Skip to content

ADR 0004: Grounding defaults to a bias-only correction, not a free-slope affine fit

Status

Accepted. The most-cited decision in this project.

Context

Grounding corrects each source toward the station with an affine map \(y \approx a + b\,x\), fitted per source × variable × lead bucket. The textbook choice — and what model output statistics (MOS) has done for decades — is to fit both parameters by least squares.

We did that first. It made forecasts worse.

grounded_equal_weight was losing to an uncorrected equal-weight blend at 48–168 h leads, and its bias column read +1.2 to +1.4 °C. The correction was injecting bias.

The mechanism, traced by inspecting fitted coefficients fold by fold, is regression dilution. Regressing truth on a noisy predictor gives

\[b_{\text{ols}} = \frac{\operatorname{cov}(x,y)}{\operatorname{var}(x)} < 1\]

essentially always, because the forecast carries error the truth does not. Fitted slopes came out at 0.76–0.89.

A slope below 1 shrinks predictions toward the training-period mean. Inside the training distribution that genuinely lowers MSE — it is Stein-like, and it is why the textbook recommends it. But it makes the correction a function of the training-period mean, and the moment the evaluation period sits in a different regime, "shrink toward the training mean" becomes a mean-dependent tilt.

The station's data made this vivid rather than subtle: truth exists only in summer 2025 and spring 2026. The training window was all-summer (mean 21.4 °C); the test folds were spring (mean 13–20 °C). So the "correction" was a warm tilt, worst exactly where the test period was coldest — one fold with test mean 13.2 °C carried a bias of +2.10 °C.

Decision

Default the slope to \(b = 1\) — a pure bias correction, \(a = \bar{y} - \bar{x}\), the mean training error.

The slope is opt-in via slope_shrinkage, \(b = 1 + \lambda(b_{\text{ols}} - 1)\), with \(\lambda = 0\) the default (BIAS_ONLY) and \(\lambda = 1\) the free fit (FREE_SLOPE).

Both variants stay registered — grounded_equal_weight and affine_equal_weight — so the leaderboard, not this document, decides when a longer and seasonally representative archive has earned the slope back.

Why this works

A bias-only correction is equivariant to level shifts. Under \(y \mapsto y + c\), \(x \mapsto x + c\), the fitted intercept \(\bar{y} - \bar{x}\) is unchanged. Change the regime and the correction is the same. The free-slope correction has no such property, which is precisely the failure above.

Measured result

Bias-only beat the free slope in every lead bucket:

bucket bias-only (now default) free slope (previous default)
24–48 h MAE 1.367, bias +0.23 MAE 1.471, bias +0.56
48–96 h MAE 1.713, bias +0.67 MAE 2.104, bias +1.45
96–168 h MAE 1.775, bias +0.26 MAE 2.143, bias +1.30
168–240 h MAE 2.345, bias −0.44 MAE 2.368, bias +1.21

Measured on 13 months of Open-Meteo Previous Runs backfill against the Crestline station, July 2026. As with every number in this documentation, this is a historical illustration from one station — see Limitations §4.1.

Consequences

Good.

  • The correction cannot re-inject a mean-dependent tilt, which is the specific failure that motivated this.
  • It is one parameter instead of two, so it is estimable on far thinner slices.
  • The behaviour is explicable to an operator in one sentence.

Costs.

  • Where a provider genuinely has a scale error — systematically compressing the diurnal range, say — bias-only cannot correct it. affine_equal_weight and harmonic_grounded_equal_weight remain available for the leaderboard to promote if that case is real.
  • On a seasonally representative archive, the free slope may well win. The default is right for the data we have, not for all data.

The generalizable lesson, which is why this ADR is cited so often: a correction fitted on an unrepresentative window is not a neutral no-op — it is an active source of error. And the only reason it was caught is that bias is reported as its own column. A leaderboard showing only MAE would have shown grounding as merely "not helping", and the mechanism would have gone unnoticed.