis denotes the original LSTs, and y-axis denotes the prediction LSTs.

1 c , 2 c
temperature of the surface, sensor R and sensor T stands for the radiance and brightness temperature at-satellite, respectively,  (11.3355 μm) is the effective wavelength for ETM+ sensor, are the constants, ε is the land surface emissivity.The atmospheric functions are described with the water vapour content: represents a location of the central pixel in a moving window, t is the acquisition date,

Table 1 .
Quantitative assessment of thermal sharpening in the testing experiment via ELM.
Note: AD is the average of the original LST value minus the predicted LST value; * significant at 0.001 level (p ＜ 0.001).
1 e and 2 e are the parameters input to the algorithm.Therefore, if the radiances of the jth L pixel at date 1 is named the conversion coefficient for the purpose of consistency,  reflects the phase shift of a pixel and is related with the thermal characteristics of land cover.Supposing s is the moving window size, if there is a pair of L and M radiance images at 0 t and a M radiance image at p t , the predicted L radiance image at p t can be predicted by the following equation: