More than 20 years ago, a paper was published in the journal Geology titled “Large-Scale Reversals in Shoreline Trends along the U.S. Mid-Atlantic Coast” (Fenster and Dolan, 1994). This paper purports to show a correspondence between a peak in the record of extratropical storm frequency and magnitude and historical shoreline change reversals toward erosion. Although we agree that large-scale changes in historical storm patterns could affect tempo and mode of shoreline changes, we believe that the methods used by the authors include an arithmetic error that calls into question their specific results regarding a correspondence between changes in extratropical storm patterns and historical shoreline change reversals toward erosion. We have prepared this critique because the Fenster and Dolan (1994) article is still being cited in the scientific literature (e.g., Antolínez et al., 2018; Sankar, Donohue, and Kish, 2018).

Methods used to calculate historical rates of shoreline change have been extensively studied over the past several decades. Several publications have focused on various aspects of historical shoreline change and erosion rate analysis, including accuracy of source data, optimum temporal spans of historical and recent data, appropriate statistical methods, and whether maps or imagery displaying poststorm shorelines should be included in the data sets (see Hapke et al., 2011, or Crowell, Leatherman, and Douglas, 2019, for recent summaries and citations). Statistical methods used in these studies have ranged from simple endpoint rate techniques and linear regression to newer, more complex methods that incorporate projected accelerations in sea-level rise or that use Bayesian networks to produce probabilistic forecasts of future shorelines.

In their 1994 paper, Fenster and Dolan sought to improve upon linear methods for quantifying shoreline change trends by employing a statistical modeling technique known as the minimum description length (MDL) criterion (Rissanen, 1978). The MDL method is a type of complexity–penalty model criterion that is used to determine the straight or curved line (polynomial) that best fits the data set being examined. In short, the MDL method selects the best-fit line or polynomial by determining whether the increase in complexity of the model is justified by the increase in model precision (Crowell, Douglas, and Leatherman, 1997; Fenster, Dolan, and Elder, 1993; Rissanen, 1978). Fenster and Dolan (1994) applied the MDL criterion to a set of nine shoreline reaches along the U.S. East Coast from southern New Jersey to the North Carolina–South Carolina border, and for Cape Canaveral, Florida. The temporal range of the shoreline data spans up to 60 years (i.e. 1930–90), with the data (as few as four or more shoreline positions through time) spaced along the shore at 50-m intervals. From the abstract of Fenster and Dolan (1994, p. 545), we learn the following:

In the main body of the text, Fenster and Dolan (1994, p. 545) note that based on their review of a database of extratropical storm frequency, “storm frequency had steadily increased from 1954 until it peaked during the 1960s when more larger magnitude storms occurred than at any other time during the period of record.” The authors further state the following:

In short, it is understood that the peak in storminess in the 1960s led to “a ubiquitous shoreline trend toward greater erosion” (our italics).

Unfortunately, our read of the entire paper calls into question Fenster and Dolan's assertions “that 62% of the shorelines have become more erosional or less accretional” (abstract) and, more significantly, that a peak in storminess in the 1960s led to “a ubiquitous shoreline trend toward greater erosion.” For example, in the paper, the authors note that the trend distribution of MDL-modeled shorelines is as follows:

However, the authors further note that of the 60.6% of the coast that is modeled by a quadratic polynomial, 62% of the shorelines underwent a change from “accretion to erosion, an acceleration in the rate of erosion, or a deceleration in the rate of accretion.” They also state, “Conversely, 38% of the coast [modeled by the quadratic polynomial] has undergone a change from erosion to accretion, an acceleration in the rate of accretion, or a deceleration in the rate of erosion.” Consequently, the preceding distribution can be rewritten as follows:

Alternatively, in terms of the percentage of the coast experiencing trend reversals (ignoring the cubic trend reversals), the distribution can be rewritten as follows:

In other words, only 37.6% of the coast as modeled by MDL (not 62%, as stated in the abstract) suggest trend reversals toward greater erosion. Clearly this is not evidence of a “ubiquitous shoreline reversal toward greater erosion.”

Notwithstanding the arithmetic error, Fenster and Dolan (1994) provide results that indicate 60.6% of the shorelines show a reversal in long-term change trend, which peaked in 1967 (average), toward either greater erosion or greater accretion. Is this evidence of a correspondence between a peak in extratropical storm frequency that occurred in the 1960s and any type of shoreline change reversal (i.e. “system state change”)?We direct the reader to Crowell, Douglas, and Leatherman (1997), who tested the utility of the MDL model for shoreline positional forecasting using systematically depleted tide gauge data to mimic the temporally sparse and random historical shoreline data sets that are typically available.

A principal conclusion in our paper (Crowell, Douglas, and Leatherman, 1997) was that in most cases, linear regression gave better forecasting results than the MDL approach. In addition, and more relevant to this letter, we noted that the choice of the estimate of noise variance (sigma prior) used in the MDL criterion has a profound impact on the determination of the best-fit model. Of 24 tide gauge stations that were analyzed, theMDL criterion produced 20 quadratic fits and 4 linear fits when a sigma prior of 5 was used. A sigma prior of 10 resulted in 13 quadratic fits and 10 linear fits (plus one cubic fit). A sigma prior of 16 resulted in just 8 quadratic fits plus 15 linear fits (and one cubic fit). Crowell, Douglas, and Leatherman (1997) also tested sigma priors of 19 and 50, which resulted in 6 and 0 quadratic fits, respectively. In summary, large values of sigma prior will favor constant or linear models, whereas small values of sigma prior will favor quadratic and cubic models.

Crowell, Douglas, and Leatherman (1997) concluded in their analyses that when using sigma priors of 5.0 and 10.0, the MDL criterion produced inferior results because the low estimate of measurement noise tended to find inflections that did not appear to be real in the depleted tide gauge data sets (sampled to mimic available historical shoreline change data sets). Fenster and Dolan (1994) used sigma priors of 7.0 and 8.5 (and as few as four shoreline position positions per section), which may have also identified questionable inflections. Furthermore, if they had used higher values of sigma priors, they undoubtedly would have produced results showing a higher percentage of linear and/or stable fits. Accordingly, we believe that the MDL criterion as used by Fenster and Dolan (1994) fails to convincingly show that powerful storms that peaked in the 1960s produced a system change over a large part of the U.S. mid-Atlantic coast.

NOTES

The views expressed in this letter to the editor are those solely of the authors and do not necessarily represent those of the Federal Emergency Management Agency.