Weather is the state of the atmosphere at a specific place and time, while climate is its average over a large area and a long period. Chaos in the atmosphere was discovered by Lorenz back in the 1960s, but his model described only air, not the ocean. The ocean covers more than 70% of the planet's surface and actively exchanges heat and momentum with the atmosphere. El Niño is the most striking example of this exchange: warm Pacific waters cause droughts, floods, and hurricanes worldwide. This work sits at the intersection of research on El Niño predictability and the distinction between weather and climate, but goes further: it attempts to show that chaos is not tied to one location but can travel.
The authors use three coupled tools: an advection equation for sea surface temperature (SST), the Vallis model for ENSO, and the Lorenz system for the atmosphere. The advection equation describes how temperature is transported by currents; they add an external chaotic signal or make the current speed unpredictable. To prove the existence of chaos, they apply recent results on 'unpredictable functions'—trajectories that behave like random ones but are generated by a deterministic system. They solve the equations numerically with specific parameters and plot graphs showing irregular oscillations. The Vallis model reduces to the Lorenz equations, so chaos in it is already known; the authors couple it with other models to demonstrate the transfer of chaos.
Numerical experiments show that chaos can transfer from one system to another. If a chaotic signal from the logistic map is added to the advection equation, the sea surface temperature begins to oscillate unpredictably. The same happens if the current speed is made chaotic. Coupled advection equations, where one is chaotic and the other is not, lead to chaos 'infecting' the calm system. The Vallis model with parameters B=102, C=3 is chaotic; if coupled with another Vallis model that is not chaotic by itself (B=20, C=7), the second becomes chaotic as well. Similarly, chaos transfers from ocean to atmosphere: if a signal from the chaotic Vallis model is added to a Lorenz system with nonchaotic parameters, the atmospheric model starts behaving chaotically. Conversely, atmospheric chaos can make an ocean model chaotic. Key numbers: parameter r=0.35 in the Lorenz system makes it nonchaotic, but after coupling with a chaotic ocean it exhibits irregular oscillations; in the Vallis model chaos arises at B=102, C=3, while at B=20, C=7 the system is stable until coupled with a chaotic neighbor.
The work shows that chaos is not a local property of a single model but a contagious phenomenon. If one part of the climate system is chaotic, it can transmit unpredictability to neighboring parts through physical connections (heat exchange, wind friction on water). This explains why weather forecasts are limited to a few days even with perfect observations: chaos spreads across the entire planet. Unlike adjacent studies that examined chaos in individual models or sought sources of ENSO irregularity, here a mechanism for global spread of chaos through coupled systems is proposed. This is a new perspective on climate unpredictability as a network effect.
In the future, simplified models (Vallis, Lorenz) could be replaced with more realistic climate models to test whether chaos transfer persists. It is also interesting to explore whether chaos can be controlled: if small perturbations in one place change the behavior of the whole system, it might be possible to mitigate extreme events. The authors mention that chaos control in the Lorenz system is still poorly developed, and this direction could be the next step.
The results are important for meteorology, oceanography, and climatology: they provide a mathematical justification for global unpredictability. They may also be useful in dynamical systems theory, where the transfer of chaos between coupled subsystems is studied.
The next step is to include more components of the climate system (ice, biosphere) in the model and check how chaos spreads in a more complete network. It is also worth studying the possibility of controlling chaos with small external perturbations.
The work addresses the fundamental problem of climate predictability: how far into the future can we see if the system is chaotic? It also relates to the question of the nature of ENSO irregularity: is it an intrinsic property of the system or a consequence of external noise? The proposed mechanism of chaos transfer may help explain the observed synchronization of climate anomalies across different oceans.
Lorenz, who discovered chaos in the atmosphere, posed the famous question: 'Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?' This work shows that chaos can also travel through the ocean: warm water in the Pacific can make weather in the distant Atlantic unpredictable.
The idea of global climate connectivity echoes Kim Stanley Robinson's novel 'Forty Signs of Rain', where scientists try to understand and predict abrupt climate changes caused by nonlinear interactions between ocean and atmosphere.