Ayesha S. Genz

The Predictive Accuracy of Shoreline Change Rate Methods and Alongshore Beach Variation on Maui, Hawaii

Abstract Beach erosion has direct consequences for Hawaiis tourist-based economy, which depends on the attraction of beautiful sandy beaches. Within the last century, however, beaches on Oahu and Maui have been narrowed or completely lost, threatening tourism and construction development. In order for the counties and state of Hawaii to implement coastal regulations to prevent infrastructure damage, it is necessary to find a statistically valid methodology that accurately delineates annual erosion hazard rates specific to Hawaii. We compare the following erosion rate methods: end point rate (EPR), average of rates (AOR), minimum description length (MDL), jackknifing (JK), ordinary least squares (OLS), reweighted least squares (RLS), weighted least squares (WLS), reweighted weighted least squares (RWLS), least absolute deviation (LAD), and weighted least absolute deviation (WLAD). To evaluate these statistical methods, this study determines the predictive accuracy of various calculated erosion rates, including the effects of a priori knowledge of storms, using (1) temporally truncated data to forecast and hindcast known shorelines and (2) synthetic beach time series that contain noise. This study also introduces binning of adjacent transects to identify segments of a beach that have erosion rates that are indistinguishable. If major uncertainties of the shoreline methodology and storm shorelines are known, WLS, RWLS, and WLAD better reflect the data; if storm shorelines are not known, RWLS and WLAD are preferred. If both uncertainties and storm shorelines are not known, RLS and LAD are preferred; if storm shorelines are known, OLS, RLS, JK, and LAD are recommended. MDL and AOR produce the most variable results. Hindcasting results show that early twentieth century topographic surveys are valuable in change rate analyses. Binning adjacent transects improves the signal-to-noise ratio by increasing the number of data points.

Historical Shoreline Change, Southeast Oahu, Hawaii; Applying Polynomial Models to Calculate Shoreline Change Rates

Abstract Here we present shoreline change rates for the beaches of southeast Oahu, Hawaii, calculated using recently developed polynomial methods to assist coastal managers in planning for erosion hazards and to provide an example for interpreting results from these new rate calculation methods. The polynomial methods use data from all transects (shoreline measurement locations) on a beach to calculate a rate at any one location along the beach. These methods utilize a polynomial to model alongshore variation in the rates. Models that are linear in time best characterize the trend of the entire time series of historical shorelines. Models that include acceleration (both increasing and decreasing) in their rates provide additional information about shoreline trends and indicate how rates vary with time. The ability to detect accelerating shoreline change is an important advance because beaches may not erode or accrete in a constant (linear) manner. Because they use all the data from a beach, polynomial models calculate rates with reduced uncertainty compared with the previously used single-transect method. An information criterion, a type of model optimization equation, identifies the best shoreline change model for a beach. Polynomial models that use eigenvectors as their basis functions are most often identified as the best shoreline change models.

Toward Parsimony in Shoreline Change Prediction (I): Basis Function Methods

Abstract Single-transect methods of shoreline change prediction are unparsimonious, i.e., they tend to overfit data by using more parameters than necessary because they assume that both signal and noise at adjacent transects are independent. Here we introduce some new methods that reduce overfitting by expressing change rate as a linear sum of basis functions. In the method of IC-binning, the basis functions are boxcars—an information criterion is used to assign contiguous alongshore locations into bins within which change rate is constant; the resulting rate is discontinuous but may be useful for beach management. In the polynomial method, the basis functions are polynomials in alongshore distance, and the change rate varies continuously along the beach. In the eigenbeaches method, the basis functions are the principal components of the matrix of shorelines. To choose the number of basis functions in each method, and to compare methods with each other, we use an information criterion. We apply these new methods to shoreline change on Maui Island, Hawaii, briefly here, and in more detail in a companion paper. The polynomial method works best for short beaches with rates that vary slowly in the alongshore direction while eigenbeaches works best for shorelines that are long, or have rates that vary rapidly in the alongshore direction. The Schwarz information criterion and the AICu version of the Akaike information criterion performed well in tests on real data and noisy synthetic data.

Toward Parsimony in Shoreline Change Prediction (II): Applying Basis Function Methods to Real and Synthetic Data

Abstract There is a need to supply coastal managers with statistically defensible hazard predictions that can be used to implement coastal setbacks and other management policies. The goal of this article is to evaluate the widely used single-transect method, as well as several new methods: t-binning, IC-binning, polynomial methods, and eigenbeaches, to identify which method(s) best predicts a 50-year eroded shoreline position. The polynomial and eigenbeach methods allow for acceleration (the rates vary with time). The methods are compared using data from nine beaches on Maui, Hawaii, and four sets of synthetic data. Evaluations of the methods are based on an information criterion, color maps of residuals, long-term (50 year) predictions, and cross-validating the most recent shoreline, which has a short-term span of 5–9 years. The newer methods identified significant rates at 74% of the transects, vs. 0% for single-transect on beaches in Maui, Hawaii. The cross-validation results showed that the polynomial and eigenbeach methods, without acceleration, best predicted the most recent shoreline. Contrary to the cross-validation results, synthetic results showed that the polynomial and eigenbeach methods with acceleration predicted the 50-year shoreline better than methods without acceleration. Nonacceleration methods predicted short-term positions better, and acceleration methods predicted long-term positions better. We conclude that the polynomial and eigenbeach methods improve the significance of the rates compared with the single-transect method.

Bringing Sea-Level Rise into Long Range Planning Considerations on Maui, Hawaii

Maui’s coastal lands, along with many others worldwide, are under tremendous pressure from expanding development and accelerating coastal erosion. While it may be perceived by the public that the lands most at risk from sea-level rise are those immediately bordering the coastline, the threat to low-lying areas from a rising water table inland of the coast may also be great. Maui planning officials have begun to recognize that regardless of the uncertainty over projected rates of sealevel rise, threats associated with rising sea level should be identified and mitigated through a combination of modeling, mapping, and direct observation. This paper provides a review of current sea-level rise science and describes the scientific and management approaches being undertaken by Maui County to better understand potential risks associated with rising seas and account for these projections in long-range planning. INTRODUCTION In 2003, Maui County became the first county in the state of Hawaii to adopt a science-based approach to determining construction setbacks on coastal properties (Norcross-Nu’u and Abbott 2005). High-resolution annual erosion rate data spaced at

Measuring Historical Shoreline Change, Applying New Polynomial Change Models: Southeast Oahu, Hawaii

Digital aerial photo mosaics and NOAA topographic survey charts (t-sheets) are used to map historical shoreline positions on southeast Oahu, Hawaii. The new PX (Polynomial in alongshore X) and PXT (Polynomial in X and Time) shoreline change rate methods are applied to calculate shoreline change rates from the time series of historical shoreline positions. These new methods utilize all historical shoreline data from a beach to calculate shoreline change rates and can find acceleration in the shoreline change rate with time. The methods are shown here and in previous works to produce more parsimonious models and more statistically significant and defensible rates than the previously used ST (Single-Transect) shoreline change rate calculation method. The ability to model acceleration in shoreline change rates with time provides insight into shoreline change processes, which was previously theoretical or observed in only small-scale studies. An overview of the methods is presented along with results from shoreline change analysis of four beach study sites on the southeast Oahu, Hawaii, shoreline.