Guest post by David Middleton
Models often get a bad rap among skeptics, largely because climate models have demonstrated an epic failure in predictive skill. However, models are extremely valuable scientific tools, particularly when used heuristically. Models are learning tools.
Generally speaking models fall into two general categories:
- Forward problems.
- Inverse problems.
From Wikipedia, the free encyclopedia
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in computer tomography, source reconstructing in acoustics, or calculating the density of the Earth from measurements of its gravity field.
It is called an inverse problem because it starts with the results and then calculates the causes. This is the inverse of a forward problem, which starts with the causes and then calculates the results.
Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They have wide application in optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, and many other fields.
In oil & gas exploration, we make extensive used of inverse models. We start with a result (seismic amplitude anomaly) and then try to calculate the causes (oil, gas, tabular salt, oyster beds, geopressure, tuff, marl, etc.). One of the most widely used tools is called a “fluid replacement model.” Using sonic and density logs from an existing well drilled through the objective section, we can mathematically substitute oil and gas for brine in wet sands and generate a synthetic seismic anomaly to compare with the real seismic anomaly. While these models are very useful, sometimes you will get a result that just doesn’t make sense. If a model defies realistic geology, it’s probably wrong. I wondered if we could do the same sort of thing to climate data.
Climate Sensitivity Inverse Model
In a fluid replacement model, we replace one fluid with another to see what the real data would look like with different fluid contents. In my climate model, I simulated what a climate reconstruction would look like without the industrial era rise in atmospheric CO2. I used two transient climate response cases 1) 1.35 °C and 2) 3.5 °C per doubling of atmospheric CO2.
This yielded two equations for ΔT:
- ΔT = 1.9476*ln(CO2) – 10.954 for TCR = 1.35 °C
- ΔT = 5.0494*ln(CO2) – 28.398 for TCR = 3.50 °C
Using CO2 data from Law Dome (MacFarling Meure et al., 2006) and a Northern Hemisphere climate reconstruction (Ljungqvist 2010), calculated the CO2-driven temperature component and then subtracted it from the reconstructed temperatures.
The removal of a 1.35 °C TCR yields reasonable result. The removal of a 3.50 °C TCR yields a temperature much colder than the nadir of the Little Ice Age. This seems massively unlikely. (When I applied this to Greenland ice core temperatures (Alley, 2000 and Kobashi et al., 2010) using a 2X polar amplification, the model yielded temperatures equivalent to the Bølling-Allerød glacial interstadial.)
Zooming in on the “Anthropocene,” it appears that a high TCR (alarmist) world would already be buried under a mile of ice, if not for anthropogenic augmentation of the so-called greenhouse effect.
If my methodology is valid, it seems highly probable that the climate is relatively insensitive to atmospheric CO2. This would seem to validate recent observation-based climate sensitivity estimates, which indicate rather low TCR and ECS values.
- I use the phrase “so-called greenhouse effect” because it doesn’t really work like a greenhouse… Not because I deny its existence.
- If I’ve made any glaring errors, please point them out.
- For the purpose of this exercise, I am assuming that the Law Dome ice core has adequate resolution to yield an accurate depiction of pre-industrial atmospheric CO2.
 Ljungqvist, F.C. 2010.
A new reconstruction of temperature variability in the extra-tropical
Northern Hemisphere during the last two millennia.
Geografiska Annaler: Physical Geography, Vol. 92 A(3), pp. 339-351,
September 2010. DOI: 10.1111/j.1468-0459.2010.00399.x
 MacFarling Meure, C., D. Etheridge, C. Trudinger, P. Steele,
R. Langenfelds, T. van Ommen, A. Smith, and J. Elkins. 2006.
The Law Dome CO2, CH4 and N2O Ice Core Records Extended to 2000 years BP.
Geophysical Research Letters, Vol. 33, No. 14, L14810 10.1029/2006GL026152.
 Science News
 Featured Image