Modelling glacier-wide annual mass balance of continental-type glaciers in China using a deep neural network

Abstract. Glacier mass balance is crucial for climate and hydrological research. Although data-driven techniques have advanced mass balance estimation, their reliance on comprehensive and reliable training datasets still limits their practical application. In this study, a lightweight feed-forward fully connected neural network (FF-FCNN) was developed to simulate glacier-wide annual mass balance using multi-temporal meteorological variables from ERA5-Land, MODIS-derived summer mean albedo, and topographical attributes from ASTGTM_003 as input features, with 180 glaciological observations from ten continental-type glaciers in China as reference data. To mitigate overfitting in the “small-sample, high-dimensional” scenario, key meteorological variables were selected using the Pearson correlation analysis combined with the Random Forest (RF) algorithm, and several strategies including Gaussian noise injection, L1 regularization, and early stopping were incorporated into the model architecture. Two training dataset construction strategies were evaluated to address temporal inconsistencies in albedo data, and both results demonstrated that the FF-FCNN effectively avoids overfitting and maintains stable and reliable performance. Under the reduced-sample strategy, the FF-FCNN significantly outperformed the Random Forest model (R² = 0.82, RMSE = 0.19 m w.e., MAE = 0.15 m w.e.). Spatial and temporal cross-validations further confirmed the robustness and generalization capability of the proposed model. Although the dynamic loss-based weighting strategy enhanced the model’s ability to capture pronounced interannual variability in glacier mass balance, reproducing extreme values ​​remains challenging under severely limited sample conditions. Overall, the proposed framework provides a feasible pathway for estimating regional glacier mass balance in high-altitude and cold regions where observations are scarce.