Browsing by Author "Murray, A Brad"

Complex feedbacks dominate landscape dynamics over large spatial scales (10s – 100s km) and over the long-term (10s – 100s yrs). These interactions and feedbacks are particularly strong at land-water boundaries, such as coastlines, marshes, and rivers. Water, although necessary for life and agriculture, threatens humans and infrastructure during natural disasters (e.g., floods, hurricanes) and through sea-level rise. The goal of this dissertation is to better understand landscape morphodynamics in these settings, and in some cases, to investigate how humans have influenced these landscapes (e.g., through climate or land-use change). In this work, I use innovative numerical models to study the larger-scale emergent interactions and most critical variables of these systems, allowing me to clarify the most important feedbacks and explore large space and time scales.

Chapter 1 focuses on understanding the shoreline dynamics of pocket (embayed) beaches, which are positioned between rocky headlands and adorn about half the world’s coastlines. Previous work suggested that seasonality or oscillations in climate indices control erosion and accretion along these shorelines; however, using the Coastline Evolution Model (CEM), I find that patterns of shoreline change can be found without systematic shifts in wave forcings. Using Principal Component Analysis (PCA), I identify two main modes of sediment transport dynamics: a shoreline rotation mode, which had been previously studied, and a shoreline “breathing” mode, which is newly discovered. Using wavelet analysis of the PCA mode time series, I find characteristic time scales of these modes, which emerge from internal system dynamics (rather than changes in the wave forcing; e.g., seasonality). To confirm the breathing mode’s existence, I retroactively identified this mode in observations of pocket beach shoreline change from different parts of the world. Characterization of these modes, as well as their timescales, better informs risk assessment and coastal management decisions along thinning shorelines, especially as climate change affects storminess and wave energy variations across the world.

Chapter 2 moves slightly inland to examine how coastal marshes, which provide numerous ecosystem services and are an important carbon sink, respond to climate change and anthropogenic influences. Specifically, I focus on how increasing concentrations of atmospheric CO2 affect marsh resilience to increased rates of sea-level rise relative to inorganic sediment availability and elevated nitrogen levels. Using a meta-analysis of the available literature for marsh plant biomass response to elevated levels of CO2 and nitrogen, I incorporated these effects into a coupled model of marsh vegetation and morphodynamics. Although nitrogen’s effect on biomass and marsh accretion rates is less clear, elevated CO2 causes a fertilization effect, increasing plant biomass, which enhances marsh accretion rates (through increased rates of both in- organic and organic sedimentation). Findings from the model experiments suggest that the CO2 fertilization effect significantly increases marsh resilience to sea-level rise; however, reduced inorganic sediment supply (e.g., through land-use change or damming) still remains a serious threat to marsh survival).

Almost half a billion people live on or near river deltas, which are flat, fertile landscapes that have long been ideal for human settlement, but are increasingly vulnerable to flooding. These landscapes are formed by the repeated stacking of sedimentary lobes, the location and size of which are formed by river channel avulsions, which occur when the river changes course relatively rapidly. Despite the importance of avulsions to delta morphodynamics, we do not fully understand their dynamics(specifically, avulsion location and timing). In order to investigate the relative influence of rivers and waves on delta morphology and avulsion processes, I develop the River Avulsion and Floodplain Evolution Model (RAFEM) and couple it to CEM to create a new morphodynamic river delta model.

In Chapter 3, I use the new coupled fluvial-coastal model to examine the upstream location of avulsions over a range of sea-level rise rates and wave energies. In model experiments, the longitudinal river profile adjusts as the river progrades, causing a preferential avulsion location where the river aggradation relative to the floodplain topography is most rapid. This avulsion length scale is a function of the amount of in-channel sedimentation required to trigger an avulsion, where a larger amount of aggradation required necessitates a greater amount of pre-avulsion progradation. If an avulsion is triggered once aggradation reaches half bankfull channel depth, the preferential length scale is around a backwater length, which scales well with laboratory and field observations.

In Chapter 4, I explore how a wide range sea-level rise rates and wave climates affect both delta morphology and avulsion dynamics with the coupled model. Surprisingly, I find that increasing sea-level rise rates do not always accelerate avulsions. In river-dominated deltas, avulsion time scales tend not to decrease, as upslope river mouth transgression counteracts base-level driven aggradation. I also find that both the sign and magnitude of the wave climate diffusivity affects both avulsion dynamics and large-scale delta morphology. My findings highlight not only important differences between river and wave-dominated deltas, but also prototypical deltas and those created in the lab. Because the wave climate, sea-level rise rate, and amount of in-channel aggradation required to trigger an avulsion all affect rates of autogenic variability operating within the delta, each of these forcings has important implication for avulsion dynamics and stratigraphic interpretation of paleo-deltaic deposits.

Sorted bedforms are spatial extensive (100 m-km) features present on many inner continental shelves with subtle bathymetric relief (cm-m) and localized, abrupt variations in grain size (fine sand to coarse sand/gravel). Sorted bedforms provide nursery habitat for fish, are a control on benthic biodiversity, function as sediment reservoirs, and influence nearshore waves and currents. Research suggests these bedforms are a consequence of a sediment sorting feedback as opposed to the more common flow-bathymetry interaction. This dissertation addresses three topics related to sorted bedforms: 1) Modeling the long-term evolution of bedform patterns, 2) Refinement of morphological and sediment transport relations used in the sorted bedform model with `machine learning'; 3) Development of a new sorted bedform model using these new `data-driven' components.

Chapter 1 focuses on modeling the long term evolution of sorted bedforms. A range of sorted bedform model behaviors is possible in the long term, from pattern persistence to spatial-temporal intermittency. Vertical sorting (a result of pattern maturation processes) causes the burial of coarse material until a critical state of seabed coarseness is reached. This critical state causes a local cessation of the sorting feedback, leading to a self-organized spatially intermittent pattern, a hallmark of observed sorted bedforms. Various patterns emerge when numerical experiments include erosion, deposition, and storm events.

Modeling of sorted bedforms relies on the parameterization of processes that lack deterministic descriptions. When large datasets exist, machine learning (optimization tools from computer science) can be used to develop parameterizations directly from data. Using genetic programming (a machine learning technique) and large multisetting datasets I develop smooth, physically meaningful predictors for ripple morphology (wavelength, height, and steepness; Chapter 2) and near bed suspended sediment reference concentration under unbroken waves (Chapter 3). The new predictors perform better than existing empirical formulations.

In Chapter 3, the new components derived from machine learning are integrated into the sorted bedform model to create a `hybrid' model: a novel way to incorporate observational data into a numerical model. Results suggest that the new hybrid model is able to capture dynamics absent from previous models, specifically, the two observed end-member pattern modes of sorted bedforms (i.e., coarse material on updrift bedform flanks or coarse material in bedform troughs). However, caveats exist when data driven components do not have parity with traditional theoretical components of morphodynamic models, and I address the challenges of integrating these disparate pieces and the future of this type of `hybrid' modeling.

My doctoral work stems from an original motivation to understand more closely why some areas of sandy coastlines erode and others accrete<—>an intriguing fundamental question and one of societal relevance wherever human coastal infrastructure exists. What are the physical processes driving shoreline change, and over what spatial and temporal scales are they manifest? If forces driving the littoral system change, how does the shoreline respond? Can we attribute observed patterns of shoreline change to a particular process?

Recent novel numerical shoreline-evolution modeling demonstrated that wave-driven gradients in alongshore sediment transport could produce self-organized, emergent features on spatial scales from sand waves to large-scale capes [Ashton et al., 2001], introducing a new theoretical perspective to the cross-shore-oriented considerations of the coastal scientific community. The unexpected model results inspired fresh hypotheses about shoreline pattern formation and the forcing mechanisms behind them.

One overarching hypothesis was that under regimes of high- and low-angle deep-water incident waves, alongshore shoreline perturbations grow or diffuse away, respectively. To test the hypothesis we looked for a correlation between shoreline curvature (showing perturbations to a nearly straight coastline) and shoreline change in observed measurements. High-resolution topographic lidar surveys of the North Carolina Outer Banks from 1996<–>2006 allowed robust, quantitative comparisons between shoreline surveys spanning tens of kms. In Chapter 1 [Lazarus and Murray, 2007] we report that over the last decade, at multi-km scales along the barrier islands, convex-seaward promontories tended to erode and concave-seaward embayments accrete<—>a pattern of diffusion consistent with the smoothing effects of alongshore-transport gradients driven by a low-angle wave climate. Why then, after a decade or more of smoothing, do plan-view bumps in the shoreline still persist? In Chapter 2 [Lazarus et al., in review] we compile evidence suggesting that (a) a framework of paleochannels may control the areas of persistent multi-km-scale shoreline convexity that (b) in turn drive decadal-term transient changes in shoreline morphology by (c) affecting gradients in wave-driven alongshore sediment transport.

In Chapter 3, a third investigation of large-scale coastal behavior, we explore an existing premise that shoreline change on a sandy coast is a self-affine signal wherein patterns of changes are scale-invariant, perhaps suggesting that a single process operates across the scales. Applying wavelet analysis<—>a mathematical technique involving scaled filter transforms<—>we confirm that a power law fits the average variance of shoreline change at alongshore scales spanning approximately three orders of magnitude (5<–>5000 m). The power law itself does not necessarily indicate a single dominant driver; beach changes across those scales likely result from a variety of cross-shore and alongshore hydrodynamic processes. A paired modeling experiment supports the conclusion that the power relationship is not an obvious function of wave-driven alongshore sediment transport alone.

Our tests of theory against field observations are middle steps in pattern-to-process attribution; they fit into a larger body of coastal morphodynamic research that in time may enable shoreline-change prediction. Present hydrodynamic models are still too limited in spatial and temporal scope to accommodate the extended scales at which large morphological changes occur, but more integrated quantitative models linking bathymetry, wave fields, and geologic substrate are underway and will set the next course of questions for the discipline.

Scientists expect temperatures on Earth to get substantially warmer over the course of the 21st century, causing storm systems to intensify and sea-level rise to accelerate--these changes will likely have dramatic impacts on how the coastlines of tomorrow will evolve. Humans are also playing an increasingly important role in shaping Earth's coastal systems. Coastal scientists have only a general understanding of how these three factors--humans, storms, and sea-level rise--will alter the evolution of coastlines over the coming century, however. I conduct numerical modeling experiments to shed light on the relative importance of these factors on the evolution of coastline geomorphology.

In a series of experiments using a numerical model of large-scale (1 to 100's km) and long-term (years to centuries) coastline evolution that results from gradients in alongshore sediment transport, I explore how the patterns and rates of shoreline erosion and accretion are affected by shifts in 'wave climate' (the mix of influences on alongshore sediment transport of waves approaching from different directions) induced by intensified storm systems and the direct manipulation of the shoreline system by humans through beach nourishment (periodically placing sand on an eroding beach). I use a cuspate-cape coastline, similar to the Outer Banks, North and South Carolina, USA, as an important case study in my experiments. I observe that moderate shifts in the wave climate can alter the patterns of shoreline erosion and accretion, potentially increasing migration rates by several times that which we see today, and nearly an order-of-magnitude larger than sea-level rise-related erosion alone. I also find that under possible wave climate futures, beach nourishment may also induce shoreline change on the same order of magnitude as does sea-level rise.

The decision humans make whether or not to nourish their beach often depends upon a favorable economic outcome in the endeavor. In further experiments, I couple a cost-benefit economic model of human decision making to the numerical model of coastline evolution and test a hypothetical scenario where two communities (one 'rich' and one 'poor') nourish their beaches in tandem, under different sets of economic and wave climate parameters. I observe that two adjacent communities can benefit substantially from each other's nourishment activity, and these effects persist even if the two communities are separated by several tens of kilometers.

In a separate effort, I employ techniques from dynamic capital theory coupled to a physically-realistic model of coastline evolution to find the optimum time a community should wait between beach nourishment episodes ('rotation length') to maximize the utility to beach-front property owners. In a series of experiments, I explore the sensitivity of the rotation length to economic parameters, including the discount rate, the fixed and variable costs of beach nourishment, and the benefits from beach nourishment, and physical parameters including the background erosion rate and the exponential rate at which both the cross-shore profile and the plan-view coastline shape re-adjusts following a beach nourishment episode ('decay rate' of nourishment sand). Some results I obtained were expected: if property values, the hedonic value of beach width, the baseline retreat rate, the fixed cost of beach nourishment, and the discount rate increase, then the rotation length of nourishment decreases. Some results I obtained, however, were unexpected: the rotation length of nourishment can either increase or decrease when the decay rate of nourishment sand varies versus the discount rate and when the variable costs of beach nourishment increase.

Low-lying coastal landforms such as barrier islands and river deltas are attractive sites for human habitation and infrastructure. They are also highly vulnerable to both climate change impacts such as rising sea levels or increases in storm intensity and anthropogenic impacts such as changes in sediment supply. In this dissertation I aim to improve understanding of some of the primary drivers of the evolution of low-lying coastal landforms over varying space (1-100s km) and time (decadal to millennial) scales. I focus in Chapter 2 on the influence of shoreline curvature and resulting gradients in alongshore sediment transport on shoreline change; in Chapter 3 on the influence of wave-edge erosion on back-barrier marsh resilience; and in Chapters 4 and 5 on the cohesive effects of vegetation on river deltas.

Sandy coastlines, often associated with low-lying barrier islands that are highly vulnerable to sea level rise and storms, can experience high rates of shoreline change. However, they also attract human habitation, recreation, and infrastructure. Previous research to understand and quantify contributions to shoreline erosion has considered factors such as grain size, underlying geology, regional geography, sea level rise, and anthropogenic modifications. Shoreline curvature is often not considered in such analyses, but subtle shoreline curvature (and associated alongshore variation in relative offshore wave angles) can result in gradients in net alongshore transport which can cause significant erosion or accretion. In Chapter 2, we conducted a spatially extensive analysis of the correlation between shoreline curvature and shoreline change rates for the sandy shorelines of the US East and Gulf coasts. For wave-dominated, sandy coasts where nourishment and shoreline stabilization do not dominate the shoreline change signal, we find a significant negative correlation between shoreline curvature and shoreline change rates over decadal to centurial and 1-5 km temporal and spatial scales. This indicates that some of the coastal erosion observed in these areas can be explained by the smoothing of subtle shoreline curvature by gradients in alongshore transport. In other settings, this signal can be obscured by tidal, anthropogenic, or geologic processes which also influence shoreline erosion. While limited in practical application to long, sandy shorelines with limited human stabilization, these results have widespread implications for the inclusion of shoreline curvature as an important variable in modelling and risk assessment of long-term coastal erosion on sandy, wave-dominated coastlines.

The marshes and bays in the back-barrier environment between barrier islands and the mainland can also experience wave-driven erosion, and their dynamics are coupled to those of barrier islands. Previous results show that overwash provides an important sediment source to back-barrier marshes, sustaining a narrow marsh state under conditions in which marsh drowning would otherwise occur. In Chapter 3, I expand the coupled barrier island-marsh evolution model GEOMBEST+ to explore the effects of wind waves on back-barrier marshes. I find that the addition of marsh-edge erosion leads to wider, more resilient marshes and that horizontal erosion of the marsh edge is a more efficient sediment source than vertical erosion of the marsh surface as it drowns. Where marshes and bays are vertically keeping up with sea level, and the net rate of sediment imported to (or exported from) the basin is known, the rate of marsh-edge erosion or progradation can be predicted knowing only the present basin geometry, sea-level rise rate, and the net rate of sediment input (without considering the erosion or progradation mechanisms). If the rate of sediment input/export is known, this relationship applies whether sediment exchange with the open ocean is negligible (as in basins dominated by riverine sediment input), or is significant (including the loss of sediment remobilized by waves in the bay). Analysis of these results reveals that geometry and stratigraphy can exert a first order control on back-barrier marsh evolution and on the marsh-barrier island system as a whole, and provides new insights into the resilience of back-barrier marshes and on the interconnectedness of the barrier-marsh system.

Coastal wetlands such as marshes are also an important component of river deltas. Like barrier islands, these low-lying landscapes are both attractive to human settlement (providing fertile farmland, fisheries, hydrocarbon reserves, and many other services) and prone to hazards such as flooding and land loss. Delta evolution is governed by complex interactions between coastal, marine, and fluvial processes, many of which are still not well understood. In Chapters 4 and 5, I use the delta-building model DeltaRCM to explore the effects of vegetation, specifically its ability to introduce cohesion, on delta morphology and the dynamics of delta distributary networks. The use of this rule-based model allows me to simplify vegetation dynamics and effects in order to enhance the clarity of potential insights into which processes or interactions may be most important in the context of vegetation as a cohesive agent.

Cohesive sediment exerts a significant influence on delta evolution, increasing shoreline rugosity and decreasing channel mobility. Vegetation has been assumed to play a similar role in delta evolution, but its cohesive effects have not been explicitly studied. In Chapter 4, I use DeltaRCM to directly explore two cohesive effects of vegetation: decreasing lateral transport and increasing flow resistance. I find that vegetation and cohesive sediment do alter delta morphology and channel dynamics in similar ways (e.g. more rugose shorelines, deeper, narrower, less mobile channels), but that vegetation may have additional implications for deltaic sediment retention and stratigraphy, by confining flow and sand in channels. My results suggest that sediment composition is a first-order control on delta morphology but vegetation has a stronger influence on channel mobility timescales. To fully understand the cohesive influences acting on a delta, the influence of vegetation should be considered in addition to fine sediment.

In Chapter 5, I explore the cohesive effects of vegetation on delta evolution under different environmental conditions. The dynamics and evolution of deltas and their channel networks are controlled by interactions between a number of factors, including water and sediment discharge, cohesion from fine sediment and vegetation, and sea level rise rates. Vegetation’s influence on the delta is likely to be significantly impacted by other environmental factors. For example, increasing sea level or sediment discharge increases aggradation rates on the delta, and may result in sediment transport processes such as deposition and erosion, both of which can kill vegetation, happening more rapidly than vegetation growth. I conduct two sets of experiments; in the first, I explore the interactions between vegetation and sea level rise rate, and in the second, between vegetation and rate of sediment and water discharge. As expected, I find that sea level rise decreases vegetation’s ability to stabilize channels but that vegetation can still exert a strong influence on the delta at low rates of sea level rise. This limit appears to be higher for channel dynamics than delta morphology, supporting the findings of Chapter 4. In addition, I propose two new insights into delta evolution under different discharge conditions with and without vegetation. First, without vegetation, I observe a shift in avulsion dynamics with increasing water discharge: from a few active channels supplemented by overbank flow and undergoing episodic avulsion (with low discharge) to many active channels experiencing frequent local and partial avulsions (with high discharge). Second, with vegetation, increased sediment discharge and associated aggradation results in more frequent switching of the dominant channels, but also prevents vegetation from establishing in non-dominant channels, resulting in more frequent channel reoccupation and therefore in channel network planform stability. These insights have important implications for understanding the distribution of water, sediment, and nutrients on deltas in the face of future changes in climate, human modifications of fluxes of sediment and water to the coast, and especially for restored or engineered deltas with controlled water or sediment discharges.