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a b s t r a c t a r t i c l e i n f oThe Bruun Rule (Bruun, 1954(Bruun, , 1962) provides a relationship between sea level rise and shoreline retreat, and has been widely applied by the engineering and scientific communities to interpret shoreline changes and to plan for possible future increases in sea level rise rates. The Bruun Rule assumes that all sand removed from the upper profile is deposited offshore as sea level rises, although overwash during storms and landward Aeolian transport clearly indicate otherwise. Herein, we examine processes associated with sandy beach evolution in response to relative sea level rise and propose a modified form of the Bruun Rule that considers the full range of parsing cross-shore transport, from completely seaward to completely landward depending on the prevailing storm and surge conditions and whether there is a surplus or deficit of sand in the profile with respect to the equilibrium beach profile. A methodology is proposed that more appropriately represents the long-term processes and beach response. However, an improved quantitative understanding of landward transport is required for optimal application of the proposed method.Published by Elsevier B.V.

The sediment budget is fundamental in coastal science and engineering. Budgets allow estimates to be made of the volume or volume rate of sediment entering and exiting a defined region of the coast and the surplus or deficit remaining in that region. Sediment budgets have been regularly employed with variations in approaches to determine the sources and sinks through application of the primary conservation of mass equation. Historically, sediment budgets have been constructed and displayed on paper or maps. Challenges in constructing a sediment budget include determining the appropriate boundaries of the budget and interior cells; defining the possible range of sediment transport pathways, and the relative magnitude of each; representing the uncertainty associated with values and assumptions in the budget; and testing the sensitivity of the series of budgets to variations in the unknown and temporally-changing values. These challenges are usually addressed by representing a series of budget alternatives that are ultimately drawn on paper, maps, or graphs. Applications of the methodology include detailed local-scale sediment budgets, such as for an inlet or beach fill project, and large-scale sediment budgets for the region surrounding the study area. The local-scale budget has calculation cells representing features on the order of 10s to 100s of meters, and it must be shown separately from the regional sediment budget, with cells ranging from 100s of meters to kilometers. This paper reviews commonly applied sediment budget concepts and introduces new considerations intended to make the sediment budget process more reliable, streamlined, and understandable. The need for both local and regional sediment budgets is discussed, and the utility of combining, or collapsing, cells is shown to be beneficial for local budgets within a regional system. Collapsing all cells within the budget creates a ''macrobudget,'' which can be applied to check for overall balance of values. An automated means of changing the magnitude of terms, while maintaining the same dependency on other values within the sediment budget, is presented. Finally, the need for and method of tracking uncertainty within the sediment budget, and a means for conducting sensitivity analyses, are discussed. These new concepts are demonstrated within the Sediment Budget Analysis System with an application for Long Island, New York, and Ocean City Inlet, Maryland.