The model layer — the forecast systems, calibrated and scored

2026–27, blended

Dec–Feb, climate divisions

FieldLayer

Skill, winter by winter

Leave-one-year-out, 1993–2016

Model against history, on the same winters

Ranked probability skill score for the thirds of Dec–Feb temperature and precipitation against climatology (0 = no better, 1 = perfect), each layer scored exactly as it is published: the thirds of the 1991–2020 winters, with each winter's trend level; the history layer is the atlas's own composite of that winter's El Niño or La Niña group, unshrunk. Each winter was forecast without itself (trend, thirds and composite refitted without it). The last column is the history layer's weight in the blend, w = RPSS_history / (RPSS_history + RPSS_model) with negative skill counted as zero, measured on the El Niño winters: 2026–27 is one, and that is the regime the history layer is built for.

Places	Field	Model	History	Model, El Niño winters	History, El Niño winters	History weight

History weight: from El Niño-winter skill. El Niño winters in the hindcast: every winter NOAA's ONI classes as El Niño (weak to very strong), 1993–94 to 2015–16. Only two of them were strong, 1997–98 and 2015–16, which is why the history layer needs the models this year.

Model by model

Copernicus and NMME, one vote each

Each system alone, calibrated the same way

Ranked probability skill for the thirds of Dec–Feb temperature and precipitation at the 344 climate divisions, each winter forecast without itself (0 = no better than climatology). A system with no skill it can show gets a regression slope of zero from the calibration, so its score sits just below zero. The layer combines systems, and the combination scores better than most of its members.

System	Group	Hindcast	Members	Temperature	Temperature, El Niño	Precipitation	Precipitation, El Niño	In the layer

Does NMME help?

The whole layer was built twice, with the Copernicus systems alone and with the NMME models added, each calibrated, scored and gated the same way. NMME stays in only if both gates still pass and no blended score (all winters or El Niño winters, any level, the book) drops by more than . The rule was set before the comparison was run.

Blended skill	Copernicus alone	With NMME	Change

Is a 60% really 60%?

The reliability gate

The Season Book blend

Brier skill by family

How the book's families weigh the two layers

For the Season Book the model reweights history: each past winter counts in proportion to how likely its temperature and precipitation are under the calibrated forecast, and a line's probability is the weighted share of winters, shifted to today's climate, that cleared it. Both layers are scored on the same 1993–2016 winters (Brier skill against the base rate) and blended family by family, weighted by their skill in the El Niño winters.

Family	Model	History	Model, El Niño winters	History, El Niño winters	History weight

More winters than history

UNSEEN tails from the SEAS5 reforecast

600 simulated winters, tested before they are trusted

Many Season Book ladders end in a rung that no more than one of the nine strong El Niño winters on record ever reached. History cannot price those well. UNSEEN (Thompson et al. 2017; Kelder et al. 2020) uses a model's reforecast instead: ECMWF's SEAS5 re-ran every winter from 1993–94 to 2016–17, 25 times each from a September start, which gives 600 simulated winters. They are used only where they pass a fidelity test. Draw 24 winters from the 600, 10,000 times over, and the observed 1993–2016 mean, spread, skewness and kurtosis must each fall inside the range of those draws. The simulated winters are then filtered to the ones in which the model's own El Niño was strong, and that filter is trusted only where the model's strong El Niños shift the winter about as far as the real ones did (the El Niño signal test).

The fidelity test, station by station

Top four rows: the grey bar is the central range of each statistic across 10,000 draws of 24 simulated winters (98.75%, so that all four together are a 95% test), and the dot is the observed 1993–2016 value. Last row, the El Niño signal test: the bar is the range the observed shift may take around the model's strong-El-Niño shift (1.96 combined standard errors), and the dot is the observed shift, the mean of the nine strong El Niño winters since 1957. A dot outside its bar fails.

Station

Tail prices: UNSEEN against history

For the book's tail rungs (lines that 0 or 1 of the nine strong El Niño winters cleared), the share of strong-El-Niño simulated winters, set in today's climate, that clear the line. The interval resamples whole winters, because most of these simulated winters come from just two real ones, 1997–98 and 2015–16. Families other than winter temperature pass through each station's own observed link to Dec–Feb temperature and precipitation. That link has to explain at least 40% of the variance and pass the same fidelity test, or the rung stays "from history only".

Out of sample, 2017–2025

Nine winters no fit ever saw

The first independent test of the layer

Everything above was fitted and scored on 1993–2016. ECMWF's SEAS5 has issued a real forecast every September since, and none of those forecasts was used to fit anything here. So each winter from 2017–18 to 2025–26 can be forecast the way the layer would have done it at the time, then checked against what happened. Only SEAS5 can be tested this way: the other Copernicus systems' and CCSM4's forecasts for those years are not in our store. The history layer is scored on the same winters, with each scored winter left out of its record, and it is handed the winter's observed El Niño or La Niña class, so it knows something SEAS5 had to forecast.

Winter by winter

Ranked probability skill for the thirds of Dec–Feb temperature and precipitation at the 344 climate divisions (0 = no better than climatology, above 0 = better), Brier skill for every Season Book line at the stations, and how often the observed station values fell inside UNSEEN's central 90%. Each winter is forecast from the September start of that year.

Winter	ENSO, observed	SEAS5 Niño-3.4	Temperature		Precipitation		Season Book		Inside UNSEEN 90%
Winter	ENSO, observed	SEAS5 Niño-3.4	Model	History	Model	History	Model	History	Inside UNSEEN 90%

2023–24: the one strong El Niño in the sample

All nine winters together

Pooled skill with 90% intervals from resampling the nine winters. "As published" scores the odds the way they are shown, against the 1991–2020 thirds with each winter's trend level, as the 1993–2016 table above does; knowing that winters have warmed is worth something to both layers there. "Detrended" scores only the year-to-year departures from the trend line, the model's own signal.

Places	Field	Scored as	Model	History	Blend	Model − history	1993–2016, model

Were the observed winters inside UNSEEN's spread?

Is a 60% still 60%?

Method

Systems: the ten Copernicus C3S seasonal systems and the NMME models that are not already among them, one vote per underlying model. NMME's CFSv2 is Copernicus's ncep-2, and its Canadian pair (GEM5.2-NEMO and CanESM5) is eccc-4 and eccc-5, so they are not counted twice. Each system's anomaly is taken against its own 1993–2016 hindcast mean, which removes its bias. NMME comes from the Forecast Network's store (COLA-RSMAS CCSM4 and CESM1) and the IRI Data Library (NASA GEOS-S2S; GFDL SPEAR, whose newest start is July, so it votes two months lagged and is calibrated on July-start hindcasts).
Calibration: at every place, observed Dec–Feb temperature and precipitation (NOAA nClimDiv; RCC-ACIS at stations) and the multi-system mean are both detrended. The observed anomaly is regressed on the model's with no intercept. The slope is shrunk by the factor with the best pooled leave-one-year-out score, and the spread is the leave-one-year-out error. That is the same detrended space the history layer uses, so the two can be blended.
The gates (Build Plan, Nov 5): reliability on 1993–2016 (upper-third probabilities in ten bins: slope 0.7–1.3, mean absolute bin error at most 0.07), and every Season Book ladder monotone after blending.
UNSEEN tails: SEAS5's daily reforecast from the September and October starts, 50 members × 36 winters (1981–2016) = 1,800 simulated winters, read from Planette's cloud copy of the Copernicus archive (the October start joined after a pooling test set in advance: its members are as independent of September's as September's are of each other, its climate is the same, and it covers Nov–Mar; the August start does not reach March). Every Season Book family is computed from the model's own days at each station's nearest 1° cell (the Dec–Feb mean of the daily high and low; the lowest low, the days with a high of 32 °F or less, heating degree days and precipitation over Nov–Mar; snowfall from the model's snowfall water equivalent at 10:1 times a factor fitted to the station). Each family is bias-corrected to the station's own 1981–2016 record (the model's trend line swapped for the observed one; precipitation and snow scaled to the observed mean; the ice-day threshold moved until the mean count matches; spread matched only if the spread test fails), tested for fidelity and for the El Niño signal, and filtered to winters in which the member's own Dec–Feb Niño-3.4 was at least +1.5 °C. Prices are kernel-smoothed shares of those winters. A tail rung takes the UNSEEN price as its model price; the family's blend weight is unchanged. If that makes a ladder step the wrong way, the model prices on that ladder are pooled (pool-adjacent-violators), and the count is shown above. Details: docs/MODEL_LAYER_V2.md.
Out of sample: SEAS5's real-time forecasts for 2017–18 to 2025–26 (51 members, September starts) were never used in any fit. They are calibrated as the layer calibrates, scored against nClimDiv and RCC-ACIS, and compared with the history layer run with each scored winter left out.
Not yet in: NOAA's SFS (its reforecast is not public yet).

The forecast systems, calibrated and scored.