Martin D. Hurst

Using hilltop curvature to derive the spatial distribution of erosion rates

[1] Erosion rates dictate the morphology of landscapes, and therefore quantifying them is a critical part of many geomorphic studies. Methods to directly measure erosion rates are expensive and time consuming, whereas topographic analysis facilitates prediction of erosion rates rapidly and over large spatial extents. If hillslope sediment flux is nonlinearly dependent on slope then the curvature of hilltops will be linearly proportional to erosion rates. In this contribution we develop new techniques to extract hilltop networks and sample their adjacent hillslopes in order to test the utility of hilltop curvature for estimating erosion rates using high-resolution (1 m) digital elevation data. Published and new cosmogenic radionuclide analyses in the Feather River basin, California, suggest that erosion rates vary by over an order of magnitude (10 to 250 mm kyr � 1 ). Hilltop curvature increases with erosion rates, allowing calibration of the hillslope sediment transport coefficient, which controls the relationship between gradient and sediment flux. Having constraints on sediment transport efficiency allows estimation of erosion rates throughout the landscape by mapping the spatial distribution of hilltop curvature. Additionally, we show that hilltop curvature continues to increase with rising erosion rates after gradient-limited hillslopes have emerged. Hence hilltop curvature can potentially reflect higher erosion rates than can be predicted by hillslope gradient, providing soil production on hilltops can keep pace with erosion. Finally, hilltop curvature can be used to estimate erosion rates in landscapes undergoing a transient adjustment to changing boundary conditions if the response timescale of hillslopes is short relative to channels.

Objective extraction of channel heads from high-resolution topographic data

Fluvial landscapes are dissected by channels, and at their upstream termini are channel heads. Accurate reconstruction of the fluvial domain is fundamental to understanding runoff generation, storm hydrology, sediment transport, biogeochemical cycling, and landscape evolution. Many methods have been proposed for predicting channel head locations using topographic data, yet none have been tested against a robust field data set of mapped channel heads across multiple landscapes. In this study, four methods of channel head prediction were tested against field data from four sites with high-resolution DEMs: slope-area scaling relationships; two techniques based on landscape tangential curvature; and a new method presented here, which identifies the change from channel to hillslope topography along a profile using a transformed longitudinal coordinate system. Our method requires only two user-defined parameters, determined via independent statistical analysis. Slope-area plots are traditionally used to identify the fluvial-hillslope transition, but we observe no clear relationship between this transition and field-mapped channel heads. Of the four methods assessed, one of the tangential curvature methods and our new method most accurately reproduce the measured channel heads in all four field sites (Feather River CA, Mid Bailey Run OH, Indian Creek OH, Piedmont VA), with mean errors of −11, −7, 5, and −24 m and 34, 3, 12, and −58 m, respectively. Negative values indicate channel heads located upslope of those mapped in the field. Importantly, these two independent methods produce mutually consistent estimates, providing two tests of channel head locations based on independent topographic signatures.

Hillslopes Record the Growth and Decay of Landscapes

Gotta Get Up to Get Down By examining high-resolution satellite topography data of a ridge along the San Andreas Fault in California, Hurst et al. (p. 868) demonstrate how hill slope curvature may be used to infer long-term rates of tectonic uplift and erosion. Numerical modeling shows a lag phase between uplift events and changes in morphology, which, combined with the observational data, shows that topography can reveal whether landscapes are active or decaying. These fundamental relationships may help to improve seismic hazard forecasts or to interpret topographic data collected on other terrestrial planets. Changes in tectonic rates can be quantitatively derived from hillslope morphology. Earths surface archives the combined history of tectonics and erosion, which tend to roughen landscapes, and sediment transport and deposition, which smooth them. We analyzed hillslope morphology in the tectonically active Dragon’s Back Pressure Ridge in California, United States, to assess whether tectonic uplift history can be reconstructed using measurable attributes of hillslope features within landscapes. Hilltop curvature and hillslope relief mirror measured rates of vertical displacement caused by tectonic forcing, and their relationships are consistent with those expected when idealizing hillslope transport as a nonlinear diffusion process. Hilltop curvature lags behind relief in its response to changing erosion rates, allowing growing landscapes to be distinguished from decaying landscapes. Numerical modeling demonstrates that hillslope morphology may be used to infer changes in tectonic rates.

Recent acceleration in coastal cliff retreat rates on the south coast of Great Britain

Significance Cliffed coasts erode when attacked by energetic waves. Cliff retreat threatens coastal assets and livelihoods. Understanding rates of past erosion is vital to quantifying these risks, particularly when confronted with expected increases in storminess and sea level, and given continued human occupation and engineering of coastal regions. Historical observations of cliff retreat span 150 y at most. We derived past cliff retreat rates over millennial time scales for chalk cliffs on the south coast of Great Britain by interpreting measured cosmogenic nuclides with numerical models. Our results provide evidence for accelerated erosion in recent centuries, which we suggest is driven by reduced sediment supply and thinning of beaches in the face of environmental and anthropogenic changes. Rising sea levels and increased storminess are expected to accelerate the erosion of soft-cliff coastlines, threatening coastal infrastructure and livelihoods. To develop predictive models of future coastal change we need fundamentally to know how rapidly coasts have been eroding in the past, and to understand the driving mechanisms of coastal change. Direct observations of cliff retreat rarely extend beyond 150 y, during which humans have significantly modified the coastal system. Cliff retreat rates are unknown in prior centuries and millennia. In this study, we derived retreat rates of chalk cliffs on the south coast of Great Britain over millennial time scales by coupling high-precision cosmogenic radionuclide geochronology and rigorous numerical modeling. Measured 10Be concentrations on rocky coastal platforms were compared with simulations of coastal evolution using a Monte Carlo approach to determine the most likely history of cliff retreat. The 10Be concentrations are consistent with retreat rates of chalk cliffs that were relatively slow (2–6 cm⋅y−1) until a few hundred years ago. Historical observations reveal that retreat rates have subsequently accelerated by an order of magnitude (22–32 cm⋅y−1). We suggest that acceleration is the result of thinning of cliff-front beaches, exacerbated by regional storminess and anthropogenic modification of the coast.

Exploring the sensitivities of crenulate bay shorelines to wave climates using a new vector-based one-line model

We use a new exploratory model that simulates the evolution of sandy coastlines over decadal to centennial timescales to examine the behavior of crenulate-shaped bays forced by differing directional wave climates. The model represents the coastline as a vector in a Cartesian reference frame, and the shoreface evolves relative to its local orientation, allowing simulation of coasts with high planform-curvature. Shoreline change is driven by gradients in alongshore transport following newly developed algorithms that facilitate dealing with high planform-curvature coastlines. We simulated the evolution of bays from a straight coast between two fixed headlands with no external sediment inputs to an equilibrium condition (zero net alongshore sediment flux) under an ensemble of directional wave climate conditions. We find that planform bay relief increases with obliquity of the mean wave direction, and decreases with the spread of wave directions. Varying bay size over 2 orders of magnitude (0.1–16 km), the model predicts bay shape to be independent of bay size. The time taken for modeled bays to attain equilibrium was found to scale with the square of the distance between headlands, so that, all else being equal, small bays are likely to respond to and recover from perturbations more rapidly (over just a few years) compared to large bays (hundreds of years). Empirical expressions predicting bay shape may be misleading if used to predict their behavior over planning timescales.

Spatio-temporal Variability in the Tipping Points of a Coastal Defense

ABSTRACT Brown, J.M.; Prime, T.; Phelps, J.J.C.; Barkwith, A.; Hurst, M.D.; Ellis, M.A.; Masselink, G., and Plater, A.J., 2016. Spatio-temporal Variability in the Tipping Points of Coastal Defense. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 1042 - 1046. Coconut Creek (Florida), ISSN 0749-0208. To enable effective adaptive management, early warning of when a ‘tipping point’ within a systems defense may occur is vital. A tipping point is a critical threshold at which the state of a system is altered, perhaps irreversibly. After the extremity of the UKs 2013/2014 winter, many coastal systems have undergone a change in state. For example, the conversion of a sandy beach into a rocky platform or an increase/decrease in flood hazard due to a defense breach or new intervention. Coastal monitoring networks around the UK have enabled data collection of these extreme events to drive model applications to assess plausible changes in coastal conditions that trigger a sudden change in a systems state and conditions that enable recovery. Using available UK monitoring networks and a numerical approach, we focus on Dungeness and Rye Bay, a region of high value in terms of habitat and energy, to assess (i) how the natural variability within the profile of the gravel barrier modifies the overwash rates that can occur and (ii) how ambitious human intervention that re-scape the geomorphic character of the shoreline could impact the critical point at which overwash occurs.

Development of an automatic delineation of cliff top and toe on very irregular planform coastlines (CliffMetrics v1.0)

We describe a new algorithm that automatically delineates the cliff top and toe of a cliffed coastline from a digital elevation model (DEM). The algorithm builds upon existing methods but is specifically designed to resolve very irregular planform coastlines with many bays and capes, such as parts of the coastline of Great Britain. The algorithm automatically and sequentially delineates and smooths shoreline vectors, generates orthogonal transects and elevation profiles with a minimum spacing equal to the DEM resolution, and extracts the position and elevation of the cliff top and toe. Outputs include the non-smoothed raster and smoothed vector coastlines, normals to the coastline (as vector shape files), xyz profiles (as comma-separated-value, CSV, files), and the cliff top and toe (as point shape files). The algorithm also automatically assesses the quality of the profile and omits lowquality profiles (i.e. extraction of cliff top and toe is not possible). The performance of the proposed algorithm is compared with an existing method, which was not specifically designed for very irregular coastlines, and to manually digitized boundaries by numerous professionals. Also, we assess the reproducibility of the results using different DEM resolutions (5, 10 and 50 m), different user-defined parameter sets related to the degree of coastline smoothing, and the threshold used to identify the cliff top and toe. The model output sensitivity is found to be smaller than the manually digitized uncertainty. The code and a manual are publicly available on a GitHub repository.

Sediment accumulation in embayments controlled by bathymetric slope and wave energy: Implications for beach formation and persistence: PRESTON ET. AL. BEACH FORMATION AND OFFSHORE SLOPE

High energy, rocky coastlines often feature sandy beaches within headland‐bound embayments. Not all such embayments have beaches however, and beaches in embayments can be removed by storms and may subsequently reform. What dictates the presence or absence of an embayed beach and its resilience to storms? In this paper, we explore the effect of offshore slope and wind conditions on nearshore sediment transport within idealised embayments to give insight into nearshore sediment supplies. We use numerical simulations to show that sand can accumulate near shore if the offshore slope is >0.025 m/m, but only under persistent calm conditions. Our modelling also suggests that if sediment in an embayment with an offshore gradient steeper than 0.025 m/m is removed during a period of persistent stormy conditions, it will be unlikely to return in sub‐decadal timescales. In contrast, sediment located in embayments with shallower gradients can reform swiftly in both calm and stormy conditions. Our findings have wide implications for contemporary coastal engineering in the face of future global climate change, but also for Quaternary environmental reconstruction. Our simple method to predict beach stability based on slope can be used to interpret differing responses of embayments to periods of changing coastal storminess such as the medieval climate anomaly‐little ice age (MCA‐LIA) transition.