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
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
• A new Bayesian machine learning
(BML) framework is developed
to accommodate the shortage of
observations when training neural
• The new BML forecast significantly
outperforms model-based ensemble
predictions and standard machine
• The new BML algorithm reduces
forecast uncertainty and overcomes
the spring predictability barrier to a
Supporting Information may be found
in the online version of this article.
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.
Received 6 APR 2021
Accepted 5 AUG 2021
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