Was the flood of Noah global or local?

You make the assumption that there was a flood at all.

But maybe the flood is just a metaphor, a story. Which would lead to a different question: What does the story mean? It could be meant either way, without a real flood.

Since the ancient Jews didn't know the whole earth, how could they know whether the whole world was covered with water to begin with? Nobody knew Mt. Everest then, nobody in that region knew Japan, China, North or South America.

Without modern information technology, and without witnesses to ask later, it is impossible to know what was covered with water. But witnesses would be a contradiction to the idea that the whole earth population was killed.

I'm going to offer a different perspective:

The third century apologist Origen of Alexandria argued that certain Bible stories included "stumbling blocks" that made them impossible to take literally, in order to guide us to seek the spiritual meaning:

[D]ivine wisdom took care that certain stumbling-blocks, or interruptions, to the historical meaning should take place, by the intro­duction into the midst (of the narrative) of certain impossibilities and incongruities; that in this way the very interruption of the narrative might, as by the interposition of a bolt, present an obstacle to the reader, whereby he might refuse to acknowledge the way which conducts to the ordinary meaning; and being thus excluded and debarred from it, we might be recalled to the beginning of another way, in order that, by entering upon a narrow path, and passing to a loftier and more sublime road, he might lay open the immense breadth of divine wisdom. —Origen, De Principiis, Book IV

Under this approach, the Noah story has many such stumbling blocks. Besides questions of where the water went, there are matters of:

• how hard it would have to rain to produce that much water in 40 days (more than a foot per hour)
• how animals from the other continents could have gotten to the ark
• where could Noah have gotten enough grain to feed them all
• how an olive tree could have survived under flood waters for half a year so the dove could find a leaf

So with that in mind, I'd say that the text clearly defines it as a global flood, to lead us to a deeper meaning.

There are two views on this topic, the local and global. Those that support local flood theory have the following thesis:

Since the geographical perspective of ancient people was more limited than that of contemporary readers, it is possible that the flood, while universal from their viewpoint, did not cover the entire globe¹.

They base this view on verse Genesis 41:57 which says:

And all the world came to Egypt to buy grain from Joseph, because the famine was severe everywhere.

Of course "all the world" clearly refers to the eastern Mediterranean seaboard. So comparing this verse with Genesis 8:9 make some people to believe in a local flood.

In the other hand the verse you mentioned says: "The waters rose and covered the mountains to a depth of more than fifteen cubits." Of course this creates a problem with the above theory. If “the mountains of Ararat” (Genesis 8:4) refers to the range that includes present-day Mount Ararat in Turkey (elevation 16,854 feet or 5,137 m), the amount of water necessary to cover it would be at least 16,854 feet above sea level.

A try to fit the literal explanation with logic is made by "Insight on the Scriptures", there we read:

It is believed that there was a time when the oceans were smaller and the continents were larger than they are now, as is evidenced by river channels extending far out under the oceans. It should also be noted that scientists have stated that mountains in the past were much lower than at present, and some mountains have even been pushed up from under the seas. As to the present situation, it is said that “there is ten times as much water by volume in the ocean as there is land above sea level. Dump all this land evenly into the sea, and water would cover the entire earth, one and one-half miles deep.” (National Geographic, January 1945, p. 105) So, after the floodwaters fell, but before the raising of mountains and the lowering of seabeds and before the buildup of polar ice caps, there was more than enough water to cover “all the tall mountains,” as the inspired record says².

In any case we can trust the biblical account for Noah and flood because Jesus, Luke, Ezra, Isaiah, Ezekiel, Paul & Peter mentioned this event or Noah as real person.

¹Crossway Bibles: The ESV Study Bible. Wheaton, IL : Crossway Bibles, 2008, S. 62

² Insight on the Scriputes, Vol.1 p. 610 Deluge

It's a global flood. There are several logical points why.

First, the gathering of all of the animals in the world would be useless, if the Flood was only a local flood. If the Flood was only local, not all of the animals would drown, and thus, bringing all the animals of the World on the ark would have been a useless act.

Secondly, if the Flood was only local, would all the people die? Obviously not. There'd be other people in the world that wouldn't have died besides Noah.

Thirdly, if the Flood was only local, why did Noah have to spend 100 years to build a massive ark, when all he had to do, was merely pack his bags and walk to some other place on Earth? Consequently, why build a massive 400 ft. Ark, if it's only a local flood?

Lastly if the Flood was local then did God break his promise not to Flood the world again? Hasn’t the Mesopotamian Valley been flooded many times since Noah?

Now, the major problem that you posed, was that , where did all the water go?

Edit:, Due to Caleb's statement, I looked it up, and found this:

Even if the glaciers and ice caps melted, the oceans would only rise some 70 m (230 ft), yet Mt Everest rises 8,848m (29,029 ft) above sea level.

It may surprise you to learn that we don’t need any more water to cover the earth. There is already enough.

The reason water doesn’t envelop the globe now is that the earth’s surface is uneven. The ocean basins sit low and the continents sit high. Some mountains are especially high and some ocean trenches are very deep, but these extremes do not account for a large percentage of the earth’s surface (see graph).

If the earth’s surface were even, then there is enough water in the oceans to cover the globe to a depth of about 3 km.

This suggests that, during the Flood, the ocean floor moved vertically relative to the continents, something mentioned in the Bible (Psalm 104:8 NASB).

In the first half, the pre-Flood ocean basins rose and the pre-Flood continents eroded down until water covered everything.

That does not mean the earth’s surface would have to be completely even. The ocean basins would have only had to rise enough for the water to cover everything.

Then, in the second half of the Flood, other parts of the earth’s crust sank. The water flowed off our continents into new ocean basins. Movement of the earth’s crust at this time also pushed up new mountain ranges, including the one that is home to Mt Everest.1

So where did all the water go? It is in the ocean.

Just for the reader, Psalm 104 : 6-8 states:

Thou coveredst it with the deep as [with] a garment: the waters stood above the mountains.

7 At thy rebuke they fled; at the voice of thy thunder they hasted away.

8 They go up by the mountains; they go down by the valleys unto the place which thou hast founded for them.