By Daniel Brouse and Sidd Mukherjee
March 24, 2026
This paper presents a physics-based framework for understanding anthropogenic climate change through energy balance, rate dynamics, and force scaling. While the radiative basis of global warming is well established, we argue that the most critical—and underappreciated—dimensions of climate change lie in (1) the acceleration of system change via feedback-driven compression of doubling times, and (2) the nonlinear scaling of physical damage through momentum transfer and drag physics. By reframing climate change as a problem of energy accumulation (joules) and energy redistribution, we provide a unified interpretation of intensifying impacts across atmospheric, hydrological, and geophysical systems.
Anthropogenic global warming is no longer meaningfully debated within the scientific community. The primary driver is fossil fuel combustion, and the causal mechanism is well constrained.
The isotopic signature of atmospheric carbon dioxide provides direct evidence. Fossil carbon is depleted in ¹³C and contains no measurable ¹⁴C due to radioactive decay over geological timescales.
The radiative forcing from CO₂ is quantified by:
ΔF = 5.35 ln(C / C0) [W/m²]
Where:
This relationship defines the perturbation to Earth’s energy balance.
At its core, climate change is an energy imbalance problem:
ΔE = Ein - Eout
Where:
All energy within the climate system is measured in Joules (J):
1 J = 1 kg·m²/s²
The term global warming is therefore incomplete. Temperature is only the initial signal. The more fundamental process is the accumulation and redistribution of energy across multiple physical domains.
Historical analysis alone is insufficient to describe current climate dynamics. The rate of change, and more importantly the acceleration of that rate, provides deeper insight.
In systems governed by feedback, doubling time is defined as:
Td(t) = ln(2) / k(t)
Where:
As feedback mechanisms strengthen, k(t) increases, and doubling time compresses.
Empirical observations across multiple datasets indicate accelerating change:
Estimated doubling times have evolved as follows:
| Period | Approximate Doubling Time |
|---|---|
| Early industrial era | ~100 years |
| ~2010 | ~10 years |
| Mid-2020s | ~2–5 years |
Under compressed doubling intervals (~1.5–2 years), cumulative impacts increase as:
2^6-fold = 64 (per decade)
This represents nonlinear escalation, not linear change.
Observed global mean sea-level rise:
| Period | Rate |
|---|---|
| 20th century | 1.2–1.7 mm/yr |
| 1990s | ~3.1 mm/yr |
| 2024 | ~5.9 mm/yr |
This progression demonstrates not only exponential growth, but acceleration of the exponential itself.
A critical but underemphasized consequence of increased system energy is the amplification of mechanical forces.
p = m · v
Where:
As atmospheric moisture increases (~7% per 1°C warming), raindrop mass increases, leading to greater momentum transfer upon impact.
The drag equation governs force in fluid systems:
Fd = (1/2) · ρ · v² · Cd · A
Where:
Key implication:
Force ∝ v²
Small increases in velocity produce disproportionately large increases in force.
Density further amplifies effects:
Thus, moving water exerts dramatically greater force than wind at equivalent speeds.
Damage is governed not by linear change, but by nonlinear force amplification.
Excess trapped energy is not static—it is continuously transformed:
This reflects a fundamental principle:
Climate change is the redistribution of energy across coupled physical systems.
By 2025, global mean temperature exceeded 1.5°C above pre-industrial levels. While numerically small, this shift represents a major perturbation in a nonlinear system.
Small increases in temperature produce large changes in:
These gradient shifts drive:
The result is the emergence of what are more accurately described as:
Extreme energy events
Understanding climate change requires a shift in perspective:
The governing quantity is not degrees Celsius, but joules.
ΔE = Ein - Eout
As long as ΔE remains positive, energy accumulates.
As energy accumulates, it redistributes.
As it redistributes, it amplifies force, motion, and instability.
Climate change is therefore not simply warming.
It is the rapid escalation of energy within a complex system—
and the increasingly violent ways that energy is expressed.
The detailed math:
Emergent Climate Dynamics: The Nonlinear Acceleration of Climate Impacts
* 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.
Tipping points and feedback loops drive the acceleration of climate change. When one tipping point is toppled and triggers others, the cascading collapse is known as the Domino Effect.