Mathematical rule said to be widely and wrongly used to forecast future beach erosion

A decades-old mathematical model is being inappropriately used in at least 26 nations to make potentially costly predictions about how shorelines will retreat in response to rising sea levels, two coastal scientists contended in the Friday, March 19, 2004, issue of the research journal Science.

“Models can be a hazard to society, and this is certainly an example of such,” wrote Orrin Pilkey of Duke University’s Nicholas School of the Environment and Earth Sciences, and J. Andrew Cooper of the Coastal Research Group at the University of Ulster in Northern Ireland, in a Perspectives commentary.

The mathematical equation, called the Bruun rule, “is a ’one model fits all’ approach unsuitable in a highly complex natural environment with large spatial variations in shoreline retreat,” the two authors added. “Even under ideal conditions … the rule has never been credibly shown to provide accurate predictions.”

Pilkey, a retired geology professor who still directs Duke’s Program for the Study of Developed Shorelines, said in an interview that the rule was developed in the 1960s by Per Bruun, a Danish civil engineer who was long active in Florida beach preservation projects.

According to Pilkey, the Bruun rule stipulates that it is the slope of the “shoreface” — the broad front of a beach extending down into the water to a depth of about 10 yards — that controls how and how quickly a beach “erodes,” meaning how it retreats landward as sea level rises.

“There is no relationship between the shoreface slope and the rate of erosion,” he said. “We know that each shoreline is different, and one model cannot possibly explain every shoreface. It’s ludicrous. And yet it’s being defended by a number of people.”

Their commentary also said the Bruun rule is intended “to be deployed only under a limited range of environmental circumstances (such as uniform sandy shorefaces with no rock or mud outcrops). Unfortunately, these constraints on its use are widely ignored, and it has been applied to such diverse coastal types as mud flats, rocky coasts and coral atolls.

“Even under ideal conditions, however, the rule has never been credibly shown to provide accurate predictions,” the commentary added.

Two ways of predicting the retreat of shorelines are actually in “widespread practice,” the authors noted. One way is the Bruun rule. The other method is to use a beach’s past behavior to “extrapolate” its future erosion trends. They asserted that extrapolation also “has problems” in that past data is incomplete, and different parts of a single beachfront may erode at different rates.

“We advocate recognition and acceptance that we cannot actually predict shoreline retreat related to sea level rise,” Pilkey said, quoting from their commentary. “It’s too complex.

“What startles me is why people think they can take a mathematical equation that requires only a navigation chart and actually predict what sea level rise will do. The answer is because everybody thinks that if it’s done mathematically it’s sophisticated and state-of-the-art.

“One of the big lessons here is that sometimes intuition based on experience on a given shoreline is a lot better than a mathematical model.”

Cooper consulted available information with the aid of an Internet computer search service to come up with the estimate that the Bruun rule is in use in 26 countries, Pilkey said.

Their commentary noted that much of the developed world has experienced “a four-decade rush to the shore, with concomitant beachfront development and exponentially increasing total values for beachfront, real estate, infrastructure and buildings.”

This development has “unfortunately coincided with the century of accelerated global sea level rise,” it added. That coincidence “means that the prediction of the future rate of shoreline retreat has become a major societal priority.”