Comparison of Methods for Reconstructing MODIS Land Surface Temperature under Cloudy Conditions

Abstract

Land surface temperature (LST) is a vital parameter associated with the land–atmosphere interface. The Moderate Resolution Imaging Spectroradiometer (MODIS) LST product can provide precise LST with high time resolution, and is widely applied in various remote sensing temperature research. However, due to its inability to penetrate the cloud and fog, its quality is not able to meet the requirements of actual research. Hence, obtaining continuous and cloudless MODIS LST datasets remains challenging for researchers. The critical point is to reconstruct missing pixels. To compare the performance of different methods, first, three kinds of methods were used to reconstruct the missing pixels, namely, temporal, spatial, and spatiotemporal methods. The predicted values using these methods were validated by the automatic weather system data (AWS) in the Heihe river basin of China. The results demonstrated that, compared with other methods, linear temporal interpolation using Aqua data had the best performance in MODIS LST reconstruction in the Heihe river basin, with an RMSE of 7.13 K and an R² of 0.82, and the NSE and PBias were 0.78 and −0.76%, respectively. Furthermore, the interpolation method was improved using adaptive windows and robust regression. First, the international Geosphere–Biosphere Program (IGBP) classification was employed to distinguish the different land surface types. Then, the invalid LST values were reconstructed using adjacent days’ effective LST values combined with a robust regression. Finally, a mean filter was applied to eliminate outliers. The overall results combined with ERA5 data were validated by AWS, with an RMSE of 6.96 K and an R² of 0.79 and the NSE and PBias were 0.77 and −0.20%, respectively. The validation demonstrated that the scheme proposed in this paper is able to accurately reconstruct the missing values and improve the accuracy of the interpolation method to a certain extent when reconstructing MODIS LST.

1. Introduction

Land surface temperature (LST) is one of the most important parameters associated with the land–atmosphere interface, and has important research significance in many fields, including climate, ecology, hydrology, and habitat chemistry [1,2,3]. It reflects the physical process of the interaction between the land surface and the atmosphere on regional and global scales, and is an indispensable and important parameter for the study of climate change, the urban heat island effect, and so on [4,5,6].

In recent years, with the rapid development of remote sensing technology, the acquisition of LST no longer depends on the radiometers at weather stations, but on satellite datasets from around the world. Remote sensing is playing an increasingly important role in thermal infrared research associated with LST [7]. Currently, the available LST satellite datasets include the Moderate-Resolution Imaging Spectrometer (MODIS), the Advanced Very-High-Resolution Radiometer (AVHRR), and the Advanced Along-Track Scanning Radiometer (AATSR) [8]. Among these, the MODIS sensors carried on the Terra and Aqua satellites are one of the most widely used sources of satellite-derived LST, because of their superior spatial and temporal resolution. MODIS provides multiple daily LST products from thermal infrared bands using a split window algorithm [9,10]. However, the algorithm is only effective when the data have been acquired under clear-sky conditions. In the case of cloudy weather or other atmospheric interference with radiation transmission, the retrieval of LST is greatly affected. As a result, MODIS LST suffers from contamination by cloud-top temperature, which leads to the greater or lesser appearance of null-value pixels in the LST products [11,12]. Only under clear-sky conditions do pixels in LST products have valid values. For regions with undesirable weather conditions that lead to extensive cloud cover, little valid information can be found in daily LST products [10]. Cloudy-sky conditions have a greatly negative influence on these regions, because their presence means the surface energy is not truly reflected, which greatly limits the subsequent applications in related fields [13]. Therefore, the MODIS LST products need to be improved in order to overcome these limitations before being used in research. In other words, research into MODIS LST reconstruction is of great significance [11].

At present, mainly interpolation methods are used in the reconstruction of MODIS LST, and many novel interpolation methods have been proposed for daily MODIS LST reconstruction [14,15,16] that only use limited spatiotemporal information. Methods for the reconstruction of MODIS LST can be divided into three kinds of methods: spatial, temporal, and spatiotemporal [12]. For temporal methods, invalid values are estimated on a pixel-by-pixel basis, and the values of geographically adjacent pixels are not considered. Spatial methods only consider the values of adjacent pixels and do not include values from different periods [17]. Spatiotemporal methods consider neighboring pixels in both the temporal and spatial domains. Among the spatial methods, a method based on the assumption that LST is related to elevation was proposed by Linghong et al., 2012 [18]. For each invalid pixel, an adaptive window was used to recover it based on the linear relationship between other valid pixel values with elevation. On this basis, ordinary least squares (OLS) regression is performed, in which LST is modeled as a linear function of elevation. Then the missing value can be interpolated on the basis of evaluation of the exported function at the elevation of the pixel center. Among the temporal methods, Arroyo, 2016 [19] and Zhang et al., 2015 [20] adopted the Linear Temporal method. For each invalid value on the image, the rate of change in the LST between the closest preceding and succeeding 8-day periods with data is determined, and a linear equation is constructed. The linear equation can be used to fill in the missing value based on the temporal distance between the period in question and the LST of the most recent period with data. Based on this idea, a more sophisticated temporal approach (Harmonic Analysis of Time Series) was used. Yan et al. [21] and Maffei et al. [22] used the Savitzky-Golay (S-G) method and the Harmonic Analysis of Time Series (HANTS) to interpolate daily invalid data, respectively. Among the spatiotemporal methods, Zeng et al., 2014 [10] proposed a novel interpolation approach. An adaptive window is established with invalid pixels as the center to search for effective and similar pixels geographically. At the same time, combined with the effective images on adjacent days, the search process of effective pixels is completed together. If the maximum window is reached without a pixel threshold being met, the search process continues using the image of another clear-sky day until the threshold is met. As a result, the missing surface temperature value can be reconstructed using data from another period, and a linear connection established from similar pixels. This method has been widely applied in MODIS LST research in different geographical regions [23,24,25]. Mukherjee et al., 2014 [26] associated LST with normalized difference vegetation index (NDVI). The second-order polynomial regression relationship was fitted between LST and NDVI to reconstruct the invalid values of LST.

Currently, there is no unified and fixed method for the reconstruction of MODIS LST, and it is still necessary to compare the advantages and disadvantages of other methods. The purpose of this study is to propose a novel reconstruction method for MODIS LST by contrasting the commonly used methods (linear interpolation, smoothing filter, fitting, and fusion) and making full use of the spatiotemporal advantage. The Heihe River Basin (HRB), located in the northwestern arid and semi-arid regions of China, was selected as the study area. We reconstructed the MODIS LST products from 2016 to 2019 and validated the reconstructed results using in situ observations from an automatic weather station (AWS) [27,28]. Section 2 introduces the research area, remote sensing data, and station measurements. Then, the performances of LST reconstruction using the temporal, spatial, and spatiotemporal methods are compared and analyzed. Finally, a new method based on classification and an adaptive window is proposed. In Section 3, the performance of different reconstruction methods is systematically evaluated using daily LST measurements from the AWS station. Then, the variation law of soil moisture with LST on different underlying surfaces is analyzed. Section 4 discusses the advantages and limitations of different methods. In Section 5, we provide a conclusion and analyze the performance of each method in MODIS LST reconstruction in the Heihe River Basin.

2. Materials and Methods

2.1. Study Area

The Heihe River Basin (HRB) is located in the middle of the Hexi Corridor in arid and semi-arid areas of northwest China, and is located between 97.1° E to 102.0° E and 37.7° N to 42.7° N. It is about 390 km wide from east to west and 510 km long from north to south. The region covers an area of approximately 143,000 km², and is the second-largest inland river basin in China. The terrain in the Heihe River Basin is high in the south, low in the north, high in the west, and low in the east. The Qilian Mountains in the south have the largest change in altitude and are the main source of snowmelt water in the basin. The annual average temperature, rainfall, and evaporation potentials for the study area are 7.5 °C, 136.8 mm, and 1840.1 mm, respectively.

There are abundant geomorphic types in the region, including glaciers, frozen soils, alpine meadows, forests, irrigated crops, riparian ecosystems, deserts, and gobi. Different regions have different surface landscapes and different water and soil conditions. As a result, the reconstruction performance can be thoroughly tested. Figure 1 shows the land use types of the Heihe river basin and distribution of sites.

2.2. AWS Measurements

The AWS measured the land surface temperature (LST) and soil moisture (SM) for the purpose of validation. The surface temperature from AWS was measured using a thermal infrared thermometer. The soil moisture was measured using a soil moisture probe buried underground. The AWS observations were averaged to a frequency of half an hour. The validation data obtained at eight weather stations from 2016 to 2019 were used in this study, namely: Arou, Daman, Dashanglong, Huazhazi, Hunhelin, Zhangye, Yakou, and Sidaoqiao [27,28]. Detailed information regarding the seven sites is presented in

Table 1. Site location and underlying surface information of Heihe River Basin.

Station	Land Cover	Longitude (E)	Latitude (N)	Elevation (m)
Arou	Alpine meadow	100.4643	38.0473	3033
Daman	Cropland	100.3722	38.8555	1556
Dashalong	Swamp meadow	98.9406	38.8399	3739
Huazhaizi	Barren land	100.3201	38.7659	1731
Hunhelin	Populus Euphratica and Tamarix	100.1335	41.9903	874
Zhangye	Wetland	100.4464	38.9751	1460
Yakou	Alpine meadow	100.2421	38.0142	4148
Sidaoqiao	Tamarix	101.1374	42.0012	873

.

2.3. The Satellite and Other Auxiliary Data

The MODIS 500-m-resolution daily land surface reflectance (MOD09GA) and 1-km-resolution land surface temperature (MOD11A1 and MYD11A1) were used for LST reconstruction calculation. The LST data from the MOD11A1 product and the MYD11A1 product were adopted, and these were acquired by the Terra and Aqua satellites, respectively. The Terra and Aqua satellites have equatorial crossing times of 10:30 a.m. and 1:30 p.m., respectively. The original MODIS data have 12 bands in total, and the LST data were calculated using the “LST_Day_1km” band combined with a scale factor of 0.02. The MODIS Normalized Difference Vegetation Index (NDVI) was computed using the the reflectance of near-infrared and red bands. All MODIS data were obtained from the Application for Extracting and Exploring Analysis Ready Samples (AppEEARS) (https://lpdaacsvc.cr.usgs.gov/appeears/ (accessed on 1 August 2021)).

The advanced microwave scanning radiometer 2 (AMSR2) is a remote sensing sensor mounted on GCOM-W1, which is used to measure the weak microwave radiation on the earth’s surface and in the atmosphere (https://gportal.jaxa.jp/gpr/search/ (accessed on 1 September 2021)). AMSR2 measures vertically and horizontally polarized brightness temperatures at 6.925, 10.65, 18.7, 23.8, 36.5, and 89.0 GHz. In this study, the LST inversion scheme proposed by Holmes (2009), that is, that the AMSR2 brightness temperature product in the 37 GHz vertical polarization channel and the actual LST have a certain linear relationship, was used to retrieve surface temperature, will be employed in the following study [29].

ERA5 is the fifth-generation ECMWF atmospheric reanalysis of the global climate (https://cds.climate.copernicus.eu/ (accessed on 1 August 2021)). The reanalysis combines model data with observations from across the world into a globally complete and consistent dataset. ERA5 data provide hourly estimates of atmospheric, terrestrial, and marine climate variables. The earth data are accurate to a 30 km grid, including 137 layers of atmospheric data. The skin temperature was adopted in this study.

All of the images were geometrically rectified to the Universal Transversal Mercator projection (UTM Zone 47N) by the Pixel Information Expert (PIE) remote sensing image processing platform and resampled to a resolution of 1 km using the cubic convolution method by means of ENVI to maintain consistency with the MODIS data.

2.4. Methods

In this study, MODIS LST was first reconstructed using four common interpolation methods, namely, linear temporal interpolation, smoothing filter, fitting, and fusion, in order to compare the performance of these methods. Among them, the Savitzky-Golay method and HANTS were used for filtering in order to compare the performance of these two filtering methods. Fitting was performed on the basis of the relationship between LST and NDVI over a series of times. The fusion used AMSR2 data and ERA5 data. Then, a new interpolation method was applied with the advantages of both time and space. This method takes the central pixel from missing values and uses the image of another clear-sky day as the fill LST to reconstruct the invalid values. The reconstruction is based on the assumption that a ground feature’s surface temperature will change linearly, and that equivalent changes will occur for nearby similar features. As a result, the missing surface temperature value can be recovered using data obtained for a different time, and a linear relationship can be established using the closest matching pixels. To make the reconstruction results more accurate, we first carried out different land cover classifications in the Heihe River Basin. For the selection of images on another clear-sky day, we assumed that the correlation between the two images was highest within 10 days. Therefore, the image with the most effective pixels acquired within 10 days was selected as the fill LST. For each missing value, the nearest similar pixels were searched on the basis of the classification results. Local robust regression was then performed on similar pixels to reconstruct the missing value. Figure 2 shows the overall method flow chart of this research.

2.4.1. Temporal Method

In this study, the temporal method, linear time interpolation and smoothing filtering were used.

Following the procedure described by Klingseisen, 2010 [30] and Zhang et al., 2015 [20], the invalid pixel was taken as the center, and the period of the effective pixel at the same position was determined and used to derive a linear equation to estimate the LST value of the invalid pixel. Because it is rare for a pixel to have an invalid LST value for two consecutive 10-day periods, most estimations were completed by taking the average of two values that were close to one another in time.

The smoothing filters used in this study were the HANTS and SG filters. The core algorithms of HANTS are the least squares method and Fourier transform. The points in the LST value that are greatly affected by cloud pollution are removed through iterative fitting by means of the least squares method, and the curve decomposition and reconstruction are performed with the help of forward and inverse Fourier transforms in the time and frequency domains in order to achieve cloud removal and the reconstruction of a time-series of remote sensing images. There are 5 parameters to be input into the HANTS algorithm: the number of frequencies (NOF), high/low suppression flag (SF), valid data range (VDR), fit error tolerance (FET), and degree of over-determinedness (DOD) [31]. A value of ‘Low’ was used for SF, since undetected clouds result in unusually low LST values. A range of −50 °C to 70 °C was set for VDR to omit unusual temperatures during the computational process. Values of 6 °C and 7 °C were used for the FET and DOD, respectively.

The core idea of the Savitzky-Golay (S-G) filter is to filter the data in the window by means of weighting, but the weightings are determined by means of the least-squares fitting of a given high-order polynomial. The advantage of this is that it is possible to preserve the change information of the signal more effectively while filtering and smoothing. There are 5 parameters to be input into the S-G algorithm: Nleft, Nright, Order, and Degree. Nleft and Nright represent the number of data points to the left and right of each point to be included in the filter, respectively, the default of which is 5. Order is an integer specifying the order of the desired derivative. For smoothing, an order of 0 is used. To find the smoothed first derivative of the signal, an order of 1 is used; for the second derivative, order 2 is used, etc. Degree is an integer specifying the degree of the smoothing polynomial. Typical values are 2 to 4. Lower values for Degree will produce smoother results but may introduce bias, while higher values for Degree will reduce the filter bias, but may ‘overfit’ the data and give a noisier result.

2.4.2. Spatial Method

In contrast to the other two interpolation methods, fitting establishes the relationship between the data and LST by introducing external effective data to recover the invalid value of LST. Mukherjee et al. [26] fitted LST and NDVI using linear regression and quadratic polynomial regression, respectively. Therefore, the invalid value of LST can be calculated by the regression equation and the effective value of NDVI. For each LST image with missing pixel values, there is a corresponding NDVI image. During reconstruction, the relationship between LST and NDVI is fitted using the effective pixels on the target LST image and the NDVI image at the same position. As a result, the invalid pixel on the target LST can be calculated using the effective value of the same position on the NDVI image.

2.4.3. Spatiotemporal Method

Gao et al. [32] used the spatial and temporal adaptive reflectance fusion model (STARFM) to fuse the NDVI and LST from clear days’ Landsat and MODIS data. The basic idea of the model is to combine the advantages of Landsat’s high spatial resolution and MODIS’s high temporal resolution. Through the use of a mathematical model, the reflectivity data at the coarse spatial resolution of the predicted date are combined by using multiple pairs (two pairs, in practice) simultaneously during the observation period. The model makes the best of the advantages of high spatial resolution of Landsat and high temporal resolution of MODIS for data fusion. MODIS itself has a high temporal resolution, but there are few high-quality images. The temporal resolutions of AMSR2 and ERA5 data are also very high, and there are no invalid values in the data itself. Based on this idea, we introduce different data to fuse MODIS LST, and then compare the fusion results of the two data sources.

2.4.4. A Method Based on Classification and Adaptive Window

Reconstruction takes the classification results as the reference, and defective LST images can be filled using high-quality images obtained at a different time. For each missing value, similar pixels are defined as the closest effective pixels in the same class. To search for similar pixels, an adaptive window is used for both the target LST and the fill LST. The number of point pairs obtained by searching is defined as K, and a threshold value is set for K. The window size is initially set to a particular value, and if the threshold K is not satisfied, it is increased by two pixels. Because a large window size will take a long time to compute, a maximum window size can be defined. If the maximum window size is reached and threshold K is still not met, this signifies that this reference LST is not acceptable for this position; as a result, the missing value will be filled during post-processing.

In the reconstruction process, threshold K is a crucial parameter. The size of the searching window will likewise be smaller with a smaller threshold. Due to the high spatial correlation of LST, the linear connection will fit better if similar points are concentrated in a short window. However, if the threshold is not high enough, a small number of outliers can cause a lot of havoc with the linear relationship. As a result, the threshold should be suitably modified to ensure accuracy. Based on our experience, K should be set to between 20 and 30 in most circumstances to obtain good results.

Some invalid values cannot be recovered, because a suitable fill LST cannot be found. The invalid pixels in this area can be reconstructed by establishing their linear relationship with AMSR2 or ERA5 data within 10 days. Specifically, the time coordinates of the target LST and the fill LST are determined, and these two coordinates are taken as the starting point and endpoint of the timeline, respectively. All daily AMSR2 and ERA5 data on this timeline are extracted. We take the LST value of AMSR2 or EAR5 at the same position as the invalid pixel value as the ordinate and the position on the time axis as the abscissa; then, we determine a linear equation that simulates the changing trend of LST during this period. As a result, the LST value of invalid pixels can be calculated on the basis of the linear equation and its position on the time axis.

Ideally, most invalid pixels can be recovered using the above method. Except for some outliers, almost all missing values will be recovered. This is because when most similar pixels are far away from the target pixel, the linear relationship is unrealistic. To solve this problem, we establish a 3 × 3 pixel mean filter centered on outliers to remove these abnormal values.

3. Results

3.1. Validation of the Temporal and Spatial Methods

Ground measurement validation is essential for confirming the accuracy and applicability of different reconstruction methods. The land surface temperature can be obtained from AWS ground observation or calculated on the basis of four-component radiation data. Because there may be some uncertainty in the calculation process, AWS observation data was selected for the validation of LST reconstruction in this paper. Figure 3 and Figure 4 present a comparison of the LST results obtained using the temporal and spatial methods, as well as the AWS ground measurement results, for the eight sites from 2016 to 2019. Each site validated the reconstruction results obtained from the Terra and Aqua satellites. Taking the Terra satellite as an example, the overall root mean square error (RMSE) of the estimated cloudy-sky LST of the fitting algorithm was 13.12 K, with a percentage bias (PBias) of −3.76%, and a determination coefficient (R²) of 0.76, based on the ground measurements from the eight sites from 2016 to 2019. However, the validation results of LST estimated using linear temporal interpolation, HANTS and SG filter, and ground measurements showed that the deviation between them was not large. Among them, the overall RMSE of the three (10.70 K vs. 10.93 K vs. 11.04 K), R² (0.87 vs. 0.87 vs. 0.86), and PBias (−3.24% vs. −3.34% vs. −3.39%) did not exhibit much difference. The negative PBias values indicated that these methods overestimated LST. This illustrates that for the cloudy-sky pixels, part of the solar radiation will be absorbed by the clouds before reaching the land’s surface, causing the temperature of the cloud-covered pixels to be lower than the surrounding clear-sky pixels. However, whether the spatial method or the temporal method is used, the reconstruction of the cloudy-sky pixels is dependent on the value of nearby clear-sky pixels. As a result, the estimated LST will be slightly higher than the actual LST. In addition, the overall Nash–Sutcliffe efficiency (NSE) of the fitting algorithm was not high, at only 0.22. This value is close to 0, which means that the fitting estimation value is close to the average value of the observation value, that is, the overall result is credible, but the simulation error of the process is high. In other words, simply borrowing the information from spatially neighboring pixels based on the vegetation indices may not be accurate for reconstruction. Because LST is the result of the comprehensive action of multiple factors, such as soil moisture, albedo, evapotranspiration, etc., there is no completely decisive role or influence. However, the NSE when using linear temporal interpolation, HANTS, and SG filters remained between 0.44 and 0.48. Compared with the fitting algorithm, they had higher reliability, but this was not satisfactory.

At the same time, similar conclusions can be obtained from the data of the Aqua satellite after validation. However, compared with the Terra data, the NSE values for linear temporal interpolation, HANTS, and SG filter using the Aqua data were significantly improved (between 0.71 and 0.78, where values close to 1 mean that the algorithm has high reliability). On the other hand, the overall RMSE of these algorithms decreased significantly (between 7.13 K and 7.98 K), and so did that of the fitting algorithm.

Table 2. The general performance results of reconstructed LST using the temporal and spatial methods based on Terra data from 2016 to 2019.

Satellite	Site	Statistics	Methods
			Fitting (NDVI)	Linear Temporal Interpolation	HANTS	SG
Terra	Arou	R2	0.64	0.77	0.81	0.82
		RMSE	12.71	9.27	9.01	9.00
		NSE	0.02	0.48	0.51	0.51
		PBias	−3.39%	−2.45%	−2.46%	−2.44%
	Daman	R2	0.88	0.89	0.88	0.88
		RMSE	10.05	8.49	8.88	9.12
		NSE	0.41	0.58	0.53	0.50
		PBias	−0.36%	−2.56%	−2.67%	−2.27%
	Dashalong	R2	0.62	0.79	0.76	0.76
		RMSE	13.74	10.74	11.27	11.35
		NSE	−0.53	0.06	0.01	0
		PBias	−4.21%	−3.43%	−3.55%	−3.58%
	Huazhaizi	R2	0.82	0.84	0.81	0.80
		RMSE	12.00	12.35	13.16	13.17
		NSE	0.23	0.19	0.06	0.06
		PBias	−3.44%	−3.71%	−3.96%	−4.01%
	Hunhelin	R2	0.91	0.91	0.93	0.93
		RMSE	12.41	13.47	13.47	13.64
		NSE	0.41	0.30	0.34	0.32
		PBias	−3.84%	−4.23%	−4.34%	−4.47%
	Sidaoqiao	R2	0.91	0.94	0.94	0.93
		RMSE	11.51	10.26	10.37	10.62
		NSE	0.48	0.41	0.58	0.56
		PBias	−3.65%	−3.30%	−3.35%	−3.43%
	Yakou	R2	0.45	0.72	0.80	0.80
		RMSE	20.72	11.69	11.52	11.52
		NSE	−3.1	−0.30	−0.18	−0.19
		PBias	−6.50%	−3.83%	−3.87%	−3.87%
	Zhangye	R2	0.83	0.90	0.87	0.87
		RMSE	9.45	8.12	8.64	8.83
		NSE	0.46	0.60	0.54	0.52
		PBias	−2.68%	−2.45%	−2.58%	−2.63%
	Overall	R2	0.76	0.87	0.87	0.86
		RMSE	13.12	10.70	10.93	11.04
		NSE	0.22	0.48	0.45	0.44
		PBias	−3.76%	−3.24%	−3.34%	−3.39%

and

Table 3. The general performance results of reconstructed LST using temporal and spatial methods based on Aqua data from 2016 to 2019.

Satellite	Site	Statistics	Methods
			Fitting (NDVI)	Linear Temporal Interpolation	HANTS	SG
Aqua	Arou	R2	0.44	0.61	0.62	0.62
		RMSE	10.38	7.21	6.84	6.85
		NSE	0.12	0.58	0.62	0.62
		PBias	−0.79%	0.39%	0.30%	0.27%
	Daman	R2	0.66	0.78	0.69	0.68
		RMSE	8.28	6.1	7.16	7.22
		NSE	0.56	0.76	0.66	0.65
		PBias	−0.67%	−0.38%	−0.64%	−0.66%
	Dashalong	R2	0.46	0.71	0.52	0.52
		RMSE	9.66	6.45	7.92	7.95
		NSE	0.33	0.70	0.52	0.52
		PBias	−0.87%	0.21%	−0.34%	−0.37%
	Huazhaizi	R2	0.72	0.79	0.67	0.66
		RMSE	8.61	7.36	9.20	9.21
		NSE	0.71	0.79	0.66	0.66
		PBias	−0.21%	−0.18%	−0.54%	−0.58%
	Hunhelin	R2	0.88	0.87	0.86	0.86
		RMSE	8.31	9.18	9.73	9.74
		NSE	0.74	0.69	0.66	0.66
		PBias	−1.81%	−2.14%	−2.38%	−2.45%
	Sidaoqiao	R2	0.86	0.90	0.88	0.87
		RMSE	7.05	5.90	6.44	6.46
		NSE	0.78	0.85	0.82	0.82
		PBias	−1.29%	−1.00%	−1.13%	−1.19%
	Yakou	R2	0.24	0.69	0.71	0.70
		RMSE	19.91	7.23	7.61	7.62
		NSE	-2.79	0.5	0.48	0.48
		PBias	−5.22%	−1.52%	−1.80%	−1.81%
	Zhangye	R2	0.75	0.79	0.71	0.71
		RMSE	8.12	7.00	8.13	8.12
		NSE	0.52	0.64	0.50	0.50
		PBias	−1.61%	−1.41%	−1.73%	−1.78%
	Overall	R2	0.64	0.82	0.76	0.76
		RMSE	10.63	7.13	7.97	7.98
		NSE	0.51	0.78	0.71	0.71
		PBias	−1.50%	−0.76%	−1.03%	−1.07%

summarize the statistical validation results of the two methods combined with Terra and Aqua data, respectively.

3.2. Validation of the Spatiotemporal Method

Compared with the above method, for the STARFM algorithm using ERA5, the overall performance of LST fused with Terra data was relatively poor.

Table 4. The general performance results of reconstructed LST based on ERA5 data using STARFM from 2016 to 2019.

Method	Satellite	Sites
		Statistics	Arou	Daman	Dashalong	Huazhaizi
STARFM (ERA5)	Terra	R2	0.68	0.79	0.12	0.74
		RMSE	12.24	11.52	48.38	16.2
		NSE	0.08	0.2	−17.19	−0.43
		PBIAS	−3.33%	−3.33%	−2.56%	−4.91%
		Sites
		Statistics	Hunhelin	Sidaoqiao	Yakou	Zhangye	Overall
		R2	0.9	0.93	0.71	0.87	0.4
		RMSE	15.2	11.41	14.59	10.51	21.28
		NSE	0.16	0.5	−0.9	0.32	−1.1
		PBIAS	−4.84%	−3.71%	−4.73%	−3.30%	−3.83%
	Satellite	Sites
		Statistics	Arou	Daman	Dashalong	Huazhaizi
	Aqua	R2	0.53	0.74	0.55	0.8
		RMSE	8.34	7.81	9.14	7.67
		NSE	0.42	0.6	0.36	0.76
		PBIAS	−0.04%	−0.85%	−1.27%	−0.98%
		Sites
		Statistics	Hunhelin	Sidaoqiao	Yakou	Zhangye	Overall
		R2	0.91	0.91	0.64	0.84	0.79
		RMSE	10.37	6.34	8.83	7.74	8.34
		NSE	0.61	0.82	0.3	0.55	0.68
		PBIAS	−2.95%	−1.28%	−2.14%	−1.83%	−1.40%

summarizes the validation statistics of LST reconstructed by STARFM using ERA5 data at eight sites. Among them, the R², RMSE, and NSE were 0.4, 21.28 K, and −1.10, respectively. A negative NSE value indicates that the algorithm cannot be trusted. The main reason for this is that the performance of the STARFM algorithm at the Dashalong site was much worse than the other sites, lowering the overall level. In addition, for Aqua data, the overall performance of STARFM was at a relatively good level. The R², RMSE, and NSE were 0.79, 8.34 K, and 0.68, respectively. Compared with the other sites, the gap was not big for the Dashalong site, but it was also at the lowest level. This is mainly because the STARFM algorithm cannot take into consideration the influence of elevation. The altitude of the Dashalong site is 3739 m. The altitudes of the Arou site and the Yakou site also reach 3033 m and 4148 m, respectively. However, the altitude of the other sites is only about 1500 m or even lower. Therefore, the performance at these three high-altitude sites was not as good as that at other sites. For other methods, the influence of elevation is also a factor.

Figure 5 presents a comparison between the reconstructed LST obtained using Terra and Aqua data with the ground measurements. Overall, the performance when using Aqua data was better than that when using Terra data. This can be attributed to the fact that, during the day, the temperature reaches its highest point at around 2 p.m., which is the transit time of the Aqua satellite. As the temperature increases, the air density and humidity decrease. The factors that weaken solar radiation, such as water vapor and aerosol in the air, will be reduced. This is particularly evident in arid inland areas far from the sea.

In addition, we also used AMSR2 data to verify the reconstruction performance of the STARFM algorithm. AMSR2 data is carried on the GCOM-W1 satellite, and its transit time is close to that of Aqua. Therefore, we only validated the data for the afternoon. Figure 6 shows the results of this. On the basis of the results, the performance of the three sites (Arou, Dashalong, and Yakou) with high altitudes was still relatively poor. However, compared with each site, the performance when using AMSR2 data was relatively better than that when using ERA5 data.

3.3. Validation of the CAAW Method

Recent studies have improved the interpolation method by considering the elevation factor, and a number of improved interpolation methods, such as kriging, have also been employed [33,34]. Elevation chosen over all other LST-related parameters. This is because the elevation is a measurable variable that is linked to LST [35,36]. Land surface-property-based approaches are more adaptable to a wider range of situations than elevation-based methods. Although the physical features of land surfaces are complicated to quantify, classification algorithms are able to differentiate them qualitatively. On the basis of this idea, we improve the interpolation method and propose a classification-based LST reconstruction method.

We used a method based on classification and adaptive window to reconstruct the LST of the Heihe River Basin from 2016 to 2019. Figure 7 shows a comparison of reconstructed LST using classification and adaptive window with the LST measured by AWS at eight sites from 2016 to 2019.

Table 5. Validation of reconstructed LST using classification and adaptive window from 2016 to 2019.

Site	Data	Statistics
		R2	RMSE	NSE	PBIAS
Arou	ERA5	0.57	8.54	0.39	1.35%
	AMSR2	0.57	8.56	0.38	1.35%
Daman	ERA5	0.80	5.75	0.78	0.28%
	AMSR2	0.80	5.75	0.78	0.28%
Dashalong	ERA5	0.58	7.69	0.51	0.30%
	AMSR2	0.58	7.69	0.51	0.31%
Huazhaizi	ERA5	0.76	7.40	0.70	−0.53%
	AMSR2	0.76	7.4	0.71	−0.84%
Hunhelin	ERA5	0.84	7.26	0.81	−0.87%
	AMSR2	0.84	7.24	0.81	−0.86%
Sidaoqiao	ERA5	0.89	5.35	0.88	−0.37%
	AMSR2	0.90	5.27	0.88	−0.36%
Yakou	ERA5	0.62	7.62	0.51	−0.89%
	AMSR2	0.62	7.57	0.51	−0.88%
Zhangye	ERA5	0.86	5.48	0.78	−0.91%
	AMSR2	0.86	5.47	0.78	−0.91%
Overall	ERA5	0.79	6.96	0.77	−0.20%
	AMSR2	0.79	6.95	0.77	−0.20%

summarizes the validation results obtained when using this method combined with the AMSR2 and ERA5 data, respectively. As can be seen from Table 5, there is no significant difference between the performances obtained when using ERA5 and AMSR2. Combining Table 3 and Table 4, we compared the five reconstruction methods described above (fitting, linear temporal interpolation, HANTS, SG filter, and STARFM) with this method. Overall, the method based on classification and adaptive window has a similar accuracy to that of other methods. Taking the ERA5 data as an example, in terms of model reliability, the R² and NSE of this method were 0.79 and 0.77, respectively, second only to the values of 0.82 and 0.78 obtained for linear temporal interpolation. However, the RMSE of this method is slightly lower than that of linear temporal interpolation (6.96 K vs. 7.13 K), and the degree of overestimation is decreased (−0.20% vs. −0.76%). For each station, the accuracy of the method based on classification and adaptive window is better than that of other methods for stations with low altitudes. For the three stations at higher altitudes (Arou, Dashalong, Yakou), the accuracy of this method was slightly lower than that of linear temporal interpolation, but it was also better than the other methods. Overall, the performance of the method based on classification and adaptive window was relatively better than that of the other methods.

We used the method based on classification and adaptive window to obtain daily LST from 2016 to 2019. Figure 8 shows the spatial distribution of the reconstructed LST based on the methods described above. To better analyze the temporal and spatiotemporal changes of LST in the Heihe River Basin, we randomly selected four days of the year, one in the spring (19 April), one in the summer (15 July), one in the autumn (18 October), and one in the winter (24 February). It can be seen from Figure 8 that the changes in surface temperature in the Heihe River Basin still conformed to those characteristic of a temperate continental climate. It is cold in winter, and the temperature reaches its lowest values, while it is hot in summer, and the temperature reaches its highest values. The distribution of temperature in the whole basin still exhibits obvious characteristics. The Qilian Mountain area in the upper reaches has greater precipitation and a glacier meltwater supply. The underlying surface is mostly vegetation and forests, and the temperature is the lowest in the whole basin. The underlying surface in the middle and lower reaches is mostly bare land, with less precipitation and strong evaporation. It receives sunlight for a long time, so the temperature in this area is the highest in the whole basin.

The results show that the method based on classification and adaptive window is able to recover invalid and abnormal pixels affected by clouds over a large area, and generate an LST spatial distribution map. Because the input data are continuous, this method is able to provide a continuous spatiotemporal graph. A few regions have different spatial distributions due to the use of different methods, but overall, LSTs reconstructed using different methods still have similar spatial distribution characteristics. However, due to the low spatial resolution of MODIS data, the details of the image cannot be easily distinguished.

3.4. Analysis of LST Variation Characteristics Based on Soil Moisture

Among the many factors affecting surface temperature, soil moisture is an important factor, especially in arid areas. Both agricultural activities and geological surveys depend significantly on the moisture content of soil [37]. Sun et al. [38] believed that there was a certain spatial correlation between soil moisture (SM) and land surface temperature. It is generally believed that SM has a positive relationship with thermal inertia at the surface. As a result, a drop in SM causes a decrease in thermal inertia and an increase in the diurnal range of LST. However, the actual changes need to be analyzed according to the specific environment. To analyze the influence of soil moisture on LST, we selected the data of 2 cm soil moisture, because the soil moisture in this layer is closer to the surface moisture, and is therefore more useful for analyzing the impact of soil moisture on LST. We selected three sites (Arou, Daman, and Huazhaizi) representing different underlying surfaces (alpine meadow, cropland, and bare land) to analyze the impact of soil moisture on LST. Figure 9 presents a comparison of SM with LST reconstructed by classification and adaptive window.

The underlying surface of the Arou Site is grassland, and the surface type is relatively uniform, so the inter-annual change in soil moisture is also relatively uniform. During spring, with the increase in LST, the melting of frozen soil in winter is an important reason for the increase in SM. Summer is a hot and rainy season, but on days of high temperature with no rain, SM will decrease. With the arrival of autumn and winter, the precipitation will decrease, LST will gradually decrease, and SM will also decrease. The change in SM throughout the whole area mainly depends on the freeze–thaw cycle of water and rainfall. The underlying surface of the Daman Site is cropland. In around March, SM will usher in a peak, which is mainly due to irrigation for the upcoming sowing season. With the arrival of the summer rainy season, the LST reaches its maximum value in the year. When crops are harvested in autumn, the underlying surface of the ground gradually changes from crops to bare soil. On the soil surface without vegetation cover, soil moisture will accelerate the loss. SM decreases and LST decreases. However, in 2018, SM was significantly different from in other years, remaining at a low value for the whole year. This may be due to the heterogeneity of the irrigation area and the change in planting density. The change in SM throughout the whole area is mainly dependent on irrigation and rainfall. The underlying surface of the Huazhaizi Site is bare land, so the evaporation is at a high level and SM is at a low level throughout the year compared with the other two sites. However, SM will still reach its maximum in the rainy season. The change in SM throughout the whole region is mainly dependent on evaporation and precipitation.

4. Discussion

The reconstruction of land surface temperature was carried out based on different scales, and the reconstruction performance was also different. The reconstruction methods used in this study were based on three different scales: temporal, spatial, and spatiotemporal scales. For the temporal scale, we compared three methods: linear temporal interpolation, HANTS, and SG filter. Among them, the performance of linear temporal interpolation was the best, because it constructs a function in the period of valid data, and invalid values are simulated by the valid value closest to the invalid pixel. Therefore, linear temporal interpolation has a higher correlation with time compared with the other two methods. As for smoothing filters, there is no significant difference between HANTS and SG filters. From Figure 3, although the accuracy of these three methods does not exhibit much difference, from a temporal perspective, linear temporal interpolation can keep the details of LST changes, the smoothing filter will eliminate the details of LST change, only retaining the overall change trend. The results of linear temporal interpolation will be more in line with the actual situation of LST change. However, a smoothing filter is not necessarily worse than linear temporal interpolation. In some specific cases, such as in a period of effective data, there are a large number of polluted images, and the effective data available for linear temporal interpolation are limited. At this point, we can use a smoothing filter to simulate invalid values with limited effective values. In other words, when the number of days of effective images is very small, the performance of the smoothing filter may be better than that of linear temporal interpolation.

For the spatial scale, we used a simple fitting method based on NDVI, but the performance of this method was not satisfactory. On the one hand, for the data required for fitting, only using NDVI is not enough, because LST is the result of the joint action of many factors (such as evapotranspiration, soil moisture, etc.), and more factors should be considered in the fitting. On the other hand, from a spatial perspective, the correlation between valid and invalid values may not be as direct as the temporal method, because fitting is performed based on the number of effective values in a certain area centered on invalid values. For example, in a 3 × 3 window, there are eight pixels directly related to an invalid pixel. There may be invalid values in these eight pixels. Meanwhile, surface reflectance in a remote sensing image is spatially dependent, meaning that pixel locations that are close together are more comparable than pixel sites separated by greater distances. The fewer effective pixels available, the worse the reconstruction effect. However, the temporal method only needs to find a certain number of valid values near the invalid values on the time axis of a section of valid data. Pixels that have a direct impact on the reconstruction effect will not be like that of the fitting. Moreover, the change in LST itself over time has a certain regularity. Therefore, without considering other factors, only depending on temporal or spatial information, the temporal method performs better than the spatial method in reconstructing invalid pixels.

For the spatiotemporal scale, we used STARFM to reconstruct LST. Although STARFM makes full use of temporal and spatial information, it has a certain uncertainty. From Figure 8, it can be seen that there are some outliers in the results of reconstruction using the STARFM. Wang and Huang [39] analyzed the uncertainty of the STARFM algorithm and proposed a novel model to improve this algorithm. First, in the process of searching similar pixels, STARFM does not consider the land cover type of the pixel. Kriging was developed to achieve the best linear unbiased prediction (BLUP) and to determine the appropriate weights based on the fitted semivariance–distance relationship. Kriging can also be used to calculate the kriging variance, or reduced estimation variance, which can be used as a measure of prediction uncertainty. The prediction model combined with Kriging can distinguish the areas with and without land cover change, considering the structural similarity of the whole changed land cover area and predicting the changed area more accurately in the process of searching for spectrally similar pixels. Second, because the heterogeneous portions surrounding the margins have fewer coincident identical pixels, the shapes and edges of the surface objects have higher uncertainty. In contrast, homogeneous areas with a denser distribution of similar pixels and unchanged land cover areas have lower uncertainties. As can be seen in Figure 8, the outliers in the results of STARFM are concentrated in the edge area of the image. The densities and variabilities of similar pixels in the vicinity of the prediction site determine the prediction uncertainty [40]. In general, pixels with more coincident variations and denser nearby similar pixels will have lower prediction uncertainty [41]. Finally, because of variances in land surface reflectance between two observation dates, higher changes in surface reflectance lead to larger uncertainty in the fusion results.

Through the comparison of the validation statistics in the results, it can be determined that the method based on classification and adaptive window can improve the accuracy of the interpolation method to a certain extent. First, in terms of spatial scale, this method uses classification to distinguish pixels of different land cover types, avoids pixels of different land types from participating in the reconstruction of invalid values, and improves the spatial correlation between effective pixels and invalid pixels. Second, for the selection of adaptive window size, we set the maximum window to 9 × 9. On the one hand, for the threshold K (20), its proportion in the window will not appear too low. In this way, cases where the effective pixels searched for re too far away from the invalid pixels can be avoided, reducing the spatial correlation between them. On the other hand, if the window is set too large, the calculation time will be greatly increased, which will affect the efficiency of the reconstructed method. Finally, in terms of temporal scale, we selected the image having the clearest sky pixels in 10 days near the invalid pixel as the fill LST, because for the Heihe River Basin, there are rarely clouds for 10 consecutive days. In addition, if the time series is set too large, it will also reduce the time correlation between effective pixels and invalid pixels.

Because there are no obvious differences between the cloud-top temperature of thin cloud and the actual LST, the influence of thin cloud on the surface temperature can almost be ignored [42]. However, the reconstruction of LST in this study was aimed at all pixels with cloud coverage, and did not consider the impact of the extent of the cloudiness in the images on the reconstruction method. As can be seen from Figure 9, soil moisture also shows a certain regular change with changing LST. Soil moisture is an important parameter affecting LST change, especially in arid and semi-arid areas. The analysis of soil moisture on different underlying surfaces in the Heihe River basin can lead to a better understanding of the impact of LST on soil moisture change. Especially in agricultural areas, it plays a vital role in surface evapotranspiration monitoring, agricultural irrigation management, crop yield prediction, climate change, drought, and hydrological processes.

5. Conclusions

Land surface temperature (LST) is an extremely important parameter that controls the atmospheric surface water heat balance. It has an extremely wide application value in the fields of earth resources and the environment, ecosystems, hydrological cycles, and so on. However, due to the inevitable cloud pollution of satellite remote sensing data, in areas covered by clouds, there will be a large number of null and invalid values in the LST retrieved from thermal infrared remote sensing data, which will reduce its accuracy, thus affecting the wide application of LST products. Therefore, it is of great significance to be able to reconstruct the invalid value of LST.

In this paper, the missing pixels of MODIS LST in the Heihe River Basin from 2016 to 2019 were reconstructed using temporal, spatial, and spatiotemporal methods, and the performance obtained when using data acquired by Terra and Aqua was compared. Three methods were used for the temporal scale: linear temporal interpolation, HANTS, and SG filter. The spatial and spatiotemporal methods used fitting and STARFM, respectively. On the basis of the results, the linear temporal interpolation performed best among these methods, and the performance when using Aqua data was better than when using Terra data, with an RMSE of 7.13 K and an R² of 0.82, and the NSE and PBias were 0.78 and −0.76%, respectively. There are no obvious differences in the performance of the two smoothing filters (HANTS and SG). The overall results combined with Aqua data were as follows: R² (0.76 vs. 0.76), RMSE (7.97 K vs. 7.98 K), NSE (0.71 vs. 0.71), and Pbias (−1.03% vs. −1.07%). The overall performance of the fitting method was the worst among these methods, with an RMSE of 10.63 K and an R² of 0.64, and the NSE and Pbias were 0.64 and −1.50%, respectively. On the one hand, it is not enough to only consider NDVI in the fitting process, because LST is the result of the joint action of many factors. On the other hand, in terms of spatial scale, the number of effective pixels related to invalid pixels will directly affect the effect of reconstruction. The temporal method can be used to complete the reconstruction only by relying on the effective pixels near the invalid pixels in time, and the change in LST over time has a certain regularity. For STARFM, we used ERA5 and AMSR2 data, respectively. Although STARFM can make full use of temporal and spatial information, its performance is not as good as linear temporal interpolation, because STARFM itself has a certain uncertainty. STARFM cannot distinguish the surface types of different pixels, and the prediction uncertainty of image edge pixels is high. Furthermore, we proposed a new method based on classification and adaptive window to complete the reconstruction of LST. The process of classifying and searching for similar pixels can improve the correlation between invalid pixels and effective pixels to a certain extent. Taking ERA5 data as an example, compared with linear temporal interpolation, the overall accuracy of this method was improved to a certain extent, with an RMSE of 6.96 K, an R² of 0.79, and an NSE and Pbias of 0.77 and −0.20%, respectively.

This study compared the performance of different LST reconstruction methods. Finally, a new method based on classification and adaptive window was proposed based on a spatiotemporal scale. On the basis of the results, this method can indeed improve the accuracy of interpolation to a certain extent, thus providing a new concept for MODIS LST reconstruction in the Heihe River Basin and other parts of the world.