基于时间序列LSTM模型的ENSO指数预报试验The Prediction of ENSO Indexes Based on Time Series LSTM Model

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To improve the prediction ability of El Niño-Southern Oscillation (ENSO), we use the Niño 3.4 and Southern Oscillation indexes during 1951-2008 to build time series long short-term memory (LSTM) model, and forecast that during 2009-2018. The analysis shows the time series LSTM model has a good forecasting ability for Niño 3.4 index in advance of 1 - 12 months, though underestimates the amplitude of the super El Niño event during 15/16 year. While time series LSTM model can only predict the SOI in advance of 1 - 3 months to a certain extent, because of the high frequency seasonal variability in SOI index. Further experiment proves that the 7-month run-mean SOI is also can be predicted well by time series LSTM model, similar with the Niño 3.4 index. Comparing with other statistical forecasting models, the time series LSTM model is efficient and convenience with ad-vantages in ENSO prediction.

1. 引言

2. 模型介绍

$\begin{array}{l}{i}_{t}=\sigma \left({W}_{i}{x}_{t}+{U}_{i}{h}_{t-1}+{b}_{i}\right)\\ {f}_{t}=\sigma \left({W}_{f}{x}_{t}+{U}_{f}{h}_{t-1}+{b}_{f}\right)\\ {u}_{t}=\mathrm{tanh}\left({W}_{u}{x}_{t}+{U}_{u}{h}_{t-1}+{b}_{u}\right)\\ {o}_{t}=\sigma \left({W}_{o}{x}_{t}+{U}_{o}{h}_{t-1}+{b}_{o}\right)\\ {c}_{t}={f}_{t}\odot {c}_{t-1}+{i}_{t}{u}_{t}\\ {h}_{t}={o}_{t}\odot \mathrm{tanh}\left({c}_{t}\right)\end{array}$ (1)

Figure 1. The schematic diagram of DNN and RNN

3. 实验过程

3.1. 数据介绍

ENSO是一种发生在热带太平洋的海气相互作用过程，因此有许多定义从不同角度来描述了ENSO事件。在海洋中，最具代表性的描述是Niño 3.4指数，其定义是5˚N~5˚S，170˚W~120˚W区域海表面温度距平场的空间平均。而在大气中，最具有代表性的描述是南方涛动指数(Southern Oscillation index，简称SOI)，其定义为达尔文岛和塔希提岛标准化海平面气压异常场的差值(塔希提岛-达尔文岛)。因此，本文采用了由美国国家大气研究中心(National Center for Atmospheric Research，简称NCAR)提供的Niño 3.4指数，作为海洋中ENSO事件的指标，和来自美国海洋与大气中心(National Oceanic and Atmospheric Administration，简称NOAA)提供的SOI指数，作为大气中ENSO事件的衡量指标。两种指数的起止时间均为1951年1月至2018年12月。

Figure 2. The mean (a), standard deviation (b), maximum (c), minimum (d) in train (red) and test (green) set of Niño 3.4 and SOI index

3.2. 模型训练

4. 结果分析

Figure 3. Prediction results and observed Niño 3.4 index

Figure 4. Prediction results and observed SOI index

Figure 5. The correlation coefficient and root-mean-square error between prediction results and observed Niño 3.4 index or SOI

Figure 6. The power spectra density of Niño 3.4 (red) and SOI (green) index

Figure 7. Prediction results and observed 7-months run-mean SOI index

5. 结语

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