The Terrifying Math Behind the Sudden Spike in Global Warming

Between 2023 and 2025, the Earth’s climate system broke its own mathematical boundaries. Global surface temperatures shattered records by margins so large that veteran climatologists were left searching the data for instrument errors. The year 2024 finished as the warmest since records began in 1850, soaring 1.29 degrees Celsius above the 20th-century average, while 2025 closely followed as the third-warmest year on record—even as a cooling La Niña pattern gripped the tropical Pacific.

The heat was not confined to the air. The oceans, which absorb roughly 90% of the excess heat trapped by greenhouse gases, swallowed an additional 23 zettajoules of energy between 2024 and 2025. To put that abstract unit into perspective, 23 zettajoules is roughly equivalent to 210 times the annual electricity generation of the entire human race. As John Abraham, a professor of thermal sciences at the University of St. Thomas, remarked upon reviewing the 2025 ocean heat data: "Holy shit, the oceans are hot."

To get the global warming spike explained properly, the scientific community has split into two heavily armed analytical camps. Both sides look at the exact same terrifying arithmetic of Earth's Energy Imbalance (EEI)—the net surplus of incoming solar radiation over outgoing thermal radiation—but they draw radically different conclusions about the mechanics driving it.

One camp, led by former NASA climate scientist James Hansen, argues that the baseline rate of anthropogenic warming has drastically accelerated due to the sudden removal of reflective aerosol pollution over the oceans. The other camp, representing a large swath of mainstream modelers including Michael Mann and researchers at the University of Miami, counters that the spike is a colossal, yet temporary, thermodynamic burp caused by natural ocean oscillations stacking on top of steady, unaccelerated background warming.

By examining these two frameworks side by side, we uncover a deeply unsettling picture of planetary physics, public health tradeoffs, and the limits of modern climate modeling.

The Forcing Multiplier: The Aerosol Unmasking Theory

James Hansen’s thesis rests on a dark paradox of environmental policy: pollution was keeping the planet cool.

For decades, the global shipping industry burned bunker fuel rich in sulfur. When combusted, this fuel released sulfur dioxide into the atmosphere, creating fine sulfate aerosols. These suspended particles did two things. First, they directly reflected incoming solar radiation back into space. Second, and more importantly, they seeded highly reflective, low-lying marine clouds—often visible from space as long, white "ship tracks."

In 2020, the International Maritime Organization (IMO) enforced strict new regulations cutting the maximum sulfur content of marine fuels from 3.5% to 0.5%. The public health benefits were immediate and undeniable, saving tens of thousands of lives annually from respiratory and cardiovascular diseases linked to air pollution.

But Hansen and his co-authors argue this clean-up triggered a catastrophic climate shock. By clearing the skies of sulfate aerosols, humanity inadvertently stripped away a reflective shield that had been masking a significant portion of our greenhouse gas warming.

The Math of the Faustian Bargain

Hansen refers to this tradeoff as a "Faustian bargain." His calculations suggest that mainstream climate science has systematically underestimated how much cooling these aerosols provided.

When observing the Earth's Energy Imbalance using precise satellite data and deep-diving Argo ocean floats, Hansen's team noted a severe darkening of the planet (decreased albedo). Earth was absorbing vastly more solar energy after 2015, and particularly after 2020. Hansen estimates that the reduction in marine aerosols caused an increase in climate forcing of at least 0.5 Watts per square meter (W/m²), and possibly up to 1 W/m².

To contextualize a forcing of 1 W/m²: it is equivalent to instantly increasing atmospheric CO2 by more than 100 parts per million.

This leads to Hansen's most controversial mathematical claim. The Intergovernmental Panel on Climate Change (IPCC) operates on a "best estimate" of climate sensitivity, assuming that doubling atmospheric CO2 will lead to about 3.0°C of warming. Hansen, calculating the sheer volume of heat unmasked by the disappearing aerosols, argues that paleoclimate evidence points to a climate sensitivity of 4.8°C (±1.2°C). If Hansen is right, the models relied upon by global governments are running dangerously cold, and the Paris Agreement’s goal of limiting warming to 1.5°C is already mathematically impossible without direct geoengineering interventions.

The Oscillating Engine: The ENSO Accumulation Theory

Contrasting sharply with Hansen’s theory of fundamental acceleration is the natural variability argument. Researchers in this camp look at the same 2023–2025 anomaly and see the fingerprints of the El Niño-Southern Oscillation (ENSO), operating exactly as the laws of fluid dynamics dictate.

Shiv Priyam Raghuraman, a researcher at the University of Miami, led a study explicitly isolating the causes of the surface temperature jump. By running climate models completely stripped of human influences, his team demonstrated that global warming spikes of this magnitude still occur naturally.

The mechanics here rely on the ocean's ability to act as a thermal battery. From 2020 to 2022, the Earth experienced a rare "triple-dip" La Niña. During La Niña, strong trade winds push warm surface water toward the western Pacific, causing cold, deep water to upwell in the east. This cools global average surface temperatures, but crucially, it does not stop the planet from absorbing heat. Instead, the heat is driven deep into the ocean volume.

When the system snapped into a strong El Niño in 2023, the trade winds weakened. The vast reserve of hot water that had been shoved into the western Pacific sloshed back across the ocean, spreading a massive layer of anomalous heat across the surface. Tom Di Liberto, a meteorologist with Climate Central, described the transition: "When there is a transition from La Niña to El Niño, it’s like the lid is popped off."

The Probability of the Spike

Raghuraman’s statistical analysis revealed a 10% probability that a temperature spike occurs when an El Niño is immediately preceded by a long La Niña. To these researchers, the math suggests that the baseline rate of anthropogenic warming has remained steady at around 0.20°C per decade since the 1970s. The recent extremity is simply what happens when a massive natural heat release rides on top of an already elevated anthropogenic baseline.

Michael Mann points out that the total warming seen over the past two years fits comfortably within the upper bounds of existing IPCC model projections. To the ENSO-focus camp, declaring that warming has permanently "accelerated" based on a three-year anomaly is a statistical error—confusing a noisy, high-amplitude wave for a shift in the underlying tide.

Comparing the Frameworks: Spatial Signatures and Energy Ledgers

To evaluate these competing views, we must look at where the heat actually went, and how the models handled the geography of the warming.

The North Atlantic Anomaly

During the peak of the 2023–2024 warming, Sea Surface Temperatures (SSTs) in the North Atlantic went literally off the charts, exceeding previous records by margins of up to 1°C in certain zones.

The Aerosol View: Hansen’s supporters point directly to this region as smoking-gun evidence for their theory. The North Atlantic is one of the most heavily trafficked maritime shipping corridors on Earth. It is precisely where the greatest reduction in sulfur aerosols occurred post-2020. The localized extremity perfectly matches the geographic footprint of the lost ship tracks.
The Natural Variability View: Mainstream modelers counter that the North Atlantic warming was largely driven by a weakening of the Azores High—a semi-permanent pressure system. Weaker winds reduced the amount of Saharan dust blowing over the ocean (another natural aerosol) and reduced evaporative cooling on the ocean surface. They argue that atmospheric circulation changes, driven by the ENSO transition, account for the bulk of this localized heating.

Earth's Energy Imbalance (EEI)

Both theories must account for the persistent, massive increase in EEI. Between 1960 and 2025, ocean heat absorption increased from a rate of 0.14 W/m² to 0.32 W/m².

The Aerosol View: The sudden jump in absorbed solar radiation (shortwave energy) is too large and abrupt to be explained by greenhouse gases alone, which primarily trap outgoing thermal radiation (longwave energy). The rapid darkening of the planet is a distinct symptom of missing clouds.
The Natural Variability View: A 2026 study in Nature Geoscience calculated that roughly three-quarters of the change in Earth's energy imbalance in recent years can be attributed to the long-term human-caused climate trend combining with the shift from a three-year La Niña to El Niño. The lack of cloud cover over the Pacific during this transition allowed more sunlight in, increasing the imbalance without requiring a massive miscalculation of aerosol forcing.

If you want the global warming spike explained by a single variable, the data refuses to comply. The reality likely involves the two mechanisms compounding each other. The aerosol reduction primed the planet to absorb extra solar radiation exactly when the La Niña cycle was burying that heat in the ocean. When El Niño arrived, it detonated an energy stockpile that had been supercharged by clearer skies.

The 2025 Data: A Warning from the Deep

The trajectory of ocean temperatures into 2025 provides a critical stress test for both theories. By late 2024 and into 2025, the El Niño pattern had dissipated, giving way to weak La Niña conditions. According to historical patterns, surface temperatures should have plummeted.

They did not plummet.

While global annual mean sea surface temperature in 2025 was 0.12°C lower than in 2024, it remained anomalously high—ranking as the third warmest on record and 0.49°C above the 1981–2010 baseline. More alarming was the deep ocean data. The upper 2,000 meters of the water column absorbed an additional 23 zettajoules of heat between 2024 and 2025, compared to an increase of 13 zettajoules between 2023 and 2024.

This relentless accumulation of oceanic heat regardless of surface phenomena lends weight to the idea that the underlying planetary imbalance is intensifying. The ocean acts as the Earth's thermal flywheel; it is highly resistant to sudden temperature changes due to the immense specific heat capacity of water. The fact that roughly 33% of the global ocean area ranked among its historical top three warmest conditions in 2025 proves that the energy driving the recent spike has not radiated back into space. It has taken up residence in the sea.

The consequences of this stored heat are already materializing. Warmer water occupies more volume, driving thermal expansion that accelerates sea-level rise. It also supercharges the hydrological cycle. The heat transfer from a 23-zettajoule anomaly means exponentially more moisture evaporating into the atmosphere. In 2025, this translated directly into severe flooding across Southeast Asia, the Pacific Northwest, and unprecedented thermodynamic extremes globally.

The Policy Tradeoffs: Inaction vs. Geoengineering

The most profound difference between the aerosol acceleration theory and the natural variability theory is what they demand from global policymakers.

If the natural variability theorists are correct, the current crisis, while severe, is proceeding according to the physics predicted by the IPCC. The solution remains difficult but straightforward: rapidly decarbonize the global economy, transition to renewable energy, and brace for the impacts of a world warming at 0.20°C per decade. Once the ENSO cycle settles, the spikes will smooth out into the established upward slope.

If Hansen’s acceleration theory is correct, the policy implications are terrifying. Getting the global warming spike explained through the loss of sulfur emissions implies that cutting CO2 emissions now will not be fast enough to prevent catastrophic tipping points. Because aerosols wash out of the atmosphere in weeks, while CO2 remains for centuries, cleaning up industrial pollution actually accelerates warming in the short term.

This math drives Hansen to a highly controversial conclusion: humanity must actively intervene in the Earth’s radiation budget. He argues for the research and deployment of solar radiation management (SRM), a form of geoengineering. This could involve intentionally spraying seawater into the lower atmosphere to artificially brighten marine clouds, or injecting sulfur dioxide into the stratosphere to mimic the cooling effect of volcanic eruptions.

The mainstream climate community largely recoils from this proposition. Intervening in the stratosphere could disrupt global precipitation patterns, potentially collapsing the Asian monsoon systems that billions rely upon for agriculture. Furthermore, geoengineering does nothing to address ocean acidification caused by CO2 absorption. Yet, if the Earth is crossing a threshold where climate sensitivity is near 4.8°C, the risk calculations of geoengineering versus unchecked warming will undergo a brutal reassessment.

Navigating the Thermal Margin

The fierce debate over the 2023–2025 anomaly forces us to confront the limitations of our predictive models. Climate models are extraordinary feats of computational physics, but they are tuned to historical data. When society enacted a sudden, global change to shipping fuels, we initiated an unprecedented atmospheric experiment. When the Pacific Ocean held a La Niña pattern for three years, it wound a thermal spring tighter than at any point in the observational record.

The math behind the sudden spike serves as a stark audit of the planet's energy ledger. The incoming solar radiation, the missing marine clouds, the sloshing of equatorial Pacific waters, and the steady, smothering blanket of carbon dioxide have combined to push the Earth system out of its previous equilibrium.

As we look toward the remainder of the 2020s, the debate over whether the underlying warming rate has formally "accelerated" or merely "pulsed" may become entirely academic. The zettajoules of heat banked in the oceans over the last three years cannot be un-absorbed. They will continue to fuel extreme weather, melt glacial ice, and rewrite coastal maps for centuries. When the next El Niño inevitably forms, it will not be pulling from the ocean temperatures of the 20th century, but from a deeply altered, hyper-energized sea. The true terror of the math is not just how fast the numbers are rising, but how stubbornly they refuse to come back down.