The "beauty" of a conspiracy theory is that no matter what evidence is presented, there is a "talk around" for the believer. No matter what answer is given, they will have a more conspiratorial rebuttal for that. To suggest that HAARP is anything beyond "an ionospheric research program jointly funded by the US Air Force, the US Navy, the University of Alaska and the Defense Advanced Research Projects Agency (DARPA). Its purpose is to analyze the ionosphere and investigate the potential for developing ionospheric enhancement technology for radio communications and surveillance purposes (such as missile detection)." without anything to go on is a great hallmark of "making stuff up."
AS REQUESTED: Info about HAARP and what they do.
What is HAARP?
HAARP stands for The High Frequency Active Auroral Research Program. The goal of this program is to further advance our knowledge of the physical and electrical properties of the Earth's ionosphere which can affect our military and civilian communication and navigation systems. The HAARP program operates a world-class ionospheric research facility located in Gakona, Alaska.
Is HAARP a classified project?
HAARP is not classified. There are no classified documents pertaining to HAARP. The Environmental Impact Process (EIP) documents have always been, are now, and will always be completely descriptive of the program in its entirety. The EIP documents are a matter of public record.
What kind of research will be conducted at the HAARP facility?
The research to be conducted at HAARP falls into two broad categories:
The study of basic natural processes that occur in the ionosphere under the natural but much stronger influence of solar interaction. This includes studying how the natural ionosphere affects radio signals with the goal of developing techniques that may be available for mitigating these effects to improve the reliability and/or the performance of communication and navigation systems.
Development of technology to use effects produced through ionospheric interactions. One example of this is learning how to generate new signals in the ELF range for the real application of subsurface communications.
BACK TO CONSPIRACY THEORIES: As we understand weather and earthquakes, there is no known mechanism by which HAARP can accomplish either conspiracy goal. Since HAARP uses EM, it does not fall into any known application for having an actual effect on weather (Wiki). As for using any sort of EM to control earthquakes, most of this stems from theoretical work that there may be some precursors to earthquakes. (Wiki) Although, if this was reliable, I am quite certian Japan would also have this level of technology, and would have actually used it to warn their population prior to the 11 MAR 11 earthquake.
Does that mean that the research these agencies do can't go beyond analyzing the ionosphere for those particular applications? No. They may indeed find some interesting applications that they weren't aware of before starting the study. Is there anything nefarious going on? Well, wanting to detect missiles, and perhaps enabling covert communications could be considered "nefarious" by some, but not beyond the scope of what agencies such as the USAF, USN, and DARPA do all the time.
So if the government claims HAARP is ionospheric research, and a conspiracy theorists claims it's meant to control the Yellowstone Caldera, what answer should any reasonable person give? A simple "no" will of course be met with "the government is lying" response, and no matter what is shown to the believer, they will claim that there is something hidden. In these cases, it is standard policy to ignore these fringe elements because engaging them is ultimately more destructive than just ignoring them.