I think system dynamic approach is the best way for you.because your interest issue is a dynamic problem and they relate to each other in more than one way. vensim is a free software for modeling system dynamic (SD) problem .

http://www.systemdynamics.org/

The correlation between all indicators of environmental degradation way (pollution, over-exploitation of resources and elimination of excessive amounts of waste into the environment)

I think you need to define climate change in terms of ecological parameters, such as those used by Koppen and refined by Trewartha. Fortunately, there is a substantial body of recent literature on the subject.

In my opinion Belda et al have done the best exercise in defining climate regions based on climate parameters that are ecologically significant.

Also, Belda avoided defining cells so small that they reach what would obviously be spurious precision. But it remains debatable what level of precision would have real meaning given the sparsity of climate data outside the US, Europe and a few other places, such as Asian Turkey. This itself is a worthy subject for study.

Reference: Belda, M., Holtanová, E., Halenka, T. and Kalvová, J., 2014. Climate classification revisited: from Köppen to Trewartha. Climate research, 59(1), pp.1-13.

Paper: http://www.int-res.com/articles/cr_oa/c059p001.pdf

The URL may take a little patience. The web site is also worth exploring.

I am retired, but if I were to pursue your question, I would attempt to repeat their study using updated climate data, which is now available. I would use the same periods they used (1900-1930 and 1975-2005). The reason is that the data set they used is now known to have a wet bias that exaggerates the change in ecological impacts. The update to the climate data corrected the wet bias.

So repeating the Belda study with updated climate data (presumably precipitation) would be an efficient way to reconstruct Koppen-Trewartha ecological regions.

If you are interested in following this up, let me know and I will pass on what I have to help you get started. My Excel spreadsheet is a bit of a mess, but I could tidy it a little. Have a look at the Belda paper to see if it is relevant to your interests.

Hello Masnat,

Like Pooneh above, if you are interested in quantitative modelling, I suggest you look into dynamic modelling, e.g. system dynamics. Surely there are many static modelling approaches (including regression models, or indicators), but 'impact' depends on dynamic co-adaptation of human and environmental systems, which is a dynamic problem. I would also suggest adopting a participatory modelling approach (see, for example attached file), which is a particularly powerful (albeit challenging) way to do modelling.

There is also scholarship on qualitative models (fuzzy logic, participatory approaches, etc), but you would get less of a "measure", than an understanding of impact pathways. 

You can get an overview of three quantitative modelling approaches in the book chapter below. 

I hope this helps as a start.

Best wishes,

Giuseppe.