# Help in understanding this. Is this just an empirical observation on climate sensitivity?

I was reading this on realclimate.org.

My question on the below is this. Physics can tell you the radiative forcing of CO2, which is $$\small\mathsf{5.35ln(Cnew/Cpreindustrial)}$$. This tells you how much radiative forcing to expect for an increase of CO2 (=$$\small\mathsf{C_{new})}$$ over pre-industrial levels (C preindustrial, usually 280 ppm). This formula provides an unambiguous answer of radiative forcing.

But... there is a question that then arises about what warming is associated with this particular level of radiative forcing. This appears to be an empirical matter, looking at past fluctuations of CO2 and associated temperatures. This is the climate sensitivity. There are lots of studies on this, with a now-accepted range of 1.5-4.5 °C. But the reason there is some disagreement about this is that it is an empirical question, not so much a physics one, right?

Here's the realclimate piece:

Blockquote

As the name suggests, climate sensitivity is an estimate of how sensitive the climate is to an increase in a radiative forcing. The climate sensitivity value tells us how much the planet will warm or cool in response to a given radiative forcing change. As you might guess, the temperature change is proportional to the change in the amount of energy reaching the Earth's surface (the radiative forcing), and the climate sensitivity is the coefficient of proportionality:

dT = λ*dF

Where 'dT' is the change in the Earth's average surface temperature, 'λ' is the climate sensitivity, usually with units in Kelvin or degrees Celsius per Watts per square meter (°C/[W/m2]), and 'dF' is the radiative forcing.

So now to calculate the change in temperature, we just need to know the climate sensitivity. Studies have given a possible range of values of 2-4.5 °C warming for a doubling of CO2 (IPCC 2007). Using these values it's a simple task to put the climate sensitivity into the units we need, using the formulas above:

λ = dT/dF = dT/(5.35 * ln[2])= [2 to 4.5 °C]/3.7 = 0.54 to 1.2 °C/(W/m2)

Using this range of possible climate sensitivity values, we can plug λ into the formulas above and calculate the expected temperature change. The atmospheric CO2 concentration as of 2010 is about 390 ppmv. This gives us the value for 'C', and for 'C0' we'll use the pre-industrial value of 280 ppmv.

dT = λ*dF = λ * 5.35 * ln(390/280) = 1.8 * λ

Plugging in our possible climate sensitivity values, this gives us an expected surface temperature change of about 1–2.2 °C of global warming, with a most likely value of 1.4 °C. However, this tells us the equilibrium temperature. In reality it takes a long time to heat up the oceans due to their thermal inertia. For this reason there is currently a planetary energy imbalance, and the surface has only warmed about 0.8 °C. In other words, even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6 °C until it reached this new equilibrium state (confirmed by Hansen 2005). This is referred to as the 'warming in the pipeline'.