Science is only applicable to physical phenomena with physical causes due to consistent natural law; "supernatural" is a term for things that don't meet that description. At most -- e.g., for physical phenomena with nonphysical causes, or causes that are not governed by consistent natural law -- a scientific approach to supernatural will simply identify gaps in the ability to construct a scientific model no different than if the governing natural law were not correctly identified out the physical causes were outside our current ability to detect.
The issue is not the interest of scientist, is the applicability and function of the method known as "science".
Global flooding isn't inherently a supernatural event, and can be investigated with science, but science cannot, by its very nature, address any supernatural cause, ask it can do is produce a natural model of causation.
Let us suppose that it is possible to "petition the Lord with prayer", to quote Morrison. For example, do prayers from strangers help someone recover from an illness?
We can test two populations, ones who receive stranger prayer, and ones who do not, and see if one population gets better treatment. We can look at the epidemiology to see if people from one religion, who practice healing prayer, have different health outcomes than those who do not. (This is tricky but not intractable because there is more than one factor at play.)
Thus we have the ability to detect if there is something outside of the current model. Detecting failures of the current model is part of science, even when it it cannot produce a better model other than "here there be dragons." What's at issue is that so far those gaps seem to get smaller and smaller the more we look into them. Hence the phrase "God of the gaps."
We of course have many examples of thing which were outside of the then-current understanding of science. The "ultraviolet catastrophe" is a classic example. The irreconcilability of general relativity and quantum mechanics is another.
But we did not call that "supernatural", even though when we knew there was a gap in our understanding.
At this point, global flooding of the sort discussed would have to be a supernatural event. There is no place for the water to come from or go to. There is no physical trace of such an event. Therefore, it would either require planetary engineering of the sort more appropriate for science fiction, or some sort of magical or divine intervention.
> Let us suppose that it is possible to "petition the Lord with prayer", to quote Morrison.
That's obviously possible.
What's subject to debate is whether that action in the material universe produces any change in outcomes in the material universe.
> We can test two populations, ones who receive stranger prayer, and ones who do not, and see if one population gets better treatment. We can look at the epidemiology to see if people from one religion, who practice healing prayer, have different health outcomes than those who do not. (This is tricky but not intractable because there is more than one factor at play.)
Sure.
> Thus we have the ability to detect if there is something outside of the current model.
Science is all about detecting things outside the current model, creating a hypothetical models which include those things, validating whether they explain observed realities better than the current model, and updating models.
OTOH, once it does so, the new model is still, by definition, a naturalistic model which excludes the supernatural. If intercessory prayer has an influence on health effects, not only can science detect it -- but by detecting it can quantify it (even if the necessary model is one of changes in the probability distribution of outcomes, not a simple direct consistent change in outcomes) and incorporate it into a naturalistic model.
> At this point, global flooding of the sort discussed would have to be a supernatural event. There is no place for the water to come from or go to.
No, it wouldn't. The lack of knowledge of the details of the mechanism or explanation for something which is nevertheless an element of the best model does not suddenly make the incompletely-explained thing supernatural; otherwise, things like the Planck constant are "supernatural".
The issue is not the interest of scientist, is the applicability and function of the method known as "science".
Global flooding isn't inherently a supernatural event, and can be investigated with science, but science cannot, by its very nature, address any supernatural cause, ask it can do is produce a natural model of causation.