Spectral Quantification of Nonlinear Behaviour of the Nearshore Seabed and Correlations with Potential Forcings at Duck, N.C., U.S.A

Local bathymetric, quasi-periodic patterns of oscillation are identified from 26 years of monthly profile surveys taken at two shore-perpendicular transects at Duck, North Carolina, USA. The data cover both the swash and surf zones. Singular Spectrum Analysis (SSA) and Multi-channel Singular Spectrum analysis (MSSA) methods are applied, on the shoreface, to three potential forcings: the monthly wave heights, the monthly mean water levels and the large scale atmospheric index known as the North Atlantic Oscillation. The patterns within these forcings are compared to the local bathymetric patterns; it is found that the patterns extracted using SSA and MSSA agree well with previous patterns identified using wavelets and confirm the highly non-stationary behaviour of beach levels at Duck. This is followed by analysis of potential correlations between the local bathymetry (at the two transects) and hydrodynamic and atmospheric patterns. The study is then extended to all measured bathymetric profiles, covering an area of 1100 m (alongshore) by 440 m (cross-shore). MSSA showed no collective inter-annual patterns of oscillations present in the bathymetry and the three potential forcings. Annual and semi-annual cycles within the bathymetry are found to be strongly correlated with the monthly wave height, in agreement with the SSA findings. Other collective intra-annual cycles besides the semi-annual were identified; they were all correlated with the North Atlantic Oscillation.

[1]  Donald G. Bailey,et al.  An Inter-Site Comparison of Net Offshore Bar Migration Characteristics and Environmental Conditions , 1999 .

[2]  R. Gilmore,et al.  The Topology of Chaos: Alice in Stretch and Squeezeland , 2002 .

[3]  W. Birkemeier.  Time Scales of Nearshore Profile Changes , 1984 .

[4]  J. W. Tukey,et al.  The Measurement of Power Spectra from the Point of View of Communications Engineering , 1958 .

[5]  Kathelijne Mariken Wijnberg,et al.  Intersite comparison of interannual nearshore bar behavior , 2003 .

[6]  F. Cayocca,et al.  Long-term morphological modeling of a tidal inlet: the Arcachon Basin, France , 2001 .

[7]  Hiroshi Akima,et al.  A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures , 1970, JACM.

[8]  L. Wright,et al.  Morphodynamic variability of surf zones and beaches: A synthesis , 1984 .

[9]  D. Sornette,et al.  Data-adaptive wavelets and multi-scale singular-spectrum analysis , 1998, chao-dyn/9810034.

[10]  William A. Birkemeier,et al.  Beach and nearshore survey data : 1985-1991 CERC Field Research Facility / by Guan-hong Lee, William A. Birkemeier, Coastal Engineering Research Center ; prepared for U.S. Army Corps of Engineers. , 1993 .

[11]  D. Bailey,et al.  A Review of Net Offshore Bar Migration with Photographic Illustrations from Wanganui, New Zealand , 1999 .

[12]  David Ruelle,et al.  Deterministic chaos: the science and the fiction , 1995 .

[13]  R. Kirby,et al.  Medium timescale stability of tidal mudflats in Bridgwater Bay, Bristol Channel, UK: Influence of tides, waves and climate , 2008 .

[14]  P. Mote,et al.  Intraseasonal variations of water vapor in the tropical upper troposphere and tropopause region , 2000 .

[15]  G. Różyński.  Data-driven modeling of multiple longshore bars and their interactions , 2003 .

[16]  R. Dean,et al.  Shoreline variability via empirical orthogonal function analysis: Part I temporal and spatial characteristics , 2007 .

[17]  William A. Birkemeier,et al.  Beach and nearshore survey data, 1981-1984, CERC Field Research Facility / by Peter A. Howd, William A. Birkemeier, Coastal Engineering Research Center ; prepared for Department of the Army, US Army Corps of Engineers. , 1987 .

[18]  R. Holman,et al.  The spatial and temporal variability of sand bar morphology , 1990 .

[19]  Michael Ghil,et al.  ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES , 2002 .

[20]  B. G. Ruessink,et al.  Multivariate analysis of nonlinearity in sandbar behavior , 2008 .

[21]  Ying Li,et al.  Multi-scale variability of beach profiles at Duck: A wavelet analysis , 2005 .

[22]  Shirley Dowdy,et al.  Statistics for Research , 1983 .

[23]  Robert F. Cahalan,et al.  Sampling Errors in the Estimation of Empirical Orthogonal Functions , 1982 .

[24]  Robert J. Nicholls,et al.  Evaluation of depth of closure using data from Duck, NC, USA , 1998 .

[25]  Douglas L. Inman,et al.  Edge waves and crescentic bars , 1971 .

[26]  Coherent Coastal Sea-Level Variability at Interdecadal and Interannual Scales from Tide Gauges , 2006 .

[27]  Michael Ghil,et al.  Intraseasonal oscillations in the global atmosphere. I - Northern Hemisphere and tropics , 1991 .

[28]  M. Ghil,et al.  Trends, interdecadal and interannual oscillations in global sea-surface temperatures , 1998 .

[29]  Magnus Larson,et al.  Forced and self-organized shoreline response for a beach in the southern Baltic Sea determined through singular spectrum analysis , 2001 .

[30]  H. N. Southgate,et al.  Fractal properties of coastal profile evolution at Duck, North Carolina , 2000 .

[31]  R. Holman,et al.  Remote Sensing of Nearshore Bar Systems—Making Morphology Visible , 1987 .

[32]  Grzegorz Różyński,et al.  Long-term evolution of Baltic Sea wave climate near a coastal segment in Poland; its drivers and impacts , 2010 .

[33]  Kathelijne Mariken Wijnberg,et al.  Extracting decadal morphological behaviour from high-resolution, long-term bathymetric surveys along the Holland coast using eigenfunction analysis , 1995 .

[34]  A. Long,et al.  Sea level is not level: the case for a new approach to predicting UK sea-level rise , 2008 .

[35]  William A. Brenneman.  Statistics for Research , 2005, Technometrics.

[36]  B. G. Ruessink,et al.  The behaviour of a multiple bar system in the nearshore zone of Terschelling, the Netherlands: 1965–1993 , 1994 .

[37]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[38]  Aslak Grinsted,et al.  Nonlinear Processes in Geophysics Application of the Cross Wavelet Transform and Wavelet Coherence to Geophysical Time Series , 2022 .

[39]  Giovanni Coco,et al.  A mechanism for the generation of wave‐driven rhythmic patterns in the surf zone , 2000 .

[40]  A J Bowen,et al.  Simple Models of Nearshore Sedimentation, Beach Profiles and Longshore Bars , 1980 .

[41]  G. Plaut,et al.  Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere. , 1994 .

[42]  B. Latteux,et al.  Approaches to long-term modelling of coastal morphology : A review , 1993 .

[43]  R. D. Shand.  Bar Splitting: System Attributes and Sediment Budget Implications for a Net Offshore Migrating Bar System , 2024, Journal of Coastal Research.

[44]  G. Różyński,et al.  Quasi-Seasonal Morphological Shore Evolution Response to Variable Wave Climate , 1999 .

[45]  Medium-term variations of bar properties and their linkages with environmental factors at Hasaki, Japan , 2008 .

[46]  R. Nicholls,et al.  Storm-driven variability of the beach-nearshore profile at Duck, North Carolina, USA, 1981-1991 , 1998 .

[47]  R. Holman,et al.  Bars, bumps, and holes: Models for the generation of complex beach topography , 1982 .

[48]  G. Różyński.  Long-term shoreline response of a nontidal, barred coast , 2005 .

[49]  Michele Capobianco,et al.  Analysis of field data of coastal morphological evolution over yearly and decadal time scales. Part 2 Non-linear techniques , 2003 .

[50]  Jose M. Horrillo-Caraballo,et al.  An investigation of the link between beach morphology and wave climate at Duck, NC, USA , 2008 .

[51]  R. A. Holman,et al.  High‐energy nearshore processes , 1986 .

[52]  Generation and nonlinear evolution of shore-oblique/transverse sand bars , 2006, Journal of Fluid Mechanics.

[53]  A. Bowen,et al.  Edge waves and surf beat , 1978 .

[54]  M. Allen,et al.  Distinguishing modulated oscillations from coloured noise in multivariate datasets , 1996 .

[55]  D. Ruelle,et al.  The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[56]  R. Nicholls,et al.  Storms, Storm Groups and Nearshore Morphologic Change , 1999 .

[57]  R. Vautard,et al.  Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series , 1989 .

[58]  Sanjay S. P. Rattan,et al.  Non-linear complex principal component analysis of nearshore bathymetry , 2004 .

[59]  Nicholas C. Kraus,et al.  Temporal and spatial scales of beach profile change, Duck, North Carolina , 1994 .

[60]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[61]  Nathaniel G. Plant,et al.  A simple model for interannual sandbar behavior , 1999 .

[62]  Aart Kroon,et al.  Barred beaches , 2002 .

[63]  J. Horrillo-Caraballo,et al.  Statistical analysis and forecasts of long-term sandbank evolution at Great Yarmouth, UK , 2008 .

[64]  B. G. Ruessink,et al.  The behaviour of nearshore bars on the time scale of years: a conceptual model , 2000 .

[65]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[66]  Roshanka Ranasinghe,et al.  The Southern Oscillation Index, wave climate, and beach rotation , 2004 .

[67]  D. Reeve,et al.  An investigation of the multi-scale temporal variability of beach profiles at Duck using wavelet packet transforms , 2007 .

[68]  Suzanne J.M.H. Hulscher,et al.  Understanding coastal morphodynamics using stability methods , 2003 .

[69]  D. Inman,et al.  Description of seasonal beach changes using empirical eigenfunctions , 1975 .

[70]  Steve Elgar,et al.  Observations of sand bar evolution on a natural beach , 1998 .

[71]  J. Rogers.  The Association between the North Atlantic Oscillation and the Southern Oscillation in the Northern Hemisphere , 1984 .