Coastal Erosion Hazard
This section describes the method and results for the historical shoreline change at Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP.
Shoreline change evaluations are based on comparing historical shorelines derived from processed vertical aerial photography. Historical shorelines generally represent the period of the last 70 years. Long-term rates of change are calculated using most shorelines (1940's to most recent shoreline) using the standard single-transect (ST) method as well as an alternative method incorporating principal component analysis (EX). Short-term rates of change are calculated using most shorelines (1940's to most recent shoreline) using an advanced form of EX called EXT. The historical rates of change presented in this report represent past conditions and therefore are not intended for predicting future shoreline positions or rates of change.
Compilation of historical shorelines
Coastal scientists in universities and government agencies have been quantifying rates of shoreline movement and studying coastal change for decades. The most commonly used sources of historical shoreline data have traditionally been NOAA Topographic Sheets (T-sheets, see Shalowitz, 1964) and vertical aerial photographs. Ideally, extraction of past shoreline positions from these data sources involves geo-referencing and removing distortions from maps and aerial photographs, followed by digitizing the shoreline position. Depending on coastal location, data source, and investigator, different proxies for shoreline position are used to represent the position of the shoreline at the time the map or photo was produced. Time series of shoreline positions document coastal change and are interpreted to improve our understanding of shoreline stability. Common shoreline proxies include the high water line (for discussion of the high water line (HWL) see Shalowitz, 1964), a wet-dry line, the first line of vegetation, the toe or crest of the abutting dune, a low water line such as the toe of the beach, a cliff base or top, and a tidal datum or elevation – typically the location where the plane of mean high water (MHW) intersects the beach face.
Delineation of aerial photo based shoreline
In Hawai‘i, the high reflectivity of Hawaiian white carbonate beaches reduces the visibility of the HWL on contact prints of historical aerial photography (Fletcher et al. 2003). Norcross et al. (2002) and Eversole (2002) found that the low water mark (LWM), or toe of the beach, played a significant role as a pivot point for along-shore transportation processes at their study sites of Kailua, Oahu and Kaanapali, Maui respectively. High water clarity and the absence of significant flotsam in Hawaiian waters allow the delineation of the LWM on historical 0.5 m orthorectified aerial photomosaics as a color (Black and White or Color) tone change at the base of the foreshore, most easily identified during a wave runup on the beach.
Uncertainties and errors
Several sources of error impact the accuracy of historical shoreline positions and final shoreline change rates. We define two types of uncertainty: positional uncertainty and measurement uncertainty. We quantify 7 different sources of error in identifying shoreline positions on aerial photographs and T-sheets (3 positional and 4 measurement errors). The 7 different sources of errors are summed in quadrature (the square root of the sum of the squares) to get a total positional uncertainty . Table 8 contains values of each error for Kaloko-Honokōhau NHP and Pu‘ukoholā Heiau NHS.
Positional uncertainty is related to all features and phenomena that reduce the precision and accuracy of defining a representative shoreline position in a given year. These uncertainties mostly center on the nature of the shoreline position at the time an aerial photo is collected. Influences on position include the stage of tide, the incidence of storms, and the seasonal state of the beach.
Seasonal error is quantified by using summer and winter beach profiles (or shoreline positions from aerial photographs). Many beaches have seasonal cycles where they accrete in summer and erode in winter (or vice versa). Because the availability of high resolution aerial photographs is limited for the two national parks, the selection of aerial photographs cannot be based on seasonal time frames. To account for the shifts in shoreline position due to seasons, the seasonal error is the standard deviation of a randomly generated uniform distribution with minimum and maximum values equal to the mean plus two times the standard deviation of the difference in the seasonal shoreline positions.
Tidal fluctuation error is only calculated for aerial photographs. The aerial photographs were obtained without regard to tidal cycles, which can result in inaccuracies on the digitized shoreline. The horizontal movement of the LWM during a spring tidal cycle was estimated based on the morphology of the different beaches within each study area. Because the tides are cyclical fluctuating between low and high, there is an equal chance of taking a photograph of the shoreline at different stages of the tides. Therefore, the tidal error is the standard deviation of a randomly generated uniform distribution with minimum and maximum values equal to two times the horizontal movement of the LWM.
Digitizing error is the error associated with digitizing the shoreline. Only one analyst digitizes the shorelines for all photographs and T-sheets to minimize different interpretations from multiple users. The error is the standard deviation of the differences between repeat digitization measurements. The error is calculated for photos/T-sheets at different resolutions.
Pixel error is the pixel size of the image. The pixel size in orthorectified images is 0.5 m, which means anything less than 0.5 m cannot be resolved.
Rectification error is calculated from the orthorectification process. Aerial photographs are corrected, or rectified, to reduce displacements caused by lens distortions, earth curvature, refraction, cameral tilt, and terrain relief using remote sensing software. The Root Mean Square (RMS) values calculated by the software are measures of the misfit between points on a photo and established ground control points (GCP). The rectification error is the RMS value.
T-sheet plotting error is only calculated for T-sheets. The error is based on Shalowitz (1964) thorough analysis of topographic surveys. There are three major errors involved in the accuracy of T-sheet surveys: (1) measuring distances has an accuracy of 1 m, (2) planetable position has an accuracy of 3 m, and (3) delineation of the actual high water line has an accuracy of 4 m. The three errors are summed in quadrature to get the plotting error.
These errors are random and uncorrelated and may be represented by a single measure calculated by summing in quadrature (the square root of the sum of the squares). The total positional uncertainty is:
For aerial photographs,andare omitted. For T-sheets, and are omitted.
These uncertainty values can be propagated into the shoreline change result using the analysis methods discussed below. The resulting uncertainty of the rate will incorporate the uncertainty of each shoreline and the uncertainty of the model.
Table 8 . Range of errors for Kaloko-Honokōhau NHP and Pu‘ukoholā Heiau NHS.
Magnitude Ranges (m) |
||
Source |
KAHO |
PUHE |
Es, Seasonal Error |
± 2.9 |
± 1.7 |
Etd, Tidal Error |
± 5 |
± 5 |
Ec, T-sheet Conversion Error |
N/A |
N/A |
Ed, Digitizing Error |
± 0.8 – 1.7 |
± 0.8 |
Ep, Pixel Error |
± 0.5 |
± 0.5 |
Er, Rectification Error |
± 0.9 – 5 |
± 0.4 – 2.6 |
Ets, T-sheet Plotting Error |
N/A |
N/A |
Analysis methods
Single-Transect (ST) method
For the single-transect method (ST) a rate is calculated at each transect spaced every 20 m alongshore. A rate is calculated at each transect location regardless of the effects of shoreline positions at adjacent transects. Several different statistical methods can be used to calculate the rate at each transect (e.g., End-Point Rate (EPR), Ordinary Least Squares (OLS), and Weighted Least Squares (WLS)). The change-rate approach used for the ST analysis of Kaloko-Honokōhau NHP and Pu‘ukoholā Heiau NHS is WLS.
One assumption of ST is that shoreline behavior at one transect is independent of shoreline behavior at an adjacent transect. However, rarely does a single transect behave independently from neighboring transects, as sediment transport usually affects shorelines in the cross-shore and alongshore directions. One way to determine whether transects along a beach are independent or not is to determine the spatial correlation distance. If the correlation distance is greater than the transect spacing, then the assumption for ST fails and ST is over-fitting the data (Frazer et al. in press).
Rate uncertainty is high with ST since the rate is calculated using between four and ten shoreline positions at one transect. With less information (about adjacent shoreline position), the uncertainty will be greater. Hence many rates with ST will not be significant.
Eigenbeaches (EX and EXT): Alternatives to ST method
Eigenbeaches is an alternative method that incorporates all data within a beach system to calculate a rate at each transect. For a comprehensive description of Eigenbeaches, see Frazer et al. (in press). Eigenbeaches uses a linear sum of basis functions on a finite scale to determine shoreline change. Basis functions are building blocks that are used in a function. For Eigenbeaches, the principal components of the shoreline data (or eigenvectors) are the basis functions, and are used to model the rate in the alongshore direction (spatially along the transects).
This method reduces the number of parameters needed to describe shoreline change on a beach. If there are 30 transects on a beach, ST calculates a rate at each transect, making the number of rate terms equal to 30 to describe shoreline change. The number of parameters in Eigenbeaches is limited to the number of shorelines present at a specific beach. If there are 30 transects, but 10 shorelines, the maximum number of basis functions that describes the rate term is equal to 10. The reduction in terms and the increase in data points in Eigenbeaches reduce the uncertainty values of the shoreline change rate (Frazer et al. in press).
There are two types of Eigenbeaches: (1) EX – rates are modeled in the alongshore direction (X) using basis functions, but the rates are constant through time (Figure 38); (2) EXT – rates are modeled in the alongshore direction (X) using basis functions, and the rates change with time (T) using a quadratic fit (i.e., acceleration) (Figure 39). Both EX and EXT use the same basis functions. Because the basis functions are the principal components of the shoreline data, using the same data set to calculate the rates and their uncertainties is inappropriate, hence shoreline data is divided into two data sets. The first data set is used to generate the basis functions, which are then used to model the second data set. We use an information criterion (IC) to determine the number of basis functions needed to model the data. An IC is a test statistic that determines the best model from a group of models that are not necessarily nested (Sugiura 1978, Hurvich and Tsai 1989).
Figure 38 . EX fit at each transect. The rates are modeled spatially along the transect location, but are constant through time.
Figure 39 . EXT fit at each transect. The rates are modeled spatially along the transect location, and are modeled with a quadratic fit though time.
Before running EX or EXT, we use ST to determine the spatial correlation distance. Transects are usually closely spaced and shoreline measurements from these transects can be correlated in the alongshore direction. To calculate the correlation distance, ST is first run to determine the data residuals. A decaying exponential function is fit to the autocorrelation of the data residuals . The best-fit exponential decay is the correlated data error with equation: , where and are transect locations, and is the estimated correlation distance. In computing ST, we use WLS to calculate the rate at each transect. WLS takes into account the uncertainty at each time position (covariance matrix) and propagates it into the model. The resulting rate and rate-uncertainty incorporate the uncertainty of the model and the uncertainty in the time positions. For EX and EXT, we combine the correlated data errors with the uncertainty in the time position in the covariance matrix. Because this matrix is more complicated, we use Generalized Least Squares (GLS) to calculate the rate terms (WLS is a simplified form of GLS).
Eigenbeaches has similar limitations to ST despite improvements in calculating uncertainty and not assuming transects are independent. Both methods are susceptible to outliers, whether the outlier is statistical or based on a priori knowledge (i.e., storms). Both methods use least squares, which assumes Gaussian errors. Robust methods such as Least Absolute Deviation (LAD) and Least Median of Squares (LMS) can be applied to both methods to overcome limitations. LMS finds statistical outliers and removes them from the data. LAD does not discard data, rather it puts less emphasis than least squares on outlier points.
Reporting ST, EX and EXT results
ST and EX results are used for long-term predictions because it is more reliable than EXT (Genz et al. in press; Romine et al., accepted). Genz et al. (in press) found that EX did better than EXT in cross-validating the most recent shoreline. Romine et al. (accepted) found that EXT rates were strongly influenced by more recent shoreline data and was a better indicator of change that was occurring at a more recent, short-term time scale. Therefore, we use EX for long-term predictions and EXT for short-term changes. Rates reported with EXT are the rates at the most recent time position.
Similar to ST, EX and EXT do not smooth rates in the alongshore direction. EX and EXT use eigenvectors of the shoreline data to model rates in the alongshore direction. Any discontinuities present in the alongshore direction will be embedded in the eigenvectors. Hence, the resulting EX and EXT rates are not smoothed. If other basis functions were used (e.g., Legendre polynomials or trigonometric functions), the rates would be smoothed in the alongshore direction. A disadvantage of smoothing within the analysis is that if there is a discontinuity (e.g., hardened shoreline affects one segment of the beach causing a significant rate shift), the basis function methods that smooth would be susceptible to ringing and the resulting rates would not reflect the alongshore variation. However, many coastal managers prefer smoothed rates in the alongshore direction for policy purposes.
A smoothing technique can be applied to ST, EX and EXT rates after the analyses are complete. The rates are smoothed using a center-weighted five-point moving average (Rooney et al. 2003). The weighting scheme is 1, 3, 5, 3, 1 for each set of transects. We present the ST and smoothed EX rates in the results representing long term historic trends in shoreline position while EXT is presented to indicate recent shoreline trends.
Rectification of vertical aerial photography
Historical and modern aerial photographic coverage of Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP areas was achieved using two methods (Table 9). Historical imagery of Kaloko-Honokōhau NHP was received via DVD from the National Park Service (NPS). The received imagery was georeferenced but lacked camera calibration and geometric information for each scene. Data were visually inspected using modern (2006) satellite imagery and the 2002 imagery from NPS. Inspection focused on the comparison of hard shoreline and geologic features such as headlands and reef along the coast. Significant offset (excess of 5 m) was found for several images. Those images were ‘refined' using ESRI ArcMap georeferencing tool to locate ground control points on the stable features visible in both the historical images and modern satellite imagery. The images were processed using a 3rd Order Polynomial solution and checked for shoreline feature matching. Final images are included in Appendix C.
Vertical aerial imagery of Pu‘ukoholā Heiau NHS was acquired from local vendors and received as digital image scans on DVD. Following the orthorectification methods used by Fletcher et al. (2003) in their shoreline mapping on Maui, integrated coastal digital elevation models and a modern (2006) satellite image were used in the processing. Resulting map-correct images and mosaics were inspected using the satellite reference image and comparing the locations of stable features visible in both the reference and processed images. Final images are included in Appendix C.
Table 9 . Imagery acquired for Pu‘ukoholā Heiau NHS and Kaloko-Honokōhau NHP areas. Delineated into two groups: Reference Imagery and Processed Imagery.
AREA |
REFERENCE IMAGERY |
PROCESSED IMAGERY |
PUHE |
2006 Quickbird Satellite |
1949, 1950, 1966, 1970, 1975-June, 1975-Nov, 1977, 1981, 1987, 1989, 1990, 1998, 2006 |
KAHO |
2006 Quickbird Satellite |
1950, 1954, 1965, 1968, 1970, 1980, 1987, 1988, 1992, 2000, 2002 |
ST, EX and EXT results at Kaloko-Honokōhau NHP and Pu‘ukoholā Heiau NHS
The low water mark (LWM) is used as the shoreline change reference feature (SCRF) for this study. Transects are spaced every 20 m alongshore. Results are presented on poster maps, as individual ‘transect plots', and in table form (see Appendix D). There were no consistent trends found at a scale that includes both study areas, rather Kaloko-Honokōhau NHP and Pu‘ukoholā Heiau NHS are unique in morphology, shoreline history, and responses to periodic events. The EX method is used to project an erosion hazard line at CI 95% and is used in the area descriptions.
Kaloko-Honokōhau NHP
The Kaloko-Honokōhau NHP study area extends from Noio Point (just south of Honokōhau Harbor) to just north of Kaloko Fishpond. The coastline is composed of carbonate sand beach in the south (Honokōhau Beach), low basalt headlands at Kaloko Point and basalt fronted supratidal carbonate beach in the north. Two sections of shoreline were selected for analysis: (1) Maliu Point to just north of ‘Aimakapā Fishpond, including Honokōhau Beach (transects 0 – 63; Figure 40) in the south; (2) the supratidal beach between just north of Kaloko Fishpond (transects 66 – 87; Figure 41).
Figure 40 . Maliu Point to north of ‘Aimakapā Fishpond shoreline positions, transects and results. Shoreline change rates are displayed in graph form offshore. Each bar corresponds to a transect location (yellow shore-normal lines) on the shoreline. Negative rates (erosion) are indicated in red. Positive rates (accretion) are indicated in blue.
Figure 41 . North of Kaloko Fishpond shoreline positions, transects and results. Shoreline change rates are displayed in graph form offshore. Each bar corresponds to a transect location (yellow shore-normal lines) on the shoreline. Negative rates (erosion) are indicated in red. Positive rates (accretion) are indicated in blue.
The thin carbonate beach between Maliu Point and north of ‘Aimakapā Fishpond is experiencing long term erosion (EX) at an average rate of -0.8 ± 0.1 ft/yr. Recent shoreline data indicate a slight slowing of this trend at an average recent change rate (EXT) of -0.4 ± 0.1 ft/yr. At the southern end of Honokōhau Beach is ‘Ai‘ōpio Fishtrap. Aerial photography from 1950 to present show sand migrating north along the beach and out to ‘Aimakapā Fishpond area exposing several cultural sites to minor wave action. This portion of shoreline has experienced long term erosion (EX) at an average rate of -0.7 ± 0.1 ft/yr. The average EXT change rate at this section of shoreline in 2006 is -0.4 ± 0.4 ft/yr.
The ‘Aimakapā Fishpond is marked on the seaward side by Honokōhau Beach. This ~550 ft section of the beach (transects 33 – 41) has been moderately stable over the period of study with an average long term shoreline change rate (EX) of -0.3 ± 0.1 ft/yr. Recent data suggests it continues to be stable with an average rate (EXT) of 0.5 ± 0.2 ft/yr.
The northern segment of Kaloko-Honokōhau NHP (transects 66 – 87) is active during storm and large swell events. It extends northward from Kaloko Fishpond. This section of coast is relatively stable with long (EX) and short term (EXT) average rates of change within the range of uncertainty (EX = -0.1 ± 0.1 ft/yr and EXT = -0.1 ± 0.3 ft/yr).
Pu‘ukoholā Heiau NHS
The Pu‘ukoholā Heiau NHS study area is comprised of two separate carbonate sand beaches. Pelekane Beach (Figure 42) prior to construction of Kawaihae Harbor in the 1950's is noted as a thin black sand beach that stretched along the shoreline the length of the present day harbor. Today's Pelekane Beach was created with carbonate spoil from reef dredging during harbor construction. 1970 data were removed from analysis due the apparent result of a episodic event severely altering the beach. This is possibly due to the 1968 tsunami. Analysis of Pelekane Beach for this study begins with 1966 data, the first aerial coverage identified after the creation of the harbor and beach creation. Since 1966, Pelekane beach has been accreting at a long (EX) and short term (EXT) average rate of 1.4 ± 0.7 ft/yr.
Figure 42 . Pelekane Beach shoreline positions, transects and results. Shoreline change rates are displayed in graphs offshore. Each bar corresponds to a transect location (yellow shore-normal lines) on the shoreline. Negative rates (erosion) are indicated in red. Positive rates (accretion) are indicated in blue.
South along the low rocky shoreline, lies Spencer State Beach Park at Ohaiula Beach (Figure 43). Although Spencer State Beach Park is not within park boundaries, it was included in the study in order to document changes in areas abutting the park that might have future effects on the park. This small pocket beach of carbonate sand has experienced long (EX) and short term (EXT) erosion with an average rate of -0.8 ± 0.5 ft/yr.
Figure 43 . Ohaiula Beach shoreline positions, transects and results. Shoreline change rates are displayed in graphs offshore. Each bar corresponds to a transect location (yellow shore-normal lines) on the shoreline. Negative rates (erosion) are indicated in red. Positive rates (accretion) are indicated in blue.