InSAR Error Budget Calculator

Every deformation number in a report is an estimate, and reviewers increasingly refuse estimates without an uncertainty statement attached. The error budget is that statement made systematic: you list every mechanism that corrupts the measurement, assign each a realistic one-sigma magnitude, and combine them into a single total uncertainty with an explicit breakdown of which mechanisms dominate. This tool performs the combination for you — five standard InSAR error sources, root-sum-square mathematics, a contribution pie chart that shows instantly whether your precision claim is limited by the atmosphere or by your own geometry assumptions — and writes the summary paragraph for the report.

The mathematical model is simple and worth stating plainly, because its simplicity is what makes it defensible. If the error sources are statistically independent, their variances add: σ_total = √(Σ σᵢ²). The share of each source is its variance divided by the total variance, so shares always sum to 100% and the dominant mechanism is the one whose square dominates. That last observation matters practically: quadrature combination forgives you moderate uncertainty in minor sources, but the largest source sets the floor — halving a 6 mm atmospheric term buys you far more than eliminating a 1 mm orbit term entirely. When you need to improve a project's precision claim, spend effort where the pie chart is fat.

When you should use this tool

• Writing the quality-assurance section of a monitoring report, where each deformation rate needs a stated uncertainty with a defensible breakdown.
• Answering the pre-award question "how precise will InSAR be on this site?" — the budget shows which correction investments (weather-model atmospheric correction, better DEM, longer archives) actually move the total.
• Comparing configurations: compute the budget twice — with and without an atmospheric correction, at two incidence angles — and the share chart quantifies the improvement.
• Preparing for review: an explicit budget with named sources pre-empts the vaguest but most damaging question, "how accurate is this really?".

When NOT to use this tool

• As evidence of achieved accuracy. A budget is a design-stage statement of expected error, not a validation result; achieved accuracy comes from the GNSS Validation tool against real observations.
• With sources that are not independent. Correlated errors do not add in quadrature — if two of your terms share a driver (say, DEM error and incidence-angle error both stemming from one bad geolocation), the quadrature model underestimates the total. Merge them or widen one honestly.
• For single-epoch claims using velocity-calibrated defaults. The default values sit at screening magnitudes for Sentinel-1 small-baseline processing; your project's parameters — baseline distribution, coherence levels, correction models — may be better or worse. Edit every line.

The five sources & where their defaults come from

DEM error enters through the residual topography phase; small-baseline strategies that keep perpendicular baselines short suppress it strongly, which is why the default is modest. Orbit error reflects residual satellite-position uncertainty after precise orbit products — small for Sentinel-1 with POEORB, and it mainly manifests as long-wavelength ramps. Atmospheric delay is the heavyweight in most real budgets: turbulent wet delay and stratified troposphere can easily contribute several millimetres per epoch in humid or high-relief terrain, and this is the term that weather-model corrections (ERA5, GACOS-class products) attack. Decorrelation noise covers temporal and geometric loss of coherence, which depends on land cover, time interval and baseline spread — it shrinks as your archive grows. Incidence-angle error is the projection uncertainty you already met in the LOS Converter: |v · tan θ| · dθ, which is why it scales with the deformation magnitude itself and grows toward far range. Every default in the tool is a screening-level typical magnitude, labelled as such; the credible move is to replace each with a value justified by your own processing parameters and cite that justification.

Step-by-step usage & output

1. Enter the five one-sigma values in the unit that matches your report — millimetres per epoch for single-measurement claims, mm/yr for velocity claims. Keep the unit consistent across sources.
2. Compute. The results table lists each source with its magnitude and variance share; the pie chart makes the hierarchy visible; the total appears above with the unit label.
3. Export the Markdown summary — it names the dominant source and carries the screening-default caveat, so the report cannot be accused of overstating rigor.
4. Iterate: adjust the source you intend to improve (atmospheric correction is the usual candidate) and watch the total respond. Two or three such comparisons usually settle the processing plan.

A worked example you can reproduce

Run the tool with its opening defaults and you get a concrete illustration of the whole point of budgeting. The five screening defaults produce a total uncertainty of roughly 7 mm, with the atmospheric term alone contributing about two-thirds of the variance while the orbit term is nearly invisible. The engineering reading is immediate: buying a better orbit product would be money spent on the thin slice of the pie, whereas an atmospheric correction that halved the atmospheric term would pull the total down by a fifth or more. That asymmetry — small sources barely matter, the dominant source defines your ceiling — is the single most useful thing an error budget teaches, and the pie chart teaches it without a single line of text. Repeat the exercise with your own project values; the conclusion you can defend in a review is not the total itself but the demonstrated reasoning of which correction to buy next.

Common pitfalls & mistakes

• Double counting. If your atmospheric term already includes the DEM-correlated stratified component, do not add it again under DEM error. Define each source's scope once, in writing.
• Unicorns in the small print. Quoting σ_total = 0.4 mm/yr from optimistic defaults impresses nobody who has measured real atmospheric signal. The pie chart's honesty is the product; use realistic values.
• Mixing epochs and velocities. Per-epoch errors and per-year rates are different quantities; converting between them requires the observation span, not a unit relabel.
• Forgetting the spatial structure. Atmospheric error is spatially correlated — it inflates gradients near the deformation feature less than point velocities far from any reference. State the scope of the budget.

Frequently asked questions

Why root-sum-square and not linear addition?

Independent random errors add in variance, not in magnitude; linear addition would dramatically overestimate the total. The model's honesty lives in the independence assumption — check it.

My dominant source is atmospheric. What now?

That is the normal finding. Weather-model corrections, dense time-series averaging and spatial filtering are the standard levers; recompute the budget with the post-correction magnitude.

Should the budget include unwrapping errors?

They are not Gaussian and resist a σ. Handle them as events — the Time-series tool's step detection flags candidates — rather than folding them into the budget.

How does this connect to the GNSS comparison?

The GNSS Validation tool measures the achieved σ; the budget predicts it. When the measured value far exceeds the prediction, one of your source assumptions is wrong — usually the atmosphere.

Can I add a sixth source?

Not in the form, but the arithmetic is trivial: add its square into the sum. The Markdown report lists shares explicitly, so a manual extension stays auditable.

Related tools

Use alongside the LOS Converter (whose incidence-uncertainty column implements one of the five sources) and the GNSS Validation tool (which measures what this tool predicts). The Sample dataset guide