Coastal Erosion Rate Estimator
Turn dated shoreline surveys into erosion rates and a setback year, or estimate sea level rise recession with the Bruun rule.
🏖️ What is a Coastal Erosion Rate?
Coastal erosion rate is the speed at which a shoreline moves landward over time, normally given in metres per year. Because a shoreline can also advance seaward, coastal scientists usually speak of a shoreline change rate, which is negative for erosion and positive for accretion. The rate is found by comparing the position of the shoreline on maps, aerial photographs, satellite images or GPS surveys taken on different dates. All positions are measured along a transect from a fixed baseline, so that every survey is compared on the same footing. This is the approach used by the U.S. Geological Survey in its Digital Shoreline Analysis System (DSAS), which defines three standard statistics that this calculator reproduces: the net shoreline movement (NSM), the end point rate (EPR) and the linear regression rate (LRR).
These numbers matter to anyone who builds, insures or manages land near the water. Planners use them to draw setback lines for houses and roads, engineers use them to size beach nourishment, insurers and lenders use them to judge long-term risk, and researchers use them to separate the effect of storms, sediment supply and sea level rise. The survey mode here takes up to six dated shoreline positions, fits a least-squares line, and tells you the rate, how well the data fit a straight line, the standard error of the slope, the projected position in a year of your choice and the year the shoreline reaches a building or road at a given distance from the baseline.
The second mode applies the Bruun rule, proposed by Per Bruun in 1962. It is a simple geometric model for how far a sandy shoreline retreats when sea level rises. The idea is that the beach profile keeps its equilibrium shape: as water rises, sand is eroded from the upper beach and dune and deposited offshore until the seabed has risen by the same amount as the sea. Because beach slopes are gentle, the horizontal retreat is many times larger than the vertical rise. The rule is widely used for screening, and also widely criticised, so this page states its limits clearly.
Three cautions apply. First, a rate is only as good as the record behind it. Shorelines mapped with different indicators, or surveyed just before and after a storm, can give a misleading slope. Second, a straight-line fit hides cycles and steps, which is why R squared and the standard error are shown. Third, projecting a rate forward assumes that the causes stay the same, which rarely holds for decades. Typical long-term rates vary enormously, from nearly stable shores to several metres a year on exposed sandy coasts, and cliffs and deltas behave differently again, so always rely on your own measured data instead of a general figure.
📐 Formula
The Bruun rule is a coarse two-dimensional equilibrium-profile estimate. It assumes a closed sediment budget and ignores longshore transport, inlets, overwash, structures and sediment supply, so use it as a first screening number and not as a design value.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Eroding Sandy Coast
Six surveys from 1955 to 2024, shoreline falling from 120 m to 71 m from the baseline, building at 30 m, projected to 2050
Example 2 — Accreting Delta
Four surveys from 1975 to 2020, shoreline growing from 410 m to 590 m, setback 30 m, projected to 2050
Example 3 — Cliff Coast
Cliff-top surveyed in 1998, 2008 and 2024 at 42, 38.5 and 26 m from the baseline, house at 10 m, projected to 2045
Example 4 — Bruun Rule for 0.5 m of Sea Level Rise
S = 0.5 m, active profile L = 300 m, dune height B = 2 m, closure depth h = 8 m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the difference between EPR and LRR in shoreline change?
The end point rate (EPR) divides the net distance between the oldest and newest shoreline by the elapsed time, so it uses only two surveys. The linear regression rate (LRR) is the slope of the least-squares line through every survey, so it uses all of them and is less sensitive to one odd date. Both are in metres per year.
What is net shoreline movement (NSM)?
NSM is the distance in metres between the oldest and the newest shoreline at the same transect, with no reference to time. A negative NSM means the shoreline moved landward (erosion) and a positive NSM means it moved seaward (accretion). Dividing NSM by the time between the two surveys gives the EPR.
How do I calculate the shoreline erosion rate from historical surveys?
Measure the distance from one fixed baseline to the shoreline on each survey date, then enter the year and distance in the table. The calculator fits a straight line to the points. Its slope is the LRR, and (x_last - x_first) / (t_last - t_first) is the EPR. A negative value means erosion.
Why is erosion negative in this calculator?
Distances are measured seaward from the baseline, so a shoreline that moves landward gets closer to the baseline and its distance decreases. A falling distance gives a negative slope, which this tool labels erosion. A rising distance gives a positive slope, labelled accretion. This follows the usual USGS DSAS sign convention.
How many shorelines do I need for a reliable rate?
Two shorelines are enough to compute an EPR and an NSM, but they give no measure of scatter. Three or more are needed for the standard error of the slope, and more surveys spread across several decades give a far more trustworthy LRR. Agencies often favour LRR when enough shoreline dates exist.
How is the year the shoreline reaches a setback calculated?
The calculator solves the regression line x(t) = x_mean + LRR (t - t_mean) for the year when the position equals your setback distance. It only reports a year when the shoreline is currently seaward of the setback and the trend is erosional. Otherwise it says the setback is already reached or not reached.
What does R squared tell me about a shoreline trend?
R squared is the fraction of the variation in shoreline position that the straight line explains. A value near 1 means the surveys fall close to a line and the rate is steady. A low value means the shoreline moves in steps or cycles, and a single linear rate may be a poor description.
What is the Bruun rule?
The Bruun rule (Bruun, 1962) says that when sea level rises by S, a sandy profile shifts landward and upward so that its shape is preserved. The shoreline recession is R = S L / (B + h), where L is the horizontal width of the active profile, B is the berm or dune height and h is the closure depth.
What is the depth of closure in the Bruun rule?
The depth of closure h is the water depth beyond which waves rarely move enough sand to change the seabed over the period of interest. It marks the seaward end of the active profile. Typical values for open sandy coasts are of the order of several to ten or more metres, and depend on the wave climate.
Is the Bruun rule accurate?
It is a coarse, two-dimensional first estimate and has been debated for decades. It assumes a closed sediment budget, an equilibrium profile and that sand moves only across the shore. It ignores longshore transport, rocky or armoured shores, inlets, overwash and sediment supply, so use it only for screening.