Lighthouses that lost their ground to the seaThe shoreline retreats. The tower can move too.

A lighthouse stands closer to the sea, or further from it. Did the sea take the ground, or did someone move the tower? The gap alone will not tell you. Split it into two movements, measured from one fixed anchor.

Model diagram: not a map and not a measurement. An original drawing based on invented figures. The axis is in metres from anchor 0 and increases towards the sea. The structure symbol is not to scale; only its axis counts.

anchor 0 (black post, fixed)
shoreline in measurement A (dashed)
shoreline in measurement B (solid)
tolerance band A, ±uA around shoreline A (dots)
tolerance band B, ±uB around shoreline B (solid fill)
area between shorelines A and B
structure A (outline)
structure B (filled)

Gap-only mode: the blue line B′ is the shoreline calculated on the assumption that the structure stood still; the grey line and grey outline are the actual measurement B.

shoreline

15 m

retreated landward

outside tolerance ±4 m

structure

35 m

relocated landward

outside tolerance ±4 m

gap

+20 m

from 25 to 45 m

outside tolerance ±8 m

Both have changed: the shoreline and the structureThe gap grew by 20 m: +35 m from moving the structure and −15 m from the movement of the shoreline. Note: the gap changed in the opposite direction to what the shoreline movement alone would suggest. All of this is in the model, on invented figures.

Set two measurements from the same anchor

Model scenario

How you read the change in the gap

Showing both measurements: shoreline and structure separately.

Measurement A · dashed Shoreline [m from anchor] Structure [m from anchor] Reading tolerance ± [m]

Measurement B · solid Shoreline [m from anchor] Structure [m from anchor] Reading tolerance ± [m]

Shoreline: retreat landward by 15 m · structure: relocation landward by 35 m · gap: +20 m. Both have changed: the shoreline and the structure.

Where the change in the gap comes from

Gap A structure → shoreline, first measurement25 m
Shoreline movement retreat reduces the gap−15 m
Relocation of the structure landward movement increases the gap+35 m
Gap B second measurement45 m

change in gap +20 m = structure movement +35 m − shoreline retreat 15 m

The bars share one scale in metres (from 0 to 100 m); they show gaps, not coordinates from the cross-section.

From the gap alone

I assume the structure stood still.

Shoreline: seaward shift of 20 m

Structure: 0 m (assumed, not measured)

From two measurements

Shoreline and structure separately.

Shoreline: retreat landward by 15 m

Structure: relocation landward by 35 m

The gap alone misjudges the shoreline movement by 35 m, which is exactly the movement of the structure.

Without JavaScript: five model scenarios

The interactive cross-section requires JavaScript. Below are the results of five scenarios built from invented figures (metres from the anchor, tolerance ± for each date). Movement landward is counted as positive; change in gap = structure movement − shoreline retreat.

Both movements: Shoreline 80 → 65 m (retreat 15 m), structure 55 → 20 m (relocation 35 m), tolerance ±2 m. Gap 25 → 45 m: +20 m, even though the shoreline retreated.
Shoreline only: Shoreline 85 → 65 m (retreat 20 m), structure stays at 40 m. Gap 45 → 25 m: −20 m, the whole change comes from the shoreline.
Structure only: Shoreline stays at 80 m, structure 55 → 20 m (relocation 35 m). Gap 25 → 60 m: +35 m, shoreline with no resolved change.
Constant gap: Shoreline 80 → 60 m (retreat 20 m), structure 45 → 25 m (relocation 20 m). Gap 35 → 35 m, even though both objects moved.
Reading noise: Shoreline 75 → 73 m, structure stays at 30 m, tolerance ±5 m for each date. The 2 m change falls within the combined tolerance of ±10 m: result unresolved.

Three real-world leads and what you cannot read from them

Cape Hatteras

USA · foreign case study, no map

The National Park Service describes the 1999 relocation of the lighthouse and its complex in North Carolina as a response to the threat of erosion [2]. This is a documented engineering decision in which the change in distance from the sea had two causes at once. The figures in the cross-section above are not its measurements, and the page does not place this site on any map. description carried over from V2 · to be verified

Rozewie

Poland · no measurement series

The museum describes 200 years of the light at Rozewie, from 1822 [3]. This is the history of the light, not evidence that the ground under the tower was lost or that it was moved. The materials for this task contain no measurement series for any Polish lighthouse, so the page shows neither a Polish gap nor a rate of retreat. description carried over from V2 · to be verified

Cliffs

Methodology · PIG-PIB

PIG-PIB distinguishes rockfalls, debris falls and landslides, and describes monitoring of cliffs by laser scanning [1]. The coordinate of the shoreline is not the same as cliff loss: a change can come from the definition of the waterline, tides or sediment dynamics, and mass movement occurs in sudden steps. description carried over from V2 · to be verified

Assumptions and limits of the model

Units and axis. Everything is in metres from anchor 0, and the axis increases towards the sea. The anchor is fixed in both measurements. If the benchmark moved, the whole calculation would lose its meaning, and with real data the anchor's stability would first have to be demonstrated.
Formulas. Shoreline retreat R = shoreline A − shoreline B, structure relocation M = structure A − structure B (both positive landward), gap shoreline − structure. The change in the gap always equals M − R.
Reading tolerance. Each of the four readings has an error of up to ±u for its date. I add the intervals in the worst case, without statistics: R and M have a tolerance of ±(uA + uB), and the change in the gap ±2(uA + uB). When |result| falls within the tolerance, the page says “unresolved”, not “zero” and not “detected”. This is a simplification, not a confidence interval.
Time. The dates of the measurements are not entered, so there is no timeline and no rate in metres per year. There is also no forecast of when the tower will reach the sea: a linear extrapolation from two points would be guesswork.
A shoreline is not erosion. In this model the shoreline is a coordinate. A shift does not prove cliff erosion, and the absence of a shift does not prove safety.
No safety assessment. The page has no “safe distance” threshold. Observe cliffs only from marked trails, because edges are subject to sudden rockfalls.
Data. All figures in the scenarios are invented for the purposes of the exercise. The drawing is an original diagram, not a verified map or a georeferenced plan.

What is no longer here compared with V2

Saving to and reading from browser storage, and copying the report: removed, because these are two states without personal data that are easy to re-enter with a scenario button. Nothing is saved.
Free-text measurement labels: removed, because they did not change any result.
The 15 m “exercise threshold”: removed, because it looked like a safety standard. It was replaced by the reading tolerance, which really does decide whether a change is resolved.
Four equal tiles with numbers: replaced by three measures (shoreline, structure, gap) under the drawing, plus bars on a single axis.
Kept: the four coordinates and tolerances, the calculation of the components of the change in the gap, the scenarios (pure shoreline change, relocation, compensation, noise), the sources and the foreign status of Cape Hatteras.