How Deep Is Earth’s Thermal Inertia?

In working on my last post, I discovered that global temperature or, more exactly the world surface temperature within a height of 2 meters, warms and cools at a rate of more than 10°C per year every year. To me this seemed too fast. The large size of the seasonal change seemed inconsistent with the smaller change over 25 years as if the two timescales had different thermal inertias. This post investigates how the planet reacts to fluctuations in Earth’s energy imbalance (EEIMB), which is absorbed solar radiation (ASR) minus the emitted thermal radiation (ETR). https://ceres.larc.nasa.gov/

Naively, I would think that the “depth” of the response and, therefore, the magnitude of the thermal inertia would vary inversely to the timescale of the fluctuation, i.e. thinner depth, and smaller inertia for shorter timescales. With its slow steady increase superimposed on a yearly fluctuation, the EEIMB of the previous 25 years provides the experimental evidence to characterize the thermal response (https://climatereanalyzer.org/about/)on two different time scales.

Long-Term Warming: Like a Deep Layer of Water

In the previous post, I showed that global temperature closely follows cumulative energy, which is the integral of EEIMB, Earth’s Energy Imbalance with the sun, as measured by the NASA CERES project. Here, again, is that comparison of global temperature, T, and cumulative energy (ΔQ).

Over the past 25 years, global temperature has increased by about 0.62°C, while the planet has retained about 21 watt-years per square meter of extra energy.

Thermal inertia is basically how much a system resists a temperature change when energy is added or removed. The Earth’s climate is complex, but I am going to compare it to a layer of water. We all know it takes longer to heat a deep pot of water to a boil than a shallow one. We have a feel or experience with the heat capacity of water.

To put numbers to it: it takes 4,184 joules of energy (what we call a “calorie” in diet and exercise) to warm up 1 kilogram of water 1°C. A cubic meter of water is about 1000 kilograms, so heating up a cubic meter by 1°C requires about 4.184 million joules. A watt is a joule per second, so if we add energy to a layer of water at the rate of 1 watt per square meter for a whole year, that is a “watt-year” of energy per square meter, about 31.56 million joules. One watt-year per m² of retained energy would raise the temperature of a 7.542-meter-deep layer of water by 1°C. The temperature rise of a layer of water depends on its depth; a deeper layer will heat up more slowly because there is more mass to absorb the energy. If one knows the number of watt-years and the temperature rise, one can do the math to get the depth of water.

For example, if an area absorbs one watt-year per square meter and its temperature rises by 10°C, that is equivalent to a water layer about 0.754 meters deep. If the same energy caused a 100°C rise, the water layer would only be about 0.0754 meters deep.

Now looking at Earth’s climate: Over the past 25 years a gain of about 0.62°C after absorbing about 21 watt-years per square meter of extra energy. So, in my way of looking at it, the climate system has a thermal inertia which is roughly equivalent to that of a 255-meter-deep layer of water. Of course, the real climate involves ocean, land, ice, and atmosphere plus a non-uniform temperature, but it makes sense. A 255-meter-deep layer of water has a large thermal inertia. It explains a slow warming of 0.62°C in 25 years.

Seasonal Swings: A Much Shallower Response

What about the large, 3.8°C, rapid, seasonal swing in average global temperature, though? How does it compare with the seasonal swing in cumulative retained energy and what magnitude thermal inertia does that imply?  To isolate seasonal variations from the long-term trends, one could subtract a trend line, but subtracting the one year running averages might to be a better way. Here is global temperature with running average in blue.

Here is cumulative energy, the integral of the Earth’s Energy Imbalance (EEIMB) with the sun, with the 12-month running average in blue.

Next, after subtracting the running average, are the isolated seasonal variations of global temperature (ΔT, red line) and of cumulative energy (ΔCE, blue line) shown together on the same graph. Although the scaling is different and there is a phase lag, the swings in temperature can be seen to track the magnitude and shape of the swings in cumulative energy.

Here are the average seasonal variations of temperature and cumulative energy.

Compare the axis on either side of the graph. From coolest to warmest, the average temperature swing since 2000 has been 3.85°C. The average swing in cumulative energy has been 2.68 W-Year/m². The maximum temperature follows or lags the maximum in cumulative energy by about ¼ year.

Using the same logic as before to compare the thermal inertia of the atmosphere to that of a layer of water, if swings of 2.68 watt-years per m² cause 3.85°C swings in temperature then climate’s thermal inertia is equivalent to that of a 5.26- meter-deep layer of water.

Conclusion: Climate Thermal Inertia Changes with Timescale

The thermal inertia of the climate is not a fixed number. It depends on how fast the energy imbalance is changing.  A rapid change causes a shallower response with smaller thermal inertia than a slow change.

• For seasonal changes, the climate’s response is like a 5.26-meter layer of water, quick and relatively shallow.
• For long-term changes, such as the past 25 years, the climate response is like a 255-meter of water, slow and much deeper.

This helps explain why we see such large seasonal temperature swings, i.e. 3.85°C, for small energy swings, i.e. 2.68 watt-years per m², but only small temperature shifts over decades for a larger change of energy. The faster the energy change, the larger the response in temperature, but the shallower in depth.  A slow steady change accumulated 7.8 times more energy, i.e. 21 watt-years per m², over a 25-year period into the climate system, but, due to more time, it was distributed deeper into the ocean and the lands with a mass or heat capacity equivalent to 48.5 times deeper water. The net effect of the slow heating was 0.62°C of global warming.

The rapid seasonal changes we experience are nothing new – they have been happening like clockwork for millennia, driven by Earth’s orbit around the sun. These ups and downs come and go each year, and over time, they average out to nearly zero. They are part of the natural rhythm of the climate.

What is different – and concerning – is the slow, steady warming that has emerged in recent decades. This is not part of the usual cycle. Over the past 25 years, global temperature has risen by 0.62°C, a rate that is more than 45% faster than in previous decades. And if we zoom in even closer, the past 10 years have seen an even faster rate of warming.

This is not just a gradual change – its an accelerating one. The seasonal ups and down may be familiar, but the underlying warming trend is something new. It is slow, insidious, and picking up speed.