Uncertainty-aware few-shot snow depth estimation in complex terrains via generative-Bayesian deep learning

• Novel Generative-Bayesian Few-Shot Framework for robust, uncertainty-aware SD estimation. • Where-Way-What Strategy identifies gaps, generates samples, and trains reliable models. • cWGAN-GP produces realistic and diverse SD time-series samples for scarce regions. • Bayesian BiGRU enhances generalization with calibrated, interpretable uncertainty. • Achieves MAE < 2 cm and strong robustness across complex, data-limited terrains. Accurate snow depth (SD) estimation is critical for understanding cold-region hydrology, land–atmosphere interactions, and cryosphere dynamics. Deep learning (DL) offers transformative potential for remote sensing SD estimation, yet sparse, uneven, and terrain-dependent in-situ measurements make it a typical few-shot problem, limiting generalization and predictive reliability. To address this, we propose a Generative-Bayesian Framework for Few-Shot SD Estimation (GB-FSSD) that integrates physically consistent generative data augmentation with uncertainty-aware recurrent modeling. GB-FSSD mitigates scarcity, imbalance, and limited representativeness through targeted synthetic sample generation. Guided by a Where-Way-What strategy: (i) Where , underrepresented Alpine and Forest regimes are identified via sample-space representativeness analysis; (ii) Way , a conditional Wasserstein GAN with gradient penalty (cWGAN-GP) generates physically plausible and statistically consistent synthetic sample time series; (iii) What , a Bayesian bidirectional GRU is trained on the augmented dataset, with optimal augmentation scales determined by predictive accuracy and uncertainty. Applied to China’s 2019–2020 snow season, GB-FSSD achieves MAE < 2 cm, R 2 > 0.84, and average predictive uncertainty ∼ 0.46 cm, demonstrating robust generalization under data-limited conditions. By integrating spatial representativeness analysis, generative augmentation, and uncertainty-aware modeling, GB-FSSD provides a scalable and generalizable framework for Earth Observation-based geophysical variable estimation, with broad applicability to cryosphere and Earth system studies.