Predicting El Niño is one of the most challenging problems in climatology. The phenomenon occurs in the tropical Pacific every 2–7 years and affects ecosystems, agriculture, and economies worldwide. Dynamical and statistical models predict events well up to six months ahead, but before spring there is the so-called predictability barrier: from February to May, accuracy drops sharply. This work stands alongside studies using climate network links and machine learning for early warnings of drought and El Niño. The difference is that here, for the first time, it is possible to predict not only the onset but also the strength of the event with a one-year horizon.
The authors introduce a measure of systemic sample entropy (SysSampEn) to assess the complexity of a system of 22 time series of temperature anomalies in the Niño 3.4 region (5°S–5°N, 170°W–120°W). SysSampEn generalizes sample entropy and cross-entropy: it measures how similar subsequences of length m remain similar over an additional p points, considering pairs from the same or different series. Parameters m (30 or 60 days), p (15 or 30 days), effective series length $l_{eff}$, and threshold γ are tuned using two accuracy tests: the spatial asynchrony test (comparing systems from neighboring and random points) and the temporal disorder test (adding noise). Four datasets are used: ERA-Interim, ERA5 (air temperature at 1000 hPa), ERA5 SST, and JRA55-do SST, covering 1984–2018.
A strong positive correlation is found between the entropy of the previous calendar year and the magnitude of El Niño. For ERA-Interim with parameters m=60 days, p=15 days, $l_{eff}$=345 days, γ=9, the correlation reaches r=0.99 (on average across datasets, r=0.90). Forecasting event onset with a one-year horizon yields 9 out of 10 correct onset predictions and 21 out of 24 correct no-event predictions. Magnitude prediction using leave-one-out has an RMSE of 0.23°C. For the 2018 event, a weak El Niño with magnitude 1.11±0.23°C is predicted, matching observations. Older entropy definitions (average SampEn or average Cross-SampEn) yield correlations of only 0.42, highlighting the advantage of the new approach.
The work shows that the complexity of the temperature field in the Niño 3.4 region a year before the event contains information about the future strength of El Niño. This is the first method that allows predicting magnitude with a one-year horizon, overcoming the spring barrier. Unlike related studies that focus only on event onset or use neural networks, here a physically interpretable complexity measure is proposed. The method can be extended to other complex systems where spatiotemporal synchronization is important.
SysSampEn might allow even earlier El Niño predictions if half-year data are used: the correlation remains high for some parameters, though accuracy decreases. The authors hypothesize a link between entropy and oceanic turbulence: strong El Niños are associated with intense turbulence, which reduces horizontal temperature gradients and hence entropy. Testing this hypothesis requires further research with climate models and observations.
The method could improve long-term El Niño forecasts for agriculture, water resource management, and preparedness for extreme weather events. It also offers a new tool for analyzing complexity in other natural and engineered systems.
The method needs to be validated on independent data and in real time for future events. The relationship between SysSampEn and physical mechanisms, such as turbulence and ocean heat buildup, also warrants investigation.
A key unresolved problem in climatology is overcoming the spring predictability barrier for El Niño. This work shows that a complexity measure can bypass this barrier, but the physical mechanism linking entropy to magnitude remains an open question. Also open is the method's applicability to other climate phenomena, such as La Niña or the Pacific Decadal Oscillation.
For the 1997 event, one of the strongest of the century, the previous year's entropy was the highest in the entire observational record. The SysSampEn value for 1996 was 1.25, nearly twice that of years without El Niño.
In Kim Stanley Robinson's novel 'Forty Signs of Rain', scientists attempt to predict abrupt climate changes using nonlinear data analysis methods. SysSampEn is a real step in this direction: a complexity measure that reveals signals where classical models are blind.