|MadSci Network: Physics|
According to my handy dandy copy of The Effects of Nuclear Weapons, the answer is messy. So, I'll go over the example in the book to give you an idea what would happen. First off, we assume a ground shot similar to the Trinity test with a yield around 20 kilotons. We will also assume that they are not completely insane and do this when it is dry to minimize rain out on their own soil. Given what the prevailing winds are in that region, we will also assume that the shot is done near the east coast of the Korean peninsula. With a 15mph wind, the primary fall out will be in an area ~16 miles wide and ~150 miles long. At this contour, the dose rate is about 1 R/hr shortly after the shot. The debris that makes it to the upper atmosphere will spread over many hours/days for quite some distance. The problem here is that there are so many variables with the weather that exact maps of radioactive fallout hot spots are something that must be done after the fact. However, to answer your question, Japan is going to be really angry given that the heart of their agricultural land is more or less directly in the path of prevailing winds and will receive non-trivial fallout contamination. We aren't talking about massive amounts of cancer or severe long-term effects, but I seriously doubt anyone would be willing to eat the food for a while. We will certainly be able to detect radioactive debris (in incredibly tiny quantities) across all of the US. By the time it gets here, however, it won't be enough to cause a measurable health effect. After some time, the stuff that rises on the center of the plume will spread across the entire northern hemisphere and take years to completely drain out. There is surprisingly little exchange between the northern and southern hemispheres, so below the equator you won't really see anything detectable. Hope for a below ground test. Scott Kniffin Radiaiton Effects and Analysis Group NASA Goddard Space Flight Center
Try the links in the MadSci Library for more information on Physics.