Abstract
The effect of topographic correction (TOC) has a profound influence on the quantitative application of remote sensing image. With regard to the invalid evaluation of the TOC model with such a single topographic correction assessment (TCA) method, we have selected five TCA indexes from five different perspectives: the difference in mean radiance radiometry between sunlit and shaded slopes, the cosine empirical relationship, stability, heterogeneity, and outlier ratio. The entropy weight method was used to assign weight to each TCA indexes, and the comprehensive evaluation value (CEV) of TOC for each band of remote sensing image was obtained by weighted superposition. After that, the weight of each band of the remote sensing image is determined by the entropy weight method, and the CEV of the TOC of the remote sensing image is obtained by weighting and superposition, so as to realize the effect evaluation of the six TOC models of C, SCS + C, VECA, Teillet, Minnaert, and Minnaert + SCS. The results indicate that the proposed method can effectively evaluate the correction effect of the TOC model. Results indicate that the SCS + C model has the best correction effect, while the Minnaert model performs the worst. The results generated from the Minnaert + SCS, Teillet, and Minnaert models typically show inferior quality. The SCS + C, VECA, and C models are better suited for generating images with high spectral fidelity, and these three correction models are recommended for TOCs over mountainous areas.
1 Introduction
The development of remote sensing technology has provided more effective and largescale monitoring methods for the general survey of different areas, such as agricultural and forestry resources, geological exploration, and environmental monitoring [1]. However, remote sensing images require complex preprocessing after acquisition before being used to accurately reflect the actual information [2]. When the remote sensing image is of a rugged mountainous area, violent terrain undulation will cause an uneven illumination on the ground. Therefore, real objects cannot be truly reflected in the image [3]. This topographical effect seriously affects the quantitative analysis of remote sensing images. In consequence, to obtain accurate spectral information of ground objects from remote sensing images, it is necessary to perform topographic correction (TOC) on the images to eliminate the influence of topography [4].
Since the 1980s, scholars have studied how to accurately obtain remote sensing reflectance of mountainous surfaces and have established a variety of TOC models to eliminate the effects of terrain in remote sensing images and reduce the differences in the reflectance of the same surface type. TOC models consist of statistical and physical models [5]. The advantages of statistical models are few parameters, simple calculations, and strong applicability, but without adequate theoretical foundations and a sufficient understanding and knowledge of the physical mechanisms [6,7]. For example, statistical models have used the high correlation between the radiance value of the remote sensing image and the cosine value of the sun’s incidence angle to construct the correction model of the shadow area. Representative examples include the Teillet and VECA models [8,9]. Physical models include the Lambertianbased model and nonLambertianbased model depending on whether the nonLambertian characteristics of the surface are considered when the model is constructed. The most representative Lambertian models are the cosine and SCS models, but these two models ignore the influence of scattered radiation, so the correction effect in practical applications is often unsatisfactory [10,11,12]. The improvement of the model by introducing the empirical coefficient C to describe the characteristics of surface scattering radiation can solve the problem of overcorrection to a certain extent. However, the real surface is nonLambertian, with two directional reflectivities of the earth’s surface [13,14]. For that reason, some scholars have constructed a series of nonLambertian correction models based on directional reflectivity, such as the Minnaert series model and BRATC model [15,16].
With the establishment of a series of TOC models, the effective evaluation of the performance of TOC models has become a focal point [3,9,17]. According to the linear correlation between the radiance of the remote sensing image and the cosine of the sun’s incident angle, scholars have often used the slope of the linear regression equation of the two factors before and after TOC and the change in the correlation coefficient to express the TOC effect of the TOC models [9]. In addition, the correction effect of the TOC model can be reflected to a certain extent with statistical methods, such as using the coefficient of variation in image pixels within the same land cover type to indicate the heterogeneity of remote sensing images or using the average value of pixel radiance to evaluate the stability of the images [18,19]. The application effect of the resulting image of the TOC can also be used as an evaluation strategy for the TOC model. For example, the results of TOC model can be determined by comparing the landcover classification accuracy of the image before and after the TOC [20,21,22]. This evaluation strategy is controversial because TOC does not significantly improve the classification accuracy of land cover [22,23]. In fact, a single model for evaluation will often lead to unreliable results because different evaluation strategies for the same TOC model come to varying conclusions. This also affects the true judgment regarding the performance of the TOC model. Therefore, some scholars have attempted to describe the correction effect of the TOC model through multicriteria evaluations, but this method can only analyze the evaluation results of each topographic correction assessment (TCA) method individually and cannot obtain a comprehensive evaluation value of the TOC model [24,25]. Furthermore, because the calculation of the TOC is based on a single band, people tend to use the results of a single band or simply list the effects of all bands and analyze them separately to evaluate the TOC models [9,11]. Consequently, even if a series of TOC models are quantitatively evaluated, the results obtained remain ambiguous. Hence, there is an urgent need to establish a method that can effectively evaluate the performance of the TOC model in view of the current problem that a single TCA method cannot effectively evaluate the TOC model.
This article proposes a comprehensive evaluation method for a remote sensing image TOC model based on the entropy weight method, which quantitatively evaluates the TOC effect of the Teillet, VECA, C, SCS + C, Minnaert, and Minnaert + SCS models. In this study, five TCA models were selected based on two aspects: direct and indirect evaluations. The direct evaluation model quantitatively evaluates the difference in the mean radiance of the shady slope and sunny slope, which is based on the topographic effect of the remote sensing images. The indirect evaluation model evaluates the TOC model laterally, including the correlation between the image radiance and the incident angle cosine, the stability of the TOC model, the heterogeneity of the corrected image, and the proportion of outliers generated by the TOC model. By assigning weights to the five TCA models, the influence of each model in the comprehensive evaluation was determined. The entropy method has proven to be a scientific and objective weighting process, and the evaluation values of all the models were weighted and superimposed to obtain the TOC comprehensive evaluation value (CEV) of each band. Similarly, each band was integrated based on the entropy weight method, and a CEV of the TOC of the TOC model was obtained.
2 Study area and data
2.1 Study area
The experimental area (
Figure 1
2.2 Data preprocessing
The Landsat8 OLI remote sensing images used in this study were taken on December 8, 2020, downloaded from the website of the United States Geological Survey (USGS, https://glovis.usgs.gov/). The solar elevation angle of the image was 37.26°, and the solar azimuth angle was 155.71°. The DEM data in the study area were obtained from the Geospatial Data Cloud (http://www.gscloud.cn/), and the resolution of the digital elevation model (DEM) was 30 m × 30 m. The obtained Landsat8 OLI remote sensing image and DEM data are cropped to the size of the study area, and then the remote sensing image and DEM data are geometrically registered to match the pixel positions. In the next step, based on the image offset and gain coefficients, the digital number (DN) value of the remote sensing image is converted into the pixel radiance value through a linear conversion formula, and the image radiance value is used for TOC calculations [26]. The maximum likelihood ratio method was used to supervise and classify the remote sensing images of the study area to obtain the land cover data. The land cover types were divided into four types: forest land, bare land, water area, and residential land, and the area of the four land cover types accounted for 79.486, 16.746, 1.432, and 2.336%, respectively. The confusion matrix was used to evaluate the classification accuracy, and the overall accuracy reached 95.89%.
3 Methods and models
3.1 Direct evaluation model
According to the definition of TOC, the image after TOC should meet the characteristics of the same type of ground feature radiance on slopes with direct sunlight and nonilluminated slopes [24]. More than 70% of the ground feature types in the study area were forest land, which is widely distributed on the shaded and sunny slopes of the mountains. Therefore, according to the principle of TOC, the difference in the mean radiance radiometry between the sunlit and shaded slopes (SSR) is used as the direct evaluation index of the TOC model [27,28]. The calculation equation for SSR is
where sunlit and shady represent the mean radiances of the pixels on the sunny and shaded slopes before and after TOC, respectively. When the value of SSR is 0, the terrain effect completely disappears. In this study, sunny and shaded slopes were divided according to the solar azimuth angle at the time of imaging. The sun slope was taken as the area of ±30° of the sun azimuth angle, and the corresponding shaded slope was taken as the back of the sun slope area.
3.2 Indirect evaluation model
3.2.1 Cosine experience relationship evaluation
The linear correlation between the image pixel radiance and the cosine of the sun’s incident angle was used to quantitatively evaluate the effect of the TOC. Theoretically, a good TOC model can effectively reduce the slope and correlation coefficient of the linear equation. For that reason, this study introduces the relative correction extent (RCE) as an index to quantitatively evaluate the TOC model. RCE represents the degree of change in the slope of the linear equation before and after the TOC, which can effectively reflect the effect of the correction [29]. The equation for the RCE is as follows:
where
3.2.2 Stability evaluation
When evaluating the advantages and disadvantages of the TOC model, whether the stability of the image pixel radiance before and after the correction can be maintained must be considered. The study area was divided into four land cover types. Although the surface of the water is always flat, it is essential to maintain the stability of the water body radiance during the calibration process. The difference in the radiance median (MRD) of the internal pixel radiance of each land cover type was selected as the index to evaluate the stability of the TOC method. For an outstanding TOC model, the pixel radiance of the remote sensing image after TOC should maintain good stability; that is, the MRD should be as close to 0 as possible [18]. The MRD equation is as follows:
where
3.2.3 Heterogeneity evaluation
After the TOC, the heterogeneity of the radiance of each land cover in the remote sensing image should be reduced [30]. The interquartile range of radiance difference (IQRD) of the pixel radiance of each land cover type was selected as the index to evaluate the internal heterogeneity of the remote sensing images. The IQRD equation is
where
3.2.4 Outlier ratio
The outlier values produced by TOC have a significant influence on the quality of the remote sensing images. Pixels with a radiance value greater than the original image maximum value or less than the original image minimum value in the resulting image were defined as outlier pixels [31]. The outlier ratio (OR) was used as the evaluation index for the TOC model. A good TOC model should produce fewer outliers. The equation for OR is
where NUM represents the number of image pixels, and
3.3 Comprehensive evaluation method of TOC model based on entropy weight method
The evaluation results obtained by using a single indicator are usually not objective, because the evaluation results obtained by selecting different TCA indicators are different. To solve this problem, we developed the comprehensive evaluation method of TOC model based on entropy weight method (Figure 2). The comprehensive evaluation method comprehensively considers five TCA indexes, which can measure the performance of the TOC model. In order to measure the contribution of each TCA index in evaluating each band of remote sensing image, we use entropy weight method to assign weight to each TCA index, and then superimpose these TCA index values to obtain CEV of each band. CEV can express the correction effect of TOC model objectively and quantitatively. The entropy weight method provides an objective and effective way of weighting that determines the weight based on the hidden information in the data, and the process is not affected by human factors. Furthermore, the entropy method can effectively explain the results, and there is no loss of information; therefore, it is widely used in various fields [32,33]. The construction process of the comprehensive TOC model evaluation method based on the entropy weight method is shown in Table 1 [34]. The TOC model’s CEV was used for a comprehensive evaluation. The larger the CEV, the better the TOC effect of the TOC models.
Figure 2
Table 1
Process  Instruction  Equation 

Step 1  Five TCA index values were standardized using Zscore standardization method. In the equation,


Step 2  Calculate the proportion


Step 3  Calculate the entropy value


Step 4  Calculate the information entropy redundancy


Step 5  Calculate the weight of the jth TCA model. In the equation, m is the number of TCA indicators 

Step 6  Calculate the CEV of TOC for each band of the remote sensing image CEV_{
b
}. In the equation, b (


Step 7  The above process is repeated to calculate the weight value of each band of the remote sensing image


4 Results and discussion
4.1 TCA models evaluation value
It is generally believed that after TOCs, the pixel radiance of the shady slopes will be enhanced, while that of the sunny slopes will be inhibited. Thereby the radiance of the pixels on the shadow and sunny slopes of the image is balanced to eliminate the influence of the terrain. This is not always the case. As shown in Figure 3, compared with the uncorrected image, the SSR of the resultant image after the TOC is significantly closer to 0, indicating that each TOC model can effectively reduce the SSR of the remote sensing image. However, in most wavebands, the SSR after the TOC is negative; that is, the average radiance of the pixels on a shaded slope is higher than the average radiance of pixels on a sunny slope, and there is a significant overcorrection phenomenon. Especially in Band1, the SSR of the Minnaert and Minnaert + SCS models reached –0.31, and its absolute value exceeded the SSR of the uncorrected image. In other words, the remote sensing image corrected by the Minnaert and Minnaert + SCS models in Band1 was worse than the original. However, in Band3, Band4, and Band7, the Minnaert and Minnaert + SCS models have the best correction effect, which demonstrates that the band difference is a critical factor for a TOC model. In contrast, the SCS + C, C, Teillet, and VECA models were relatively stable.
Figure 3
The cosine empirical relationship evaluation method was used to quantitatively evaluate the remote sensing images obtained by the six TOC models and calculate the RCE of each image according to the slope of the linear equation. The results are shown in Figure 4. The ideal TOC model should completely eliminate the correlation between the radiance of the remote sensing image pixel and the cosine of the incident angle; that is, the RCE should reach 100%. As illustrated in Figure 4, the RCEs of the six TOC images are all greater than 0, which means that all the models could effectively perform TOCs on remote sensing images. Except for the C model and the VECA model, where the RCEs are 54.01 and 46.72% in Band7, respectively, the RCE of the other models are all above 65%. The performances of the TOC models in different wavebands vary significantly. For example, the RCE of the SCS + C model exceeded 90% in the first four bands but did not reach 80% in the shortwave infrared (SWIR) band, with the worst performance in the SWIR2 band reaching only 68.06%. The C and VECA models also exhibited poor corrections in the SWIR band. Only the Teillet model could maintain a high RCE in each band.
Figure 4
An excellent TOC model should be able to ensure the stability of remote sensing images before and after the correction. If the mean value of the pixel radiance of the remote sensing image after TOC changes significantly, it means that the radiance value of most of the pixels has been greatly increased or decreased. Therefore, it is difficult to quantitatively invert the images after the TOC. The application area obtained credible results. Figure 5 displays the MRD of the resulting images of the six TOC models. The MRD of most of the TOC models is less than 10%, which is an acceptable result. The C model and the Minnaert model have high MRD values in all bands and have an obvious trend of increasing gradually from Bands1–7. In Band7, which has the highest MRD value, the MRD values of the two models reached 17.87 and 56.99%, respectively. The performance of the Minnaert + SCS model was the opposite. From Bands1–5, the MRD value exhibits a trend of gradually approaching 0 from –9.18%. The SCS + C, Teillet, and VECA models have good correction effects in all the wavebands and could effectively maintain the stability of the radiance of the pixels in each land cover type.
Figure 5
The interquartile range of pixel radiance reflects the internal heterogeneity of the remote sensing images to a certain extent. By calculating the IQR of each land cover type, we obtained the areaweighted IQRD within the land cover category using the proportion of the land cover area. The calculation results are presented in Figure 6. Most of the TOC models caused an increase in the image IQRD, but the performance of the TOC models fluctuated in different spectral bands. In Band1, all the models except the SCS + C model caused a reduction in the IQRD of the image, which indicates that the heterogeneity within the image increased after the TOC due to overcorrection. The same phenomenon also appears in the Minnaert model of Band6 and Band7. Among all the TOC models, only the SCS + C model could maintain a positive IQRD in each spectral band. Furthermore, the VECA and Minnaert + SCS models maintained a better correction effect in the six bands other than Band1.
Figure 6
We calculated the proportion of outliers in the correction result image for each TOC model (Figure 7). The number of outlier pixels often restricts the actual application of an image. The proportion of outliers in most of the TOC models was controlled to be below 1%, indicating that the six TOC models had good correction effects in most cases. However, in some bands, the OR index of the Minnaert model and the Minnaert + SCS model far exceeded those of the other models. In Band1, the OR index of the Minnaert + SCS model reached 16.05%, and that of the Minnaert model exceeded 5%. This demonstrates that the correction performance of these two models in individual bands is poor. However, the OR index in Band3 to Band7 performs well, which also reflects the significant difference in the band between the two models. The proportion of outliers in the Teillet model from Bands1–7 exhibited an increasing trend, reaching the highest value of 2.24% in Band7.
Figure 7
Comprehensively considering the evaluation results of the five TCA models, it was found that the correction effect of the TOC model demonstrated significant differences between the bands. The SSR, IQRD, and OR evaluation indices all have abnormal evaluation values in Band1, while the RCE and MRD have better results in Band1. As in previous studies, the SWIR band tends to have poor correction effects, possibly because these bands respond more intensely to the effects of the terrain [35]. However, it is surprising that the performance of the Minnaert + SCS model is relatively poor in most bands, and the SWIR band often has a better correction effect. Therefore, the Minnaert + SCS model can be considered for targeted TOCs of the SWIR band in subsequent studies. The SCS + C, VECA, and C models could maintain good stability in different wavebands. Hence, it is recommended to use these TOC models to ensure the effect of TOCs when correcting singleband images. In addition to the differences between the TOC models in the bands, the results obtained when using different TCA models for the evaluation were also significantly different. For example, the C model performs well in the SSR evaluation, which can effectively reduce the difference in the mean radiance of the shady and sunny slope pixels of the image, but it performs poorly in terms of stability. This is a shortcoming of using a single TOC evaluation model. In conclusion, the results of this study highlight the differences between different TOC models in various bands of remote sensing images. In previous studies, the evaluation value of a certain band of remote sensing images was often used to explain the performance of the TOC model, which is improper and may even lead to incorrect conclusions. For that reason, it is necessary to comprehensively consider the performance of all the bands when evaluating the effect of the TOC model.
4.2 CEV of each band of TOC models
The results of using the entropy method to weigh the five TCA models corresponding to each band of remote sensing images are listed in Table 2. The TCA indexes of each band of remote sensing image were weighted and superimposed to obtain the CEV of all the spectral bands. The results are presented in Figure 8. The SCS + C model has an advantage in almost every band, except that it ranks second in Band6 and Band7, and the CEV in the other bands is the highest. The CEV value of the VECA model in each band is lower than the SCS + C model, but it still has obvious advantages compared to other models. In the seven spectral bands, the CEV value of the C model is slightly lower than the VECA model, but higher than the Teillet model and the Minnaert model. The Teillet model and the Minnaert model performed poorly in all the seven bands, and the CEV value of the Minnaert model in band6 was much lower than other TOC models.
Table 2
TCA  Band1  Band2  Band3  Band4  Band5  Band6  Band7 

RCE  0.0521  0.1205  0.1403  0.1426  0.0763  0.1309  0.1262 
SSR  0.2485  0.1810  0.1739  0.1170  0.3002  0.1701  0.1025 
MRD  0.2414  0.2529  0.1926  0.2188  0.3347  0.3141  0.2805 
IQRD  0.1339  0.0997  0.1001  0.0819  0.0739  0.0786  0.0838 
OR  0.3241  0.3459  0.3930  0.4397  0.2149  0.3063  0.1070 
Figure 8
Notably, the VECA and C models have similar trends, maintaining a stable CEV among the seven bands, and there is no outstanding or poor performance in a certain band. SCS + C, VECA, and C models are preferred for TOC of singleband images, because they can guarantee better correction results in all the bands. The performances of the Teillet, Minnaert, and Minnaert + SCS models between the bands are extremely unstable; in particular, the Minnaert + SCS model has the lowest CEV in Band1 and Band2, while the CEV in Band6 and Band7 is higher than in other models. Consequently, we can consider using the Minnaert + SCS model to perform TOC on the SWIR band of Landsat images in subsequent research.
4.3 CEV of TOC models based on entropy weight method
To obtain the CEV value of the entire remote sensing image and then comprehensively evaluate the TOC model, the entropy weight method was used to calculate the weight of the band CEV value. The calculation results are presented in Table 3. As shown in Figure 9, the SCS + C model has the best TOC effect in the study area, and the Minnaert model has the worst performance. Therefore, the comprehensive evaluation method for TOC model of remote sensing image based on entropy weight method can obtain accurate evaluation results, and can express the correction effect of the TOC model through quantitative values. In general, the CEV of the six TOC models presents an arrangement of SCS + C > VECA > C > Minnaert + SCS > Teillet > Minnaert, which is mostly consistent with the results of the previous studies [10,24,36]. The CEV value of the SCS + C model is much higher than other TOC models, so the correction effect of the SCS + C model has obvious advantages. The C model often had the best correction effect in previous studies. In this study, the CEV was below the SCS + C and VECA models. There may be two reasons: one is that the C model performs poorly in terms of stability, and MRD occupies a higher weight in the five TCA models, so the CEV obtained is not prominent; the other is that it may be related to the land cover of the study area. The SCS + C model is more in line with the terrestrial growth of trees, so it is distributed in woodlands. The effect of widearea correction is better. Because more than 70% of the land cover in the study area is forest land, it is reasonable that the SCS + C model based on the SunCanopySensor principle has the best correction effect in the area, while the C model is inferior in comparison. Notably, the VECA model has a CEV second only to the SCS + C model. This is because the VECA model performs better in the evaluation results of any TCA model. Although the Teillet model has a high RCE in the evaluation of cosine empirical relation, it performs poorly in controlling the outliers. Meanwhile, the Teillet model is unstable in the performance between bands and has the lowest CEV in Band3, Band4, and Band7. Therefore, the CEV of the Teillet model is low. Obviously, Minnaert model has the lowest CEV, because the evaluation results of Minnaert model in most TCA indicators are not ideal. However, the Minnaert + SCS model has better CEV than the Minnaert model because it comprehensively considers the characteristics of the terrestrial growth of trees.
Table 3
BAND  Band1  Band2  Band3  Band4  Band5  Band6  Band7 

Weight  0.1374  0.1164  0.1924  0.1363  0.1129  0.1405  0.1641 
Figure 9
In this study, a comprehensive evaluation method of the TOC model was constructed based on the entropy weight method. The method comprehensively considers five quantitative evaluation indices of the TOC effect, which can comprehensively and objectively evaluate the TOC model effectively. At present, the commonly used objective weighting methods mainly include the entropy method and principal component analysis (PCA) method. The PCA method uses a few principal components to explain the information in multiple variables, but it is inevitable that there is information loss. Furthermore, the application of the PCA method is more dependent on data quality, and its versatility is poor. TOC is mostly applied to areas with complex terrain. These areas not only have a large number of pixels, but also the brightness values of the pixels often vary. As a result, the calculation results of TOC often have poor data quality. Therefore, the entropy weight method is more suitable for TOC model evaluation. The entropy method determines the weight according to the amount of information inside the indicator system; however, in practical applications, the amount of information of the indicator does not fully represent the importance of the indicator. As shown in Table 2, the OR model has the highest weight in Bands1–4, and the MRD model has the highest weight in Bands5–7, but the TCA model with more information has a greater influence in the comprehensive evaluation. However, this is difficult to determine. Therefore, it is necessary to develop a new and more persuasive method for empowerment. Furthermore, compared with the direct averaging of the evaluation results of multiple evaluation strategies in some studies, this method considers the differences between evaluation strategies and between various bands, and the results are more scientific. The comprehensive evaluation method proposed in this study can avoid the interference of human factors to the greatest extent, which can include multiple dimensions of evaluation indicators and ensure the objectivity of the calculation process. This is the first and most critical step in the credibility of the comprehensive evaluation results of TOCs.
Simultaneously, land cover data also affects the accuracy of the evaluation of the TOC model. In this study, the radiance change in the water body was considered in the quantitative evaluation value, while the water body was not considered in most studies, because it is generally believed that the water surface is always level [24,37]. In fact, after the TOC, the pixel radiance on the water surface becomes uneven, which is also a reflection of the correction effect of the TOC model. This is because an excellent TOC model should not significantly change the radiance of the water surface before and after TOC. The classification of land cover types in the study area is affected by the resolution of the image. Only types with dominant areas can be classified, and a more detailed classification cannot be performed accurately, which may affect the results of the evaluation. Therefore, it is necessary to obtain map data with higher accuracy in the research of other regions and a more precise classification of land cover types.
5 Conclusion
An effective evaluation of the performance of the TOC models for remote sensing images is the basis for the development and application of TOC models. This research proposes a comprehensive evaluation method of TOC models based on the entropy weight method, which can integrate multiple evaluation strategies to evaluate the performance of TOC models objectively and effectively. The key contributions of this research include two aspects: one is to establish a comprehensive evaluation method of the TOC model based on the entropy weight method, which realizes the quantitative evaluation of TOC models, and the second is to use a comprehensive evaluation method to analyze the TOC model and resulting image to provide a basis for the selection of the TOC model.
This study verified the effectiveness of the comprehensive evaluation method. The comprehensive evaluation method based on the entropy weight method has proven to be scientific and can effectively integrate the results of multiple evaluation strategies. The results of a comprehensive evaluation of the study area suggest that the SCS + C model has the best comprehensive effect, followed by the VECA model. There is only a small gap between the C and VECA models. Furthermore, the C and VECA models exhibited a similar trend between bands. Therefore, the two models can be substituted for each other when the accuracy requirements are not high. The comprehensive correction effects of the Minnaert + SCS model, Teillet model, and Minnaert model are lower than the average level, and it is not recommended to use these in TOCs. However, the correction effect of the Minnaert + SCS model in the SWIR band is better than that of the other models, so the SWIR band can be used in a targeted manner. The SCS + C, VECA, and C models can maintain good stability between different bands of remote sensing images. The correction effects of the other TOC models in the different bands vary significantly. Therefore, it is recommended to use these three TOC models when performing TOC on singleband images. For further research, we intend to evaluate the application effects of TOC models in different terrain and geomorphic regions based on the comprehensive evaluation method proposed in this article to explore the most suitable TOC models for different terrains and geomorphic regions and to provide a more direct method for the selection of remote sensing image TOC models.
Acknowledgments
The research was supported by the National Natural Science Foundation of China (71704177). And be grateful for the data provided by the platform the United States Geological Survey and the Geospatial Data Cloud.

Funding information: This study was supported by the National Natural Science Foundation of China (71704177).

Author contributions: J. J. Huang and M. K. Yao managed the entire research project and also analyzed and considered the research materials. M. Zhang and L. L. Kuang performed software operations. H. Zhou completed the formal analysis, and F. W. Ye provided the experimental data. All authors have read and agreed to the published version of the manuscript.

Conflict of interest: Authors state no conflict of interest.
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