We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119 , 64–80 ( doi:10.1061/(ASCE)0733-9429(1993)119:1(64) )). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Climate change and population growth are degrading coastal ecosystems and increasing risks to communities and infrastructure. Reliance on seawalls and other types of hardened shorelines is unsustainable in an era of rising seas, given the costs to build and maintain these structures and their unintended consequences on ecosystems. This is especially true for communities that depend on coastal and marine ecosystems for livelihoods and sustenance. Protecting and restoring coral reefs and coastal forests can be lower cost, sustainable alternatives for shoreline protection. However, decision-makers often lack basic information about where and under what conditions ecosystems reduce risk to coastal hazards and who would benefit. To better understand where to prioritize ecosystems for coastal protection, we assessed risk reduction provided by coral reefs, mangroves, and seagrass along the entire coast of The Bahamas, under current and future climate scenarios. Modeled results show that the population most exposed to coastal hazards would more than double with future sea-level rise and more than triple if ecosystems were lost or degraded. We also found that ecosystem-based risk reduction differs across islands due to variation in a suite of ecological, physical, and social variables. On some populated islands, like Grand Bahama and Abaco, habitats provide protection to disproportionately large numbers of people compared to the rest of the country. Risk reduction provided by ecosystems is also evident for several sparsely populated, remote coastal communities, which in some cases, have large elderly populations. The results from our analyses were critical for engaging policy-makers in discussions about employing natural and nature-based features for coastal resilience. After hurricanes Joaquin and Matthew hit The Bahamas in 2016 and 2017, our assessment of coastal risk reduction and the multiple benefits provided by coastal ecosystems helped pave the way for an innovative loan from the Inter-American Development Bank to the Government of The Bahamas to invest in mangrove restoration for coastal resilience. This work serves as an example for other regions and investors aiming to use assessments of ecosystem services to inform financing of natural and nature-based approaches for coastal resilience and climate adaptation.

The problem of determining the threshold of motion of a sediment particle resting on the bed of an open channel has historically been dominated by an approach based on the time–space-averaged bed shear stress (i.e. Shields criterion). Recently, experimental studies have promoted an alternative approach to predict the dislodgement threshold, which is based on the impulse of the flow-induced force. Nonetheless, theoretical analyses accompanying these studies result in complex expressions that fail to provide a direct estimate of said impulse threshold. We employ the work–energy principle to derive a prediction of the fundamental impulse threshold that the destabilising hydrodynamic force must overcome in order to achieve full particle dislodgement. For the bed configuration studied, which is composed of spheres, the proposed expression depends on the mobile particle’s size and mass, and shows excellent agreement with experimental observations previously published. The derivation presented in this paper may thus represent a robust theoretical framework that aids in the reinterpretation of existing data, as well as in the design of future experiments aimed at analysing the importance of hydrodynamic impulse as a criterion for prediction of particle dislodgement.

Saltation models provide considerable insight into near-bed sediment transport. This paper outlines a simple, efficient numerical model of stochastic saltation, which is validated against previously published experimental data on saltation in a channel of nearly horizontal bed. Convergence tests are systematically applied to ensure the model is free from statistical errors emanating from the number of particle hops considered. Two criteria for statistical convergence are derived; according to the first criterion, at least $10^3$ hops appear to be necessary for convergent results, whereas $10^4$ saltations seem to be the minimum required in order to achieve statistical convergence in accordance with the second criterion. Two empirical formulae for lift force are considered: one dependent on the slip (relative) velocity of the particle multiplied by the vertical gradient of the horizontal flow velocity component; the other dependent on the difference between the squares of the slip velocity components at the top and bottom of the particle. The former is found to give more stable results. A parameter study indicates that the saltation length has a minimum value with increasing particle diameter (at non-dimensional $D_* \sim 12$) for a given transport stage. Variations in the friction coefficient and collision line level have negligible effect on the saltation statistics within the ranges considered. Regression equations are obtained for each of the saltation characteristics. Finally, the model is used to evaluate the bed load transport rate, which is in satisfactory agreement with common formulae based on flume data, especially when compared against other saltation-derived expressions.Comment: Published in ASCE Journal of Hydraulic Engineering, J. Hydraul. Eng. 201