How can I gather information for a quantitative research if a hypothesis that I've chosen is: "There will be a positive correlation between low pressure systems and rain occurring."
You will need to gather weather information, from the National Weather Service, perhaps, on barometric measurements and precipitation. You might want to do several different geographic areas or focus on one area in particular. Also, you will have to decide what particular time period you want to focus on, going back in the past to the archives kept, or going forward for a few weeks or months in the future. If you choose to go forward, bear in mind that the sequestration is probably going to have an effect on the service's ability to function, so perhaps going back is a better prospect. If your hypothesis is correct, it should be correct no matter where you take your sampling, and it should be correct over all periods of time.