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.

I’m trying to understand the climate sensitivity. To me it is too vague a concept. It is the increase or decrease in global surface temperature due to a given climate forcing. By convention, the given climate forcing is equated to that of a doubling of the concentration of CO₂ in the atmosphere. Apparently, climate sensitivity includes all feedbacks. Its ok that it includes a humidity feedback, i.e. the feedback which arises because the solubility of water in air and the evaporation rate of water are temperature dependent. It also includes cloud feedbacks. Apparently, though, it includes feedbacks that may take a really long time or feedbacks that may vary due to other conditions. For example, ice sheets take a long time to melt away. Also, the vulnerability of ice sheets change depending the current global temperature. Some feedbacks change the average reflectivity, the albedo, of the earth. Some affect the earth’s emissivity. I would be satisfied to know the response of the earth’s emissivity to a doubling of the concentration atmospheric CO₂. For small changes, that’s equivalent to knowing the value of “B” in the following equation.

Where x is the base 2 log of CO₂ concentration.

The current value of earth’s emissivity is defined by applying the Stefan-Boltzmann equation to the earth. At equilibrium the radiation from the earth must balance the radiation received from the sun.

T is earth’s average surface temperature. Epsilon is the earth’s average emissivity. Sigma is the Stefan-Boltzmann constant. TSI is the total solar irradiance at the position of the earth. The solar irradiance is intercepted on a disk the size of the earth, but, since the earth spins, it is absorbed over a sphere. The area ratio of the disk to the sphere is ¼. Alpha, the albedo, is the fraction of incoming radiation that is simply reflected back into space. Solving for epsilon gives the following equation for emissivity.

Satellites measure the current value of alpha at about 0.3. The current value of TSI is about 1361 W/m₂ . Current average global temperature is about 287°K. Therefore, from the above equation the current value of emissivity is about 0.619. Solving the above equation for T gives

If we knew the value of “B” we could the obtain the (partial?) climate sensitivity by taking the partial derivative of T with respect to x, the base 2 log of CO2.

Or substituting the above values

So, the partial climate sensitivity due to the effect of CO₂ on emissivity is 116 times “B”. The previous equations can be used to calculate emissivity knowing solar irradiance, average global temperature, and albedo. Although there are good records of irradiance and global temperature, I haven’t found good records or even good estimates of albedo. Albedo could vary for a number of reasons, such as ice sheet extent, black carbon on snow, cloudiness response, and aerosols from volcanoes and human emissions. The longest record I found was satellite measurements from 2000 to 2011. During that period, it remained relatively constant at about 0.3. The following graph shows calculated emissivity, assuming albedo has remained constant, plotted versus the base 2 logarithm of atmospheric CO₂. Since 1958 the levels of CO₂ in the atmosphere have been very precisely measured, so only data from 1958 to 2019 is plotted.

The result is a straight line with scatter. The correlation coefficient between the calculated emissivity and the log of CO₂ is 0.9. A least square fit gives “B”, i.e. the slope, a value of 0.021. Multiplying by 116 gives an estimate of 2.44 to the (partial?) climate sensitivity with the assumption that albedo stayed constant at 0.3.

A value of 2.44 for the climate sensitivity is surprisingly close to 2.36, the 1967 result for CO₂between 300 and 600ppm, fixed relative humidity, and average cloudiness in S. Manabe and R. T. Wetherald. That paper assumed that relative humidity would remain constant with small increases in atmospheric temperature. Since water solubility in air increases with an increase in temperature, absolute humidity increases if relative humidity remains the same. Manabe/Wetherald computed eight values for the climate sensitivity to atmospheric CO₂. Four conditions were fixing absolute humidity, fixing relative humidity, having average cloudiness, and having clear skies. Two ranges in CO₂ were 300 to 500ppm and 300 to 600 ppm. I’ll focus on the 300 to 600 ppm values. In the case of absolute humidity remaining constant the chemical sensitivity was 1.33 for average cloudiness and 1.36 for clear skies. In the more likely case of relative humidity remaining constant the chemical sensitivity was 2.36 for average cloudiness and 2.92 for clear skies. The above 2.44 result derived from the NASA temperature record is in remarkable agreement with the Manabe/Wetherald value of chemical sensitivity for average cloudiness. This agreement could be luck. Average albedo could have changed between 1958 and now. Also there are other greenhouse gases other than CO₂. The proper way to determine climate sensitivity is include all the variables in realistic models. I did this exercise as a sanity check. The result was within the margins of sanity.

It is unsatisfactory, however, that I did not include other greenhouse gases, since they contribute to the climate forcing of the greenhouse effect. Including them would logically reduce the above climate sensitivity. Fortunately, NOAA has estimated an equivalent CO₂ concentration for all greenhouse gases for the period from 1700 to present. They didn’t show the numerical data, but I estimated it from their graph. Below is a comparison of CO₂ concentration and CO2 equivalent concentration from NOAA/ESRL.

Using my estimate of CO₂ equivalent from the NOAA/ESRL graph, I calculated emissivity for the 1958 to present time period again assuming an albedo of 0.3 for that time period. This time I included both the NASA and the Berkeley global temperature records. Here is the result after plotting the values versus the logarithm to base 2 of CO₂ equivalent concentration.

The result was a straight line with scatter. The correlation coefficient was 0.875. From a least square fit of the data, this time, the slope “B” was determined as 0.0138. Again, multiplying by 116 gives a climate sensitivity of (116×0.0138) of 1.6°C. It again meets the sanity check. This value is less than the Manabe/Wetherald result for constant relative humidity and average cloudiness, but it is higher than their result for constant absolute humidity and clear skies. It also falls within the likely range of 1.5°C to 4.5°C stated in the IPCC Fifth Assessment report.

Tag: climate sensitivity

Paris Climate Goals? DOE “Assessment”