I have been working with a simple model for temperature that has the earth responding logarithmically to CO2 forcing (for example, depending on the parameters that I use, it might warm by 40 per cent of the expected total warming in the first 10 years and then by another 30 per cent of the expected total warming in the next 90 years) and then running that model using different climate sensitivities.
Climate sensitivity is commonly defined as the predicted climate response to a forcing and in the case of CO2 it is put as X degrees per doubling.
The values for X that I have tried range from one to 10.
The CO2 data I am taking from Manua Loa.
At the moment I have having some difficulty getting my model to come close to matching observations if I use a low climate sensitivity. I can almost do it if I have a very fast response time. For example, if I choose a climate sensitivity of two degrees per doubling and I have the vast majority (80 per cent) of the temperature response occuring within 50 years, with more than 50 per cent of that in the first decade, I can fit the model to the current observed temperature. But the rate of warming that this produces for the last 50 years is still too low.
However, even here there is a problem: the rate of observed change is still faster than my model shows.
The better fits are with higher climate sensitivities, but even there things are not perfect. (Note: I would not expect them to be so, as my model is leaving out climate variability, but they are still not good enough for my purposes).
This seems reasonable: based on our observations of temperature and atmospheric CO2 concentrations over the last 130 years and the linear fit between the two, a sensitivity of two degrees would seem to be implied. However, this would seem to suggest an almost instantaneous response to CO2. If instead some kind of logarithmic fit was used, I wonder what result we would end up with?
I am assuming that there is a major problem with a model such as this. Hansen seems to use a linear model, with different slopes at different periods of time (for example, four per cent of the response per year for the first decade, followed by about .4 per cent of the response per year for the rest of the century). According to him, other models use much longer response times, at least for the second half of the response.
If anyone has any advice on this, that would be appreciated. I can obviously provide the full model (which is not very full or large) to anyone who wishes to see it.