Any force or power above nature as we know it, or something of a phenomenon known to exist but defies physical explanation is how i define supernatural.
Also if its natural then it must be in accordance with nature.
Great!
You've made it more interesting.
Phenomenon
A phenomenon is any thing which manifests itself. Phenomena are often, but not always, understood as "things that appear" or "experiences" for a sentient being, or in principle may be so.
The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon.
In contrast to a phenomenon, a noumenon cannot be directly observed. Kant was heavily influenced by Gottfried Wilhelm Leibniz in this part of his philosophy, in which phenomenon and noumenon serve as interrelated technical terms. Far predating this, the ancient Greek Pyrrhonist philosopher Sextus Empiricus also used phenomenon and noumenon as interrelated technical terms.
Scientific
In scientific usage, a phenomenon is any event that is observable, however common it might be, even if it requires the use of instrumentation to observe, record, or compile data concerning it. For example, in physics, a phenomenon may be described by a system of information related to matter, energy, or spacetime, such as Isaac Newton's observations of the moon's orbit and of gravity, or Galileo Galilei's observations of the motion of a pendulum.
Another example of scientific phenomena can be found in the experience of phantom limb sensations. This occurrence, the sensation of feeling in amputated limbs, is reported by over 70% of amputees. Although the limb is no longer present, they report still experiencing sensations. This is an extraordinary event that defies typical logic and has been a source of much curiosity within the medical and physiological fields.
So Dark Matter, and Dark Energy are noumenons, not phenomenons.
What I find interesting in this is that a phenomenon can be personal - that is - experienced personally even if not observed, or manifest to others - like seeing "ghost" or having an apparent physical experience with an unseen force, for example. Hence, it is possible it can be supernatural... or not - but possible.
How would it be determined, if there is no way to test it.
Another example...
Say people, actually thousands of people, witness the ocean part - split in two. No one has an explanation - it totally baffles scientists. It's a phenomenon, but it defies physical explanation, as
@osgart puts it. What do we call call the event? Can we call it a natural event because we observed it? Furthermore, if we cannot explain it, we likely can't explain the force behind it.
What is it?
Currently, the "fuel" that is speculated to have started the "Big Bang" has never been observed, nor manifest. What do we call this?
Do we put it in the category which many put the multiverse?
"
Extreme multiverse explanations are therefore reminiscent of theological discussions. Indeed, invoking an infinity of unseen universes to explain the unusual features of the one we do see is just as ad hoc as invoking an unseen Creator."
— Paul Davies, The New York Times, "A Brief History of the Multiverse"