First, let me just state that the questions you have listed above are covered in about 15 credit hours of graduate school work, hundreds of peer reviewed journal articles, numerous textbooks, etc. I'll do my best to keep things simple and answer questions (and try to do so without equations). First, what is data assimilation, analysis, and initialization? These are not all the necessarily the same thing, and it's good if we can get some nomenclature sorted out to help keep the discussion clea