{"id":10235,"date":"2024-07-20T12:44:00","date_gmt":"2024-07-20T11:44:00","guid":{"rendered":"https:\/\/klima-fakten.net\/?p=10235"},"modified":"2024-07-20T12:44:01","modified_gmt":"2024-07-20T11:44:01","slug":"how-large-is-the-greenhouse-effect-in-germany-a-statistical-analysis","status":"publish","type":"post","link":"https:\/\/klima-fakten.net\/?p=10235&lang=en","title":{"rendered":"How large is the Greenhouse Effect in Germany? — A statistical Analysis."},"content":{"rendered":"
\"image_print\"<\/a><\/div>\n\n\n

High correlation as an indication of causality?<\/h4>\n\n\n\n

The argument that CO2<\/sub> determines the mean global temperature is often illustrated or even justified with this diagram, which shows a strong correlation between CO2<\/sub> concentration and mean global temperature, here for example the mean annual concentration measured at Maona Loa and the annual global sea surface temperatures:<\/p>\n\n\n\n

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

Although there are strong systematic deviations between 1900 and 1975 – 75 years after all – the correlation has been strong since 1975.
If we try to explain the German mean temperatures with the CO2<\/sub> concentration data from Maona Loa available since 1959, we get a clear description of the trend in temperature development, but no explanation of the strong fluctuations:<\/p>\n\n\n\n

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

The „model temperature“ \"\hat{T}_i\" estimated from the logarithmic CO2<\/sub> concentration data \"ln(C_i)\" measured in year \"i\" using the least squares method<\/a> is given by
\u00a0\"\hat{T}_i = 7.5\cdot ln(C_i)- 35.1\" (\u00b0C)

\u00a0If we add the annual hours of sunshine as a second explanatory variable, the fit improves somewhat, but we are still a long way from a complete explanation of the fluctuating temperatures. As expected, the trend is similarly well represented, and some of the fluctuations are also explained by the hours of sunshine, but not nearly as well as one would expect from a causal determinant:<\/p>\n\n\n\n

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

The model equation for the estimated temperature \"\hat{T}_i\" becomes with the extension of the hours of sunshine \"S_i\" to
\"\hat{T}_i = 5.8\cdot ln(C_i) + 0.002\cdot S_i - 28.5\"  (\u00b0C)
The relative weight of the CO2<\/sub> concentration has decreased slightly with an overall improvement in the statistical explanatory value of the data.<\/p>\n\n\n\n

However, it looks as if the time interval of 1 year is far too long to correctly treat the effect of solar radiation on temperature. It is obvious that the seasonal variations are undoubtedly caused by solar radiation.
 The effects of irradiation are not all spontaneous; storage effects must also be taken into account. This corresponds to our perception that the heat storage of summer heat lasts for 1-3 months and that the warmest months, for example, are only after the period of greatest solar radiation. We therefore need to create a model based on the energy flow that is fed with monthly measured values and that provides for storage.<\/p>\n\n\n\n

Energy conservation – improving the model<\/h4>\n\n\n\n

To improve understanding, we create a model with monthly data taking into account the physical processes (the months are counted with the index variable \"i\" ):<\/p>\n\n\n\n