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- Objective
- Shoreline change rate methods
- Prediction of known positions
- Synthetic time series analysis
- Binning adjacent transects
- Erosion Hazard Maps
- Conclusion

- Find the most appropriate shoreline change rate method that describes beach change in Hawaii
- Forecasting known data points
- Using synthetic data to predict true rate

- Study the effects of a priori (storms, tsunamis) outliers
- 1960 Tsunami – North Shore
- 1963 Kona storms – Kihei, West Maui (Rooney, 2002; Eversole and Fletcher, 2002)

- Identify regions of a beach that have indistinguishable change rates (binning)
- Create Erosion Hazard maps that incorporate rate method and binning

Kihei: South Swells, refracted North Swells and kona storm waves

West Maui: North Pacific swells, south swells and kona storm waves

North Shore: North Pacific swells, tradewind waves

Foster and Savage, 1989

Fenster et al., 1993

Forecasting Methodology

Step 1: Remove a known data point

Remove

Forecasting Methodology

Step 1: Remove a known data point

Forecasting Methodology

Step 2: Calculate the shoreline change rate

Forecasting Methodology

Error in Prediction (EIP) = Predicted – Actual

Step 3: Calculate the predicted shoreline and compare it to the actual shoreline

Forecasting Results

- For most regions, OLS, WLS, RLS, RWLS, JK, EPR, and LAD are statistically insignificant at the 95% Confidence Interval
- MDL and AOR have the highest mean |EIP|
- Hardened beaches have lower mean |EIP| than natural beaches

Kihei

Forecasting Results

- Average improvement for all methods when a priori outliers removed range from < 0.1 m to 15 m
- OLS, RLS, WLS, RWLS, JK, and LAD have minimal improvements (avg = 0.7 m)
- Each beach reacts differently to storm: a little more than half the beaches showed no significant improvements.

Kihei

Synthetic Analysis

An alternative to Forecasting analysis

Generate a synthetic shoreline time series

Slope = 0.1 m/yr

Intercept = 75 m

Synthetic Analysis

Using various distributions, generate noise into the time series

= real position

= noisy position

Synthetic Analysis

Calculate trend fits with erosion rate methods

Compare slope of fits to true slope

Add more noise and repeat

Add storm point in middle, then at end and repeat

Synthetic Results

- Less Noise
- No storm
- 1000 synthetic time series
- = true slope of 0.1 m/yr

Synthetic Results

- More Noise
- No storm
- 1000 synthetic time series
- = true slope of 0.1 m/yr

Synthetic Results

No Storms

Storm - MID

Storm- END

WLS, RWLS,

WLAD

WLS, RWLS,

WLAD, OLS,

RLS, JK,

LAD, EPR

RWLS, RLS,

WLAD, LAD

Less Noise

WLS, RWLS,

WLAD, OLS,

RLS, JK,

LAD, EPR

WLS, RWLS,

WLAD, RLS,

JK, OLS

WLS, RWLS,

WLAD, RLS,

JK, OLS,

LAD

More Noise

Based on Synthetic and Forecasting work, we choose RWLS as our

rate method because we know uncertainties, but not storm effects.

Available Methods:

OLS, RLS, WLS, RWLS, LAD, WLAD, JK

Are

Uncertainties

Known?

Yes

No

Are Storms

Known?

Are Storms

Known?

Yes

No

Yes

No

Choose WLS,

RWLS, or WLAD

Choose RWLS

or WLAD

Choose OLS, JK,

RLS, or LAD

Choose RLS

or LAD

Outliers

- Two types of outliers: a priori and statistical outliers
- A priori outliers based on historical data and confirmed by tide gauge records
- U.S. East Coast studies show that removal of these outliers improve forecasting predictions by 15-30 m. We show an improvement of 0.7 m

Zhang et. al, 2002

Outliers

- Statistical outliers based on residuals and are important because Least Squares are susceptible to outliers
- RLS and RWLS remove statistical outliers by estimating true standard deviation (σ) of population.
- For small sample size, less certainty of true σ, causing removal or retention of too many outliers
- Conclusion: increase sample size (bin)

- Identifying statistical outliers is less accurate with only 5-9 unevenly spaced points
- We group regions of a beach that have indistinguishable erosion rates to better identify the trend of the data by increasing the signal

Binning Analysis

- Start with a window spacing of 4 transects and use Students t-test to compare its rate to the rate of the rest of the beach
- Shift window by 1 transect and repeat t-test. Window is shifted in increments of 1 transect until the last 4 transects are grouped together
- Increase window size by 2 transects and process is repeated

R=binned erosion rate

T-test compares R1 to R2

Binning Analysis

- Vertical lines = transects
- Horizontal lines = transect windows where binned rate is statistically different from binned rate of the rest of the beach

Binning Analysis

- Within each window size, a t-test is performed on any overlapping transects

Binning Analysis

- If overlapping transects are statistically insignificant, they are grouped together as one bin (A)
- If overlapping transects are statistically different, they are grouped separately (B)
- Another t-test is performed on any overlapping transects at different window sizes (Comparison of A and B)

Binning Analysis

- Bins that are found to be statistically insignificant are clustered together and a rate is calculated for that region (1 and 2)
- Transects that fall in both clusters are considered transitional zones

Binning Analysis

- Each cluster is assigned a color and each transect within the cluster is given a shade of that color
- Transect shade corresponds to frequency of windows that intersect the transect
- Groups A and C represent two distinct colors
- Group B represents the overlap between Groups A and C

0.10 m/yr

Erosion

0.25 m/yr

Erosion

0.19 m/yr

Erosion

Binning Results

- Binned vs Unbinned
- 84% of binned rates significant vs. 38% unbinned rates significant (95% C.I.)
- 0.1 m decrease in uncertainties with binned rates compared to unbinned rates
- Binned Beaches
- 15 beaches binned – 8 from Kihei, 4 from West Maui, and 3 from the North Shore.
- Kihei further categorized in two geographical groups within study site– 4 central beaches and 4 southern beaches

Binning Results

- Summary of bin trends

Binning Results

Kaanapali Beach

An example at one Beach

- Eversole and Fletcher (2003) identify an inflection point at Kaanapali Beach where the seasonal volume trend reverses. They also conclude that the net annual sediment transport is northward
- We observe an erosive south and accretive north
- The region encompassing the inflection point switches from erosion to accretion

-0.070 m/yr

Inflection

point

-0.165 m/yr

0.104 m/yr

Available Methods:

OLS, RLS, WLS, RWLS, LAD, WLAD, JK

Are

Uncertainties

Known?

Yes

No

Are Storms

Known?

Are Storms

Known?

Yes

No

Yes

No

Choose WLS,

RWLS, or WLAD

Choose RWLS

or WLAD

Choose OLS, JK,

RLS, or LAD

Choose RLS

or LAD

Bin Transects to identify segments of a

beach that have indistinguishable erosion rates

Erosion Hazard Maps

Calculate 50 yr predicted position and its uncertainty from binned data

Erosion Hazard Maps

- Map Assumptions
- Erosion is constant
- No shoreline change due to storms

Available Methods:

OLS, RLS, WLS, RWLS, LAD, WLAD, JK

Are

Uncertainties

Known?

Yes

No

Are Storms

Known?

Are Storms

Known?

Yes

No

Yes

No

Choose RLS

or LAD

Choose WLS,

RWLS, or WLAD

Choose RWLS

or WLAD

Choose OLS, JK,

RLS, or LAD

Bin Transects to identify segments of a

beach that have indistinguishable erosion rates

Calculate 50 year position and its uncertainty

from trend line of binned data

Project 50 year position and uncertainty

on map

Erosion Hazard Map

- YESUNCERTAINTIES and NOSTORMS = weighted, robust methods (RWLS or WLAD)
- YESUNCERTAINTIES and YESSTORMS = weighted methods (WLS, RWLS or WLAD)
- NOUNCERTAINTIES and NOSTORMS = unweighted robust methods (RLS or LAD)
- NOUNCERTAINTIES and YESSTORMS = unweighted methods (OLS, JK, RLS or LAD)
- MDL and AOR produce the most variable results
- Increasing sample sizes in a RWLS or RLS analysis improves the identification of statistical outliers
- Binning increases sample sizes and improves the signal-to-noise ratio
- Erosion Hazard Maps are useful for coastal management purposes

- Committee Members – Chip Fletcher, Rob Dunn, John Rooney, and Neil Frazer
- University of Hawaii Sea Grant College, USGS, Maui County
- Coastal Geology Group
- Joe Genz
- GG faculty and students
- Family and Friends

Questions….