{"id":6276,"date":"2021-07-25T21:03:18","date_gmt":"2021-07-25T20:03:18","guid":{"rendered":"http:\/\/klima-fakten.net\/?p=6276"},"modified":"2021-07-27T13:52:35","modified_gmt":"2021-07-27T12:52:35","slug":"temperature-and-co2","status":"publish","type":"post","link":"https:\/\/klima-fakten.net\/?p=6276&lang=en","title":{"rendered":"Global Temperature predictions"},"content":{"rendered":"
\"image_print\"<\/a><\/div>\n\n\n

Questioning the traditional approach<\/h4>\n\n\n\n

The key question to climate change is how much does the \"CO_2\" content of the atmosphere influence the global average temperature?<\/strong> And in particular, how sensitive is the temperature to changes in \"CO_2\" concentration?
We will investigate this by means of two data sets, the HadCRUT4 global temperature average data set, and the CMIP6 \"CO_2\" content data set.
The correlation between these data is rather high, so it appears to be fairly obvious, that rising \"CO_2\" content causes rising temperatures.
With a linear model it appears easy to find out how exactly temperatures at year i \"T_i\" is predicted by \"CO_2\" content \"C_i\" and random (Gaussian) noise \"\epsilon_i\". From theoretical considerations (radiative forcing) it is likely that the best fitting model is with \"log(C_i)\":
\"T_i = a + b\cdot log(C_i) + \epsilon_i\"
The constants a and b are determined by a least squares fit (with the Python module OLS from package statsmodels.regression.linear_model):
a=-16.1, b=2.78
From this we can determine the sensitivity, which is defined as the temperature difference when \"CO_2\" ist doubled:
\"\Delta(T) = b\cdot log (2) °C = 1.93 °C\"
This is nearly 2 \u00b0C, a number close to the official estimates of the IPCC. <\/p>\n\n\n\n

What is wrong with this, it appears to be very straightforward and logical?<\/strong>
We have not yet investigated the residue of the least squares fit. Our model says that the residue must be Gaussian noise, i.e. uncorrelated.
The statistical test to measure this is the Ljung-Box test. Looking at the Q-criterion of the fit, it is Q = 184 with p=0. This means, that the residue has significant correlations, there is structural information in the residue, which has not been covered with the proposed linear model of log(\"CO_2\") content<\/strong>. Looking at the diagram which shows the fitted curve, we get a glimpse why the statistical test failed:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

We see 3 graphs:<\/p>\n\n\n\n