Some Christians believe Noah's flood was a local event rather than a global flood.
What physical or geological evidence has been given by such Christians to support their position?
There are two variants of the "local flood" view. One variant is that Genesis 6-9 refers to an actual flood that was large-scale but not global, and the other is that the Noah story is fiction, but derived from the memory of a large flood in the past.
Both variants point first to evidence found in the geological column. In particular:
1) All of the early contributors to geology were Christians who believed in a global flood before they began studying rock columns. Buffon, Hutton, Lyell, Agassiz, and Kelvin all became convinced after seeing the rock layers that a single global flood could not have produced them.
2) Some formations, such as the Grand Canyon, include layers of desert sandstone in between layers of marine sediments. Yet YECs claim the entire formation was laid down in one global flood. Grey Neyman of Old Earth Ministries explains the problem:
3) Other areas, such as the Gulf of Mexico, have thick layers of salt. Salt deposits are created when water evaporates. Gregg Davidson and Ken Wolgemuth, writing for BioLogos, explain why this is a problem for flood geology:
4) Among the deposits are layers of igneous rock, formed by volcanic eruptions. When volcanoes erupt, they release greenhouse gases. The number of eruptions necessary to produce all the igneous layers found in the geological column, if they all happened within the same year, would produce enough CO2 to kill Noah and his family. Glenn Morton, writing for Old Earth Ministries, has the details:
5) Industrial geologists looking for oil deposits use temperature differences in boreholes to determine the age of the sediment they're drilling through. It's kind of complicated, but Willy Fjeldskaar, writing for Age of Rocks, explains:
As the heat radiates up from the earth's core, the rocks in lower layers retain a certain percentage. The longer the rocks have been buried, the more heat they will have accumulated. In the short time span proposed by YECs, there's simply not enough time for the sediments to have reached the temperatures geologists find in the boreholes:
6) The total amount of water on and in the earth is not nearly enough to produce a global flood. Hugh Ross of Reasons to Believe explains the problem:
That's a sample of the evidence against a global flood. Some Christians take the idea of a local flood further, attempting to find evidence of a large local flood in the geological record.
Greg Neyman of Old Earth Ministries lays out the parameters:
Neyman calculates that Noah, standing on the deck of the ark, would have been able to see a mountain 95 miles away. That gives us a ballpark estimate of how much area the flood would have to include to cover the highest mountains.
There is some evidence of massive flooding in the Middle East in the distant past. One conjecture which has received a lot of attention recently is the Black Sea deluge hypothesis. Geologists have found some evidence of a massive flood following an inrush of water from the Mediterranean about 7600 years ago, causing the Black Sea to overflow.
There's some evidence that glacial melting caused the Caspian Sea to flood the surrounding area somewhere between 9000 and 17,000 years ago.
Hugh Ross favors the Black Sea hypothesis, while Neyman favors the Caspian. Critics (including YECs) point out that there is no clear evidence that either flood could have produced enough water to cover the mountains and wipe out all of human civilization.
The lack of archaeological evidence for a global flood.
Here's an interesting article I came across which discusses several ancient myths and likely corresponding floods including the Black Sea event: http://discovermagazine.com/2012/jul-aug/06-biblical-type-floods-real-absolutely-enormous
The Black Sea deluge hypothesis suggests the Black Sea may have suddenly and violently flooded due to it being below sea level at one point, thus possibly providing material for the story of Atrahasis, Gilgamesh, and the latter story of Noah.
Naturally if you lived in a little hut on the shores of the Black sea when this may have happened it would not be completely irrational for you believe the whole world has flooded.
Archaeologists argue over whether it happened or not.