Geographers need to determine where floodwaters will begin to congregate across the land (as in, not in existing stream beds but leading up to them), and if those places are where the soil isn’t covered up with tarmac, concrete, or structures, you can bring in tractors with PTO augers to bore holes up to a metre deep. Clear away the accumulated dirt on one side of the hole - where the water is flowing across ground from, usually uphill - and you can have many “drainage sinks” in an area which can hold the water and let it seep better into the soil instead of running off and back into the oceans. Once things calm down and these holes dry out, push the soil back in.
Long-term, the same can be done with concrete dry wells with grates on top of them.
IIRC California is also considering this as a method for catching those massive rain events in order to hold the water long enough for it to have some sort of a chance of re-charging their underground aquifers. Now these will be dry wells the size of skyscrapers, not the size of barrels, but the principle is the same: give rainwater a fighting chance to be absorbed by the ground instead of just running off into the ocean.