Forest height retrieval under zero baseline InSAR: A reduced-order coherence framework

Within the Sentinel User Preparation- Synthetic Aperture Radar (SUPSAR) programme, this study addresses a fundamental and timely challenge: how to retrieve forest height robustly from the near-zero baseline, repeat-pass interferometric configurations that will dominate the coming Copernicus SAR System-of-Systems. Sentinel-1, the upcoming ROSE-L mission, as well as NISAR, all operate with tightly controlled orbital tubes and regular revisit cycles, providing dense temporal sampling but limited spatial baselines. While this configuration enables systematic global monitoring, it renders classical geometric PolInSAR approaches ill-conditioned, as volume decorrelation becomes weak and height sensitivity diminishes.

Given the operational reality of 6–12 day repeat cycles and small perpendicular baselines, there is an urgent need for simple, stable, and physically consistent methods tailored to zero- or near-zero-baseline InSAR. The method should exploit temporal decorrelation behavior rather than geometric decorrelation, operate reliably under dual-polarimetric constraints, and remain extensible to multi-frequency configurations. Developing these frameworks is critical for ensuring that the Sentinel-1 and ROSE-L System-of-Systems can deliver continuous forest structure monitoring at continental to global scales.

We propose a reduced-order coherence modelling strategy for forest height estimation based upon a parameter reduction of the Random Motion over Ground (RMoG) temporal decorrelation model. Instead of directly inverting the full nonlinear scattering formulation, which contains multiple interacting physical parameters and leads to an underdetermined problem under limited observability, we reformulate the interferometric coherence as a compact height-dependent polynomial representation. Through a systematic series expansion and parameter aggregation, the complex set of attenuation, motion variance, and ground-to-volume terms is collapsed into two effective coefficients that preserve the physical behavior of the model while dramatically reducing inversion dimensionality.

This reduced parameterization transforms forest height retrieval under small-baseline conditions into a well-posed, numerically stable estimation problem. The framework is designed to operate on time-series stacks, where multiple repeat-pass interferometric pairs are jointly exploited to enhance robustness and mitigate noise. Height can then be retrieved through constrained numerical optimization, enabling consistent estimation even under dual-polarimetric acquisition modes.

In addition to deterministic inversion, we introduce a physics-guided deep learning extension in which neural networks are trained to estimate the reduced-order coefficients rather than height directly. This preserves physical interpretability while improving robustness to noise, seasonal variability, and modelling approximations. The approach remains analytically constrained, avoiding black-box regression and ensuring compatibility with multi-temporal and multi-frequency observations.

The reduced-order framework is inherently extensible. It supports single-frequency (C- or L-band) operation and can be naturally extended to dual-frequency synergy, where shared canopy height is estimated jointly from C- and L-band time-series. The formulation also accommodates multi-polarization observables and enables systematic assessment of orbit phasing strategies, temporal baselines, and frequency combinations in line with SUPSAR objectives.

By converting small-baseline interferometric coherence into a reduced, physically interpretable height model, this work opens a practical pathway for operational forest height monitoring within the Sentinel-1 and ROSE-L System-of-Systems. The approach advances state of the art beyond classical geometric PolInSAR, aligns with the high temporal density of current and future SAR missions, and establishes a scalable framework for synergistic multi-frequency forest monitoring in preparation for the next generation of Copernicus SAR capabilities