Paris Climate Goals? DOE “Assessment”

Supposedly, “climate science is baaaack.” The DOE has published a new climate assessment report that conflates “nuance” with delaying climate action. It exaggerates scientific uncertainty, overstates the benefits of CO₂, and emphasizes the risks of climate action while downplaying the risks and costs of inaction. Here is a direct quote:

“Mainstream climate economics has recognized that CO₂-induced warming might have some negative economic effects, but they are too small to justify aggressive abatement policy and that trying to ‘stop’ or cap global warming even at levels well above the Paris target would be worse than doing nothing.”

So, what are those targets, and how are we doing?

The Paris Agreement is a legally binding international treaty on climate change, adopted in 2015 by 196 parties, including the United States—which has now exited the agreement twice. Its main goal is to limit global warming to well below 2°C, preferably to 1.5°C, compared to “pre‑industrial” levels. The agreement also calls for adaptation to climate change.

It sounds clear enough—except for one big question: what exactly were pre‑industrial temperatures?

The Pre-Industrial Mystery

Strangely, despite how central that number is, the Paris Agreement never pinned it down. There is no official baseline, no agreed‑on thermometer reading from the past. And that leaves a serious problem: how can we know how close we are to the target if we do not know where we started?

To get some clarity, I did what the agreement did not: translate the abstract 1.5°C and 2.0°C goals into actual global average temperatures, using the best available data.

Why “Anomalies” Instead of Temperatures?

When scientists report global temperatures, they usually do not give you the actual average temperature in °C. Instead, they report anomalies—the difference from a reference period, usually a few decades with good thermometer coverage.

Why? Because thermometers are finicky. A few feet of elevation, a patch of urban pavement, or a nearby tree line can throw off the reading. Working with anomalies lets scientists track changes more accurately, without being skewed by where a thermometer happens to sit.

This method has been excellent for spotting long‑term trends. But recently, climate science has given us a way to track real temperatures directly.

ERA5

Thanks to climate reanalysis—a blend of weather observations and computer models—we can now estimate daily average surface air temperatures worldwide. ERA5, from the European Centre for Medium‑Range Weather Forecasts, is among the most respected reanalyses.

I use ERA5’s 2-meter surface air temperature (the air temperature about 6 feet above ground) and smooth seasonal ups and downs with a one‑year running average. The result: a reliable estimate of real global temperature.

Before Fossil Fuels

To find the “pre‑industrial” temperature the Paris Agreement implies, I used the PAGES2k reconstruction. This global project combines climate proxies—tree rings, ice cores, and sediments—to estimate global temperatures year by year back to the year 1.

PAGES2k reports anomalies relative to 1961–1990. To get real °C values, I anchored PAGES2k to ERA5 by matching their average values over the overlapping years (1941–2017). The adjustment required was +13.822°C.

Here is the result for recent times.

The Pre-Industrial Baseline

Defining “pre‑industrial” is imprecise, but I followed a common approach: use everything before large‑scale fossil fuel burning began. I set the cutoff at 1764.

Many reports use 1850–1900 as a proxy for “pre‑industrial,” mainly because that’s when thermometer records become reliable. But by the mid‑1800s, the Industrial Revolution was underway, and greenhouse gas concentrations had already risen. In other words, 1850–1900 was already warmer than true pre‑industrial conditions.

Averaging the reconstructed temperatures for the 1,000 years before 1764 (764–1763) gives a global 2‑meter temperature of about 13.5°C. See below.

This lets us translate the Paris targets into real temperatures:

• 1.5°C above pre‑industrial → 15.0°C

• 2.0°C above pre‑industrial → 15.5°C

How Close Are We?

Earth’s temperature naturally swings by ~3.9°C seasonally. That means the 1.5°C Paris goal (15.0°C annual average) corresponds to a daily range from ~13.0°C in early January to ~16.9°C in late June.

Comparing these to ERA5:

• 2024: Averaged ~0.1°C above the 1.5°C target.

• 2025 (to date): Averaging ~0.03°C below the 1.5°C target—slightly better, but still hovering near the threshold.

We have essentially reached the 1.5°C goal in real temperatures.

Energy Imbalance and Future Warming

Earth is still absorbing more solar energy than it emits to space. To reach energy balance, global temperature must rise toward:

where ASR is absorbed solar radiation, ETR is emitted thermal radiation, and T is current absolute temperature.

In 2025, the fourth root of the ASR/ETR ratio is ~1.0015, implying a future equilibrium of:

Given current trends, 15.5°C (2°C above pre‑industrial) may be unavoidable by ~2033.

Summary: Should We Use Real Temperatures Instead of Anomalies?

By translating the Paris Agreement limits into real temperatures (15.0°C and 15.5°C) we gain a clearer, more intuitive benchmark. Based on ERA5 and PAGES2k, true pre‑industrial global temperature was ~13.5°C.

Using real temperatures:

• 2024 exceeded the 1.5°C target.

• 2025 is hovering near it.

Global temperature naturally swings by 3.9°C annually, so a fixed target must be interpreted with that in mind.

Conclusion

Expressing climate goals in real temperatures makes them easier to communicate and compare with datasets like ERA5. By this measure, we are right on the edge of failing Paris goals.

The DOE report implies that exceeding these targets—even well above them—will not be too harmful and that trying to prevent it would be too costly. It uses scientific uncertainty as a reason to delay action.

Where I see the real uncertainty is in the report’s conclusions.

Represent Us

As my granddaughters are happily enjoying summer camp, I am watching the news about missing girls at a summer camp after Texas flash floods. Did they have NOAA weather radio? Are there rules for summer camps? Is there a way I can help? Can government do something? I think it should. Government is how we cooperate on a local or national basis, but I am not going to advocate for any political party.

My golf buddies know better than to discuss politics, but last week I heard a commotion at the other end of the table. It was something political. One of my friends started pointing at each of us one by one saying “conservative, conservative, liberal, conservative,…” When he got to me, he paused for a while, then he said “I think you are a …” Yes, he made a guess. I looked at him and said “there are more than two choices.” He answered “no there aren’t.”

We get so mad at the “other side”! We are not listening to each other! My suggestion here is that government should Represent Us. , so, I wrote an essay on the topic. It expresses what I think is the cause of polarization and a course to a better direction. What do you think? Please comment.

Representative Democracy? Ha! We are blowing it!

Somewhere along the way, we convinced ourselves that there are only two sides to everything. Maybe it is just easier that way. Easier to sort the world into good and evil, red, and blue, us and them, this side of the aisle and that side. But easy does not mean right—or rational. And in our politics, this rigid two-sided mindset has become not just lazy, but dangerous. We have created a country so divided it feels broken, and we have built a system that rewards the worst of us, simply because we cannot imagine anything beyond the false binary we have inherited. We are blowing it—and it is time to say so.

We talk as if every issue can be resolved by picking a side. You are either right or wrong, Republican or Democrat, liberal or conservative, left or right, red, or blue. Even the word “bipartisan”—which we are told is the gold standard of compromise—still assumes only two camps. That is not compromise; that is dueling monopolies coming to a temporary truce. There’s no room in this system for nuance, complexity, or fresh thinking. It’s a straitjacket on our democracy, and we have strapped it on ourselves.

The result? A political ecosystem that selects for extremism. When the only real competition is between two parties, the incentives tilt toward whichever candidate can rally the loudest, most committed base. That means primaries dominated by the fringes and general elections where voters are forced to pick “the lesser of two evils.” Moderate voices, independent thinkers, and problem-solvers are squeezed out or silenced. We don’t get leaders who represent our full spectrum of views—we get cartoonish avatars of team red or team blue.

This is not just a frustrating process—it is deeply undemocratic. Most Americans hold complex, blended views. They might be economically conservative but socially liberal, or vice versa. They might agree with Democrats on climate and Republicans on crime. But our political system flattens all that out. If you do not fit neatly into one of two boxes, you get no real voice, no real representation.

So how do we fix this? We start by redesigning the system itself—building a democracy that assumes more than two perspectives and empowers voters to reflect that complexity. Imagine an electoral system rooted in proportional representation, where seats in Congress are awarded based on the actual share of votes different parties receive, not a winner-takes-all, district-by-district death match. This would encourage a multi-party landscape: not just Democrats and Republicans, but Greens, Libertarians, Social Democrats, Moderates, Independents, and others.

To complement that, we implement ranked-choice voting (RCV), where voters can rank candidates in order of preference. No more spoiler effect. No more “wasting your vote.” If your top choice does not win, your vote transfers to your next preferred candidate. This encourages civility, coalition-building, and broader appeal—because to win, a candidate must be not just someone’s first choice, but also an acceptable second or third.

But here is the crucial point: RCV only works when voters have a real menu of choices—not just two candidates who survived the same old binary battle. That means our open primaries must advance more than two candidates to the final ballot. The ideal number? Five.

With Final Five Voting, the top five finishers in a nonpartisan open primary move on to the general election. Why five? Because it hits the sweet spot: enough to create meaningful choice, ideological diversity, and genuine competition—but not so many that voters get overwhelmed. It lets independents and third parties break through. It allows moderates to survive. It gives ranked-choice voting room to work its magic—finding not the loudest candidate, but the one who can unite a majority.

This setup also tones down the scorched-earth campaigning. To win in a Final Five system, candidates need to appeal beyond their base and earn second- or third-choice rankings from voters outside their tribe. That changes how people run, how they govern, and how they treat one another.

We pair this with independent redistricting commissions to end the gerrymandering madness that locks voters into rigged districts and fuels political extremism. And we ditch closed partisan primaries, embracing open primaries where every voter, regardless of affiliation, helps decide who makes the ballot.

Together, these changes would shatter the illusion of two sides. They would allow new ideas to surface, new voices to rise, and new coalitions to form. They would not guarantee perfect outcomes—but they would make better outcomes possible. Outcomes based on deliberation, diversity, and compromise—not just tribal loyalty.

Our system was never meant to be static. The Founders did not pretend they had all the answers; they built a framework designed to adapt and improve. That is why the Constitution begins with a mission: to form a more perfect Union. They knew that democracy is not a finished product—it is a living process. And when our institutions no longer serve the people with fairness, representation, and wisdom, it is not betrayal to reform them—it is fidelity to the American idea.

And yet, instead of working together to modernize that idea, too many Americans are reaching for something darker. In a moment of historic gridlock—when the three branches of government seem locked in endless paralysis—millions of our fellow citizens are turning, astonishingly, toward authoritarianism. They see strength where there is force, decisiveness where there is cruelty, and order where there is obedience. It is a dangerous illusion, born of frustration, and it should shake us to the core. Because when democracy fails to function, demagogues rush to fill the void.

That is why we cannot afford to keep pretending that our system is fine. The greatest choice we face today is not left or right. It is whether we give in to decline and division—or rise to the challenge of reimagining our democracy. One that reflects the full complexity, diversity, and intelligence of the American people. One that earns back their trust—not through fear or force, but through real representation, real problem-solving, and real choices. One that restores three functioning branches of government—led by people who respect the institutions they serve and the humanity of those they disagree with.

We are blowing it. But we still have time to turn it around.

Clouds

Upon seeing liquid water at the bottom of a glass of crushed ice, most people would understand that the melting ice will not stop melting unless the temperature is reduced below freezing. The Greenland ice sheet has lost 5500 billion tons of water since 2000. It now occasionally rains even where the ice is thickest. Greenland ice is melting and it will not stop melting because Greenland temperatures are not decreasing. The earth’s energy imbalance with the sun is increasing. If heat were being added to the atmosphere at a steady rate, then global temperature would only be increasing at a constant rate. It is not. Heat is being added at an increasing rate. The earth has been and is warming at an accelerating rate. This is the opposite of what is needed to stop climate change.

Will clouds save us? It seems reasonable that higher evaporation rates from a warming climate would produce more clouds and that more clouds would resist further warming by reflecting more of incoming solar radiation. Another idea, originally proposed by the MIT professor Richard Lindzen, is that warming sea surface would concentrate tropical convection and reduce the type of clouds (Cirrus) that block infrared radiation from the earth. Either effect, i.e. reflecting more sunlight or allowing more thermal radiation to escape, would provide negative feedback to oppose global warming. NASA CERES satellites have provided measurements relevant to these two hypotheses. They have monitored Earth’s reflected short wave and emitted long wave radiation for both “all sky” and “clear sky” conditions since the year 2000. The “clear sky” condition means no clouds, so the effect of clouds can be inferred.

Albedo

The fraction of short-wave solar radiation reflected by the earth is called the albedo. A higher albedo means a brighter, but cooler, planet because what is not reflected is absorbed and heats the planet. The albedo for both “all sky” and “clear sky,” i.e. no clouds, conditions are shown below.

The albedo of “all sky” condition is 85% higher (brighter) than the “clear sky” condition. The albedo of clouds varies widely from 0.1 and 0.9, depending on density. This data indicates that on average the albedo of clouds is higher than the average albedo of earth surfaces. Clouds keep the earth cooler, but do they help reduce current warming? If a warming earth created more clouds of similar albedo, then “all sky” albedo should increase. However, albedo for both “all sky” and “clear sky” conditions has decreased since 2000. Below is the 12 month running averages of each divided by albedo in year 2000 to show the relative decrease.

The decline in clear-sky albedo may reflect reduced surface reflectivity-such as less or dirtier ice-or a decrease in atmospheric aerosols. Aerosols are suspended particles that scatter incoming solar radiation back into space, contributing to earth’s reflectivity. However, the observed decrease decline in all-sky albedo has been relatively steeper than that of clear sky albedo, suggesting either a reduction in over all cloud coverage or a shift to less reflective clouds. For instance, if average cloud albedo remained constant at 0.36, the measured drop in all-sky albedo would imply that cloud cover decreased from 67.1 % in 2000 to 64.7% by the end of 2024. The idea that an increase in clouds would counteract global warming is contradicted. Although the earth warmed since 2000, albedo has not increased. The effectiveness of clouds to reflect solar radiation has decreased.

Effective Emissivity

The influence of clouds on Earth’s energy balance can be seen in their effect on effective emissivity, defined as the ratio of emitted longwave thermal radiation to the product of the Stefan-Boltzmann constant and global temperature raised to the fourth power. This ratio provides a measure of the greenhouse effect’s strength. Here is the effective emissivity for both clear-sky and all-sky conditions since 2000. Average global surface measurements were from Climate Reanalyzer.

Interestingly, all-sky effective emissivity is about 10% lower than clear-sky emissivity, meaning that clouds tend to enhance the greenhouse effect by trapping outgoing infrared radiation. Despite this, both all-sky and clear-sky emissivity have been declining since 2000, indicating an overall strengthening of the greenhouse effect. See the relative running average for both below.

The decline in all-sky emissivity has been less steep than the decline in clear-sky emissivity—implying that clouds have partially offset the worsening greenhouse effect.

Clouds form around aerosols, which act as nucleation sites for water vapor. A reduction in atmospheric aerosols could be limiting cloud formation. Another contributing factor may be a shift in cloud type, as suggested by Lindzen’s “iris hypothesis,” in which warming reduces high cirrus cloud coverage and allows more thermal radiation to escape.

Combined Factor

The overall radiative effect of clouds can be assessed using the combined factor: the inverse of emissivity multiplied by one minus albedo. This combined factor represents how clouds influence both incoming solar reflection and outgoing thermal radiation.

The all-sky combined factor is about 6% lower than the clear-sky value, indicating that, on balance, clouds exert a cooling influence on the planet. The relative running average for both is shown below.

Both all-sky and clear-sky combined factors have been increasing since 2000, with all-sky rising slightly faster. This suggests that while clouds have slightly weakened their cooling role by reflecting less sunlight (reduced albedo), they have also helped to mitigate the strengthening greenhouse effect. Overall, these opposing changes in cloud behavior have nearly canceled each other out in terms of their net effect on global warming. In other words, the overall effect of clouds has been near neutral. Clouds are not saving us from global warming.

Seasonal Variation from Running Average

Without comment, here are the seasonal variations of albedo, effective emissivity, and combined factor.

Seasonal Temperature Changes and Earth’s Eccentric Orbit

The Earth’s Orbit and Seasonal Radiative Balance

I wanted to better understand why global temperature was highest when Earth was farthest from the sun, so this post is not about climate change. Instead, it explores the annual timing of the Earth’s natural warming and cooling cycle-driven by the elliptical orbit of the Earth around the Sun. The analysis focuses on deviations from the running average of radiative fluxes and global surface temperature, isolating orbital effects on Earth’s energy balance. For each type of measurement, I used Principal Component Analysis (PCA) to obtain the dominant seasonal variation, applying PCA to multiyear data after subtracting the one-year running average.

NASA’s CERES satellite system provided continuous measurements of incoming and outgoing radiation from March 2000 to July 2024. (Hopefully this effort will continue or be renewed by other systems when satellites reach end of life.) The measurements include incoming solar flux and the Earth’s reflected short wave and emitted long wave radiation, reported for both “all sky” and “clear sky” conditions. This analysis uses “all sky” data only.

Solar radiation received by Earth varies with its distance from the Sun, following the inverse square law. The Earth’s orbit is elliptical, with an eccentricity of 0.01672, making it nearly circular. While small, this eccentricity causes seasonal changes in solar flux. Calculating the Earth-Sun distance over time requires accounting for the eccentricity, the earth’s orbital period (365.256363 days) and the variable orbital speed (faster near perihelion, slower near aphelion). Finally, Moon’s orbit around the Earth causes a wobble in Earth’s orbit around the Sun so that the day of perihelion varies from year to year. The effect of eccentricity on angle is shown below.

Because the earth’s eccentricity is so small, the ellipse angle is always within 1° of the angle calculated assuming a circular orbit. Although the correction is small, I kept it.

The influence of the moon’s orbit on the day of the perihelion is not as easily predicted. The Moon not only causes the Earth’s axis of rotation to wobble slowly (26,000 years per cycle), it also slightly oscillates the Earth’s distance from the sun. The effect of this oscillation on day of perihelion since 2000 is shown below. Of less importance here is that, because of axis precession, the time of perihelion advances by one day every 58 years.

On average right now perihelion occurs around January 4 with aphelion approximately 183 says later, around July 6.

Below is the Earth-Sun distance versus time of year assuming an orbit eccentricity of 0.01672 and perihelion on Jan. 4. The unit of distance is the astronomical unit, au, which is the average distance between Earth and Sun.

Seasonal Incoming Solar Radiation

Here is the NASA CERES measurement for incoming solar radiation over the past 25 years.

Below is what PCA (Principal Component Analysis) shows for the annual variation of incoming solar radiation (circles). Also plotted is the annual variation of inverse square of orbital distance (blue line).

The CERES data shows a seasonal variation in incoming solar flux that closely follows that predicted based on orbital distance. The maximum and minimum dates agree with January 4 and July 6. The “neutral times,” when incoming radiation equals the average, are March 2 and September 4. Between Sept. 4 and Mar. 2, the earth receives more than the average. The rest of the time it receives less.

Net Radiative Flux

Global temperature is determined by net flux: the difference between incoming radiation and the outgoing reflected plus emitted radiation. If net flux were zero then the earth’s global temperature would remain unchanged. As seen below, the one year running average (blue) of net flux has been increasing, but net flux mostly oscillates around zero.

Here is how net flux deviates from average (circles and red line) compared with the annual variation of inverse orbital distance squared (blue line).

The seasonal variation of the net flux is 23% less than the seasonal variation of incoming solar. The neutral points are shifted to Apr 17 and Aug 31.

Cumulative Heat

Global temperature does not react instantly to net radiative flux. Instead, cumulative heat, the integral of net flux over time, determines warming or cooling. Here is the cumulative heat and its one year running average (blue).

It has been increasing since 2000 at an accelerating rate (with seasonal oscillations).

Below is its seasonal oscillation (circles and red line) compared with net flux (blue line).

The dates of maximum and minimum retained heat correspond to the neutral points of net flux, near April 17 and August 31. How do these dates, April 17 and August 31, compare with dates of maximum and minimum global or world temperature? Not good.

Global Surface Temperature

Climate Reanalyzer publishes ERA5 daily surface temperature estimates for 6 geographical areas, namely for the world, northern hemisphere, southern hemisphere, tropics (latitudes 23.5°S-23.5°N, about 26% of the earth’s surface), Artic (66.5-90°N, about 13% of the earth’s surface), and Antarctic (66.5-90°S, also about 13% of the earth’s surface). The estimates go back to 1940. Below is the seasonal variation of surface temperature for the northern hemisphere, the southern hemisphere, and the world.

The seasonal variation (root mean square) of the northern hemisphere is 2.4 times larger than that of the southern hemisphere. Note that the seasonal difference between the north and south hemispheres is mostly due to the tilt of the earth’s axis of rotation. The highest temperature for the northern temperature occurs about June 29. This makes sense since the summer solstice is June 21.

The world surface temperature is the average of the northern and southern hemispheres, so its seasonal variation is less than that of either northern or southern hemispheres, but, because of the elliptical orbit, it is not zero. The dates for maximum and minimum world or global temperature are Jun 25 and Jan 10. So why does that not track with the dates of maximum and minimum cumulative heat, April 17 and August 31? Is the heat concentrated differently than the temperature? The answer can be yes due to differing heat capacitances of Earth’s regions. So where is the heat concentrated in April?

Below is the seasonal variation of surface temperature for antarctica, the artic, and the tropics.

The seasonal variations for the Arctic and Antarctic regions (rms of 10.7 and 7.3 °C) are greater than for that of the tropical region (rms of 0.36°C), but neither show a peaking of temperature near April 17. The tropics, however, does peak at April 23, which is close to the April 17 date. This supports the idea that tropical regions are first to absorb and retain the heat, which then distributes globally.

Linear Combination

Cumulative heat should be a linear combination of temperature changes across regions, weighted by heat capacities. Here is a linear fit using the seasonal temperature variations in tropics, northern hemisphere, and southern hemisphere. Note that the area of tropics (latitudes 23.5°S-23.5°N) includes 13% of each hemisphere, so the areas of the three, namely tropics, northern hemisphere, and southern hemisphere, but are not independent.

Summary

This post analyses natural seasonal changes in Earth’s radiative energy balance due to its elliptical orbit using satellite and surface temperature data.

Incoming solar radiation peaks near perihelion (Jan 4) and dips near aphelion (July 6).
Cumulative heat from the net radiative flux reaches max near April 17 and min near August 31.
Globally averaged surface temperature, however, lags due to regional differences in heat capacity-with the tropics playing a key role in early heat retention. The max and min dates are June 25 and January 10.

The Earth’s elliptical orbit, though close to circular, creates significant and measurable seasonal oscillations in energy balance and surface temperature.

Water

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.

2024

Hottest Year on Record and Accelerating Global Warming

The year 2023 was officially the hottest in human history. However, 2024 has already surpassed that milestone. The following graph compares daily global temperatures of 2024 (blue points) with 2023(green points). On average, 2024 was hotter than 2023 by 0.113°C – a significant jump compared to the average warming rate of 0.02°C per since 1975. Only 118 days of 2023 were warmer than their 2024 counterparts. Before 2023, the hottest year was 2016, but only 40 days in 2016 were hotter than in 2024. No year before 2014 had days that surpassed 2024’s temperatures. Thus, we now have a new hottest year in recorded history.

Global Warming Trends Since 2015

Despite worldwide efforts to reduce warming under the Paris Agreement, global temperatures have continued to rise at an accelerating pace. Since 2015, the average rate of warming has been faster than during the preceding 40 years. This trend is visible when global temperatures are averaged over different time periods, as shown in the following graph:

Blue lines: Ten-year averages.
Green lines: Five-year averages.
Red lines: Two-year averages.

From 1945 to 1975, the blue lines are close together, indicating slow warming. Between 1975 and 2015, the blue lines are evenly spaced, showing a steady warming of about 0.17°C per decade. However, the most recent step (2015-2025) shows a larger temperature increase of 0.357°C – more than double the previous rate. One step alone does not provide sufficient evidence of an accelerating warming rate unless the cause of the warming is increasing.

Understanding Energy Imbalance and Global Warming

The root cause of global warming is Earth’s energy imbalance (EEIMB): the difference between absorbed solar radiation (ASR) and emitted thermal radiation (ETR). When EEIMB is positive, the planet absorbs more energy than it emits, leading to warming. Conversely, a negative EEIMB results in cooling.

If the energy imbalance remains constant, global temperature would rise at a steady rate. However, a growing EEIMB implies an accelerating rate of warming. Since 2000, NASA has been monitoring radiation fluxes at the top of the atmosphere, making it possible to track this imbalance alongside temperature changes.

Seasonal variations in EEIMB are driven by Earth’s elliptical orbit, which causes a 6.5% fluctuation in incoming solar radiation from January to July. Although seasonal variations in EEIMB explain the 4.2°C swing in global temperature each year, the response of average global temperature to changes in EEIMB is counterintuitive. As seen in the first graph, the Earth’s surface is warmest in July when the planet is farthest from the sun and it is coolest in January when the planet is closest.

Plotted together below, for a typical year, is the rate of temperature change, i.e. the first derivative, – black line and smoother blue line – and the energy imbalance, EEIMB – red line.

There is a noticeable phase lag: the fastest warming occurs about 61 days after the maximum positive imbalance, and the fastest cooling occurs about 116 days after the maximum negative imbalance. This must be due to a thermal inertia of Earth’s systems, particularly the oceans, which absorb and release heat over extended periods. Remarkably, the planet can warm or cool at rates as high as 10°C per year – an astonishingly rapid change compared to the long-term warming of just 2°C over a century.

Increasing Energy Imbalance and Accelerating Warming

If the positive and negative swings of the energy imbalance remained equal year over year, there would still be a seasonal swing to global temperature, but there would be no year-to-year warming. Since 2000, however, the 12-month running average of EEIMB has been a net positive. If the EEIMB net positive were stable, global warming would follow a linear trajectory. In fact, a 12-month running average of EEIMB shows a steady increase, indicating that the imbalance is not stabilizing.

Global temperature increase depends on cumulative retained energy, the integral (ΔQ) of the EEIMB. In the 12-month running average of the integral of the energy imbalance, shown below, the parabolic shape is visibly evident.

The cumulative retained energy over the past 25 years is equivalent to the energy of a 20-watt bulb shining on every square meter of the Earth’s surface for 20 years. In the following graph a one year running average of temperature is compared with the cumulative energy (ΔQ). The scaling for the cumulative energy is adjusted to fit the temperature in the least squares sense. It shows that global temperature has risen in proportion to cumulative energy, following the same parabolic trajectory.

Three potential future scenarios are shown in the graph below:

Accelerating (parabolic) path: If current trends continue, temperatures will rise even faster.
Linear path: Temperature increase at a constant rate.
Equilibrium path: Temperatures stabilize if greenhouse gas and albedo effects stop changing.

Currently we are on an accelerating path. In all scenarios, global temperatures will exceed the critical 1.5°C threshold in fewer than 10 years.

The Drivers of Increasing Energy Imbalance

The increase in EEIMB is not due to changes in incoming solar radiation, which has remained constant at 340.2 W/m² +/-0.03% over the past 25-years. Instead, the widening gap between ASR and ETR is the driver:

ASR (Absorbed Solar Radiation): Reflectivity (albedo, α) has decreased, allowing more solar energy to be absorbed.
ETR (Emitted Thermal Radiation): While ETR has increased in response to warming, it has not kept pace with ASR. This disparity is partly or completely due to the greenhouse effect, which reduces Earth’s effective emissivity (ε).

The energy balance, EEIMB, is the difference between absorbed solar radiation, ASR, and emitted thermal radiation, ETR. The following graph shows 12-month running averages of ASR and ETR. It is the same graph as in Berkeley Earth Global Temperature Report for 2024, but I have added two additional curves.

Both ASR and ETR have been increasing, but not at the same rate, so the gap between them is widening. ASR, the fraction of incoming solar radiation not reflected into space, is increasing because the earth is reflecting less radiation. Earth’s reflectivity, α, dropped from 0.621 in 2000 to 0.615 in 2025 (see graph for albedo below). ETR, the emitted thermal radiation is also increasing, but not keeping up with the ASR. A definition of Earth’s effective emissivity, ε, is that ETR should equal εσT⁴, where σ is the Stefan-Boltzmann constant. The quantity εσT⁴ closely tracks ETR only if ε is a gradually decreasing quantity. The emissivity of the earth is affected by the greenhouse gas effect, so I modeled ε using atmospheric CO₂as a proxy for all greenhouse gasses. From that model, emissivity decreased from 0.621 in 2000 to 0.618 in 2025 (see graph for emissivity below). This change aligns with rising CO2 levels, 369.7ppm in 2000 to 425.9ppm in 2025.

Conclusion

The accelerating rate of global warming is driven by a persistent and growing energy imbalance. Both albedo and emissivity have been decreasing, exacerbating this imbalance. Without immediate and effective action, the planet will continue a path of accelerating warming, with consequences for ecosystems, economies, and human well-being.

Accelerating Global Temperature

Global temperature shows signs of accelerating. Here I use a simple model of the atmosphere to explore the reason. Assume an earth modeled by a spherical shell, very well insulated on the inner surface, so that its temperature is only determined by the radiant energy entering and leaving its outer surface. A change in temperature of the shell will be proportional to the cumulative change in energy.

ASR is absorbed solar radiation and ETR is emitted thermal radiation. These fluxes have been measured by the NASA CERES program since 2000. The following graph shows the 12-month running average of the energy imbalance (ASR – ETR) by year.

The cumulative energy is the integral of this curve shown in the following graph.

Note that the cumulative energy seems to have a quadratic dependence with time. It is accelerating. As shown in the next graph a plot of the 12-month running average of 2m mean global temperature versus the corresponding cumulative energy shows a reasonable straight-line dependence.

In fact, the least square fit of global temperature with cumulative energy had a smaller standard deviation (0.095) than either a straight line fit of temperature by year (0.101) or a quadratic fit (0.0964).

The next graph shows global temperature and the fit of global temperature with cumulative energy (blue line). The lavender lines show quadratic and straight-line extensions of global temperature. Note that the quadratic extension is essentially the same 2^nd order polynomial line as the line of cumulative energy. A green line shows a rise to an equilibrium temperature if albedo and emissivity were to remain constant. Right now, that equilibrium temperature would be slightly above the 1.5-degree Paris goal.

Global temperature is accelerating at a quadratic rate because the earth’s cumulative energy imbalance is increasing at a quadratic rate. In previous posts I showed that the effect of albedo decrease has slightly exceeded the effect of greenhouse gases on emissivity since 2000. Whether linear or quadratic, global temperature is heading toward 2°C above preindustrial levels between 2035 and 2060

Out on a Limb

Albedo and Emissivity

Is my previous analysis using CERES measurements of earth’s absorbed and emitted radiations and the ERA5 global mean surface air temperature at a height of 2 meters correct?

Ultimately, for the temperature of the roughly 2-meter shell of atmosphere within which we live to remain stable, the absorbed solar ration, ASR, must be balanced by the earth’s emitted thermal radiation, ETR. ASR is a fraction of the incoming solar radiation. Similarly, ETR is a fraction of the thermal radiation emitted by the 2-meter shell of atmosphere. In my analysis I have been defining albedo and effective emissivity as

and

where

IN = Incoming solar flux

ETR = Emitted Thermal Radiation, Top of the atmosphere long wave flux – all sky

and

ASR = Absorbed Solar Radiation, (Incoming Solar flux) minus (Top of the atmosphere short wave flux – all sky)

are from CERES and T is the global mean surface air temperature at a height of 2 meters. I made estimates for albedo and emissivity in creating the following graph, which is based on one found here: https://berkeleyearth.org/global-temperature-report-for-2023/. The absorbed solar radiation (ASR) was compared to the incoming solar flux (IN) times a linearly increasing constant, 0.705 in 2000 and 0.7105 in 2024, corresponding to albedo values of 0.295 and 0.2895. Similarly, the emitted thermal radiation (ETR) was compared to T⁴ using an effective emissivity linear with log of atmospheric CO₂. The fitted values for the emissivity decreased from 0.620 in 2000 to 0.617 in 2024.

These values of albedo and emissivity seemed reasonable. I felt confidant using the above definitions to create the following two graphs for albedo and emissivity. Again, the seasonal variations are suppressed by using 12 month running averages.

For albedo I found a value of 0.294 decreasing at the rate of 0.000233 times the number of years since 2000. For effective emissivity I found a value of 0.621 decreasing at the rate of 0.000137 times the number of years since 2000. The variation of atmospheric CO₂ is so consistent with time that it can be used as an independent variable for a least square fit. I found the fit to emissivity as 0.762 minus 0.0239 times the natural log of the concentration. A plot of the CO₂ concentration (12 month running average), on the same graph as emissivity, falls nearly on the linear least square fit line for emissivity.

So how do these definitions hold up with the literature? Finding anything by internet search to corroborate either result was disappointing. In this reference, Measuring Earth’s Albedo, only a small random anomaly from a nominal value of 0.3 for the earth’s albedo was found in the period between March 1, 2000 and December 31, 2011. That is a clearly different result. I found no source that used the same definition for either effective emissivity or albedo. Maybe someone knowledgeable will comment.

Progress in Curbing CO2

In a post during the COVID pandemic I commented on the unreasonable consistency with which atmospheric CO₂ has increased as seen in the Keeling curve. I modeled the Keeling curve up to 2020 by a second order polynomial plus a seasonal variation which increased linearly with CO₂. I had expected a measurable deviation from that trend after the reduced economic activity during the pandemic. I observed none. Since then, there has not been any progress. The following graphs show the lack of progress in curbing the accelerating increase of CO₂. Unless that changes in the following seven years, I estimate no chance in avoiding a 2°C global temperature anomaly from preindustrial times (see previous posts on “Setpoint”). I hope I am wrong.

Global Temperature Setpoint

How Fast is the Setpoint Increasing?

A recent post in Open Mind estimates that global temperature is increasing at 0.032°C per year. In the last post I showed that, if all conditions remained the same, then the earth would warm to a “setpoint” temperature, T_eq , at which its emitted thermal radiation would equal the absorbed solar radiation.

The setpoint temperature has already passed 1.5°C above the preindustrial temperature. It is no longer possible to avoid passing 1.5°C without reducing the greenhouse effect or increasing earth’s albedo. So how fast is the setpoint temperature increasing?

Here is the setpoint since 2000 along with a straight line fit. The rate of increase of the setpoint is 0.0395°C per year.

If the trends in albedo and effective emissivity remain the same then the setpoint will exceed 2°C by 2033. In the last post I showed that, absorbed solar radiation has increased faster than the greenhouse effect, 0.791% vs 0.531% since 2000.