Floods reaching five feet above the current high tide line will become increasingly common along the nation’s coastlines well before the seas climb by five feet. Over the last century, the nearly eight-inch rise of the world’s seas has already doubled the chance of “once in a century” floods for many seaside communities.

We hope that with enough time, most of our great coastal cities and regions will be able to prepare for a five-foot increase. Some will not. Barriers that might work in Manhattan would be futile in South Florida, where water would pass underneath them by pushing through porous bedrock.

According to Dr. Schaeffer’s study, immediate and extreme pollution cuts — measures well beyond any discussion now under way — could limit sea level rise to five feet over 300 years. If we stay on our current path, the oceans could rise five feet by the first half of next century, then continue rising even faster. If instead we make moderate shifts in energy and industry — using the kinds of targets that nations have contemplated in international talks but have failed to pursue — sea level could still climb past 12 feet just after 2300. It is hard to imagine what measures might allow many of our great coastal cities to survive a 12-foot increase.

WE might find comfort in the fact that this is just one set of projections, and projections are notoriously tough to get right. But a second study that also came out this past summer erases any such comfort.

Led by the geochemist Andrea Dutton and published in the journal Science, the second paper uses deep history, not model projections, for clues to the future. About 125,000 years ago, before the last ice age, there was a warm period that lasted 10,000 to 15,000 years. It was perhaps a little warmer than today, but cooler than the temperatures that climate scientists expect later in this century without sharp pollution cuts. Dr. Dutton’s research strongly reinforces a prior study led by one of us, which found that the warm-period sea levels rose roughly 20 to 30 feet higher than those of today. We just don’t have a clear picture of how fast that could happen again.