Mapping Large-Scale Pantropical Forest Canopy Height by Integrating GEDI Lidar and TanDEM-X InSAR Data

doi:10.21203/rs.3.rs-3306982/v1

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Mapping Large-Scale Pantropical Forest Canopy Height by Integrating GEDI Lidar and TanDEM-X InSAR Data

https://doi.org/10.21203/rs.3.rs-3306982/v1

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Our ability to infer the impact of land use changes such as deforestation and reforestation on concentrations of atmospheric CO₂ rests upon accurate and spatially resolved estimates of forest structure, namely canopy height, aboveground biomass (AGB) and biomass density (AGBD). Since April 2019, NASA’s Global Ecosystem Dynamic Investigation (GEDI) mission has been collecting billions of lidar waveforms over the Earth’s temperate and pantropical forests. However, GEDI is a sampling mission and there are large gaps between tracks, as well as those caused by clouds. As a result, the standard gridded height products created from this mission are at 1 km resolution which provides nearly continuous coverage, but which may be too coarse for some applications. One way to provide wall-to-wall maps at finer spatial resolution is through fusion with other remotely sensed data that are responsive to ecosystem structure. The TanDEM-X twin satellites (abbreviated as TDX for convenience all through this study) have provided an unprecedented dataset of global SAR interferometry at X-band since 2010 and have been shown to be highly sensitive to height and other ecosystem structure, but with limited accuracy as compared to lidar. Building on our previous research for fusion of TDX and GEDI, we present a new method of mapping high spatial resolution forest heights across large areas using data from these two missions. Our method uses GEDI waveforms to provide the vertical profile of scatterers needed to invert a physically-based model to solve for canopy height. We assess the impact of using profiles generalized over large areas and develop a calibration method based on GEDI canopy heights to improve model performance. Our method reduces regional errors in forest height caused by the limited penetration capability of the X-band signal in dense tropical forests and the impact of terrain slope using adaptive wavenumber (k_Z)-based calibration models and over 2 years of GEDI height observations. In comparison to applying a general country-scale calibration model, the adaptive method selects more representative calibration coefficients for different forest types and landscapes. We apply the method over the entirety of Gabon, Mexico, French Guiana and most of the Amazon basin to produce continuous forest height products at 25m and 100 m. We find that the regional calibration approach produces the best results with a bias of 0.31 m, RMSE = 8.48 m (30.02%) at 25 m and a bias of 0.46 m, RMSE = 6.91 m (24.08%) at 100 m when cross-validated against airborne lidar data. In comparison to existing height data products that have used Machine Learning based approaches to fuse GEDI with passive optical data, such as Landsat and Sentinel-2, our methods produce maps with greatly reduced bias, lower RMSE, and they do not saturate for tall canopy heights up to 56 m. An important feature of this study is that our canopy height product is complemented with an uncertainty of prediction map which is a measure of the predictor’s uncertainty around the actual value rather than the standard error (a square root of estimated variance which quantifies the predictor’s expectation) used by earlier studies. The approach outlined here shows how the integration of GEDI data with TDX InSAR images enables high-resolution mapping of wall-to-wall forest canopy heights, providing an essential foundation for the global mapping of aboveground biomass.

Forestry

Geographic Information Systems

Forest height

Fusion

Lidar

GEDI

InSAR

TanDEM-X

Model-based inference

Acquiring high-resolution and accurate data on forest structure in the pantropics is essential for improving the quantification of terrestrial carbon stocks and change (Pugh et al., 2019; Tagesson et al., 2020). Such information also has practical applications, such as estimating forest timber volume, assessing forest degradation, deforestation and regrowth, and modeling primary production, biodiversity and other key ecosystem variables (Asner et al., 2012; Goetz and Dubayah, 2011). In addition, these data are essential for the production of jurisdictional forest biomass and carbon stock estimates, which can help with the production of countries’ National Determined Contribution reports (Secretariat, 2022) and to help achieve the UN Sustainable Development Goals (Olabi et al., 2022).

Airborne lidar campaigns using small-footprint or medium-footprint waveform sensors deliver accurate canopy structural information and enable the estimation of high-quality reference biomass (Duncanson et al., 2020; Fatoyinbo et al., 2021; Huang et al., 2019; Ojoatre et al., 2019), but are limited in spatial extent particularly over tropical regions. Space-based lidar can measure forest structure and biomass consistently at the global scale. The GLAS (Geoscience Laser Altimeter System) instrument onboard NASA’s ICESat mission and, more recently, the ATLAS instrument onboard the ICESat-2 mission have successfully measured forest structure, but are not optimized for vegetation mapping and have quite limited spatial mapping (Narine et al., 2020; Simard et al., 2011).

NASA’s Global Ecosystem Dynamics Investigation (GEDI) instrument is a vegetation-optimized lidar onboard the International Space Station (ISS). Since April 2019, GEDI has provided billions of lidar waveform observations of ecosystem structure between 51.6° N and 51.6° S latitudes (Dubayah et al., 2022a). The GEDI mission provides a variety of products on ecosystem structure including canopy height, canopy cover and vertical profile, canopy leaf area index and profiles and aboveground biomass (AGB) (Dubayah et al., 2020, 2022a). However, although GEDI provides vastly better spatial coverage than previous spaceborne lidar missions, it is also a sampling mission with 60 m gaps along each of its 8 tracks, 600 m spacing between tracks, and variable spacing between the orbital swaths of these 8 tracks, which varies as a function of latitude. Additionally, persistent clouds create gaps in coverage, especially over the tropics. For these reasons, GEDI’s standard, gridded ecosystem products are produced at 1 km resolution which provides near continuous mapping.

Many applications require higher spatial resolution and this has motivated much research into fusion methods that combine the highly accurate but sparse estimates from GEDI with wall-to-wall high-resolution imagery from other sensors. These methods have used passive optical, stereo, and SAR imagery, often in machine learning or other advanced statistical frameworks (Francini et al., 2022; Shendryk, 2022). For example, the first one is the 30-m Global Forest Canopy Height for 2019 by Potapov et al., (2021) which was produced by integrating GEDI data and Landsat data using a bagged regression tree ensemble model. Another product is the 10-m Global Canopy Top Height map for the year 2020 estimated from fusing GEDI with Sentinel-2 multi-spectral imagery using a probabilistic deep learning (Lang et al., 2022). However, ideal ancillary data to map forest structure should be not merely spatially continuous but also (a) less influenced by clouds and (b) sensitive to vertical vegetation structure. While time series of optical imagery, including spatial texture measures, have proven to be somewhat indirectly responsive to height, they may not capture the full range of height and can be limited in areas of high canopy cover, resulting in saturation of predicted heights (Bullock et al., 2020; Chi et al., 2015; Nguyen et al., 2020).

Interferometric Synthetic Aperture Radar (SAR), known as Interferometric SAR or InSAR, has shown to accurately capture the vertical structure of forest canopies. However, its accuracy is influenced by two factors: the wavelength of the radar waves and temporal decorrelation. The wavelength determines the radar's ability to penetrate through the canopy (Jedlovec, 2009), while temporal decorrelation results in a loss of coherence necessary for modeling canopy structure (Simard et al., 2012). Lower-frequency waves like P- and L-band are more sensitive to the tree trunk, underlying ground, and their interaction, while higher-frequency waves like C- and X-band are more sensitive to the crown composed of leaves and branches. However, at each frequency, all components of the tree and the ground contribute to the scattering of the radar signal received (Treuhaft and Siqueira, 2000). This necessitates algorithms capable of separately estimating different types of canopy height and ground elevation. Multiple studies have developed algorithms that use various sources of information such as multi-polarization InSAR (PolInSAR), multi-baseline InSAR/PolInSAR, multi-baseline tomography SAR (TomoSAR) (Reigber and Moreira, 2000; Neumann et al., 2009; Pardini and Papathanassiou, 2012; Kugler et al., 2014; Soja and Ulander, 2016; Pardini et al., 2017;) as well as lidar (Askne et al., 2013, 2017; Qi and Dubayah, 2016; Pulella et al., 2017; Bispo et al., 2019) to identify and remove the ground. These studies were limited to areas where such data sources were available. Forest height estimation has been achieved without the need to identify and remove the ground by utilizing the TanDEM-X (TDX) X-band InSAR coherence magnitude and a physical InSAR scattering model (Chen et al., 2021, 2016; Olesk et al., 2016; Schlund et al., 2019; Gómez et al., 2021). This is significant because TDX is a spaceborne InSAR mission that avoids issues with temporal decorrelation and has the potential for global-scale application. Studies have shown the potential of combining data from GEDI and TDX to map forest structure (Qi et al., 2019a) and biomass (Qi et al., 2019b), but these studies were limited to specific study sites and a few TDX acquisitions. With the availability of abundant GEDI data, further research is needed to evaluate the effectiveness of GEDI and TDX data fusion in larger areas and countries.

The efficacy of GEDI-TDX fusion can be attributed to several factors: 1) InSAR coherence has relatively higher sensitivity to forest structure and biomass than optical or SAR backscatter signals (Raveendrakumar et al., 2022); 2) Lidar and InSAR are similar in the capability of measuring forest vertical structure, although working at different viewing geometry and wavelength (Pardini et al., 2019); 3) TDX interferometer provides unprecedent high-quality interferometric coherence with no temporal decorrelation and high spatial resolution (Chen et al., 2019); 4) The baseline of TDX Interferometer has large variability due to the tandem satellite configuration (as opposed to the fixed baseline used by the earlier SRTM mission (Kobrick, 2006)), allowing for a wide variability of spatial baselines (Zink and Moreira, 2013) which is essential for accurate height retrievals.

Both missions are still operational and have had coincident acquisitions since 2019, which facilitates fusion. However, our earlier studies were conducted over selected experimental sites using simulated GEDI data derived from airborne laser scanning data within a simulator (Hancock et al., 2019), and was based on Random Volume over Ground (RVoG) model (a simplified physical model) which inverts less-accurate canopy height when the assumptions of the scattering model are violated (Pardini et al., 2019). The potential and performance of this type of fusion has not been evaluated using on-orbit GEDI data over large areas.

This study investigates the performance of GEDI-TDX data fusion over forests in Central Africa, Central and South America, including the Amazon Basin at 25 and 100 m resolution. We use a model-based forest height inversion framework where the GEDI lidar waveforms are used to approximate the X-band vertical reflectivity. This provides a key, missing element when using single single-baseline single-polarized TDX InSAR that allows for the inversion of canopy height from interferometric coherence. The inverted TDX height is then calibrated with actual GEDI canopy heights using adaptive regional models and TDX wavenumber k_Z as a calibration factor, resulting in final GEDI-TDX (GTDX, hereafter) fusion height maps at 25 m and 100 m. The study is conducted across four pantropical countries/regions: Gabon, Mexico, French Guiana, and Amazon Basin. Our results of the fusion product are validated against independent airborne lidar canopy height for accuracy assessment. Our height canopy map product is complemented with an uncertainty of prediction map, expressed as the RMSE, that was derived under the same closed-form parametric statistical inference framework developed around the GEDI mission (Dubayah et al., 2022a; Patterson et al., 2019; Saarela et al., 2022).

2.1 Study sites

Our study is conducted over four countries/regions: Gabon, Mexico, French Guiana and Amazon Basin. These sites vary greatly in topographic, climatic and ecosystem conditions, providing a broad range of vegetation cover, structure, and terrain complexity for understanding forest structure mapping from GEDI-TDX data fusion (Fig. 1).

In Gabon, forests cover ~ 88.5% of the country’s surface area, which is about 267,667 km². The aboveground biomass of Gabon varies from a few Mg/ha in savanna sites to about 600 Mg/ha in areas of older growth forests (Mitchard et al., 2012). The tallest trees reach above 60 m, while the average height of the canopy remains about 30–40 m at 1-ha scale (Fatoyinbo et al., 2021). The topography of Gabon is also diverse, alternating between large flat plains and steep sloping terrains (Wasik et al., 2018).

In Mexico, forests cover a surface area of ~ 640,000 km², occupying around 30% of Mexico's land surface. Forest ecosystems in Mexico diversify from the arid zones in the northwest to the humid rainforest in the southeast, comprising a vast variety of vegetation with tree heights ranging between 60m in coniferous forests to 1.3 m in xerophilous scrubs. Mean tree heights measured in the field range from ~ 5–10 m (Barreras et al., 2022).

French Guiana is situated on the northeastern coast of South America, bounded by Brazil to the south and east. Most of French Guiana is low-lying, except for mountains in the south that reach an elevation of ~ 700 m. Dense tropical forests (mainly hardwoods) cover 90% of the land area and canopy heights were estimated to have a mean of approximately 31 m, reaching a maximum of ~ 69 m. The lower canopy heights over the coastal marsh areas in the northeastern part of French Guiana were observed to have a maximum tree height of ~ 20 m (Fayad et al., 2014). Only 2.6% of the French Guiana forest cover has been lost since the 1990s, which is the lowest rate in South America.

The Amazon Basin covers an area of ~ 6.3 million km² in South America, located in the countries of Bolivia, Brazil, Colombia, Ecuador, French Guiana, Guyana, Peru, Suriname, and Venezuela. Broadleaf tropical rainforest covers most of the Amazon Basin, with an area of ~ 5.5 million km². The Amazon biome also includes savannas, floodplain forests, grasslands, swamps, bamboos and palm forests. The majority of the rainforest is contained in Brazil (60%), followed by 13% in Peru, 10% in Colombia and minor amounts in other countries. The distribution of canopy heights for closed forest canopies in the basin is slightly skewed toward taller heights; 50 percent of stands have a mean canopy height between about 25 and 35 m (Helmer and Lefsky, 2006), with the tallest tree reaching up to ~ 88.5 m (Gorgens et al., 2019). Since 1970, an extensive extent of over 760,000 km² of forest cover has been lost in the Amazon basin due to anthropogenic processes (Conrado da Cruz et al., 2020).

2.2 Land, Vegetation and Ice Sensor (LVIS) data

Airborne lidar data provided reference canopy height for validating the GEDI lidar canopy height and the fused GTDX canopy height (Lang et al., 2022; Lovell et al., 2003; White et al., 2016). In Gabon, we used NASA Land, Vegetation, and Ice Sensor (LVIS) medium-footprint (~ 22 m diameter with 9 m separation) lidar observations acquired in the AfriSAR campaign, a joint effort between NASA and the European Space Agency (ESA) in support of ESA BIOMASS, NASA-ISRO Synthetic Aperture Radar (NISAR) and NASA GEDI missions. The data were collected over multiple experimental sites, including Lope, Mabounie, Mondah, Pongara and Rabi in 2016 (Fatoyinbo et al., 2017). We averaged the LVIS RH98 metric to create reference canopy height maps at 25 m and 100 m resolutions for Gabon.

LVIS data (nominal spatial resolution 20 m) were collected over French Guiana in August 2021 during the GEDI USA and French Guiana 2021 Campaign (Blair, J. B and Hofton, M., 2020). The campaign covered large areas or with flights under GEDI orbits for the calibration/validation of the GEDI L1/L2 data. These LVIS acquisitions filled the reference data gaps in South America tropical forests. We used the averaged LVIS RH98 metric to create reference canopy height maps at 25 m and 100 m resolutions for French Guiana.

2.3 Small-footprint airborne laser scanning (ALS) data

NASA Goddard’s LiDAR, Hyperspectral & Thermal Imager (G-LiHT) provided data for Mexico. The VQ-480 (Riegl USA, Orlando, FL, USA) airborne laser scanning (ALS) instrument onboard G-LiHT acquired a high sample density (∼12 pulses/m²) of small footprint laser pulses (∼10 cm diameter with 0.23 m along-track spacing and 0.57 m across-track) and records up to eight discrete returns for each given pulse, creating a continuous, canopy height surface layer model (CHM) at 1 m horizontal spatial resolution (Cook et al., 2013). We used this 1-m CHM product from G-LiHT to extract the 98th percentile height within each 25 m grid (to be consistent with the use of RH98 metric for LVIS data) and calculated the average height at 100 m to produce the reference canopy height maps for Mexico.

CHM derived from ALS data collected across the Brazilian Amazon was published in September 2022 (Reis et al., 2022). Each transect (width on the ground was approximately 494 m) covered 375 ha (12.5 km × 300 m) by emitting full-waveform laser pulses (footprint < 30 cm) with an averaged point density of four returns per square meters. Horizontal and vertical accuracy were controlled to be under 1 m and under 0.5 m, respectively. We used the 1-m CHM product to extract the 98th percentile height within each 25 m grid. Reference canopy heights were created at both 25 m and 100 m resolutions for the Amazon Basin.

2.4 GEDI data

GEDI Version 2 footprint data (Dubayah et al., 2021b, 2021a) collected between April 2019 and August 2021 were used in this study. The geolocation error associated with GEDI footprint-level measurements has been improved over time, and currently the geolocation error for Version 2 data is estimated to be ∼10 m (1-sigma, Beck et al., 2020). We utilized the GEDI L1B (Geolocated Waveform Data Global Footprint Level) and L2A (Elevation and Height Metrics Data Global Footprint Level) products, and filtered these based on data quality flags and the beam sensitivity (defined as maximum canopy cover that can be penetrated) (Dubayah et al., 2021a, b). The L1B product was used to estimate the vertical reflectivity of scatterers, which is needed for the TDX height inversion process (3.1), whereas the RH98 metric of the L2A product was employed to establish calibration models with the inverted height (3.2). The RH98 metric was chosen here for consistency with previous GEDI studies because it provides a more reliable and less noisy estimation of canopy height than RH100. Applying a threshold of 0.95–1 for sensitivity, we used approximately 1.9, 59.8, 0.9 and 143.9 million shots in Gabon, Mexico, French Guiana and the Amazon Basin, respectively (Fig. 2 (a)).

GEDI footprint canopy heights were averaged respectively at 25 m and 100 m resolutions to calibrate the GEDI-TDX relationship models, i.e. the 25-m GEDI canopy height and TDX inverted height were utilized in creating the 25-m calibration model whereas the 100-m GEDI and TDX height grids were employed in establishing the 100-m calibration model (3.2). Comparing the averaged GEDI grids against wall-to-wall airborne lidar measurements, we quantified the impact the number of GEDI shots has on the mean height for a grid cell (Fig. 3). We found that requiring too many GEDI shots in a grid cell will limit the number of grid cells available for calibration (Fig. 2 (b)); conversely using grid cells with too few shots will produce less precise means (Fig. 3). At the 25 m resolution, a single GEDI shot covers nearly the entire grid cell, so any cell with ≥ 1 was used. At the 100 m resolution, we required at least two or more GEDI shots to include that grid cell for calibration to balance the coverage and accuracy of the training data. These GEDI calibration data were found to have biases of about 0.02–0.8 m and RMSEs of about 6–7 m over the study sites. Although given earlier literature (Silva et al., 2018) and the available data, using grid cells with three or more shots at 100 m resolution seems a more reasonable choice, large contiguous areas (> 50 km) were lacking samples across the range of expect height variation at this threshold. The same reason holds for our use of 0.95 as a cutoff for sensitivity over all forest sites, which is different from GEDI L4B that used 0.98 as the cutoff over broadleaf (Dubayah et al., 2022b).

2.5 TDX data

Conventional Coregistered Single look Slant range Complex (CoSSC) data products acquired in a HH polarized stripmap mode during the global DEM (Krieger et al., 2013) and change DEM (Lachaise et al., 2021) TDX mission phases between 2011 and 2019 have been used to derive interferometric coherence and effective vertical wavenumber k_Z for inverting forest canopy height. We processed around 30,000 TDX acquisitions in the four study sites acquired along ascending and descending orbits with a typical resolution of about 3m in range and azimuth selected to have suitable acquisition geometries (k_Z of ~ 0.05–0.25; Height of Ambiguity of ~ 25 m–125 m). There is a time difference of approximately 1–10 years between TDX and GEDI. The impact of such difference on our fusion product and the procedures taken in this study to address it is discussed in 3.3.

For each TDX acquisition, we applied the interferometric processing summarized in 8 steps as shown Fig. 4 (a). In step 7, about 64 looks were used to compute the corrected interferometric coherence at a final resolution of 25 m × 25 m. The major output parameters of the processing chain are the calibrated and geocoded (complex) interferometric coherence and k_Z (terrain corrected) (Fig. 4), which are subsequently used to derive forest height at 25 m based on the inversion algorithm described in Section 3.1 (Choi et al., 2023). The code was executed on a Server with two Intel® Xeon® Gold 6130 CPU with 756 GB RAM, taking about 10 minutes to process a single scene.

We derive forest height from TDX interferometric coherence based on a structure-based framework that exploits radar reflectivity profiles derived from GEDI lidar waveforms (see 3.1). To minimize errors across the full range of canopy height, we apply a spatial-adaptive correction for the inverted TDX height using regional GEDI-TDX calibration models and generate the final GTDX fusion height map at both 25 m and 100 m (see 3.2). We validate each height product using canopy height derived from independent ALS/LVIS data by height classes and ecosystem types (see 3.4). Maps of uncertainty of prediction are also provided together with each fusion height product at the respective resolution following method described in Appendix A. Grid-level uncertainty estimation

3.1 Structure-based framework for TDX height inversion

To retrieve height from TDX InSAR data, a Fourier relationship is established between the volume decorrelation contribution of the interferometric coherence (γ_Vol,) and the vertical reflectivity profile f(z), which represents the vertical distribution of scatterers seen by the radar (e.g., TDX) at a given polarization and imaging geometry under given scattering and attenuation processes (Chen et al., 2021; Garestier and Le Toan, 2010; Pardini et al., 2017):

$$\left|{\stackrel{\sim}{\gamma }}_{Vol}\left({k}_{Z}\right)\right|=\left|\frac{{\int }_{0}^{{h}_{V}}f\left(z\right){e}^{i{k}_{z}z}dz}{{\int }_{0}^{{h}_{V}}f\left(z\right)dz}\right|$$

where h_V is the canopy height to be inverted and k_Z is the vertical wavenumber. In the case of using single-polarized TDX acquisitions, the inversion of canopy height h_V from γ_Vol is an under-determined problem since f(z) is also unknown.

One way to overcome this is to approximate the vertical reflectivity profile f(z) in (1) with the GEDI lidar waveforms. It is clear that the TDX vertical reflectivity profiles and the GEDI waveforms are not the same. However, the high attenuation at both frequencies makes both sensitive to the geometric architecture of the canopy and introduces a certain similarity that is supported by the similar spatial resolution both are measured. This has been already demonstrated to be able to provide meaningful height estimates in (Guliaev et al., 2021). However, as the GEDI waveform measurements are spatially discrete, in order to obtain a spatially continuous solution by (1), a mean reflectivity profile representative of a larger area is derived by using all GEDI waveforms within that area. Here, for the generation of the mean reflectivity the approach proposed in (Guliaev et al., 2021) is adopted using the low order eigen-profiles obtained from the Eigen-decomposition algorithm on the profile covariance matrix formed from the GEDI waveforms within a given area. A simpler alternative approach to obtain the mean reflectivity profile could be to average across all GEDI waveforms within the area. Before using the derived mean profile in (1), an attenuation correction has to be performed accounting for the fact that while in open canopy forest conditions, the ground contribution is overrepresented in the GEDI profiles, in denser and/or closed canopy forest conditions the ground contribution in the GEDI waveforms is weaker than the one expected at X-band (vertical) reflectivity. This is because of the difference in the effective attenuations of the side-looking TDX and the nadir looking GEDI propagation. An empirically derived attenuation factor is used for this correction, which is set at a universal value of 0.1 dB/m for all scenes (Choi et al., 2023). The corrected mean profiles are finally used in (1). A more detailed description and discussion can be found in (Choi et al., 2023). Next, we applied Eq. (1) to derive canopy height at 25 m from TDX interferometric coherence using the extinction-corrected f(z). The inversion was implemented by means of a 2D lookup table, with interpolation performed afterwards for inconsistent inversion areas (Choi et al., 2023).

3.2 Regionalized calibration for GTDX height estimation

It is clear that the use of a single “mean” reflectivity profile is not able to track the spatial forest structure heterogeneity within the scene. A local discrepancy of the "mean" reflectivity profile used for inversion and the underlying reflectivity leads to a biased estimate, expressed as a forest height over- or under-estimation. In scenes with a very heterogeneous forest structure the local biases appear as an overall increased variance rather than a bias (Choi et al., 2023; Guliaev et al., 2021). It is important to note here that for the generation of large-scale forest height maps from TDX single-pol single-baseline data, a compromise always has to be made, as the problem is under-determined. The use of the mean reflectivity profile is one of the possible compromises. The advantage of the proposed approach is that it allows unbiased height estimates over larger areas at the cost of a high(er) variance.

Even if, as discussed above, the height bias can be kept rather small over the extent of a single or a few TDX scenes, the mismatch between the "mean" reflectivity profiles used and the underlying reflectivity and/or uncompensated residual decorrelation contributions will introduce large scale estimation biases if the spatial baseline of the TDX images becomes too large or too small. In a final step, these large-scale biases are compensated by using the height estimates at the GEDI footprints. The correction is applied on the unitless product h_V*k_Z, which is directly related to the inversion of (1): the product of the GEDI footprint height estimates with the (local) vertical wavenumber k_Z is used to calibrate the product of the TDX estimated heights h_V with the vertical wavenumber k_Z. In this way, large-scale biases are accounted for in a single step, by means of a single correction applied to the entire set of inverted heights, without having to distinguish between different height ranges or vertical wave numbers (Choi et al., 2023; Guliaev et al., 2021).

A recent study demonstrated that applying a country-scale GEDI-TDX calibration that uses k_Z as a correction factor was able to reduce these errors and improve the accuracy of canopy height estimation (Choi et al., 2023). While a country-scale model is simpler, it ignores the power of having a vast amount of spatially distributed waveforms that may be used to provide more local calibrations. It is therefore of great interest to assess the improvements that may result from a regionalized calibration approach to map canopy height with the goal of improving forest types that are even if both difficult to model (e.g. heterogeneous, flooded or very tall stands) and may be spatially concentrated. Note that our study areas and a real pantropical estimation includes not only forests but also landcover types such as woodlands, savanna, agriculture, etc.

We implement a regional calibration approach at both the 25 m resolution and the 100 m resolution. A 100 m height product (based on 100 m calibration) helps overcome two issues that can dominate at the 25 m resolution. First, GEDI geolocation accuracies are on the order of 10 m which is a significant fraction of the cell size. The impacts of this level of geolocation are greatly reduced when GEDI shots are aggregated to 100 m. Secondly, TDX and GEDI have dissimilar viewing geometries and see different vertical distributions of canopy scatterers. GEDI’s viewing angles are limited to within about 5 deg of nadir, and thus sees a different vertical cross section of forest as compared to slant range imaging from TDX. Such differences are reduced when averaging to 100 m.

Our regional calibration method uses a moving window approach to calibrate each grid cell. The window is centered on the cell and utilizes a specific model for that cell. The size of the window is adjusted dynamically to ensure a sufficient number of GEDI samples within the window, creating a stable model. The optimal window size depends on factors including the local distribution of GEDI shots and the homogeneity of forest type, canopy density, slope, and other conditions. If the window is too small, the models may be statistically unstable and the predictions noisy. Conversely, an excessively large window may result in overgeneralized models that do not consider local conditions affecting canopy height in the grid cell (in the case of the non-regional model, the window size is essentially the area of the entire country). Furthermore, as depicted in Fig. 2, GEDI tracks and clouds are not distributed evenly, leading to gaps of varying sizes that necessitate variable-sized windows.

We design a procedure to adaptively determine the size of the moving window locally. To constrain the computational cost required for selecting the window size, we limit the options to a range of 2 km–50 km, with intervals of 4 km (see Fig. 5 for an example of using a 2-km moving window size). From these options, we choose the optimal window size for each central grid based on two priorities: (1) higher values of r², which measure the correlation between the predicted height and GEDI height within the window, and (2) lower values of RMSE, which quantify the differences between the predicted height and GEDI height within the window. We then employ the optimized model to estimate the final GTDX height using the inverted TDX height and k_Z. In cases where none of the window size options provides enough GEDI samples for model fitting (a minimum of 30 samples is required) or yielded a model with satisfactory goodness-of-fit metrics (r² and RMSE values compared to those from the predicted height based on the country-scale calibration model within the window), we resort to the country-scale calibration model to estimate the GTDX height.

3.3 Uncertainty estimation

As previously mentioned, there are two parallel procedures being conducted. The first involves selecting a moving window size and fitting models at a 25-m spatial resolution, while the second involves the same process but at a 100-m spatial resolution. This means that four map products are generated independently: two based on regional- and country-scale model calibration fitted at 25-m resolution and the other two using the 100-m calibration models.

Because these processes are conducted in parallel and independently, there is no concern regarding spatial autocorrelation since no aggregation has occurred. However, if the 25-m predictions are aggregated to create the 100-m map product, it would be necessary to approximate the spatial autocorrelation of residual errors to estimate uncertainty at the 100-m resolution (Appendix A. Grid-level uncertainty estimation).

In accordance with the conventional model-based inference paradigm, the actual canopy height for a grid cell is considered a realization from a random variable (Appendix A. Grid-level uncertainty estimation). The expectation of this variable may differ from the specific outcome of that grid cell. This means that the predictor's expectation is not necessarily the same as the actual value at the grid cell level, even if the calibration model is unbiased (Saarela et al., 2022). Therefore, unlike previous studies that provide the standard error as a measure of uncertainty around the expectation of the predictor, we provide an uncertainty measure around the actual value.

It should be noted that earlier studies on the GEDI mission have conducted simulation analyses to demonstrate that the 1-km grid is large enough, with a sufficient number of pixel population, to obtain a standard error that is approximately equal to the estimated uncertainty based on the model-based theoretical outline (Patterson et al., 2019). That is why the GEDI mission reported standard error as a complement to the L4B product (Dubayah et al., 2022b).

3.4 Validation of GTDX height products

Detailed local comparisons of model coefficients between regional- and county-scale model are performed to analyze the impact of regional calibration for the inverted TDX height. Both height products are validated against ALS/LVIS data at 25 m and 100 m.

To address the time discrepancy between the TDX (2011–2019) and GEDI (2020–2021), we use the global 2000–2020 land cover and land use change dataset derived from Landsat images (Potapov et al., 2022) to identify forest areas that were disturbed between 2011 and 2020 and re-validate the results to ensure the accuracy and reliability of our product. Specifically, we exclude any areas that have experienced disturbances and thoroughly analyze the overall enhancement achieved across all study sites. Moreover, we provide supplementary data on these disturbed areas as complementary information for our products, granting users the ability to make informed decisions about the utilization of height estimates for a particular location. Regarding the intact forest specifically, the average growth of trees has been projected to the modeled heights (i.e. the years of 2020–2021) through the use of regionalized GEDI-TDX models.

To assess potential improvements in the use of InSAR imagery vs. passive optical fusion approaches we compare our results with the global height maps discussed earlier: 1) 30-m ‘GLAD’ canopy height, derived through the integration of GEDI data and Landsat time-series (Potapov et al., 2021); 2) 10-m “ETH Zurich” canopy height, estimated from fusing GEDI with Sentinel-2 imagery using a probabilistic deep learning (Lang et al., 2022). All these maps are compared against the reference lidar data.

4.1 TDX height from structure-based inversion

Based on the method described in 3.1, we calculated mean profiles from GEDI for each TDX acquisition and inverted TDX height from interferometric coherence at 25 m. Inverted height maps from each TDX acquisition were combined to 1°× 1° tiles (see Fig. 6 for an example of such tile). TDX forest/non-forest (FNF) maps were used to mask out settlement and water (marked red and blue respectively in Fig. 6) in the inversion process (Martone et al., 2018).

Biases of about − 10.6 m to -1.5 m (at 25 m) and − 9.7 m to -0.5 m (at 100 m) were observed for the inverted TDX height before calibration with GEDI canopy heights, which may be related to the use of an unfitted reflectivity profile, the limited penetration capability of X-band or the impact of terrain slopes. These biases were found to be the largest over the countries with the highest canopy cover, French Guiana, followed by Gabon and Amazon Basin, and the smallest over Mexico. We established calibration models based on height*k_Z relationships between GEDI and TDX, i.e. GEDI_height*k_Z ~ a + b*TDX_height*k_Z (Fig. 6) to lower these biases (Choi et al., 2023) (3.2). The estimated intercept (a) and slope (b) were then used in the height relationship GTDX_height = a*1/k_Z+b*TDX_height to estimate the GTDX height. Larger a (absolute) and b values were found in French Guiana and Gabon (Fig. 6), which may be related to a higher degree of compensation for such biases. This agrees with our finding that applying locally-calibrated models benefits the mitigation of regional errors across landscapes, using spatially-varying a and b values (Fig. 7).

4.2 GTDX canopy height based on regional calibrations

We established height*k_Z relationships between GEDI and TDX using our regionalized, moving window approach and created the final GTDX height product, applying k_Z-based correction to each inverted TDX height cell at 25 m (Fig. 8) and 100 m.

Table 1: r² of TDX height, GTDX height from country-scale calibration, and GTDX height from regional calibration against ALS/LVIS height at both 25 m and 100 m. Best height model is highlighted in red.

r²	TDX		GTDX Country-Scale		GTDX Regional
r²	25 m	100m	25 m	100m	25 m	100m
Gabon	0.53	0.59	0.55	0.63	0.59	0.65
Mexico	0.31	0.31	0.35	0.34	0.39	0.41
French Guiana	0.23	0.32	0.24	0.33	0.26	0.35
Amazon Basin	0.31	0.37	0.24	0.31	0.36	0.44

Table 2: RMSE of TDX height, GTDX height from country-scale calibration, and GTDX height from regional calibration against ALS/LVIS height at both 25 m and 100 m. Best height model is highlighted in red.

RMSE (m)	TDX		GTDX Country-Scale		GTDX Regional
RMSE (m)	25 m	100m	25 m	100m	25 m	100m
Gabon	12.82	11.74	8.74	7.44	8.35	6.88
Mexico	7.15	6.40	7.66	7.51	7.11	6.38
French Guiana	13.33	11.74	8.20	6.61	7.97	6.39
Amazon Basin	13.20	11.15	10.40	8.54	9.30	7.56

We validated the inverted TDX height and the GTDX height estimated respectively with country-scale and regional calibration models against independent ALS/LVIS canopy heights at 25 m and 100 m. The TDX heights correlated moderately well with the reference lidar heights, but there were variations by country (Table 1). The validation RMSEs were somewhat large (Table 2) and likely illustrate the limitations of using X-band data penetration in closed canopies, among other factors (and why Mexico had the lowest RMSE given its more open canopy structures). Except for Mexico, the RMSEs decreased significantly with country-scale calibration, and continued to decrease, though not as much, with the application of regional calibration. The latter led to an overall accuracy improvement of up to 22.5% and 35.0% at 25 m and 100 m respectively.

We compared the difference of GTDX height estimated with country-scale calibration and with regional calibration respectively against ALS/LVIS height by different forest types and height classes (see Fig. 9 first row). We found that GTDX height estimated with regional calibration model consistently demonstrates smaller differences against ALS/LVIS height than the country-scale GTDX model heights. However, both GTDX estimates showed different frequency distribution of heights from GEDI and ALS/LVIS heights over low stands (less than around 10 m) (see Fig. 9 second row). This is maybe related to our selection of TDX acquisitions with smaller baselines which produced smaller vertical wavenumbers for the purpose of minimizing bias in tall canopies at the expense of short canopies. Most of the vertical wavenumbers realized in the standard DEM mode of TDX are not large enough to avoid underestimation of low forest stands (Choi et al., 2023), discussed in detail in Discussion. Errors related to these are reflected in the variance of GEDI-TDX calibration model and subsequently included in the estimated uncertainty for each grid cell (Appendix A. Grid-level uncertainty estimation).

Using the global land cover and land use change dataset, our analysis revealed that a relatively small proportion of approximately 3.09% of the study areas experienced disturbance between 2011 and 2020. Specifically, we observed 1.55% in Gabon, 0.80% in French Guiana, 1.45% in Mexico, and 3.83% in the Amazon Basin with disturbance occurred. To ensure the accuracy of our product, we conducted a re-validation process that excluded the disturbed areas. The results indicated an overall improvement in RMSE of about 0.1 m across all four sites. This demonstrates the consistency and reliability of our final product, even when accounting for areas of disturbance. For transparency and enhanced usability, information regarding the disturbed areas is provided as a mask layer for our height product. This feature enables users to access prior knowledge and make informed decisions regarding the reliability of height estimates for specific locations.

We estimated uncertainty of prediction for the GTDX height at both 25 m (Fig. 8 (a) second row) and 100 m, following the method described in Appendix A. Grid-level uncertainty estimation Mean uncertainty estimates over forested areas were found to be highest over Amazon Basin and the lowest over Mexico at both resolutions, which was consistent with RMSE estimated from cross-validating against ALS/LVIS data (Table 1).

4.3 Comparison with other global height maps

We compared the GTDX height product (regional-calibrated) and the aforementioned global canopy height products (“GLAD” and “ETH”) respectively against reference airborne lidar canopy heights (Fig. 10). We found that GLAD canopy height had good performance over areas with low canopy height but saturated beyond about 35 m (Fig. 10 (a)). The ETH height also showed signs of saturation beyond 40 m, but less than the GLAD map. However, it had a much larger bias than the GLAD product and significantly overestimated heights in the lower range (Fig. 10 (b)). GTDX canopy height is unbiased (Fig. 10 (a)) and shows much less saturation with height than either product at both resolutions (Fig. 10 (b)). Note that both disturbed and undisturbed areas were considered during the validation process of our height products, ensuring a fair and accurate comparison against other maps.

Most of the recent approaches to multimodal fusion, that is using data from various sensors and their varying modes of data acquisition, have been based on machine learning methods, often using readily available passive optical data or, less commonly, backscatter SAR as ancillary data. Interferometric SAR by its very nature should be more responsive to ecosystem structure, and thus more suitable for fusion in these methods. However, issues with temporal decorrelation have limited its application. The TDX sensors avoid this problem but their operation in X-band presents limitations with canopy penetration. While machine learning and statistical approaches may be employed for estimating heights using fusion with accurate height data from GEDI, per se, this ignores the fact that well-developed, physically based models of radiative transfer exist for height inversion. Exploiting the constraints such parametric models impose on the fusion process underpins our efforts here.

While there have been other studies on InSAR-lidar fusion research, our research is the first to successfully implement GEDI-TDX fusion on a large scale for forest height estimation. In comparison to existing extensive/global-scale height products, the level of accuracy attained in this study is unparalleled, specifically for forests with heights exceeding 20 m. Our results show that our fusion of GEDI and TDX data provides gap-free, high-resolution estimates of canopy across large areas, and with better accuracy and less bias than methods using passive optical data. Importantly, our methods also appear to not saturate at high heights and to avoid excessive overestimation at lower canopy heights. These findings, lower RMSE, less bias, and less saturation all point to the possibility of creating global mosaics forest of height and products derived from height, such as biomass, using fusion of the two missions. Given the complexity of our fusion process held against, say, the seemingly simpler approach of machine learning using readily available ancillary data, the question may be asked if the improvement in results is worth the effort. Our results suggest that it is.

A second question concerns the efficacy of regionalized vs. country-scale calibration. Although country-scale calibration had higher RMSEs compared to regional calibration (about 5% higher in Gabon, 8% in Mexico, 3% in French Guiana and 12% higher in Amazon Basin at 25 m), in absolute terms these differences, while not negligible, were not so great. More importantly, the comparison in Fig. 7 shows differences in the spatial distribution of heights. The regional approach results in more tall canopy heights though not in all areas. Intuitively we would expect that for a location with taller trees, models based on GEDI data that are nearby and sampling those tall trees should capture their frequency better than a country-level model. This is consistent with other research using fusion of GEDI with Landsat data which showed that models calibrated within a smaller geographic extent (e.g., at 1–10 km scale) had higher accuracy compared to larger-scale models (Healey et al., 2020). The generality of this finding is not known and needs further research, but brings us to the issue of non-representative sampling by GEDI.

Regionalized model accuracy depends on the availability and quality of GEDI data in that region. We have discussed the large gaps that result from the GEDI sampling pattern and also from clouds. As these gaps get larger the model window must also get larger to encompass enough GEDI shots for model building. Model accuracy may be compromised if the included training data do not adequately represent forest cover type and density for the condition of the center grid cell. The inclusion of land cover maps may help in these cases by identifying which GEDI observations in the area are of the same type, and weighting these more heavily especially if window sizes are increased to provide more observations.

Another issue is the impact of errors in GEDI height estimates. While GEDI was designed to retrieve canopy top heights to within 1–2 m, these accuracies are not constant and vary as a function of the GEDI waveform quality, which in turn is dependent on slope, canopy cover, whether the estimate is from a strong or coverage beam, canopy cover, day vs. night and atmospheric optical depth. Height errors resulting from these factors may appear as noise (that is random) or as a bias, and these then propagate into calibration models. A related factor is the relatively wide pulse width of the GEDI incident waveform, which limits the ability of the instrument to resolve low lying (< 5 m) canopy heights (Li et al., 2023).

At the 25 m footprint scale the geolocation accuracy of the GEDI footprints is an important factor. As discussed earlier, GEDI data are geolocated to about 10 m accuracy (1 sigma). For 25 m grid cells this mismatch can result in significant differences in both the calibration process (where TDX data are collocated with GEDI data) as in the validation process (where GTDX estimates are compared to airborne lidar (Roy et al., 2021)). This error is greatly reduced for 100 m grid cells and further reductions in geolocation error (below 8 m) are expected in subsequent processing of the data.

Another indicator of the validity of our estimation process is to compare GTDX heights with the frequency distribution of heights from lidar. Our estimates did not accurately capture the distribution of low (less than around 10 m) canopy heights relative to lidar estimates (Fig. 11). This is likely the result of our preference to avoid bias in tall canopies at the expense of short canopies by choosing baselines (the distance between the two TDX sensors for the interferometry) that produced smaller vertical wavenumbers. The vertical wavenumber k_Z plays an important role in the accuracy of forest height estimation, as it defines the height range with optimal performance. Large vertical wavenumbers favor the estimation performance of low forest stands, but result in higher estimation variance for tall stands, often associated with underestimation. Conversely, small vertical wavenumbers allow unbiased height estimation of tall stands, but lead to overestimation of low stands. The latter essentially pushes the lower heights into higher height bins in the frequency distribution. In many cases, the vertical wavenumbers realized in the standard DEM mode of TDX are not large enough to avoid underestimation of low forest stands (Choi et al., 2023). The regionalized models employed in the current study use simple linear regression, and TDX height and 1/k_Z as predictors. This approach might be sensitive to errors contained in the training data and may have limitations in mapping the shortest and tallest forests. In the absence of new TDX scenes with other baselines, it may be possible to improve results by including other variables in the model, such as canopy cover and horizontal texture information from TDX.

In this paper, we have demonstrated a method for mapping height at high resolution across entire countries based on fusion of spaceborne GEDI lidar measurements and high-resolution TDX InSAR images. TDX single polarimetric InSAR data can successfully map high-resolution pantropical forest height over large spatial scales by incorporating GEDI-simulated reflectivity profiles. While further research is needed to refine elements of our approach, the improvements outlined here justify continued effort on this path.

A concluding consideration is the downstream use of these maps for biomass estimation either through the use of the GTDX height fields with height-to-biomass allometries, or via statistical models that use GEDI footprint estimates of biomass to train predictive models based on these height fields. In either case, a concern is the temporal mismatch between GEDI and TDX. For this study we chose scenes with the most advantageous baseline configuration, regardless of date of acquisition. This mismatch may be problematic if the goal is a baseline map of biomass for a particular epoch. In this case, care must be used to take into account potential canopy changes, such as deforestation or regrowth that may have occurred between the TDX and GEDI observation periods, both for creating calibration models and for assessing biomass changes. While potentially a source of uncertainty, if done carefully, the temporal nature of TDX heights calibrated from GEDI provides an unprecedented opportunity to create epochal biomass maps from its two previous observation cycles as well as its current cycle (2023–2025). The GEDI mission is further scheduled to go offline and place in storage on the ISS in March of 2023 and to be redeployed in late 2024, potentially obtaining new observations through 2026 and beyond for fusion with TDX and other sensors. Along these lines, we note that the technique utilized in this study can be effectively applied in conjunction with data obtained from the P-band BIOMASS SAR mission (Quegan et al., 2019) and the L-band NASA/ISRO NISAR mission (Rosen et al., 2016), both scheduled for launch in 2024. The possibility thus exists for further SAR-lidar fusion mid-decade using near contemporaneous observations from the confluence of these missions, highlighting the priority of fusion frameworks such as presented here.

Competing interests: The authors declare no competing interests.

Acknowledgements

This work was funded by NASA’s Carbon Monitoring System (CMS) (Grant # 80NSSC20K0023) and NASA's Global Ecosystem Dynamics Investigation mission (Contract #NNL 15AA03C). TerraSAR-X/TanDEM-X data were provided and pre-processed by Microwaves and Radar Institute of the German Aerospace Center (DLR).

Data Availability Statement

Global Land Cover and Land Use 2019 Data is available at https://glad.earthengine.app/view/global-land-cover-land-use-v1; LVIS data can be obtained at: http://lvis.gsfc.nasa.gov/; Canopy Height Model derived from ALS data collected across the Brazilian Amazon is published at https://doi.org/10.5281/zenodo.7104044; The G-LiHT data is openly available at https://gliht.gsfc.nasa.gov/; Version 2 GEDI L1B is available from https://lpdaac.usgs.gov/products/gedi01_bv002/; Version 2 GEDI L2A is available from https://lpdaac.usgs.gov/products/gedi02_av002/; GEDI-TDX fusion forest canopy height and RMSE maps are available at https://appex.umd.ourecosystem.com/interface/.

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Mapping Large-Scale Pantropical Forest Canopy Height by Integrating GEDI Lidar and TanDEM-X InSAR Data

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Abstract

Figures

1 Introduction

2 Study Sites and Datasets

2.1 Study sites

2.2 Land, Vegetation and Ice Sensor (LVIS) data

2.3 Small-footprint airborne laser scanning (ALS) data

2.4 GEDI data

2.5 TDX data

3 Methods

3.1 Structure-based framework for TDX height inversion

3.2 Regionalized calibration for GTDX height estimation

3.3 Uncertainty estimation

3.4 Validation of GTDX height products

4 Results

4.1 TDX height from structure-based inversion

4.2 GTDX canopy height based on regional calibrations

4.3 Comparison with other global height maps

5 Discussion

6 Conclusions

Declarations

Acknowledgements

Data Availability Statement

References

Supplementary Files

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