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.

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.

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.