FourCastNet V2 Small: AI Weather Model

• The paper reveals that FourCastNet V2 Small exhibits a systematic cold bias in 2 m temperature forecasts, effectively simulating climates from 15–20 years earlier.
• It employs a spherical Fourier neural operator (SFNO) architecture trained on ERA5 reanalysis data at 0.25° resolution to predict global atmospheric conditions.
• The study highlights that limited modern extreme-heat samples in training cause a tail-specific bias, underestimating warm extremes in current climates.

Searching arXiv for the cited FourCastNet/SFNO papers to support the article with current references. FourCastNet V2 Small, referred to as FourCastNet in the evaluation under discussion, is an AI weather model assessed for boreal winter land-temperature prediction outside its training period in "Forecasting the Future with Yesterday's Climate: Temperature Bias in AI Weather and Climate Models" (Landsberg et al., 26 Sep 2025). In that study, FourCastNet is examined as a short-range forecasting system trained on historical ERA5 reanalysis from 1979–2015 and evaluated on forecasts for 2020–2025, with particular emphasis on its 2 m temperature output. The central finding is that the model produces a systematic cold bias in modern conditions, such that its predicted winter temperatures resemble climates from approximately 15–20 years earlier than the period being forecast, with larger regional lags in some areas (Landsberg et al., 26 Sep 2025).

1. Architectural characterization

FourCastNet V2 Small employs a Spherical Fourier Neural Operator (SFNO) architecture, which learns convolution-like operators in the spectral domain on the sphere (Landsberg et al., 26 Sep 2025). Within the study, this architectural choice is presented as the basis for a global weather-modeling system operating on gridded atmospheric fields rather than as a local or regional predictor.

The model is trained on ERA5 reanalysis fields at 0.25° horizontal resolution. The input variables include standard atmospheric prognostic quantities such as geopotential heights, wind components, temperature, humidity, and surface diagnostic fields, while the evaluation considered here focuses on the 2 m temperature output (Landsberg et al., 26 Sep 2025). The output used in the analysis consists of 6-hourly forecasts of 2 m air temperature, from which daily means are computed.

A plausible implication is that the SFNO formulation is intended to exploit the global geometry of the sphere while preserving computational tractability in spectral space. In the present evaluation, however, the significance of the architecture is not framed primarily in terms of efficiency or benchmark skill, but in terms of how a historically trained global AI weather model behaves when applied to a more recent climate regime (Landsberg et al., 26 Sep 2025).

2. Training data, preprocessing, and optimization

The training data period is ERA5 reanalysis from January 1, 1979 through December 31, 2015, centered around 1997 (Landsberg et al., 26 Sep 2025). This temporal centering is important because the later interpretation of forecast bias is explicitly tied to the gap between the model’s training climatology and the warmer evaluation period.

Inputs and targets are re-gridded to a uniform 0.25° grid on the sphere, and standard normalization, using mean and standard deviation, is applied per field using the 1979–2015 climatology (Landsberg et al., 26 Sep 2025). The network is trained autoregressively with 6-hour timesteps, minimizing mean squared error over all resolved variables.

The autoregressive update rule is given as

$x_{t+6\text{h}}=\mathcal{F}_\theta(x_t),$

which is composed repeatedly to obtain forecasts at later lead times (Landsberg et al., 26 Sep 2025). The optimization objective is defined as mean squared error across all lead times and all grid points:

$$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$

This training setup matters for the later bias analysis because the model is optimized against the historical distribution represented in 1979–2015 ERA5 rather than against explicitly warmed or scenario-conditioned states. The paper’s interpretation of bias is therefore linked directly to the statistical support of the training set (Landsberg et al., 26 Sep 2025).

3. Forecast production and evaluation protocol

Forecasts are initialized daily at 00 UTC using NOAA GFS analysis fields, after which FourCastNet iteratively predicts forward in 6-hour increments (Landsberg et al., 26 Sep 2025). The evaluation analyzes 2-day lead forecasts, corresponding to $8\times 6$ h steps, and 9-day lead forecasts, corresponding to $36\times 6$ h steps. Daily mean temperature is obtained by arithmetic averaging of the four 6-hour forecasts within each UTC day.

The analysis concerns boreal winter, specifically DJF days from December 2020 to February 2025 (Landsberg et al., 26 Sep 2025). Mean temperature bias at each grid point is defined as the time-mean difference between model forecast and ERA5:

$$b(\varphi,\lambda) \;=\; \overline{T_{\mathrm{model}}(\varphi,\lambda,t)} - \overline{T_{\mathrm{ERA5}}(\varphi,\lambda,t)}.$$

Global mean bias is computed as the cosine-latitude-weighted average:

$$\overline{b} \;=\; \frac{\int_{-\pi/2}^{\pi/2}\!\int_{0}^{2\pi} b(\varphi,\lambda)\,\cos\varphi\,d\lambda\,d\varphi} {\int_{-\pi/2}^{\pi/2}\!\int_{0}^{2\pi} \cos\varphi\,d\lambda\,d\varphi}.$$

To quantify how far the forecasts resemble an earlier climate, the study introduces a climate-shift, or lag, estimate by sliding a 5-year window through ERA5 and identifying the window that minimizes the root-mean-square difference between the model’s DJF mean and the corresponding ERA5 window mean (Landsberg et al., 26 Sep 2025). If $T_{\mathrm{mod}}$ is the 2020–2025 mean and $T_{\mathrm{ERA5}}^{(w:w+4)}$ the ERA5 mean over years $w$ through $w+4$, the best-match lag $$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$0 is defined by

$$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$1

with climate-shift measured as $$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$2 years (Landsberg et al., 26 Sep 2025).

This evaluation protocol is notable because it does not treat bias solely as an average error statistic. Instead, it reframes error as a mismatch in climatological era, thereby connecting forecast performance to the problem of extrapolating beyond the training distribution.

4. Temperature bias structure

The principal reported result is a global mean cold bias in FourCastNet’s boreal-winter land-temperature forecasts outside the training period (Landsberg et al., 26 Sep 2025). The global mean bias is $$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$3 K at 2-day lead and $$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$4 K at 9-day lead. Spatially, the cold bias is nearly hemisphere-wide over land in boreal winter, with the largest negative departures, approximately $$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$5 K, over parts of North America and Eurasia.

The lagged-climate analysis shows that FourCastNet’s 2020–2025 DJF temperatures most closely resemble ERA5 from 2000–2005, corresponding to a 15–20 year lag (Landsberg et al., 26 Sep 2025). In the Eastern U.S. ($$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$6N–$$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$7N, $$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$8W–$$\mathcal{L}(\theta) \;=\; \frac{1}{N_{\mathrm{batch}}} \sum_{i=1}^{N_{\mathrm{batch}}} \sum_{\tau\in\{\text{6h,12h,\dots}\}} \Bigl\|\mathcal{F}_\theta^{(\tau)}(x^{(i)}_0)-x^{(i)}_\tau\Bigr\|_2^2.$$9W), the predictions resemble the 1995–2000 climate, corresponding to a 20–25 year lag.

These results are summarized below.

Quantity	FourCastNet result
Global mean bias, 2-day lead	$8\times 6$0 K
Global mean bias, 9-day lead	$8\times 6$1 K
Broad spatial pattern	Nearly hemisphere-wide land cold bias in boreal winter
Largest negative departures	Approximately $8\times 6$2 K over parts of North America and Eurasia
Best-match ERA5 climate window	2000–2005
Implied climate lag	15–20 years earlier
Eastern U.S. best-match climate	1995–2000
Eastern U.S. lag	20–25 years

The study interprets this as a "lagging climate" effect: the model forecasts modern winters as though they belonged to an earlier climatological regime (Landsberg et al., 26 Sep 2025). This suggests that, under the evaluation conditions used, the model does not simply exhibit random forecast error; it displays a systematic tendency to revert toward the cooler historical climate represented in its training data.

5. Distributional asymmetry and extreme-heat behavior

The cold bias is not uniform across the temperature distribution. For FourCastNet, the bias is strongest in the hottest predicted temperatures, indicating limited training exposure to modern extreme heat events (Landsberg et al., 26 Sep 2025). In 9-day forecasts, the hottest 10% of predicted temperatures are on average 0.91 K colder than ERA5, whereas the coldest 10% of forecasts show negligible bias, with $8\times 6$3 K.

The regional manifestation of this asymmetry is particularly clear in the Southeastern U.S., where the hottest-tail bias can exceed $8\times 6$4 K, while the cold-tail bias remains within $8\times 6$5 K (Landsberg et al., 26 Sep 2025). The study further reports that, globally, there are approximately 2–3 times more training samples as cold, defined as at or below the 10th percentile of 2020–2025 ERA5, than as hot, defined as at or above the 90th percentile, indicating that the cold-tail pull is a regression toward the cooler training mean.

This distributional structure matters because it distinguishes a tail-specific generalization failure from a uniform calibration offset. The model is comparatively well behaved in the cold tail yet underestimates warm extremes, which aligns with the interpretation that the most modern high-temperature states are underrepresented in the historical training sample (Landsberg et al., 26 Sep 2025).

6. Interpretation, limitations, and proposed remedies

The study attributes cold-bias amplification at high temperatures to limited examples of modern extreme-heat events in FourCastNet’s 1979–2015 training set, such that predictions are "anchored" to the cooler training-distribution mean (Landsberg et al., 26 Sep 2025). The 15–20 year shift is interpreted as evidence that the model has difficulty extrapolating beyond the range of its historical training climatology, which is centered around 1997.

This framing places the model within a broader methodological limitation of AI weather and climate systems trained exclusively on historical data. Although FourCastNet is evaluated as a weather model with short lead times, the paper argues that the same issue becomes visible when the target period is climatologically more modern than the training period. A plausible implication is that short-range forecast skill and robustness to nonstationary climate drift are related but distinct properties.

The paper outlines several corrective strategies for this failure mode (Landsberg et al., 26 Sep 2025). One is to augment training inputs with future-warmer climates, such as climate-model simulations, in order to populate extreme-heat regimes. A second is to apply "climate-invariant" transformations to inputs and outputs so that the network learns anomalies relative to evolving climatology. A third is to incorporate explicit forcing, such as CO$8\times 6$6 trajectories, or physically informed parameterizations to reduce reliance on purely historical data.

The overall conclusion is circumscribed rather than universal: while FourCastNet achieves state-of-the-art skill in short-range forecasting, care must be taken when using it for climates that lie outside its training envelope, particularly for extreme-temperature prediction and future-climate applications (Landsberg et al., 26 Sep 2025). The significance of the result is therefore methodological as much as empirical. It identifies a concrete pathway by which a high-performing AI forecast model can remain skillful in the short range yet systematically misrepresent the mean state and warm tail of a later climate.