If in a certain desert area the lightening strike rate becomes high after the establishment of of coal power plants, what kind of correlations can be drawn? What links have been established previously through research?
Good question the link may exist or not exist. It is not a linear problem but nonlinear. Lightening depend on several factors rather than co2 concentration. In some areas and cases there might be no correlation but other cases negative or positive correlations. It is complecated to be addressed in isolation without including the other ingredients of development ligthening bearings clouds
As Philbert states, it is an interesting question. However, how do you answer it? It isn't practicable to perform an experiment. None of the likely variables are amenable to experimental modification. You can't change the CO2 content of the atmosphere, or other lightning related factors, at will and see by how much lightning strike frequencies change. If you try to use historical data be aware that very many other confounding variables will be changing at the same time, making it nearly impossible to extract meaningful information from your results...