FuXiWeather2: Learning accurate atmospheric state estimation for operational global weather forecasting

Xiaoze Xu; Xiuyu Sun; Songling Zhu; Xiaohui Zhong; Yuanqing Huang; Zijian Zhu; Jun Liu; Hao Li

cs.LGMar 16, 2026

FuXiWeather2: Learning accurate atmospheric state estimation for operational global weather forecasting

Authors: Xiaoze Xu, Xiuyu Sun, Songling Zhu, Xiaohui Zhong, Yuanqing Huang, Zijian Zhu, Jun Liu, Hao Li

Organizations: Shanghai Academy of Artificial Intelligence for Science, Shanghai, & 200232, China. · Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai & 200433, China. · FuXi Intelligent Computing Technology Co., Ltd., Shanghai & 200233, China.

Abstract

Numerical weather prediction has long been constrained by the computational bottlenecks inherent in data assimilation and numerical modeling. While machine learning has accelerated forecasting, existing models largely serve as "emulators of reanalysis products," thereby retaining their systematic biases and operational latencies. Here, we present FuXiWeather2, a unified end-to-end neural framework for assimilation and forecasting. We align training objectives directly with a combination of real-world observations and reanalysis data, enabling the framework to effectively rectify inherent errors within reanalysis products. To address the distribution shift between NWP-derived background inputs during training and self-generated backgrounds during deployment, we introduce a recursive unrolling training method to enhance the precision and stability of analysis generation. Furthermore, our model is trained on a hybrid dataset of raw and simulated observations to mitigate the impact of observational distribution inconsistency. FuXiWeather2 generates high-resolution ( $0.25^{\circ}$ ) global analysis fields and 10-day forecasts within minutes. The analysis fields surpass the NCEP-GFS across most variables and demonstrate superior accuracy over both ERA5 and the ECMWF-HRES system in lower-tropospheric and surface variables. These high-quality analysis fields drive deterministic forecasts that exceed the skill of the HRES system in 91% of evaluated metrics. Additionally, its outstanding performance in typhoon track prediction underscores its practical value for rapid response to extreme weather events. The FuXiWeather2 analysis dataset is available at https://doi.org/10.5281/zenodo.18872728.

Figures & tables

Figure 1: Overview of the FuXiWeather2 system . (A) Input observations. The system ingests multi-source data, including remote sensing and in-situ measurements. A hybrid dataset, combining real-world observations and physical simulations, is utilized during training, while only real-world observations are used during inference. (B) Model architectures and cycling mode. The system consists of a multi-branch U-Net for data assimilation (DA) and a Swin U-Transformer for forec asting. The DA module integrates observations with short-range background forecast to generate analysis, which then drive the forecast module to produce the next-step background. Both modules operate in an interleaved cycling manner, continuously generating stable analysis fields. The entire process is optimized via a recursive unrolled end-to-end training paradigm. (C) Supervision signals. During training, FuXiWeather2 employs dual supervision, leveraging both global reanalysis products and discrete in-situ observations. (D) Medium-range autoregressive forecasting. Initialized by the analysis, the forecast module generates 10-day global forecasts through an autoregressive approach.

Category	Variable Name (Abbr.)	Module	I/O Role
Upper-air *	Geopotential ( $Z$ )	Assim & Fcst	In & Out
	Temperature ( $T$ )
	U-wind component ( $U$ )
	V-wind component ( $V$ )
	Relative humidity ( $R$ )
Surface	2-meter temperature ( $T_{2m}$ )	Assim & Fcst	In & Out

Table 1: Data utilized in the assimilation and forecast modules of FuXiWeather2. This table summarizes the data categories, their corresponding functional modules, and their roles as either inputs (In) or outputs (Out).

Category	Instrument	Platform	Provider	Assimilation Variable	Window (h)
Satellite	ATMS	NOAA-20, NPP	NOAA	Brightness Temperature	$[t_{0}-3,t_{0}+5)$
	AMSU-A	NOAA-15/18/19, METOP-B/C	NOAA	Brightness Temperature	$[t_{0}-3,t_{0}+5)$
	MHS	NOAA-19, METOP-B/C	NOAA	Brightness Temperature	$[t_{0}-3,t_{0}+5)$
	MWTS-III *	FY-3E	CMA	Brightness Temperature	$[t_{0}-3,t_{0}+5)$
	MWHS-II *	FY-3E	CMA	Brightness Temperature	$[t_{0}-3,t_{0}+5)$
	SSMIS	DMSP-F17/F18	NOAA	Brightness Temperature	$[t_{0}-3,t_{0}+5)$

Table 2: Detailed specifications of the observational datasets assimilated in FuXiWeather2. The system directly assimilates satellite Level-1 brightness temperatures and refractivity data, thereby avoiding reliance on retrieved products that may be influenced by external numerical weather prediction (NWP) priors. In-situ observations provide direct measurements.

t_{0}

denotes the analysis time.

Figure 2: Temperature (A) and humidity (B) Jacobian functions for the selected 38 IASI channels. A total of 38 channels are included, consisting of 21 channels in the $CO_{2}$ absorption band (650-770 $cm^{-1}$ , red lines), 16 channels in the water vapor absorption band (1210-2020 $cm^{-1}$ , green lines), and 1 atmospheric window channel (943.25 $cm^{-1}$ , blue line).

Figure 3: Loss weights for observational supervision. (A–E) Loss weights for upper-air variables across 13 pressure levels. (F) Loss weights for surface variables. For surface variables, a uniform weight of 0.2 is assigned. For upper-air variables, considering the land–atmosphere interaction, the weights decrease with increasing altitude; specifically, the weights decay linearly with height and remain constant at 0.02 above the 500 hPa level.The maximum weights for relative humidity ( $R$ ), U-wind component ( $U$ ), V-wind component ( $V$ ), and geopotential ( $Z$ ) are set to 0.1, whereas temperature ( $T$ ) is assigned a higher maximum weight of 0.2. This higher weighting for $T$ accounts for its superior spatial continuity, which enhances the spatial representativeness

Figure 4: Schematic of the pipeline parallelism strategy for recursive unrolled training. (A) Partitioning of the model across GPUs for assimilation cycles. (B) Data flow across modules and GPUs during forward propagation. FuXiWeather2 distributes the tightly coupled assimilation and forecasting modules across four GPUs. GPU1 and GPU2 serve as assimilation devices, while GPU3 and GPU4 act as forecasting devices. Each module is further divided into two sequential blocks. The

\times 4

symbol denotes the continuous execution of four assimilation cycles, where the forecast output cyclically feeds back into the assimilation module.

Figure 5: Observation-based verification for global analysis. (A–J) Time-averaged normalized root mean square error (RMSE) differences (A-E) and RMSE time series (F-J) of 12-hour forecasts using in-situ observations as ground truth. (K, L) Time-averaged normalized RMSE differences (K) and RMSE time series (L) of 12-hour forecasts using COSMIC-2 refractivity data as ground truth. (M, N) Time-averaged normalized RMSE differences (M) and RMSE time series (N) of analysis fields using YunYao refractivity data as ground truth. Gray, blue, green, and red lines represent GFS, HRES, ERA5, and FuXiWeather2, respectively. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC. In panels L and N, dash-dotted, dashed, and solid lines denote the 850, 500, and 300 hPa pressure levels, respectively. In panels A-E, K and M, 13 pressure levels are displayed, with shaded areas represent the three times the 95% confidence intervals of the t-test. Evaluation is conducted on 12-hour forecast fields (A-L) for observations already assimilated (radiosonde, land station, marine platform, and COSMIC-2 GNSS-RO) to ensure independence. For YunYao GNSS-RO data, which remain unassimilated by all products, the evaluation is performed directly on the (re)analysis fields (M and N).

Figure 6: Global analysis verification using in-situ observations as ground truth (A–O) Time-averaged root mean square error (RMSE, A-E), standard deviation (STD, F-J), and mean bias error (MBE, K-O) of 12-hour forecasts. (P–T) Time-averaged number of observations used for validation. Radiosonde observations are used as the ground truth for upper-air variables across 13 pressure levels, while the combination of land station and marine platform observations serves as the ground truth for surface variables. Gray, blue, and red lines represent GFS, HRES, and FuXiWeather2, respectively. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC and is performed on the 12-hour forecast fields, as the in-situ observations have already been assimilated into all the analysis products.

Figure 7: Global analysis verification using GNSS-RO observations as ground truth (A–C) Time-averaged root mean square error (RMSE, A), standard deviation (STD, B), and mean bias error (MBE, C) of 12-hour forecasts using COSMIC-2 refractivity data as ground truth. (D) Time-averaged number of COSMIC-2 observations used for validation. (E–G) Time-averaged RMSE (E), STD (F), and MBE (G) of (re)analysis fields using YunYao refractivity data as ground truth. (H) Time-averaged number of YunYao observations used for validation. Gray, blue, green, and red lines represent GFS, HRES, ERA5, and FuXiWeather2, respectively. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC across 13 pressure levels. For COSMIC-2 GNSS-RO data, the evaluation is conducted on the 12-hour forecast fields because these observations have already been assimilated into all the analysis products (A-D). For YunYao GNSS-RO data that have not been assimilated by any product, the evaluation is performed directly on the (re)analysis fields (E-H).

Figure 8: Observation-based verification of 12-hour forecasts generated by FuXi-Short, initialized with ERA5 and FuXiWeather2 analysis fields (FuXiWeather2-fc0). (A–O) Time-averaged normalized root mean square error (RMSE) differences (A-E), normalized standard deviation (STD) differences (F-J) and mean bias error (MBE, K-O) using in-situ observations as ground truth. (P-R) Time-averaged normalized RMSE differences (P), normalized STD differences (Q) and MBE (R) using COSMIC-2 refractivity data as ground truth. Green and red lines represent ERA5 and FuXiWeather2, respectively. The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In panels A-J, P and Q, the shaded areas represent the 95% confidence intervals of the t-test

Figure 9: Observation-based verification of 12-hour forecasts generated by FuXiWeather2’s forecast model, initialized with ERA5 and FuXiWeather2 analysis fields (FuXiWeather2-fc0). (A–O) Time-averaged normalized root mean square error (RMSE) differences (A-E), normalized standard deviation (STD) differences (F-J) and mean bias error (MBE, K-O) using in-situ observations as ground truth. (P-R) Time-averaged normalized RMSE differences (P), normalized STD differences (Q) and MBE (R) using COSMIC-2 refractivity data as ground truth. Green and red lines represent ERA5 and FuXiWeather2, respectively. The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In panels A-J, P and Q, the shaded areas represent the 95% confidence intervals of the t-test

Figure 10: Global analysis verification using ERA5 as ground truth (A–F) Time-averaged latitude-weighted root mean square error (RMSE) for five upper-air variables (A-E) across 13 pressure levels and four surface variables (F). Gray, blue, and red lines represent GFS, HRES, and FuXiWeather2, respectively. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC.

Figure 11: Comparison of surface variables at 00 UTC, 1 August 2023. (A-D) Global distributions of 2-meter temperature ( $T_{2m}$ ) and wind fields for GFS, HRES, ERA5, and FuXiWeather2. (E) Global distributions of $T_{2m}$ observations. (F-I) Global distributions of the differences between the analysis and observations for GFS, HRES, ERA5, and FuXiWeather2. (J-N) $T_{2m}$ and wind fields distribution over United State for GFS, HRES, ERA5, and FuXiWeather2. (N) $T_{2m}$ observation distribution over United State. (O-R) Differences between the analysis and observations over United State for GFS, HRES, ERA5, and FuXiWeather2. In panels A-D and J-M, within the wind vector plots, a long barb represents 4 m/s, a short barb represents 2 m/s, and a pennant indicates 20 m/s. In panels F-I, and O-R, dots marked with black outlines indicate wind speed biases exceeding 2 m/s between the analysis field and the station observations.

Figure 12: Comparison of 10-day forecast performance. (A–P) Globally-averaged and latitude-weighted root mean square error (RMSE, A-H) and anomaly correlation coefficient (ACC, I-P) for selected variables. The figure displays four surface variables: 2-meter temperature ( $T_{2m}$ , A and I), 10-meter U-wind component ( $U_{10m}$ , B and J), 10-meter V-wind component ( $V_{10m}$ , C and K), and mean sea-level pressure ( $MSLP$ , D and L), as well as four key upper-air atmospheric variables: temperature at 850 hPa ( $T850$ , E and M), relative humidity ( $R$ ) at 850 hPa ( $R850$ , F and N), U-wind component at 850 hPa ( $U850$ , G and O), and geopotential at 850 hPa ( $Z500$ , H and P). Gray, blue, and red lines represent GFS, HRES, and FuXiWeather2, respectively. The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC with a 6-hour forecast step. All forecasts are verified using their own analysis fields as the ground truth.

Figure 13: Comparison of 10-day forecast performance between FuXiWeather2 and HRES, verified using their own analysis fields as ground truth. (A-F) Globally averaged, latitude-averaged root mean square error (RMSE) change rates of FuXiWeather2 relative to HRES for upper-air variables (A-E) across 13 pressure levels and surface variables (F). (G-M) Globally averaged, latitude-averaged anomaly correlation coefficient (ACC) change rates of FuXiWeather2 relative to HRES for upper-air variables (G-K) and surface variables (M). The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC with a 6-hour forecast step

Figure 14: Comparison of 10-day forecast performance between FuXiWeather2 and HRES, verified using ERA5 as ground truth. (A-F) Globally averaged and latitude-averaged root mean square error (RMSE) change rates of FuXiWeather2 relative to HRES for upper-air variables (A-E) across 13 pressure levels and surface variables (F). (G-M) Globally averaged and latitude-averaged anomaly correlation coefficient (ACC) change rates of FuXiWeather2 relative to HRES for upper-air variables (G-K) and surface variables (M). The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC with a 6-hour forecast step

Figure 15: Comparison of std-based forecast activity for upper-air variables. The figure presents the globally-averaged and latitude-weighted forecast activity for forecasts generated by the FuXiWeather2 and HRES over a 10-day forecasts, covering five upper-air variables across 3 pressure levels. The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC with a 6-hour forecast step. Forecast activity is scaled relative to HRES activity.

Figure 16: Comparison of std-based forecast activity for surface variables. The figure presents the globally-averaged and latitude-weighted forecast activity for forecasts generated by the FuXiWeather2 and HRES over a 10-day forecasts, covering four surface variables. The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC with a 6-hour forecast step. Forecast activity is scaled relative to HRES activity.

Figure 17: Comparison of typhoon cyclone (TC) track forecasts. (A) TC tracks in IBTrACS. (B–D) 24-hour TC track forecasts for GFS (B), HRES (C), and FuXiWeather2 (D). (E) TC track forecasts for Typhoon SAOLA, initialized at 00:00 UTC on August 27, 2023. (F) TC track forecasts for Typhoon HAIKUI, initialized at 12:00 UTC on August 29, 2023. (G) Along-track errors of TC track forecasts. Black, grey, blue, and red represent IBTrACS, GFS, HRES, and FuXiWeather2, respectively. The evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC with a 6-hour forecast step. In Panels E and F, The forecast lead times are truncated at the time of typhoon landfall. For Typhoon SAOLA (E), a 7-day forecast is presented, with lead times of 0–5 days denoted by dots and 5–7 days by triangles. For Typhoon HAIKUI (F), a 5-day forecast is displayed. In panel G, the shaded areas represent the standard deviation of the errors.

Figure 18: Impact of simulated observations on analysis accuracy. The heatmap displays the percentage change in root mean square error (RMSE) for the assimilation model trained on a hybrid dataset (comprising both real and simulated observations) relative to the baseline model (trained solely on real observations), with ERA5 used as the ground truth. The plot shows five upper-air variables across 13 pressure levels. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC. Blue shading (negative values) indicates that the inclusion of simulated data results in a reduction of analysis errors.

Figure 19: Sensitivity analysis of satellite instruments for the assimilation model trained on real observations. The heatmap displays the percentage change in root mean square error (RMSE) of the analysis fields after excluding a specific satellite instrument during the cyclic data assimilation and forecast phase, with ERA5 reanalysis used as the ground truth. The differences are calculated relative to a control experiment that assimilates all available satellite instruments. Red (blue) shading indicates a degradation (improvement) in performance following the data exclusion. Results cover five upper-air variables across 13 vertical pressure levels. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC. The symbol $\times$ denotes cases where the difference is not statistically significant, based on the t-test at the 95% confidence level.

Figure 20: Sensitivity analysis of satellite instruments for the assimilation model trained on hybrid observations. The heatmap displays the percentage change in root mean square error (RMSE) of the analysis fields after excluding a specific satellite instrument during the cyclic data assimilation and forecast phase, with ERA5 reanalysis used as the ground truth. The differences are calculated relative to a control experiment that assimilates all available satellite instruments. Red (blue) shading indicates a degradation (improvement) in performance following the data exclusion. Results cover five upper-air variables across 13 vertical pressure levels. The evaluation spans a one-year testing period at 00:00 and 12:00 UTC. The symbol $\times$ denotes cases where the difference is not statistically significant, based on the t-test at the 95% confidence level.

Figure S1: Spatial distribution of time-averaged root mean square error (RMSE) for relative humidity ( $R$ ). (A-C) RMSE of HRES (A) and FuXiWeather2 (B) forecasts, along with their differences (C) at 300 hPa. (D-F) RMSE of HRES (D) and FuXiWeather2 (E) forecasts, along with their differences (F) at 500 hPa. (G-I) RMSE of HRES (G) and FuXiWeather2 (H) forecasts, along with their differences (I) at 850 hPa. a, b and c (columns 1, 2, and 3) represent 1-day, 3-day, and 5-day lead times, respectively. the evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In RMSE maps, darker red indicates higher errors; in difference maps, blue (red) denotes regions where FuXiWeather2 (HRES) performs better. In panels C, F and I, stippling highlights regions where FuXiWeather2 significantly outperforms HRES (t-test, 95% confidence level)

Figure S2: Spatial distribution of time-averaged root mean square error (RMSE) for temperature ( $T$ ). (A-C) RMSE of HRES (A) and FuXiWeather2 (B) forecasts, along with their differences (C) at 300 hPa. (D-F) RMSE of HRES (D) and FuXiWeather2 (E) forecasts, along with their differences (F) at 500 hPa. (G-I) RMSE of HRES (G) and FuXiWeather2 (H) forecasts, along with their differences (I) at 850 hPa. a, b and c (columns 1, 2, and 3) represent 1-day, 3-day, and 5-day lead times, respectively. the evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In RMSE maps, darker red indicates higher errors; in difference maps, blue (red) denotes regions where FuXiWeather2 (HRES) performs better. In panels C, F and I, stippling highlights regions where FuXiWeather2 significantly outperforms HRES (t-test, 95% confidence level)

Figure S3: Spatial distribution of time-averaged root mean square error (RMSE) for geopotential ( $Z$ ). (A-C) RMSE of HRES (A) and FuXiWeather2 (B) forecasts, along with their differences (C) at 300 hPa. (D-F) RMSE of HRES (D) and FuXiWeather2 (E) forecasts, along with their differences (F) at 500 hPa. (G-I) RMSE of HRES (G) and FuXiWeather2 (H) forecasts, along with their differences (I) at 850 hPa. a, b and c (columns 1, 2, and 3) represent 1-day, 3-day, and 5-day lead times, respectively. the evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In RMSE maps, darker red indicates higher errors; in difference maps, blue (red) denotes regions where FuXiWeather2 (HRES) performs better. In panels C, F and I, stippling highlights regions where FuXiWeather2 significantly outperforms HRES (t-test, 95% confidence level)

Figure S4: Spatial distribution of time-averaged root mean square error (RMSE) for U-wind component ( $U$ ). (A-C) RMSE of HRES (A) and FuXiWeather2 (B) forecasts, along with their differences (C) at 300 hPa. (D-F) RMSE of HRES (D) and FuXiWeather2 (E) forecasts, along with their differences (F) at 500 hPa. (G-I) RMSE of HRES (G) and FuXiWeather2 (H) forecasts, along with their differences (I) at 850 hPa. a, b and c (columns 1, 2, and 3) represent 1-day, 3-day, and 5-day lead times, respectively. the evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In RMSE maps, darker red indicates higher errors; in difference maps, blue (red) denotes regions where FuXiWeather2 (HRES) performs better. In panels C, F and I, stippling highlights regions where FuXiWeather2 significantly outperforms HRES (t-test, 95% confidence level)

Figure S5: Spatial distribution of time-averaged root mean square error (RMSE) for V-wind component ( $U$ ). (A-C) RMSE of HRES (A) and FuXiWeather2 (B) forecasts, along with their differences (C) at 300 hPa. (D-F) RMSE of HRES (D) and FuXiWeather2 (E) forecasts, along with their differences (F) at 500 hPa. (G-I) RMSE of HRES (G) and FuXiWeather2 (H) forecasts, along with their differences (I) at 850 hPa. a, b and c (columns 1, 2, and 3) represent 1-day, 3-day, and 5-day lead times, respectively. the evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In RMSE maps, darker red indicates higher errors; in difference maps, blue (red) denotes regions where FuXiWeather2 (HRES) performs better. In panels C, F and I, stippling highlights regions where FuXiWeather2 significantly outperforms HRES (t-test, 95% confidence level)

Figure S6: Spatial distribution of time-averaged root mean square error (RMSE) for surface variables. (A-C) RMSE of HRES (A) and FuXiWeather2 (B) forecasts, along with their differences (C) for mean sea-level pressure ( $MSLP$ ). (D-F) RMSE of HRES (D) and FuXiWeather2 (E) forecasts, along with their differences (F) for 2-meter temperature ( $T_{2m}$ ). (G-I) RMSE of HRES (G) and FuXiWeather2 (H) forecasts, along with their differences (I) for 10-meter U-wind component ( $U_{10m}$ ). a, b and c (columns 1, 2, and 3) represent 1-day, 3-day, and 5-day lead times, respectively. the evaluation spans a one-year testing period, including forecasts initialized at 00:00 and 12:00 UTC. In RMSE maps, darker red indicates higher errors; in difference maps, blue (red) denotes regions where FuXiWeather2 (HRES) performs better. In panels C, F and I, stippling highlights regions where FuXiWeather2 significantly outperforms HRES (t-test, 95% confidence level)

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