Cumulative versus transient shoreline change : dependencies on temporal and spatial scale

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 116 (2011): F02014, doi:10.1029/2010JF001835.Using shoreline change measurements of two oceanside reaches of the North Carolina Outer Banks, USA, we explore an existing premise that shoreline change on a sandy coast is a self-affine signal, wherein patterns of change are scale invariant. Wavelet analysis confirms that the mean variance (spectral power) of shoreline change can be approximated by a power law at alongshore scales from tens of meters up to ∼4–8 km. However, the possibility of a power law relationship does not necessarily reveal a unifying, scale-free, dominant process, and deviations from power law scaling at scales of kilometers to tens of kilometers may suggest further insights into shoreline change processes. Specifically, the maximum of the variance in shoreline change and the scale at which that maximum occurs both increase when shoreline change is measured over longer time scales. This suggests a temporal control on the magnitude of change possible at a given spatial scale and, by extension, that aggregation of shoreline change over time is an important component of large-scale shifts in shoreline position. We also find a consistent difference in variance magnitude between the two survey reaches at large spatial scales, which may be related to differences in oceanographic forcing conditions or may involve hydrodynamic interactions with nearshore geologic bathymetric structures. Overall, the findings suggest that shoreline change at small spatial scales (less than kilometers) does not represent a peak in the shoreline change signal and that change at larger spatial scales dominates the signal, emphasizing the need for studies that target long-term, large-scale shoreline change.Our thanks to the NSF (grant EAR‐04‐ 44792) for funding this researc

Upper-Truncated Power Law Distributions

Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhibit a fall-off from a power law at the largest object sizes. Previous work has often either ignored the fall-off region or described this region with a different function. We demonstrate that when a data set is abruptly truncated at large object size, fall-off from a power law is expected for the cumulative distribution. Functions to describe this fall-off are derived for both linearly and logarithmically binned data. These functions lead to a generalized function, the upper-truncated power law, that is independent of binning method. Fitting the upper-truncated power law to a cumulative number-size distribution determines the parameters of the power law, thus providing the scaling exponent of the data. Unlike previous approaches that employ alternate functions to describe the fall-off region, an upper-truncated power law describes the data set, including the fall-off, with a single function

Geologic Structure and Hydrodynamics of Egmont Channel: An Anomalous Inlet at the Mouth of Tampa Bay, Florida

High-resolution bathymetry surveys of Egmont Channel were conducted in 1999 and 2001 using a Kongsberg Simrad EM 3000 multibeam bathymetric system. These data were supplemented with other bathymetry data, seismic profiles, underwater scuba observations, and current velocity data, in order to investigate the geologic and hydrodynamic characteristics of Egmont Channel. Bounded to the north by a linear steep scarp (∼38°) and by a more gradual slope (\u3e10°) to the south Egmont Channel is an asymmetric tidal inlet and the main shipping channel for Tampa Bay, Florida. The cross sectional area (17,964 m2) and the tidal prism (6×108 m3) for Egmont Channel were derived in this study. Currents measured at Egmont Deep and the Sunshine Skyway Bridge (∼11 km away) with Acoustic Doppler Current Profilers, have a high correlation (97%) indicating the current velocities at Sunshine Skyway Bridge can be used as a proxy for current velocities at Egmont Deep. Seismic profile data indicate that both the mouth of Tampa Bay and the bay proper contain many stratigraphically controlled depressions. Egmont Deep is located at one of these depressions. Bathymetry and seismic data indicate that the main ebb jet for Egmont Channel is deflected northward by a local stratigraphic high located at the north end of Egmont Key. The repeated high-resolution multibeam bathymetric surveys document sediment bedform migration. The bottom characteristics of the deep fluctuate due to the erosion and deposition of gravelwaves. Analysis of seismic data and SCUBA observations suggest that the most likely origin for Egmont Deep is a combination of erosion-resistant limestone strata interspersed with pockets of dissolution which is overlain by an irregular bed of mobile sediments. The strong tidal current scour maintains the depth of the feature and assures that any sediment that becomes incorporated in the deep is short-lived

Comparisons of Gravity Anomalies at Pseudofaults, Fracture Zones, and Nontransform Discontinuities from Fast to Slow Spreading Areas

Published mechanisms for rift tip propagation at spreading centers include extensional deformation and an initial period of slow spreading. We investigate whether the gravity signal and inferred crustal structure at pseudofaults formed in medium to superfast spreading environments resemble the gravity signal at fracture zones or nontransform discontinuities formed in slow spreading environments. We find that altimetry-based gravity anomalies on the Mathematician, Bauer, Easter, Juan Fernandez, and northern Chile Ridge pseudofaults, located in 75–150 mm/yr (full rate) seafloor spreading environments, are similar in amplitude and form to Atlantic fracture zones with 20–30 mm/yr spreading rates. A 5–15 mGal positive mantle Bouguer anomaly is observed on the pseudofault bounding the eastern Juan Fernandez microplate, comparable to those at some similar age-offset nontransform discontinuities in slow spreading environments. Our results suggest that the deeps associated with active propagating rift tips result from both a dynamic mantle component and anomalous crust, the latter of which remains frozen at pseudofaults. We predict that any pseudofaults with age offsets more than ∼1 m.y. and not coincident with hotspot volcanism will be associated with thin (and possibly unusually dense) crust, even in superfast seafloor spreading environments