Statistical modeling of the long-range-dependent structure of barrier island framework geology and surface geomorphology

Abstract

Shorelines exhibit long-range dependence (LRD) and have been shown in some environments to be described in the wave number domain by a power-law characteristic of scale independence. Recent evidence suggests that the geomorphology of barrier islands can, however, exhibit scale dependence as a result of systematic variations in the underlying framework geology. The LRD of framework geology, which influences island geomorphology and its response to storms and sea level rise, has not been previously examined. Electromagnetic induction (EMI) surveys conducted along Padre Island National Seashore (PAIS), Texas, United States, reveal that the EMI apparent conductivity (σa) signal and, by inference, the framework geology exhibits LRD at scales of up to 101 to 102 km. Our study demonstrates the utility of describing EMI σa and lidar spatial series by a fractional autoregressive integrated moving average (ARIMA) process that specifically models LRD. This method offers a robust and compact way of quantifying the geological variations along a barrier island shoreline using three statistical parameters (p, d, q). We discuss how ARIMA models that use a single parameter d provide a quantitative measure for determining free and forced barrier island evolutionary behavior across different scales. Statistical analyses at regional, intermediate, and local scales suggest that the geologic framework within an area of paleo-channels exhibits a first-order control on dune height. The exchange of sediment amongst nearshore, beach, and dune in areas outside this region are scale independent, implying that barrier islands like PAIS exhibit a combination of free and forced behaviors that affect the response of the island to sea level rise.