Methods and systems to improve grounded-weather-forecast¶

Research synthesis, 2026-07-18. Four parallel literature/web sweeps (statistical post-processing & combination; online learning & conformal calibration; nowcasting & PWS quality control; data sources & ML weather models) mapped onto this codebase's measured failure modes. Complements — and in places supersedes — docs/improvement-plan.md; a cross-reference table is at the end.

0. Diagnosis: why it currently underperforms¶

From the code, the leaderboards, and docs/limitations.md:

1. Grounding — the core thesis — is losing. grounded_equal_weight trails raw equal_weight at 24–96 h (MAE 1.367 vs 1.336 at 24–48 h; 1.713 vs 1.593 at 48–96 h, with DM p = 0.001). Cause: AffineGrounding fits one static intercept per (source, variable, lead bucket) over all history, so diurnal and seasonal bias structure averages to ~zero and the seasonally unrepresentative window injects error instead of removing it.
2. The live leaderboard is empty. The archive is too young to form folds, so nothing can be promoted and predict serves degraded equal weight.
3. Providers are redundant (error correlations 0.5–0.9; effective ensemble size ~1.8 of 8), so weighting schemes have almost nothing to win, and provider-column spread is a dishonest uncertainty signal.
4. Anchoring is unfitted and unevaluated. τ comes from a grid search that the synthetic backfill (24 h-multiple leads only) can never exercise below 24 h; the minutely product double-anchors and uses a never-fitted constant.
5. No calibrated probabilistic output. CRPS/PIT/reliability are implemented but unwired; no method emits quantiles.
6. The self-improvement loop is open. "Online" experts are batch-replayed from a uniform prior at every serve; self-verification is written to a report and never fed back; promotion does argmin-MAE with one DM test (winner's curse across 12 methods × 10 buckets).
7. Truth is trusted on faith. Radiation-shield heating, gauge undercatch, and slow sensor drift are acknowledged but undetected (no external cross-check, no physical error model).

The literature has direct, proven answers to every one of these. The headline finding: the operational state of the art (NOAA's National Blend of Models) is architecturally almost exactly this project — adaptive decaying-average bias correction per input, then mild inverse-MAE weighting — which both validates the design and hands it a recipe for the parts that are failing.

1. Fix grounding: adaptive, diurnally-aware bias correction (highest priority)¶

Three independent research threads converged on the same answer.

1a. Hour-of-day-keyed decaying-average (EWMA) bias correction — the operational default¶

Maintain bias[source, var, lead_bucket, hour_bin] ← (1−w)·bias + w·(fcst − obs) with w ≈ 0.02–0.1. This is literally what NCEP has run operationally since 2006 (NAEFS; Cui, Toth, Zhu & Hou 2012, Wea. Forecasting) and what the NBM uses per grid point/projection/element (Veenhuis slides, NBM algorithm description).

Why it beats the current static fit and the planned harmonic fit:

• No training window to choose. Lang et al. 2020, NPG — evaluated at mountain stations — shows sliding short windows are the worst scheme for seasonally varying error; adaptive/EWMA and smooth-seasonal coefficients are the fixes. This is exactly the §4.1 grounding failure.
• Survives archive gaps (state goes stale, re-converges in ~1/w days) and adapts to season drift automatically — no phase model needed.
• 4–8 hour-of-day bins per lead bucket restore the diurnal structure the current per-bucket intercept averages away, at the cost of a handful of online scalars per source.

Converges in ~2–8 weeks of data; degrades gracefully to zero correction. Register as e.g. ewma_grounded_equal_weight beside the current methods.

1b. The published single-PWS template: moving-average bias + lead-time Kalman filter¶

Alerskans & Kaas 2021, Met. Apps compared six adaptive schemes on 100 private weather stations — the closest published analog to this project. Winner: a long-memory moving-average bias term (≈ §1a) plus a lead-time Kalman filter that propagates today's observed short-lead error to longer leads, explicitly designed to need "no long record of observations." Their MA+KF decomposition maps 1:1 onto grounding + anchoring. Supporting lineage: Homleid 1995 (eight time-of-day bias states — the diurnal KF), Crochet 2004 (adaptive per-station estimation of the KF noise variances, i.e. the gain and decay are fitted, not hand-set — operational at met services for decades).

1c. SAMOS: standardized-anomaly grounding — the batch/mountain-terrain alternative¶

Transform obs and each source to standardized anomalies w.r.t. smooth harmonic-in-(hour, day-of-year) site climatologies, then fit one small regression valid across all seasons/hours (Dabernig, Mayr, Messner & Zeileis 2017, QJRMS; developed for Alpine terrain; modern extension MIXSAMOS-GB 2024). The bias model no longer needs to learn the diurnal cycle — it is removed before fitting, so all rows pool into one seasonally valid fit. Key trick for the thin station record: build the climatology from the provider archive or ERA5 rather than station obs (the harmonic climatology has only ~10 dof). Météo-France's operational QRF similarly works in forecast-anomaly space (Taillardat & Mestre 2020). Cheap parametric middle road: add 4–6 sin/cos(hour, doy) terms to the intercept (tsEMOS shows this significantly beats static EMOS — Jobst, Möller & Groß 2024).

Recommendation: implement §1a first (days of work, no new deps, matches the NBM), register the improvement plan's harmonic/solar variant as the batch challenger informed by §1c, and let the leaderboard arbitrate. Fold §1b's lead-time KF into the anchoring redesign (§3).

2. Fix data starvation: diverse sources, honest ensembles, deeper backfill¶

The scarcest resources are (i) genuinely decorrelated sources and (ii) honest spread. Both became cheap in 2025–2026.

2a. ML-model ensembles via the Open-Meteo Ensemble API — zero new auth¶

The Ensemble API (free non-commercial, same client already in use) now returns individual members for, among others:

One call per cycle for four families ≈ 200 members from independent modeling systems: an honest predictive distribution to calibrate against the station, replacing the structurally under-dispersed provider-column spread. Caveat: Open-Meteo retains only the latest run for individual members — poll and archive them (mean/spread or quantiles per variable × lead is enough).

2b. NBM as ingredient and benchmark¶

NBM v5.0 (operational May 2026) is a bias-corrected mega-blend at 2.5 km with percentile elements — exactly what this project builds, with vastly more inputs. Trivial access: NBM text bulletins (NBH/NBS/NBE/NBP) for the nearest of 9,000+ stations, plain text over HTTPS from NOMADS; GRIB via Herbie or AWS byte-range. If the blend cannot beat station-grounded NBM, that is the leaderboard's most informative row.

2c. Backfill that fills the sub-24 h gap¶

The Previous Runs backfill only populates ≥24 h buckets — the reason anchoring is unevaluated. Two fixes:

• dynamical.org: free, keyless, analysis-ready Zarr/Icechunk archives on AWS — GEFS (35-day, 31 members) + GEFS analysis, HRRR back to 2014, AIFS-ENS archived since Jul 2025 (catalog), and MRMS. Full forecast cycles at native (6-hourly) steps → real 0–24 h leads for backtesting, and ensemble history to pre-train spread models before the live archive matures. Point extraction is a few lines of xarray.
• GribStream (free tier / ~$10+ mo): as-of historical forecast queries for NBM/GFS/HRRR — NBM backfill, since NOAA's public NBM archives were discontinued.
• Open-Meteo Historical Forecast + Single Runs APIs (docs): archives of the exact models already polled (most from Jan 2024; full single runs archived from Apr 2026) — backfill every provider column that is an Open-Meteo model in one weekend job.

2d. Neighbor-station truth via Synoptic¶

Synoptic Data free tier (5k requests + 5M service units/month; open-access public networks free; MesoWest classic was retired 2025): RAWS/SNOTEL/DOT neighbors near the site that no consumer API carries, via SynopticPy. Feeds the truth-QC layer (§5) and an elevation-aware truth panel. api.weather.gov station observations remain the free METAR fallback.

2e. Minutely precipitation with radar information¶

Cheapest first step: Open-Meteo minutely_15 — in North America this is real HRRR 15-minutely sub-hourly output (radar-assimilating), not interpolation (blog). The full option later: MRMS PrecipRate (1 km / 2-min, on AWS and dynamical.org) + pysteps optical-flow extrapolation of a small patch around the site — with a beam-blockage check first at 1400 m (a 2025 W&F paper tunes STEPS for MRMS: WAF-D-24-0240.1).

Also worth a look: weatherapi's negative error correlation with every other provider (−0.32 vs met_norway) — either it is the one genuinely diverse source in the current set or its ingestion (timestamp semantics?) is broken. Both possibilities are high-value to resolve.

3. Make anchoring real: fitted decay, trend state, single pass¶

The theory result that organizes everything: if the obs-minus-blend residual is stationary AR(1) with lag-1 autocorrelation ρ, the optimal anchor is exactly exponential decay with rate −ln ρ — so the current shape is right, but the constant must be fitted as the residual ACF, and the documented deviations from AR(1) are precisely the improvements:

1. Fit τ from the residual ACF now. The ACF of r(t) = obs − blend at lags 1 min–6 h estimates ρ(τ) per variable (day/night separately) with no short-lead forecast archive needed. Near-zero code risk; kills the never-fitted constant.
2. Persist, then ramp — not decay-from-zero. INCA (validated in the eastern Alps — Haiden et al. 2011, WAF) carries the observed level forward with the NWP tendency for ~2 h, then ramps the residual out by ~6 h. NOAA's LAMP fits per-lead regression weights obs↔MOS and finds observation information persists to ~12–20 h for temperature (LAMP background) — an argument against forcing the anchor to zero by 3 h (_ANCHOR_MAX_LEAD).
3. Anchor level + damped trend. Replace the level-only residual with a damped-Holt (level, trend, damping φ) state on the 1-min residual series — uses the observed derivative the station uniquely provides, while damping prevents runaway extrapolation (fpp3 ch. 8; fit via statsmodels ETS in weeks of data).
4. One anchoring pass. Anchor once at the minutely level against the un-anchored hourly path and aggregate minutely→hourly (the IMPROVER lesson: each processing step applied once, then blend — BAMS 2023). Fixes the double-anchor and the interp-clamp defects structurally.
5. Probabilistic anchoring, later. Nipen, West & Stull 2011, WAF is the probabilistic generalization: model the verifying CDF value as a fitted first-order Markov process — updated forecasts sharpen for the first hours and relax back to the base forecast.
6. Start logging live issued paths immediately (already partly done via predict_history) and, after ~60–90 days, fit inverse-MSE lead weights w(τ) = MSE_NWP/(MSE_now + MSE_NWP) per variable and day/night — the LAMP/Kober-style empirical crossover (typically ~3–6 h for temperature, ~1–3 h for precip).

Precipitation onset/cessation nowcast (new capability): logistic recalibration of provider minutely PoP against tipping-bucket wet/dry outcomes (~50–100 wet hours suffice for two parameters), plus a gauge-state-conditioned override — if the bucket is tipping and a provider says dry within 10 min, trust the bucket with a ~20–30 min decaying override.

4. Ship calibrated uncertainty¶

Sequenced by data appetite:

1. EMOS/NGR first (Gneiting et al. 2005): μ = a + b·blend, σ² = c + d·spread, CRPS-fit on a seasonally weighted 40–60 day window — the original design point was thin data. Four parameters per variable × lead bucket; feeds the already-implemented CRPS/PIT metrics. With real ensemble spread from §2a, d becomes meaningful (with provider-column spread expect d ≈ 0 — the shared-parent caveat).
2. IDR / EasyUQ as the zero-tuning benchmark (Henzi, Ziegel & Gneiting 2021, JRSS-B; Walz et al. 2024, SIAM Review; isodisreg on PyPI): calibrated conditional CDF from the single blend covariate, no hyperparameters — the universal baseline any fancier distributional method must beat.
3. Online conformal wrapper for guaranteed coverage under drift. The recommended stack from the 2021–2024 literature: SAOCP (Bhatnagar et al., ICML 2023) or conformal PID control (Angelopoulos, Candès, Tibshirani, NeurIPS 2023 — benchmarked on temperature forecasting, code at conformal-time-series) per variable × lead bucket, ~10 floats of state each; per-hour-of-day coverage verified via conditional-guarantees conformal (Gibbs, Cherian & Candès, JRSS-B 2025) rather than 24 Mondrian bins that shatter a thin sample. Batch baseline via MAPIE / crepes. Note the improvement plan's plain-ACI choice is superseded: ACI's single learning rate oscillates or lags; DtACI/SAOCP remove the knob.
4. QRA for quantiles straight from point providers (Nowotarski & Weron 2015; lasso-regularized for collinearity — Uniejewski & Weron 2021): pinball regression on provider points; GEFCom-winning pedigree; LightGBM quantile mode with a monotone constraint on the blend feature is the nonlinear variant. Always sort quantiles (monotone rearrangement).
5. CRPS Learning as the unifying upgrade (Berrisch & Ziel 2023, J. Econometrics): quantile-wise BOA with smoothing across levels — turns the existing BOA/fixed-share/sleeping machinery into the probabilistic blender itself, with forgetting built in. A 2026 successor, AdaWeather (arXiv:2606.02663), gets log-regret against the best static mixture on temperature — direct evidence the GBM-vs-experts dichotomy should eventually be unified.
6. Defer neural distributional methods (DRN, BQN, transformers — every success pools hundreds of stations or years), D-vine copulas, and BMA (weights degenerate under near-duplicate members). Reconsider analog ensembles (Delle Monache et al. 2013) at the ~12-month archive mark. Operational warning from Météo-France: minimizing CRPS alone does not guarantee reliability — keep reliability tests beside CRPS in promotion (Zamo, Bel & Mestre 2020).

5. Trust the truth: a station-QC layer with physics and neighbors¶

Everything upstream optimizes toward the station; if the station drifts, the whole system calibrates to a broken sensor. Three cheap, proven defenses:

1. Radiation-shield error model (detection + correction). Daytime error of passively ventilated shields ≈ f(solar S, wind u), classically increasing in S and decreasing in u (1–3 °C at high-S/low-u for consumer shields; BAST 2022 regression method). The station has the co-located anemometer (and pyranometer): regress daytime residual on S/(1+u); a significant positive slope that grows over months is the failing-shield signature; the fitted curve doubles as a correction and as inflated observation-error variance so sunny-calm observations anchor more weakly.
2. Neighbor cross-check. MET Norway's titanlib buddy check / Spatial Consistency Test (designed for sparse mountain networks; Båserud et al. 2020) against 3–10 lapse-adjusted Synoptic/METAR neighbors (§2d), as a daily cron: 30-day median of station-minus-consensus, alert on drift > ~1 °C. The single-station-applicable core of CrowdQC+ (Fenner et al. 2021): a rolling ≥72 h correlation with a reference series (neighbor or the blend itself) below ~0.9 flags a failing sensor even when values stay plausible — the direct answer to "a failing radiation shield can look plausible for months."
3. Gauge undercatch and rain QC. WMO-SPICE transfer functions (catch efficiency as a function of wind and temperature — Kochendorfer et al. 2018, HESS) apply directly because the anemometer is co-located; PWSQC's false-zero / high-influx filters (de Vos et al. 2019, GRL) with provider/radar QPE as the "neighbor."

6. Self-improvement: true online state, drift alarms, honest promotion¶

1. Replace batch replay with delayed-feedback online updates. Flaspohler et al., Online Learning with Optimism and Delay, ICML 2021 was developed for weather forecasting with late-arriving truth: DORM+ / AdaHedgeD are tuning-free with optimal regret under delay, and "delay as optimism" (use the last resolved loss as a hint) cancels much of the delay penalty. Code: poold. Concretely: per (variable × lead bucket), persist expert weights + a queue of outstanding (issue-time, pending-losses) records; when truth resolves, pop and apply the update. Removes the per-serve refit and activates the dormant ArtifactStore machinery.
2. Two-tier drift detection for provider backend swaps. The delayed-truth trap: residual-based detection lags by the lead time. So (i) fast alarm on provider-vs-consensus deviation at issue time (a swap is visible against the other 7–12 providers within hours), triggering down-weight; (ii) slow confirmation on truth-based residuals (BOCPD — Adams & MacKay 2007 — or Page-Hinkley / ADWIN via river / Frouros), triggering a grounding-state reset. ADWIN's adaptive window length is directly "how much history is still valid for grounding."
3. Promotion: sequential Model Confidence Sets instead of argmin-MAE + one DM test. MCS (Hansen, Lunde & Nason 2011, Econometrica; Python: model-confidence-set, arch.bootstrap.MCS) returns the set statistically indistinguishable from best — thin data ⇒ larger set ⇒ keep the incumbent. The e-process sequential MCS (JRSS-B 2025) is valid at every look, so promotion can re-run after every backtest refresh with no alpha-spending bookkeeping. Stopgap this week: Harvey–Leybourne–Newbold small-sample DM correction + Benjamini–Hochberg across the slice grid. Report winner's-curse-corrected scores for whatever is promoted (Andrews, Kitagawa & McCloskey 2024, QJE).
4. Soft promotion as the default posture. Since full-information losses for all methods arrive with every resolved forecast, a second-level fixed-share aggregation over the 12 methods gives drift-adaptive "soft promotion" with regret guarantees; reserve hard promotion (interpretability, cost) for the sequential-MCS gate.
5. DM autocorrelation fix (from the improvement plan, confirmed): HAC lag from the valid-time overlap structure, or collapse to one loss per valid_time.

7. Blending: what not to build¶

The combination literature blesses the current outcome and warns against the obvious next steps:

• Equal-ish weights are near-optimal at this correlation and sample size. Weight-estimation error, not method choice, is what loses (Claeskens et al. 2016); with ρ ≈ 0.9 the optimal-weight variance explodes, and Smith & Wallis 2009 explicitly endorse ignoring error covariances on short samples. The NBM itself uses only decaying-average bias + inverse-MAE EWMA weights — no covariance terms. The planned Ledoit–Wolf inverse_covariance blender is still worth registering as the honest test, but expectations should be low; cap its weight deviations from 1/K.
• Do build the 20%-trimmed mean. Zero parameters, small consistent gains, and real protection when a provider misbehaves (Jose & Winkler 2008) — the best effort/benefit ratio in the whole combination axis, and a better degraded-mode default than plain equal weight.
• Cluster providers by error correlation and keep one per cluster (subset selection beats fancy weighting under near-duplicates — Radchenko, Vasnev & Wang); this also raises the effective ensemble size behind any spread estimate.
• Skip BMA (weights degenerate on near-duplicate members). Skip full-cov GLS until years of archive exist.

8. Cross-reference with docs/improvement-plan.md¶

9. Sequenced roadmap¶

Ordered by (impact ÷ effort), respecting data availability:

The polling cron remains the binding constraint (docs/limitations.md §1) — items 1 and 4 are the two actions that make the wait productive rather than idle.