According to me climate science is natural science and nothing more or less than that.
It is true that climate science, besides many other sciences determine policies in economy, social issues and not to forget environmental issues as well, just to name a few. But a mix of climate science with social or even political sciences is lethal for climate science. The only driver for climate science is climate, nothing else. Politicians and sociologists, must act and perform their research according to the results and findings in climate science and certainly not the reverse.
This assumes some hierarchy between sciences. According to me this hierarchy originates from the development over the last 3000 years of the different scientific disciplines in natural sciences. Man started with philosophy about 3000 to 2000 years ago. That type of philosophy was a mix of natural and human sciences. Later on, in the European Middle Ages, a first split-off occurred when physics came into being as an independent science branch of philosophy, with the discoveries in astronomy and mechanics. The next natural science one to split off the philosophy tree was chemistry, followed by biology. Biology came into being fully with Darwin's theory on Natural evolution during the European 19th century. Climate sciences are a 19th and 20th spin-off of physical science. Hence, no mix with sociology nor political science.
So that's in a nutshell my view on the hierarchy in sciences, largely determined by their evolution and origin along the time axis of human existence. Within this framework climate science is completely independent from the human and economical sciences. It is dependent only on other branches of the natural sciences like physics and statistics.
you asked an interesting question which requires a lot of debate and still will not be answered.
To begin with I believe that Science is one and is time to start correlate and compare findings from seemingly different "sciences".
If the aim of science is to investigate the results of physical phenomena on man (maybe this is the only science we can do considering the subjectivity of the observer) then climate science and social science can be interrelated.
There is a certain effect of climate and geography on dominant mentality of people.
Frank expressed a well considered concept for categorizing natural sciences. There is a logic to separating natural science research from the ultimate users. It may keep this science more objective. However, as Petros notes, there is an 'aim' to science, and if there isn't more coordination between research and application, the science is misused, and I think that should concern the scientist.
In the US today, many of our "leaders" hold science in contempt, and make 'decisions' contrary to good science, good logic, or good morals, including any kind of social consciousness. It's truly appalling. How did this happen?
I think that perhaps part of Frank's concern may be that if you link natural and social science too much, that this may be a cause of the divestiture of hard science, and the predominance of the kind of anti-scientific 'thinking' that goes on in the US Congress, and elsewhere. But I think that Petros and I hope for less of a complete collapse of scientific thinking. After all, the social sciences include the use of statistics - which if done properly will enlighten rather than obfuscate - and the anti-scientific 'movement' we see is no more good social science than it is good natural science.
So "Is climate science equal to natural science plus polical or social science?" Well, to say that theoretical climate science is its own branch of natural science is logical, but in practice, it better be well communicated to the other sciences if it is to be useful. Thus, in practice one might take the broader view.
Note that though "political science" may carry the connotation of pushing biased and unscientific points of view for 'political gain,' it should not be that way, and we do not need to be satisfied with that.
Climate science is a branch of the natural sciences or more accurately a group of disciplines ranging from astronomy through physics to zoology, a true A to Z of scientific disciplines . Understanding the changes in climate requires a huge multidisciplinary approach since no single cause can be observed and the range of effects is truly enormous.
The problem however with the political and social science involvement is that in politics vested interests and ideologies often overwhelm the 'real' science. While the effects of natural science impact hugely on social sciences here, such as in designing strategies for coping with climate change the politics is more disingenuous.
Politics and science have always been a difficult match.