One of the main reasons that climate change and global warming have become such a well publicised phenomenon is that at its core it is very easy to understand. It is not like quantum physics where the major concepts require an intense amount of study and intellect. All one needs to do to understand climate change is read a few articles and watch An Inconvenient Truth.
Therefore if the average individual wanted to create their own program for the research into climate change then there would be few obstacles in their way. However, there are a number of things that they would have to be aware of before trying to achieve this endeavour.
First and foremost the program would require some form of funding. There are a number of bodies that give out research grants to climate based research. Since this is scientific topic that has much popularity in many different sectors it is likely to gain some financial backing if you can prove it is a sound project.
The other issue to consider is who may want to shut this research down. There are some governments that do not want the truth about climate change to be publicised. This is usually because it would negatively effect their investments. Therefore the country the program is based on will be a factor on its success.
There may also be fossil fuel companies who want to actively prevent the research from being done. Therefore anyone wanting to create their own climate program will need to prepare for attacks from these entities in terms of negative publicity and possible legal action.
The most important thing to do is to make sure that the research is scientifically sound. The data will need to be peer reviewed and obtained in an honest way under industry standard conditions.