One of my favorite sentences from the great author Heinrich Spoerl’s book “Die Feuerzangenbowle” (1933) is the physics professor Bömmel. Explaining the working of the steam engine he begins with “Da stelle mer uns janz dumm” (approximate translation “Let’s start by assuming we are completely stupid”).
The primordial question about an eventual anthropogenic caused global warming is the temperature increase following rising atmospheric CO2 concentrations (or more correctly “mixing ratios”). The IPCC assumes that AGH (anthropogenic greenhouse gases) and predominantly CO2 are the principal driver of the last 150 years warming of about 0.7°C. We know from laboratory experiments that the radiative forcing F (in W/m-2) produced by CO2 is proportional to the (natural) logarithm of its concentration. Generally it is assumed that dF = 5.35*ln(CO2new/CO2old), and that global temperature increase dT is proportional to dF: dT = lambda* dF, where lambda is the much debated (equilibrium) climate sensitivity. Lambda is not only much debated, but the last 30 years of multi-billion officially fostered climate research has not lowered the “consensus” estimate range (about 1.5 to 4.5 °C). Now politicians eager to avoid planetary Armageddon and to show their environmental care have only one simple question: “by how much will the globe warm when our emissions increase atmospheric CO2 by so and so much?”. Alas, their only acceptable counselor (the IPCC) can only give an answer based on models (an answer the IPCC calls a scenario to avoid that satanic word “prediction”).
So we will follow professor Böhmer’s dictum and “da stelle mer uns janz dumm”. Let us look at the past data since 1850, and use the Hadcrut4 data set for global temperatures (this dataset is used by the IPCC) and also an officially accepted CO2 variation data set (the Mauna Loa series extended backwards to 1850). I will use Prof. Humlum’s excellent website www.climate4you.com (a website that shines like a rare true scientific beacon in midst global activism and hysterical enviro-angst). We will use two periods with much different CO2 increases: 1850 to 1945 where CO2 increases from 290 to 310 ppmV (let’s not object to these numbers, even if they are still open to debate), and 1945 to 2013, where the CO2 concentrations go from 310 to 397 ppmV. The global temperature increases by 0.3 K (or °C) during the first period, and by +0.4 K during the second.
Now let us take the simplistic model: dT = k* ln(dCO2) where the d means a delta: dT = temperature difference, same for dCO2. I know, this model differs from the expression given above; it is an “janz dumme” hypothesis which will be subjected to observational verification.
The first period allows to calculate the factor k which is equal to k = dT/ln(dCO2) = 0.3/ln(20) = 0.1.
Let us take this result to calculate the temperature increase that a CO2 swing from 310 to 397 ppm would yield: dTcalc = 0.1*ln(87) = 0.45 K. The observational data give dT = 0.40 K, very, very close to the simplistic calculation. Our zero-dollar model is more or less verified by the second period of nearly 70 years.
fig. Global temperature anomalies (Hadcrut4 series) for 1850 to present with CO2 increase.
Now we will look into the crystal ball and predict how much warming a CO2 doubling from the pre-industrial (1850) baseline will cause (if everything continues as it has during the last 163 years):
dT = 0.1*ln(580-397) = 0.52 K. This will be the warming from today on if CO2 levels rise to 580 ppmV. IPCC’s “business as usual” scenario A1TI predicts this mixing ratio for 2050, and about 1000 ppmV for 2100. Now 1000 ppmV seems ***BIG***, but our model shows that it will correspond to a warming of only dT = 0.1*ln(1000-397) = 0.64 K from today’s situation. This means a total warming of 0.7 + 0.64 = 1.34 °C in respect to the cold, end of little ice age pre-industrial times if we do nothing. Hardly anything to shudder and scream about!