Long-term prediction of El Niño-Southern Oscillation using reservoir computing with data-driven realtime filter

TL;DR

This study tackles the challenge of long-term ENSO forecasting by introducing a data-driven realtime filter that uses only past information to extract mid- to long-term signals, coupled with a delay-coordinate reservoir computing model. Hyperparameters for both the filter and the reservoir are optimized via Bayesian optimization (Optuna), enabling forecast horizons up to $24$ months with robust performance measured by all-season correlation $C(\\mu)$. The results demonstrate a passband in the $4$–$8$ year range, a backward shift of about $5$ months, and a $C(\\mu)$ exceeding $0.5$ for up to $29$ months, highlighting the method’s potential for realtime, data-driven long-term climate forecasting. The approach is argued to be broadly applicable to other complex, high-dimensional dynamical systems beyond ENSO.

Abstract

In recent years, the application of machine learning approaches to time-series forecasting of climate dynamical phenomena has become increasingly active. It is known that applying a band-pass filter to a time-series data is a key to obtaining a high-quality data-driven model. Here, to obtain longer-term predictability of machine learning models, we introduce a new type of band-pass filter. It can be applied to realtime operational prediction workflows since it relies solely on past time series. We combine the filter with reservoir computing, which is a machine-learning technique that employs a data-driven dynamical system. As an application, we predict the multi-year dynamics of the El Niño-Southern Oscillation with the prediction horizon of 24 months using only past time series.

Figures (7)

• Figure 1: Optimization of filter performances. a) A filtered time series data $y^*$ (black thick line) is classified into discrete values $\tilde{y}$ (blue dots). b) Concept of the key and value: The indefinite factor of the filter is reduced statistically by maximizing \ref{['objective function']}, which represents the highest rate at which a key pattern $\sigma^L_n$ is followed by one of the values $\{a_k\}^K_{k=1}$ at the subsequent time step.
• Figure 2: Schematic diagram of reservoir computing. In training phase ($t<t_0$), optimal value of $\mathbf{W}_{\text{out}}$ is determined using the input time series with prescribed random matrix $\mathbf{A}$ and $\mathbf{W}_{\text{in}}$. In the prediction phase ($t\ge t_0$), the dynamics of the filtered time series are inferred recursively by the optimized model of the output matrix, which is denoted as $\mathbf{W}^*_{\text{out}}$.
• Figure 3: Characteristics of the new realtime filter. (a) The weight function in terms of time step and (b) frequency response function of the weight function. The weight function for $t \ge 0$ is zero so that the filtered time series does not include information from the future. The left endpoint of the weight function is also determined by Optuna in the parameter $w$.
• Figure 4: Comparison between the original and filtered realtime SST anomaly. (a) The time series of original (black) and filtered (red) indices from 1980 to 2022. (b) Lag correlation between the two time series over the entire data period. When the lag $\lambda$ is positive, it corresponds to delaying the original time series by $\lambda$ steps.
• Figure 5: Prediction skill of the data-driven model. All-season correlation skill for ecch forecast lead time is obtained from 180 predictions between January 2001 and December 2015 based on Eq. (\ref{['eq_corr']}). The red line shows the prediction obtained using the optimal matrices $\mathbf{W}_{\text{in}}$ and $\mathbf{A}$, which were determined simultaneously with the hyperparameters during the model selection process. The blue solid line represents the average of the correlation skill when randomly generated 100 combination of $\mathbf{W}_{\text{in}}$ and $\mathbf{A}$ are used with the same hyperparameters as in Table \ref{['param_model']}, while the blue shading indicates the range of ±1 standard deviation. The horizontal gray dashed line denotes a correlation of 0.5, displayed as a benchmark for the model’s prediction capability.

Theorems & Definitions (1)

• Remark 2.1