Global fine beam dual-polarization (FBD) SAR images with a spatial grid of 10 × 3 m (for range and azimuth directions) were collected by the ALOS-1 satellite from 2007 to 2010, with a repeat cycle of 46 d. To generate a forest height mosaic, 100 cross-polarized ALOS-1 InSAR scenes (identified by one pair of frame and orbit numbers) were processed to cover the New England region in the US, whereas more than 600 InSAR scenes were processed for covering the northeast of China. The InSAR preprocessing was done by the Jet Propulsion Laboratory (JPL)'s InSAR Scientific Computing Software (ISCE) software (Rosen et al., 2012). It was reported by Lei and Siqueira (2014) that the ALOS-1 InSAR observations acquired during the summer/fall time frame of 2007 and 2010 tended to have higher InSAR coherence. In practical processing, multiple cross-polarized interferograms during the lifetime of ALOS-1 (2007–2011) were formed and processed for each scene based on different combinations of acquisition dates, allowing for the identification of the best InSAR pair for each ALOS-1 observation scene.

As a follow-on mission to ALOS-1, ALOS-2 had a shorter revisiting period (14 d), resulting in a better InSAR correlation behavior. The acquisition started from 2016, allowing for nearly concurrent observations with respect to GEDI samples. However, the acquisition strategy and limited access to the high-resolution dual-polarized strip-map data have made it more difficult to form proper InSAR pairs and perform large-scale mapping. The grid of ALOS-2 images in FBD mode is at a grid of 8 × 4 m for range and azimuth directions. A window size of 4 × 8 looks is used for the coherence estimation, resulting in an average pixel size of 30 m.

In this study, the use of limited ALOS-2 data is devoted to demonstrating the proposed approach in the ideal case. The large-scale mapping capabilities were demonstrated using free-access ALOS-1 data over the temperate forest regions. It is also noted that there is a time discrepancy between the acquisition dates of ALOS-1 and GEDI. This discrepancy is addressed using the twofold solution as detailed in Sect. 3.3. As for the abrupt discrepancy due to forest disturbance (e.g., logging, deforestation, and fire) that usually results in no/short vegetation with small backscatter values, replacing the InSAR inverted forest estimates with those derived from the appropriate ALOS-2 backscatter mosaic map for short vegetation (as shown in Sect. 3.1) can detect the disturbed forest areas, so the study area is mainly concentrated on temperate and boreal forests, the heights of mature temperate forests (intact forest landscape) remain almost stable with slight changes. Nevertheless, a simulation in Sect. 3.4.3 shows that the approach of this study can approximate the height of the forests subject to natural growth at a regional scale. In other words, all the InSAR-based height inversions are calibrated to the acquisition time of GEDI and thus best compared with the concurrent airborne lidar validation data.

As the first spaceborne lidar mission to characterize ecosystem structure and its dynamics, the NASA's GEDI mission was launched in December 2018. GEDI provides near-global measurements of forest structure metrics from 51.6° S to 51.6° N until 2024. With three lasers mounted, eight parallel tracks of samples at a footprint of 25 m are simultaneously collected. The spatial separation between samples during one data take is 60 m in the along-track direction and 600 m in the cross-track direction. The GEDI RH98 metric is selected as an appropriate proxy for indicating forest canopy height within each footprint because it has a lower sensitivity to errors as compared to the RH100 metric (Hofton et al., 2020). After filtering out GEDI samples with lower penetration sensitivities (e.g., 95 % sensitivity, 50 m maximum elevation difference between GEDI and TanDEM-X measurements), the remaining L2A version 2 GEDI samples are used for calibrating the inversion model.

A significant amount of airborne full-waveform lidar data was collected across the US using the LVIS sensor. The lidar data were processed into RH98 maps with a 25 m grid. Specifically, lidar data over the Howland Forest site in Maine were obtained in 2009. LVIS data acquired in 2021 for GEDI calibration cover all the other forest sites in the New England region, which were classified into four parts based on the state boundaries of New Hampshire, Vermont, Massachusetts, and Connecticut.

In some sites, small-footprint lidar data have to be used for validation. The validation at the WNMF site utilized GRANIT lidar data, which has a 2 m footprint and was acquired in 2011. All the forest heights in northeastern China were validated using small-footprint lidar data. The airborne lidar data, with an average point density of 6 pts m⁻² over Hubao National Park, were acquired using an airborne lidar system owned by the Chinese Academy of Forest Inventory and Planning. The observations covering all other forest sites in the northeastern China were acquired during 2017–2022 using the airborne remote sensing system developed by the Chinese Academy of Forestry (Pang et al., 2016), which has an average point density of 12 pts m⁻². It should be noted that validating the forest height estimates against airborne LVIS observations is not straightforward as the footprint of these airborne data is much smaller than the footprint of GEDI. To address this footprint difference, an equivalent RH98 metric (referred to as ERH98 hereafter) needs to be extracted at the position of the 98th percentile of the lidar waveform or from the histogram formed by high-resolution canopy height model (CHM) estimates within a matching footprint size. Following this procedure, all small-footprint lidar data were reprocessed to generate forest height estimates based on the ERH98 metric using a 25 m footprint

Non-forest areas including waterbodies and urban areas were masked out using the 2021 National Land Cover Database (Homer et al., 2015) and the 2021 ESRI Global Land Cover Map (Karra et al., 2021).

This study used the global radar backscatter products generated by JAXA using ALOS-1/2 FBD images (Shimada et al., 2016) after radiometric and geometric calibration (including slope effects correction). Specifically, the global cross-polarized backscatter products from 2019 and 2020 over the northeast of the US and China were utilized to obtain height estimates of short vegetation. These 2-year products were used to account for missing data gaps and backscatter calibration inconsistencies and to best match the acquisition time of the validation airborne lidar data.

The acquisition times between repeat-pass InSAR and spaceborne lidar usually do not overlap in practice. For example, the ALOS-2 InSAR acquisitions would match those of GEDI ideally; however, there are not many ALOS-2 InSAR pairs available in the data archive that are freely accessible. In contrast, ALOS-1 InSAR pairs are consistently available covering the study regions; however, there is an approximate 10-year time gap. To address this issue, a twofold solution is provided in Sect. 3.4. The temporal evolution of forests is primarily influenced by two factors: forest disturbance (including deforestation) and natural growth. Forest disturbance leads to forest loss and, in some cases, conversion to other land uses, such as bare ground. This change is poorly characterized by the signal model (3) and must be addressed in advance.

The height of the bare ground and short vegetation (≤10 m) (Lawrence, 2013; Allaby, 2012) is better inverted by jointly using the SAR backscatter and spaceborne lidar data compared to the InSAR correlation-based approach (Lei, 2016). Moreover, annual global backscatter products are available from the archive of JAXA, enabling the fusion of the ALOS-2 SAR backscatter information and spaceborne lidar under nearly concurrent acquisition conditions. Figure 8 presents an example of forest loss detection by SAR backscatter-based inversion within the New England region: the majority of forest disturbance areas as defined by the global forest change products (Hansen et al., 2013) were detected by the backscatter-based estimates. Based on the statistics over the New England region, 72 % of disturbed areas have been detected using the backscatter-based estimates.

Short forests undergoing rapid temporal height variations within short intervals cannot be adequately captured by current ALOS-1/2 datasets. These dynamic changes can be better resolved using dense time series data from TanDEM-X (Treuhaft et al., 2017; Lei et al., 2018), Sentinel-1 (Bhogapurapu et al., 2024), and the forthcoming NISAR mission.

The natural growth of forests remains another concern. In temperate forest regions, the intact forest landscape (IFL), along with forest height, remains quite stable and only changes slightly as trees grow (Potapov et al., 2008; Riofrío et al., 2023). In the New England region, the growth rate was found to be inversely proportional to forest height. This finding is based on a comparison between ICESat-1 or LVIS lidar data acquired before 2009 and LVIS lidar data collected in 2021. Using these datasets, the temporal evolution of forest height at two epochs is modeled as follows: 11hvt2=hvt1+G⋅t2-t1, where hv represents the time-dependent forest height and t1andt2 denote the initial and subsequent epochs, respectively. Although the forest growth rate is derived by comparing pre- and post-growth states, it can be modeled based only on forest height data from either epoch, for example, using the initial forest height hvt1: 12G=a⋅hvt1+b, where a and b are linear coefficients. If a dense time series of forest height data over certain forest land cover is provided, the above equation can be constructed in a differential form as 13∂hv∂t=a⋅hv+b.

This ordinary differential equation yields the following expression: 14hvt1=ba+Ht2e-at2-t1-ba.

This expression aligns with the Hossfeld model. However, it requires statistical data on annual growth rates, which is often unavailable on a large scale in practice. When the parameter a is small, Eq. (14) simplifies to the form presented in Eq. (12). Evaluation in the New England region indicates the absolute value of a is less than 0.02. By substituting Eq. (12) into the signal model, the following modified model is obtained: 15γt&vHVt1=St1⋅sinchvt2-b⋅dt1-a⋅dt⋅Ct1, where γt&vHVt1 represents the InSAR coherence at initial time t1, and it follows that the model is shifted and scaled with respect to original model (3); dt=t2-t1.

As a representative example, Fig. 9 illustrates the fitted forest growth rate (G=-0.0134⋅hvt1+0.464; unit: m yr⁻¹) for the forest height interval with the highest density at the Harvard Forest site in Massachusetts. This analysis compares LVIS lidar data acquired in 2009 and 2021 after filtering out disturbed forests areas (G≤-0.1 m yr⁻¹) and short vegetation hv≤10m. To illustrate how the InSAR correlation observations from ALOS-1 data are linked to GEDI forest estimates (with time gap of around 10 years), a simulation can be performed by inserting the fitted growth rate into model (15) and settings St1=0.9 and Ct1=11. Figure 10 presents the simulated results of original sinc model and its modified version. It follows that the forest height below b⋅dt cannot be well characterized. This value usually ranges from 8 to 15 in the investigation over the New England region. This finding also highlights the importance of utilizing backscatter information to estimate the heights of short forests in this case. We remark that natural growth functions are highly species-specific. From a practical inversion perspective, the application of the modified model requires precise detailed statistics of natural growth across various forest types on a large scale. However, such data are currently unavailable as existing spaceborne lidar datasets lack collocated measurements from two distinct time periods. In the absence of comprehensive forest growth data, this model is not yet recommended for direct large-scale use. Instead, it can be integrated into the framework of the original model by adjusting temporal parameters. The following subsection provides simulation examples to demonstrate this adaptation.

Without detailed forest growth statistics, this subsection demonstrates that the modified sinc model can be well approximated in the framework of the original sinc model but with updated parameters S′,C′ using simulations. This enables large-scale application achieved in the framework of the original model without detailed growth statistics.

It is almost impossible to derive S′ and C′ based on a direct one-to-one analytical transformation between models (15) and (3). Instead, such parameters can be determined by aligning the original model and modified model at two fixed points. For example, Fig. 11 presents the resolved parameters when the alignment is performed for two points at 10 and 30 m for global fitting at three typical forest sites (e.g., scenes with large forest height ranges). The best approximation is observed at the Howland Forest site, where the forest height changes slowly. Model mismatches are observed at 20 m at other two forest sites. This can be addressed by aligning two models for each short interval. Figure 12 presents the behavior of newly fitted parameters when aligning either a short forest interval (e.g., 10–15 m) or a tall forest interval (e.g., 25–30 m). The results suggest that the modified sinc model is better approximated through piecewise fitting, emphasizing the importance of local fitting to approximate modified models for a short height range within relatively homogeneous forest areas. Notably, S′ increases and even exceeds 1, particularly for taller trees, deviating from its original physical definition S′≤1 (e.g., only due to moisture-induced dielectric decorrelation in the original model). As seen in the behavior of the fitted parameters for each short interval x,x+5 in Fig. 13, the C′ parameter is larger than the original parameter C for short vegetation but approaches C as vegetation height increases, while the S′ parameter is close to the original S parameter for short trees and becomes biased for tall trees. For the three forest sites analyzed, the White Mountain National Forest shows a larger forest height change rate, leading to a greater deviation between the fitted parameters S′,C′ and the original parameters S,C.

Figure 17 presents density scatterplots comparing forest height estimates (derived from ALOS-1 mosaics or ALOS-2 single-scene inversions where suitable InSAR pairs are available) across all test sites in the New England region of the US. Error metrics for these estimates are reported in the corresponding scatterplots.

In short, the proposed inversion approach is capable of estimating forest height with an RMSE of 3–4 m in areas such as Howland and Harvard Forest sites, characterized by relatively flat topography and minimal human activity influence. In contrast, hilly or suburban areas, such as WMNF, GMNF, and Naugatuck State Forest (NSF) sites, exhibit slightly lower accuracy (RMSE 4–5 m). The ALOS-2-based inversion generally presents superior performance due to enhanced InSAR correlation behavior resulting from shorter temporal baselines and less temporal discrepancy between radar and lidar data. For ALOS-1 inversion, the time mismatch between ALOS-1 and GEDI data is not a fatal problem as the inversion is carried out for temperate regions where the intact forest landscapes and forest height (of mature forests) remain stable. While our solution for addressing forest growth may not fully resolve temporal uncertainties, the resulting errors remain relatively minor, as evidenced by an RMSE of 3–4 m. This is also supported by the finding that the ALOS-1-based inversion is occasionally more accurate than ALOS-2-based estimates.

In addition, we evaluate the inversion performance of two widely recognized global forest products: the GEDI-Sentinel (ETH) product (Lang et al., 2022) and the GEDI-Landsat (GLAD) product (Potapov et al., 2021). As shown in Table 4, both products exhibit significant biases across forest sites in the New England region compared with our ALOS-1-based estimates. Specifically, the GLAD product systematically underestimates canopy height, likely due to saturation effects in dense canopies, while the ETH product demonstrates larger systematic biases, consistently overestimating canopy height at all sites. These findings are consistent with the analysis by Qi et al. (2025). In contrast, our inversion method achieves lower RMSE and smaller biases in most cases, with the exception of Naugatuck State Forest. At this site, hilly topography and suburban land cover likely contribute to reduced inversion accuracy. Notably, the ETH product exhibits lower SD and higher height-related R2 values, which is likely attributable to its integration of high-resolution Sentinel-2 data.

The Howland Forest was selected as one of the representative test sites, continuing from previous efforts in developing the inversion approaches (Lei et al., 2018; Lei and Siqueira, 2022). Comparing results from these earlier studies with the current work allows for an evaluation of performance improvements. A strip of LVIS lidar data acquired in 2009 was used as the reference to assess the inversion accuracy of both the ALOS-1-based forest height mosaic map and the ALOS-2-based inversion from a single pair of ALOS-2 data (frame: 890, orbit: 37). The comparison between the inverted forest height estimates, and the LVIS lidar data is presented in Fig. 18, generating the differential height maps between the inversion and the lidar data as shown in Fig. 19a and b. For quantitative analysis, density scatterplots and corresponding statistical error metrics comparing inversion results with validation data are displayed in the first row of Fig. 17.

The comparison reveals that the ALOS-1-based mosaic inversion estimates forest height with an RMSE of 3.8 m. In contrast, the ALOS-2-based single-scene inversion achieves enhanced accuracy (RMSE = 3.6 m), likely due to improved correlation from its 14 d temporal baseline. To compare these results against our earlier work (Lei et al., 2019), we applied the global-fitting-based inversion method (in the left panel of Fig. 20), which yielded an inversion accuracy of RMSE = 4.38 m at an aggregated pixel size of 0.81 ha. This demonstrates that the global-to-local two-stage inversion approach significantly improves inversion accuracy, particularly over tall forest regions.

By synergistically combining SAR data with GEDI samples, this methodology not only resolves the wall-to-wall mapping limitations inherent to GEDI's discrete sampling, but also improves inversion precision. As shown in the right panel of Fig. 20, the 30 m interpolated GEDI-based forest height maps still face discontinuity problems. However, an accuracy improvement of up to 20 % has been achieved for ALOS-2-based estimates. This enhancement stems from the refined characterization of temporal parameters S,C enabled by leveraging GEDI's dense spatial sampling, as shown in Fig. 21. As anticipated in Sect. 3.4.3, the saturation behavior of S parameters arises from approximating modified forest growth model (15) using original model (3) in the local window with taller forests.

The Harvard Forest site was selected to evaluate the inversion in a region characterized by high biomass up to 400 Mg ha⁻¹ (Tang et al., 2021). Figure 22 presents the LVIS validation data acquired in 2021 covering the Harvard Forest area in panel (a) and the forest height estimates extracted from the ALOS-1 mosaic and the ALOS-2 single-scene inversion results (frame: 2770, orbit: 141) in panels (b) and (c). The comparison of ALOS-1 and ALOS-2 inversion results against the validation data is illustrated in the differential height maps in Figure 23. The density scatterplots from these two comparisons are given in the second row of Fig. 17.

Both the ALOS-1 mosaic and ALOS-2 single-scene inversion are capable of estimating forest height with an RMSE of 4 m. The biased estimates occurred in taller forest stands may be attributed to the degraded sensitivity of GEDI measurements over dense forest stands (Fayad et al., 2022).

The evaluation of the forest height inversion will also be extended to mountainous areas such as the WMNF site, considering the potential challenges GEDI and InSAR observations might face in these regions. These challenges include GEDI's geolocation shifts and slope effects as well as the radar's viewing geometry problems (e.g., layover, shadow, and foreshortening).

A high-resolution canopy height model (CHM), derived from small-footprint GRANIT lidar data, serves as the validation reference. As outlined in Sect. 2.2.3, due to the footprint difference between small-footprint lidar data and GEDI observations, an equivalent RH metric must be extracted within the same footprint size as GEDI observations to ensure comparability. Without this adjustment, directly comparing GEDI-based forest height inversions with the reprojected CHM (via resampling or multi-pixel averaging) introduces significant bias. Figure 24 illustrates the difference between the ERH98 metric and the mean value (or ERH50 metric) in panel (a) and shows the maps of these two metrics in panels (b) and (c). Notably, ALOS-1-based forest height estimates (Fig. 24d) align closely with the ERH98 metric (Fig. 24b). The differential map between the ALOS-1 mosaic and GRANIT ERH98 map is shown in Fig. 25, and the associated density scatterplot can be found in the third row of Fig. 17.

Forest height estimates across all sites across the northeast of China were validated against ERH98 metrics derived from small-footprint airborne lidar data. Density scatterplots as well as error metrics for the representative forest sites are summarized in Fig. 26. The highest accuracy was observed at the Mengjiagang Forest site, achieving an RMSE of 3.32 m and an R2 of up to 0.84. Most inversions exhibit a slight negative bias, likely due to GEDI's reduced signal penetration capability compared to airborne lidar. Slightly less accurate estimates are provided by the ALOS-2-based inversion at the Saihanba forest site, which is attributed to the limited overlapping area between the ALOS-2 single-scene inversion and ALS validation observations. This limitation arises from the distribution of heterogeneous land cover influenced by human activities. Overall, forest height estimates align closely with ERH98 lidar benchmarks, with accuracies of 3–4 m (even below 3.5 m at three sites) and R2 predominantly exceeding 0.65.

Notably, inversion performance in northeastern China surpasses results from GEDI calibration sites in the northeastern US, likely due to fewer forest disturbance in the selected represented forest sites (See Fig. 4) compared to those in the northeastern US, as shown in Fig. 3.

Hubao National Park is selected as it represents one of the typical temperate regions with the richest biodiversity in terms of wildlife and plants in the Northern Hemisphere. Figure 27a displays an ERH98 map derived from reprocessed 1 m resolution canopy height model (CHM) data acquired in 2018 using a window size same as GEDI footprints. Panels (b) and (c) present forest height estimates from ALOS-1 single-scene inversion (Frame 860, Orbit 421) and ALOS-2 single-pair InSAR data (Frame 860, Orbit 130), respectively. The detailed differential height maps are provided in Fig. 28.

As shown in the density scatterplots (see the bottom row of Fig. 26), both ALOS-1 mosaic and ALOS-2 single-scene inversions align closely with ALS-derived ERH98 data, achieving accuracies of 3.5–3.8 m with an R2 of up to 0.7. These results demonstrate the inversion precision comparable to airborne lidar measurements across both short and tall vegetation types. Differential height maps highlight discrepancies in transitional zones between forested and bare surfaces, underscoring the need for higher-spatial-resolution data integration (e.g., fusing TDX-GEDI data; Hu et al., 2024; Lei et al., 2021; Qi et al., 2025) to refine estimates in such areas.

Slightly better performance for ALOS-1-based inversion is attributed to the fact that the ALOS-1 InSAR data archive offers the possibility of picking out the best InSAR pair with better correlation behavior; however, the availability of proper ALOS-2 InSAR data is limited.

A second case study examines the Genhe Forest Bureau situated in northeastern China within one of the country's northernmost boreal forest regions. Figure 29 presents the (a) reference ERH98 map derived from 1 m resolution airborne lidar data, (b) forest height estimates from the ALOS-1-based mosaic, and (c) results from the ALOS-2 single-scene inversion. Differential height maps are shown in Fig. 30. The spatial distribution of forest heights in both ALOS-1 and ALOS-2 inversions closely matches the reference ERH98 map, though primary discrepancies occur in short vegetation and bare surfaces, which is likely linked to anthropogenic disturbances.

Quantitative validation (see the third row of Fig. 26) confirms strong agreement between inverted and reference forest height estimates, with an RMSE of 3.6 m and an R2 of 0.65, demonstrating the method's effectiveness and accuracy in boreal ecosystems.