Abstract Stochastic simulation has been employed for producing long-term records and assessing the impact of climate change on hydrological and climatological variables in the future. However, traditional stochastic simulation of hydroclimatological variables often underestimates the variability and correlation structure of larger timescale due to the preservation of long-term memory. However, the Long Short-Term Memory (LSTM) model, one type of recurrent neural network (RNN), employed in different fields, exhibits a remarkable long-term memory characteristic owing to the recursive hidden and cell states. The current study, therefore, applied the LSTM model to the stochastic simulation of hydroclimatological variables to examine how good the LSTM model can preserve the long-term memory and overcome the drawbacks of conventional time series models. The simulation involved a trigonometric function and the Rossler system as well as real case studies for hydrological and climatological variables. Results showed that the LSTM model reproduced the variability and correlation structure of the larger timescale as well as the key statistics of the original time domain better than the traditional models. The hidden and cell states of the LSTM containing the long-memory and oscillation structure following the observations allows better performance compared to the other tested conventional models. This better representation of the long-term variability can be critical in water manager since future water resources planning and management is highly related with this long-term variability. Thus, it is concluded that the LSTM model can be a potential alternative for the stochastic simulation of hydroclimatological variables. Also, note that another long-term memory model such as Gated Recurrent Unit can be also applicable.

中文翻译：

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使用深度学习模型再现水文气候变量长期记忆的随机模拟

摘要 随机模拟已被用于产生长期记录和评估未来气候变化对水文和气候变量的影响。然而，由于长期记忆的保留，传统的水文气候变量随机模拟往往低估了较大时间尺度的变异性和相关性结构。然而，长短期记忆 (LSTM) 模型是一种用于不同领域的循环神经网络 (RNN)，由于递归隐藏和单元状态，它表现出显着的长期记忆特性。因此，当前的研究将 LSTM 模型应用于水文气候变量的随机模拟，以检验 LSTM 模型在保持长期记忆和克服传统时间序列模型的缺点方面的效果如何。模拟涉及三角函数和罗斯勒系统以及水文和气候变量的真实案例研究。结果表明，LSTM模型比传统模型更好地再现了较大时间尺度的可变性和相关性结构以及原始时域的关键统计数据。与其他经过测试的传统模型相比，包含长记忆和振荡结构的 LSTM 的隐藏状态和单元状态在观察之后具有更好的性能。由于未来的水资源规划和管理与这种长期可变性高度相关，因此更好地表示长期可变性对于水资源管理人员来说至关重要。因此，得出的结论是，LSTM 模型可以成为水文气候变量随机模拟的潜在替代方案。另请注意，另一种长期记忆模型（例如门控循环单元）也适用。