A Leakage-Free, Delta-Based Deep Learning Framework for Long-Term Lake Volume Prediction

A Leakage-Free, Delta-Based Deep Learning Framework for Long-Term Lake Volume Prediction Lakes are vital freshwater resources whose long-term storage dynamics are increasingly influenced by hydroclimatic variability, making accurate lake volume forecasting essential for sustainable water resources management. This study investigates whether a delta-based prediction strategy, in which monthly lake volume changes (ΔLV) are predicted instead of absolute lake volumes, improves long-term forecasting performance. Monthly hydroclimatic observations for Lake Beyşehir (Türkiye) covering 1965–2023 were used to develop Long Short-Term Memory (LSTM), Bidirectional Long Short-Term Memory (BiLSTM), and Gated Recurrent Unit (GRU) models under both direct and delta prediction strategies. Model performance was evaluated for different optimization algorithms and antecedent sequence lengths using RMSE, MAE, NSE, KGE, and PBIAS. Results showed that the delta-based strategy consistently outperformed direct prediction by more effectively capturing temporal variations in lake storage. The best-performing model, BiLSTM with a 24-month input sequence, achieved an RMSE of approximately 80 hm³, an NSE of 0.966, a KGE of 0.982, and a PBIAS of 0.44% during testing. These findings demonstrate that predicting monthly lake volume changes substantially improves long-term forecasting accuracy while reducing systematic prediction bias. The proposed framework provides a robust and transferable approach for lake volume forecasting and offers valuable support for sustainable lake management under changing hydroclimatic conditions.无数据泄漏、基于差分的深度学习框架用于长期湖泊水量预测 湖泊是至关重要的淡水资源，其长期储水动态日益受到水文气候变化的影响，因此精准的湖泊水量预测对水资源可持续管理至关重要。本研究探讨了基于差分的预测策略——即通过预测月湖泊水量变化量（ΔLV）而非绝对湖泊水量——能否提升长期预测性能。本研究以土耳其贝谢伊尔湖（Lake Beyşehir）1965-2023年的月尺度水文气象观测数据为基础，分别采用直接预测和差分预测两种策略，构建了长短期记忆网络（Long Short-Term Memory, LSTM）、双向长短期记忆网络（Bidirectional Long Short-Term Memory, BiLSTM）以及门控循环单元（Gated Recurrent Unit, GRU）模型。本研究针对不同优化算法及前期序列长度，采用均方根误差（RMSE）、平均绝对误差（MAE）、纳什效率系数（NSE）、克林-古普塔效率系数（KGE）以及相对偏差（PBIAS）对模型性能进行评估。研究结果表明，基于差分的预测策略能够更有效地捕捉湖泊储水的时间变化特征，因此其性能始终优于直接预测策略。测试阶段，表现最优的模型为输入序列长度为24个月的双向长短期记忆网络（BiLSTM），其均方根误差约为80 hm³，纳什效率系数为0.966，克林-古普塔效率系数为0.982，相对偏差仅为0.44%。上述研究结果表明，预测月湖泊水量变化量可显著提升长期预测精度，同时降低系统性预测偏差。本研究提出的框架为湖泊水量预测提供了一种稳健且可迁移的方法，可为水文气候变化背景下的湖泊可持续管理提供重要支撑。