Cumulative Time-series Subsidence Calculator

Velocity maps summarise a deformation story in one number per point — and in doing so they hide the part of the story that matters most to an engineer: when the motion happened, whether it was steady or accelerating, and whether the record contains a discontinuity that no velocity can represent. A point averaging 10 mm/yr of steady subsidence and a point that sat still for two years and then dropped 60 millimetres in a wet season share the same velocity. Only the time series separates them. This tool imports the multi-epoch displacement series your processor exported, fits each point's trajectory, compares the first-half and second-half rates to detect acceleration, watches for single-epoch steps that usually mean unwrapping trouble, and draws every trajectory with its linear baseline so the behaviour is visible at a glance.

It occupies the temporal stage of the workflow — after the LOS Converter has produced consistent vertical series, alongside the Hazard Classifier's spatial view. The two are complementary: the classifier tells you where to look, this tool tells you how the motion unfolded there. As with every tool on this site, the series never leave your browser.

When you should use this tool

• You have SBAS or PS time-series exports (cumulative displacement per epoch per point) and need per-point rates, acceleration flags and a clean figure for the report.
• A hazard-classified zone needs a temporal characterisation before you recommend field inspection — accelerating points and steady points deserve different urgency.
• You suspect unwrapping or atmospheric events in the record and need a systematic scan for discontinuities across all points, not a manual click-through of a hundred charts.
• You are preparing a monitoring baseline: knowing which points behaved linearly over the archive period tells you which are trustworthy reference candidates.

When NOT to use this tool

• Your data is a single displacement pair or a velocity layer — there is no time dimension to analyse here. Import a proper per-epoch series.
• The epochs are irregular and sparse (fewer than roughly six epochs). Half-span rate comparison needs enough points on each side to fit meaningfully; with three epochs the acceleration flag is numerology.
• You expect the acceleration flag to carry regulatory meaning. It is a screening indicator from a defined arithmetic comparison, and it must be confirmed — the flags direct field attention, they do not conclude.

How the detection actually works

Each point's epochs are sorted in time and converted to decimal years. A least-squares line over the full record gives the headline rate in mm/yr; that is the number to compare against the velocity maps you already have. The acceleration test then fits separate lines to the first half and the second half of the record: if the second-half rate is more negative than the first-half rate by more than the acceleration threshold (default 3 mm/yr), the point is flagged as accelerating. The half-span choice is deliberate — it is robust to seasonality on either side, cheap to explain in a review, and impossible to tune into self-deception without noticing. The step test watches consecutive epochs: a single-interval jump larger than the step threshold (default 15 mm) is flagged with its date, because an isolated discontinuity in an otherwise smooth series is far more likely an unwrapping or network error than real geology. Steps take precedence over the acceleration label in the display for exactly that reason.

Reading the chart & the summary

The chart stacks every point's cumulative displacement curve with its full-record linear fit as a dashed line. Three signatures cover most engineering narratives: a flat noisy line (stable — a candidate reference point), a straight descending line (steady subsidence — quote the fitted rate), and a curve that steepens (accelerating — quote both half-rates and the crossover period). A curve with a clean jump should trigger a look at the raw interferograms around the flagged date before any interpretation. The summary table gives every number the chart displays — epoch count, total displacement, headline rate, both half-rates and the flags — and the CSV export carries them all, one row per point.

What the demo shows, point by point

The demonstration series — six points over twelve monthly epochs — is built so that every detection mechanism fires exactly once, which makes it a calibration target for your own threshold tuning. Two points are stable: their curves are flat noise, their rates near zero, their flags linear. Two are steady subsiders: clean straight lines whose fitted rates land in the −10 to −15 mm/yr band, flagged linear — these are your honest, quotable results. One accelerates: its curve steepens visibly, the second-half rate comes out several mm/yr more negative than the first half, and the accelerating flag fires. The last point is linear except for a single 18 mm jump mid-record — below nothing you would notice in a velocity map, above the step threshold — and it surfaces as a step flag with the date attached. Run the demo, open the summary CSV, and confirm you can reproduce each flag from the numbers: that ten-minute exercise is the fastest way to understand precisely what the tool will and will not tell you about a real monitoring record.

Common pitfalls & mistakes

• Seasonal masquerade. Groundwater-driven sites oscillate; a half-span fit can dress a seasonal cycle up as acceleration. Check whether the steepening coincides with a wet season before escalating.
• Reference-point contamination. If the scene's reference point itself moves, every series inherits it. Validate the reference against the GNSS Validation tool first.
• Threshold blindness. The default acceleration threshold of 3 mm/yr suits mm-level Sentinel-1 work on temperate sites; noisy tropical scenes may need a wider threshold, and high-quality urban stacks a narrower one. State the threshold with the results.
• Treating steps as geology. Until the interferograms around the flagged date are checked, a step is a data-quality hypothesis, not a finding.
• Mixed time windows. Points with different observation periods (new buildings, mission gaps) produce rates over different baselines — the span column exists so you can spot them.

Frequently asked questions

Must the displacement series be cumulative, or per-interval?

Cumulative, as SBAS/PS processors export. If your source gives per-interval increments, cumulate them before import — the tool's plots and statistics assume a running sum.

Why a linear fit and not something fancier?

Because the deliverable is a report number a reviewer can recompute with two statistics functions. Piecewise and periodic models are valuable, but they add assumptions this screening stage cannot defend.

Can I analyse more than six points at once?

Yes — the six-curve demo is for readability. Real imports of hundreds of points work; the chart legend scrolls, and the table carries every point regardless.

What acceleration threshold should I use?

Start at 3 mm/yr, then check the flagged points against the chart. If the flags are catching seasonal wiggles, widen; if genuine accelerations slip through, narrow. Record the final value.

Do the flags survive export?

Yes — the CSV includes both half-rates, the accelerating boolean and the step date, so the classification logic is fully auditable offline.

Related tools

The LOS Converter produces the consistent vertical series this tool expects; the Hazard Classifier provides the spatial view that tells you which of these temporal stories happens where; the GNSS Validation tool anchors the rates against ground truth.