Fine-Resolution Forest Height Estimation by Integrating ICESat-2 and Landsat 8 OLI Data with a Spatial Downscaling Method for Aboveground Biomass Quantification

Abstract

Rapid and accurate estimation of forest aboveground biomass (AGB) with fine details is crucial for effective forest monitoring and management, where forest height plays a key role in AGB quantification. In this study, we propose a random forest (RF)-based down-scaling method to map forest height and biomass at a 15-m resolution by integrating Landsat 8 OLI and Ice, Cloud and Land Elevation Satellite-2 (ICESat-2) LiDAR data. ICESat-2 photon data are used to derive canopy parameters along 15-m segments, which are considered sample plots for the extrapolation of discrete forest height. Fourteen variables associated with spectral features, textual features and vegetation index are extracted from pan-sharpened Landsat 8 images. A regression function is established between these variables and ICESat-2-derived forest height to produce a 15-m continuous forest height distribution data based on the 30-m forest height product using the RF algorithm. Finally, a wall-to-wall forest AGB at 15-m spatial resolution is achieved by using an allometric model specific to the forest type and height. The Jilin Province in northeast China is taken as the study area, and the forest AGB estimation results reveal a density of 61.15 Mg/ha with a standard deviation of 89.46 Mg/ha. The $R^2$ between our predicted forest heights and the ICESat-2-derived heights reaches 0.93. Validation results at the county scale demonstrate reasonable correspondence between the estimated AGB and reference data, with consistently high $R^2$ value exceeding 0.65. This downscaling method provides a promising scheme to estimate spatial forest AGB with fine details and to enhance the accuracy of AGB estimation, which may facilitate carbon stock measurement and carbon cycle studies.

1. Introduction

The forest ecosystem plays a prominent role in regulating global carbon cycle [1]. Forests absorb and store carbon dioxide from the atmosphere, contributing to their ecological and economic value. Aboveground biomass (AGB) serves as an important indicator for measuring a forest’s carbon sequestration capacity and quantifying its contribution to the carbon cycle [2]. Accurately assessing forest AGB at a spatial level is essential for forest resource management, monitoring, biodiversity conservation and carbon neutralization [3]. Developing a rapid and accurate technique for fine-resolution AGB mapping is critical for estimating forest carbon stock estimations and studying carbon cycle.

Traditionally, forest AGB is calculated based on in-situ measurements at the plot level. Allometric equations are used to convert tree characteristics, such as tree height and diameter, into forest AGB [4]. Although this method provides accurate biomass estimate results, it is time-consuming and labor-intensive [5,6]. It lacks the ability to provide spatially continuous distribution information of forest AGB. Remote sensing technologies offer advantages in rapidly observing large-scale Earth’s surface [7,8]. It is potential to extrapolate AGB estimations from the plot to the regional level using remote sensing techniques. However, current remote sensing instruments do not directly provide forest AGB information. An effective approach is to build regression relationships between remotely sensed data and biomass, using field sample to estimate AGB [9]. In this approach, relevant features extracted from remote sensing data are considered independent variables, and AGB values from in-situ measurements are considered dependent variables. Previous studies explored machine learning methods, such as neural networks, k-nearest neighbors and support vector machines, which are nonparametric methods, for simulating forest AGB from remote sensing signals [10,11]. Particularly, the random forest (RF) algorithm is widely used because of its robustness to sample distribution and its ability to mitigate model overfitting [12].

Various remote sensing techniques have been investigated for forest AGB estimation in recent years, including optical, radar and LiDAR remote sensing techniques [13]. Optical remote sensing captures reflectance signals from the forest canopy [14]. Spectral reflectance from optical data can indicate forest distribution and state of vegetation growth, playing a fundamental role in remote sensing-based forest parameter inversion [12]. Optical data usually exhibit limited sensitivity to high biomass levels due to saturation problems [15]. Another method for regional forest AGB estimation using optical data is to classify forests into different subtypes and assign rough AGB results per subtype based on statistics from field inventory data [16]. Synthetic aperture radar (SAR) remote sensing is an alternative approach for assessing forest AGB because it captures backscattering features of the vegetation canopy, which indicate various aspects of forest stand structures [17]. SAR detects ground vegetation information using specific frequency bands, which are generally unnecessary for forest AGB estimation [18]. In addition, forests are mainly distributed in complex topography, and the impacts of altitude variation in topography restrict SAR application for forest AGB estimation [19]. LiDAR systems can capture the vertical structure of trees by recoding signals from canopy tops and ground surfaces. LiDAR data are generated as point clouds with small footprints or waveforms with large footprints. LiDAR is more suitable and provides more accurate measurements of forest height and AGB compared with optical and SAR remote sensing techniques [20]. Airborne LiDAR can estimate forest height with high precision but is usually limited to local areas due to its high cost [21]. Spaceborne LiDAR, such as Ice, Cloud and Land Elevation Satellite-2 (ICESat-2), offers the advantages of free accessibility and wide observation, making it popular for obtaining spatially vertical information on trees on a large scale [22]. However, LiDAR data are discrete and lack spatially continuous measurements [12].

Combining data from different systems is necessary to develop spatial forest AGB estimation at large scale, given the shortcomings of each remote sensing system. Optical remote sensing systems provide wall-to-wall observation, which complements the sparse coverage of LiDAR remote sensing systems. Conversely, LiDAR can directly measure forest height from space. Numerous studies have demonstrated the potentials of fusing optical and LiDAR data for forest height estimation and AGB mapping. For example, ref. [5] adopted ICESat Geoscience Laser Altimetry System (GLAS) data to extrapolate AGB value from inventory plots and mapped AGB based on corresponding forest types extracted from Landsat 7 ETM+ images. Ref. [23] predicted forest biomass at a grid size of 500 m in northeastern China using GLAS and MODIS data, reporting a satisfactory fitting result with an $R^2$ value of 0.86. Ref. [24] developed a simulated ICESat-2 vegetation canopy product and generated 30-m resolution AGB maps using spectral variables from Landsat TM images. Despite substantial progress, existing remote sensing-based AGB estimation results suffer from coarse spatial resolution, leading to mixed attributions within pixels and reduced calculation accuracy [25]. The use of moderate resolution data also limits the sensitivity of optical sensing to biomass, especially in characterizing complex forest structures within pixels, particularly in fragmented landscapes [26]. On the contrary, high-resolution images contain rich textural information, which is beneficial to non-saturating modeling of forest height and biomass [27]. Thus, refining the details of forest AGB mapping using high-resolution remote sensing data and developing fine spatial resolution forest AGB estimation techniques are necessary.

In this study, we propose an RF-based down-scaling method to map 15-m resolution forest height and biomass by combining Landsat 8 OLI and ICESat-2 LiDAR data. The main difference between this study and previous ones is that the regression relationship is established between Landsat-derived variables and the 15-m ICESat-2 derived forest height, based on the 30-m forest height product [28]. This approach allows for downscaling the forest height during the regression progress, accurately inferring fine data from relative coarse data. The methodology of this study consists of four main steps: (1) preparation of sample data of forest height from ICESat-2; (2) extraction of variables from Landsat 8 OLI data; (3) modeling the regression relationship between variables and 15-m forest height and down-scaling 30-m forest height data using the RF algorithm; (4) extrapolating continuous forest height from discrete ICESat-2 data and then estimating wall-to-wall forest AGB using an allometric model. In summary, our main contribution is the development of a new feasible method to estimate forest height with fine spatial resolution (15 m), which helps for accurate forest AGB quantification. The proposed method is validated by considering Jilin Province in northeast China as the case area, resulting in the production of a 15-m forest AGB map for the study area.

2. Data and Methods

In this study, ICESat-2 and Landsat 8 OLI data are integrated for spatial forest AGB estimation. Canopy parameters along 15-m segments are initially derived from the ICESat-2 photon data, which serve as sample plots for forest height extrapolation. Fourteen variables, including spectral features, textual features and vegetation index, are extracted from pan-sharpened Landsat 8 images. Subsequently, a regression function is established between the 14 variables and ICESat-2 derived forest height for down-scaling to produce a 15-m continuous forest height map on the basis of 30-m forest height product by using the RF algorithm. The 30-m forest height product is a free dataset developed by [28], which is mapped by the neural network guided interpolation method with the fusion of the Global Ecosystem Dynamics Investigation, ICESat-2 and Sentinel-2 data. Finally, a 15-m wall-to-wall forest AGB estimation is achieved using an allometric model specific to the forest cover type and height. The flowchart of this study is shown in Figure 1.

2.1. Forest Canopy Height Extraction from ICESat-2 Data

ICESat-2 is a spaceborne LiDAR system that utilizes photon-counting LiDAR technology [29]. It is equipped with an advanced terrain laser altimeter system (ATLAS), which emits laser pulses at a rate of 10 kHz, allowing it to capture dense photon point cloud data by observing a small spot with a high pulse repetition rate. Along its track, ATLAS transmits three pairs of beams in parallel, with each pair separated by 3.3 km and each beam within a pair being separated by 90 m. This arrangement generates footprints spaced at 0.7 m intervals with a radius of 8.5 m, providing information about the ground. ICESat-2 provides 22 data products categorized into four levels, named ATL01–ATL22. For this study, the ATL03 and ATL08 data from July 2020 to September 2020 are used for modeling 15-m forest height. These data can be freely downloaded from the official National Snow and Ice Data Center’s ICESat-2 website (https://nsidc.org/data/icesat-2 (accessed on 5 September 2022)).

ATL03 contains global positioning photon data that capture geospatial information (e.g., latitude, longitude and height) of photon clouds. ATL08 is a level 3A product that provides height estimation segments related to topography and vegetation along the track using 100-m intervals. Each photon in the ATL08 data can be linked to the corresponding ATL03 data using a unique index [30]. ATL03 and ATL08 are input into the PhoREAL software with a 15-m interval to obtain 15-m height estimation data. Each photon is classified into four categories, namely, noise, ground, canopy and top of canopy, based on a photon classification technique. The computation result of ATL03 and ATL08 is denoted as ATL03_08, which provides essential height parameters (e.g., maxima, minima and means of height) of photons per 15 m, specifically related to canopy height. In preprocessing, the footprints corresponding to canopy heights less than 2 m or belonging to non-forested areas are initially filtered out [31]. ICESat-2 ATL03_08 data may contain atmospheric and solar background noise due to the inherent limitations of the photon-counting LiDAR system [32]. The box-plot algorithm is applied to exclude outlier footprints and improve data quality. Uncertainty estimation for footprints is performed on the basis of corresponding ATL08 products, and footprints with uncertainty less than 5% are removed. The attributes of various photons from a segment may have remarkable differences. Segments in ATL03_08 data with canopy heights exceeding 1.5 times the heights of the corresponding segments in ATL08 data are eliminated to ensure a stable estimation. The remaining footprints in ATL03_08 data are considered sample plots for forest height modeling and variable extraction. The “true value” of the samples used in this study is determined by considering the 98% of maximum canopy height rather than the maximum canopy height because completely removing solar background noise is challenging, and using the maximum canopy height directly can introduce errors [31]. Finally, a total of 16,002 sample plots that note information about canopy height and corresponding predictor variables (Section 2.2) are selected within the study area (Figure 2). These sample plots are randomly split into two parts using a ratio of 75%/25% to assess the model’s performance. The training data consist of 75% of the sample plots and are utilized to develop the relationship between ICESat-2-derived forest height and variables during the downscaling of coarse resolution forest height data. The remaining 25% of the sample plots are used for model performance validation.

2.2. Variables Derived from the Landsat 8 OLI Images

Preparing optical remote sensing data in wall-to-wall forest height and AGB estimation is necessary because discrete ICESat-2 footprints cannot provide continuous coverage. Moderate-resolution Landsat 8 OLI data have been widely applied in large-scale mapping studies due to their availability and advantages in providing extensive coverage. In this study, 32 cloud-free Landsat 8 OLI images covering the study area between July and September in 2020 were obtained from the United States Geological Survey website (https://earthexplorer.usgs.gov/ (accessed on 5 September 2022)) (Figure 3). These images are processed using radiometric calibration and atmospheric correction methods in ENVI 5.3 software to transform satellite digital numbers into surface reflectance. All images are mosaicked together using the seam-line feathering algorithm and clipped by a mask of the study area. An image pan-sharpening operation is conducted to obtain more detailed surface information. Landsat 8 OLI data covering the study area with a spatial resolution of 15 m × 15 m are generated by fusing multispectral and panchromatic images.

Fourteen relevant variables are selected on the basis of considerations of spectral characteristics, texture features and vegetation index, aiming to infer the distribution of forest height at a resolution of 15 m from 30 m forest height data (

Table 1. Variables used for forest height modeling.

Variable Types	Variables	Abbreviation	Equation
Spectral features	Coastal, blue, green, red, NIR, SWIR1, SWIR2	B1, B2, B3, B4, B5, B6, B7	–
Textual features	Mean	MEA	${\displaystyle \sum _{i=0}^{N-1}}{\displaystyle \sum _{j=0}^{N-1}}{i\times P}_{i,j}$
	Homogeneity	HOM	${\displaystyle \sum _{i=0}^{N-1}}{\displaystyle \sum _{j=0}^{N-1}}\frac{P_{i,j}}{1+{(i-j)}^2}$
	Angular second moment	ASM	${\displaystyle \sum _{i=0}^{N-1}}{\displaystyle \sum _{j=0}^{N-1}}{P_{i,j}}^2$
	Contrast	CON	${\displaystyle \sum _{i=0}^{N-1}}{\displaystyle \sum _{j=0}^{N-1}}{P}_{i,j}{(i-j)}^2$
	Entropy	ENT	${\displaystyle \sum _{i=0}^{N-1}}{\displaystyle \sum _{j=0}^{N-1}}{-P}_{i,j}\times \ln P_{i,j}$
	Variance	VAR	${\displaystyle \sum _{i=0}^{N-1}}{\displaystyle \sum _{j=0}^{N-1}}{P}_{i,j}\times {(i-\mathrm{M}\mathrm{E}\mathrm{A}\mathrm{N})}^2$
Vegetation index	Normalized difference vegetation index	NDVI	$\frac{B5-B4}{B5+B4}$

Note: $N$ is the number of gray levels, and $P_{i,j}$ is the normalized gray level value of the cell $(i,j)$ of the GLCM.

). Spectral variables are widely applied in forest AGB modeling because they capture signals from canopy tops and reflect spatial continuity of the canopy [18,33]. Spectral information is valuable for inverting vegetation parameters, such as leaf area index and growing stock volume, and it has the potential to evaluate forest parameters [34,35]. The seven bands (i.e., coastal, blue, green, red, NIR, SWIR1 and SWIR2) of Landsat 8 data after image processing are used to provide canopy spectral reflectance information. Previous studies suggested that the inclusion of textural information can improve the accuracy of forest height and AGB prediction by effectively identifying forest stand structures, such as height and density [17,36]. The gray level co-occurrence matrix (GLCM) [37] can indicate textual information in images, and six texture statistics related to GLCM are computed based on the first principal component of seven bands. The extracted textures include the mean (MEA), homogeneity (HOM), angular second moment (ASM), contrast (CON), entropy (ENT) and variance (VAR) of GLCM. The GLCM textures are calculated for each pixel using a moving window with a size of 5 × 5 and a stride of 1 [38]. Additionally, vegetation index is used along with spectral and textural features to estimate fine forest height. Vegetation indices, such as the normalized difference vegetation index (NDVI), can reveal the growth status of vegetation, closely relate to forest AGB and prove useful for forest parameter modeling [39,40]. NDVI data are obtained by calculating the normalized difference between the red and NIR bands. Further details regarding all the variables are summarized in Table 1.

2.3. Spatially Continuous Forest Height Modeling by RF

In this study, Landsat 8 OLI and ICESat-2 data are combined to estimate a continuous distribution of forest height distribution at a spatial resolution of 15 m using the RF model. In the RF regression, the forest height derived from ICESat-2 data is considered the dependent variable, and the 30-m forest height data and multiple variables extracted from the Landsat 8 OLI data are used as inputs for modeling the 15-m forest height.

RF [41] is an ensemble model consisting of classification and regression trees [42], which serve as the base learners and construct diverse decision trees from different subsample spaces. RF prediction is performed by averaging the results of all decision trees. RF is known for its insensitivity to noise, resistance to overfitting problems and ability to maintain high predictive accuracy due to the ensemble learning strategy [43]. The success of RF in forest height and AGB estimation studies has been widely reported [44,45,46].

The core idea behind RF is to build and train a series of unrelated decision trees. The RF uses the bootstrap resampling technique to repeatedly and randomly select samples from the original training data, generating sample subsets. Decision trees are fitted on each subset separately to establish fitting functions. The diversity of sample subsets contributes to reducing the model’s variance and mitigating the overfitting problem. The remaining samples at each bootstrap iteration are referred to as out-of-bag (OOB) data, which are used to estimate the error rate of the RF to avoid overfitting problems. The generalization error $\epsilon$ of RF is defined as follows:

$$\epsilon \le \frac{\rho \left(1-s^2\right)}{s^2},$$

(1)

where $\rho$ represents the average correlations between base decision trees in the RF and $s$ is the average estimation of fitting powers of decision trees.

RF introduces a random selection strategy by perturbing the variable space to further reduce the generalization error. This indicates that a subset of variables is randomly selected to construct decision trees. Thus, the splitting nodes in each decision tree may be different, increasing the diversity of the base learner in the RF model. The RF method constructs decision trees using the classification and regression tree algorithm, which aims to split the data into homogeneous datasets with respect to the target variable using input variables. The classification and regression tree adopts the Gini index to measure the homogeneity of nodes in trees, where a smaller Gini value indicates higher homogeneity. The minimization of the Gini value is the optimization direction of RF. The Gini index of a dataset $T$ is calculated as follows:

$$\mathrm{G}\mathrm{i}\mathrm{n}\mathrm{i}\left(T\right)=1-\sum _{i=1}^I{p}_i^2,$$

(2)

where $p_i$ represents the probability of class $i$ in $T$.

When a node divides the dataset $T$ into two parts, denoted as $T_1$ and $T_2$, the Gini index after the node split is expressed as follows:

$$\mathrm{G}\mathrm{i}\mathrm{n}\mathrm{i}\left(T_1,T_2\right)=\frac{\left|T_1\right|}{\left|T\right|}\mathrm{G}\mathrm{i}\mathrm{n}\mathrm{i}\left(T_1\right)+\frac{\left|T_2\right|}{\left|T\right|}\mathrm{G}\mathrm{i}\mathrm{n}\mathrm{i}\left(T_2\right).$$

(3)

As trees grow and nodes split, the Gini value of the child nodes becomes smaller than that of the parent node, indicating a Gini decay in the dataset. The RF algorithm evaluates the importance level of input variables relative to the target variable by summing up the Gini decay for each single variable over all decision trees.

RF defines two important parameters for model implementation: $M_{try}$ and $N_{tree}$. $M_{try}$ controls the number of variables to be input into decision trees at each iteration. $N_{tree}$ is the number of decision trees used to construct the RF model. Through trial-and-error tests, $M_{try}$ and $N_{tree}$ are set to 5 and 200, respectively.

The coefficient of determination ($R^2$) and root mean square error ($RMSE$) are used as performance metrics to evaluate the performance of the RF-based height estimation model. On the basis of validation data, the discrepancies between the predicted canopy height from the RF model and the canopy height derived from ICESat-2 data are estimated, and $R^2$ and $RMSE$ are computed as follows:

$$R^2=1-\frac{{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2},$$

(4)

$$RMSE=\sqrt{\frac{{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{n}},$$

(5)

where $y_i$ represents the canopy height derived from ICESat-2 data, $\widehat{y_i}$ is the predicted height, $\overline{y}$ represents the mean of all canopy height values and $n$ is the number of samples.

2.4. Allometric Model for AGB Estimation

In this study, a two-step allometric model is introduced to transform forest heights into AGB [47]. The stem biomass ${AGB}_{stem}$ is calculated and adopted as an intermediate variable to derive a pair of equations for indirect estimation of AGB from heights. The forest height as an important parameter that explains approximately 87% of the variation in stem biomass, and the stem biomass reflects the nearly overall AGB situation [47]. This approach allows for the separation of error source in AGB estimation, reducing the calculation bias. The forest AGB estimation from forest heights using the two-step allometric model is expressed as follows:

$${AGB}_{stem}=a{H}^b,$$

(6)

$${AGB}_{above}=m{AGB}_{stem}^n,$$

(7)

where $H$ represents the forest canopy height. ${AGB}_{above}$ and ${AGB}_{stem}$ are the aboveground and stem biomass densities, respectively. The parameters $a$, $b$, $m$ and $n$ are used for AGB calculation and are associated with different forest cover types. In the study area, four main forest cover types are considered: deciduous broadleaved forest (DBF), evergreen coniferous forest (ECF), deciduous coniferous forest (DCF) and mixed forest (MF). The following parameter values are set for each forest cover type based on the study by [47]. For DBF: $a=0.43, b=1.96, m=1.7, n=0.94$. For ECF: $a=1.77, b=1.48, m=3.1, n=0.81$. For DCF: $a=2.17, b=1.36, m=2.09, n=0.89$. For MF: $a=0.68, b=1.79, m=1.71, n=0.95$.

3. Study Area

This study is conducted in Jilin Province, located in Northeast China (40°52′–46°18′ N and 121°38′–131°19′ E) (Figure 4). Jilin Province is one of the most important forestry provinces in China. It covers an area of approximately 187,400 km² and exhibits terrain elevation that decreases from southeast to northwest. The area is characterized by three types of landforms, namely, eastern mountainous landform, central hilly landform and western plain landform, with altitude ranges of 600–1000, 300–400 and 120–200 m, respectively. The province experiences a temperate continental monsoon climate with an average temperature of 5.2 °C and an average annual precipitation of 500 mm.

Jilin Province has a forest coverage rate of approximately 45% and a total forest stock volume of 1.96 billion m³. The forest types in the area are diverse and vary spatially due to differences in terrain and climate. Forests are mainly distributed in the Changbai Mountain in the eastern area. The Changbai mountain is home to 3980 species of forest plants, with mixed broadleaved and Korea pine forest being the dominant vegetation types. Particularly, the broadleaved forest is characterized by species, such as Fraxinus mandshurica Rup., Phellodendron amurense Rupr., Juglans mandshurica Maxim., Betula platyphylla Sukaczev, Tilia amurensis Rupr., Tilia mandshurica Rupr. & Maxim., Acer tegmentosum Maxim. and Populus davidiana Dode. The coniferous forest is mainly composed of Pinus koraiensis, Picea asperata and Abies fabri. In the low mountain and mound area of the middle-eastern Jilin Province, the originally broadleaved forest has been changed to secondary mixed broadleaved forests dominated by poplar, birch and larch plantations. The Mongolian oak sparse forest in the central area has been transformed in farmland shelterbelts dominated by poplar. The natural elm forest in the western area has been replaced by shelterbelts composed of poplar and willow. Regarding the vertical distribution of forest vegetation, the secondary mixed broadleaved forest is found in areas below 500 m. Mixed broadleaved forests and Korea pine forests are widely distributed at altitudes ranging from 500 m to 1100 m. The mountainous boreal forest dominates the area between 1100 and 1800 m. The subalpine Erman birch forest is located between 1800 and 2100 m. To estimate forest AGB using the allometric model, the forest cover types in the study area are reclassified into five classes, namely DBF, ECF, DCF and MF, according to [48] (Figure 4).

4. Results and Discussion

4.1. Importance Evaluation of Variables

Different variables have varying impacts on the performance of the forest height estimation model, and selecting an appropriate combination of variables can significantly improve its accuracy. The RF algorithm provides valuable information on the statistical importance of each variable by calculating the decrease in OOB accuracy when the variable is eliminated. Variables that lead to substantial OOB error decreases are assigned high importance levels, indicating their remarkable contribution to forest height estimation. Understanding the contributions of variables to forest height prediction can also shed light on forest AGB modeling because forest height is positively correlated with forest AGB. The importance ranking of variables using the RF algorithm is shown in Figure 5. All variables exert a positive influence on forest AGB prediction, with spectral features demonstrating greater importance compared with other types of variables. The red and NIR bands contribute the most to forest AGB estimation, with importance values of 12.93% and 10.29%, respectively. Other bands, such as B1, B7 and B3, exhibit moderate levels of importance ranging from 6.39% to 9.12%. The NDVI variable ranks third and yields an importance value of 10.14%. NDVI has been proven to be an essential variable in estimating forest parameters due to its close association with vegetation characteristics, such as leaf area index and growing stock volume [49]. With the exception of MEA (7.63%) surpassing the importance of the B2 band, other texture features obtain relatively lower importance levels, all below 6%. All variables are retained for forest height modeling and AGB estimation because they provide useful and reasonable information. The results show that spectral features outperform texture feature in forest AGB estimation, which is consistent with previous studies [50,51]. Particularly, a study by [47] also reported that variables derived from the red band achieve the highest ranking for estimating forest AGB, aligning with our results. Ref. [52] identified the spectral features as the most important variable in predicting forest height and AGB. This result can be attributed to the use of fine-resolution images, which enhance the role of the spectrum in capturing detailed observations and reflectance contributions from forests. By contrast, the coarse resolution may result in mixed spectral attributes within pixels, leading to confusion between forests and other ground objects, such as grass, thereby constraining the contributions of spectrum [53]. However, the results of this study contradict some forest AGB studies that have identified textural features as the most important predictors [54]. Texture features have the capability to capture forest structures and distinguish trees from other vegetation classes, such as grass and crops [16]. Although no definitive conclusions regarding the variable importance ranking have been drawn, we believe that the cooperation of spectral and texture variables is beneficial for enhancing the accuracy of AGB prediction [54,55,56].

The forest height is divided into six groups in intervals of 5 m to examine the contribution of input variables along the height distribution (Figure 6). In terms of heights below 5 m, NDVI (18.41%) demonstrates the highest importance score, followed by the B5 band (12.32%), which is a useful indicator related to vegetation health. In forest AGB studies, AGB is an important parameter that reflects the productivity and health status of forest ecosystems, with healthy trees contributing positively to AGB. As the quantification of forest AGB is closely linked to forest height, variables related to vegetation health can serve as the auxiliary information in the downscaling modeling of forest height. However, after this height interval, the ranks of the two variables decrease initially and then increase slightly. For height ranges between 5 and 20 m, the B4 band plays the most important role in modeling forest height, with importance scores exceeding 10%. Above 5 m, the importance of the B1 and B2 bands increases, reaching their maximum contributions when the forest height reaches 20 m. These results demonstrate that different bands possess varying predictive power as forest height changes, despite the indispensability of spectral variables in forest height modeling. For example, NDVI and NIR bands are more sensitive to low forest height but exhibit limitations in predicting moderate forest height. Conversely, the red band produces opposite results compared with NDVI and NIR bands. By comparison, textural variables show less contribution than spectral variables along different height distributions.

4.2. Model Performance Evaluation

The RF algorithm provides a measure similar to $R^2$, called percent variance explained (PVE), to evaluate the goodness of fit. PVE is calculated using the ICESat-2 training data to analyze the model’s fitting power. In this study, the RF model yields a PVE value of 93.56% when inferring forest height at a 15-m resolution, suggesting satisfactory fitting results. Additionally, $R^2$ and $RMSE$ of the RF-based forest height estimation model are calculated using ICESat-2 validation data. The estimated forest height from the RF model is plotted against the ICESat-2 derived height in Figure 7. The estimated height shows a strong correlation well with the ICESat-2-derived height, with $R^2=0.93$ and $RMSE=$ 1.15 Mg/ha. The results suggest that the RF achieves accurate performance in forest height estimation, which is consistent with the findings from related studies [44,52]. The results demonstrate the feasibility of inferring fine-resolution forest height distribution from 30-m resolution forest height data by integrating continuous Landsat 8 OLI data and dispersed ICESat-2 data, providing a new approach for estimating forest AGB.

4.3. Spatial Forest AGB Estimation

Once the RF-based model is successfully trained and evaluated, it is used to assign a unique forest height value to each pixel at a 15 m × 15 m resolution across the entire study area. The spatial distribution of forest height (Figure 8) is produced at a 15-m resolution using the RF method with 14 variables. The measured forest height values range from 0 m to 35.90 m, with a mean value of 7.33 m and a standard deviation of 9.2 m. On the basis of the resulting forest height map, the 15-m resolution forest AGB distribution is generated using the allometric model (Figure 9). The simulated forest AGB in the study area ranges from 0 to 331.12 Mg/ha, with the 25% and 75% percentile values of 112.91 Mg/ha and 209.87 Mg/ha, respectively. The average forest AGB is 61.15 Mg/ha, with a standard deviation of 89.46 Mg/ha. In summary, the forest AGB levels increase from the northwest to the southeast in the study area. Total forest carbon stock in the study area in 2020 estimated to be 57.3 TgC in 2020 by summing the AGB of all pixels and using a carbon stock transformation coefficient of 0.5 [57].

In the spatial forest AGB estimation, forest canopy height is considered a good predictor of forest biomass [58]. Many studies have investigated the ICESat-2-based canopy height extraction methods and adopted canopy height-related metrics as independent variables to explain AGB. For example, ref. [46] used ICESat-2 height metrics, such as minimum, maximum, mean and percentile heights, to predict AGB and achieved an $R^2$ value of 0.62. With the complement of continuous optical remote sensing data, discrete ICESat-2 data can be extrapolated to provide wall-to-wall coverage of forest AGB [59]. For example, ref. [60] successfully explored the synergies of Landsat 8 and ICESat-2 data for quantifying vegetation AGB in dryland environments. Ref. [32] combined nine vegetation indices from Sentinel-2 data and 15 height metrics from ICESat-2 data for AGB modeling, resulting in an $R^2$ value of 0.68 and an $RMSE$ value of 25.14 mg/ha. The complex nonlinear relationship between remote sensing variables and forest AGB can be effectively simulated to produce spatial AGB distribution by using machine learning based regression methods (e.g., RF) [12,18,61]. However, existing studies have been limited in their mapping resolution because they depend on the ICESat-2 ATL08 product, which only provides forest height estimation segments at 100-m resolution [24,46]. In this study, an innovative attempt is made to infer fine-resolution forest AGB from existing 30-m forest height data by integrating 15-m Landsat 8 OLI data and ICESat-2 data. ICESat-2 ATL03 and ATL08 data are used to produce 15-m segment height estimations, which serve as sample plots. Fourteen variable layers at 15-m resolution are used as auxiliary data to convert the 30-m forest height data into 15-m forest height data through nonlinear regression. From this, a 15-m continuous forest AGB distribution map is obtained. Our method relates image variables to forest height rather than AGB because forest height is a critical parameter in AGB quantification, and our primary goal is to contribute to AGB estimation by inferring a fine-resolution forest height distribution from coarse-resolution forest height data. Additionally, directly collecting field data and quantifying forest AGB within field plots for remote sensing-based AGB modeling remain challenging. This study introduces a new approach to achieve wall-to-wall forest AGB mapping with improved resolution.

4.4. Accuracy Assessment of Forest AGB Map

Three public forest AGB products are adopted as reference data, including China forest AGB mapping (CFAM) data [49], global forest AGB mapping (GFAM) data [62] and GEOCARBORN data [63], to validate the accuracy of the resulting AGB map. Detailed information on these validation data is provided in

Table 2. Information about the reference data.

Information	CFAM	GFAM	GEOCARBORN
Spatial resolution	1 km	0.01°	0.01°
Remote sensing data	ICESat GLAS MODIS Landsat 4–5 TM	ICESat GLAS MODIS InSAR Landsat 7 ETM+ Envisat ASAR	Envisat ASAR
Mapping technique	Random forests algorithm	Error removal and weighted linear averaging algorithm	BIOMASAR algorithm
AGB ranges within the study area	0–166.04 Mg/ha	0–220.23 Mg/ha	2.84–151.31 Mg/ha
25%–75% percentiles of AGB within the study area	67.72–110.69 Mg/ha	95.57–149.16 Mg/ha	72.71–101.82 Mg/ha
$R^2$	0.75	0.61	0.45
Date of the product	2015	2020	2010
Reference source	[49]	[62]	[63]

. A total of 73 validation plots from forest areas are randomly selected for validation. The unit sizes for validation are set to 8 m × 8 m, 10 m × 10 m and 12 m × 12 km, respectively, to calculate the mean forest AGB within each unit. The estimated AGB presents a remarkable correlation with the three reference data at various unit sizes (Figure 10). The $R^2$ values between our AGB estimates and CFAM, GFAM and GEOCARBORN data range from 0.54 to 0.67, 0.78 to 0.83 and 0.85 to 0.86, respectively. Particularly, our AGB estimates exhibit high consistency with GEOCARBORN data, with an average $R^2$ value of 0.85 and an average $RMSE$ value of 3.91 Mg/ha. The results show that the $R^2$ values tend to increase as the unit size enlarges. This phenomenon can be attributed to the advantageous effect of large spatial units in mitigating localized variations in forest AGB density. We further observe that our results tend to overestimate forest AGB compared with the three reference data, despite yielding high regression coefficients. Our result also has larger ranges, quarter percentile and three-quarter percentile, than reference data (Table 2). This overestimation can be attributed to the coarse resolution (e.g., 1 km × 1 km) of the reference data, which can cause the forest AGB levels within pixels to be over-smoothed. For example, non-forested areas within pixels can reduce the remote sensing signal intensity of the pixels classified as forest, resulting in an underestimation of the AGB value. In comparison, our results have a higher resolution (15 m × 15 m), enabling a more detailed depiction of the surface situation and accurate estimations of forest height and AGB estimations. Therefore, our results present a reasonable level of overestimation compared with the reference data. This highlights the necessity of developing fine spatial resolution forest AGB mapping.

Moreover, the accuracy of our AGB map is evaluated at the county scale using the above validation data. Counties with AGB < 10 Mg/ha are excluded from the validation due to sparse forest coverage. The estimated AGB presents reasonable correspondence with the validation data in 29 counties (Figure 11). When compared with the CFAM data, the $R^2$ and $RMSE$ of regression are 0.66 and 12.08 Mg/ha, respectively. Using the GFAM data, $R^2$ and $RMSE$ of regression reach 0.91 and 10.78 Mg/ha, respectively. When compared with the GEOCARBORN data, $R^2$ and $RMSE$ of regression are 0.66 and 6.67 Mg/ha, respectively. The AGB values in approximately half of the counties are overestimated, whereas the other half are underestimated on the basis of the validation data. Three counties, namely, Fusong, Helong and Huinan, exhibit remarkable differences in validation, with absolute differences exceeding 50 Mg/ha. However, most counties present low differences (<20 Mg/ha in absolute), indicating a strong correlation between our results and the validation data.

5. Conclusions

This study develops a fine resolution forest height estimation approach to contribute to AGB quantification by combining ICESat-2 data and optical Landsat 8 OLI data using a spatial downscaling scheme. Jilin is chosen as the case area. The discrete ICESat-2 photon data provide forest canopy height measurements in 15-m segments, establishing correlations with 30-m resolution forest height data using the RF algorithm by considering 14 variables derived from the pan-sharpened Landsat 8 OLI data. This allows us to achieve the downscaling process from coarse data to fine data. RF presents promising regression results between the estimated and ICESat-2-based forest height data, yielding an $R^2$ of 0.93 and an $RMSE$ of 1.15 Mg/ha. Wall-to-wall fine-resolution forest AGB mapping is achieved through extrapolation of ICESat-2-derived forest height and the use of an allometric model. Our AGB estimation corresponds reasonably well with the reference data, and the $R^2$ is higher than 0.65 in most cases. The proposed scheme facilitates accurate and fine estimation of forest AGB for studying forest carbon stocks. Also, the results from this study demonstrate the value of combining discrete ICESat-2 data and continuous Landsat 8 OLI data for fine resolution forest AGB estimation. In the future, the proposed method will be further validated and applied to other large-scale areas.