My question is based on how to model the phenomenon, what kind of GIS Software to be used, what are the parameters to be identified and procedures to adopt.
There are many softwares that are capable of modeling climate phenomena some of them are free wares (QGIS, ILWIS etc) where are others are licensed (ESRI products). You could try any of them...
regarding parameters to be used - it would largely be based on the phenomena you are trying to model. basically you would require the atmospheric parameters like temperature, rainfall and humidity along with the base LULC. you could then identify the dependent variables for the phenomena under study and use it as inputs in any of the climate models.
One recommendation would be to explore the possibility of using IDRISI software. It has some very good modeling capabilities but am not sure of its specificity to model climate phenomena.
You ask a very broad question. The choice of software really depends on the kind of phenomena you are studying. Dr. Heejun Chang (http://web.pdx.edu/~changh/) at my University has done a lot of work on hydrologic changes with GIS tools. His website and work may give you some ideas.
When you talk about Climate, you are talking about a non-linear coupled Earth system with all its complex processes and natural variability. It deals with more quantitative parameterisation and assimilation of parameters into the models. There are many parameters and many models. So you should be sure of your area of interest.
You should go to Global Climate Observing System (GCOS) site and find out which are critical parameters for climate modeling. There are atleast 26 Essential Climate variables which are amenable for Earth Observation satellite measurements.
http://www.wmo.int/pages/prog/gcos/index.php?name=ObservingSystemsandData
The most important thing is that these parameters have to be monitored for long time and one should remove the effect of natural variability. World over efforts are on to create Fundamental Climate Data Records which are inter-calibrated and validated. As for as I know, the GIS is not the answer today as it has largely restricted itself to mapping and change detection. The climate modelers do not use the same datum as well. I suggest you also see the website of Group on Earth Observation (GEO) and Global Earth Observation System of Systems (GEOSS).
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