State-Space Unlearning for Non-Stationary Bias in Land Surface Forecasting

Operational land surface forecasting systems built on Mamba-family Structured State Space Models absorb non-stationary confounding events (unrecorded irrigation booms, dam-operation shifts, sensor recalibrations) into their state-transition matrices, silently biasing NDVI, LST, and crop phenology predictions long after the physical cause ends. This paper introduces SSU-LSF (State-Space Unlearning for Land Surface Forecasting), the first machine-unlearning framework purpose-built for geoscientific Mamba-based SSMs. We develop EKFac influence functions specialized to the Mamba state matrices via a closed-form matrix-exponential gradient, use spectral-radius-weighted elbow thresholding to localize a temporal confounding footprint Phi, and apply Hessian-free projected gradient ascent within a KL-divergence trust region augmented by spatial total-variation (TV) regularization. Proposition 1 establishes that residual confounding is bounded by Obig((1-ρ(barA)Tc)/((1-ρ(barA))μ)big), which grows with the window length Tc. Across three heterogeneous benchmarks and eleven baselines, SSU-LSF achieves confounding reduction rates of 0.773 (CropHarvest), 0.821 (NDVI-LST), and 0.859 (ERA5), with worst-case clean-domain RMSE degradation of 4.2% on ERA5, converging in 3--5 epochs at 8.4× lower GPU-cost per unlearning request than full retraining. Code: https://github.com/Anidipta/SSU-LSF