Space-time variability of coastal morphology:
results from video remote sensing
Presented as partial fulfillment of the requirements for the degree of Doctor in Science at the Instituto Oceanográfico da Universidade de São Paulo, with emphasis in Geological Oceanography
Adviser:
Prof. Dr. Eduardo Siegle
Universidade de São Paulo Adviser:
Prof. Dr. Robert Holman
Oregon State University (USA)
São Paulo
INSTITUTO OCEANOGRÁFICO
Space-time variability of coastal morphology: results from
video remote sensing
Cássia Pianca Barroso
Presented as partial fulfillment of the requirements for the degree of Doctor of Philosophy in Oceanography at the Instituto Oceanográfico da Universidade de São Paulo, with emphasis in
Geological Oceanography.
Evaluated in / /
Prof. Dr. Grade
Prof. Dr. Grade
Prof. Dr. Grade
Prof. Dr. Grade
” Persistence is the road to accomplishment "
Acknowledgments iii
Abstract v
Resumo vii
List of Figures xv
List of Tables xvi
List of Symbols xvii
1 Introduction 1
1.1 Argus video remote sensing . . . 2
1.2 General Goals . . . 4
1.3 Thesis Outline . . . 4
2 Shoreline Variability From Days to Decades: Results of Long-term Video Imaging 5 2.1 Introduction . . . 5
2.2 Shoreline Extraction Model . . . 7
2.2.1 ASLIM . . . 9
2.3 Description of the data set . . . 12
2.3.1 Duck Beach - North Carolina (USA) . . . 12
2.4 Quality control . . . 18
2.5 Comparison against ground truth . . . 19
2.6 Results . . . 20
2.6.1 Wave Forcing . . . 21
2.6.3 Cross-Spectrum between Forcing and Response . . . 46
2.7 Discussion . . . 52
3 Applying the shoreline extraction model (ASLIM) to a reflective and cuspy beach: Massaguaçu - Brazil 54 3.1 Introduction . . . 54
3.2 Massaguaçu Beach . . . 54
3.3 Results and Discussion . . . 59
4 Mobility of Meso-scale Morphology on a Microtidal Ebb Delta Measured Using Remote Sensing 65 4.1 Introduction . . . 65
4.2 Regional Setting . . . 67
4.3 Observational Data . . . 68
4.3.1 Remote Sensing Argus System . . . 71
4.3.2 Comparison between Argus and survey data . . . 77
4.4 Migration patterns . . . 79
4.5 Lag least squares analysis (LLSA) of Migration Rates . . . 84
4.6 Results . . . 87
4.7 Discussion . . . 92
5 Final Remark 95 5.1 Conclusions . . . 95
5.2 Future Works . . . 98
I would like to thank Rob Holman for all support, dedication, questions answered, knowl-edge shared, for receiving me in Corvallis, believing in my capacity, giving me the opportunity to work with the data from Duck and New River Inlet, for making me think like a scientist, and for our enjoyable meetings always finishing with the phrase: "make me famous". I am very happy I had the opportunity to work with him during my PhD. I would also like to thank Kathy Holman for the cordiality, support, and the delicious dinners.
I would like to thank Eduardo Siegle for the support, enjoyable times, sharing his knowl-edge, ideas, for giving me the opportunity to work with the Argus Station at Massaguaçu, and pursue a PhD.
I thank John Stanley for receiving me so well in CIL and Corvallis, for giving me all the support, for giving me Bauducco cookies when I was missing Brazil, for the long conversations (many of them in "Portuguese-English"), and for his funny stories.
I would like to thank Peter Ruggiero, Tuba Ozkan-Haller and Mick Haller for receiving me on the coastal group and sharing their knowledge. I thank Dan Cox, for helping with the wave tank and with suggestions regarding swash processes. I thank Paul Komar, by the casual conversations, his interest in my work, his suggestions, and for receiving me so well.
To all the friends that accompanied me during this journey, especially the Corvallis friends that made the end enjoyable: the Amorim sisters (Mariana and Clarice), Ludi, Fábio Mineo, Ive, Fábio, Cleuzir, Adriana, Bruno, Maria, Gizele, Bianca Terra, Yhasmin, Célio, Lina, An-dré Belejo, Jennica, Dylan, Jennifer Van Wakeman, Elizabeth McHugh, Jennifer Veilleux, Byungho, Wei Li, Atul, Chris Ordonez, Bret, Tiffany, Rodrigo, Dani, Thais, Julio, Mousa, Jehan, Drew, Meagan, Silvia, Cheryl Harrison, among others. To my friends in Brazil: Natali, Zezinha, Rafa Soutelino, Juliana, Luis Felipe, Fabíola, Raquel, Fabrício Sanguinetti, Marin, Márcio, Talitha, Paulo Henrique, Pitu, Mariana Coppede, Leornardo Samaritano, and the great
The CIL group, for receiving me: Meg Palmsteen, Greg Wilson, Jeremy Mull, Heather Baron, Rebecca, Colleen, Sarah, Cameron, Gabriel, Kate, Adam, Erica, Jacob, Dylan, Manuel, Jeff, Nick, Guillhermo and David.
To Piero, for being this wonderful person in my life, for supporting me in all moments, both easy and tough ones, for dealing with my stress in these last 4 months, for all the help, suggestions, for teaching many things, having always believed in me, not letting me give up, for always reminding me why I was doing a PhD. Thanks Piero, for being my best mate, friend and teacher, without you none of this would have been possible.
To my parents, Alcides and Ana, and the "adoptive" ones, Décio and Sônia, for full support, love, believing in me, helping and allowing me to continue this journey. To my brother Rafael and sister-in-law, Ana Paula, for supporting me and being always there when I needed.
The ability to predict changes of the coastal morphology has been restricted by the lack of observational data in a sufficient spatial and temporal coverage. With the advent of remote sensing, the low spatial and temporal resolution could be overcome, especially with the devel-opment of video cameras to study nearshore environments. The goals of this thesis are, using remote sensing techniques, to (1) develop a robust method for extracting shoreline locations; (2) analyze a unique 16 and 26-year record of daily to hourly video images; (3) characterize the space-time scales of shoreline variability at a representative site at Duck, NC; (4) test this method at a reflective and cuspy beach at Massaguaçu Beach located at Brazilian coast; (5) describe recent observations of meso-scales morphology associated with tidal inlets using an innovative optical method and document rates and patterns of migration of these features at New River Inlet, NC.
A model was developed, called ASLIM (Augmented ShoreLine Intensity Maxima) to ex-tract the shoreline positions based on fitting the band of high light intensity in time exposure images to a local Gaussian fit with a subsequent Kalman filter to reduce noise and uncertainty. The ASLIM model showed good agreement with survey data (correlation coefficient of 0.85, significant at 95% confidence level). Wave forcing was characterized in terms of the significant wave height and the cross-shore and longshore components of wave energy flux. 66% of the shoreline variability was explained by periods longer than the annual cycle, despite the fact that wave forcing is dominated by shorter periods. The first EOF mode of shoreline variability con-tained 49% of the variance and represented the cross-shore movement (landward- seaward) of the shoreline. The second mode (26% of the variance) is associated with alternating accretion signals on either side of the pier, while the next two higher EOFs (7% and 5.6%) describe the local pier effects. The pier was found to have a significant influence on shoreline behavior that extends out to 500 meters, nearly twice the length scales assumed by previous studies. The
resulting in a seasonally-reversing sediment accumulation on the up-drift side. Erosion signals on the down-drift side of the pier were found propagate away from the pier at 1200 m/year. A shoreline erosion trend that was found only on the north side of the pier may be related to the trend found in the alongshore transport, that it is increasing toward the north and is being blocked by the pier. The ASLIM method was also tested at Massaguaçu Beach and showed to be a valuable tool to investigate shoreline variability processes.
Our observations, at New Rivet Inlet (NC), revealed a complex set of swash bars and meso-scale sand banks that migrated in a coherent clockwise pattern with movement in offshore re-gions being away from the inlet mouth while nearshore migration was back toward the inlet. To quantify migration rates and patterns objectively based on sequences of time exposure images, a Lagged Least Squares Algorithm (LLSA) was developed that found the vector migration rate for which the suite of lagged images were most similar, computed on a tile-by-tile basis. The mean migration rate was found to be 1.53 m/day (standard deviation of 0.76 m/day). 72% per-cent of estimated rates were greater than 1.0 m/day, 31% perper-cent were larger than 2.0 m/day, and the maximum rate round was 3.5 m/day, averaged over 23 days. Alongshore averages of cross-shore migration rates showed a node at 110 m from the shoreline that separates migration away from the inlet (offshore) from migration toward the inlet near the shore. The circular pattern of migration appeared to be consistent with expected residual flow on an ebb delta.
A habilidade de prever mudanças morfológicas nas regiões costeiras é restringida pela falta de dados observacionais com suficiente resolução espacial e temporal. Com o desenvolvimento do sensoriamento remoto, esse problema pode ser minimizado, especialmente com o uso de câmeras de video para o estudo de regiões costeiras. Os objetivos dessa tese são, através do uso de images de video, (1) desenvolver um método robusto para extrair a localização da linha de costa; (2) analisar um conjunto de dados inéditos de 26 anos de imagens diárias; (3) caracteri-zar as escalas espaciais e temporais da variação da linha de costa em um local representativo, a praia de Duck, NC; (4) testar esse método em uma praia reflectiva e com cúspides, a praia de Massaguaçu localizada no litoral brasileiro; (5) descrever recentes observações de feições mor-fológicas de meso-escalas associadas a um canal de marés usando uma técnica óptica inovadora e documentar as taxas e padrões de migração dessas feições morfológicas em New River Inlet, NC.
Um modelo foi desenvolvido, chamado ASLIM (Augmented ShoreLine Intensity Maxima) para extrair as posições da linha de costa baseado na intensidade máxima observada nas ima-gens de exposição (timex) através de um ajuste Gaussiano com um subsequente filtro Kalman filtro, este para reduzir incertezas e ruídos. O ASLIM quando comparado com dados do levanta-mentos batimétricos mostrou um boa correlação com coeficiente de 0.85, esstatisticamente sig-nificativo). As ondas foram caracterizadas em termos da altura significativa e os componentes longitudinal e transversal do fluxo de energia da onda (PxePy, respectivamente). Menos de 2%
da altura da onda é explicada por escalas maiores do que um ano. 66% da variância foi explicada por períodos maiores do que o ciclo anual, apesar do fato das forçantes (ondas) serem domi-nadas por períodos curtos (menores que 20 dias). O primeiro modo da EOF para a variação da linha de costa contém 49% da variância e representou o movimento transversal da linha de costa. O segundo modo (26% da variância) está associado com a alternância de sinais de acresção em
píer. O píer apresentou uma influência significativa no comportamento da linha de costa, à qual estende-se a 500 metros ao norte e sul do píer, duas vezes mais do que os valores assumidos por estudos anteriores. O píer restringe o transporte longitudinal sazonal entre a parte sul (verão) e a parte norte (inverno), resultando em uma acumulação de sedimentos sazonalmente reversa no lado up-drift da deriva. Sinais de erosão foram encontrados ao lado down-drift do píer e que propagam-se 1200 m/ano para longe do píer. A linha de costa apresentou uma tendência à erosão apenas no lado norte do píer, esta erosão pode estar relacionada com a tendência de aumento do transporte longitudinal para o norte, que é bloqueado devido ao píer, gerando uma acumulação na parte sul do píer e erosão na parte norte. O método ASLIM também foi testado na Praia de Massaguaçu e mostrou ser uma valiosa ferramenta para investigar variabilidade da linha de costa.
Nossas observações em New River Inlet (NC), revelaram um complexo de bancos de espra-iamento e feições arenosas de meso-escalas que migraram em um padrão coerente horário onde nas regiões offshore migraram em direção contrária a desembocadura do rio enquanto que as feições na região próxima a costa, migraram em direção ao canal. Para quantificar de forma objetiva as taxas e padrões de migração um algoritmo foi desenvolvido (LLSA - Lagged Least Square Algorithm) usando sequências de imagens de exposição (timex). Esse método compara diferentes imagens que possuem diferentes intervalos de tempo, e encontra o intervalo (lag) onde essas imagens são similares. A taxa média de migração encontrada foi de 1.53 m/dia (com desvio padrão de 0.76 m/dia). 72% das taxas estimadas foram maiores que 1.0 m/dia, 31% foram maiores que 2 m/dia, e as taxas máximas encontradas foram 3.5 m/day, em 23 dias. As taxas de migração média longitudinais mostraram um nó em 110 metros da linha de costa que separa as feições que migram para longe do canal (offshore) e para a linha de costa. O padrão circular pareceu ser consistente com o fluxo residual esperado em um delta de maré vazante.
2.1 Example ASLIM position estimates (a) showing a rectified time exposure im-age (timex) overlain with the instantaneous shoreline (red line) extracted using ASLIM and the location of an example cross-shore transect (black), while (b) shows the example intensity profile at y = 997.5 m (black), the Gaussian fit (red) and the region of interest (green). . . 10 2.2 Map of Duck Beach located on the east coast of United States, in the state of
North Carolina. The black triangle indicated the location of the 8 meter Array pressure gauges and the red circle is the waverider buoy at 17.4 meter depth. The black line is the FRF research pier. The yellow star indicates the location of the video tower. The yellow triangles indicate the surveys profiles used to validate the ASLIM model. The lower panel is a map of the bathymetry at 07 February, 2011. . . 13 2.3 Measured tides at Duck Beach during the 26 years of data. . . 15 2.4 Example of the five types of images collected by the Argus System at Duck
(lower) and a rectified timex image (upper). . . 16 2.5 Resolution maps for Duck area showing the resolution in meters in the
cross-shore (white) and alongcross-shore (black) directions. The red box is the region of interest. . . 17 2.6 Temporal variability of pixel resolution for a camera 0 location at x = 120 and
y = 900. . . 17 2.7 Two examples from Duck showing images with poor quality that were discarded
from the data set. In each image, the upper panel is the rectified timex images with poor quality, and the lower panel is the histogram of the error variance of the predicted state (R). The dash red line indicates the 40% value. . . 19
95% confidence intervals of 0.78 and 0.88; and slope of 0.90). The dash gray line indicates along the 1:1 relationship. . . 20 2.9 Wave conditions at Duck extracted from the FRF’s 8m Array pressure gauges:
(a) significant wave height (m), (b) peak period (s), (c) wave direction (degrees), (d) cross-shore wave energy flux (W/m) and (e) alongshore wave energy flux (W/m). Data gaps mostly correspond to days with no data. Positive alongshore wave energy flux corresponds to transport to north, while negative cross-shore wave energy flux is associated with transport towards the shore. The large spike at the end of thePy record corresponds to Hurricane Sandy. . . 22
2.10 Wave rose of significant wave height (left) and wave period (right). The dash line represent the Duck coastline in relation to the true north. . . 23 2.11 Annual signal of the wave parameters: (a) significant wave height (m), (b) wave
period (s), (c) wave direction (deg), (d) cross-shore wave energy flux (W/m), and (e) alongshore wave energy flux (W/m). Solid lines show the monthly means while dashed lines are spaced one standard deviation away. The hori-zontal line in panel c indicates the direction of shore normal. . . 24 2.12 Number of storms with waves > 2 meters and duration > 8 hours by months for
Duck, during the years of 1980 to 2014. . . 25 2.13 (a) Power spectral density for the wave height, and (b) for the cross-shore (black
line) and alongshore wave energy fluxes (red line). The dashed gray lines are indicative of the annual, semi-annual and 20 days frequencies, respectively. . . 26 2.14 Space-time plot of the shoreline position as a function of alongshore location
and time. The FRF pier is shown by the black line in the middle of the plot and the data sets for 26 years and 16 years are illustrated by the red and green rectangles, respectively. For reference, a rectified timex image is provided at the bottom. Hot colors indicate seaward shoreline positions while cold colors indicate that landward shoreline positions. White indicates regions of no data. . 28 2.15 Mean shoreline positions for the 16 years (long black line) and the 26 years
sition for the 16 years data set as a function of longshore location. The black contours are the cumulative probability. . . 30 2.17 The alongshore-averaged shoreline position <xˆo >y (t)for the 26-year (blue
line) and 16-year (red line) data sets. . . 31 2.18 Slopes from the linear regression as a function of alongshore locations and 95%
confidence levels (red and green dash lines) for the 26 and 16 year data sets (short lines correspond to the 26 year data set). The FRF pier location (thick black line) is plotted for reference. . . 32 2.19 Space-time plot of the shoreline deviations as a function of alongshore location
and time. Cold colors indicate a erosive position and hot colors accretionary deviations of shoreline position. . . 33 2.20 Monthly averaged shoreline deviations. Hot colors indicate accretion (seaward
positions) and cold colors indicate erosion (landward position). . . 35 2.21 Power spectra of the base shoreline for 26 years (a) and 16 years (b). The red
lines are the alongshore-averaged PSDs and the gray lines represent the PSDs (dof = 2) of each of the 181 (upper panel) and 601 (lower panel) y-locations. The 95% confidence interval applies to the average spectra. . . 37 2.22 Space-frequency plot of the power spectrum (dof = 10) for the 16 years data.
The dash black lines represent the division between the cycles: weather and intra-annual (20 days line), intra-annual and inter-annual (1 year line, which also represent the annual cycle). The dash gray line is the 2 cycle per year, i.e, the semi-annual harmonic. Hot colors correspond to higher variance and cold colors to lower variance values. . . 39 2.23 (Amplitudes (a;A =√2V ar) and percentages of variance (b) as a function of
alongshore positions for each the 4 bands studied. The line colors and the text are in agreement. . . 40 2.24 Wavenumber power spectral density for 16 years data. The red line is the
2.27 Comparison between the first EOF scores (red) and the alongshore-averaged shoreline times series (blue). . . 44 2.28 Power Spectra for the four EOF scores time series. The dashed gray lines are
indicative of the annual, semi-annual and 20 days frequencies, respectively. . . 45 2.29 Coherence-squared between shoreline data (16 years data set) and wave height
(a), cross-shore wave energy flux (b) and alongshore wave energy flux (c). The white color corresponds to the 95% confidence level. Hot colors correspond to high coherence and cold colors small coherence below the 95% confidence level. 46 2.30 Coherence and phase between wave height (16 years) and EOF scores time
series. The dashed gray lines represent the annual, semi-annual and 20 days frequencies, respectively. . . 49 2.31 Coherence and phase between Px (16 years) and EOF scores time series. The
dashed gray lines represent the annual, semi-annual and 20 days frequencies, respectively. . . 50 2.32 Coherence and phase between Py (16 years) and EOF scores time series. The
dashed gray lines represent the annual, semi-annual and 20 days frequencies, respectively. . . 51
3.1 Map of Massaguaçu Beach. The red triangle indicates the Argus Station and the black triangle is the WWW3 grid location at isobath 75 meters. . . 55 3.2 Predicted tide for Massaguaçu Station. . . 55 3.3 Wave conditions at Massaguaçu Station extracted from WWW3: significant
wave height (m), peak period (s) and wave direction (degrees). . . 57 3.4 Wave rose of significant wave height (left) and wave period (right). The dash
line represent the Massaguaçu coastline in relation to the true north. . . 57 3.5 Massaguaçu Station, illustrating the tower where the cameras were installed and
the Brisa Hotel. . . 58 3.6 Example of the five types of images collected by the Argus System at
cross-shore (white) and alongshore (black) directions. The red box is the region of interest (ROI). . . 59 3.8 Two examples from Massaguaçu showing images with poor quality that were
removed from the data set. . . 60 3.9 Example ASLIM position estimates showing a rectified time exposure image
(timex) overlain with the instantaneous shoreline (red line) extracted using ASLIM. 60 3.10 Space-time plot of the shoreline positions as a function of alongshore location
and time. For reference, a rectified timex image is provided at the bottom. Hot colors indicate seaward shoreline positions while cold colors indicate landward shoreline positions. White indicates regions of no data. . . 61 3.11 Mean shoreline positions for Massaguaçu data sets. The dashed red lines
repre-sent±one standard deviation. . . 62 3.12 Shoreline distribution (colored contours) and cumulative probability density
functions (black contours) for the shoreline position for Massaguaçu as a func-tion of longshore locafunc-tion. . . 62 3.13 The alongshore-averaged shoreline position < xˆo >y (t)for the 3-year record
for Massaguaçu. . . 63 3.14 EOF weights for the first four modes for Massaguaçu. . . 63 3.15 EOF scores time series of the four modes for Massaguaçu. . . 64
4.1 Map of NRI. The aerial photo shows the position of the ebb shoals, the Argus Station (yellow star) and the AWAC wave buoy from WHOI (yellow circle). The WaveRider buoy location from CDIP (Station #190) is represented with a red asterisk on the middle map. The aerial photo was obtained from Gordon Farquharson (Applied Physics Laboratory - University of Washington). . . 68 4.2 Water level measured at New River Inlet during the experiments obtained from
the AWAC. . . 69 4.3 Time series of wave conditions (Hmo, Tp and direction) during the New Rivet
River Inlet. The top panel is a merged geo-rectified Timex image that combines the six views. White regions correspond to regions of enhanced breaking over shoals. The red box shows the region of interest for later analysis. The image has been rotated 90o for better visualization, so offshore is now the bottom of
the figure. . . 72 4.6 Resolution Map for NRI area showing the resolution in meters in the
cross-shore (white lines) and alongcross-shore (black lines) directions. . . 73 4.7 Region of interest. Shoal regions appear white due to the wave dissipation over
the shallow depths. The green line is an example alongshore-oriented pixel transect at roughly x= -90 m while the red line indicates an example cross-shore pixel transect at y = -540 m. Both were used to show below the presence of meso-scales variability in the area of interest and the magnitudes of dominant length scales. . . 75 4.8 These figures are related with the cross-shore pixel transect at y = -540 m. On
the top is the cross-shore profile illustrating the existence of the bumps, i.e., the shoals along the profile. On the bottom is the power spectra density to quantify the wavelength bands of energy of these shoals. . . 76 4.9 These figures are related with the alongshore pixel transect around x = -90 m
and x = -100 m. On the top is the alongshore transect illustrating the existence of shorter scales morphologies along the shoreline. On the bottom is the power spectra density to quantify the wavelength bands of energy to the shorter scales features. . . 77 4.10 Comparison between an example survey for 05/10/2012 and Argus data over
the entire RIVET experiment region. . . 78 4.11 Comparison between the survey for 05/10/2012 and Argus data over the area of
interest, the southerly lobe of the ebb delta. . . 78 4.12 Comparison between survey data (black line) and timex image (pixel intensities;
-540 and (bottom panel) y = -700 m. Time proceeds from the top to the bot-tom of the page. Movement of features down to the left corresponds to shore-ward migration while down to the right indicates seashore-ward migration. Horizontal banding is caused by lighting fluctuations, for example sunny or cloudy days. . 81 4.14 Time-space plots of alongshore vectors of pixel intensities at: (top panel) x =
-70 m and (bottom panel) x = 120. Time proceeds from top to bottom. The inlet is in the direction of positive y so feature movement down to the right cor-responds to migration toward the inlet while down left means movement away from the inlet. Horizontal striping corresponds to lighting variations from day to day including the two bright areas on the right of Figure 14a that correspond to morning sun glare. . . 83 4.15 Example of a sum of squares deviation surface (χ(U,V)). The minimum value
represents the velocity values (U˜ andV˜)of minimum variance (the least squares estimate) found for this case. The white ’X’ represents the minimum variance for this example. . . 86 4.16 Migration rates calculated using the full stack method (top panel) and pair-wise
method (bottom panel). . . 88 4.17 Map of percentage of good data returned from the 23-day data set for the
pair-wise method. . . 89 4.18 Map of the magnitudes of migration rates around the region of interest for the
pair-wise method. . . 90 4.19 Histogram of the migration rates magnitudes for the pair-wise method . . . 90 4.20 The cross-shore averaged U-component as a function of the alongshore
2.1 Wave statistics during the period of study based on a daily wave time series. . . 23 2.2 Amplitudes (Amp) and percentages of the variance (% Var) explained by each
cycle for the wave parameters:Hsig,PxandPy . . . 27
2.3 Alongshore-averages of amplitudes and percentages of variance explained for each frequencies bands for the shoreline response data. . . 38 2.4 Percentages of variance explained by each EOF mode at each four cycles. . . . 46
3.1 Wave statistics during the roughly three-year period of this study at Massaguaçu Beach. . . 56
4.1 The table shows the wave statistics during the period of the experiments at NRI. 70
x: cross-shore location; y: alongshore location;
I(x, y, t′): time exposure image (timex);
I(x, y′, t′): intensity profiles;
b
I(x, y′, t′): normalized intensities;
A(y, t′): amplitude of the Gaussian function;
L(y, t′)width of the Gaussian function;
xs: center peak location;
ˆ
xs(y, t′): tide-dependent shoreline position;
ˆ
xo(y, t′): base shoreline location;
zt(t): tidal elevation;
β: foreshore slope;
e
x(ot): new estimate of the Kalman filter;
e
x(t−1)
o : prior estimate of the Kalman filter;
K: Kalman filter gain P−
t : error variance of the prior estimate;
t: time;
R: error variance of the new estimate; Q: process error;
∆t: time interval since the last estimate;
|P|: wave energy flux;
Px: cross-shore wave energy flux;
Py: alongshore wave energy flux;
αand Dir: wave direction;
T p: wave period;
Amp: amplitude from the power spectra; V ar: variance;
<xˆo>y (t): alongshore-averaged shoreline position;
x′
o(y, t): shoreline deviations;
xo(y): time-mean shoreline;
Ψ(x, y, t): map of image intensity;
∆t: time difference between images;
χ: sum of squares deviation; U: cross-shore velocity; V: longshore velocity;
xoandyo center locations of the sub-windows;
dxanddy: tile sizes; I: sub-images;
ˆ
I: normalized intensities of the sub-images; ¯
I: mean of intensities within the tiles;
σI: standard deviation of intensities within the tiles;
Introduction
The coastal zone is the transitional area between land and oceanic environments and it is extremely dynamic. Most of the world population lives in or near these regions, thus they are important for economic and social reasons. A better understanding of these places is required for the proper management to preserve them for future generations. The interest over these regions had intensified recent years due to the climate changes issues such as an increase on hurricanes occurrence, loss of coastal areas due to erosion, change of the wave climate and sea level rise.
The processes that occur in these coastal environments are responsible for its complexity and diversity. The interaction between the dominant will govern these environments in different configurations, such as, sand and rocky beaches, marshes, mangroves, estuaries and tidal inlets. These processes can vary at time scales from seconds (waves, turbulent processes) to geological periods (climate change, sea level rise), and space scales from meters to 10’s of kilometers.
Understanding how the shoreline varies over time is crucial for coastal zone management. The stability of a beach is strictly related with the shoreline variability, and this is related with the wave regime over the beach and the resultant sediment distribution. Many previous studies have related beach behavior to the summer-winter model (e.g. Komar (1998)), where beaches during the summer are shaped by accretional processes due to calm waves conditions, and erosional processes during energetic winter waves. However, recent observations have revealed the existence of inter-annual and decadal morphologic processes (e.g. offshore progressive sand bars over periods of several years to decades), that can not be described by the summer-winter model (Plant & Holman, 1996).
Another important environment in the coastal regions are the tidal inlets. They provide a passageway for ships and small boats to travel between the open ocean and sheltered waters so are vital to a nation’s commerce, recreation and safety. Tidal inlets have the potential to develop on any depositional shoreline where sediment supply is adequate and where the antecedent topography and sea level fluctuations allow the correct geometry to develop (Boothroyd, 1985). The dynamics of these environmentals are well documented, however most of them have been focused on the macro-scale morphology of ebb shoals and channels. Little is known of the existence or characteristics of smaller meso-scale morphology. The topography of these features is difficult to measure directly, but can be derived from remote sensing imagery (Woodroffe, 2002).
The main obstacle to obtaining information on the coastal variability is the lack of large temporal and spatial measurements using conventional methods. Surveys have high costs and depending on the place that instruments are deployed, they can become outdated within a few hours due to highly energetic waves and turbulent nature of the surf zone. With the advent of remote sensing, the low spatial and temporal resolution could be overcome, especially with the development of video cameras to study nearshore environments. This technique has low cost, easy maintenance, high spatial and temporal resolution, even in storms conditions.
For the preservation of beaches and protection of coastal properties, the increase for infor-mation in how these places change and with what rates these changes occur, makes the use of remote sensing a great tool. In the following section, the Argus video remote sensing, the technique utilized in this present work, will be introduced.
1.1 Argus video remote sensing
The motivation to build a camera system for coastal zone monitoring came from the diffi-culty of studying physical processes on beaches on the West Coast of the United States under extreme wave conditions. The first ideas appeared in the beginning of the 80’s by the coastal group of the Oregon State University (CIL; http://cil-www.coas.oregonstate.edu) and developed into a system called Argus Station.
consists of a number of video cameras attached to a host computer that serves as both system control and communication link between the cameras and central data archives (Holman and Stanley, 2007). Argus stations have been installed in many countries around the world, such as United States, Australia, New Zealand, England, Netherlands, Brazil.
The nearshore exhibits many optical signatures that can be exploited. Ocean waves are visible to the eye due to variations in the reflection coefficient of water with sea surface slope (Holman and Stanley, 2007). The camera can capture wave breaking . Since waves break in shallow water, locations of concentrated breaking indicate positions of submerged sand bars (Lippmann & Holman (1989b)). Foam left by breakers can be seen to drift along the beach with longshore currents in ways that can be measured (Chickadelet al. (2003)).
Five products are routinely collect by the Argus Stations each hour of daylight: (1) instanta-neous images (snapshots); (2) time exposure images (timex) which are obtained by the average of snapshots over 10 minutes; (3) 10-min variance images; (4) brightest and (5) darkness images found from the extremes of intensity variations during the sampling period. A snapshot image is usually collected at the beginning of each hour for each camera to record the conditions and provide a picture of the site that can be used to interpret other collected data. The timex images are the most used product of Argus Stations. Collected every hour or half-hour, each image represents the mathematical time-mean of all of the frames collected at 2 Hz over a 10-minute period of sampling. This processing yields a much clearer view of pattern of wave dissipation and hence the sand bars locations, rip channels (Lippmann & Holman (1989b)) and shoreline positions. Long time series of timex images have provided excellent, low-cost datasets of mor-phodynamic variability over time scales from days to decades (Holman & Stanley (2007))
The basis of video image processing is the quantification of intensity variability of an im-age into a two-dimensional array of picture elements, or pixels. The successful use of video image requires an understanding of temporal aspects of video sampling, spatial aspects and the transformation between image and real-world coordinates and most importantly the relation-ship between image data and geophysical signals of interest. A more detailed discussion on the history, capabilities and the many applications of Argus imagery in research is given in Holman
1.2 General Goals
The goals of this thesis are, using remote sensing techniques, to (1) develop a robust method for extracting shoreline locations; (2) analyze a unique 16 and 26-year record of daily to hourly video images; (3) characterize the space-time scales of shoreline variability at a representative site at Duck, NC; (4) test this method at a reflective and cuspy beach at Massaguaçu Beach located at Brazilian coast; (5) describe recent observations of meso-scales morphology asso-ciated with tidal inlets using an innovative optical method and document rates and patterns of migration of these features at New River Inlet, NC.
1.3 Thesis Outline
Shoreline Variability From Days to
Decades: Results of Long-term Video
Imaging
2.1 Introduction
About two-thirds of the world’s population lives in the coastal regions. These regions are important both economically and socially and require enlightened management to preserve their value for future. Beaches occur on practically all coasts of the world and but are inherently variable, as sand is constantly shifted by waves, wind and nearshore currents (Komar, 1998). An understanding of the processes that govern wave motions, nearshore currents, sediment transport and the resulting morphological variability is required to preserve these environments. The shorelines along coastal regions can erode or accrete as a result of these nearshore processes. These changes can occur on temporal scales from long-term (years and decades) to seasonal variability that repeats on an annual cycle to short-term (days and months, storm events). Spatial scales of variability span from meters for beach cusps to the many kilometers of shoreline evolution. Erosion can reduce beaches areas and destroy houses and commercial properties along the coastlines. Traditionally it was assumed that coastal variability was domi-nated by seasonal, or summer-winter cycles (Komar, 1998), where summer or calm conditions are characterized by a wide berm and smooth offshore profiles while during winter or storm con-ditions the berm is destroyed, the beaches are narrow and steep and sand bars, when present,
migrate offshore.
For most practical purposes, the shoreline is considered to be the key representative of the varying beach and is often the legal separation of property and the ocean. Thus, from the coastal management point of view, it is important to know where the shoreline is, where it has been in the past and where it will be in the future. The location of the shoreline can be used to quantify historical rates of changes (Moore, 2000) and give information about the beach volume and width (Smith & Jackson, 1992). For more than 150 years, the shoreline was defined as the position of high water level (HWL) because it could be visually identified in the field. With the introduction of measurement techniques such as LIDAR and GPS, the shoreline became defined on the basis of an elevation or a tidal datum, such as mean high water (MHW) (Hapke
et al. , 2006). The Dutch define the Momentary CoastLine (MCL) as an integrated measure of the volume of sediment within the active shoreline region (Min V & W, 1990), a measure that is insensitive to details of profile shape so a better basis for coastal zone management deci-sions like shoreline nourishment. Thus, the shoreline definition can vary depending on the data source available and the detection technique used. A complete review of shoreline definitions is reported by Boak & Turner (2005). Shoreline position is one of the most commonly monitored and generally accepted indicators of coastal change (Morton, 1996).
The ability to predict changing coastal morphology has been restricted by the lack of ob-servational data, especially over the multi-decade time scales that are important to coastal zone management. Common recent techniques such as LIDAR, aerial photography, satellite images and airborne radar can cover large spatial scales but are sparse in time due to prohibitive costs. GPS surveys require that expensive survey teams go out into the field, so can only be done infre-quently. However, the advance of digital imaging technologies has made it possible to collect high-frequency, long-duration images of coasts at low cost, greatly increasing the capability to monitor detailed changes in the coastal system. The objective of this paper is to analyze a unique 26-year record of daily to hourly video images by extracting shoreline locations using a new method described below. This data set will then be used to characterize the space-time scales of shoreline variability at a representative site at Duck, NC.
compar-ison with ground truth data. In the following section, we will present and describe the results, presenting the data in a sense of spatial and temporal variability of the wave forcing and then the shoreline response, a correlation between them and an EOF analysis of the shoreline pattern. We close with a discussion and conclusions.
2.2 Shoreline Extraction Model
Because shoreline location is a key measure of coastal health and because it is visible in video images, a number of methods have been previously tested for quantifying shoreline lo-cation from image data. Plant & Holman (1997) following by Madsen & Plant (2001) devel-oped a technique to exploit the white foam generated by swash motions at the shoreline in a shore-parallel band of high light intensity which is very clear on time exposure images on steep beaches. They named this band the shoreline intensity maximum (SLIM). The SLIM method will be discussed again in the next paragraphs. Turneret al. (2001) used a method based on color discrimination wherein the relative amount of red and blue light was used to distinguish the sand and water surfaces. They called their method the CCD Model (Color Channel Diver-gence). Aarninkhof (2003) developed a method called Pixel Intensity Clustering Model (PIC Model) that it is also based on the color difference between wet and dry beach sand but with the distinction defined by a statistical cluster analysis. Finally, Kingston (2003) used an artificial neural network (ANN) to differentiate wet from dry pixels and identify the shoreline position, using manually-selected regions of sand and water to train the network before it was applied to an extensive image archive. Most recently, Plantet al. (2007) compared these four differ-ent shoreline mapping methods in each of the four differdiffer-ent places they were developed and concluded that the shoreline detection methods provided similar results but with slightly differ-ent relative cross-shore displacemdiffer-ents at each location, and the intertidal bathymetry estimated with any of the methods ought to be inter-comparable and complementary over a wide range of geomorphic and environmental conditions.
to analyze, it was important to develop a method for shoreline extraction that is automated and robust.
Plant & Holman (1997) introduced a method to extract the cross-shore location of this ShoreLine Intensity Maximum from a sequence of time exposure images. They noted that sim-ply using the location of maximum intensity in a swash search region would return noisy results associated with small fluctuations in the shore break intensity profile. Instead, they pointed out that the results would be more robust if they fit a parabola to the intensities near the shoreline and used the maximum in the fitted function to define the SLIM position. They found the mea-surement error for individual shoreline estimates in a field comparison to be about 0.10 m in the vertical. This method was updated by Madsen & Plant (2001) who used, instead of a parabola to fit the intensities, the superposition of a quadratic and Gaussian-shaped function where the quadratic modeled the background intensity in the near-shoreline region and the Gaussian repre-sented the intensity maximum above that background. Results were similar to Plant & Holman (1997), with a mean error (0.12 m in the vertical) when compared with surveys data.
Our approach will also base estimates of shoreline location on the band of high light inten-sity on timex images but will model the local maximum as a Gaussian but without the parabolic background profile. A second and more important change will be the implementation of a Kalman filter to reduce noise and uncertainty in the resulting time series of shoreline measure-ments. We called our method the Augmented Shoreline Intensity Maximum, or ASLIM.
The Kalman filter was introduced in 1960 (Kalman, 1960) as a statistically robust method of merging predictions of the state of a system or variable (for us, the shoreline location) with new measurements of that state, acknowledging that both the predictions and measurements have associated errors. The impact of the new measurement depends on a Kalman gain (K) that sensibly balances the two sources of error. Kalman filtering allows the automated shoreline es-timation to deal sensibly with estimates of widely ranging accuracy, for example automatically ignoring very poor results from rainy or foggy days. Kalman filters have been widely applied to coastal geophysical applications, especially in data assimilation with numerical models (Chen
2.2.1 ASLIM
The first step on the algorithm is to load the rectified time exposure image I(x, y, t′) for
timet′. For each alongshore location (y′) in the image, the cross-shore (x) intensity profiles
I(x, y′, t′) were extracted. The intensities were then normalized from 0 to 1,I(x, yb ′, t′). The
Figure 2.1:Example ASLIM position estimates (a) showing a rectified time exposure image (timex) overlain with
the instantaneous shoreline (red line) extracted using ASLIM and the location of an example cross-shore transect
(black), while (b) shows the example intensity profile at y = 997.5 m (black), the Gaussian fit (red) and the region
of interest (green).
To improve the fit, the search area within the ROI was restricted to the region of a local peak and adjacent slopes. The initial guess at the peak location was defined by a change of slope (dI
dx)from positive to negative, and the region of analysis spanned to the surrounding inflection
points. After defining this curvature region, a non-linear least square fit to a Gaussian function was performed in the vicinity of the local maximum of the curvature using the function.
b
I(x, y′, t′) = A∗exp
−(x−xs)2
L
(2.1)
the center peak location. Figure 2.1b shows an example of the Gaussian function fitted over the normalized intensity profile for y = 997.5 m.
TheAvalues were constrained to range between 0 to 1 (since the intensities were previously normalized) and theLto range from 1 and 20, where 20 is a typical extreme standard deviation for a shore-break Gaussian (Madsen & Plant, 2001). The results from the fit function were the tide-dependent shoreline positionxˆs(y, t′), values forA(y, t′)andL(y, t′)and the variance of
each estimate (σ2
A,σL2,σ2ˆxs).
Because the xˆs position is dependent of the tidal level, causing daily shoreline position
variations, the tidal effect was removed and results were expressed in terms of a base shoreline location,xˆo(y, t′):
ˆ
xo(y, t′) = ˆxs(y, t′) +
zt(t)
β (2.2)
wherezt(t)is the tidal elevation andβ is the foreshore slope. A climatological value ofβ was
chosen as 1:12.5, based on previous results by Plant & Holman (1997) and Holland (1998). The last step is the implementation of the Kalman filter to reduce the uncertainty associated with each instantaneous measurement, some of which will be inevitably be poor due to weather conditions. The Kalman filter equation that updates our prior estimate of shoreline location is:
e
x(ot) =xe(t−1)
o +K(ˆx(ot)−ex(ot−1)) (2.3)
wherexe(ot)is the new estimate, xe(ot−1) is the prior estimate and K is the Kalman filter gain that
compares the credibility of the new estimate with the prior estimate and is obtained from:
K = P
−
t
P−
t +R
(2.4)
P−
t is the error variance of the prior estimate, updated to time, t, and R is the error variance
of the new estimate. The value ofP was known at the previous time step,t−1, but will have become more uncertain since then due to unmodeled natural processes. This increase in error variance is modeled as:
P−
t =Pt−−1+Q∗ △t (2.5)
last step of the process is to update P, the error variance of the estimate, since it has been improved by the incorporation of the new measurement. This is done by:
Pt+= (1−K)∗Pt− (2.6)
The measurement error, R, could be obtained from any of the confidence intervals (σ2
A,
σ2
L, σ2ˆxs) calculated from the parameters found on the least square curve fit. Initially, the value σ2
ˆ
xs was used but proved to be unrealistically small. Instead, it was assumed that the error in shoreline position would be better represented by the width of the shore break, soRwas taken as the valueL2.
The process error,Qmust represent the expected variability on the shoreline due to natural shoreline processes. Because shoreline change depends of the wave conditions, for example, erosion during storms, the significant wave height was taken into account for theQcalculation (Q=Qsh2∗Hmo2 , whereQshwas subjectively chosen to be 21/dayfor Duck).
Results for the first time exposure image of the time series must be digitized manually since there is no prior seed for either finding the peak sub-region or for the Kalman filter pro-cess. Since the measured shoreline was manually digitized, the error was estimated to be small (Pt=1 = 12m2).
According to equation 2.4, ifP−
t is much smaller thanR, the Kalman filter gain (K) tends
to zero and the new estimate (xe(ot)) is trusted much less than, the prior estimate (ex(ot−1)) is trusted
more, and thusxe(ot) =xeo(t−1)(see equation 2.3). In contrast, ifPo(t−1)is much larger thatR, the
Kalman gain (K) tends to one and the new estimate is trusted more.
2.3 Description of the data set
2.3.1 Duck Beach - North Carolina (USA)
Figure 2.2: Map of Duck Beach located on the east coast of United States, in the state of North Carolina. The
black triangle indicated the location of the 8 meter Array pressure gauges and the red circle is the waverider buoy
at 17.4 meter depth. The black line is the FRF research pier. The yellow star indicates the location of the video
tower. The yellow triangles indicate the surveys profiles used to validate the ASLIM model. The lower panel is a
Duck beach is oriented north-northwest to south-southeast, and according to Miller (1999), the research pier is oriented69.78◦east-northeast of true north and is considered shore normal to
the beach. Thus the Duck beach is oriented−20.3◦north-northwest of true north. The foreshore
is relatively steep at 1:12.5 (Plant & Holman, 1997; Holland, 1998), flattening offshore where one or two sand bars are commonly present and vary on both annual and inter-annual time scales (Alexander & Holman, 2004). Beach sediments are composed of fine to coarse sand (Stauble, 1992). The beach has a bimodal grain size distribution material with the main component around 0.25 mm and a secondary component near 1.0 mm (Miller, 1999).
The wave regime is dominated during the summer time by waves approaching from S and have an average significant wave height around 1 meter. During the rest of the year, this beach commonly experiences storm conditions with waves approaching from NE and occasional hur-ricanes and tropical storms with wave approach from the S. Wave data were collected from two instruments deployed by the FRF crew: a waverider buoy (36o11.30’ N,75o44.60’ W) at 17.4
m depth and an 8 m array with 15 pressure gauges (both instruments are shown at figure 2.2). For this present study, the data from the 8 m array is the one used. However, this instrument became inoperative in January of 2012 and the wave time series were extrapolated with the data collected by the waverider buoy. Other data gaps found on the 8 m array collection were also interpolated with waverider buoy data.
Figure 2.3:Measured tides at Duck Beach during the 26 years of data.
The Argus Station at Duck has been in continuous operation since 1986 and has seen a considerable evolution in both technology and video coverage since that time (see Holman & Stanley (2007) for a discussion of the historical evolution of Argus data collection). From 1986 to 1992 images were captured by videotape and post-processed into useful image products. A single camera viewed the beach to the north of the 43 m FRF observation tower, just to the north of the FRF pier. In 1992, data collection was automated but continued with single camera coverage until 1995 when offshore and southward-facing cameras were added, still leaving data gaps to the northeast and southeast. These were filled in 1997 with the addition of two further cameras to form a five-camera set that spanned the full coastal field view. In 2005, the older analog cameras were replaced by higher resolution digital cameras that have run since that time. Each image has ground control points (GCP’s) which are used to determine the camera’s orientation relative to the ground topography. These GCP’s allow for a photogrammetric trans-formations of image coordinates to ground coordinates according to the method outlined in Hollandet al. (1997).
foam over these features, and also for observing variability in the shoreline since the white shore break has been shown to occur near the still water shoreline (Plant & Holman, 1997).
Figure 2.4: Example of the five types of images collected by the Argus System at Duck (lower) and a rectified
timex image (upper).
Figure 2.5:Resolution maps for Duck area showing the resolution in meters in the cross-shore (white) and
along-shore (black) directions. The red box is the region of interest.
2.4 Quality control
The data were partitioned into subsets before and after 1997 because before 1997 the station had less than 5 cameras (only one up to 1995, then three) and because image resolution and frequency improved significantly in later years at the Duck Argus Station. Over the many years of data collection, images were sometimes unusable for a variety of reasons including fog or rain. While the Kalman filter deals with quality variations, it was determined that sufficiently bad images such as foggy days should be omitted from further analysis based on objective quality control measures. Quality control was based on the error variance (R) which depended
on the width of the Gaussian function asL2. It was found that when more than 40% of the values
of measured error variance in a histogram were between 350 and 400 (i.e., near the maximum Lvalue based on,L= 20 m), the images were of poor quality (rainy day, glare day, or loss of shoreline tracking). These images were considered bad data and were eliminated.
Figure 2.7 shows two examples from Duck, of poor quality images that were discarded and their associated histograms. For the pre-1997 Duck data, 20.20% of the data were discarded (3574 out of 17695 shorelines extracted). After 1997, 11.02% of the data were removed (5745 out of 52138 estimates shorelines).
Figure 2.7:Two examples from Duck showing images with poor quality that were discarded from the data set. In
each image, the upper panel is the rectified timex images with poor quality, and the lower panel is the histogram of
the error variance of the predicted state (R). The dash red line indicates the 40% value.
2.5 Comparison against ground truth
A comparison between ASLIM results and survey data was used to validate our shoreline
model. The surveys were carried out by the FRF crew using the LARC (http://www.frf.usace.army.mil/larc/larcsystem.stm), and the data are referenced at NAV88 datum, with the shoreline located at z = 0 m. Five
shows the location (yellow triangles) of the 5 profiles. Figure 2.8 shows the relation between the ASLIM positions and the shoreline obtained by the surveys at the 5 profiles. The results ob-tained by the ASLIM model showed good agreement with the surveys data, with a correlation coefficient of r = 0.85, with 95% confidence intervals of 0.78 and 0.88, rmse error of 5.1 meters and a least square slope of 0.90. TheR2 was equal 0.92.
Figure 2.8: Comparison between surveys data and ASLIM model (R2 = 0.92; r = 0.85 with 95% confidence intervals of 0.78 and 0.88; and slope of 0.90). The dash gray line indicates along the 1:1 relationship.
2.6 Results
2.6.1 Wave Forcing
Figure 2.9 shows the daily wave data collection for Duck extracted from the FRF’s 8m Array pressure array. Because there was no alternate source of wave direction data during the data gap from January,1988 to September, 1988, the wave analysis will be restricted to the period between September, 1988 to December, 2012. The lower panel shows the wave energy flux (|P|) which was decomposed into a cross-shore (Px =|P|cos(α)) and alongshore (Py =|P|sin(α))
components, where α is the wave direction, measured positive counter-clockwise from shore normal (the x-axis is positive towards offshore and y-axis is positive towards north-northwest). Significant wave heights can reach values over 5 meters. We also see an annual signal where lower energy waves come from one direction in one season and a different direction and more energy later. On the wave energy flux figures, we observed thatPx, as expected, is more intense
with transport towards the shoreline (negative sign). Py is less intense with transport most
frequently towards north-northwest. The average alongshore transport was 932.56 W/m with a standard deviation of 4989.4 W/m and the average cross-shore transport was -9319 W/m with a standard deviation of 16301 W/m (Table 2.1).
Mean and standard deviations as well as 24-year trends were computed for each variable and are listed in Table 2.1. The means are based on the daily time series from figure 2.9. From the table, we observe that the mean wave height is 0.88±0.55 meters and mean period for the regions is 9±2.24 seconds and the predominant wave direction is from east-northeast (the wave direction is based on the true north). This predominant direction can also be observed through the wave directional probability distribution illustrated in figure 2.10, where most of the wave distribution are located between east-northeast. The time series were also tested for the presence of trends (Table 2.1). For the wave heights the trend was 5.7x10−4with 95% of confidence level
of 4.6x10−3 m/year; for wave period the slope was 1.8x10−2 with 95% of confidence level of
9x10−3 s/year and for wave direction the trend was 0.18 with 95% of confidence level of 0.18
degrees/year. Px had a slope of -33.84 with 95% of confidence level of 87.93 W/year and for
(a) (b)
(c)
(d) (e)
Figure 2.9: Wave conditions at Duck extracted from the FRF’s 8m Array pressure gauges: (a) significant wave
height (m), (b) peak period (s), (c) wave direction (degrees), (d) cross-shore wave energy flux (W/m) and (e)
alongshore wave energy flux (W/m). Data gaps mostly correspond to days with no data. Positive alongshore
wave energy flux corresponds to transport to north, while negative cross-shore wave energy flux is associated with
Table 2.1:Wave statistics during the period of study based on a daily wave time series.
Wave Parameter Mean Std Max Min Range Trend
Hsig (m) 0.88 0.55 5.21 0.18 5.03 5.7x10−4 ±4.6x10−3
Tp (s) 9.03 2.24 19.0 3.35 15.61 1.8x10−2 ±9x10−3
Dir (deg) 79.30 18.62 152.62 8 144.62 0.18±0.18
Px (W/m) -9319 16301 -93.08 -2.93x105 2.93x105 -33.84±87.93
Py (W/m) 932.49 4989.4 2.27x105 -56881 2.84x105 59.64±15.77
Figure 2.10:Wave rose of significant wave height (left) and wave period (right). The dash line represent the Duck
coastline in relation to the true north.
The annual cycle of wave forcing data can be found by averaging values partitioned by month (Figure 2.11). Wave heights show a seasonal cycle and are more energetic and stormier (higher standard deviation) during fall and winter time and less energetic and stormy during the spring-summer. Monthly-averaged wave direction follows a similar cycle with wave ap-proach coming from more southerly directions during the summer months and near shore nor-mal through the more energetic months. Average wave periods are surprisingly uniform through the year.
This pattern is also observed in the cross-shore and longshore wave energy fluxes (Px and
Py) which are directly dependent of the wave direction and wave height. Cross-shore wave
energy flux is small and steady during the spring-summer and large and variable during the fall-winter. The monthly-averaged alongshore wave energy flux (Py) is always slightly to the
is still commonly from the south.
(a) (b)
(c)
(d) (e)
Figure 2.11:Annual signal of the wave parameters: (a) significant wave height (m), (b) wave period (s), (c) wave
direction (deg), (d) cross-shore wave energy flux (W/m), and (e) alongshore wave energy flux (W/m). Solid lines
show the monthly means while dashed lines are spaced one standard deviation away. The horizontal line in panel
c indicates the direction of shore normal.
duration > 8 hours) for Duck, during the years of 1980 to 2014. Late spring and summer are quiet months while storms are spread fairly evenly throughout the rest of the year. March is historically the stormiest month.
Figure 2.12: Number of storms with waves > 2 meters and duration > 8 hours by months for Duck, during the
years of 1980 to 2014.
Figure 2.13 shows the power spectral density (PSD) ofHsig,PyandPx. In all cases, the peak
energy lies at 1 and 2 cycles per year corresponding to the annual cycle and its first harmonic. The spectrum forHsig is generally flat (white) up to a frequency of 20 cycles per year (up to the
weather band) before falling by about two orders of magnitude over the next decade, consistent with a power law off−2 over the weather band. The PSD for the cross-shore and alongshore
wave energy flux present the same pattern, but with Px being about ten times as energetic.
Decay of energy in the weather band is weaker, being approximatelyf−1forP
(a)
(b)
Figure 2.13: (a) Power spectral density for the wave height, and (b) for the cross-shore (black line) and
along-shore wave energy fluxes (red line). The dashed gray lines are indicative of the annual, semi-annual and 20 days
Table 2.2 shows the amplitudes (Amp=√2V ar) and percentages of the variance explained
by each cycle forHsig, cross-shore and alongshore wave energy flux. Despite showing the
low-est spectral levels, the weather cycle explains the larglow-est fraction (roughly 2/3) of the variance for the three parameters due to the wide frequency range over which it acts (total variance in a band is the area under the spectrum in that band). The intra-annual cycle is the next-most important contributor followed by the annual and then inter-annual cycles.
One conclusion of this analysis is that the vast majority of variability in forcing is at annual or shorter scales with only 1-2% of the variability at inter-annual time scales. This would imply that the shoreline response should similarly lack inter-annual variability.
Table 2.2: Amplitudes (Amp) and percentages of the variance (% Var) explained by each cycle for the wave
parameters:Hsig,PxandPy
Hsig Px Py
Cycles Amp (m) % Var Amp (m) % Var Amp (m) % Var
Inter-annual 0.09 1.47 2847.1 1.52 1143.4 2.63
Annual 0.18 5.38 3587.8 2.42 515.18 0.53
Intra-annual 0.44 32.35 12489 29.35 3369.60 22.81
Weather 0.60 60.79 18826 66.69 6061.30 73.80
2.6.2 Shoreline Response
This section describes the response of the shoreline at Duck to the wave forcing described above. Figure 2.14 is a space-time plot, or timestack, which shows the time dependence of shoreline position as a function of alongshore position. This figure also shows analysis parti-tions into two data sets (26 years and 16 years) that represent the full 26 year period for which data were available for y >= 800 m, and the 16 years of data for which better camera coverage allowed analysis over the full 1500 m alongshore distance.
for example the shoreline immediately north of the pier being typically landward of that on the south side.
In the following, we will parse the shoreline signals into the mean and deviations about the mean, then analyze both the longshore and temporal variability and their relationship to wave forcing.
Figure 2.14:Space-time plot of the shoreline position as a function of alongshore location and time. The FRF pier
is shown by the black line in the middle of the plot and the data sets for 26 years and 16 years are illustrated by the
red and green rectangles, respectively. For reference, a rectified timex image is provided at the bottom. Hot colors
indicate seaward shoreline positions while cold colors indicate that landward shoreline positions. White indicates
Figure 2.15 shows the mean shoreline positions and its standard deviation for both data sets. The influence of the pier is apparent and appears to cause approximately 15 m excursion anoma-lies in the adjacent several hundred meters, in contrast to the original long, straight shoreline that was found prior to the FRF pier construction in 1977 (Mason, pers. comm.). The statistics in the region of overlap at y >= 800 m show small differences (∼3 m) presumably associated with the stronger accretionary signal in the early 1990’s. The standard deviation (dashed gray lines) appear surprisingly alongshore-uniform at 9 m±1 m for y < 800 m and broadening by 2 m to the north.
Figure 2.15: Mean shoreline positions for the 16 years (long black line) and the 26 years (short solid line) data
sets. The dash gray lines represent±one standard deviation. The FRF pier (blue line) is plotted for reference.
Figure 2.16:Shoreline distribution and cumulative probability density for the shoreline position for the 16 years
data set as a function of longshore location. The black contours are the cumulative probability.
Temporal variability
The time variability of alongshore-average shoreline position<xˆo>y (t)is shown in figure
2.17 for both data sets. We observe that the expected annual signal is not apparent. Instead, the shoreline response appears to be dominated by inter-annual signals at near-decade time scales and a later trend, in contrast to the near absence of an inter-annual component in the forcing. The higher recent erosion rates for the 26 year data set (y≥800 only) is related to the late erosion to the north of the pier, a trend not equally seen to the south.
Figure 2.17:The alongshore-averaged shoreline position<xˆo>y(t)for the 26-year (blue line) and 16-year (red line) data sets.
Figure 2.18: Slopes from the linear regression as a function of alongshore locations and 95% confidence levels
(red and green dash lines) for the 26 and 16 year data sets (short lines correspond to the 26 year data set). The FRF
pier location (thick black line) is plotted for reference.
In the following analysis, we wish to examine the shoreline variability about the mean shore-line. We will refer to this as shoreline deviations (x′
o(y, t)), obtained by:
x′
o(y, t) = xbo(y, t)−xo(y) (2.7)
wherexo(y)is the time-mean shoreline andxbo(y, t)are the shoreline positions as a function of
time and y.
Figure 2.19 shows a space-time plot of the shoreline deviations as a function of alongshore location and time. In this figure, cold colors indicate a landward, or erosive position, and hot colors seaward, or accretionary, deviations of shoreline position. This figure is similar to figure 2.14 but without the distraction of the mean shoreline structure.
of sediment between the north and south sides of the pier are more apparent, for example in 1999 and 2002.
Figure 2.19:Space-time plot of the shoreline deviations as a function of alongshore location and time. Cold colors
indicate a erosive position and hot colors accretionary deviations of shoreline position.
and erosion to the north. Thus, accretion on one side will be accompanied by erosion on the other, illustrating the influence of the pier in partially blocking alongshore transport. From this figure, we note that the region of the pier influence is at least 500 m, much larger than the in-fluence region assumed in a number of publications (e.g. Plantet al. (1999) estimated 200 m; Miller & Dean (2007) found 300 m). The erosion signal from July to December to the north of the pier features a landward shoreline anomaly of about 5 m that progresses away from the pier at approximately 100 m per month. An equivalent but weaker winter erosive signal on the south propagates away from the pier at about 50 m per month.
(a)
(b)Annual signal removed (c) Annual and semi-annual signals
re-moved
Figure 2.20:Monthly averaged shoreline deviations. Hot colors indicate accretion (seaward positions) and cold
colors indicate erosion (landward position).
Power spectra for the shoreline data is shown in figure 2.21. Gray lines are over-plots of spectra for each alongshore location while the red spectra in both figures are the alongshore-averaged power spectra for both data sets. The dominant characteristic of these spectra is the surprisingly linear decay (in a log-log format) of variance with frequency, consistent with a power law format,f−α. From the least-squares slope fit for the 26 year data set, the coefficient
be -1.74±0.015 with anR2 of 0.93.
The annual cycle is apparent in both data sets while the semi-annual harmonic (2 cy-cles/year), present in the wave forcing records, is not visible in the shoreline response. The spectra also show inter-annual energy located in broad peaks such as the one centered on the period of 7 years (figure 2.21a) and one centered at 4 years in the PSD for the 16 year data set. There is also a narrow peak at the period of 14.78 days in figure 2.21a that is not apparent in the shorter data set, figure 2.21b. This is actually a frequency alias due to the once-per-day data sampling strategy used between the years of 1986 to 1993. This sampling rate implies in an under-sampling of the M2 tide with a predicted alias to a period of 14.78 days, the same as observed. Despite the attempted removal of tidal effects in computing xˆo, the assumption of
(a)
(b)
Figure 2.21:Power spectra of the base shoreline for 26 years (a) and 16 years (b). The red lines are the
alongshore-averaged PSDs and the gray lines represent the PSDs (dof = 2) of each of the 181 (upper panel) and 601 (lower
panel) y-locations. The 95% confidence interval applies to the average spectra.
