Objectives  The random volume over ground (RVoG) model is widely used in forest height inversion with polarimetric interferometric synthetic aperture radar (PolInSAR). The model assumes that the forest is a random uniform homogeneous body and the extinction coefficient in the model is a constant with‍out considering the effects of forest vertical heterogeneity and terrain slope. This paper proposes a prom‍is‍ing multi-baseline (MB) algorithm for forest height inversion based on a slope-RVoG (S-RVoG) model with linearly varying extinction.

  Methods  The effects of terrain slope and forest vertical heterogene‍ity on forest height inversion with the RVoG model are considered in the proposed algorithm. Firstly, the terrain slope is introduced to rectify the effective vertical wavenumber, and the S-RVoG model is derived on the basis of the basic RVoG model. Secondly, the linearly varying extinction coefficient, which is assumed to vary linearly with the forest height, is introduced into the S-RVoG model, and it can be solved by the Gaussian error function. Finally, MB PolInSAR datasets are used to solve the parameters of the S-RVoG model with linearly varying extinction, and the forest height can be obtained by the MB three-stage algorithm with coherence separation product criterion. The P-band F-SAR airborne PolInSAR datasets obtained by the 2016 AfriSAR campaign of the European Space Agency are selected for experimental verification.

  Results  The results of four MB algorithms, namely MB RVoG, MB S-RVoG, MB RVoG with linearly varying extinction, and MB S-RVoG with linearly varying extinction, are compared. The root mean square error (RMSE) and the relative error are used to evaluate the accuracy of the obtained forest height. (1) The forest height calculated by the MB RVoG algorithm is a significant overestimation, with RMSE of 6.57 m and relative error of 16.8%. (2) The RMSE of the MB S-RVoG algorithm is 5.97 ‍m, and the relative error is 15.1%. The accuracy is improved by about 10% with the addition of terrain slope correction. (3) The MB RVoG algorithm with linearly varying extinction has RMSE of 4.71 m and relative error of 11.0%. Compared with the conventional MB RVoG algorithm, it improves the accuracy by about 28.3%. (4) The RMSE of the MB S-RVOG algorithm with lin‍ear‍ly varying extinction is 4.27 ‍m, and the relative error is 9.9%. Compared with the results of the MB RVoG algorithm and the MB S-RVOG algorithm, the accuracy is improved by about 35% and 28.4%, respectively.

  Conclusions  The RVoG model is widely used in PolInSAR forest height inversion. The MB S-RVOG algorithm with linearly varying extinction considers the effects of terrain slope and forest vertical heterogeneity simultaneously and introduces linearly varying extinction and terrain slope to correct the mod‍el, which makes up for the deficiency of the tradition‍al RVoG model. The results show that the S-RVOG model with linearly varying extinction performs better in tropical forests with high forest density and great forest height.