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Background: Determining the spatial distribution of tree heights at the regional area scale is significant when performing forest above-ground biomass estimates in forest resource management research. The geometric-optical mutual shadowing (GOMS) model can be used to invert the forest canopy structural parameters at the regional scale. However, this method can obtain only the ratios among the horizontal canopy diameter (CD), tree height, clear height, and vertical CD. In this paper, we used a semi-variance model to calculate the CD using high spatial resolution images and expanded this method to the regional scale. We then combined the CD results with the forest canopy structural parameter inversion results from the GOMS model to calculate tree heights at the regional scale. Results: The semi-variance model can be used to calculate the CD at the regional scale that closely matches (mainly with in a range from − 1 to 1 m) the CD derived from the canopy height model (CHM) data. The difference between tree heights calculated by the GOMS model and the tree heights derived from the CHM data was small, with a root mean square error (RMSE) of 1.96 for a 500-m area with high fractional vegetation cover (FVC) (i.e., forest area coverage index values greater than 0.8). Both the inaccuracy of the tree height derived from the CHM data and the unmatched spatial resolution of different datasets will influence the accuracy of the inverted tree height. And the error caused by the unmatched spatial resolution is small in dense forest. Conclusions: The semi-variance model can be used to calculate the CD at the regional scale, together with the canopy structure parameters inverted by the GOMS model, the mean tree height at the regional scale can be obtained. Our study provides a new approach for calculating tree height and provides further directions for the application of the GOMS model. Keywords: Geometric-optical mutual shadowing (GOMS) model, Semi-variance model, Canopy diameter, Tree height, Regional scale Introduction total resource utilization, biomass productivity, spatial Tree height is one of the main forest vertical structural distribution, death,rebirth,etc.(Enquist etal. 1998;Enquist parameters, and it can reflect the overall state of the forest et al. 2009; Enquist and Niklas 2001; Muller-Landau et al. structure. Moreover, tree height is the main input param- 2006;West etal. 2009). Research on tree height has far- eter for estimating forest volume and forest above-ground reaching significance for the study of forest ecosystems. biomass (AGB). It also represents a natural characteristic of The main methods of obtaining tree height in forest theallometricgrowthmechanism and an indicator of forest studies include field measurements, statistical model estimates, and physical model inversions based on field- * Correspondence: songjl@bnu.edu.cn measured data or remote sensing data. A total station State Key Laboratory of Remote Sensing Science, Jointly Sponsored by device is an instrument that is often used to measure Beijing Normal University and Aerospace Information Research Institute of tree height in the field and it provides direct, current, Chinese Academy of Sciences, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China accurate and reliable data for determining the three- Full list of author information is available at the end of the article © The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Li et al. Forest Ecosystems (2021) 8:24 Page 2 of 19 dimensional coordinates of a tree. Although the field scales is critical for improving forest studies and measurement method can obtain tree height with high developing long-term strategies for forest ecosystem accuracy, the detected area is limited due to the substan- protection. tial technical requirements and material resource costs. The geometric-optical mutual shadowing (GOMS) In forest science studies, statistical regression methods model increases the suitability of the geometric-optic have been widely used to investigate vegetation parame- model for highly dense canopy forests (Li and Strahler ters of forests, and according to the principles of tree 1992) and is particularly suitable at the regional scale. growth, the tree height in a specific zone is highly corre- The GOMS model describes the tree canopy 3-D lated with numerous forest parameters, including the structure and successfully establishes the relationship diameter at breast height (DBH) (Ercanlı 2020) and between forest structure parameters (e.g., average vege- stand age (Xiong et al. 2016). Richard (Carmean and tation coverage, average tree height, crown size) and the Lenthall 1989; Payandeh 1974; Payandeh and Wang canopy bidirectional reflection distribution function, 1994a), Logistic (Chen et al. 1998; Nigh and Sit 1996; yielding the relationship between canopy structure Thrower and Goudie 1992; Wang and Klinka 1995), and parameters (e.g., clear height, crown radius, forest Weibull (Payandeh and Wang 1994b; Yang et al. 1978) canopy distribution) and the canopy reflection character- are the most frequently used statistical models to esti- istics (Li and Strahler 1985). Then, forest canopy struc- mate tree height. However, these statistical models are tural parameters can be inverted by the GOMS model. primarily based on field measurements, and obtaining However, the GOMS model can obtain only the ratio the stand age and DBH at the regional scale is unfeas- between different canopy structural parameters, such as ible. Statistical models are not well-suited for calculating b/R and h/b, in which R represents the horizontal radius tree height at the regional scale. With the development of an ellipsoidal crown, b represents the vertical half axis of remote sensing science and technology, remote sens- of an ellipsoidal crown, and h represents the height at ing data have been widely used to retrieve tree height. which a crown center is located (Li et al. 2015). To Laser radar technology is the main method for obtain- obtain tree height, field-measured data and LiDAR data ing high-resolution tree height data, and researchers are required to provide the canopy diameter (CD) or have developed numerous algorithms to derive tree clear height (Fu et al. 2011; Ma et al. 2014). Realistically, height from LiDAR data (Nelson et al. 1997; Nilsson in tree height studies, high-accuracy field-measured data 1996). Airborne laser scanning (ALS) provides 3D struc- and LiDAR data are not always available at the regional ture information as well as the intensity of the reflected scale. Easily and cheaply providing CD or other canopy light and has become established as an important instru- structure parameters as prior knowledge for the tree ment in forestry applications (Edson 2011). ALS has height calculation process through the GOMS model is been successfully used to estimate the canopy height, an important and meaningful research direction in tree leaf area index (LAI), biomass and other variables height studies. Therefore, in this study, we attempted to (Dubayah et al. 2010; Lefsky et al. 2005; Lefsky et al. build a method for calculating the CD or clear height 2007; Ma et al. 2014; Riaño et al. 2004). Data from ALS with optical remote sensing data instead of field- can provide precise individual tree detection (ITD), and measured and LiDAR data; then, tree height at the researchers use the spectral (Breidenbach et al. 2010; regional scale can be easily obtained using the GOMS Heinzel and Koch 2012; Leckie et al. 2003) and intensity model. We learned from the research of Song et al. information (Huo and Lindberg 2020) for ITD studies. (2010), who successfully calculated CD by using high- Lefsky et al. (2002) showed that together with the re- resolution imagery, and applied the CD calculation mote sensing of topography, the three-dimensional method to the regional scale. We chose the Dayekou structure and function of vegetation canopies can be dir- forest study site as a study area, used a semi-variance ectly measured and forest stand attributes accurately model to calculate the CD, and then extended this predicted. Means et al. (1999) reported that compared method to the regional scale. Then, combined with the with field-measured tree height, large-footprint, airborne canopy structural parameters inverted by the GOMS scanning LiDAR can be used to precisely characterize model, including b/R and h/b, tree height (H = h + b) stand structure with R equal to 0.95. However, the weak could be calculated. The accuracy of the estimated tree penetration of laser pulses in dense forest coverage height was validated using canopy height model (CHM) makes it difficult to obtain the forest canopy vertical data derived from LiDAR data. structural parameters using this method, and the high cost and the lack of mapping capacity also limit the ap- Materials and methods plication of ALS at regional and global scales (Sun et al. Study site 2006; Swatantran et al. 2011). Thus, developing a The study site, Dayekou forest (100° E, 38.6° N), is method to obtain tree height at regional and global located in the Qilian Mountain area of Gansu Province, Li et al. Forest Ecosystems (2021) 8:24 Page 3 of 19 China. The Heihe Basin is the second largest inland river Field-measured data (Chen and Guo 2008) were used to basin of the arid region in northwestern China, with construct a prior knowledge database of the canopy annual precipitation of 140 mm (Li and Xu 2011) in the structural parameters for the GOMS model. middle valley. Dayekou is located in the middle valley of The protocols for each instrument used in the sample the Heihe River Basin, and most of the area is covered plots and the sample-plot layouts were as described in a by forest and upland meadow. The main vegetation previous study (Fu et al. 2011). types in the Dayekou forest are Picea crassifolia, shrubland and upland meadow, and the dominant forest Bidirectional reflectance data and high spatial remote type is P. crassifolia. sensing data The locations of the field measurement sample plots In this research, both bidirectional reflectance data and are shown in Fig. 1. One super sample plot sized 100 optical high spatial resolution remote sensing data were m × 100 m is located within the yellow line surrounding used. The detailed information on the datasets is the pixels as indicated within the Dayekou site. The provided in Table 1. Moderate-resolution Imaging super sample plot was divided into 16 parts, each sized Spectro Radiometer (MODIS) and Multi-angle Imaging 25 m × 25 m. In each small sample plot (B 1–16), all Spectro radiometer (MISR) reflectance products were parameters related to trees were measured, including used to build the multi-angle bidirectional reflectance LAI and canopy structure parameters (tree height, (BRF) datasets (Fu et al. 2011; Li et al. 2015), which were canopy diameter, etc.). The field-measured canopy struc- the input data in the canopy structure parameter inver- ture parameters measured in these super sample plots sion process performed by the GOMS model. SPOT-5 are described in the section of field-measured data. The data can be used to acquire the spectral information (G, super sample plots were relatively homogeneous. C, Z and T) (Fu et al. 2011), and we also used the SPOT-5 image to perform the supervised classification Data foundation with the Environment for Visualizing Images (ENVI; Field-measured data Exelis, Inc., Boulder, CO, USA) to provide the landcover Field measurements in the super sample plots were information for the CD calculation process in the performed in June 2008. The measured geometrical section of tree height and CD results derived from the structural parameters included the horizontal radius of CHM data (Fig. 11). Airborne CCD multi-band imagery the tree crown (R), tree height (H), clear bole height (h), (Li et al. 2017; Xiao 2018) was used to calculate the and DBH. The height of each tree in the super sample spatial variation in the study area with the semi-variance plots was measured via a laser altimeter (TruPulse 200, model in the section of tree height and CD results Laser Technology Inc. (LTI), Norristown, PA USA). derived from the CHM data (Fig. 2) (Song et al. 2010). Fig. 1 Standard false color image (SPOT-5) of the experimental sites. The super sample plot is outlined in black. The area outlined in yellow of this map is the same as that of the CCD image shown in Fig. 2 Li et al. Forest Ecosystems (2021) 8:24 Page 4 of 19 Table 1 List of remote sensing data sensors receive the ground reflection and the crown reflection in the field of view A (“A” is the assumption Data Acquisition time Spatial resolution (m) that the area of the field of view is A). BRF datasets 1 May to 28 July 2008 500 (MODIS) Considering the 3-D forest canopy structural parame- 1000 (MISR) ters, the influence of sky light, and multiple scattering, SPOT 10 August 2008 10 the received signal of A can be defined as a combination Airborne CCD 26 July 2012 0.2 of the four area-weighted components: Airborne LiDAR data 28 June 2008 0.5 S ¼ K G þ K C þ K Z þ K T ð1Þ g c z t Airborne LiDAR data provided the CHM information to estimate the accuracy of the tree height inversion where S refers to bidirectional reflectance factor (BRF); results. K , K , K , and K are the proportions of sunlit back- g c z t ground, sunlit crown, shaded background, and shaded Methods crown, respectively; and G, C, Z and T are the contribu- GOMS model and inversion strategy tions of the sunlit background, sunlit crown, shaded The GOMS model was constructed based on the Li- background, and shaded crown, respectively (Li and Strahler geometric-optical model (Li and Strahler 1992), Strahler 1986). which assumes that the reflectance of a pixel can be Assuming that the tree crown shape is ellipsoidal modeled as a sum of the reflectance of its individual (Fig. 3a), K , K , K and K can be expressed by a com- g c z t scene components weighted by their respective areas bination of the forest canopy structural parameters such within the pixel (Li and Strahler 1985) and that the vege- as R, b, h and n (the number of crowns per unit area). tation canopy bidirectional reflectance distribution func- In the GOMS model, the ellipsoid model is simplified tion (BRDF) characteristics at the pixel scale can be into a spheres model (Fig. 3b); then, K , K , K and K g c z t explained by the geometric-optical principle. The can be expressed as: Fig. 2 CCD image of the Dayekou site Li et al. Forest Ecosystems (2021) 8:24 Page 5 of 19 Fig. 3 a Forest canopy shape as an ellipsoid. b A single sphere viewed at position v and illuminated at position i (Li and Strahler 1992). θ and θ i v are the revised solar zenith angle and view zenith angle, respectively. ∅ and ∅ are the solar azimuth and view azimuth, respectively. ∅ −∅ is i v i v the azimuthal difference between the illumination and viewing directions. τ and τ are the sunlit shadow and viewed shadow, respectively. The i v shaded area is the mutual shadowing area of the sunlit shadow and viewed shadow affects the outward width of the hot spot; and Δh/b K ¼ expðÞ − n ½ τ þ τ − OðÞ θ ; θ ; ∅ −∅ð2Þ g i v i v i v describes the discrete degree of the crown height distri- where bution and affects the bowl-shape of the BRDF (Δh is the variance of the h distribution in one pixel) (Li et al. τ ¼ πR = cosθ ð3Þ i i 2015). θ and ∅ are the local slope and aspect, respect- s s ively. θ , ∅ , θ and ∅ are the solar zenith angle, solar τ ¼ πR = cosθ ð4Þ i i v v v v azimuth, view zenith angle, and view azimuth, respect- and O(θ , θ , ∅ −∅ ) is the shaded area in Fig. 3b. ∅ i v i v i ively (Fu et al. 2011; Ma et al. 2014). In this study, we and ∅ are the solar azimuth and view azimuth, respect- v assume that the reflected intensities of the shadow on ively, and θ and θ are the revised solar zenith angle and i v the ground and on the canopy are the same (i.e., Z view zenith angle, respectively: equals T). Thus, the model is simplified with three area- weighting components (G, C and Z). − 1 θ ¼ tan ðÞ b=R tanθ ð5Þ i i The multi-stage, sample-direction dependent, target- decisions (MSDT) inversion method (Li et al. 1997) was − 1 θ ¼ tan ðÞ b=R tanθ ð6Þ adopted to segment invert the observation data and the v v parameters in the GOMS model. In this method, the ′ ′ where θ and θ are solar zenith angle and view zenith most sensitive observation data were used to invert the i v angle, respectively. most sensitive parameters; then, the previous inversion results were used as the prior knowledge in the next par- DE 1 ! ameter inversion stage. The parameter inversion order is K ¼ 1 − exp − n 1 þ i ; v τ ð7Þ c v based on the uncertainty and sensitivity matrix (USM), DE which presents the sensitivity of the parameters to the 1 ! K ¼ exp − n 1 þ i ; v τ − expðÞ − n τ t v v observational data in different viewing directions. The USM function can be expressed as ð8Þ ΔBRFðÞ p; q K ¼ 1 − K − K − K ð9Þ z g c t USMðÞ p; q ¼ ð11Þ BRF ðÞ p exp Then, the GOMS model can be expressed by the func- tion below: where ΔBRF(p, q) is the maximum difference of BRF cal- culated by the model when only parameter q changes in S ¼ f θ ; ∅ ; θ ; ∅ ; θ ; ∅ ; nR ; b=R; h=b; Δh=b; G; C; Z; T ð10Þ i i v v s s its uncertainty and other parameters remain fixed, and where nR represents the crown coverage condition BRF (p) is the BRF calculated by the model at the p exp th per unit area in the nadir observation, b/R affects the geometry of illumination and viewed with all parameters crown coverage density in the non-nadir direction; h/b at their expected values. Based on our previous study Li et al. Forest Ecosystems (2021) 8:24 Page 6 of 19 (Fu et al. 2011), the inversion order of all the parameters the semi-variance and can be used to study the spatial in the GOMS model is RC- > RG- > RZ and NIRC- > (b/ properties of the underlying scene (Song 2007). R, NIRZ, Δh/b)- > NIRG- nR . RC-RG-RZ refers to the A semivariogram contains three parameters: the sill, BRF information of sunlit crown, sunlit background, and the range and the nugget effect. The sill is the maximum shaded area in the red band, and the NIRC-NIRG-NIRZ value of semi-variance that presents the total variance of refers to the BRF information of the sunlit crown, sunlit the scene, and it can be calculated by the semi-variance background, and shaded area in the near-infrared (NIR) model. The range is the distance at which the semi- band. Then, the parameters in both the NIR and red variance reaches the sill value, which reflects the scale bands were used to calculate h/b. From the inversion characteristics of the scene. When the distance between order results, R (R = CD/2) was not a very sensitive points in space is equal to or greater than the range, parameter in the GOMS model; thus, using the CD pro- these points can be considered to be independent of vided by other data sources as prior knowledge in the each other. The nugget effect is the semi-variance at lag GOMS model inversion procedure to calculate tree zero. height would not cause substantial error. The semi-variance model is defined as follows: Semi-variance model γ ðÞ h ¼ EfðÞ ðÞ x − fðÞ x þ h ð12Þ The semi-variance model is a tool to build the relation- ship between the underlying scene and the image spatial where γ (h) is the semi-variance for points with lag h in properties and the image spatial properties can be mea- space, f(x) is the realization of a spatial random function sured by calculating the spatial variation of a spatial ran- at location x,f(x + h) is the realization of the same func- dom variable. In a remote sensing image, each digital tion at another point with lag h from x, and E(.) denotes number (DN) is linked to a unique location on the the mathematical expectation (Song et al. 2010). ground and can be considered the realization of a spatial Based on the semi-variance model and the theory of random function: DN =f(x ), where DN is the digital Jupp et al. (1988, 1989), the disc scene model was devel- i i i number for the i pixel, x is the geographic location oped, which simplifies the representation of a forest th i vector for the i pixel, and f is the random spatial func- scene. The model assumes a scene that is composed of th tion. The DN of a remotely sensed image can be treated discs, and the brightness value of a disc does not change as a spatial random variable. Therefore, the image spatial in overlapped areas. The model is constructed from the properties can be estimated by calculating the spatial relationship between the scene structure and the spatial variation in DN. characteristics of image DNs. Based on the disc scene A semivariogram (Fig. 4) is a plot of semi-variance model, Song et al. (Song 2007; Song et al. 2002; Song against the lag that separates the points used to estimate and Woodcock 2003) developed a model that relates the Fig. 4 Typical shape of a semivariogram over a stationary scene (Song 2007) Li et al. Forest Ecosystems (2021) 8:24 Page 7 of 19 ratio of the sill at two spatial resolutions to the diameter h s ¼ ð16Þ of the object as follows: tD p1 cos ¼ s ð17Þ λA T − 1 1 D 0 2 tTðÞ t e dt z1 In Eq. (13), the ratio of the sill of the regularized vario- ¼ ð13Þ tD C p2 z2 R λA T − 1 gram of two different spatial resolutions would be solely tTðÞ t e dt determined by the scene structure, which is independent of the brightness value of the pixels. Therefore, the ratio of image variances can be used to estimate the tree where D and D are the pixel sizes of the two spatial p1 p2 crown size across sensors and sites. resolutions; D is the diameter of the object (forest CD); and C and C are the sills of the regularized semivar- z1 z2 Flowchart of the methods iograms at spatial resolutions D and D , respectively. p1 p2 Figure 5 shows a flowchart of our method, which γ is used to denote the ratio (C /C ) described in z1z2 z1 z2 consists mainly of three parts: the first for the CD the latter part of the paper (e.g., γ denotes the ratio of calculation process based on the semi-variance model, the image semi-variance at a spatial resolution of 1 m to the second for the tree height estimation process that at 2 m). using the CD results from part 1 along with the in- ‘A’ represents the object area: version results obtained from the GOMS model, and the third for the tree height accuracy validation πD A ¼ ð14Þ process. In the CD calculation process, we applied the CD estimation process of Song et al. (Song 2007;Song T(t) represents the overlap function for the objects in et al. 2002; Song and Woodcock 2003)tothe Daye- the scene: kou forest site using the regularized semi-variance model and high spatial resolution CCD imagery. The h ¼ 0 optimal fitting function between the sill and the field- TsðÞ ¼ ðt − sin ðÞ t Þ h < D ð15Þ measured CD was constructed based on the 16 super h≥D sample plots. We first cut the 16 sample plots out of where the CCD image employing binarization, then Fig. 5 Flowchart of the method Li et al. Forest Ecosystems (2021) 8:24 Page 8 of 19 Fig. 6 Correlation between the tree height derived from CHM data and the field-measured tree height at the single-tree scale resampled the binary results to different spatial reso- the whole image. We also used the CD derived from lutions (1, 2, … 6 m), and finally calculated the sill ra- the CHM data to analyze the accuracy of the CD data tio value of the 16 images at a different spatial calculated based on the CCD image. resolution. Second, we built the function between the Canopy structural parameters could be inverted by the field-measured CD and the sill ratio value and se- GOMS model, and in combination with the CD results lected the best fitting relationship as the optimal fit- described above, tree height can be estimated. Finally, ting function. Using the supervised classification we used the revised CHM data derived from LiDAR to results for the SPOT-5 image, the method was ap- validate the tree height accuracy calculated by the plied first to the experimental small plot and then to GOMS model. Fig. 7 Tree height derived from the CHM data at a 25-m spatial resolution Li et al. Forest Ecosystems (2021) 8:24 Page 9 of 19 Results derived from the CHM data and the field-measured Tree height and CD results derived from the CHM data CD of the super sample plots. The single-tree points Since there was not enough field-measured tree in the CHM data with tree height error ranges height data for our study area, CHM data rather smaller than 10% compared with field-measured tree than field measurement data were used to provide heights were selected to build the function shown in the tree heights for the inversion results validation Fig. 8. The results showed that tree height derived process. Local filtering with a canopy height-based from the CHM data had a linear relationship with variable window size (Popescu et al. 2002) was used the field-measured CD values, with a high determin- to identify asingletreetoextract the single-tree ation coefficient of 0.61. Thus, we used the function height within the super sample plot. The results in Fig. 8 to calculate the CD (Fig. 9) as a reference showed that the field-measured tree height and the for the validation process of the CD results calcu- extracted single-tree height based on the CHM data lated in the section of canopy diameter results esti- have a high correlation, with an R equals value of mated by the semi-variance model. 0.72 (Fig. 6). The CHM data can be used to provide single-treescaletreeheightinformation. Canopy diameter results estimated by the semi-variance We further set the sampling unit to a size of 25 model m × 25 m and extracted all single-tree heights in each sampling unit, then calculated the mean value of all In our study, each of the super sample plots had a single trees as the mean tree height of this sampling size of 25 m × 25 m; therefore, in this part, all the unit. In this section, the function in Fig. 6 was used sample plots used to calculate the CD are 25 m × 25 to revise the CHM data. After the removal of the m. The mean field-measured CD of each sample plot non-forest pixels based on the supervised classifica- can be calculated as follows: tion results indicated in the section of supervised classification results based on the SPOT image, the sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ mean tree height distribution map of the study area 2 CD i¼1 CD ¼ ð18Þ at a 25-m spatial resolution was generated, as shown in Fig. 7. LiDAR data have typically been used to calculate CD in forest studies (Popescu et al. 2011)when where CD is the mean CD of the plot, n is the number field-measured CD values are not available. We con- of trees within the plot, and CD is the individual tree structed the relationship between the tree height CD within the stands. Fig. 8 Correlation between tree height derived from the CHM data and the field-measured CD data Li et al. Forest Ecosystems (2021) 8:24 Page 10 of 19 Fig. 9 CD derived from the CHM data based on the function indicated in Fig. 8 Optimal fitting function between the sill and field-measured on the super sample plots (e.g., sample plots No. 4 and canopy diameter No. 5 contained a large hole and presented low LAI with The optimal fitting function between the sill and the reduced canopy density), only 13 sample plots were field-measured CD is constructed based on the 16 super selected to provide the CD data for the modeling sample plots. The mean field-measured CD is calculated process. The results in Table 1 show that the ratios (γ ) according to Eq. (18). Because of the low binarization between the sill under 2-m and 5-m spatial resolution accuracy (e.g., at sample plot No. 14, the quality of the conditions are the most accurate for estimating the CD, CCD image is low) and insufficient detailed information with an R value of 0. 72 (Fig. 10). The negative Fig. 10 Relationship between γ and CD 25 Li et al. Forest Ecosystems (2021) 8:24 Page 11 of 19 Table 2 Relationship between tree crown size and image supervised classification process was employed to select variance of multiple resolution image (R is the correlation the sample plots for further CD calculation at the re- coefficient, and R is the determination coefficient) gional scale. The maximum likelihood method in ENVI 2 2 2 R RR RR R was used to perform the supervised classification with γ 0.03 0.18 γ 0.40 −0.63 γ 0.31 −0.55 SPOT-5 data (described in the section of bidirectional 1 13 26 reflectance data and 163 high spatial remote sensing γ 0.17 0.42 γ 0.54 −0.73 γ 0.59 −0.77 2 14 34 data), and the classification result is shown in Fig. 11 γ 0.30 0.55 γ 0.66 −0.81 γ 0.65 −0.80 3 15 35 (pixels in green represent the forest coverage zone). γ 0.47 0.69 γ 0.41 −0.64 γ 0.18 −0.42 4 16 36 γ 0.60 0.77 γ 0.49 −0.70 γ 0.17 −0.41 5 23 45 Canopy diameter calculation results for a small γ 0.40 0.63 γ 0.62 −0.78 γ 0.00 0.03 6 24 46 experimental plot γ 0.26 −0.51 γ 0.72 −0.85 γ 0.13 0.36 We first applied Eq. (19) to a MODIS 500-m pixel 12 25 56 within which the super sample plots were located. The correlation (R) in Table 2 indicates that when the spatial small experimental plot information is shown below in resolution of an image decreased, the sill ratio values of Fig. 12. larger CD images decreased faster than the smaller CD Based on the classification results (Fig. 12 (upper- images; this result also supports the results reported by right)), we picked out the forest pixels and set the others Song (2007). to black (DN = 0). We next performed a binarization Therefore, the optimal fitting function between CD process with the selected forest pixels by setting the sun- and the sill ratio value was: lit forest crown area to black (DN = 0) and the shaded area to white (DN = 255) (Fig. 12 (bottom-right)). We CD ¼ -0:28 γ þ 3:94 R ¼ 0:72 ð19Þ then divided the binarization results of the small experi- mental plot into 20 × 20 parts, each sized 25 m × 25 m, and resampled each forest pixel to 2-m and 5-m spatial Supervised classification results based on the SPOT image resolutions to calculate the sill ratio value (γ ) by using As described in the section of optimal fitting function the semi-variance model described in the section of between the sill and field-measured canopy diameter, semi-variance model. Then, the CD could be estimated the optimal fitting function was built based on the for the small experimental plot. The results showed that super sample plots sized 25 m × 25 m. To apply Eq. (19) the threshold of the CD value is from 0 to 4 m, with to a larger scale, selected sample plots at a larger scale most values distributed between 2 and 4 m (Fig. 13). with areas 25 m × 25 m and high forest vegetation When the CD calculated by the semi-variance model coverage, which are highly similar to the super sample was compared with the CD based on the CHM data for plots, must first be determined. Thus, in this part, a a small experimental plot (the section of Tree height Fig. 11 Supervised classification results based on the SPOT-5 image with a spatial resolution of 25 m Li et al. Forest Ecosystems (2021) 8:24 Page 12 of 19 Fig. 12 Small experimental plot information in the area within which the super sample plots were located. True color CCD image (middle), supervised classification results (upper-right) and binarization results (bottom-right) with a spatial resolution of 0.5, 25, and 0.5 m, respectively and CD results derived from the CHM data), the differ- CHM data, but these values were highly correlated, ence value (D-value) results (Fig. 14) demonstrated that with an R value of 0.79 and an RMSE of 0.37 m the difference between the two CD data points was (Fig. 15). The validation results showed that the small, with a concentrated distribution from −1to 1m. semi-variance model can be used to precisely We also compared the CD derived from the CCD calculate CD. image of the 13 super sample plots used in Eq. (19) with the CD derived from the CHM data. The re- CD calculation results at the regional scale sults showed that the CDs derived from the CCD To expand the CD calculation process to the regional image were smaller than those derived from the scale, SPOT, CCD and CHM images with the same Fig. 13 CD derived from the CCD image Li et al. Forest Ecosystems (2021) 8:24 Page 13 of 19 Fig. 14 D-value results of comparison between the two CD datasets (CD derived from the CHM data minus the CD derived from the CCD image) coverage were used. To precisely match the supervised 0.5 m, we first transferred the supervised classification classification results based on the SPOT image with results of both the SPOT data and the CCD image to a those of the CCD image used in the semi-variance spatial resolution of 0.5 m so that the CD calculated model and to perform pixel-to-pixel comparisons of the based on the CCD image could be compared with the CD data based on the CCD image with the CD data CD derived from the CHM data pixel-to-pixel. In this based on the CHM data, these data must be pre- process, the forest pixels were defined as those with processed. As the spatial resolution of the CHM data is forest vegetation coverage greater than 0.75, which Fig. 15 Correlation between CD derived from the CCD image and CD derived from the CHM data Li et al. Forest Ecosystems (2021) 8:24 Page 14 of 19 means that in the transferred supervised classification in one 500 m × 500 m pixel, the difference in CD among results, the number of forest pixels sized 0.5 m × 0.5 m is the subpixels sized 25 m × 25 m was small. Through this more than 187 for the 25 m × 25 m area. Then, the CCD method, high-accuracy CD results at a 500-m spatial image was used to calculate CD with the supervised clas- resolution could be obtained. Combined with the inver- sification results at 25-m spatial resolution according to sion results (b/R and h/b) provided by the GOMS model, Eq. (19). The calculated CD results shown in Fig. 16 tree height at a 500-m spatial resolution could be calcu- demonstrate that most pixel values were concentrated lated (Fig. 19a). We also calculated tree height based on from 2 to 4 m. the CHM data at a 500-m spatial resolution by averaging When the CD results shown in Fig. 16 were compared all single trees in one 500-m scale pixel; the results are with the CD derived from the CHM data, the D-value shown in Fig. 19b. results (Fig. 17) showed that most D-values were con- We compared the inverted tree height calculated by centrated from − 1 to 1 m, with RMSE of 1 m for all the GOMS model and the tree height derived from the data. These results showed that this method can pre- CHM data. In the pixel outlined in black (Fig. 19) cisely calculate CD at the regional scale. wherein the super sample plots were located, the tree height calculated by the GOMS model and that derived Tree height estimated results based on the GOMS model from the CHM data were 7.34 and 9.60 m, respectively. and the semi-variance model The difference between the two tree heights was small. In this paper, the BRF datasets built as described in the We also calculated the threshold of the tree height section (Bidirectional reflectance data and high spatial (equals the mean value ± standard deviation value, with remote sensing data) were at 500-m spatial resolution. the standard deviation value calculated when upscaling Of all the inversion results, the spatial resolution of all CHM tree height from single-tree point to 500-m spatial the observational data and parameters in the GOMS resolution scale) of each pixel. The relationship between model was 500 m. However, the spatial resolution of the the thresholds and the tree height calculated by the CD data calculated by the semi-variance model was 25 GOMS model is plotted in Fig. 20a. The results showed m (the Section of CD calculation results at the regional that, most of the inverted tree heights are within the scale). When combining the CD data and the GOMS threshold range, and the GOMS model will overestimate model inversion results to calculate the tree height, we tree height with low tree height pixels. Since the GOMS transferred the CD data from 25- to 500-m spatial reso- model was more suitable for a high-FVC coverage area, lution with Eq. 18. As shown in Fig. 18, the results dem- we then compared the two different tree heights among onstrated that the standard deviation of a 500-m pixel pixels with high forest coverage ratios (greater than 0.8); was mainly concentrated at 0.5 m, which reflected that the difference between them was small, with an R value Fig. 16 CD results derived from the CCD image with a 25-m spatial resolution Li et al. Forest Ecosystems (2021) 8:24 Page 15 of 19 Fig. 17 D-value results of comparison between the two CD datasets (CD derived from CHM data minus the CD derived from the CCD image) of 0.49 and RMSE of 2.44 (Fig. 20b). The low RMSE In the validation process, the data values of the CD showed that with CD provided by another data source as (the section of CD calculation results at the regional prior knowledge for the GOMS model, tree height could scale) and inverted tree height (the section of tree height be accurately calculated for dense crown areas. estimated results based on the GOMS model and the semi-variance model) results were close to those of the validation data (with low RMSE), but the R was small. Discussion We further attempted to determine which factors influ- The results described in the section of optimal fitting enced the accuracy of the inverted tree height. Two rea- function between the sill and field-measured canopy sons were identified, as discussed herein: (1) The diameter support the research of Song et al. (2007) with inaccuracy of the tree heights derived from the CHM different sample plots of different crown sizes; when the data. In the section of canopy diameter calculation re- spatial resolution of the sample plots decreased, the sill sults for a small experimental plot, local filtering with a value decreased faster with larger crown size sample canopy height-based variable window size was used to plots than with smaller ones. Moreover, in the optimal extract single-tree points, with an R of 0.72 compared fitting function, the sill ratio was closer to the real size with the field-measured tree height. Thus, the extracted of the crown canopy than the spatial resolution of the tree height used as the true tree height of one pixel sample plots. could cause errors in the later comparison process. Fig. 18 CD upscaling results from 25- to 500-m spatial resolution. Standard deviation results (a); CD upscaling results (b) Li et al. Forest Ecosystems (2021) 8:24 Page 16 of 19 Fig. 19 Tree height calculated by the GOMS model (a); tree height derived from the CHM data (b) However, due to insufficient field-measured tree height FVC (forest coverage ratio higher than 0.8), the tree heights data, these datasets must be used to perform the valid- derived from the CHM data were slightly higher overall ation. (2) The unmatched spatial resolution of different than the tree heights obtained from the GOMS model but datasets may cause errors in the data transference also showed high correlation, with an R value of 0.79 and a process. As described in the section of canopy diameter RMSE of 1.56. The results shown in Fig. 21 were better results estimated by the semi-variance model, CD results than those shown in Fig. 20b, which means that when com- must be based on the transferred CD at 500-m spatial paring tree height calculated by the GOMS model with that resolution, referring to the effective CD of a 500 m × derived from the CHM data, the accuracy uncertainty 500 m pixel, which had a different physical meaning with emerges primarily in the process of transforming CDs to the CD (true CD) in the GOMS model. This difference tree heights. However, despite the low consistency, both may cause an error when calculating tree height using RMSEs (2.44 and 1.56) shown in Figs. 20band 21 were low, these effective CD data, especially in areas with low which demonstrates that the method detailed in our study FVC. is suitable for areas with high FVC. Since the inaccuracy caused by factor (1) was inevit- able due to the shortage of field-measured tree height Conclusions data, we conducted further testing to explore the im- In this study, we provided CD data derived from a high portance of the effect of factor (2) on the inaccuracy of spatial resolution image as a priori knowledge for the the estimated tree height result. GOMS model to obtain tree height data at the regional We combined the CD data derived from the CHM data scale. We first built the optimal relationship function be- (Fig. 9) with the canopy structural parameters inversion tween the sill calculated by the semi-variance model and data derived from the GOMS model to calculate tree height the field-measured CD, and then applied the optimal and then compared these with the CHM data. The com- function at the regional scale (the section of CD calcula- parison results (Fig. 21) showed that in the pixels with high tion results at the regional scale) to obtain CD data Fig. 20 Comparison between tree heights calculated by the GOMS model and tree height threshold derived from the CHM data (a) and tree heights derived from the CHM data (forest coverage ratio greater than 0.8) (b) Li et al. Forest Ecosystems (2021) 8:24 Page 17 of 19 Fig. 21 Comparison between tree heights calculated by the GOMS model and tree heights derived from CHM data in cases for which the forest area coverage index was greater than 0.8 covering the entire image. Moreover, by combing the relevance in the field of forest studies, especially for CD results described in the section of CD calculation re- difficult-to-reach areas or for cases in which prior know- sults at the regional scale and the canopy structure pa- ledge of forest structural parameters is lacking. There- rameters (b/R and h/b) inversion results derived from fore, in a forthcoming study, we will focus on improving the GOMS model, tree height at the regional scale could the accuracy of our modeling process and obtain multi- be obtained (the section of canopy diameter results esti- angle BRF data with higher spatial resolution to perform mated by the semi-variance model). The results showed canopy structural parameter inversions. that γ (the ratio between the sill values when the Abbreviations spatial resolution of the image was 2 and 5 m) had the 2 GOMS: Geometric-optical mutual shadowing; CD: Canopy diameter; greatest R of 0.72 with the CD. Moreover, the differ- CHM: Canopy height model; DEM: Digital elevation model; RMSE: Root mean ences between the tree heights calculated by the GOMS square error; FVC: Fractional vegetation cover; AGB: Above-ground biomass; LAI: Leaf area index; DBH: Diameter at breast height; MODIS: Moderate- model and the tree heights derived from the CHM data resolution Imaging Spectro radiometer; MISR: Multi-angle Imaging Spectro were small. We also found that the calculated tree height radiometer; BRF: Bidirectional reflectance; BRDF: Bidirectional reflectance result had high accuracy in an area with high FVC, exhi- distribution function; DN: Digital number biting an RMSE of 2.44 in the pixels for which the forest area coverage index was greater than 0.8. Acknowledgements Sincere thanks to Ma Han for sharing her datasets and method and to the However, several problems remained unresolved. For researchers who performed the field-measured work of Dayekou. example, additional field-measured data are needed for the modeling process to increase the precision of the op- Authors’ contributions timal function when using the semi-variance model to Congrong Li collected and analyzed the data and wrote the first draft. Jingling Song provided the study idea. Jinling Song and Jindi Wang calculate CD. Additionally, many pixels did not match reviewed the draft. All authors read and approved the final manuscript. the assumption of the GOMS model; therefore, BRF data at a higher spatial resolution are needed for future stud- Funding ies. Moreover, inconsistencies in the spatial resolution This research was partially supported by the National Natural Science between the calculated CD results and the inversion re- Foundation of China (No. 41871231), and partially supported by the National Key Research and Development Program of China (No. 2016YFB0501502), sults of the GOMS model can also lead to inaccurate the Special Funds for Major State Basic Research Project (No. 2013CB733403). tree height calculation results. Although there are several uncertainties with the method used in this research, our Availability of data and materials project provides a novel concept for calculating tree The datasets used and analyzed during the current study are available from height cheaply and easily, which has far-reaching the corresponding author on reasonable request. Li et al. Forest Ecosystems (2021) 8:24 Page 18 of 19 Declarations accurately estimate vegetation structural attributes and should be of particular intere. 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"Forest Ecosystems" – Springer Journals
Published: Apr 1, 2021
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