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1. Introduction

As the most prominent interannual climate variability, the El Niño–Southern Oscillation (ENSO) manifests

as a basin-scale air-sea interaction phenomenon characterized by sea surface temperature (SST) anom-

alies in the equatorial central to eastern Pacific (Clarke,2008; Rasmusson & Carpenter,1982; Zebiak &

Cane,1987). It has a strong impact on climate, ecosystems, and economies around the world through global

circulation (Ashok & Yamagata,2009; Ropelewski & Halpert,1987). Classically, ENSO is regarded as a cy-

clic phenomenon (Jin,1997; Wyrtki,1975), in which the positive and negative phases are known as El Niño

and La Niña, respectively.

The traditional ensemble forecast using physics-based models has been widely used for predicting the

ENSO (Moore & Kleeman,1998; Tang etal.,2018; B. P. Kirtman & Min,2009). A hierarchy of models rang-

ing from the general circulation models (GCMs) to many intermediate and low-order models are employed

for forecasting the refined and large-scale ENSO features, respectively. However, model error, which leads

to large predictive uncertainty, is ubiquitous in these parametric models and often results in ineffective

forecasts. The model error often comes from the incomplete understanding of nature and/or the inadequate

spatiotemporal resolutions in these models (Kalnay,2003; Majda & Chen,2018; Palmer,2001). More recent-

ly, machine learning (ML) techniques have become prevalent in forecasting ENSO and many other climate

Abstract A simple and efficient Bayesian machine learning (BML) training algorithm, which exploits

only a 20-year short observational time series and an approximate prior model, is developed to predict

the Niño 3 sea surface temperature (SST) index. The BML forecast significantly outperforms model-based

ensemble predictions and standard machine learning forecasts. Even with a simple feedforward neural

network (NN), the BML forecast is skillful for 9.5months. Remarkably, the BML forecast overcomes

the spring predictability barrier to a large extent: the forecast starting from spring remains skillful for

nearly 10months. The BML algorithm can also effectively utilize multiscale features: the BML forecast

of SST using SST, thermocline, and windburst improves on the BML forecast using just SST by at least

2months. Finally, the BML algorithm also reduces the forecast uncertainty of NNs and is robust to input

perturbations.

Plain Language Summary One major challenge in applying machine learning algorithms

for predicting the El Nino-Southern Oscillation is the shortage of observational training data. In this

article, a simple and efficient Bayesian machine learning (BML) training algorithm is developed, which

exploits only a 20-year observational time series for training a neural network. In this new BML algorithm,

a long simulation from an approximate parametric model is used as the prior information while the short

observational data plays the role of the likelihood which corrects the intrinsic model error in the prior data

during the training process. The BML algorithm is applied to predict the Nino 3 sea surface temperature

(SST) index. Forecast from the BML algorithm outperforms standard machine learning forecasts and

model-based ensemble predictions. The BML algorithm also allows a multiscale input consisting of

both the SST and the wind bursts that greatly facilitate the forecast of the Nino 3 index. Remarkably, the

BML forecast overcomes the spring predictability barrier to a large extent. Moreover, the BML algorithm

reduces the forecast uncertainty and is robust to the input perturbations.

CHEN ET AL.

© 2021. American Geophysical Union.

All Rights Reserved.

A Bayesian Machine Learning Algorithm for Predicting

ENSO Using Short Observational Time Series

Nan Chen1 , Faheem Gilani2, and John Harlim3

1Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA, 2Department of Mathematics, The

Pennsylvania State University, University Park, PA, USA, 3Department of Mathematics, Department of Meteorology

and Atmospheric Science, Institute for Computational and Data Sciences, The Pennsylvania State University, University

Park, PA, USA

Key Points:

• A new Bayesian machine learning

(BML) framework is developed

to accommodate the shortage of

observations when training neural

networks

• The new BML forecast significantly

outperforms model-based ensemble

predictions and standard machine

learning forecasts

• The new BML algorithm reduces

forecast uncertainty and overcomes

the spring predictability barrier to a

large extent

Supporting Information:

Supporting Information may be found

in the online version of this article.

Correspondence to:

N. Chen,

chennan@math.wisc.edu

Citation:

Chen, N., Gilani, F., & Harlim, J. (2021).

A Bayesian machine learning algorithm

for predicting ENSO using short

observational time series. Geophysical

Research Letters, 48, e2021GL093704.

https://doi.org/10.1029/2021GL093704

Received 6 APR 2021

Accepted 5 AUG 2021

10.1029/2021GL093704

RESEARCH LETTER

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