Open Access
Add to BibSonomy
Abstract
The changing of vegetation is a sensitive signature of global warming, and satellite photon-counting laser altimeters provide an effective way to monitor the changing of vegetation. Based on the background noise difference between vegetation-covered areas and bare lands, we proposed a classification method to distinguish vegetation-covered areas from the raw photons measured by photon-counting laser altimeters in relatively flat areas. First, a theoretical noise model was established considering the influence of the sunlight incident direction and reflection characteristics of different surfaces. Second, the thresholds from the proposed theoretical model were calculated and tested to classify the along-track land-cover types for the Ice, Cloud, and Elevation Satellite-2 (ICESat-2) photon-counting laser altimeter. Then, the study areas near Seattle and Romania in summer were selected and the classification method was verified to achieve an overall accuracy of over 77% (the strong beam) and over 76% (the weak beam) for both thresholds and areas. Our method utilized the noise photons with vegetation canopy reflection information, which are enormous in quantity and easy to extract compared to the signal photons. More importantly, this method reduces the requirements of the optical images (that are used as prior knowledge). The results show that using the noise photons of the weak beam may be more potential for the classification of vegetation and land than using the signal photons of the weak beam. We extended the research on the mechanism and application of ICESat-2 in forestry.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The vegetation is an important part of the human living environment [1], afforestation can reduce air pollution [2], purify water bodies [3], conserve water [4] and soil, and regulate climate. Plants can perform photosynthesis and provide humans with primary production materials, such as wood, grain, vegetables and fruits, industrial raw materials, and medicinal materials [5]. To discover and utilize them, they must be effectively protected and studied in depth. The detection of the vegetation area is of great significance because the examination of environmental disasters (biodiversity loss, deforestation, depletion of natural resources, etc.) necessitates the computation of detection in the vegetation [6,7].
Remote sensing can be used to monitor vegetation well [8]. The most commonly used method is optical remote sensing, which has been used for vegetation classification to achieve high accuracy. However, the application of optical remote sensing also has its limitations. Except for luminous remote sensing, optical remote sensing cannot be used at night. In places where optical remote sensing images are absent, or the weather is bad (e.g., cloudy or foggy), or at night, LiDAR can make up for the defects of optical remote sensing [9]. Being able to accurately obtain three-dimensional structural information is another advantage of LiDAR, so the space-borne LiDAR has been widely used for the extraction of ground objects (e.g., vegetation) with complex three-dimensional forms. The first-generation satellite-borne LiDAR ICESat-1 has many applications in vegetation [10], but its footprint is too sparse. The second-generation satellite-borne LiDAR ICESat-2 has the advantages of multiple beams and dense footprints, which can be used to extract vegetation more finely. For instance, in this paper, we used ICESat-2 photon-counting LiDAR. To overcome the defect that the height-based classification methods [11,12] only used the geometric structure information of LiDAR signal photons and ignored the reflectance information contained in the noise photons, we first utilized the photon noise rate to classify vegetation and bare land. There were articles using photon noise rate to classify ice and snow [13,14], land and water [15], or snow and land [16]. The mechanism of target classification in these articles is that different targets have different reflectivity to sunlight, so they reflect different solar noise rates [17]. We apply the mechanism to alleviating the problem in previous studies [11,12] that classification results (especially when weak beams are used) of low vegetation and bare land are not ideal due to a lack of vegetation structure information. There is little difference in height between low vegetation and bare land, but the reflectivity of low vegetation at 532 nm is lower than that of bare land because of vegetation’s strong absorption in this band. Hence, it’s a big advantage of using our noise photon rate method (compared to the height-based methods) to separate low vegetation from the land. Another contribution of this paper is that noise photons of the weak beam were firstly utilized to do the classification.
After proposing the vegetation and land classification method based on different reflection characteristics of various land-cover types by assessing the noise rates, the method was applied to detect the along-track vegetation-covered areas and boundaries using the raw photons from the ICESat-2 LiDAR. The classification results were verified in areas near Seattle and near Romania in the summer. Finally, the factors that affect the background noise were analyzed to reveal the noise rate difference between the vegetation-covered areas and bare land.
2. Materials
2.1 Study area
In this study, two areas were used to evaluate the classification method. The first study area is near Seattle (48°25’ N, 118°8’ W) which is in America. This area is covered by low evergreen needleleaf forests and croplands (according to ICESat-2 ATL08 products) in summer. The area is about 30 square kilometers and the terrain is flat. The climate here is a temperate marine climate. On 27/08/2020 (in summer), the ICESat-2 flew over Seattle in the daytime. Figure 2(a) illustrates the Sentinel-2 imagery and one of the ICESat-2 ATLAS laser trajectories in Seattle (using a red line and with an along-track distance of approximately 8 km). In Fig. 1(a) and Fig. 1(b), the points represent the captured raw photons of the strong beam and the weak beam along the laser trajectories in Fig. 2(a).
Fig. 1. Along-track raw photon points from the ICESat-2. (a) Raw photons (the strong beam) near Seattle. (b) Raw photons (the weak beam) near Seattle. (c) Raw photons (the strong beam) near Romania. (d) Raw photons (the weak beam) near Romania.
Fig. 2. ICESat-2 ATLAS laser trajectories (using red lines) and Sentinel-2 imageries. The strong beam and weak beam of the same pair are very close, only 90 m apart, so they are represented by a red line. (a) Imagery near Seattle. (b) Imagery near Romania.
The second study area is near Romania (44°9’ N, 26°50’ E) which is in East Europe. This place is a plain area covered by land and vegetation. The area is about 20 square kilometers. The topographic relief is small and the climate is the temperate continental climate in this area. On 17/07/2020 (in summer), the ICESat-2 flew over Romania in the daytime. Figure 2(b) illustrates the Sentinel-2 imagery and one of the ICESat-2 ATLAS laser trajectories near Romania (using a red line and with an along-track distance of approximately 7 km). In Fig. 1(c) and Fig. 1(d), the points represent the captured raw photons of the strong beam and the weak beam along the laser trajectories in Fig. 2(b).
2.2 ICESat-2 / Atlas data
In this study, the ICESat-2 ATL03 datasets were used, which contain the raw photons recorded with the unique time tag, latitude, longitude, and WGS84 ellipsoid elevation. The new ICESat-2 photon-counting LiDAR has six individual transmit beams (three strong beams and three weak beams). We selected two strips of data. Figure 1 shows the data of ICESat-2 ATL03. One strip of data was acquired on 27/08/2020 (in summer), the other strip of data is acquired on 17/07/2020 (in summer). Figure 1(a) shows the along-track raw photon points from the ICESat-2 strong beam (ATL03_20200827143510_09660802_004_01, GT2L). The y-axis represents the ellipsoid height in meters, and the x-axis represents relative ICESat-2 along-track distance. These photon points were captured in the daytime when the solar-induced background noise is strong. Figure 1(b) presents the weak beam of Fig. 1(a). Figure 1(c) and Fig. 1(d), present the other strip of data (ATL03_20200717065823_03350802_004_01, GT1L/GT1R) of the second study area. It can be seen that noise photons above the land are denser than those above the vegetation in the strong beam. However, the signal photon rate of vegetation is close to the surrounding noise photon rate in the weak beam. In other words, for the weak beam, it is difficult to distinguish the vegetation structure from the raw data.
2.3 Sentinel imagery
Sentinel-2 is a polar-orbiting multi-spectral high-resolution imaging mission of the European Space Agency (ESA). It is used for land monitoring to provide images of vegetation, soil and water cover, inland waterways, and coastal areas. The Sentinel-2A satellite was launched on June 23, 2015, and the Sentinel-2B satellite was launched on March 7, 2017. The revisit time of Sentinel-2 is 5 days. The Sentinel-2 satellite carries a multispectral instrument (MSI) that can cover 13 spectral bands, including red band, blue band, green band, near-infrared band, and so on. As Fig. 2 shows, in this study, we used two imageries of Sentinel-2. Both imageries were acquired in the summer of 2020. These imageries were downloaded from Google Earth Engine, and some pre-processing has been done.
The NDVI (Normalized Difference Vegetation Index) was applied to obtain the ground truth of vegetation-cover areas in our study area [18,19]. Specifically, the NDVI was calculated based on two bands (i.e., the visible red and short-wave infrared) from the Sentinel-2 data. Then, a threshold was determined based on the frequency distribution of the NDVI for the extraction of vegetation information. The NDVI can be calculated as follows
where R corresponds to the visible red (0.65∼0.68 µm, the fourth band of Sentinel-2) and $NIR$ represents the short-wave infrared (0.785∼0.9 µm, the eighth band of Sentinel-2). Based on the satellite imageries captured in the summer of 2020, the along-track land-cover types (i.e., the bare-land or vegetation-covered area) can be obtained accordingly.3. Methods
We established the noise rate model of the vegetation area and compared it with the noise rate of the bare land, thus proposing the land-cover classification method.
3.1 Noise rate model in vegetation area
The mechanism of noise photons has been clarified [16,17], there are numerous noise photons evenly distributed in the range gate, which makes it easy to extract noise photons and estimate the noise rate. The noise rate ${f_n}$ in units of Hz usually represents the noise level of a photon-counting LiDAR and can be calculated by the mean number of noise photons within a fixed time interval. According to the classical model of Degnan [20], assuming that the ground is Lambertian, the solar-induced noise received by a LiDAR over the bare-land area can be expressed by Eq. (2).
Figure 3 demonstrates the geometry of the solar radiation reflected by the surface of the vegetation canopy and received by the laser altimeter. In Fig. 3, the right-handed coordinate system is centered at the laser beam center, with the $x$-axis pointing to the along-track direction and the $z$-axis pointing to the zenith direction.
Fig. 3. The geometry of the solar irradiance that is reflected by the surface of the vegetation canopy and received by a space-borne laser altimeter.
It should be noted that the reflectance of vegetation surface is different from that of bare land, so the noise rate model of vegetation canopy is also different. The theoretical noise rate received by a laser altimeter over vegetation-covered areas can be then calculated by replacing the land reflectivity in Eq. (2) with the BRDF (Bidirectional Reflectance Distribution Function) [21] and is expressed in Eq. (3).
The reflectance of the vegetation canopy is very special. The SAIL model [22] considers it as a function of leaf reflectivity, leaf transmittance, soil reflectivity, leaf angle distribution, leaf area index, solar azimuth angle, and observer azimuth angle. In this formula, the canopy reflectivity is calculated by the SAIL model in Eq. (4).
In the above formula, ${\rho _{leaf}}$ denotes the leaf reflectivity; ${\tau _{leaf}}$ represents the leaf transmittance; ${\rho _{soil}}$ is the background soil reflectivity; $LAD$ is the leaf angle distribution; $LAI$ is the leaf area index; ${\theta _s}$ is the solar zenith angle; ${\theta _v}$ is the observer zenith angle; ${\varphi _s}$ is the solar azimuth angle, ${\varphi _v}$ is the observer azimuth angle and $\Psi $ is the angle between the solar azimuth angle and the observer azimuth angle. If the system parameters are given, the theoretical noise rate from a bare-land and vegetation-covered surface can be calculated in different solar irradiance conditions and atmospheric transmittances.
3.2 Land-cover classification method
Based on the former analysis, the procedure of the classification method to distinguish the vegetation-covered area is illustrated in Fig. 4. The DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm [23] is a spatial density-based signal extraction method. In each divided along-track segment, the ${f_n}$ is the statistical noise rate. ${P_{th}}$ is the theoretical threshold which can be calculated using Eq. (5). The reference noise rate is calculated using the threshold and will be used to distinguish the land-cover type.
First, the auxiliary data, such as the solar zenith angle, the atmospheric transmittance, the land reflectivity, and the system parameters substituted in Eq. (2) and Eq. (3), and the theoretical threshold ${P_{th}}$ in Eq. (3) can be estimated by the ratio of ${f_L}$ to ${f_v}$ that are defined by Eq. (2) and Eq. (3), respectively. Normally, ${P_{th}}$ is larger than the noise rate ratio between the vegetation-covered area and bare-land surface, which will be quantitatively analyzed in the following section.
- 1. Calculation of noise rate. Given that the ICESat-2 ATLAS range gate is approximately 800 m in vertical, the noise photon number is counted using the photons within the vertical window at the elevation between the terrain profile and the maximum elevation. In areas above the tree height and below the ground, noise photons are distributed in large numbers. We use these noise photons to calculate the noise rate. In Eq. (6), $\varDelta N$ is the total number of noise photons within a certain elevation range, $\varDelta h$ is the certain elevation range
- 2. Determination of classification threshold. Taking the data measured in Seattle for example, the raw photons in every 10 m along-track distance were divided into a segment and the step size of the adjacent segment is set as 10 m, considering that the resolution of the sentinel image used is 10 meters and the individual vegetation is relatively small. We substitute the information (e.g., solar zenith angle) in the ATL03 product into Eq. (5) to determine the threshold ${P_{th}}$ in Fig. 4 and do the classification.
3.3 Validation and assessment
As mentioned before, we used the Sentinel-2 imagery to do validation and assessment. The NDVI (Normalized Difference Vegetation Index) was applied to obtain the ground truth of vegetation-cover areas in our study area. More specifically, the validation is shown in the results in the next part.
The threshold derived from the theoretical model was applied to detect the vegetation-covered area from raw photons of the strong beam or weak beam. In addition, the official ATL08 dataset provides rough land-cover types, which were compared with our classification results. We utilized many tools (e.g., confusion matrix [24], kappa [25]) to analyze the results. Our LiDAR classification results were verified by the truth values of NDVI obtained from the corresponding Sentinel-2 optical images. Through verification, we found that many factors will affect the accuracy of the model (e.g., leaf area index $LAI$ and soil moisture), so we conducted a coupling sensitivity analysis of multiple factors and analyzed the gap between the results of our study area and the results in other cases.
4. Results
The proposed classification method was then used to classify the land-cover types for raw photons in another ICESat-2 laser trajectory.
4.1 Classification results
In Fig. 5, the calculation results of the noise rate are illustrated. Figure 5.(a) shows the along-track raw photons from the ICESat-2 strong beam, which corresponds to the area in the yellow box in Fig. 2(a). The x-axis represents the ellipsoid height in meters, and the y-axis represents relative ICESat-2 along-track distance. Raw photons marked with green were used to estimate the noise rate. These noise photons are within the vertical window at a certain elevation range. In the same way, Fig. 5.(b) (c) (d) can be obtained.
Fig. 5. The photons used from the ICESat-2 beams. (a) The strong beam near Seattle. (b) The weak beam near Seattle. (c) The strong beam near Romania. (d) The weak beam near Romania.
In Seattle, a sampled along-track segment was enlarged to show the details in Fig. 6(a), which corresponded to the whole part of the whole trajectory in the yellow box in Fig. 2(a). The classification results from the ATL08 rough land-cover types, the threshold based on the theoretical model (the strong beam), and the threshold based on the theoretical model (the weak beam) are shown in the left, central, and right columns of Fig. 6(b), respectively. It should be noted that in Fig. 6(b), the x-axis of the central and right columns represents the noise rates in units of megahertz to demonstrate the differences between the vegetation-covered areas and bare land, whereas the x-axis of the left column (ellipsoid height in meters) is the along-track terrain surface provided by ATL08 datasets. In Fig. 6(b), the green points correspond to vegetation-covered areas, the yellow points correspond to bare land. The central and right columns in Fig. 6(b) correspond to the classification results of the strong beam and the weak beam from the threshold based on the theoretical model, respectively.
Fig. 6. Classification results of the first area. (a) Near Seattle, it corresponds to the area in the yellow box in Fig. 2(a). (b) Comparison among different classification results.
Similarly, near Romania, a sampled along-track segment was enlarged to show the details, which corresponded to the part of the whole trajectory in the yellow box in Fig. 2(b). The symbols used in Fig. 7 are identical to those in Fig. 6. Then, in two study areas, the quantitative analysis of the whole classification results is shown in Table 1 as a confusion matrix. In ${N_{ij}}$ of the confusion matrix, i corresponds to the classification result of the algorithm (1 = vegetation-covered, 2 = bare-land), j corresponds to the true cover type (1 = vegetation-covered, 2 = bare-land). ${N_{11}}$ represents the samples that belong to vegetation-covered types and were correctly classified as vegetation-covered types, ${N_{21}}$ represent the samples that belong to vegetation-covered types but were wrongly classified as bare-land types. ${N_{12}}$ and ${N_{22}}$ are counted similarly.
Fig. 7. Classification results of the second area. (a) Near Romania, corresponds to the area in the yellow box in Fig. 2(b). (b) Comparison among different classification results.
Table 1. Land-cover type classification results using the confusion matrix
In both study areas, the comparison indicates that using the threshold based on the theoretical model achieves good accuracies for the strong beam and the weak beam. Near Seattle, the trained threshold of the strong beam achieves the classification result with an Overall Accuracy of (OA = 77.24%) and Kappa coefficient of 0.5996. Near Romania, the trained threshold of the strong beam achieves the best classification result with an Overall Accuracy of (OA = 91.31%) and Kappa coefficient of 0.8247.
It can be seen that our classification results are close to the ATL08 dataset for these two study areas. The main reason for the misclassification is that the vegetation leaves are not dense enough, so the difference between vegetation reflectance and land reflectance is not significant enough. The results of using noise photons for vegetation and land classification are not bad, but they are not as good as using noise photons for ice, water, and land classification. The strong beam has stronger energy, and the difference in noise rate between vegetation and land is greater, so this method is more suitable for the strong beam than the weak beam.
4.2 Land-cover classification under various factors
The separability of vegetation and bare land is related to various factors. Each factor impacts the noise rate of photons. In consequence, we used the SAIL model [22] to make a multi-parameter sensitivity analysis of the ratio of noise rate (${f_L}/{f_v})$, the parameters included:
- 1. Leaf area index $LAI$ and soil moisture. The leaf area index ($LAI$) is the ratio of the total leaf area (only one side) of the crop per unit of land to the land area. It refers to the denseness of the leaves and affects the reflectivity at the canopy scale. The reflectivity of the soil is different when the soil moisture changes. We conduct a coupled analysis of the $LAI$ and soil moisture. As shown in Fig. 8, when the $LAI$ is greater than about 0.7 and the soil moisture is less than about 0.6, the noise rate ratio is greater than the threshold of 3. This result was obtained when solar zenith angle ${\theta _s} = 30$°, observer zenith angle ${\theta _v} = 10$° and observer azimuth angle ${\varphi _v} = 90$° (assuming that the solar azimuth angle ${\varphi _s} = 0$°). In the first study area near Seattle, it can be seen that the signal photons of vegetation canopy were fewer than those in the second study area, which means the $LAI$ was smaller than that of the second area, so the overall accuracy was not as high as that of the second area. The temperate marine climate of the first study area was wetter than the temperate continental climate of the second area, the soil in the former area was likely to be wetter, so it can also explain why the classification result of the first area was not as good as that of the latter area.
- 2. Solar zenith angle ${\theta _s}$ and $LAI$. The solar zenith angle ${\theta _s}$ will affect the degree of separation of vegetation. Because the thickness of the vegetation canopy is different under different solar zenith angles. Through coupled analysis of the solar zenith angle ${\theta _s}$ and $LAI$, we found that the model is best when the ${\theta _s}$ is about 45° and $LAI$ is bigger than around 1. As shown in Fig. 9, this result was obtained when observer zenith angle ${\theta _v} = 10$°, observer azimuth angle ${\varphi _v} = 90$° (assuming that the solar azimuth angle ${\varphi _s} = 0$°) and soil moisture was 0.5. The solar zenith angle of the second study area was closer to 45° than that of the first study area according to the time of data acquisition, which may also explain why the classification result of the second study area was better.
- 3. Limitations of the noise rate model. Firstly, the horizontal coordinate of the measured photons (i.e., the latitude value and longitude value) was calculated based on the laser pointing angle (i.e., the location of the laser beam center), and the laser footprint is approximately 17 m in diameter. This phenomenon will introduce a higher noise rate when the laser footprint is within the bare land but near the land/vegetation boundary. Secondly, our model ignored the influence of terrain slope. At the same time, the DBSCAN algorithm is not good at extracting terrain slope in the weak beam. As a result, the noise rate will gradually increase (not sharply change) when the ICESat-2 flies from the vegetation-covered area to bare land, and vice versa. In the classification process, we have considered this phenomenon, and a threshold ${P_{th}}$ is calculated. Secondly, it is found through analysis that this method is not applicable in some cases, such as when vegetation is very sparse or soil moisture is very large. It is very difficult for dry dense forests and wet barren land to exist in one area at the same time. It is common in nature that the reflectance of land is 1.5 times that of vegetation, so we use the threshold method, which is a little different from Zhang's methods [15,16]. In future experiments, it is possible to find an ideal study area in the desert oasis.
5. Conclusions
In this paper, the theoretical model of the solar-induced background noise arising from the vegetation surface reflection of ICESat-2 LiDAR is proposed for the first time. According to the proposed model, the noise level from the vegetation surface is influenced by the solar zenith angle, the observer zenith angle, $LAI$, $LAD$ and so on. The study areas in Seattle summer were selected and the classification method was verified to achieve an overall accuracy of over 77% of the strong beam and over 76% of the weak beam. Meanwhile, the study areas near Romania in summer were selected and the classification method was verified to achieve an overall accuracy of over 91% of the strong beam and over 82% of the weak beam. Through sensitivity analysis, it is found that when the $LAI$ is greater than about 0.7, the soil moisture is less than about 60%, and the solar altitude angle is about 45°, the model can distinguish vegetation and bare land well.
This method utilizes noise photons and only consumes little processing capacity while achieving excellent classification accuracy. The noise photons are not useless, they contain the radiation information of sunlight, which is different from the geometric information recorded by signal photons. In addition, the classification method has great potential to detect low vegetation. The weak beams are firstly used in land-cover classification based on the background noise rate of ICESat-2 photon-counting LiDAR. It can be seen that using a weak beam for vegetation and land classification based on the background noise rate can obtain an accuracy not far from that of a strong beam.
Funding
Research Group of Short Pulse Laser Technology of Chinese Academy of Sciences, Condition Guarantee and Finance Department (No. GJJSTD20200009); National Key Research and Development Program of China (No. 2021YFF0704600); National Natural Science Foundation of China (42171352).
Acknowledgments
We thank the NASA National Snow and Ice Data Center (NSIDC) for distributing the ICESat-2 data and Europe Space Agency (ESA) for the Sentinel-2 imagery.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. T. Braak, “The analysis of vegetation-environment relationships by canonical correspondence analysis,” Vegetatio. 69(1-3), 69–77 (1987). [CrossRef]
2. J. Yang, J. Mcbride, J. Zhou, and Z. Sun, “The urban forest in Beijing and its role in air pollution reduction,” Urban For. Urban Green. 3(2), 65–78 (2005). [CrossRef]
3. K. V. Pawar and R. V. Rothkar, “Forest conservation & environmental awareness,” Procedia Earth Planet. Sci. 11, 212–215 (2015). [CrossRef]
4. F. Chen, MM* Zhang, H. D. Guo, S. Allen, J. Kargel, U. Haritashya, and S. Watson, “Annual 30 m dataset for glacial lakes in High Mountain Asia from 2008 to 2017,” Earth Syst. Sci. Data 13(2), 741–766 (2021). [CrossRef]
5. M. Egli, L. Alioth, A. Mirabella, S. Raimondi, M. Nater, and R. Verel, “Effect of climate and vegetation on soil organic carbon, humus fractions, allophanes, impolite, kaolinite, and oxyhydroxides in volcanic soils of Etna (Sicily),” Soil Sci. 172(9), 673–691 (2007). [CrossRef]
6. D. Kumar and S. Hiranwal, “Descriptive Study and Analysis of Forest Change detection techniques using Satellite Images,” International Conference on Smart Systems and Inventive Technology (ICSSIT) IEEE. 1228–1233 (2019).
7. S. H. Khan, X. He, F. Porikli, and M. Bennamoun, “Forest change detection in incomplete satellite images with deep neural networks,” IEEE Trans. Geosci. Remote Sens. 55(9), 5407–5423 (2017). [CrossRef]
8. A. A. Gitelson, Y. J. Kaufman, and M. N. Merzlyak, “Use of a green channel in remote sensing of global vegetation from EOS-MODIS,” Remote Sens. Environ. 58(3), 289–298 (1996). [CrossRef]
9. S. Rapinel, L. Hubert-Moy, and B. Clément, “Combined use of LiDAR data and multispectral earth observer imagery for wetland habitat mapping,” ITC J. 37, 56–64 (2015). [CrossRef]
10. X. Yang, C. Wang, F. Pan, S. Nie, X. Xi, and S. Luo, “Retrieving leaf area index in discontinuous forest using ICESat/GLAS full-waveform data based on gap fraction model,” ISPRS J. Photogramm. Remote Sens. 148(FEB), 54–62 (2019). [CrossRef]
11. B. Xza, W. Cheng, N. A. Sheng, C. Fp, A. Xx, and D. Zh, “Mapping forest height using photon-counting LiDAR data and Landsat 8 OLI data: A case study in Virginia and North Carolina, USA – ScienceDirect,” Ecol. Indic. 114, 106287 (2020). [CrossRef]
12. X. Zhu, S. Nie, C. Wang, and X. Xi, “The Performance of ICESat-2's Strong and Weak Beams in Estimating Ground Elevation and Forest Height,” IEEE International Geoscience and Remote Sensing Symposium. 6073–6076 (2020).
13. R. Kwok, T. Markus, J. Morison, S. P. Palm, T. A. Neumann, K. M. Brunt, W. B. Cook, D. W. Hancock, and G. F. Cunningham, “Profiling sea ice with a Multiple Altimeter Beam Experimental Lidar (MABEL),” J. Atmos. Oceanic Technol. 95(5), 675–677 (2014). [CrossRef]
14. R. Kwok, G. F. Cunningham, J. Hoffmann, and T. Markus, “Testing the ice-water discrimination and freeboard retrieval algorithms for the ICESat-2 mission,” Remote Sens. Environ. 183, 13–25 (2016). [CrossRef]
15. Z. Zhang, Y. Ma, N. Xu, S. Li, J. Sun, and X. H. Wang, “Theoretical background noise rate over water surface for a photon-counting lidar and its application in land and sea cover classification,” Opt. Express 27(20), A1490–A1505 (2019). [CrossRef]
16. Z. Zhang, N. Xu, Y. Ma, X. Liu, W. Zhang, and S. Li, “Land and snow-covered area classification method based on the background noise for satellite photon-counting laser altimeters,” Opt. Express 28(11), 16030–16044 (2020). [CrossRef]
17. X. Yang, Y. Wang, T. Yin, C. Wang, N. Lauret, O. Regaieg, X. Xi, and J.-P. Gastellu-Etchegorry, “Comprehensive LiDAR simulation with efficient physically-based DART-Lux model (I): Theory, novelty, and consistency validation,” Remote Sens. Environ. 272, 112952 (2022). [CrossRef]
18. S. N. Goward, B. Markham, D. G. Dye, W. Dulaney, and J. Yang, “Normalized difference vegetation index measurements from the advanced very high resolution radiometer,” Remote Sens. Environ. 35(2-3), 257–277 (1991). [CrossRef]
19. S. E. Nicholson, M. L. Davenport, and A. R. Malo, “A comparison of the vegetation response to rainfall in the Sahel and East Africa, using normalized difference vegetation index from NOAA AVHRR,” Clim. Change 17(2-3), 209–241 (1990). [CrossRef]
20. J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002). [CrossRef]
21. D. K. Mcallister, A. A. Lastra, B. P. Cloward, and W. Heidrich, “The spatial bi-directional reflectance distribution function,” ACM SIGGRAPH 2002 conference abstracts and applications. 265 (2002).
22. W. Verhoef, “Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model,” Remote Sens. Environ. 16(2), 125–141 (1984). [CrossRef]
23. M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” Int. Conf. Knowledge Discovery and Data Mining. 240(6), 226–231 (1996).
24. R. G. Congalton, “A review of assessing the accuracy of classifications of remotely sensed data,” Remote Sens. Environ. 37(1), 35–46 (1991). [CrossRef]
25. A. J. Viera and J. M. Garrett, “Understanding interobserver agreement: the kappa statistic,” Family Medicine. 37(5), 360–363 (2005).
