The Human Induced Climate Change Experiment
Research and Development Incorporating Complex Social-Ecological Feedback Loops Within a Dynamic, Non-Linear System

Evolving Probability Distribution of Climate Extremes

Daniel Brouse1 and Sidd Mukherjee2

1Independent Climate Researcher, Economist, Membrane Institute, USA
2Independent Physicist, Membrane Institute, USA

Earth's Energy Imbalance

The cold-to-hot axis represents thermal energy in the climate system, not simply air temperature. Since more than 90% of the excess heat trapped by greenhouse gases is absorbed by the oceans, a hot-to-cold continuum more accurately reflects changes in the Earth's overall energy balance than air temperature alone.

It is also important to recognize that the right skew is difficult to fully illustrate in a simple two-dimensional graphic. The right tail is not merely shifting to the right—it is becoming longer, fatter, and broader. In practical terms, extreme weather events are becoming more frequent, more intense, and longer-lasting. We're also witnessing events that were once expected perhaps once or twice in a century occurring multiple times within a single year. Persistent heat domes over the United States and Europe are examples that most people can readily relate to. They illustrate not only higher peak temperatures, but also prolonged durations of dangerous heat that dramatically increase cumulative impacts on human health, ecosystems, agriculture, infrastructure, and energy systems.

It is equally important to note that the graphic is not intended to depict only hot versus cold weather. Rather, it represents a probability density distribution for the full spectrum of climate extremes. Because it is a simplified bell curve, many variables, event types, and dimensions are necessarily condensed into a single conceptual illustration. The horizontal axis represents the range of climate outcomes, while the vertical axis represents their relative probability of occurrence.

The central message is therefore not simply that the climate is becoming warmer. Rather, the underlying probability distribution itself is changing in ways that make extreme events increasingly likely. Climate events that were once considered exceptionally rare are now occurring with increasing regularity, persisting for longer durations, and producing greater human, ecological, and economic damage.

Perhaps most importantly, these extreme events are no longer acting independently—they are increasingly feeding one another through interconnected feedback loops. As the Earth's energy imbalance grows, the frequency and intensity of feedback coupling also increase. Heat fuels evaporation, evaporation intensifies atmospheric rivers, warmer oceans provide additional energy for tropical cyclones, persistent high-pressure systems strengthen heat domes, and greater atmospheric instability produces more powerful thunderstorms and lightning. These are all manifestations of the same excess thermal energy being redistributed throughout the Earth system. While the planetary energy imbalance itself is an abstract concept, these increasingly energetic transfers of heat into real-world weather extremes are phenomena that people can directly observe and experience. In that sense, atmospheric rivers, heat domes, severe thunderstorms, and lightning provide some of the clearest illustrations of how excess thermal energy is reshaping our climate.

Earth's Energy Imbalance and Feedbacks

See: The Evolving Probability Distribution of Climate Extremes: Earth’s Energy Imbalance, Statistical Skewness, and Feedback Coupling


The Evolution and Acceleration of Climate Change

Q: How fast is climate change accelerating?

A: From the Industrial Revolution through the 1990s, key climate-acceleration indicators appear to have doubled on timescales closer to a century. By the 2020s, many major warming-related impacts are doubling on timescales closer to a decade.

In effect, the leading indicators suggest a multi-stage compression of characteristic doubling times, consistent with approximately six successive halving steps (2^6) when comparing early industrial-era timescales with recent decade-scale behavior across multiple indicators. This represents a heuristic description of cumulative nonlinear compression rather than a single-step ratio, and reflects the aggregation of changes across multiple time intervals and Earth-system variables.

By 2025, analysis could move beyond purely retrospective exponential fitting toward a state-space formulation of system evolution. The Earth's climate system is undergoing a regime shift away from historically near-linear behavior toward accelerating nonlinear and compounding dynamics, characterized by systematically shrinking effective doubling times and the emergence of instantaneous-growth dynamics across coupled Earth system components.

Multiple climate indicators now point to rates of warming-related disruption far beyond those observed during the modern instrumental era. There is no well-established geological analog for a sustained, multi-variable, decade-scale pattern of accelerating change across the full Earth system at the resolution available in contemporary observations. If sustained, this may represent one of the most abrupt large-scale climate transitions in Earth’s geological history.

Many of the climate indicators traditionally used for forecasting are exhibiting increasingly nonlinear and volatile behavior. Temperature anomalies, ocean heat content, sea-level rise, atmospheric moisture, ice loss, and extreme weather patterns are showing changes that are becoming more difficult to model using assumptions based primarily on historical variability.

See: Beyond Degrees: Earth’s Climate History Is No Longer a Reliable Predictor of Its Future


Probabilistic, Ensemble-Based Climate Modeling

The shifting and expanding right tail of the probability distribution illustrates what is already being observed in the real world. As the climate warms, the entire distribution moves toward more extreme outcomes while the likelihood of high-impact events increases disproportionately.

Sidd explains GCMs:

General Circulation Models (GCMs) of Earth's climate are nonlinear and highly teleconnected. That means a small change in temperature or pressure or humidity in one small area on the globe can cause _large_ changes in conditions _anywhere_ on the globe. This phenomenon is often referred to as the Butterfly Effect -- the idea that a butterfly flapping its wings in China could ultimately contribute to a hurricane forming in the Atlantic. The complexity of these models can lead to chaotic behavior. Climate science must grapple with these models and extract results in spite of the mathematical difficulties, and there have been remarkable successes in some cases and sad failures in others. Nevertheless we must proceed.

Because Earth's climate is a chaotic, nonlinear system, long-term projections rely on ensemble modeling rather than deterministic forecasts. Statistical mechanics and chaos theory provide the framework for evaluating plausible future states. In a probabilistic, ensemble-based climate model, overlapping scenarios are expected. Individual trajectories may diverge, converge, or overlap as nonlinear feedbacks evolve. Some feedbacks accelerate over time, some exhibit accelerating acceleration, and many contain both reinforcing (positive) and stabilizing (negative) components whose relative influence changes as the climate system evolves.

Projected Temperature Ranges by 2100-2200

Projected Temperature Ranges by 2100-2200

The greatest uncertainty is no longer whether climate change will occur, but how strongly Earth’s own feedback systems will accelerate it now critical thresholds are crossed.

Earth System Response Regimes

Risk Interpretation

Most likely outcome under current policy: 3–7°C warming this century.

Preventing these outcomes requires rapid fossil fuel phase-out, carbon drawdown, adaptive infrastructure, and socio-ecological resilience.


* Our probabilistic, ensemble-based climate model — which incorporates complex socio-economic and ecological feedback loops within a dynamic, nonlinear system — projects that global temperatures are becoming unsustainable this century. This far exceeds earlier estimates of a 4°C rise over the next thousand years, highlighting a dramatic acceleration in global warming. We are now entering a phase of compound, cascading collapse, where climate, ecological, and societal systems destabilize through interlinked, self-reinforcing feedback loops.

We examine how human activities — such as deforestation, fossil fuel combustion, mass consumption, industrial agriculture, and land development — interact with ecological processes like thermal energy redistribution, carbon cycling, hydrological flow, biodiversity loss, and the spread of disease vectors. These interactions do not follow linear cause-and-effect patterns. Instead, they form complex, self-reinforcing feedback loops that can trigger rapid, system-wide transformations — often abruptly and without warning. Grasping these dynamics is crucial for accurately assessing global risks and developing effective strategies for long-term survival.

The Human Induced Climate Change Experiment

"Collapsing Doubling Times in Climate Change Impacts" identifies consumerism as the primary driver of rapid environmental degradation, fueling energy demand, resource extraction, and pollution. The analysis concludes that directly reducing overall human consumption is essential to mitigating accelerating climate change impacts.

Climate Science Resources and Overview

Easy-to-Read Resources

Climate Change Simplified

Important Information

→ Solutions to the Fossil Fuel Economy and the Myths Accelerating Climate and Economic Collapse

Feedback LoopsTipping PointsAccelerationDomino Effect
Feedback loops amplify climate change and can push interconnected Earth systems past critical tipping points. As tipping points are crossed, they can trigger additional feedback loops and destabilize other climate systems. This cascading "Domino Effect" compresses timescales, accelerates change, and increases the risk of rapid, nonlinear climate transformations.

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