version: "1.0.0" name: uncertainty-quantification description: "Uncertainty for results: error propagation, bootstrap and block-bootstrap CIs, ensemble spread, conformal prediction, native product uncertainty fields, reporting rules."

uncertainty-quantification

How results earn their error bars: invocable directly ("put a confidence interval on this") and consulted automatically whenever a quantitative result heads for a report.

The house reporting rule (hard rule)

Hard rule: invariant, universal, fires without consulting the bundle. No headline quantitative result without an uncertainty statement (an interval, a spread, or the product's native uncertainty), or an explicit one-line reason why none is available. Every stated interval carries its method and level: "0.85 +/- 0.12 PW (95% CI, moving-block bootstrap, block length 12 months)" is a result; "0.85 PW" is not. The report skill enforces this in its Results section; analysis-review checks for it after the fact.

Choosing a method

• Arithmetic on inputs with known errors: error propagation.
• A statistic of a sample or series, effectively independent samples:

bootstrap.

• A statistic of an autocorrelated series (most geophysical series):

block bootstrap.

• Multiple models or ensemble members: spread, with the small-ensemble

caveat.

• The product ships uncertainty fields: use them, starting from the

dataset concept's Uncertainty section.

• An ML or statistical prediction that needs guaranteed coverage:

conformal prediction.

Error propagation basics

Independent errors add in quadrature: sums and differences combine absolute sigmas, products and ratios combine relative sigmas; correlated inputs need the covariance term, and ignoring positive covariance understates the total. For nonlinear functions, linearization is only as good as the local derivative; when in doubt, propagate by Monte Carlo (sample the inputs, run the computation per sample, quote percentiles of the output). Monte Carlo propagation is the honest default for anything beyond simple arithmetic.

Bootstrap and block bootstrap

Plain bootstrap: resample the data with replacement, recompute the statistic, at least 1000 resamples, quote percentile bounds with the level. Valid when samples are effectively independent.

Block bootstrap is the default for time series, because geophysical series are autocorrelated and plain bootstrap destroys that structure, producing intervals that are too narrow (the classic way honest-looking error bars go wrong). Resample contiguous blocks (moving-block or circular), statistic per resample, percentile CI.

Block-length guidance: the block must exceed the decorrelation scale. Estimate lag-1 autocorrelation r1; the decorrelation time is roughly (1 + r1) / (1 - r1) samples. Choose the block at or above that, and for monthly data prefer 12 months so blocks also respect the seasonal cycle. State the block length with the interval. Two pitfalls: a trended series is not exchangeable, so detrend and bootstrap the residuals (or bootstrap the trend estimator itself); and n^(1/3)-style defaults are a floor, not a justification, when r1 is large.

Native product uncertainty fields

Consult the bundle for this dataset (standing step). Before analyzing any product, consult installed knowledge concepts first, as the consult-knowledge skill sets out, and read the product's dataset concept ## Uncertainty section: the single source for whether the product ships an uncertainty field, what it captures, and what it omits (including products that ship none, where that fact is stated plainly when quoting their numbers). Restate and cite it; no product fact is carried here.

Then apply the invariant method the concept does not restate: use the fields, do not just map them, propagate them into the derived quantity. Spatially correlated errors do not average down like white noise; a basin mean of a field with correlated errors keeps most of the error unless the product documents its error correlation scale. State the assumption used.

Ensemble spread

Spread across members (standard deviation or a percentile range) is a legitimate uncertainty statement, with a mandatory caveat: small ensembles underestimate uncertainty, both statistically (a sample spread from N members is biased low and noisy for small N) and structurally (members often share model assumptions, so the true uncertainty exceeds the spread). With fewer than about 10 members, report the range, call it a lower bound on the uncertainty, and say why. An ensemble mean is never presented without its spread.

Conformal prediction

Distribution-free prediction intervals with finite-sample coverage guarantees: model-agnostic, wraps any trained predictor, no retraining. Split conformal in one breath: hold out a calibration set, compute nonconformity scores (residuals) on it, take the appropriate quantile, and widen every prediction by that amount; coverage then holds by construction under exchangeability.

When to reach for it: ML-derived surfaces and predictions (downscaling, gap-filling, biomass and yield estimation) that must state coverage to be usable; heteroscedastic cases want conformalized quantile regression so intervals vary with the predictors. Caveat: exchangeability strains under spatial and temporal correlation; calibrate on spatially or temporally blocked splits and say so. GEE-native implementations exist for Earth observation workflows, so "we could not compute intervals at scale" is rarely a valid waiver for EO ML products. Remember cartography's pairing rule: an ML surface for stakeholders ships with its uncertainty map.

The applied framing: the carbon-credit lower bound

Carbon-credit protocols allocate credits from the lower bound of a prediction interval, not from the point estimate. An estimator with great point accuracy and no honest interval earns nothing defensible; a slightly worse estimator with tight, valid intervals is worth more credits. The general lesson prices uncertainty directly: decisions consume bounds, not points, so tightening honest intervals is scientific work with direct value, and overstating a point estimate without an interval is not a shortcut, it is an unverifiable claim.

Must NOT (hard refusals)

These are the skill's hard refusals: invariant, universal statistical gates that fire without consulting the bundle (none of them restates a dataset gotcha; product uncertainty facts are consulted, not listed here).

• Never present an ensemble mean without its spread.
• Never treat quality flags as quantitative uncertainty (they are

categorical; quality-control carries the decoding rules).

• Never report an interval without stating method and level (and block

length, for block bootstrap).

• Never run a plain bootstrap on an autocorrelated series.
• Never claim conformal coverage where exchangeability is plainly broken

and unblocked.

• Never average a spatially correlated error field down as if it were

white noise without stating the correlation assumption.