Multivariate analysis of nonlinearity in sandbar behavior

Pape, Leo; Ruessink, Gerben

doi:10.5194/npg-15-145-2008

Cited by 15 publications

(10 citation statements)

References 40 publications

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“…In most cases, the model used is a linear autoregressive model [e.g. Rubin , 1992, 1995; Bryan and Coco , 2007], but it can be nonlinear (see review in Abarbanel [1986]) or depend on second independent time series, such as a forcing time series [ Jaffe and Rubin , 1996; Pape and Ruessink , 2008]. Here, we use the simplest form, an autoregressive model, to forecast the time series, x at time t , into future time steps d : where Δ t is the time lag between points, a j+1 are coefficients, and m is the length of the sequences used to make the forecast (plaquette size or embedding dimension).…”

Section: Methodsmentioning

confidence: 99%

“…A technique that has been developed to assess the relative contribution of the global versus the local properties in a time series is nonlinear forecasting [ Farmer and Sidorowich , 1987; Sugihara and May , 1990]. This has been used to examine the behavior of a wide range of natural time series, for which techniques that require stationarity have provided limited insight: for example, phytoplankton population dynamics [ Sugihara , 1994], the electrical precursor signals to earthquakes [ Cuomo et al , 1998], synthetic swash time series [ Bryan and Coco , 2007], surf zone bar behavior [ Holland et al , 1999; Pape and Ruessink , 2008] and surf zone suspended sediment patterns [ Jaffe and Rubin , 1996]. The technique is based on the premise that, if the statistical properties of the time series vary locally, a simple data‐driven model will perform better if only trained using a fraction of the available training data set.…”

Section: Introductionmentioning

confidence: 99%

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Observations of nonlinear runup patterns on plane and rhythmic beach morphology

Bryan¹,

Coco²

2010

J. Geophys. Res.

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[1] Application of nonlinear forecasting and bispectral analysis to video observations of runup over cuspate topography shows that these alongshore patterns in the morphology are accompanied by changes to the fundamental behavior of the runup time series. Nonlinear forecasting indicates that at beach cusp horns, the behavior of swash flow is more predictable and global (meaning that characteristics of individual swash events are well represented by the behavior of the time series as a whole). Conversely, at beach cusp bays, the behavior of swash flow is less predictable and more local (meaning that the characteristics of individual swash events are best represented by the behavior of a small fraction of the time series). Bispectral analysis indicates that there is a nonlinear transfer of energy from the incident wave frequency f to the infragravity frequency ∼f/2 which only occurs in the bay, suggesting that the local behavior is caused by interactions between successive swash cycles which are magnified by channeling caused by the beach cusp geometry. The local behavior and the bispectral signatures are not present in offshore measurements, and they are not present in runup time series collected when the beach was planar. These results provide evidence that interactions between successive runups are a fundamental characteristic of beach cusp bays. Ultimately, these interactions could lead to the growth of an infragravity wave with an alongshore wavelength forced by the presence of beach cusps.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observations of nonlinear runup patterns on plane and rhythmic beach morphology

Bryan¹,

Coco²

2010

J. Geophys. Res.

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“…The analyses in the present work are based on three data sets obtained at: (1) the Gold Coast, Australia [ Turner et al , 2004], (2) Egmond, The Netherlands [ Pape and Ruessink , 2008] and (3) Hasaki, Japan [ Kuriyama et al , 2008].…”

Section: Observationsmentioning

confidence: 99%

On cross‐shore migration and equilibrium states of nearshore sandbars

2010

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[1] The location of submerged sandbars in the nearshore zone changes over time in response to variability in wave conditions. Here, cross-shore sandbar migration is studied with an empirical model consisting of a differential equation relating cross-shore sandbar migration to wave forcing. Model parameters are fitted to data sets containing multiple years of daily-observed positions of five sandbars at three field sites. From the fitted model parameters we determine the cross-shore location of zero-migration (equilibrium location), the stability of this equilibrium, and the rate (response time) at which a sandbar migrates toward or away from the equilibrium location. We find that for breaking waves a sandbar moves toward a stable, wave-height-dependent equilibrium location. For non-to slightly-breaking waves, however, a sandbar moves away from the equilibrium location, implying that the beach profile evolves toward a state without submerged sandbars. The response times can differ up to a factor three for different sandbars at a particular field site, and a factor ten between sandbars at different sites. For breaking waves, response times are found to decrease with increasing wave height from months to days, while for non-to slightly-breaking waves response times exceed several months. In general, response times remain larger than the timescale of variability in wave climate (several days), implying that sandbars spend most of their lifetime out of equilibrium with the wave forcing. The model is able to hindcast the relevant features of cross-shore sandbar migration on timescales of days to several years, and outperforms a baseline prediction of no change for all sandbars. When the equilibrium location is reached by both the hindcasted and actual sandbar, the hindcast error depends on the accuracy of the predicted equilibrium location only, and no longer on the history of accumulated errors. As a result, sandbars that occasionally reach their equilibrium location can accurately be predicted from the wave forcings over their entire lifespan. However, it is difficult to predict the exact rate of the yearly to interannual trends that are observed at two field sites, because the sandbars at these sites never reach the offshore-located equilibrium states associated with high waves.Citation: Pape, L., N. G. Plant, and B. G. Ruessink (2010), On cross-shore migration and equilibrium states of nearshore sandbars,

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“…Local wave heights were computed with the Battjes‐Janssen wave transformation model [ Battjes and Janssen , 1978; Battjes and Stive , 1985] at a fixed point 50 m offshore of the seaward end of the sandbar zone, where the waves are not yet affected by the presence of the sandbar. This procedure is explained in detail in the work of Pape and Ruessink [2008]. The time series of offshore‐measured and locally computed wave heights are depicted in Figure 1c, and the time series of offshore‐measured wave periods are given in Figure 1d.…”

Section: Observationsmentioning

confidence: 99%

Models and scales for cross‐shore sandbar migration

2010

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[1] We investigate the long-term (months to years) predictability of cross-shore sandbar migration with two models that operate on different abstraction levels: (1) a coupled, cross-shore waves-currents-bathymetric evolution model and (2) two data-driven neural network models, based on simplified cross-shore profile representations and daily averaged wave properties. For model calibration, training, and validation, we use a high-resolution 15 yearlong profile data set collected at the Hasaki Oceanographic Research Station in Japan. Sandbar behavior at this field site is characterized by cycles of net-offshore migration with a duration of 1-4 years. We find that all models can produce several general features of sandbar behavior at the studied field site, such as rapid offshore migration, slower onshore return, and net-offshore migration. However, it is difficult to quantitatively predict the offshore-directed trends in sandbar location over time scales of months to years. While simple linear models outperform more detailed nonlinear models, for all models it is difficult to predict long-term sandbar behavior, because of error accumulation in the model's processes over time. Representing processes on a more abstract level (scale aggregation) alleviates error accumulation but does not completely overcome this problem.

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Multivariate analysis of nonlinearity in sandbar behavior

Cited by 15 publications

References 40 publications

Observations of nonlinear runup patterns on plane and rhythmic beach morphology

Observations of nonlinear runup patterns on plane and rhythmic beach morphology

On cross‐shore migration and equilibrium states of nearshore sandbars

Models and scales for cross‐shore sandbar migration

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