A weather model's mistakes are predictable, and that makes them fixable

TL;DR

• Researchers report that a machine-learning post-processing layer improved weather forecasts for weeks 3–4, and that it won ECMWF's 2025 real-time forecasting competition.
• The method learns each model's average error for every location, date and probability bin, mixes in recent observations, and returns a corrected probability distribution.
• The gains are real but start from a low base. Even after correction, these forecasts beat "the historical average" only by a modest margin.

What happened

On 14 October 2026, MIT News reported that a team from Microsoft Research, MIT, Harvard, the University of Toronto, Brazil's IMPA and ECMWF had published a method in Nature for correcting weather forecasts two to six weeks ahead. The Verge also covered it. MIT says the method "doubled forecasting accuracy" when applied to a gold-standard model, and that "for the first time, the model offered an improvement over relying on climatologic averages." MIT also reports that Kenya's meteorological office has asked about using it.

Some of this can be checked and some cannot. The competition result can be checked, because ECMWF ran the AI Weather Quest and publishes its leaderboard. Two co-authors work at ECMWF. The Nature publication comes from MIT's report and the code's README; the arXiv preprint (v3, 4 September 2026) lists no journal reference. The Kenya interest is MIT's report and does not appear in the paper.

The paper in brief

Weather models lose skill quickly beyond about two weeks. At that range, small per-step errors add up to large systematic errors, and raw ensembles often do worse than simply forecasting the historical average. The paper introduces probabilistic bias correction (PBC). PBC turns any model's ensemble into probabilities for five climatological bins, then runs two lightweight corrections: Debias++ subtracts the model's historical error, and Persistence++ is a regression that mixes the model with recent observations. It projects each output back onto valid distributions and averages them. PBC improved ECMWF's dynamical model, its AI model (AIFS-SUBS) and a hybrid (PoET). An ensemble of the corrected outputs won the 2025 AI Weather Quest. The interesting part is that it works across very different input models using only averages and least squares.

The math

Setup: forecast a CDF, not a number

Take a grid cell $g$ and a target week $t$, for example average temperature over days 19–25. The thresholds $q_{t,g}(1),\dots,q_{t,g}(4)$ are the climatological quintiles: the 20th, 40th, 60th and 80th percentiles of observations near that calendar date over the past 20 years, with $q_{t,g}(5)=\infty$. The forecast is a cumulative distribution over these $K=5$ bins. $F_{t,g}(k)$ is the predicted probability that the outcome $y_{t,g}$ falls below $q_{t,g}(k)$. An ensemble of $M$ model runs becomes a CDF by counting, $F(k)=\frac{1}{M}\sum_m \mathbb{I}[\hat y_m<q(k)]$. What actually happens is recorded as a step function, $O_{t,g}(k)=\mathbb{I}[y_{t,g}<q_{t,g}(k)]$.

The score

$$\mathrm{RPS}_{t,g}=\sum_{k=1}^{K}\big(F_{t,g}(k)-O_{t,g}(k)\big)^2$$

The ranked probability score (RPS) is the squared Euclidean distance between the forecast CDF and the observed step function. It is the Brier score (MSE on probabilities) summed over every threshold. Because it works on cumulative probabilities, putting mass in a neighbouring bin costs less than putting it far away.

$$\mathrm{RPSS}=1-\frac{\sum_{t}\sum_{g} w_g\,\mathrm{RPS}_{t,g}}{\sum_{t}\sum_{g} w_g\,\overline{\mathrm{RPS}}_{t,g}}$$

$\overline{\mathrm{RPS}}$ is the score of climatology, which always forecasts $F(k)=k/K$. The weight $w_g=\cos(\text{latitude})$ corrects for grid cells shrinking toward the poles. RPSS > 0 means the forecast beats climatology, 0 means a tie, and 1 would be a perfect forecast.

Worked example. Suppose the week lands in bin 4, so $O=(0,0,0,1,1)$. Climatology $(0.2,0.4,0.6,0.8,1)$ scores $0.04+0.16+0.36+0.04=0.60$. A forecast leaning warm, with bin probabilities $(0.1,0.1,0.2,0.3,0.3)$, has CDF $(0.1,0.2,0.4,0.7,1)$ and scores $0.30$, so RPSS is 0.5 on this case. The mirror-image forecast leaning cold has CDF $(0.3,0.6,0.8,0.9,1)$ and scores $1.10$, so RPSS is −0.83. Being confidently wrong costs more than being cautious.

There is also a bias–variance view. If the outcome is truly random with $P(y<q(k))=P_k$, then $\mathbb{E}[\mathrm{RPS}]=\sum_k (F(k)-P_k)^2+\sum_k P_k(1-P_k)$. The first term is the forecast's miscalibration. The second is uncertainty that no forecast can remove. At weeks 3–4 the second term dominates, so even a perfect forecast barely beats climatology, and a small bias in the first term can erase that edge.

How a small bias erases subseasonal skill

interactive

• biased model
• bias removed (b = 0)
• climatology

Hover or drag across the chart to read values.

predictable signal μ (in climatological std devs)0.3remaining spread σ0.9

best possible RPSS:

0.0595

irreducible share of climatology's RPS:

94.1%

Debias++: add back the average error

$$\tilde F_{t^\star,g}(k)=\operatorname{clip}\Big(F_{t^\star,g}(k)+\frac{1}{|\mathcal S|}\sum_{t\in\mathcal S}\big(O_{t,g}(k)-F_{t,g}(k)\big),\;[0,1]\Big)$$

Take the model's forecast for target date $t^\star$ and add the average gap between observed and forecast cumulative probability over a training set $\mathcal S$. Here $\mathcal S$ is past dates within $s$ days of the same time of year, over the previous $Y=20$ years. The training forecasts are hindcasts: the current model rerun on past dates. Each grid cell, threshold $k$ and lead time gets its own correction. For example, suppose that around this date the model's $F(2)$ averaged 0.55 but the bottom 40% occurred only 40% of the time. Debias++ then subtracts 0.15 from today's $F(2)$. This is the textbook bias correction for an estimator, done in probability space. The window $s\in\{14,28,35\}$ is chosen by which one gave the lowest RPS over the previous three years. The algorithm also averages over forecast issuance dates, but every configuration the authors used sets that to one date, so I have dropped it.

Persistence++: regression with recent weather

$$\hat F_{t^\star,g}(k)=\operatorname{clip}\Big(\hat\beta_g^{\top}\big[1,\;C_{t^\star,g}(k),\;O^{\mathrm{lag1}}_{t^\star,g}(k),\;O^{\mathrm{lag2}}_{t^\star,g}(k),\;F_{t^\star,g}(k)\big],\;[0,1]\Big)$$

Five features go into this regression, each for threshold $k$ at cell $g$:

• an intercept;
• $C$, a 20-year observed climatology for that calendar day;
• two recent weekly observation indicators that were already fully observed when the forecast was made (I simplified the paper's lag indices);
• the model's own forecast $F$.

The weights $\hat\beta_g$ come from ordinary least squares of $O_{t,g}(k)$ on these features over the training dates. This is a linear probability model fitted separately for each location. It lets the data decide how far to trust the model compared with persistence and the seasonal norm.

Projection and averaging

Each correction is applied threshold by threshold, so the output may not be monotone. For example, $(0.15,0.42,0.38,0.75,1)$ is not a valid CDF. Isotonic regression solves $\min_{z_1\le\cdots\le z_K}\sum_k (z_k-F(k))^2$ by pooling adjacent violators. Here it pools 0.42 and 0.38 into $(0.15,0.40,0.40,0.75,1)$. This can never hurt. Every possible $O$ is itself a valid CDF, the set of valid CDFs is convex, and projecting onto a convex set never moves you farther from any point inside it. Since RPS is squared distance, the score improves or stays the same for every possible outcome. Clipping to $[0,1]$ is the same argument with a box.

Finally, PBC averages the two projected CDFs. RPS is convex in $F$, so by Jensen the average scores no worse than the mean of the two components' scores on every outcome. That does not guarantee it beats the better of the two.

No leakage, low cost. Each forecast is trained only on observations that would have been available $\ell^\star-1$ days before the target, and PBC is retrained every day. Training costs are averages and a five-feature least-squares fit per grid cell. Producing the ensembles costs far more: in recent years, ECMWF's subseasonal forecast has 101 global model runs per issue.

What the results say

• Against ECMWF's operational debiasing (2016–2024): temperature RPSS rises 26–37% from a baseline of 0.07–0.10, and pressure rises 16–32% from 0.06–0.11. Precipitation goes from near zero to consistently positive. Skill improves in 98% of grid cells for precipitation, 91–92% for temperature and 89–91% for pressure.
• AI and hybrid inputs: PBC doubles AIFS-SUBS's mean RPSS (0.03) in 2025. It lifts the already-corrected PoET by 68–98% for precipitation (baseline 0.03–0.04) and 5–7% for temperature (baseline 0.16–0.19) in 2024.
• Competition: MicroDuet, which combines PBC-ECMWF and PBC-PoET, placed first in every variable and lead time in the September–November 2025 season, ahead of 34 teams and six national centres. For precipitation it scored 0.06–0.07: twice the multi-model ensemble in week 3 and three times it in week 4. It also placed first for both lead times in the December–February season.
• Extremes: For week-3 extreme highs, Brier skill improves 51% for temperature and 39% for pressure over debiased ECMWF. Flood forecast skill rises 76–92%, while operational debiasing pushed it to near zero.

Limitations. The authors say PBC corrects predictable errors and cannot replace better models: it cannot create signal the input doesn't contain. Absolute skill stays small, so these are tilted odds on weekly averages over a 1.5° grid, not day-by-day forecasts. The AIFS-SUBS and PoET results each cover a single year (179 and about 105 target dates). MicroDuet's weighting was chosen on 2024 data. The cold-snap forecast highlighted in the paper is a single case. The ground truth is ERA5 reanalysis, not station observations.

Connecting the dots

This paper is the source of the news, not just related to it. Two of MIT's claims need qualifying. "Doubled" matches the paper's result for ECMWF's AI model, AIFS-SUBS. On ECMWF's dynamical model, the gains over operational debiasing are 16–37% for temperature and pressure, with a larger jump for precipitation only because it started near zero. MIT also writes that "no one had been able to show a model predicts weather better than long term averages," but the paper's own baselines say otherwise: debiased ECMWF, AIFS-SUBS and PoET all have positive average RPSS for some variables. The paper's narrower claim is that PBC turns raw ECMWF's negative temperature and pressure skill positive. In the competition, it beat climatology on precipitation, where all six debiased national models fell below it.

Why it matters

For forecasting centres, PBC can replace the standard debiasing step directly, and it costs very little next to running an ensemble. The authors point out that this matters for resource-constrained agencies, which is consistent with Kenya's reported interest. For ML researchers, it shows a familiar pattern. When the signal is weak, careful scoring, bias estimation without leakage and simple stacking can beat bigger models, and a valid-CDF projection gives a free improvement. Practically, two to four weeks of extra warning is the window in which farmers, grid operators and relief agencies can still act.

Things to watch: whether a national service runs PBC operationally, and whether MicroDuet holds its lead across a full year of AI Weather Quest seasons.

Go deeper

• The paper on arXiv and open-source PBC code
• MIT News coverage and The Verge's story
• Adaptive Bias Correction for Improved Subseasonal Forecasting, the earlier deterministic method that PBC builds on
• Microsoft Research's subseasonal forecasting project page, with background on MicroDuet and the AI Weather Quest