Journal of Coastal Research 25 6 1236–1253 West Palm Beach, Florida November 2009 Historical Shoreline Change, Southeast Oahu, Hawaii; Applying Polynomial Models to Calculate Shoreline Change Rates Bradley M. Romine, Charles H. Fletcher, L. Neil Frazer, Ayesha S. Genz, Matthew M. Barbee, and Siang-Chyn Lim Department of Geology and Geophysics School of Ocean and Earth Science and Technology University of Hawaii 1680 East West Road Honolulu, HI 96822, U.S.A romine@hawaii.edu ABSTRACT ROMINE, B.M.; FLETCHER, C.H.; FRAZER, L.N.; GENZ, A.S.; BARBEE, M.M., and LIM, S.-C.; 2009. Historical shoreline change, southeast Oahu, Hawaii; applying polynomial models to calculate shoreline change rates. Journal of Coastal Research, 25(6), 1236–1253. West Palm Beach (Florida), ISSN 0749-0208. 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 inter- preting results from these new rate calculation methods. The polynomial methods use data from all transects (shore- line 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 uncer- tainty compared with the previously used single-transect method. An information criterion, a type of model optimi- zation 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. ADDITIONAL INDEX WORDS: Coastal erosion, shoreline change, erosion rate, polynomial, PX, PXT, EX, EXT, ST, single-transect, information criterion, Hawaii. INTRODUCTION Tourism is Hawaii’s leading employer and its largest source of revenue. Island beaches are a primary attraction for visitors, and some of the most valuable property in the world occurs on island shores. Beaches are also central to the culture and recreation of the local population. During recent decades many beaches on the island of Oahu, Hawaii, have narrowed or been completely lost to erosion (Fletcher et al., 1997; Hwang, 1981; Sea Engineering, 1988), threatening business, property, and the island’s unique lifestyle. Results from a Maui Shoreline Study (Fletcher et al., 2003) resulted in the first erosion rate-based coastal building set- back law in the state of Hawaii (Norcross-Nu’u and Abbott, 2005). Concerns about the condition of Oahu’s beaches prompted federal, state, and county government agencies to sponsor a similar study of shoreline change for the island of Oahu. The primary goals of the Oahu Shoreline Study are to analyze trends of historical shoreline change, identify future DOI: 10.2112/08-1070.1 received 1 May 2008; accepted in revision 27 October 2008. coastal erosion hazards, and report results to the scientific and management community. It is vital that coastal scientists produce reliable, i.e., sta- tistically significant and defensible, erosion rates and hazard predictions if results from shoreline change studies are to continue to influence public policy. To further this goal, Fra- zer et al. (2009) and Genz et al. (2009) have developed poly- nomial methods for calculating shoreline change rates. The new methods may calculate rates that are constant in time or rates that vary with time (acceleration, both increasing and decreasing). The polynomial models without rate accel- eration are generally referred to as PX models (for polyno- mials in the alongshore dimension, X) and the models with rate acceleration are PXT (polynomials in X and time). The PX methods, with a linear fit in time, best characterize the trend of the whole time series of historical shorelines and, therefore, describe the long-term change at a beach. The PXT methods may provide additional information about recent change at a beach and can show how rates may have varied with time. These methods are shown here and in the Frazer et al. and Genz et al. papers (2009) to produce statistically significant shoreline change rates more often than the com- monly used single-transect (ST) method using the same data.