Measuring Climate Change Without a Ruler

[note: this was published behind the paywall last week to premium users, but it’s time for complete public release]

An Epistemological Problem at the Heart of Ocean Heat Content

The central empirical claim of modern climate science is that the Earth system is gaining energy, and that this gain is sufficiently well measured to justify strong conclusions about long-term warming.

This claim does not fail because of greenhouse physics, radiative transfer, or conservation laws. It fails—or at least becomes far less certain—because of a category error about measurement.

That error becomes obvious once one confronts the scale, dominance, and uncertainty of the ocean’s energy content.

The Ocean Dominates the Climate Energy System

More than 90% of the energy attributed to recent climate change is claimed to reside in the oceans. The atmosphere, land surface, and cryosphere together account for only a small residual fraction.

This is not controversial. It is foundational.

As a result, any claim about whether the Earth’s climate system is warming, cooling, or remaining stable is, in practice, a claim about ocean heat content.

If we do not know the ocean’s energy state with sufficient epistemic confidence, then we do not know the system’s energy state—no matter how well radiative forcing is understood.

Step 1: The Absolute Energy Scale of the Ocean

Let us begin with a physically honest question:

How much energy does the global ocean contain?

To answer this, we compute the sensible enthalpy of the ocean referenced to absolute zero, including the energy required to warm ice and melt it. This is not how oceanographers usually frame the problem—but it is how thermal energy is actually defined.

Ocean mass

The mass of Earth’s oceans is approximately:

Energy components

To bring the ocean from 0 K to its present mean temperature (~3.5 °C), three energy terms are required:

1. Warming ice from 0 K to 0 °C

Because the heat capacity of ice drops sharply toward zero at low temperature, this term cannot be calculated with a constant . A physically reasonable range yields:

This term alone carries substantial uncertainty.

2. Melting ice at 0 °C (latent heat of fusion)

This term is comparatively well constrained.

3. Warming liquid seawater from 0 °C to ~3.5 °C

This is small compared to the first two terms.

Total ocean sensible enthalpy

Summing these components:

A reasonable central estimate is:

Step 2: The Uncertainty in That Quantity

The uncertainty in absolute ocean sensible enthalpy is dominated by:

• Low-temperature heat capacity of ice,
• Reference-state assumptions,
• Simplifications required to compute a planetary-scale integral.

A conservative estimate is:

This is not a statistical error bar—it is a structural uncertainty.

Step 3: The Claimed Signal

Now compare this with the quantity that underpins modern climate attribution:

Estimated ocean heat uptake over the last ~50 years:

This is the signal.

Step 4: Putting the Scales Side-by-Side

Here is the comparison that is almost never made explicitly:

Quantity	Order of Magnitude (J)
Absolute ocean sensible enthalpy	~1027
Uncertainty in absolute enthalpy	~1026
Claimed 50-year ocean heat uptake	~1023

The ratio is unavoidable:

The uncertainty in the ocean’s sensible heat content exceeds the reported signal by roughly three orders of magnitude.

This is not a matter of better statistics. It is a matter of scale.

“But We Measure Changes, Not Absolutes”

At this point, the standard rebuttal appears:

We do not need to know the absolute heat content. We measure changes.

That sounds reasonable—until one asks what must be true for that to work.

The Wall-Mark Allegory (and Why It Fails)

Imagine measuring the growth of a child without a ruler.

Instead, you make marks on a wall as the child grows taller. Over time, the marks move upward, and you infer growth.

This works only if two conditions hold:

1. You know where the floor is.
2. The floor is not moving.

In climate science, the ocean is the wall—and the observing system is the floor.

Condition 1: Knowing where the floor is

Ocean temperature measurements over the last 50–70 years come from a sequence of fundamentally different systems:

• Ship-based mechanical instruments,
• Expendable probes with known, evolving biases,
• Sparse deep measurements,
• A modern Argo float network with different calibration regimes.

Each transition introduces offsets that must be corrected after the fact, using models.

That means the baseline is not observed. It is inferred.

Condition 2: The floor is not moving

The floor has been moving continuously:

• Instrument types changed,
• Sampling depth changed,
• Spatial coverage changed,
• Correction methods changed.

The reference frame itself has drifted.

You are no longer measuring marks on a fixed wall—you are measuring marks while the floor shifts and tilts, and then reconstructing where the floor must have been.

A Second Moving Floor: Heat Entering from Below

The epistemological problem deepens further once the bottom boundary of the ocean is acknowledged.

The ocean is not heated only from above.

Seafloor heat flux

Earth’s internal heat flow to the surface is commonly estimated at roughly:

Integrated over 50 years:

This is not negligible relative to claimed multidecadal ocean heat uptake.

Why uncertainty matters more than the mean

The critical issue is not the global mean flux—it is where and how the heat enters the ocean:

• Mid-ocean ridges with intense hydrothermal circulation,
• Ridge flanks with poorly constrained low-temperature heat transfer,
• Seamounts and submarine volcanoes,
• Vast plate interiors filled in by models due to sparse measurements.

The spatial and temporal structure of this heat input is uncertain, heterogeneous, and partially modeled rather than observed.

Epistemologically, this means the “floor” is not merely unstable—it is actively injecting heat, unevenly, through pathways that are not well constrained at climate-trend resolution.

Tightening the Comparison One Last Time

Put all relevant energy terms together:

Quantity	Energy over ~50 years
Claimed ocean heat uptake	~(3–5)×10²³ J
Seafloor heat input (order)	~7×10²² J
Uncertainty in absolute ocean enthalpy	~2×10²⁶ J

This is the full context.

The Epistemological Error

Here is the core issue, stated plainly:

Climate science treats a reconstructed differential signal as if it were a directly observed quantity, even though the signal is orders of magnitude smaller than the uncertainty of the dominant energy reservoir and comparable to poorly constrained boundary fluxes.

This is a category error.

In experimental physics or metrology, such a situation would immediately trigger questions about traceability, reference stability, and error dominance. In climate science, it is largely bypassed by redefining the problem in anomaly space and assuming stability.

That assumption is not a law of nature. It is a methodological choice.

What This Does—and Does Not—Imply

This argument does not show that the Earth is not warming.
It does not show that greenhouse forcing is irrelevant.
It does not show that climate models are useless.

What it does show is this:

From a strict epistemological standpoint, we do not know—at high confidence—whether the total energy of the Earth’s climate system is increasing, decreasing, or remaining approximately constant.

The dominant reservoir cannot be measured with uncertainty smaller than the claimed change, and one of its boundaries injects heat in ways that are incompletely observed.

That matters.

Conclusion

You can measure growth without a ruler—by making marks on a wall—but only if you know where the floor is, and only if the floor is not moving.

In climate science, the floor has moved, the wall has changed, and heat is entering from below through pathways that are not well constrained.

Until those epistemological limits are acknowledged explicitly, claims about the Earth’s energy trajectory remain inferences, not measurements.

That distinction matters.