God's Broken Promise

One of the common claims by young earth creationists is that if Noah's Flood were a local flood, then God has broken his promise many times. According to The Answers Book, chapter 10,

"If the Flood were local, God would have repeatedly broken His promise never to send such a Flood again. There have been huge 'local' floods in recent times: in Bangladesh, for example, where 80% of that country has been inundated, or Europe in 2002."(Footnote 1)

Is there any truth to this claim? Do the local floods we see today constitute a breaking of the covenant God made with Noah? First, let's read the covenant in Genesis 9:8-15.

8 Then God spoke to Noah and to his sons with him, saying,
9 "Now behold, I Myself do establish My covenant with you, and with your descendants after you;
10 and with every living creature that is with you, the birds, the cattle, and every beast of the earth with you; of all that comes out of the ark, even every beast of the earth.
11 And I establish My covenant with you; and all flesh shall never again be shut off by the water of the flood, neither shall there again be a flood to destroy the earth.