Hydroformer: Frequency Domain Enhanced Multi-Attention Transformer for Monthly Lake Level Reconstruction With Low Data Input Requirements

Abstract

Lake level changes are critical indicators of hydrological balance and climate change, yet long-term monthly lake level reconstruction is challenging with incomplete or short-term data. Data-driven models, while promising, struggle with nonstationary lake level changes and complex dependencies on meteorological factors, limiting their applicability. Here, we introduce the Hydroformer, a frequency domain enhanced multi-attention Transformer model designed for monthly lake level reconstruction, utilizing reanalysis data. This model features two innovative mechanisms: (a) Frequency-Enhanced Attention (FEA) for capturing long-term temporal dependence, and (b) Causality-based Cross-dimensional Attention (CCA) to elucidate how specific meteorological factors influence lake level. Seasonal and trend patterns of catchment meteorological factors and lake level are initially identified by a time series decomposition block, then independently learned and refined within the model. Tested across 50 lakes globally, the Hydroformer excelled in reconstruction periods ranging from half to three times the training-test length. The model exhibited good performance even when training data missing rates were below 50%, particularly in lakes with significant seasonal fluctuations. The Hydroformer demonstrated robust generalization across lakes of varying sizes, from 10.11 to 18,135 km², with median values for R², MAE, MSE, and RMSE at 0.813, 0.313, 0.215, and 0.4, respectively. Furthermore, the Hydroformer outperformed data-driven models, improving MSE by 29.2% and MAE by 24.4% compared to the next best model, the FEDformer. Our method proposes a novel approach for reconstructing long-term water level changes and managing lake resources under climate change.