Forest canopy height data are fundamental parameters of forest structure and are critical for understanding terrestrial carbon stock, global carbon cycle dynamics and forest productivity. To address the limitations of retrieving forest canopy height using conventional PolInSAR-based methods, we proposed a method to estimate forest height by combining single-temporal polarimetric synthetic aperture radar (PolSAR) images with sparse spaceborne LiDAR (forest height) measurements. The core idea of our method is that volume scattering energy variations which are linked to forest canopy height occur during radar acquisition. Specifically, our methodology begins by employing a semi-empirical inversion model directly derived from the random volume over ground (RVoG) formulation to establish the relationship between forest canopy height, volume scattering energy and wave extinction. Subsequently, PolSAR decomposition techniques are used to extract canopy volume scattering energy. Additionally, machine learning is employed to generate a spatially continuous extinction coefficient product, utilizing sparse LiDAR samples for assistance. Finally, with the derived inversion model and the resulting model parameters (i.e., volume scattering power and extinction coefficient), forest canopy height can be estimated. The performance of the proposed forest height inversion method is illustrated with L-band NASA/JPL UAVSAR from AfriSAR data conducted over the Gabon Lope National Park and airborne LiDAR data. Compared to high-accuracy airborne LiDAR data, the obtained forest canopy height from the proposed approach exhibited higher accuracy (R2 = 0.92, RMSE = 6.09 m). The results demonstrate the potential and merit of the synergistic combination of PolSAR (volume scattering power) and sparse LiDAR (forest height) measurements for forest height estimation. Additionally, our approach achieves good performance in forest height estimation, with accuracy comparable to that of the multi-baseline PolInSAR-based inversion method (RMSE = 5.80 m), surpassing traditional PolSAR-based methods with an accuracy of 10.86 m. Given the simplicity and efficiency of the proposed method, it has the potential for large-scale forest height estimation applications when only single-temporal dual-polarization acquisitions are available.
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