A data-to-forecast machine learning system for global weather

Domain: earth_science
Published: 2025-07-19
Editorial outcome: major_revision

Abstract
Weather forecasting traditionally relies on numerical weather prediction (NWP) systems that integrate global observations, data assimilation (DA), and physics-based models. However, further advances are increasingly constrained by high computational costs, the underutilization of vast observational datasets, and challenges in obtaining finer resolution. Recent advances in machine learning present a promising alternative, but still depend on the initial conditions generated by NWP systems. Here, we introduce FuXi Weather, a machine learning-based global forecasting system that assimilates multi-satellite data and is capable of cycling DA and forecasting. FuXi Weather generates reliable 10-day forecasts at 0.25° resolution using fewer observations than conventional NWP systems. It demonstrates the value of background forecasts in constraining the analysis during DA. FuXi Weather outperforms the European Centre for Medium-Range Weather Forecasts high-resolution forecasts beyond day one in observation-sparse regions such as central Africa, highlighting its potential to improve forecasts where observational infrastructure is limited.

Introduction
Accurate weather forecasting is essential for informed decision-making and serves as the foundation of early warning systems1,2 that help to mitigate the impacts of extreme weather events and save lives. Since the first successful numerical weather prediction (NWP)3 using the ENIAC computer in 19504, forecast accuracy has steadily improved5, driven by advances in data assimilation (DA), spatial resolution, computational power, observational infrastructure, and physical parameterizations. However, substantial global disparities remain, with wealthier nations benefiting from better resources and more accurate forecasting6, while many low-income countries, particularly in Africa, continue to struggle with forecasts only marginally better than climatology7. These disparities are especially concerning as many low-income countries are particularly vulnerable to the impacts of climate change and extreme weather8.

Expanding observational infrastructure could help to alleviate this issue, but the financial investment required is prohibitive for many poorer nations. Additionally, the further enhancement of traditional NWP systems is increasingly challenging owing to high computational costs and the complexities of parallelizing models on modern supercomputers9. Meanwhile, recent advances in machine learning present a promising alternative, offering more efficient and accurate forecasts using the same initial conditions as traditional NWP9,10. State-of-the-art machine learning models, such as Pangu-Weather, GraphCast, FuXi, and AIFS11–15, have demonstrated forecasting skills that rival or even surpass traditional high-resolution forecasts (HRES) from the European Centre for Medium-Range Weather Forecasts (ECMWF)16. While early machine learning applications focused primarily on deterministic forecasts, recent developments have shown their potential for ensemble forecasting as well17–19. Nevertheless, NWP models and DA systems remain indispensable because they provide the initial conditions necessary for both traditional and machine learning forecasting models20: this raises the question of whether machine learning-based DA could further improve forecast accuracy.

DA is a complex, nonlinear process that incorporates vast, multi-source, and multi-resolution observational data, often plagued by noise and missing values21, involving challenges such as distinguishing the effects of clouds on satellite radiance from those of temperature and moisture, while ensuring consistency with dynamic models to minimize error growth. Leading weather centers employ sophisticated DA methods22,23, such as hybrid four-dimensional ensemble-variational approaches24–26, which leverage ensembles of short-range forecasts to incorporate flow-dependent background error covariances and enhance forecast accuracy27–29. These methods, though effective, are computationally expensive and typically use only 5%–10% of available observational data to deliver timely analyses. This limited usage is partly due to constraints related to observation error correlations. Although progress has been made in all-sky radiance assimilation for microwave sounders, challenges remain in fully leveraging satellite data across all grids, surfaces, and channels. With the volume of observational data projected to exceed 100 terabytes per day in the coming decade30 and higher model resolutions further exacerbating computational demands31, more efficient DA systems are urgently required32.

The mathematical similarities between machine learning and DA, particularly in variational methods, have inspired efforts to improve DA efficiency through machine learning33. Early attempts focused on simplified dynamical systems, such as the Lorenz6334,35 and Lorenz9636,37 models, which are far less complex than NWP models. However, extending these approaches to operational NWP models is challenging owing to the markedly higher dimensionality of such models (on the order of 10^9)38. Recent studies have demonstrated the potential of machine learning for specific tasks within the DA workflow, such as developing linear and adjoint models for parameterizations through automatic differentiation39. The rise of machine learning forecasting models40 has reignited interest in developing fully integrated machine learning-based DA frameworks for end-to-end weather prediction.

One such attempt is FengWu-4DVar41, which uses a simplified FengWu42 model to assimilate ERA5 data43. However, its reliance on simulated observations and lower dimensionality limits its effectiveness in real-world scenarios. Aardvark Weather44 processes raw observations for forecasts but falls short of the accuracy achieved by ECMWF HRES. These cases highlight the difficulties in developing machine learning-based DA systems for real-world forecasts using actual observational data. FuXi-DA45, a machine learning-based DA framework, has shown promise by assimilating raw Fengyun-4B satellite data alongside background forecasts, but its limited spatial coverage constrains its global and cycling DA capabilities.

To address these challenges, we present FuXi Weather, an end-to-end machine learning-based weather forecasting system capable of running cycling DA and forecasting every 6 h using raw observations. FuXi Weather integrates a substantially enhanced version of FuXi-DA45 with fine-tuned FuXi. Both FuXi-DA and FuXi are trained using ERA5 reanalysis data at a spatial resolution of 0.25° as the reference. Key updates to FuXi-DA include variable- and instrument-specific encoders for diverse satellite data and a modified PointPillars46 approach for processing sparse observations. The FuXi-Short model is fine-tuned using FuXi-DA analysis for initial conditions, while a replay-based incremental learning strategy updates FuXi-DA monthly, ensuring the system’s stability as satellite data quality and availability evolve. FuXi Weather assimilates raw brightness temperature data from three polar-orbiting meteorological satellites (FengYun-3E (FY-3E), Meteorological Operational Polar Satellite-C (Metop-C), and National Oceanic and Atmospheric Administration (NOAA)-20), along with the radio occultation (RO) data from the Global Navigation Satellite System (GNSS), across all grids, surfaces, and channels under all weather conditions. This represents the first realization of all-grid, all-surface, all-channel, and all-sky DA capability. FuXi Weather demonstrates comparable 10-day forecast performance to that of ECMWF HRES, extending the skillful lead time for key variables while using considerably less observational data compared with that used by ECMWF HRES. Furthermore, FuXi Weather consistently outperforms ECMWF HRES in regions with sparse land-based observations, such as Africa, demonstrating its potential to provide more accurate forecasts and enhance climate resilience. To the best of our knowledge, FuXi Weather is the first system to successfully perform cycling DA and weather forecasting over a continuous 1-year testing period47. This achievement challenges the prevailing view that standalone machine learning-based weather forecasting systems are not viable for operational use.

Results
FuXi Weather operates in a cycling analysis and forecasting mode, utilizing the full range of available satellite data. Because DA is inherently an ill-posed problem38,48 requiring background forecasts to improve analysis accuracy, we developed a variant of FuXi-DA without these forecasts to evaluate their contribution to the DA process. This variant, which relies exclusively on observations, represents a direct-from-observation prediction approach. Performance was assessed by comparing the accuracy of analysis fields and forecasts globally and in specific regions such as central Africa and northern South America, using ERA5 as the reference. The performance of FuXi Weather was compared with that of ECMWF HRES, which was evaluated using the time series of its 0-h lead time analysis, HRES-fc0 (see Section “Evaluation method”). This comparison inherently favors HRES at early lead times, since by definition it starts with a low root mean square error (RMSE) and a high anomaly correlation coefficient (ACC). Consistent with the common practices in the NWP community, FuXi Weather was also evaluated against its analyses. Statistical significance testing was conducted following the methodology outlined by Geer49. Single observation tests validated DA responses against theoretical expectations while data denial experiments (see Supplementary Information Section 5) evaluated the impact of excluding certain observations.

Global analysis fields
This subsection evaluates the performance of FuXi Weather analyses and 42-h FuXi forecasts (initialized with ERA5), against ERA5 as the reference. Figure 1 presents the globally-averaged and latitude-weighted RMSE for two FuXi Weather configurations: one incorporating background forecasts and one without. Performance varied markedly across different variables and pressure levels. The RMSE of analysis fields relative to forecasts is higher at 850 hPa than 300 and 500 hPa, likely owing to the lower information content from satellite observations at lower altitudes.

For relative humidity (R), the analyses of FuXi Weather outperform forecasts at 300 and 500 hPa, but have slightly higher RMSE values at 850 hPa. For temperature (T), geopotential (Z), and wind components (U and V), the RMSE values are comparable to those of forecasts at higher altitudes but were consistently higher at 850 hPa. Although satellite data primarily capture temperature and moisture information, their assimilation also improves wind fields through the dynamic relationship between wind, temperature, and moisture. Wind can be inferred from temperature gradients (geostrophic balance) and the movement of atmospheric constituents, such as humidity, known as the “generalized tracer effect”23.

Incorporating background forecasts yields statistically significant improvements in the accuracy of FuXi Weather analysis fields, as demonstrated by systematically lower RMSE values. This highlights the crucial role of background forecasts in DA, which is ill-posed without prior information (as detailed in Supplementary Information Section 9). Both configurations of FuXi Weather show similar trends over time, but the analyses without background forecasts exhibit more pronounced error peaks, especially when some satellite data were missing (see Supplementary Figs. 1 and 2), underscoring the stabilizing effect of background forecasts.

The shaded area in Fig. 1 represents variations across initialization times; this is more pronounced in forecasts. Forecasts initialized at 00/12 UTC consistently outperform those at 06/18 UTC, likely because the 12-h observation windows of ERA5 (09-21 UTC and 21-09 UTC)43 provide 9 h of look-ahead time for 00/12 UTC but only 3 h for 06/18 UTC13. In contrast, the analysis fields of FuXi Weather demonstrate more consistent accuracy across initialization times, likely due to its fixed 8-h assimilation window, and its use of cycled background fields initialized from previous analyses. Additional evaluations, including the analysis activity and mean bias error (MBE), are provided in Supplementary Information Section 6.

Global weather forecasts
The primary criterion for evaluating an end-to-end weather forecasting system is its ability to provide reliable and accurate forecasts in a cycling analysis and forecasting mode. This subsection evaluates the performance of 6-h cycle forecasts generated by FuXi Weather, initialized using two types of FuXi-DA analysis fields: one incorporating background forecasts and one without. The forecasts are compared with those from ECMWF HRES.

Figure 2 shows the globally-averaged and latitude-weighted RMSE as a function of forecast lead times over 10 days. FuXi Weather forecasts are initialized using FuXi-DA analysis fields either with (red solid and green dashed lines) or without (black lines) background forecasts. Forecasts depicted by red and black lines are evaluated against ERA5, while the green dashed lines represent forecasts assessed against the FuXi-DA analyses. Statistically significant improvements in FuXi Weather forecasts (red lines) over ECMWF HRES are indicated by red dots, based on t-test at the 95% confidence level. When validated against ERA5, FuXi Weather forecasts initialized with background-inclusive analyses (red lines) consistently demonstrate lower RMSE values than those without, aligning with results in Fig. 1. Regardless of the evaluation reference (ERA5 or FuXi-DA analyses), the performance gap between forecasts (red and green dashed lines) diminishes over lead time and becomes negligible by day 10.

When evaluated against their respective analyses, both FuXi Weather and ECMWF HRES show small initial errors. Against ERA5, FuXi Weather initially shows higher RMSE values than ECMWF HRES, but outperforms ECMWF HRES after a lead time of 2–8 days, depending on the variable and pressure level. For R, FuXi Weather outperforms ECMWF HRES at lead times of 2.00, 3.25, and 2.25 days for 300, 500, and 850 hPa, respectively. For T, Z, U, and V, the critical lead times are later owing to the lower accuracy of their corresponding analysis fields. For Z, these times are 8.00, 7.75, and 7.50 days at 300, 500, and 850 hPa, respectively. The performance discontinuity on day 4 reflects the transition between FuXi-Short and FuXi-Medium forecast components.

Figure 3 shows similar trends for the globally-averaged and latitude-weighted ACC. FuXi Weather forecasts initialized without background forecasts perform worse, as expected. However, FuXi Weather forecasts initialized with analyses incorporating background forecasts, though initially less accurate than ECMWF HRES, improve over time and eventually achieve higher ACC values across all examined variables. Using an ACC threshold of 0.6 to define a skillful forecast, Fig. 4 compares skillful lead times. FuXi Weather extends skillful lead times for 7 out of 15 variables, matching ECMWF HRES for 6 others. For example, for Z500, FuXi Weather extends the skillful lead time from the ECMWF HRES value of 9.25 days to 9.50 days for forecasts initialized with background forecasts (forecasts initialized without background forecasts show a skillful lead time of only 8.25 days). Additional forecast comparisons, including spatial RMSE distributions, are provided in the Supplementary Information Section 7.

Forecast performance in central Africa
Operational evaluations of NWP systems routinely assess both global and regional performance metrics16, covering geographical areas such as Europe, North America, East Asia, and Australia. However, forecast accuracy tends to be lower in low-income countries, largely due to limited investment in weather observation infrastructure. This issue is especially concerning for many low-income countries, where agriculture is a major economic sector that relies heavily on accurate weather forecasts. Climate change further exacerbates weather-related risks, disproportionately affecting vulnerable populations with low adaptive capacities in these countries. Therefore, improving forecast accuracy in underserved regions, especially Africa, is crucial for enhancing climate resilience50,51.

This subsection compares the performance of FuXi Weather and ECMWF HRES in underserved regions, with a particular focus on central Africa. Similar to Fig. 2, FuXi Weather forecasts are evaluated against both ERA5 (red lines) and its analyses (green dashed lines). Figure 5 illustrates that, when verified against their respective analyses, FuXi Weather (green dashed lines) consistently outperforms ECMWF HRES (blue lines) in forecasting the 850 hPa u wind component (U850), 2-meter temperature (T2M), and mean sea level pressure (MSLP), throughout the 10-day forecast period. When evaluated against ERA5, FuXi Weather (red lines) has nontrivial initial error, but the magnitude and growth of this error are sufficiently modest that ECMWF HRES—even compared to its own analyses, so with inherently zero initial error—exhibits larger error after two days. In particular, FuXi Weather (red lines) achieves lower RMSE and higher ACC, with ACC values for T2M consistently exceeding 0.6 across the 10-day forecasts, indicating meaningful predictive skill. In contrast, ECMWF HRES maintains skillful T2M forecasts for approximately two days.

Forecast errors are further decomposed into systematic and random components by calculating the MBE and the standard deviation (std) of errors (STD_ERROR). Supplementary Fig. 22 reveals that FuXi Weather (red lines) exhibits both lower MBE and smaller STD_ERROR across all five evaluated variables: U850, 850 hPa temperature (T850), T2M, MSLP, and total precipitation (TP). These results suggest that FuXi Weather more effectively reduces both systematic bias and random errors compared to ECMWF HRES, contributing to its overall superior forecast performance. Improvements relative to HRES in TP forecasts are of note due to precipitation’s socioeconomic importance in central Africa, although with the caveat that HRES performance is relatively poor for TP in this region. Forecast behavior is further characterized using forecast activity40, defined as the std of forecast anomalies relative to climatological means and normalized by ECMWF HRES forecast activity. As shown in Supplementary Fig. 22, FuXi Weather normalized forecast activity values indeed drop below 1, suggesting smoother predictions relative to ECMWF HRES. This reduction in forecast activity may partially account for FuXi Weather’s improved performance. However, FuXi Weather’s superior forecast skill (red lines) over ECMWF HRES becomes evident as early as day 1, prior to any considerable reduction in forecast activity. The forecast activity of FuXi Weather decreases gradually until around day 2 and then stabilizes, indicating that FuXi Weather’s enhanced accuracy arises earlier than the substantial reduction in forecast activity and cannot be fully attributed to it.

Notably, FuXi Weather achieves superior forecasts for surface variables without assimilating surface-based observations, pointing to its strength in utilizing satellite data in regions with limited in-situ observational infrastructure. Further analysis (see Supplementary Information Section 7) reveal that FuXi Weather also outperformed ECMWF HRES in other data-sparse regions, such as tropical oceans and South America, although it is less competitive in areas with dense surface observations. In central Africa, where observational networks are sparse, the efficient use of satellite data by FuXi Weather closes the performance gap with ECMWF HRES, resulting in superior forecasts. Supplementary Fig. 23 illustrates two 10-day forecast timeseries for two randomly selected initialization times, while Supplementary Fig. 24 presents forecasts at a fixed 3-day lead time. Both figures confirm that FuXi Weather more closely aligns with its benchmark than ECMWF HRES, reinforcing the results in Fig. 5. Additionally, Supplementary Fig. 25 shows FuXi Weather’s superior performance, particularly for T2M, MSLP, and TP over northern South America, where observational coverage is also sparse relative to Europe or North America. However, the reduction in forecast activity may partially contribute to these improvements. A detailed discussion on the tradeoffs between forecast accuracy and activity is provided in Supplementary Information Section 12. While incorporating generative models or differentiable solvers for atmospheric dynamics could potentially enhance forecast activity without compromising accuracy18,52,53, an in-depth investigation of these approaches is beyond the scope of this study.

Due to substantial biases in TP data from ERA554, the Integrated Multi-satellite Retrievals for the Global Precipitation Measurement (GPM) (IMERG)55,56 is used to evaluate TP forecasts over central Africa and northern South America, respectively. As shown in Supplementary Fig. 26, FuXi Weather achieves lower RMSE than ECMWF HRES, relative to IMERG. However, both FuXi Weather and ECMWF HRES exhibit undesirably low ACC and substantial MBE when evaluated against IMERG. In FuXi Weather, this deficiency is likely inherited from its training with ERA5, underscoring the potential advantages of training with more accurate observational datasets, such as IMERG, to further improve FuXi Weather’s precipitation forecasts.

Overall, these preliminary results suggest that FuXi Weather can produce forecasts of comparable or potentially improved accuracy relative to traditional NWP systems, despite relying on substantially fewer observations. The superior performance of FuXi Weather relative to ECMWF HRES may be attributed to two primary factors: (1) enhanced ability to mitigate both systematic biases and random errors, and (2) reduced forecast activity. While further advancements, such as improving forecast activity, are necessary, FuXi Weather represents a promising and cost-effective alternative for regions with limited observational infrastructure. Future work will include further validation against independent observational datasets to better evaluate its performance advantages.

Physical consistency of analysis changes
FuXi Weather, as a data-driven machine learning system, does not inherently encode prior physical knowledge of atmospheric processes. This subsection examines the impact of assimilating a single observation on background fields and assesses whether the resulting changes align with theoretical expectations.

Two FuXi-DA runs were conducted: the first using a 6-h forecast with original observations, and the second with a perturbation introduced to raw satellite data from individual channels at a specific observation location. The differences between these two runs reflected the changes in analysis fields caused by the perturbation (details in Supplementary Information Section 4.1). The first run, initialized at 06 UTC on July 24, 2023, assimilated all available data to generate the analysis. In the second run, a +5 K perturbation was introduced into the NOAA-20 ATMS raw observation at 19.9° N, 125.5° E (marked as a purple dot in Supplementary Fig. 9), near Typhoon Doksuri over the ocean. The impact of this perturbation was evaluated by comparing outputs from both runs. The satellite observations were independently perturbed for each channel.

Figure 6 shows the horizontal and vertical distributions of changes in the analysis fields resulting from three separate perturbations, each applied to a different humidity channel. The spatial patterns of these changes in analysis fields aligned with the radiative transfer theory: an increase in brightness temperature corresponds to a decrease in humidity, resulting in less radiation absorption57. The vertical distribution showed progressive increases in the peak heights of the Jacobian functions for channels 18, 19, and 20, matched by corresponding increases in the peak heights of the humidity increments. This pattern suggests that the DA system effectively captures the varying detection altitudes of these channels. Additionally, flow-dependent characteristics were observed in the humidity field. The perturbation introduced at 05 UTC, 1 h before the analysis, generated changes in analysis fields mainly localized near the perturbation location, with a moderate eastward extension along the prevailing flow, consistent with downwind propagation. Supplementary Fig. 10 illustrates the changes in wind vector analysis fields, overlaid with relative humidity analysis fields. The perturbation results in increased northerly flow near the perturbed location. This change enhances the advection of drier air, characterized by lower relative humidity, into a more humid region. Consequently, the perturbation leads to a localized reduction in relative humidity, consistent with the results shown in Fig. 6.

In summary, FuXi Weather effectively captures the horizontal and vertical dependencies of analysis changes on satellite observations without explicitly incorporating prior knowledge. Data denial experiments (Supplementary Information Section 5) further confirm FuXi Weather’s physical consistency with satellite observations, while additional tests demonstrate the robustness of its performance.

Methods
FuXi Weather
Figure 7 illustrates FuXi Weather, which generates global weather forecasts every 6 h. It has three main components: satellite data preprocessing (detailed in Supplementary Information Section 2.1), DA via FuXi-DA, and forecasting using the FuXi model. A complete list of variables is provided in Table 1.

The preprocessing step addresses the heterogeneity in satellite data across space and time (see Fig. 8). While FuXi Weather can directly process raw observational data, the data are interpolated to a regular 0.25° grid. The system assimilates raw brightness temperature data from three polar-orbiting satellites (FY-3E, Metop-C, and NOAA-20) and GNSS-RO data68 (see Supplementary Table 1), processed using a modified PointPillars46 approach initially designed for three-dimensional point clouds69. Missing data are handled using a masking technique, assigning a value of 1 where data are available and 0 otherwise. Further details are provided in Supplementary Information Sections 1.2 and 2.1.

FuXi-DA assimilates the preprocessed data with background forecasts within 8 h to produce analysis fields. Key improvements include separate processing of different upper-air and surface variables, and a refinement module for improved accuracy (see Supplementary Information Section 2.2). The multi-branch architecture handles satellite data and meteorological variables in background forecasts separately, allowing for flexible integration of additional observations. DA is performed four times per day (at 00, 06, 12, and 18 UTC), using observations from 3 h before to 4 h after forecast initialization, generating global analysis fields at 0.25° resolution. The FuXi-Short produces 0–4 day forecasts, which serve as initial conditions for the FuXi-Medium model to generate 4–10 day predictions.

FuXi Weather is trained through joint optimization of analyses and forecasts, using ECMWF ERA5 reanalysis data at 0.25° resolution as the reference. While both the DA and forecasting components rely on ERA5 during training, the operational system operates independently of ERA5 during inference. To mimic varying operational conditions, FuXi forecasts (initialized with ERA5 data) are randomly sampled across lead times of 6 h to 5 days and used as background forecasts to train FuXi-DA. Owing to the limited amount of satellite data, FuXi-DA is trained on a 1-year dataset (June 1, 2022–June 30, 2023); this contrasts with the 37-year dataset used to train FuXi models14. A replay-based incremental learning strategy adapts the system to changes in satellite data quality and availability70,71 (see Supplementary Figs. 1 and 2), retraining FuXi-DA monthly with data from the previous year. Further details are in the Supplementary Information Section 3.2.

The FuXi-Short model is fine-tuned with FuXi-DA analysis fields to reconcile accuracy differences with ERA5 (Supplementary Information Section 3.3). During testing, FuXi Weather is initialized with zero values for cycling DA and forecasting, using one year of data spanning from July 1, 2023 to June 30, 2024.

Evaluation method
Forecasts are evaluated against benchmark datasets at corresponding forecast times. For FuXi model forecasts, whether initialized with ERA5 or analysis fields generated by FuXi-DA, ERA5 is used as the benchmark. Consistent with standard practices in NWP, FuXi Weather is also evaluated against its analyses. In evaluating the performance of ECMWF high-resolution (HRES) forecasts, the time series of HRES-fc0 data used to initialize these forecasts at time t0 is also used as the benchmark at the evaluation time t0 + τ. When FuXi and ECMWF HRES forecasts are evaluated against their respective initialization time series, both systems inherently exhibit higher accuracy at shorter lead times.

Deterministic forecasts are evaluated using established metrics, including the RMSE and ACC, defined as follows:

RMSE(c,τ) = [1/|D| * Σ_{t0∈D} (1/(H*W) * Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - A_{t0,i,j}^τ)^2)]^0.5 (1)

ACC(c,τ) = [Σ_{t0∈D} Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - M_{t0,i,j}^τ) * (A_{t0,i,j}^τ - M_{t0,i,j}^τ)] / [Σ_{t0∈D} Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - M_{t0,i,j}^τ)^2 * Σ_{t0∈D} Σ_{i=1}^H Σ_{j=1}^W (A_{t0,i,j}^τ - M_{t0,i,j}^τ)^2]^0.5 (2)

where, t0 denotes the forecast initialization time within the testing dataset (D), and τ is the forecast lead time. The climatological mean (M), calculated from ERA5 over the period 1993–2016, reflects the average conditions over these years. To better distinguish forecast performance between models with minor differences, the normalized RMSE difference between model A and baseline model B is calculated as (RMSE_A - RMSE_B)/RMSE_B. Similarly, the normalized ACC difference is calculated as (ACC_A - ACC_B)/(1 - ACC_B). A negative RMSE difference and positive ACC difference indicate that model A outperforms model B.

Furthermore, RMSE can be decomposed into systematic and random error components through calculation of the MBE and standard deviations of errors (STD_ERROR). These metrics distinguish whether forecast errors originate from consistent bias or random variations around observed values. The MBE and STD_ERROR are calculated as follows:

MBE(c,τ) = 1/|D| * Σ_{t0∈D} (1/(H*W) * Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - A_{t0,i,j}^τ)) (3)

STD_ERROR(c,τ) = [1/|D| * Σ_{t0∈D} (1/(H*W) * Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - A_{t0,i,j}^τ - MBE(c,τ))^2)]^0.5 (4)

Machine learning-based weather forecasting models often produce excessively smooth predictions as lead time increases. We quantify this forecast smoothness using two complementary activity metrics: (1) the standard deviation (std) of forecast anomalies relative to climatological means40, and (2) the RMSE between forecasts and climatological means. The std-based activity metric measures the spatial variability in forecast anomalies with respect to the climatological mean M:

ACT_STD(c,τ) = [1/|D| * Σ_{t0∈D} (1/(H*W) * Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - M_{t0,i,j}^τ)^2)]^0.5 (5)

The RMSE-based activity metric directly measures forecast deviations from climatological means:

ACT_RMSE(c,τ) = [1/|D| * Σ_{t0∈D} (1/(H*W) * Σ_{i=1}^H Σ_{j=1}^W (F_{t0,i,j}^τ - M_{t0,i,j}^τ)^2)]^0.5 (6)

To assess the quality of analysis fields, we calculate the RMSE and MBE using the same formulations as for forecast evaluation. Furthermore, we introduce analysis activity, which is defined as the ratio of the std to the climatological mean. This metric quantifies the degree to which analyses deviate from the climatological average state. The analysis activity is calculated as follows:

ACT_ANALYSIS(c,τ) = [1/|D| * Σ_{t0∈D} (1/(H*W) * Σ_{i=1}^H Σ_{j=1}^W (A_{t0,i,j}^τ - M_{t0,i,j}^τ)^2)]^0.5 (7)

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This works presents a novel method for cycling a data assimilation system using only ML models, without a physical model or traditional DA methods. This is a unique system: it takes a background field from an ML forecast, combines the background with satellite observations via ML, and produces an analysis field for initializing forecasts with an ML model. The results are impressive and this work is an exciting step forward in the field of ML for weather prediction. The paper is well-written and the conclusions are generally supported by the results.\nMajor comments\n1. What is the main reason for withholding conventional observations? What are the challenges?\n2. Supp Fig 3b and SI lines 321-328: Why do the DA windows overlap? Does this mean that some observations are effectively used twice? In traditional DA, this is generally avoided as this can cause overfitting and ultimately degrade forecast skill. Can you comment on the reasoning behind this design choice, and if observations are assimilated more than once, can you explain whether this would cause any issues or overfitting?\n3. Main text Section 3.4 needs a bit more explanation (either in the main text or SI) and I don’t fully understand Figure 4. It’s possible my misunderstanding is due to my lack of experience with satellite DA, but a bit more explanation here may be useful for other readers like me. It’s possible my misunderstanding is due to my lack of experience with satellite DA, but a bit more explanation here may be useful for other readers like me. Specific comments related to this:\na. Can you clarify whether the perturbation was introduced directly to the brightness temperature? Was the observation perturbed for all channels from NOAA-20, or for several channels separately?\nb. Related, I don’t understand Figure 4: are these “increments” from three different perturbations (to different channels)?\nc. I’m also not sure the phrase “analysis increment” is accurate here. For example, Figure 4 is not showing analysis increments in the traditional sense (analysis minus background) but rather the difference between two analysis fields (which are perturbed by a single observation). Is that the correct understanding?\nd. Finally, SI lines 518-519 mention that this perturbation was applied across a 5x5 grid point. Does this mean that the “red dot” in Figure 4 should actually be a box with sides of length 1.25deg? Are there any other implications of this choice?\n4. SI Section 6 needs clarity on difference between figs 13 and 14 and what the implication is. Specifically, SI lines 569-576 are unclear to me. It seems like this is suggesting that the first set of experiments shows how the analysis fields were degraded but the second set shows how subsequent forecasts were also degraded. But, I thought that backgrounds were not used in the second set of experiments? Can you expand on this a bit?\nMinor comments\n1. Line 38: integrates -> integrate\n2. Lines 101-109: observation error correlation is also a major reason for only assimilating a small amount of available satellite data. Is this addressed in this method?\n3. Lines 112-113: should maybe be “dynamical systems”?\n4. Line 131 and elsewhere: “cyclic DA” should maybe be “cycled DA” or “cycling DA”\n5. line 161: consider adding the satellite data preprocessing step to Figure 1?\n6. Line 165 and SI section 2.1: can you comment on why the interpolation of observational data to the model grid is necessary? Is it too difficult to have the NN do this interpolation itself?\n7. Line 167: what is meant by “data modalities”?\n8. Line 202 “referred to as the control run” I couldn’t find any other references to a “control run” in the main text; maybe this phrase should be removed here. Instead, it could be defined only for SI section 6, where it is used. This could simply be replacing SI line 537 with “…was assessed based on experiments that assimilate the full set of satellite data, which will be referred to as the control run.”\n9. Ext. Data Fig 2: Why do the 42h forecasts have lower error than the analyses?\n10. Line 223: should be “higher at 850 hPa than 300 and 500…”\n11. Line 235 “markedly enhanced the accuracy”: can you say anything about statistical significance here? If I understand correctly, the shading on Ext Data Fig 2 is the original data, not a statistical error bar.\n12. Line 243: “the figure” can you clarify if this is ED Fig 2?\n13. Line 248-250: I’m missing some intuition here. Does this imply that the background fields will be more accurate twice per day? If so, why doesn’t this translate to a more accurate analysis field as well?\n14. Lines 264-265: this wording is a bit awkward. Maybe, “…it outperformed ECMWF HRES after a lead time of 2-8 days, depending on variable and pressure level.”\n15. Line 274: analysis -> analyses\n16. Line 326: “using substantially less…”\n17. Figure 4 caption needs to be updated (it refers to the “second and fourth rows”.)\n18. Lines 354-355: I don’t see the “larger increment values downstream of the wind fields” in Figure 4. The “increments” are mostly centered on the perturbation location, or lie slightly north of the observation (but the winds appear to be generally westerly.) Can you clarify this statement?\n19. Ext Data Fig 3 caption: green -> black\n20. SI line 72: spatialtemporal -> spatiotemporal\n21. SI line 388: By “ground truth”, do you actually mean “reanalysis”?\n22. SI line 391: “similar to the those” -> “similar to those”\n23. SI Section 3.4: this section is not referred to in the main text. In SI line 451, the reference to “the main text Section 3.4” may be inaccurate. I would suggest removing this subsection or clarifying what additional information is provided in this section. Possibly the relevant sentences could be moved to SI Section 6 (data denial experiments).\n24. SI line 500: “Typically” Do you mean “Typically for satellite radiance observations,” ?\n25. SI line 510 should be “we followed”\n26. SI Section 6: Can you clarify in the text that each satellite was denied separately? This is only mentioned in the figure captions.\n27. Supp Figs 13-14: Are there any negative values? The caption of Fig 13 refers to “red shading” but there is no comparable e.g. blue shading for negative values. Also, can you add significance to these figures?\n28. Supp Figure 13 caption: clarify that this is the set of experiments that used background forecasts. Conversely, Fig 14 caption should describe that these experiments did not use background forecasts.\n29. SI Line 569: “extended Data Fig 14” should be “Fig 14”.\n30. SI lines 644-645: “…reveals that incremental learning has a more substantial positive impact than does fine-tuning alone.” Based on Supp Figs 21-22, it seems like this is the opposite? Setting 2 has much lower errors than Setting 3, which would mean that fine-tuning is more impactful than incremental learning. Can you clarify if the figure labels are correct and I’m interpreting this accurately?\n31. Throughout main text and SI: I would recommend replacing MSL with MSLP as this is more standard.\n(Remarks on code availability)\nA README for the code would be useful for the community.", "reviewer_2": "The manuscript “FuXi Weather: A data-to-forecast machine learning system for global weather” by Sun et al., 2025 is an example of a growing area of research in Machine Learning applied to Weather Prediction (MLWP). Current MLWP models need to use initial conditions from traditional NWP systems (operational or reanalysis) to start their forecasts, which makes them effectively equivalent to advanced, 4-dimentional (space plus time) post-processing tools. It is thus of interest to see whether it is possible to extend the MLWP paradigm to include an autonomous data assimilation cycle and thus closing the circle from observations to forecasts.\nThe system proposed in this manuscript would still not be completely independent of external (i.e., ECMWF ERA5) reanalysis products as it uses the FuXi model to cycle the assimilation and run forecasts and FuXi is a model trained on ERA5 fields. Additionally the Authors explicitly state: “End-to-end training of FuXi Weather optimizes both the analysis and forecasts using ECMWF ERA5 reanalysis data at 0.25. resolution as the reference.” But it would certainly be a step in that direction.\nUnfortunately, the paper does not convince me that the Authors have managed to achieve even this more limited objective.\nSpecifically, the Authors evaluate the accuracy of the analysis fields produced by FuXi Weather by comparing their errors with those of 42-hours FuXi forecasts started from ERA5 reanalysis fields and verified against ERA5 reanalyses. Looking at Extended Data Fig. 2, these errors look comparable. My interpretation is that the analyses produced by FuXi Weather are about as accurate as 2 days forecasts produced starting the model integration from ERA5 reanalysis. This is a starting point for further research, but hardly a result worth discussing on its own merits.\nFurther, when the Authors compare forecast results from FuXi Weather with those from ECMWF IFS, they are mixing the effects of two separate components, the assimilation system and the forecast model. If they want to evaluate how good the assimilation system of FuXi Weather is, then they need to use the same forecast model (in this case FuXi) started from a separate set of initial conditions (eg, ERA5) as a control. Otherwise the different characteristics of the forecast models used in the comparison muddy the conclusions. This is especially the case with MLWP models like FuXi which are known to suffer from increasing smoothness with forecast lead time and thus can game standard performance metrics.\nMore detailed comments are provided in the attached annotated version of the manuscript.\nFrom my perspective, this is a potentially interesting but very preliminary investigation and certainly at too early a stage to be considered for publication.\n(Remarks on code availability)", "reviewer_3": "The authors present an evolution of their machine-learning (ML) based forecasting system emulator Fuxi that is assimilating selected satellite based observations to create initial conditions for forecasts instead of using external analyses for initialisation. The data assimilation replacement method, called Fuxi-DA, is combined with an enhanced Fuxi forecast emulator to create the end-to-end Fuxi-Weather system that can be cycled like traditional, numerical methods based analysis-forecast systems. The output is assessed using standard forecast error metrics, and a specific focus is applied to a region in central Africa with sparse observational data coverage to test the robustness of the method.\nThe paper is complete regarding the explanation of methods, data, experiments and evaluation.\nThe Fuxi developers build on an extensive record of ML applied to weather forecasting, and they exhibit deep knowledge of the methodological frameworks applied in the numerical weather prediction (NWP) community. They have also published their results before and made code available for others to try - which is highly commendable. The paper is very well written.\nIn the attached file, I have raised several points that will need addressing before publication.\nMy greatest concern is the lack of evidence of statistical significance of forecast performance when compared against other data. More information is needed on the use of observational data in the data-assimilation process. I also wonder about the future need of data assimilation as an intermediate step between observational data records and forecast generation. Lastly, while I appreciate a special focus on central Africa for the reasons explained in the paper, the evaluation of performance for this case is not overly convincing.\n(Remarks on code availability)"}, "author_response": "Reply to Reviewer #1\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #1 (Remarks to the Author):\nThis work presents a novel method for cycling a data assimilation system using only\nML models, without a physical model or traditional DA methods. This is a unique\nsystem: it takes a background field from an ML forecast, combines the background\nwith satellite observations via ML, and produces an analysis field for initializing\nforecasts with an ML model. The results are impressive and this work is an exciting\nstep forward in the field of ML for weather prediction. The paper is well-written and\nthe conclusions are generally supported by the results.\nMajor comments\n1. What is the main reason for withholding conventional observations? What are the\nchallenges?\nResponse:\nThe primary objective of this study is to develop a cycling data assimilation and\nforecasting system that relies exclusively on machine learning models. Specifically, we\ninvestigate the feasibility of achieving this goal using only satellite data. We agree with\nthe reviewer that incorporating conventional observations, such as those from weather\nstations and radiosondes, poses additional challenges due to issues of spatial and\ntemporal sparsity, inhomogeneity, and varying data quality. These challenges\nnecessitate additional processing steps, including rigorous quality control. As part of\nour future efforts to enhance FuXi Weather, we plan to integrate additional satellite\ndatasets and conventional observations. To improve clarity, we have revised the\n\"Discussion\" section accordingly (lines 457–463).\n2. Supp Fig 3b and SI lines 321-328: Why do the DA windows overlap? Does this\nmean that some observations are effectively used twice? In traditional DA, this is\ngenerally avoided as this can cause overfitting and ultimately degrade forecast skill.\nCan you comment on the reasoning behind this design choice, and if observations\nare assimilated more than once, can you explain whether this would cause any\nissues or overfitting?\nResponse:\nWe thank the reviewer for this thoughtful comment. While overlapping DA windows\nare generally avoided in traditional DA frameworks, our experimental results suggest\nthat minor overlaps in a ML-based DA framework do not degrade performance. For\ninstance, when retraining FuXi-DA using a non-overlapping 6-hour DA window and\nevaluating its performance over a one-month period, we observed RMSE values\ncomparable to those obtained with an 8-hour DA window configuration. As shown in\nthe figures below, the differences in RMSE are marginal: for Z500, the RMSE values\nare 82.326 m² s⁻² (8-hour window) versus 84.230 m² s⁻² (6-hour window); for T850, the\nRMSE values are 1.106 K and 1.138 K, respectively. Given the negligible impact on\nperformance and the considerable computational cost associated with retraining, we did\nnot pursue further investigations.\nWe hypothesize that the reduced sensitivity of ML-based DA systems to DA window\noverlap, in contrast to traditional approaches, may arise from their ability to filter out\nprocesses associated with rapid early-time error growth in physical models, as\ndiscussed by Selz & Craig (2023, GRL). However, a comprehensive exploration of this\nmechanism is beyond the scope of the present study.\nWe have also included a corresponding statement (lines 341-344) in Section 2.2 of the\nSupplementary Information.\nReference:\nSelz, T., & Craig, G. C. (2023). Can artificial intelligence-based weather prediction\nmodels simulate the butterfly effect? Geophysical Research Letters, 50,\ne2023GL105747. https://doi.org/10.1029/2023GL105747\n3. Main text Section 3.4 needs a bit more explanation (either in the main text or SI)\nand I don’t fully understand Figure 4. It’s possible my misunderstanding is due\nto my lack of experience with satellite DA, but a bit more explanation here may be\nuseful for other readers like me. It’s possible my misunderstanding is due to my\nlack of experience with satellite DA, but a bit more explanation here may be useful\nfor other readers like me. Specific comments related to this:\na. Can you clarify whether the perturbation was introduced directly to the\nbrightness temperature? Was the observation perturbed for all channels from\nNOAA-20, or for several channels separately?\nb. Related, I don’t understand Figure 4: are these “increments” from three\ndifferent perturbations (to different channels)?\nc. I’m also not sure the phrase “analysis increment” is accurate here. For\nexample, Figure 4 is not showing analysis increments in the traditional sense\n(analysis minus background) but rather the difference between two analysis fields\n(which are perturbed by a single observation). Is that the correct understanding?\nd. Finally, SI lines 518-519 mention that this perturbation was applied across a 5x5\ngrid point. Does this mean that the “red dot” in Figure 4 should actually be a\nbox with sides of length 1.25deg? Are there any other implications of this choice?\nResponse:\na. Yes, the perturbation was introduced directly to the brightness temperature, with\nonly one channel perturbed in each experiment. To improve clarity, we have revised\nthe corresponding sentences in Section 3.4 of the main text (lines 399–400 and 408–\n409).\nb. Yes, these increments result from three separate perturbations applied to different\nchannels. To enhance clarity, we have revised the sentence in lines 410-412.\nc. We thank the reviewer for pointing out that the term “analysis increment” is\ninaccurate in this context. Accordingly, we have replaced it with a more appropriate\nexpression. Specifically, we have changed the title of Section 3.4 to “Physical\nconsistency of analysis changes”. Related revisions have been made to several\nsentences within Section 3.4 of the main text (lines 398, 402, 411–413, and 426),\nas well as in the caption of Figure 4. Corresponding revisions have also been made\nin Section 5.1 of the Supplementary Information (lines 511 and 539).\nd. Yes, the perturbation was applied over a 5x5 grid point area. In traditional DA, data\nthinning is usually performed, but we did not apply thinning in our ML-based DA.\nAs a result, observations remain relatively dense, leading to strong spatial\ncorrelations among them. Therefore, perturbing a single point may not effectively\ncapture realistic observation error structures. By perturbing a 5×5 grid area, we\nensure that the resulting impacts are more physically meaningful and better reflect\nrealistic spatial error correlations. To clarify this methodological detail, we have\nadded an explanatory statement in Section 5.1 of the Supplementary Information\n(lines 545–549).\n4. SI Section 6 needs clarity on difference between figs 13 and 14 and what the\nimplication is. Specifically, SI lines 569-576 are unclear to me. It seems like this is\nsuggesting that the first set of experiments shows how the analysis fields were\ndegraded but the second set shows how subsequent forecasts were also degraded.\nBut, I thought that backgrounds were not used in the second set of experiments?\nCan you expand on this a bit?\nResponse:\nThank you for your helpful comment regarding the clarity of our explanation. We have\nrevised the manuscript to better distinguish the two sets of experiments based on their\nuse of background fields.\nIn the first set of experiments, all runs including those that exclude specific satellite\ndata during DA, use the same background fields—specifically, the 6-hour forecasts\nfrom the control run. In contrast, the second set of experiments involves cycling DA\nand forecasts while excluding one satellite dataset in each case. As a result, the\nbackground fields vary between experiments, as they are generated independently from\neach respective cycling run rather than being fixed.\nTo clarify this difference, we have added a sentence to Section 6 of the Supplementary\nInformation (lines 580-583). Additionally, Figures 13 and 14 have also been\nrenumbered as Figures 14 and 15 in the update Supplementary Information.\nMinor comments\n1. Line 38: integrates -> integrate\nResponse: Thanks for highlighting this typo, we have fixed it.\n2. Lines 101-109: observation error correlation is also a major reason for only\nassimilating a small amount of available satellite data. Is this addressed in this\nmethod?\nResponse:\nWe thank the reviewer for the insightful comment regarding observation error\ncorrelation as a major constraint on the assimilation of available satellite data. Our study\naddresses this issue in two ways. First, the observational dataset used in our experiments\nis relatively limited, consisting of only five microwave instruments from three polar-\norbiting satellites, along with radio occultation data. Second, while our machine\nlearning approach does not explicitly account for observation error correlations, this\ncan be considered an inherent advantage of the method. The data-driven training\nprocess implicitly accounts for such correlations without requiring the specification of\nerror covariance matrices.\nTo clarify this point, we have added a sentence to the “Introduction” of the main text\n(lines 105-106) and revised the relevant sentences in the “Discussion” of the main text\n(lines 455-462).\n3. Lines 112-113: should maybe be “dynamical systems”?\nResponse: Thanks for highlighting this typo, we have replaced “dynamic systems” with\n“dynamical systems”.\n4. Line 131 and elsewhere: “cyclic DA” should maybe be “cycled DA” or\n“cycling DA”\nResponse: As suggested by the reviewer, we have replaced “cyclic DA” with “cycling\nDA” in the paper.\n5. line 161: consider adding the satellite data preprocessing step to Figure 1?\nResponse:\nWe appreciate the reviewer’s constructive suggestion. While we recognize the value of\nincluding the satellite data preprocessing step into Figure 1, this information is already\nthorougly described in Section 2.1 of the Supplementary Information. To enhance\nclarity in the main text, we have revised the corresponding sentence in Section 2 (line\n165).\n6. Line 165 and SI section 2.1: can you comment on why the interpolation of\nobservational data to the model grid is necessary? Is it too difficult to have the NN\ndo this interpolation itself?\nResponse:\nThank you for your suggestion. To clarify the rationale for interpolating observational\ndata to the model grid, we have revised the relevant sentence in the main text (lines\n169–173).\n7. Line 167: what is meant by “data modalities”?\nResponse:\nIn machine learning, the term “data modality” refers to a distinct form or method by\nwhich data are generated or represented. Meteorological observations from various\nsources constitute different modalities, as they capture diverse physical characteristics\n(e.g., visual, infrared, or point-based measurements) and originate from different\nsensing platforms (e.g., satellite-based versus ground-based instruments). To enhance\nclarity and avoid potential ambiguity, we have replaced the term \"data modalities\" with\n\"observation types\" in line 173 of the main text.\n8. Line 202 “referred to as the control run” I couldn’t find any other references\nto a “control run” in the main text; maybe this phrase should be removed here.\nInstead, it could be defined only for SI section 6, where it is used. This could simply\nbe replacing SI line 537 with “…was assessed based on experiments that\nassimilate the full set of satellite data, which will be referred to as the control run.”\nResponse:\nFollowing the reviewer’s suggestion, we have removed the phrase “referred to as the\ncontrol run” from Section 3 of the main text.\nAdditionally, we have revised the original sentence in Section 6 of the Supplementary\nInformation (lines 567-569) for improved clarity.\n9. Ext. Data Fig 2: Why do the 42h forecasts have lower error than the analyses?\nResponse:\nIn Extended Data Figure 2, the analyses represent FuXi Weather analyses, while the\n42-hour forecasts correspond to FuXi forecasts initialized using ERA5. Since FuXi-DA\nwas trained using ERA5 as the reference dataset, the FuXi Weather analyses are not\nexpected to surpass the accuracy of ERA5. Furthermore, FuXi-DA assimilates only a\nlimited subset of satellite observations. As a result, the FuXi Weather analyses\n(incorporating background forecasts) show errors comparable to those of the 42-hour\nFuXi forecasts, with differences varying by variable and pressure level.\nTo improve clarity, we have revised the caption of Extended Data Fig. 2 accordingly.\n10. Line 223: should be“higher at 850 hPa than 300 and 500…”\nResponse: Thanks for highlighting this typo, we have changed the word from “with”\nto “than”.\n11. Line 235 “markedly enhanced the accuracy”: can you say anything about\nstatistical significance here? If I understand correctly, the shading on Ext Data Fig\n2 is the original data, not a statistical error bar.\nResponse:\nWe appreciate the reviewer's comment about statistical significance. In Extended Data\nFigure 2, the shaded areas represent the original data, while the solid lines indicate 12-\npoint moving averages, as specified in the figure caption. Following the reviewer's\nsuggestion, we conducted statistical significance tests comparing FuXi Weather\nanalyses with and without background forecasts. The results show that incorporating\nbackground forecasts leads to statistically significant improvements in analysis\naccuracy.\nTo reflect these findings more clearly, we have revised the relevant sentence in the main\ntext (lines 247-249).\n12. Line 243: “the figure” can you clarify if this is ED Fig 2?\nResponse: We confirm that “the figure” indeed refers to Extended Data Fig.2. To\neliminate any ambiguity, we have revised the text to explicitly state \"Extended Data\nFigure 2\" in place of the original phrasing.\n13. Line 248-250: I’m missing some intuition here. Does this imply that the\nbackground fields will be more accurate twice per day? If so, why doesn’t this\ntranslate to a more accurate analysis field as well?\nResponse:\nWe thank the reviewer for raising this important question regarding temporal variations\nin analysis accuracy. The relatively consistent performance of the FuXi Weather\nanalyses across different initialization times can be attributed to two key aspects of our\nsystem design. First, the use of a fixed 8-hour assimilation window ensures temporal\nstability in the DA process. Second, the background forecasts used for DA are generated\nfrom previous FuXi Weather analyses rather than ERA5, resulting in more stable\nanalysis fields that are less sensitive to temporal variability than those initialized\ndirectly from ERA5.\nTo improve clarity, we have revised the corresponding sentence in the main text (lines\n260-263).\n14. Lines 264-265: this wording is a bit awkward. Maybe, “…it outperformed\nECMWF HRES after a lead time of 2-8 days, depending on variable and pressure\nlevel.”\nResponse: Following the reviewer’s suggestion, we have revised the wording in the\nmain text (lines 288-289) to improve clarity.\n15. Line 274: analysis -> analyses\nResponse: Thanks for highlighting this typo, we have changed the word from “analysis”\nto “analyses”.\n16. Line 326: “using substantially less…”\nResponse: Thanks for highlighting this issue, we have removed the word “an”.\n17. Figure 4 caption needs to be updated (it refers to the “second and fourth rows”.)\nResponse: We thank the reviewer for pointing out this inaccuracy in the figure caption.\nThe redundant word “fourth” has been removed from the caption of Figure 4.\n18. Lines 354-355: I don’t see the “larger increment values downstream of the wind\nfields” in Figure 4. The “increments” are mostly centered on the perturbation\nlocation, or lie slightly north of the observation (but the winds appear to be\ngenerally westerly.) Can you clarify this statement?\nResponse: We sincerely appreciate the reviewer's careful analysis of this point. Upon\nre-examination of Figure 4, we agree that our initial characterization of the increment\npatterns requires clarification. The increments are mainly localized near the\nperturbation location, with a secondary region of moderate increments extending\neastward in alignment with the prevailing westerly winds. This pattern contrasts with\nour earlier description, which emphasized larger downstream values.\nTo more accurately reflect these observations, we have revised the text in lines 421-423\nof the main text.\n19. Ext Data Fig 3 caption: green -> black\nResponse: We appreciate the reviewer for identifying this error in the caption of\nExtended Data Fig 3. We have corrected the color reference in the figure caption by\nreplacing “green” with “black”.\n20. SI line 72: spatialtemporal -> spatiotemporal\nResponse: We have corrected the word from “spatialtemporal” to “spatiotemporal”.\n21. SI line 388: By “ground truth”, do you actually mean “reanalysis”?\nResponse: We confirm that the term “ground truth” refers to the ERA5 reanalysis data.\nTo avoid potential confusion, We have replaced “ground truth” with “ERA5 reanalysis\ndata” in the Supplementary Information (line 403).\n22. SI line 391: “similar to the those” -> “similar to those”\nResponse: Thanks for highlighting this typo. We have removed the redundant word\n“the” in the Supplementary Information (line 407).\n23. SI Section 3.4: this section is not referred to in the main text. In SI line 451, the\nreference to “the main text Section 3.4” may be inaccurate. I would suggest\nremoving this subsection or clarifying what additional information is provided in\nthis section. Possibly the relevant sentences could be moved to SI Section 6 (data\ndenial experiments).\nResponse:\nWe are grateful for the reviewer’s observation regarding the inaccurate reference to\n“the main text Section 3.4”, which should have referred to “SI Section 6”. Following\nthe reviewer’s suggestion, we have removed this subsection from the Supplementary\nInformation.\n24. SI line 500: “Typically” Do you mean “Typically for satellite radiance\nobservations,” ?\nResponse: We thank the reviewer for this helpful clarification. As suggested, we have\nrevised the relevant text in lines 526-527 in the Supplementary Information.\n25. SI line 510 should be “we followed”\nResponse: As per the reviewer’s suggestion, we have revised the phrasing to “we\nfollowed” in line 536 of the Supplementary Information.\n26. SI Section 6: Can you clarify in the text that each satellite was denied separately?\nThis is only mentioned in the figure captions.\nResponse: Following the reviewer’s suggestion, we have added an additional sentence\nto improve clarity in line 585 of the Supplementary Information.\n27. Supp Figs 13-14: Are there any negative values? The caption of Fig 13 refers to\n“red shading” but there is no comparable e.g. blue shading for negative values.\nAlso, can you add significance to these figures?\nResponse: As suggested by the reviewer, we have updated the figures to include blue\nshading to represent negative values. We have also performed significance testing and\nused X symbols to denote where the resulting RMSE values are not statistically\nsignificant. The captions for Supplementary Figures 13 and 14 have been revised\naccordingly. These figures have also been renumbered as Figures 14 and 15 in the\nupdated Supplementary Information.\n28. Supp Figure 13 caption: clarify that this is the set of experiments that used\nbackground forecasts. Conversely, Fig 14 caption should describe that these\nexperiments did not use background forecasts.\nResponse:\nWe appreciate the reviewer’s valuable suggestion to clarify the methodological\ndistinctions between Supplementary Figures 13 and 14.\nIn the caption of Supplementary Figure 13 (renumbered as Supplementary Figure 14),\nwe have added the following text: “Each experiment uses 6-hour control forecast\nbackgrounds at analysis times, excluding one satellite data type during DA.”\nIn the caption of Supplementary Figure 14 (renumbered as Supplementary Figure 15),\nwe have included the text: “Each experiment uses cycled background fields that evolve\ndifferently depending on the excluded satellite data.”\n29. SI Line 569: “extended Data Fig 14” should be “Fig 14”.\nResponse: We thank the reviewer for highlighting this issue. And we have fixed it.\n30. SI lines 644-645: “…reveals that incremental learning has a more substantial\npositive impact than does fine-tuning alone.” Based on Supp Figs 21-22, it seems\nlike this is the opposite? Setting 2 has much lower errors than Setting 3, which\nwould mean that fine-tuning is more impactful than incremental learning. Can you\nclarify if the figure labels are correct and I’m interpreting this accurately?\nResponse:\nWe sincerely thank the reviewer for this careful examination. We confirm that the\noriginal statement was indeed the opposite. The relevant sentence (lines 712-713) in the\nSupplementary Information has been revised accordingly.\n31. Throughout main text and SI: I would recommend replacing MSL with MSLP as\nthis is more standard.\nResponse: As suggested by the reviewer, we have replaced “MSL” with “MSLP”\nthroughout the main text and SI.\nReviewer #1 (Remarks on code availability):\nA README for the code would be useful for the community.\nResponse: Following the reviewer’s suggestion, we have uploaded the README file\nfor the code to the Google Drive folder\n(https://drive.google.com/drive/folders/1q9xxKGqmR9tpjVd9R11OJ-\neKf1nU10T-?usp=sharing_eil_se_dm&ts=6800f61c).\nReply to Reviewer #2\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #2 (Remarks to the Author):\nThe manuscript “FuXi Weather: A data-to-forecast machine learning system for\nglobal weather” by Sun et al., 2025 is an example of a growing area of research in\nMachine Learning applied to Weather Prediction (MLWP). Current MLWP models\nneed to use initial conditions from traditional NWP systems (operational or reanalysis)\nto start their forecasts, which makes them effectively equivalent to advanced, 4-\ndimentional (space plus time) post-processing tools. It is thus of interest to see whether\nit is possible to extend the MLWP paradigm to include an autonomous data assimilation\ncycle and thus closing the circle from observations to forecasts.\nResponse:\nWe sincerely appreciate the reviewer’s thoughtful and constructive comments, which\nhave significantly contributed to improving the quality of our manuscript. We address\nthe key concerns below.\nThe system proposed in this manuscript would still not be completely independent of\nexternal (i.e., ECMWF ERA5) reanalysis products as it uses the FuXi model to cycle\nthe assimilation and run forecasts and FuXi is a model trained on ERA5 fields.\nAdditionally the Authors explicitly state:“End-to-end training of FuXi Weather\noptimizes both the analysis and forecasts using ECMWF ERA5 reanalysis data at 0.25.\nresolution as the reference.” But it would certainly be a step in that direction.\nUnfortunately, the paper does not convince me that the Authors have managed to\nachieve even this more limited objective.\nResponse:\nWe agree with the reviewer that the FuXi Weather system is not completely\nindependent of ERA5 during the training phase. However, during the inference phase,\nFuXi Weather operates without relying on external NWP products. To enhance clarity,\nwe have revised the relevant sentences in lines 192-196 of the main text to include this\ncaveat.\nSpecifically, the Authors evaluate the accuracy of the analysis fields produced by FuXi\nWeather by comparing their errors with those of 42-hour FuXi forecasts started from\nERA5 reanalysis fields and verified against ERA5 reanalyses. Looking at Extended\nData Fig. 2, these errors look comparable. My interpretation is that the analyses\nproduced by FuXi Weather are about as accurate as 2 days forecasts produced starting\nthe model integration from ERA5 reanalysis. This is a starting point for further\nresearch, but hardly a result worth discussing on its own merits.\nResponse:\nRegarding the accuracy of analysis fields generated by FuXi Weather, achieving\nperformance comparable to 42-hour forecasts represents a significant advancement in\ndata-driven weather prediction. FuXi Weather is initialized with zero fields and\noperates in a cycling mode, performing DA and forecasting every 6 hours over one\nyear. To our knowledge, the only other system currently pursuing a similar approach\nis that of Allen et al. (2025) (https://www.nature.com/articles/s41586-025-08897-0),\nwhich generates analysis fields with accuracy comparable to 2-day forecasts from\nECMWF HRES.\n• To provide a more comprehensive assessment, we have added Section 7 to the\nSupplementary Information, which compares the analysis activity (defined as the\nstandard deviation of analysis anomalies relative to climatological means) and\nmean bias error (as described in SI Section 4) between FuXi Weather and ECMWF\nHRES. The results demonstrate strong consistency with ECMWF HRES in terms\nof analysis activity.\n• It is worth noting that, in contrast to the extensive range of observational data used\nin generating ERA5, FuXi Weather currently relies on a limited set of satellite\nobservations. We have included a discussion of potential future enhancements,\nsuch as incorporating additional satellite data and integrating conventional\nobservations, in the revised Discussion section (lines 455–462) of the main text.\nConsidered in terms of the end-to-end system, through joint optimization of\nanalyses and forecasts FuXi Weather is able to produce forecasts that are competitive\nwith or (in certain regions/variables/lead-times) better than HRES, using only satellite\ndata in the inference stage. We hope this helps clarify the extent to which this is a\nsignificant milestone for ML systems. Revised sentences lines 192-196 are intended to\nbetter set expectations on this. At the same time, revisions in section 3.3 elaborate on\nspecifics and caveats.\nReference:\nAllen, A., Markou, S., Tebbutt, W. et al. End-to-end data-driven weather prediction.\nNature (2025). https://doi.org/10.1038/s41586-025-08897-0\nFurther, when the Authors compare forecast results from FuXi Weather with those from\nECMWF IFS, they are mixing the effects of two separate components, the assimilation\nsystem and the forecast model. If they want to evaluate how good the assimilation\nsystem of FuXi Weather is, then they need to use the same forecast model (in this case\nFuXi) started from a separate set of initial conditions (eg, ERA5) as a control.\nOtherwise the different characteristics of the forecast models used in the comparison\nmuddy the conclusions. This is especially the case with MLWP models like FuXi which\nare known to suffer from increasing smoothness with forecast lead time and thus can\ngame standard performance metrics.\nMore detailed comments are provided in the attached annotated version of the\nmanuscript.\nFrom my perspective, this is a potentially interesting but very preliminary investigation\nand certainly at too early a stage to be considered for publication.\nResponse:\nWe appreciate the reviewer’s comment on the importance of isolating the performance\nof the DA system from that of the forecast model. However, the primary objective of\nthis study is to introduce FuXi Weather, a data-to-forecast system integrating DA and\nforecasting, rather than focusing solely on the DA component.\nIn Section 9 of the Supplementary Information, we have presented a targeted evaluation\nof four training configurations, including one (Setting 3 in Supplementary Table 1 and\nSupplementary Figure 24) that uses the original FuXi forecast model (without fine-\ntuning) and is initialized using FuXi-DA analyses. This directly responds to the\nreviewer’s request for a controlled comparison to isolate the DA component’s\ncontribution.\nWe also agree with the reviewer that overly smooth forecasts remain a common\nlimitation in machine learning-based weather forecasting models. To improve the\nclarity and comprehensiveness of the manuscript, we have made the following revisions:\n• We have included a discussion in the main text (lines 375-381 and 385-387) to\ncarefully caveat the role of reduced forecast activity at long lead times in enhancing\nforecast performance.\n• To quantitatively assess forecast smoothness, We have introduced additional\nevaluation metrics in Section 4 of the Supplementary Information, including: 1)\nthe standard deviation of forecast anomalies relative to climatological means\n(Bouallègue et al. 2024), and 2) the RMSE between forecasts and climatological\nmeans (Allen et al., 2025).\n• Comparative results on forecast activity are presented in Section 11 of the\nSupplementary Information. We also analyze the trade-off between forecast\naccuracy and activity, demonstrating that it is possible to enhance forecast activity\nwithout significantly degrading accuracy. This topic remains an active area of\nresearch, which we intend to explore further in future work.\n• We have applied statistical significance testing throughout our results to strengthen\nthe reliability of our findings.\n• We have included a comparison between FuXi Weather forecasts and its analyses\nin the main text, illustrating that the initial errors are small and comparable to those\nof ECMWF HRES.\nWe do hope the reviewer will also take into account the diagnostics presented in Section\n3.4, which examines the physical consistency of analysis changes associated with\nspecific observations. Since ML DA does not inherently encode knowledge of\natmospheric processes, we advocate this type of careful cross-checks for ensuring\nphysical consistency. While this approach is standard in traditional DA, it remains\nnovel in the ML literature. While we recognize the limitations highlighted by the\nreviewer, we believe this work represents a meaningful step forward in the\nadvancement of fully data-driven weather forecasting systems.\nReference:\nAllen, A., Markou, S., Tebbutt, W. et al. End-to-end data-driven weather prediction.\nNature (2025). https://doi.org/10.1038/s41586-025-08897-0\nBen Bouallègue, Z., and Coauthors, 2024: The Rise of Data-Driven Weather\nForecasting: A First Statistical Assessment of Machine Learning–Based Weather\nForecasts in an Operational-Like Context. Bull. Amer. Meteor. Soc., 105, E864–E883,\nhttps://doi.org/10.1175/BAMS-D-23-0162.1\n1. Line 44 in the main text. Maybe \"local disparities in forecast accuracies\"\notherwise this sentence does not make sense\nResponse: As suggested by the reviewer, we have revised the wording in the abstract\nto “local disparities in forecast accuracies”.\n2. Line 134-135 in the main text. “FuXi Weather integrates a substantially enhanced\nversion of FuXi-DA [42] with fine-tuned FuXi.” Does this mean that the DA system\nis cycled based on a model trained on ECMWF ERA5 reanalysis fields?\nResponse:\nWe confirm that the DA system is cycled using FuXi-DA, which was trained with\nECMWF ERA5 reanalysis data as the reference. To improve clarity, we have added an\nadditional sentence in the main text (lines 138-139).\n3. Line 185-187 in the main text. “End-to-end training of FuXi Weather optimizes both\nthe analysis and forecasts using ECMWF ERA5 reanalysis data at 0.25° resolution\nas the reference.” This implies that FuXi Weather is still completely dependent on\nECMWF ERA5 reanalysis data to learn both the DA update and the forecast step,\nright?\nResponse:\nWe confirm that the training of FuXi Weather relies on ECMWF ERA5 reanalysis data\nfor both the DA and forecasting components during the model development. To clarify\nthis dependency, we have revised the main text accordingly: lines 138-139 in Section\n1, lines 194-196 in Section 2, and lines 472-473 in Section 4.\n4. Line 217-218 in the main text. “This subsection evaluates the analysis fields of FuXi\nWeather against 42-hour FuXi forecasts initialized with ERA5, using ERA5 as the\nbenchmark.” I do not understand what this means. One usually evaluates forecast\nagainst verifying analyses, not the other way round. Are the Authors saying that\nthey evaluate the quality of the FuXi Weather analyses against FuXi forecasts\ninitialised by ERA5 analyses valid 42 hours earlier? If this is the case, then I do\nnot see the point of the exercise.\nResponse:\nWe thank the reviewer for highlighting this point, which helped us to clarify a\npreviously ambiguous statement in the manuscript. We confirm that both the FuXi\nWeather analyses and the 42-hour FuXi forecasts (initialized with ERA5) are evaluated\nagainst ERA5, which serves as the reference. To improve clarity, we have revised the\nrelevant sentence in lines 229-230 in Section 3.1 of the main text.\nAdditionally, we have included evaluations of the FuXi Weather forecasts against its\nanalyses in Section 3.2 and 3.3 of the main text. Further details are provided in response\nto the reviewer’s subsequent comments.\n5. Line 218-221 in the main text. “Extended Data Fig.2 presents the globally-\naveraged, latitude-weighted RMSE for two FuXi Weather configurations: one\nincorporating background forecasts and one without.” My reading of Extended\nData Fig.2 is that the quality of the FuXi Weather analysis fields with/without\nbackground is for most variables/levels inferior to that of a FuXi forecast started\nfrom ERA5 analyses valid 42 hours earlier. If this interpretation is correct, the\nobvious conclusion is that FuXi Weather analyses are very poor.\nResponse:\nWe appreciate the reviewer’s careful examination of Extended Data Fig. 2 and would\nlike to provide additional context for interpreting these results.\n• The comparison between FuXi Weather's analyses and the 42-hour FuXi forecasts\n(initialized from ERA5) should be considered in the context of the observational\ndata available for assimilation. Although FuXi is trained using ERA5 as the\nreference, it currently has access to a subset of the observations included in the full\nERA5 reanalysis, particularly lacking the extensive set of conventional\nobservations. Moreover, FuXi Weather has been trained on just one year of data.\nTherefore, it is not surprising that there remains nontrivial analysis error. Although\nwe expect to improve on this in future, the current analyses are sufficiently accurate\nto yield slowly growing forecast errors, allowing FuXi’s medium-range forecasts\nto remain competitive.\n• To better illustrate this, we have added an additional curve to Figures 2 and 3 in\nthe main text, showing initial error growth relative to FuXi Weather’s own analysis.\nEven with imperfect analyses, we would argue that FuXi Weather already\ndemonstrates promising performance for medium-range forecasting.\n• We have carefully presented the relevant figures in a way that caveats the initial\nerrors in the current analyses. However, we recognize that we may have\naccidentally overstated these limitations by not including a comparable illustration\nof the differences between ECMWF HRES analyses and ERA5. To address this,\nwe have added two figures to the Supplementary Information: Supplementary\nFigure 16 shows that the FuXi analyses have activity comparable to ECMWF\nHRES, and Supplementary Figure 17 shows that the MBE relative to ERA5 is of\nsimilar magnitude between FuXi and ECMWF HRES analyses.\n• To our knowledge, the only other system pursuing a similar approach is that of\nAllen et al. (2025) which produces analysis fields with RMSE values comparable\nto those of 2-day ECMWF HRES forecasts. This comparison is directly relevant\nto our results in Extended Data Fig. 2. In our study, FuXi Weather’s analyses\noutperform the 42-hour forecasts (initialized with ERA5) for relative humidity at\n300 and 500 hPa, and demonstrate comparable accuracy for temperature,\ngeopotential, and wind at these levels. Some degradation is observed at 850 hPa,\nwhich we acknowledge as an area for improvement through the assimilation of\nadditional observations. Several differences between the Aardvark and FuXi\nWeather systems are discussed in Section 7 of the Supplementary Information.\nWhile we recognize that there remains room for further improvement, such as\nexpanding the observational dataset and the training period, we believe that FuXi\nWeather’s analyses achieve state-of-the-art performance in this rapidly evolving field.\nTherefore, we respectfully disagree with the characterization of these results as \"very\npoor”.\nReference:\nAllen, A., Markou, S., Tebbutt, W. et al. End-to-end data-driven weather prediction.\nNature (2025). https://doi.org/10.1038/s41586-025-08897-0\n6. Line 263-265 in the main text. “Although FuXi Weather initially had higher RMSE\nvalues than those of ECMWF HRES, it outperformed ECMWF HRES after a\nvariable-specific lead time, which varied according to the variable and pressure\nlevel.”\nLine 273-276 in the main text. “However, Fuxi Weather forecasts initialized with\nanalysis incorporating background forecasts, though initially less accurate than\nECMWF HRES, improved over time and eventually achieved higher ACC values\nacross all examined variables.”\nThe only way I can think of that a forecast model having worse performance in the\nfirst 5-6 days than a control then becomes better is by losing forecast activity, i.e.\nbecoming smoother with increasing forecast lead time. The Authors should provide\nforecast activity plots for all the variable shown in Figure 2 if these results are to\nbe taken at face value.\nResponse:\nWe thank the reviewer for highlighting the importance of forecast activity analysis,\nwhich provides valuable context for interpreting our results. We acknowledge that our\noriginal comparison between FuXi Weather and ECMWF HRES requires further\nclarification.\nThe apparent initial RMSE advantage of ECMWF HRES arises because its forecasts\nare evaluated against its own analyses, as noted in the caption of Figure 2. This gives\nECMWF HRES a favorable starting point, as its forecasts start with zero error relative\nto its own analysis fields. To provide a more equitable comparison, we have now\nincluded additional results in Figure 2, where FuXi forecasts are also evaluated against\nits own analyses. This adjustment allows for a more equitable assessment of the initial\nerror growth in both systems, with each forecast verified against its respective analysis.\nRegarding the reviewer's comment on forecast activity, we agree that this is an excellent\npoint. Indeed, the relative performance improvement of FuXi at longer lead times may\nbe partially attributed to reduced forecast activity, a phenomenon commonly observed\nin machine learning based weather prediction models. Additionally, FuXi demonstrates\na stronger ability to reduce both systematic biases and random errors, as evidenced by\nthe comparisons of MBE and standard deviations of error (STD ) in Extended Data\nERROR\nFigures 5 and 8.\nTo quantify the degree of reduced activity in FuXi, we have conducted a comprehensive\nforecast activity analysis for all variables shown in Figure 2, using both the std-based\nmethod (Bouallègue et al., 2024) and the RMSE-based approach (Allen et al., 2025).\nForecast activity was normalized relative to ECMWF HRES, with a value of 1\nindicating activity equivalent to ECMWF HRES and values approaching 0 signifying\nconvergence toward climatological means. These detailed results are now presented in\nSection 11 of the Supplementary Information, where we discuss the trade-off between\nforecast accuracy and forecast activity. Both the std-based and RMSE-based activity\nshow similar trends when normalized against ECMWF HRES, providing essential\ncontext for understanding the performance characteristics discussed in the main results.\nWe have revised lines 376-393 in Section 3 of the main text to provide a more refined\ndiscussion of the forecast improvements in light of this trade-off, particularly during\nthe interval before the loss of activity becomes substantial.We have also revised the\nparagraph of the Discussion section (lines 463-467) to include caveats regarding this\neffect.\n7. Fig. 2 caption. “Comparison of forecast performance among various models over\na 1-year testing period, spanning from July 03, 2023, to June 30, 2024.” There is a\nnotable and unphysical jump at forecast day 4 in the FuXi forecasts. Can the\nAuthors explain where this originates?\nResponse:\nWe appreciate the reviewer’s observation regarding the discontinuity in forecast\nperformance at day 4. This feature arises from the design of our FuXi Weather system,\nwhich employs a cascade model architecture, as described in our previous publication\n(https://www.nature.com/articles/s41612-023-00512-1). In that paper, FuXi consists of\nthree cascade models, FuXi-Short (0-5 days), FuXi-Medium (5-10 days), and FuXi-\nLong (10-15 days), each optimized for a specific forecast window. As demonstrated in\nthe Supplementary Information of this paper, 4-day forecasts generated by FuXi-Short\nwhen initialized with FuXi-DA analysis fields, achieve accuracy comparable to 5-day\nforecasts initialized with ERA5. Therefore, we implemented a configuration where\nFuXi-Short generates 0-4 day forecasts, which are then used as initial conditions for\nFuXi-Medium to produce forecasts for days 4-10. The discontinuity observed at day 4\nreflects model transition.\nTo enhance methodological clarity, we have made two revisions to the main text. In\nSection 2 of the main text, we have revised the description in lines 189-191, and in\nSection 3, we have added clarifications in lines 295-297.\nAdditionally, we have updated the captions of Figure 2, Extended Data Figure 3, and\nSupplementary Figures 21 and 22 (now renumbered as Supplementary Figures 24 and\n25) to include the following sentence: “The performance change at day 4 arises from\nthe model transition from FuXi-Short to FuXi-Medium.”\nWhile this cascaded architecture introduces a discontinuity, it allows optimized\nperformance across different forecast windows. We also appreciate this opportunity to\nclarify the methodology.\n8. Line 325-328 in the main text. “These findings suggest that FuXi Weather can\ndeliver more accurate forecasts using an substantially less data than traditional\nNWP systems, offering a cost-effective, satellite-based solution to improve forecasts\nin regions lacking observational infrastructure.” One can come up with a different\nexplanation for the results shown over Central Africa. Central Africa is in the\nTropics so the evolution of forecast errors is dominated by systematic errors and\nconditional biases. While the FuXi forecast starts from a clearly less accurate initial\nstate, the fact that FuXi has been trained on ERA5 reanalyses means that it has\nlearned to compensate for the IFS model biases. This, together with the reduced\nforecast activity of the FuXi model, can explain the results shown here.\nResponse:\nWe appreciate the reviewer’s insightful analysis regarding the potential factors\ncontributing to FuXi Weather's superior performance in central Africa. The suggestions\nabout systematic error compensation and reduced forecast activity offer valuable\nalternative interpretations that merit careful consideration. To rigorously examine these\nhypotheses, we conducted three complementary analyses.\nFirst, we have decomposed the forecast errors into systematic and random components\nby calculating the mean bias error (MBE) and the standard deviation (std) of errors\n(STD ). As illustrated in Extended Data Fig.5, FuXi Weather exhibits both lower\nERROR\nMBE and smaller STD values compared to ECMWF HRES, indicating more\nERROR\neffective mitigation of both systematic biases and random errors. For clarity, we have\nrevised lines 338-345 of the main text to explicitly state these findings.\nSecond, as presented in the updated Figure 3 and Extended Data Figure 5, we have\nexpanded the evaluation of FuXi Weather forecasts against its own analyses over\ncentral Africa. The results demonstrate that FuXi Weather (green lines) consistently\noutperforms ECMWF HRES (blue lines) throughout the entire 10-day forecast period\nwhen each is verified against its respective analyses.\nLastly, we calculated forecast activity, defined as the std of forecast anomalies relative\nto climatological means, over central Africa. The results reveal that FuXi Weather\nmaintains lower forecast activity than ECMWF HRES from the start of the 10-day\nforecast period, suggesting smoother predictions. This is a typical characteristic of\nmachine learning-based weather prediction models. Notably, FuXi Weather's superior\nskill (red lines) becomes apparent prior to any considerable reduction in forecast\nactivity. This implies that while reduced activity may favor performance at longer lead\ntimes, it does not fully account for FuXi Weather's enhanced accuracy beyond the initial\nforecast period. We have revised the lines 350-359 to improve clarity on this point.\nAdditionally, as detailed in our response to the reviewer’s Comment #6, we have\nexplored the trade-offs between forecast accuracy and activity, including preliminary\nresults on an enhancement module designed to improve forecast activity.\nWe have updated the relevant figures and corresponding text to reflect these\ncomprehensive analyses. While we acknowledge that the factors highlighted by the\nreviewer may contribute partially, our extended analyses support the original\nconclusion that FuXi Weather demonstrates robust and competitive performance in\ndata-sparse regions.\nReply to Reviewer #3\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #3 (Remarks to the Author):\nThe authors present an evolution of their machine-learning (ML) based forecasting\nsystem emulator Fuxi that is assimilating selected satellite based observations to\ncreate initial conditions for forecasts instead of using external analyses for\ninitialisation. The data assimilation replacement method, called Fuxi-DA, is\ncombined with an enhanced Fuxi forecast emulator to create the end-to-end Fuxi-\nWeather system that can be cycled like traditional, numerical methods based analysis-\nforecast systems. The output is assessed using standard forecast error metrics, and a\nspecific focus is applied to a region in central Africa with sparse observational data\ncoverage to test the robustness of the method.\nThe paper is complete regarding the explanation of methods, data, experiments and\nevaluation.\nThe Fuxi developers build on an extensive record of ML applied to weather\nforecasting,and they exhibit deep knowledge of the methodological frameworks\napplied in the numerical weather prediction (NWP) community. They have also\npublished their results before and made code available for others to try - which is\nhighly commendable. The paper is very well written.\nIn the attached file, I have raised several points that will need addressing before\npublication.\nMy greatest concern is the lack of evidence of statistical significance of forecast\nperformance when compared against other data. More information is needed on the\nuse of observational data in the data-assimilation process. I also wonder about the\nfuture need of data assimilation as an intermediate step between observational data\nrecords and forecast generation. Lastly, while I appreciate a special focus on central\nAfrica for the reasons explained in the paper, the evaluation of performance for this\ncase is not overly convincing.\nSummary:\nThe authors present an evolution of their machine-learning (ML) based forecasting\nsystem emulator Fuxi that is assimilating selected satellite based observations to create\ninitial conditions for forecasts instead of using external analyses for initialisation. The\ndata assimilation replacement method, called Fuxi-DA, is combined with an enhanced\nFuxi forecast emulator to create the end-to-end Fuxi-Weather system that can be cycled\nlike traditional, numerical methods based analysis-forecast systems. The output is\nassessed using standard forecast error metrics, and a specific focus is applied to a\nregion in central Africa with sparse observational data coverage to test the robustness\nof the method.\nThe paper is complete regarding the explanation of methods, data, experiments and\nevaluation. The Fuxi developers build on an extensive record of ML applied to weather\nforecasting, and they exhibit deep knowledge of the methodological frameworks\napplied in the numerical weather prediction (NWP) community. They have also\npublished their results before and made code available for others to try - which is highly\ncommendable. The paper is very well written.\nIn the following, I have raised several points that will need addressing before\npublication. My greatest concern is the lack of evidence of statistical significance of\nforecast performance when compared against other data. More information is needed\non the use of observational data in the data-assimilation process. I also wonder about\nthe future need of data assimilation as an intermediate step between observational data\nrecords and forecast generation. Lastly, while I appreciate a special focus on central\nAfrica for the reasons explained in the paper, the evaluation of performance for this\ncase is not overly convincing.\nGeneral comments:\n•1 Need for data assimilation: Given the recent evolution of ML-methods applied in\nweather prediction, I wonder whether there will still be a need for an explicit,\nintermediate data assimilation step in the future. The present need for this step\noriginates from numerical models requiring starting conditions to evolve the\ndifferential equations in time. ML methods do not necessarily need this unless they\ncycle through time steps like traditional systems. Recent studies seem to suggest that\nit may be advantageous to produce predictions directly from past and present observations,\nand therefore skip the data assimilation step all together (aka direct observation\nprediction, e.g. https://arxiv.org/abs/2407.15586).\nWhile this point does not negate the importance of assessing ML-methods for data\nassimilation per-se, this paper could benefit from a discussion of this topic given that\nthe target journal is Nature Comm.\nResponse:\nWe appreciate the reviewer’s insightful comment regarding the potential evolution of\nmachine learning-based weather prediction systems and the possibility of eliminating\nexplicit data assimilation (DA) steps. Indeed, recent pioneering efforts, such as\nArtificial Intelligence Direct Observation Prediction (McNally et al., 2024;\nhttps://arxiv.org/abs/2407.15586) and GraphDOP (Alexe et al., 2024;\nhttps://arxiv.org/html/2412.15687v1), have demonstrated the feasibility of generating\nweather forecasts directly from meteorological observations using machine learning.\nDeveloped at ECMWF, both approaches offer significant advantages by obviating\ntraditional DA challenges, including the estimation of error covariance matrices, and\nby enabling the assimilation of all available observations regardless of measurement\ncomplexity.\nHowever, the effectiveness of AI-DOP frameworks depends critically on two\nprerequisites: (1) sufficiently dense spatiotemporal observational coverage and (2)\naccess to long-term, high-quality historical observational records. For example,\nECMWF’s AI-DOP model is trained on 18 years of observational data (2004–2021),\ncovering all major categories used in numerical weather prediction (NWP) systems. In\ncontrast, FuXi Weather has thus far been trained on only one year of data. Explicit DA\napproaches, which typically rely on forecasting models pretrained using multi-decade\nERA5 reanalysis datasets, are better suited to scenarios with sparse or incomplete\nobservational data. Implicit DA methods require significantly larger and more\nconsistent observational datasets to learn direct observation to prediction directly.\nAdditionally, our objective requires generating forecasts that can be directly evaluated\nagainst ERA5 and compared with state-of-the-art NWP models, i.e., ECMWF HRES.\nSuch a comparison must encompass not only surface parameters measured by weather\nstations but also upper-air variables like 500 hPa geopotential height, for which direct\nobservations are unavailable.\nFollowing the reviewer’s suggestion, we have expanded the Discussion section (lines\n473–500) to explicitly address this important consideration.\n•2 Statistical significance: It is standard practice in NWP evaluation to indicate the\nstatistical significance of skill (differences). If the individual variance of two skill\nmeasures is too large, it will not allow to make statements about the significance of\ntheir difference:”Uncertainty in the measures can be indicated as confidence\nintervals or error bars calculated using approximations to statistical distributions, or\nthrough computer-intensive techniques such as re-sampling”\n( https://empslocal.ex.ac.uk/people/staff/dbs202/publications/booksreports/mailier.pdf\n).\nThis applies to all figures 2, 3 and extended figures 3, 4, 5, 8, also maps. The\ninterpretation of these figures will have to be adjusted as well as several score\ndifferences may not lead 1 to conclusions on better or worse performance. From my\nexperience, some of the stated score differences will become meaningless once\ninformation on statistical significance is added.\nResponse:\nWe appreciate the reviewer’s valuable suggestion regarding the importance of\nstatistical significance testing in NWP evaluation. We have conducted a comprehensive\nsignificance testing analysis for all relevant figures, following the established\nmethodology described by Geer (2016). This includes both the time series of forecast\nperformance (Figures 2 and 3; Extended Data Figures 2, 3, 5, and 8; and Supplementary\nFigures 14 and 15, previously numbered 13 and 14) and spatial distributions of forecast\nerrors (Supplementary Figures 18-23, previously numbered 15-20).\nIn the time series plots, statistically significant differences are now indicated by solid\ndots overlaid on the corresponding lines. In the spatial error maps, stippling has been\nadded to denote regions where differences in skill scores are statistically significant.\nWe have revised the relevant sections of the manuscript to clearly reflect these updates.\nThe inclusion of statistical significance strengthens our interpretations of the results\nwithout changing the study's main conclusions. The key differences in model\nperformance remain statistically significant, thereby increasing confidence in the\nrobustness of our evaluation.\nReference:\nGeer, A.J.: Significance of changes in medium-range forecast scores. Tellus A:\nDynamic Meteorology and Oceanography 68(1), 30229 (2016). https:\n//doi.org/10.3402/tellusa.v68.30229\n•3 Observation pre-processing: The satellite radiance observations are ’assimilated’\nin a rather unqualified way. All channels of the microwave sounding instruments are\nused even though the window channels of both temperature and humidity sounders are\nvery sensitive to surface emission that is driven by emissivity (dependent on surface\ntype, moisture, vegetation, roughness) and surface temperature. These channels are\nalso sensitive to clouds and precipitation, which greatly dilute the information content\non the five target state variables. The authors mention cross-track scanning instrument\n(scan angle) biases. Are these corrected or is it assumed that - through knowledge of\nthe scan-angle -the ML-method adjusts its weights? Can this be shown?\nThe GNSS radio occultation data is used as profiles of refractive index, and this product\nexhibits larger errors in the lower 2-3 km of the troposphere and in the upper\nstratosphere/mesosphere. Pre-processing is mentioned, but the paper does not provide\ninformation on how systematic errors associated with this data are being addressed.\nOverall, the study uses observational data in a brute-force fashion that could be greatly\nimproved on given the available knowledge from traditional data assimilation.\nResponse:\nWe appreciate the reviewer’s insightful comments about observation pre-processing.\nWhile we acknowledge that incorporating established DA knowledge into observation\nhandling could potentially enhance model performance, our approach intentionally\nadopts a more direct strategy. This design allows the model to learn the relationships\namong inputs, such as satellite observations, scan angle and spatial coordinates, and the\ntarget meteorological variables during training.\nTo assess how effectively FuXi-DA captures these relationships, we conducted a\ngradient-based sensitivity analysis. Specifically, we computed the gradients of relative\nhumidity (R) with respect to five ATMS humidity channels in the 183.31 GHz band\n(channels 18-22), scan angle, latitude, and longitude. For R at each pressure level, we\ncalculated a latitude-weighted MAE loss relative to ERA5. The resulting gradients\npreserve the input dimensions of the ATMS observations (8 × 8 × 720 × 1440, where\nthe second dimension of 8 includes five channels plus three additional dimensions for\nscan angle and spatial coordinates). To quantify the magnitude of sensitivity, we took\nthe absolute values of these gradients and aggregated them across the temporal and\nspatial dimensions (8, 720, 1440), resulting in eight gradient sums (one for each ATMS\nchannel), along with aggregated contributions from scan angle, latitude, and longitude.\nThese values were then normalized to the [0, 1] range using min-max scaling, with the\nminimum and maximum determined across all variables and channels.\nThe resulting sensitivity matrix (13 × 8) reveals the relative influence of each ATMS\nchannel, scan angle, and spatial coordinates on the analysis fields. These results confirm\nthat FuXi-DA learns to weight input in a physically meaningful manner, even without\nexplicit bias corrections.\nWe have also added a new Section 10 in Supplementary Information to provide further\nclarification on how the model accounts for potential biases and uncertainties in the\ninput data.\n•4 African case study: I understand the motivation of the regional focus when applied\nto an area that is important for society, sparsely observed and where traditional system\ndo not perform well. However, the study does not spend enough effort to fully assess\nthe African case. Fig. 3 shows performance, again without statistical significance\ninformation, a two-cycle/day skill-score pattern (?), forecasts are verified against\nanalyses that are notoriously poor in this area as opposed to (the few existing)\nobservations, and for parameters that matter less for society here than, for example,\nsoil moisture and rainfall.\nThis is not a very convincing.\nResponse:\nWe thank the reviewer for the valuable feedback regarding the African case study. We\nhave conducted additional analyses to further characterize FuXi Weather's performance\nover central Africa.\nFirst, we have updated Figure 3 to include statistical significance testing, where red\ndots indicate time steps at which FuXi Weather shows statistically significant\nimprovements over ECMWF HRES. As shown in the updated Figure 3 and Extended\nData Figure 5, we have expanded the evaluation of FuXi Weather forecasts by\ncomparing them against its own analyses. The results indicate that FuXi Weather (green\nlines) outperforms ECMWF HRES (blue lines) in forecasting U850, T2M, and MSLP\nacross the 10-day forecast period.\nTo include variables of greater societal relevance, we extended the evaluation to total\nprecipitation (TP), as FuXi Weather does not output soil moisture. The updated\nExtended Data Figure 5 presents TP forecast performance comparisons over central\nAfrica. Since ECMWF HRES-fc0 contains zero precipitation values, both models are\nevaluated against ERA5 TP. Results suggest that FuXi Weather achieves better TP\naccuracy, particularly for light precipitation events, as further illustrated in Extended\nData Figure 6.\nAdditionally, we have analyzed forecast activity, defined as the standard deviation of\nforecast anomalies relative to climatological means. This analysis reveals that FuXi\nWeather maintains lower forecast activity than ECMWF HRES over the 10-day forecast\nperiod, suggesting smoother predictions. This is a characteristic commonly observed\nin machine learning-based weather prediction models. As shown in Extended Data\nFigure 5, FuXi Weather's enhanced skill (red lines) becomes apparent before\nconsiderable reduction in forecast activity. This suggests that reduced forecast activity\nmay partially contribute to FuXi Weather’s superior performance at longer lead times.\nFurthermore, FuXi exhibits a greater capacity to reduce both systematic biases and\nrandom errors, as evidenced by the comparisons of MBE and standard deviations of\nerror (STD ) in Extended Data Figures 5 and 8.\nERROR\nWe have also explored the trade-offs between forecast accuracy and activity,\nincluding preliminary results demonstrating the efficacy of an enhancement module\ndesigned to improve forecast activity.\nWe acknowledge the reviewer's valid concern about verification against ERA5\nreanalysis data or ECMWF HRES analyses, both of which assimilate limited\nobservations in central Africa. Therefore, we have revised Section 3.3 to present more\ncautious interpretations of our results and explicitly acknowledge the limitations of our\nevaluation. Specifically:\n1) Lines 326–336 have been revised to describe the results of the expanded evaluation.\n2) We have removed the previously overstated claim: “These findings suggest that\nFuXi Weather can deliver more accurate forecasts using substantially less data\nthan traditional NWP systems, offering a cost-effective, satellite-based solution to\nimprove forecasts in regions lacking observational infrastructure.”\n3) We have added a discussion of evaluation limitations in lines 383-393, emphasizing\nthat while preliminary results indicate FuXi Weather may produce forecasts of\ncomparable or potentially superior accuracy using fewer observations, further\nvalidation with independent in-situ datasets is essential.\nThese revisions provide a more balanced interpretation. We agree that future work\nwould benefit from validation using independent observational datasets, and have toned\ndown our conclusions accordingly.\nSpecific comments:\n• L56-61/L152-154, and throughout: See General Comments on performance outcomes\ngiven statistical significance above, and from selected comments below.\nResponse:\nAs suggested by the reviewer, we have conducted significance testing for all relevant\nfigures and revised corresponding text in the manuscript.\n• L89: Please also mention efforts for ensemble forecasts towards uncertainty\nquantification for both traditional (which also feed off ensemble analyses) and ML\nmethods.\nResponse:\nFollowing the reviewer’s suggestions, we have added sentences in lines 87-89 of the\nIntroduction to describe recent efforts toward developing ensemble forecasts using\nmachine learning methods.\n• L207-212: Fuxi forecasts are evaluated with ERA-5, but ERA-5 is based on ECMWF’s\noperational system from 2016 (nearly 10 years ago!), it has fairly coarse resolution\n(nominally 31 km, but analysis increments are produced at 124 km!).\nHRES seems to be evaluated with HRES at t0. This will favour HRES, and also affect\nthe regional assessment over Africa with strong orographic variability that ERA-5 will\nnot resolve (, and for which MSL is not the best parameter to choose by the way). RMSE\nevaluations may actually suffer from higher resolution as increased variability\npenalizes RMSE.\nFurther, the NWP community does indeed evaluate forecasts with both own and\nreference analyses. Ideally, you show both and include HRES vs ERA-5.\nResponse:\nAs suggested by the reviewer, we have expanded the evaluation of FuXi Weather\nforecasts by evaluating them against its own analyses, which are represented by green\nlines in Figures 2 and 3, as well as in Extended Data Figures 3, 5, and 8.\n• Fig. 2 and others: I assume the dip in forecast skill for Fuxi at day 4 is explained by\nthe switch from Fuxi-Short to Fuxi-Medium. This information could be added in the\ncaption.\nResponse:\nFollowing the reviewer’s suggestion, we have added the following sentence to the\ncaptions of Figure 2, Extended Data Figure 3, and Supplementary Figures 24 and 25\n(previously numbered 21 and 22):\n“The performance change at day 4 arises from the model transition from FuXi-Short to\nFuXi-Medium.”\nAdditionally, we have added a sentence to the captions of Supplementary Figures 6 and\n7 (previously numbered 5 and 6).\n“The performance change at days 4 and 5 reflects the transition from FuXi-Short to\nFuXi-Medium for the respective forecasts (red and gray lines).”\n• Section 3.1: Would it not be informative to compare global analyses fields to begin\nwith, like Fuxi-DA vs ERA5 vs HRES at t0 for MSL, t2m and u/v300? This will exhibit,\nfor example, the analysis activity = standard deviation / climatological mean, which is\nimportant for RMSE evaluations, but also mean differences, for example, systematically\ncolder/warmer or windier/calmer analyses.\nResponse:\nAs suggested by the reviewer, we have conducted comprehensive comparisons of\nanalysis activity and mean bias error (MBE) between FuXi Weather and ECMWF\nHRES, as presented in the new Section 7 of the Supplementary Information. The\nmathematical formulation for analysis activity is now provided in Section 4 of the\nSupplementary Information.\n• Line 286-288: Global model performance is actually evaluated for regions, for\nexample, Europe, North America, East Asia, Australia etc. While this is not tied to\nsocioeconomic implications, it is still a regional evaluation.\nResponse:\nFollowing the reviewer’s suggestions, we have revised the sentence in lines 313-316 of\nthe main text.\n• L308-310: So where does the enhanced skill of Fuxi come from if ERA-5 is troubled\nover less well observed regions, surface in-situ observations are missing, and satellite\ndata is affected by all kinds of signals from lower atmosphere, clouds, precipitation and\nsurface characteristics (see above)?\nResponse:\nWe appreciate the reviewer’s insightful question regarding the superior forecast skill of\nFuXi Weather. As elaborated in our response to the reviewer’s comment #4 about the\nAfrican case study, we have conducted additional analyses to investigate why FuXi\noutperforms ECMWF HRES, particularly in regions with sparse surface in-situ\nobservations.\nFirst, we have decomposed forecast errors into systematic and random components\nby computing the mean bias error (MBE) and the standard deviation (std) of errors\n(STD ). Extended Data Fig.5 demonstrates that FuXi Weather exhibits both lower\nERROR\nMBE and smaller STD values than ECMWF HRES, indicating its improved\nERROR\nability to reduce systematic biases and random errors.\nSecond, we have analyzed forecast activity, defined as the std of forecast anomalies\nrelative to climatological means. The results show that FuXi maintains lower forecast\nactivity than ECMWF HRES throughout the 10-day forecast period, suggesting\nsmoother predictions. This is a characteristic often associated with machine learning-\nbased weather predictions. Notably, FuXi Weather's superior skill (red lines) becomes\napparent prior to any considerable reduction in forecast activity.\nIn summary, FuXi’s improved performance compared to ECMWF HRES is likely\nattributable to two key factors: its enhanced ability to reduce both systematic biases and\nrandom errors, and its lower forecast activity, which together contribute to more\naccurate and stable forecasts. For clarity, we have revised lines 338-359 of the main\ntext to explicitly state these findings.\n• L312: ’performed or ’outperformed’?\nResponse:\nThanks for highlighting this typo, the text has been corrected by changing “performed”\nto “outperformed”.\n• Section 3.4: I like the use of single-observation experiments. For clarity: are you\nshowing increments or increment differences between the analyses from using a\nperturbed minus an unperturbed ATMS radiance? It would be great to see whether a\n3D-Var would show the same increments or their differences.\nResponse:\nWe thank the reviewer for the valuable suggestions regarding Section 3.4. We\nacknowledge that the original use of the term “analysis increment” was inaccurate, as\nthis section actually examines differences between analysis fields, derived from\nperturbed and unperturbed ATMS radiance observations. To improve clarity, we have\ncarefully revised the terminology throughout Section 3.4 accordingly. Specifically, we\nhave changed the title of Section 3.4 to “Physical consistency of analysis changes”.\nRelated revisions have been made to several sentences within Section 3.4 of the main\ntext (lines 398, 402, 411–413, and 426), as well as in the caption of Figure 4.\nCorresponding revisions have also been made in Section 5.1 of the Supplementary\nInformation (lines 511 and 539).\nRegarding the reviewer's suggestion to compare our results with a 3D-Var system, we\nappreciate this thoughtful recommendation. However, such a comparison is technically\nchallenging, as FuXi-DA outputs atmospheric profiles at only 13 pressure levels. This\nrelatively coarse vertical resolution is inadequate for computing accurate Jacobian\nmatrices required by fast radiative transfer models typically employed in 3D-Var data\nassimilation systems. While this limitation prevents us from conducting the comparison\nin the present study, we recognize its potential value and plan to explore higher vertical\nresolution in future work to facilitate such analyses.\n• Supplement L190-193: If not treated properly (see General Comments item no. 3), the\nerror characteristics from different instruments on different satellites become merged\nwhen averaging to the Fuxi grid!\nResponse:\nWe appreciate the reviewer’s valuable suggestions. As addressed in our response to the\nreviewer’s Comment #3, we acknowledge that incorporating established domain\nknowledge from traditional data assimilation frameworks, particularly by accounting\nfor the distinct error characteristics of different satellite instruments, could further\nimprove model performance. We plan to pursue this direction in future work.\n• Supplement L211.1: I am not sure I fully understand how the PointPillars method is\napplied to GNSS RO data. Can the 3d-aspect of this be explained with a figure?\nResponse:\nWe appreciate the reviewer’s suggestion and have added Supplementary Figure 4 to\nillustrate the application of the PointPillars method in processing GNSS-RO data.\nAdditionally, we have revised the corresponding text in lines 212-245 of Section 2.1 in\nthe Supplementary Information to improve clarity and readability.\n• Supplement Section 5: This section seems too long, and 3D-Var/Jacobians are\nstandard knowledge. I suggest to reduce this section and focus on the single-\nobservation experiment set-up, a summary of the results and in how far they deviate\nfrom, say, 3D-Var.\nResponse:\nWe acknowledge the interdisciplinary nature of this study and recognize the importance\nof ensuring readability for readers who may be less familiar with specific concepts.\nTherefore, we have retained the relevant explanatory content and figures.\n2nd Review of “FuXi Weather: A data-to-forecast machine learning system for global weather”\nReply to Reviewer #1\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #1 (Remarks to the Author):\nThe authors did a lot of work clarifying parts of the manuscript based on reviewer\nsuggestions, which I appreciate. I have a few remaining comments. I appreciate the\nauthors responses and modifications to the paper, and I think the paper is nearly\nready for publication. I have only a few minor comments remaining.\nComments\n1. Lines 161-163: consider including the Slivinski et al (2025) citation here.\nResponse:\nFollowing the reviewer’s suggestion, we have added Slivinski et al (2025) citation in\nline 156 of the main text.\n2. Lines 395-396: consider replacing “indicating higher accuracy” with “relative\nto IMERG”.\nResponse:\nAs suggested by the reviewer, we have revised the original lines 395-396 (now\nrenumbered as line 341) by replacing “indicating higher accuracy” with “relative to\nIMERG”.\n3. Supplement: I think the added sentences on lines 94-101 regarding the 8h window\nwould be more natural in the DA section instead (e.g. line 348).\nResponse:\nWe appreciate the reviewer’s suggestion and we have moved the added sentences\noriginally in lines 94-101 to lines 343-351 in Section 2.2 of the Supplementary\nInformation.\n4. Supplement lines 342-345: This is inconsistent with the statement that the\nassimilation window is 8h. These lines describe a window that is 7h long.\nResponse:\nThank you for your insightful comment regarding the description of the assimilation\nwindow. We acknowledge the inconsistency and have revised the text to provide a\nclearer explanation. Specifically, satellite observations at a given time (e.g., 18 UTC)\ncorrespond to measurements collected within a one-hour window centered on that\ntime, spanning from 17:30 to 18:30 UTC.\nTo enhance clarity, we have revised the relevant sentence in the Supplementary\nInformation (lines 336-339) to: “… each within an 8-hour assimilation window that\nstarts 3 hours before and ends 4 hours after the forecast initialization time, with each\nobservation representing conditions over a one-hour interval centered on the\nobservation time.”\n5. Supplement, added Section 9: I appreciate the authors added this section. However,\nmy previous comment was more a request for the technical details of this “direct\nfrom obs” experiment. Was a different model trained for the experiments without\nbackground fields? Does the architecture of that model differ from the one with\nbackground fields? Or was the same model used, but with fewer inputs than it was\ntrained to take? Maybe I missed it, but it seems like these details would be useful\nfor interpretation of the results that background fields are helpful for forecast\naccuracy.\nResponse:\nThank you for your insightful comment regarding the need for additional technical\ndetails. In the “direct from obs” experiment, we used a separately trained model that\ndoes not incorporate background fields. This model shares the same architecture as the\none used in experiments with background fields. Following the reviewer’s suggestion,\nwe have added the following clarification to lines 679-680 of the Supplementary\nInformation:\n“The two variants of FuXi-DA are trained independently but share the same model\narchitecture described in Section 2.2.”\nReview of ’FuXi Weather: A data-to-forecast machine learning system\nfor global weather’ by X. Sun et al.,\nsubmitted to Nature Communications, NCOMMS-24-80174-T\nSummary:\nThe authors present an evolution of their machine-learning (ML) based forecasting system\nemulator Fuxi that is assimilating selected satellite based observations to create initial condi-\ntions for forecasts instead of using external analyses for initialisation. The data assimilation\nreplacement method, called Fuxi-DA, is combined with an enhanced Fuxi forecast emulator\nto create the end-to-end Fuxi-Weather system that can be cycled like traditional, numerical\nmethodsbasedanalysis-forecastsystems. Theoutputisassessedusingstandardforecasterror\nmetrics, and a specific focus is applied to a region in central Africa with sparse observational\ndatacoveragetotesttherobustnessofthemethod.\nThepaperiscompleteregardingtheexplanationofmethods,data,experimentsandevalu-\nation. TheFuxidevelopersbuildonanextensiverecordofMLappliedtoweatherforecasting,\nand they exhibit deep knowledge of the methodological frameworks applied in the numeri-\ncal weather prediction (NWP) community. They have also published their results before and\nmade code available for others to try - which is highly commendable. The paper is very well\nwritten.\nInthefollowing,Ihaveraisedseveralpointsthatwillneedaddressingbeforepublication.\nMy greatest concern is the lack of evidence of statistical significance of forecast performance\nwhen compared against other data. More information is needed on the use of observational\ndatainthedata-assimilationprocess. Ialsowonderaboutthefutureneedofdataassimilation\nas an intermediate step between observational data records and forecast generation. Lastly,\nwhile I appreciate a special focus on central Africa for the reasons explained in the paper, the\nevaluationofperformanceforthiscaseisnotoverlyconvincing.\nGeneralcomments:\n• Need for data assimilation: Given the recent evolution of ML-methods applied in weather\nprediction, I wonder whether there will still be a need for an explicit, intermediate data\nassimilationstepinthefuture. Thepresentneedforthissteporiginatesfromnumerical\nmodels requiring starting conditions to evolve the differential equations in time. ML-\nmethods do not necessarily need this unless they cycle through time steps like tradi-\ntional systems. Recent studies seem to suggest that it may be advantageous to produce\npredictions directly from past and present observations, and therefore skip the data-\nassimilationstepalltogether(akadirectobservationprediction, e.g. https://arxiv.\norg/abs/2407.15586).\nWhile this point does not negate the importance of assessing ML-methods for data as-\nsimilation per-se, this paper could benefit from a discussion of this topic given that the\ntargetjournalisNatureComm.\n• Statistical significance: It is standard practice in NWP evaluation to indicate the statisti-\ncal significance of skill (differences). If the individual variance of two skill measures is\ntoo large, it will not allow to make statements about the significance of their difference:\n”Uncertainty in the measures can be indicated as confidence intervals or error bars cal-\nculatedusingapproximationstostatisticaldistributions,orthroughcomputer-intensive\ntechniquessuchasre-sampling”(https://empslocal.ex.ac.uk/people/staff/\ndbs202/publications/booksreports/mailier.pdf).\nThisappliestoallfigures2,3andextendedfigures3,4,5,8,alsomaps. Theinterpretation\nofthesefigureswillhavetobeadjustedaswellasseveralscoredifferencesmaynotlead\n1\ntoconclusionsonbetterorworseperformance. Frommyexperience,someofthestated\nscoredifferenceswillbecomemeaninglessonceinformationonstatisticalsignificanceis\nadded.\n• Observationpre-processing: Thesatelliteradianceobservationsare’assimilated’inarather\nunqualified way. All channels of the microwave sounding instruments are used even\nthough the window channels of both temperature and humidity sounders are very sen-\nsitivetosurfaceemissionthatisdrivenbyemissivity(dependentonsurfacetype,mois-\nture, vegetation, roughness) and surface temperature. These channels are also sensitive\ntocloudsandprecipitation,whichgreatlydilutetheinformationcontentonthefivetar-\nget state variables. The authors mention cross-track scanning instrument (scan angle)\nbiases. Arethesecorrectedorisitassumedthat-throughknowledgeofthescan-angle-\ntheML-methodadjustsitsweights? Canthisbeshown?\nTheGNSSradiooccultationdataisusedasprofilesofrefractiveindex,andthisproduct\nexhibits larger errors in the lower 2-3 km of the troposphere and in the upper strato-\nsphere/mesosphere. Pre-processingismentioned,butthepaperdoesnotprovideinfor-\nmationonhowsystematicerrorsassociatedwiththisdataarebeingaddressed.\nOverall, the study uses observational data in a brute-force fashion that could be greatly\nimprovedongiventheavailableknowledgefromtraditionaldataassimilation.\n• African case study: I understand the motivation of the regional focus when applied to\nanareathatisimportantforsociety,sparselyobservedandwheretraditionalsystemdo\nnot perform well. However, the study does not spend enough effort to fully assess the\nAfrican case. Fig. 3 shows performance, again without statistical significance informa-\ntion, a two-cycle/day skill-score pattern (?), forecasts are verified against analyses that\nare notoriously poor in this area as opposed to (the few existing) observations, and for\nparametersthatmatterlessforsocietyherethan,forexample,soilmoistureandrainfall.\nThisisnotaveryconvincing.\nSpecificcomments:\n• L56-61/L152-154, and throughout: See General Comments on performance outcomes\ngivenstatisticalsignificanceabove,andfromselectedcommentsbelow.\n• L89: Please also mention efforts for ensemble forecasts towards uncertainty quantifica-\ntionforbothtraditional(whichalsofeedoffensembleanalyses)andMLmethods.\n• L207-212: Fuxi forecasts are evaluated with ERA-5, but ERA-5 is based on ECMWF’s\noperationalsystemfrom2016(nearly10yearsago!),ithasfairlycoarseresolution(nom-\ninally31km,butanalysisincrementsareproducedat124km!).\nHRESseemstobeevaluatedwithHRESatt0. ThiswillfavourHRES,andalsoaffectthe\nregional assessment over Africa with strong orographic variability that ERA-5 will not\nresolve (, and for which MSL is not the best parameter to choose by the way). RMSE-\nevaluationsmayactuallysufferfromhigherresolutionasincreasedvariabilitypenalises\nRMSE.\nFurther, the NWP community does indeed evaluate forecasts with both own and refer-\nenceanalyses. Ideally,youshowbothandincludeHRESvsERA-5.\n• Fig. 2 and others: I assume the dip in forecast skill for Fuxi at day 4 is explained by the\nswitchfromFuxi-ShorttoFuxi-Medium. Thisinformationcouldbeaddedinthecaption.\n• Section3.1: Woulditnotbeinformativetocompareglobalanalysesfieldstobeginwith,\nlike Fuxi-DA vs ERA5 vs HRES at t0 for MSL, t2m and u/v300? This will exhibit, for\n2\nexample, the analysis activity = standard deviation / climatological mean, which is im-\nportant for RMSE evaluations, but also mean differences, for example, systematically\ncolder/warmerorwindier/calmeranalyses.\n• Line 286-288: Global model performance is actually evaluated for regions, for example,\nEurope,NorthAmerica,EastAsia,Australiaetc. Whilethisisnottiedtosocioeconomic\nimplications,itisstillaregionalevaluation.\n• L308-310: SowheredoestheenhancedskillofFuxicomefromifERA-5istroubledover\nless well observed regions, surface in-situ observations are missing, and satellite data is\naffectedbyallkindsofsignalsfromloweratmosphere,clouds,precipitationandsurface\ncharacteristics(seeabove)?\n• L312: ’performedor’outperformed’?\n• Section3.4: Iliketheuseofsingle-observationexperiments. Forclarity: areyoushowing\nincrementsorincrementdifferencesbetweentheanalysesfromusingaperturbedminus\nanunperturbedATMSradiance? Itwouldbegreattoseewhethera3D-Varwouldshow\nthesameincrementsortheirdifferences.\n• SupplementL190-193: Ifnottreatedproperly(seeGeneralCommentsitemno. 3),theer-\nrorcharacteristicsfromdifferentinstrumentsondifferentsatellitesbecomemergedwhen\naveragingtotheFuxigrid!\n• Supplement L211.1: I am not sure I fully understand how the PointPillars method is\nappliedtoGNSSROdata. Canthe3d-aspectofthisbeexplainedwithafigure?\n• Supplement Section 5: This section seems too long, and 3D-Var/Jacobians are standard\nknowledge. I suggest to reduce this section and focus on the single-observation experi-\nmentset-up,asummaryoftheresultsandinhowfartheydeviatefrom,say,3D-Var.\n3\n2nd Review of ’FuXi Weather: A data-to-forecast machine learning\nsystem for global weather’ by X. Sun et al.,\nsubmitted to Nature Communications, NCOMMS-24-80174-T\nSummary:\nThe authors revised their paper in response to three reviews. The clarity of the paper has\ngreatlyimprovedbutIstillfeelthatitneedsseveralcorrectionsandchangesbeforepublication.\nComments:\n• Abstract: ECMWF would claim that they are running an all-grid, all-sky/surface, all-\nchannel forecasting system, which Fuxi is actually benefiting from because ERA-5 sup-\nplies the training data. ECMWF’s exclude selected observations because of too large\nuncertainties due to cloud/precipitation/surface contamination. However, the fact that\nFuxi includes all radiometer channels in their training (in a rather unqualified manner)\ndoes not mean that all channels contribute useful information in all situations. Fuxi\nwouldhavetomimicECMWF’sobservationscreeningtounderstandwhetherthemore\naggressiveapproachisbeneficialornot.\n• Section3.2andFig. 3: FuxiseemstooutperformECMWFmostlyfordays6andbeyond\nfor the important variables, namely geopotential height, temperature and wind. The\nmore general statements on Fuxi outperforming ECMWF in the Abstract should there-\nforebemorespecific.\nI really appreciate the addition on analysis and forecast activity that was also requested\nby Reviewer no. 2. However, when looking at Fuxi’s forecast activity, even after its en-\nhancement, it is still substantially lower than that of ECMWF. This happens to coincide\nwiththeforecastrangewhereFuxiappearstobebetter. Asoundconclusioncouldbethat\nFuxionlybeatsECMWFforecastsatforecastrangeswhereitisquieterandwilltherefore\nproducebetterRMSEs.\nTheclaimsonperformanceinbothAbstractandDiscussionneedtobeveryclearonthis.\n• Section3.3: Istillthinkthatverificationagainstanalysesintheseareasisnotveryuseful,\nandthataverificationagainstobservationswouldcarryalotmoreweight!\n• Section 3.4: I remarked in my initial review that I appreciate single-observation experi-\nments as they are informative about the sanity of the system and the information con-\ntributedbyobservationstoanalyses.\nThe choice of variable - in this case humidity - is ok, but it only shows the change of\nthe humidity analysis in response to moisture-sensitive radiance perturbations. In data\nassimilation, one would then look at the response of the wind fields because moisture\nchangesrequireadvection. Thechangeinwindswouldthereforeindicatethatthemois-\nturechangeshappenfortherightreason. Ifthisisleftout,thetestcarrieslittleinforma-\ntiononthephysicalconsistencyofthesystem.\nTherearestilltwo’increments’leftinlines416and425.\nI still think that Section 5.2 on Jacobians in the Supplementary Information is too long.\nThis is known information and may only require a single figure, a paragraph and refer-\nences.\n• A general conclusion from the experiments with and without backgrounds is that the\nassimilatedobservationaldataisclearlynotenoughtoconstraintheanalysissufficiently\nwell. ThisismentionedintheDiscussionbutshouldalsofindsitswayintotheAbstract.\n1\n3rd Review of “FuXi Weather: A data-to-forecast machine learning system for global weather”\nReply to Reviewer #1\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #1 (Remarks to the Author):\nThe authors did a lot of work clarifying parts of the manuscript based on reviewer\nsuggestions, which I appreciate. I have a few remaining comments. I appreciate the\nauthors responses and modifications to the paper, and I think the paper is nearly\nready for publication. I have only a few minor comments remaining.\nComments\n1. Lines 161-163: consider including the Slivinski et al (2025) citation here.\nResponse:\nFollowing the reviewer’s suggestion, we have added Slivinski et al (2025) citation in\nline 156 of the main text.\n2. Lines 395-396: consider replacing “indicating higher accuracy” with “relative\nto IMERG”.\nResponse:\nAs suggested by the reviewer, we have revised the original lines 395-396 (now\nrenumbered as line 341) by replacing “indicating higher accuracy” with “relative to\nIMERG”.\n3. Supplement: I think the added sentences on lines 94-101 regarding the 8h window\nwould be more natural in the DA section instead (e.g. line 348).\nResponse:\nWe appreciate the reviewer’s suggestion and we have moved the added sentences\noriginally in lines 94-101 to lines 343-351 in Section 2.2 of the Supplementary\nInformation.\n4. Supplement lines 342-345: This is inconsistent with the statement that the\nassimilation window is 8h. These lines describe a window that is 7h long.\nResponse:\nThank you for your insightful comment regarding the description of the assimilation\nwindow. We acknowledge the inconsistency and have revised the text to provide a\nclearer explanation. Specifically, satellite observations at a given time (e.g., 18 UTC)\ncorrespond to measurements collected within a one-hour window centered on that\ntime, spanning from 17:30 to 18:30 UTC.\nTo enhance clarity, we have revised the relevant sentence in the Supplementary\nInformation (lines 336-339) to: “… each within an 8-hour assimilation window that\nstarts 3 hours before and ends 4 hours after the forecast initialization time, with each\nobservation representing conditions over a one-hour interval centered on the\nobservation time.”\n5. Supplement, added Section 9: I appreciate the authors added this section. However,\nmy previous comment was more a request for the technical details of this “direct\nfrom obs” experiment. Was a different model trained for the experiments without\nbackground fields? Does the architecture of that model differ from the one with\nbackground fields? Or was the same model used, but with fewer inputs than it was\ntrained to take? Maybe I missed it, but it seems like these details would be useful\nfor interpretation of the results that background fields are helpful for forecast\naccuracy.\nResponse:\nThank you for your insightful comment regarding the need for additional technical\ndetails. In the “direct from obs” experiment, we used a separately trained model that\ndoes not incorporate background fields. This model shares the same architecture as the\none used in experiments with background fields. Following the reviewer’s suggestion,\nwe have added the following clarification to lines 679-680 of the Supplementary\nInformation:\n“The two variants of FuXi-DA are trained independently but share the same model\narchitecture described in Section 2.2.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors did a lot of work clarifying parts of the manuscript based on reviewer suggestions, which I appreciate. I have a few remaining comments.\nComments\n1. Introduction and conclusion: It could be worth emphasizing that this is the first ML system that can cycle in a DA-like system for weather forecasting (to my knowledge, at least.) Specifically, this is the only system that I know of that can produce forecast fields that feed back into the system without blowing up. This, I think, is a major achievement. For example, Slivinski et al (2025) found that most deterministic ML models blow up within a few weeks of cycling in a traditional DA system.\n2. Lines 160-161 “Furthermore, FuXi Weather’s development costs are considerably lower than traditional NWP systems.” This is not strictly true. FuXi Weather’s development relies heavily on ERA5, which built upon decades of NWP and reanalysis development. This is an important technicality, since many ML papers tend to gloss over this fact. With the exception of the AI-DOP techniques that learn directly from observations without reanalyses, every ML weather model is trained on a dataset that took years to develop and produce, and was built upon decades of knowledge.\n3. Line 208: “a 1-year data” should be maybe “one year of data”\n4. Lines 213-214: Is the variant of FuXi-DA without background forecasts discussed in the supplementary information? If not, I would consider adding it. Is this essentially direct-from-observation prediction?\n5. Extended Data Fig 2: maybe replace “FuXi analyses” with “FuXi Weather analyses” to make the distinction between the two systems more clear?\n6. Extended data Figs 5-6: I see that the authors added precipitation per a reviewer comment. However, there are some major issues with precipitation in ERA5 especially in the Tropics (Lavers et al 2022), such that this comparison is not very meaningful. I would urge the authors to consider the reviewer’s other suggestion, to compare to observations; even a gridded observational product like GPCP (https://climatedataguide.ucar.edu/climate-data/gpcp-monthly-global-precipitation-climatology-project) or IMERG (https://gpm.nasa.gov/data/imerg) would help provide context here.\n7. I still don’t understand the reasoning behind using overlapping DA windows. Why was this design choice made? Can you articulate the motivation behind this design choice in the paper? Also, I would recommend explicitly stating in the supplementary information that some observations are used more than once, if that is the case.\n8. Supplementary Info line 538: “a small perturbation at a single grid point.” If I understand correctly, this is inaccurate, since the perturbation is in fact over several grid points, correct?\n9. Captions of supp figs 18-22 and related description: May want to clarify that these are differences of RMSEs, as opposed to RMS differences, and define the direction of the difference. It would be helpful to add the description of what red vs blue means in the figure captions as well.\nReferences:\nSlivinski, Laura C., et al. \"Assimilating observed surface pressure into ML weather prediction models.\" Geophysical Research Letters 52.6 (2025): e2024GL114396.\nHuffman, George J., et al. \"Improving the global precipitation record: GPCP version 2.1.\" Geophysical Research Letters 36.17 (2009).\nKirschbaum, D.B.; Huffman, G.; Adler, R.F.; Braun, S.; Garrett, K.; Jones, E.; McNally, A.; Skofronick-Jackson, G.; Stocker, E.; Wu, H.; et al. NASA’s Remotely Sensed Precipitation: A Reservoir for Applications Users. Bull. Am. Meteorol. Soc. 2017, 98, 1169–1184.\nLavers, D.A., Simmons, A., Vamborg, F. & Rodwell, M.J. (2022) An evaluation of ERA5 precipitation for climate monitoring. Quarterly Journal of the Royal Meteorological Society, 148(748) 3124–3137. Available from: https://doi.org/10.1002/qj.4351\n(Remarks on code availability)", "reviewer_2": "I wish to thank the Authors for their detailed responses and the time and effort devoted to run the additional experiments and produce the new diagnostics.\nUnfortunately, I am still not convinced that the manuscript is ready for publication.\nMy main concern, among others, was that Fuxi-DA produces analyses that when used to initialise a forecast model generate forecasts that have ~2 days lower skill than those initialised with ERA5 initial conditions. To put things into perspective, a 2-day forecast skill drop is what we would see in a state of the art NWP DA system if all satellite observations were withheld. Bear in mind that satellite observations constitute ~95% of all assimilated observations in current operational NWP.\nThe Authors have two answers to this: 1) This is comparable to the state of the art in ML-driven DA, citing Allen et al. 2025 (https://www.nature.com/articles/s41586-025-08897-0); 2) The amount of observations assimilated by Fuxi-DA is smaller than that used in ERA5, especially considering the absence of conventional observations.\nMy perspective is that even though results of Allen et al., 2025, were not particularly convincing, results presented here do not show a significant improvement on those.\nMy suggestion to the Authors is to further develop their system by suitably extending the range of observations used, and only at that point it would be clearer whether end-to-end ML DA is a serious candidate for operational/reanalysis DA.\n(Remarks on code availability)", "reviewer_3": "[Editorial Note: the attachments are displayed at the end of the file]\n(Remarks to the Author)\nPlease see attached file.\n(Remarks on code availability)"}, "author_response": "Reply to Reviewer #1\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #1 (Remarks to the Author):\nThe authors did a lot of work clarifying parts of the manuscript based on reviewer\nsuggestions, which I appreciate. I have a few remaining comments.\nComments\n1. Introduction and conclusion: It could be worth emphasizing that this is the first ML system that can cycle in a DA-like system for weather forecasting (to my knowledge, at least.) Specifically, this is the only system that I know of that can produce forecast fields that feed back into the system without blowing up. This, I think, is a major achievement. For example, Slivinski et al (2025) found that most deterministic ML models blow up within a few weeks of cycling in a traditional DA system.\nResponse:\nWe appreciate the reviewer’s suggestion and have explicitly emphasized that FuXi\nWeather is the first machine learning system capable of performing both cycling data\nassimilation and forecasting for weather prediction. The “Abstract” (line 56),\n“Introduction” (lines 161-163) and “Discussion” (lines 468-469) sections have been\nrevised accordingly.\n2. Lines 160-161 “Furthermore, FuXi Weather’s development costs are considerably\nlower than traditional NWP systems.” This is not strictly true. FuXi Weather’s\ndevelopment relies heavily on ERA5, which built upon decades of NWP and\nreanalysis development. This is an important technicality, since many ML papers\ntend to gloss over this fact. With the exception of the AI-DOP techniques that learn\ndirectly from observations without reanalyses, every ML weather model is trained\non a dataset that took years to develop and produce, and was built upon decades of\nknowledge.\nResponse:\nWe appreciate the reviewer’s insightful comment regarding the development costs of\nML forecasting systems such as FuXi Weather. We have removed the original sentence\nin “Introduction” section and added new statements in line 502 of the “Discussion”\nsection to acknowledge that ERA5 took several decades to develop.\n3. Line 208: “a 1-year data” should be maybe “one year of data”\nResponse:\nThanks for highlighting this issue, we have fixed it.\n4. Lines 213-214: Is the variant of FuXi-DA without background forecasts discussed\nin the supplementary information? If not, I would consider adding it. Is this\nessentially direct-from-observation prediction?\nResponse:\nWe confirm that the variant of FuXi-DA without background forecasts is essentially\ndirect-from-observation prediction, and we have added this description in lines 219-\n220 in Section 3 of the main text. Following the reviewer’s suggestion, we have also\nincluded a brief discussion on the importance of background forecasts in data-to-\nforecast system in the newly added Section 9 of the Supplementary Information.\n5. Extended Data Fig 2: maybe replace “FuXi analyses” with “FuXi Weather analyses”\nto make the distinction between the two systems more clear?\nResponse:\nFollowing the reviewer’s suggestion, we have revised aption of Extended Data Fig 2\nby replacing “FuXi analyses” with “FuXi Weather analyses”.\n6. Extended data Figs 5-6: I see that the authors added precipitation per a reviewer\ncomment. However, there are some major issues with precipitation in ERA5\nespecially in the Tropics (Lavers et al 2022), such that this comparison is not very\nmeaningful. I would urge the authors to consider the reviewer’s other suggestion,\nto compare to observations; even a gridded observational product like GPCP\n(https://climatedataguide.ucar.edu/climate-data/gpcp-monthly-global-precipitation-\nclimatology-project) or IMERG (https://gpm.nasa.gov/data/imerg) would help provide context here.\nResponse:\nAs suggested by the reviewer, we have added Extended Data Fig.9, which evaluates\nprecipitation forecasts using IMERG instead of ERA5. The results yield slightly\ndifferent conclusions: while FuXi Weather continues to outperform ECMWF HRES in\nterms of RMSE, it shows lower ACC and higher absolute MBE.\nThese findings are discussed in the revised Section 3.3 (lines 391-401), where we\ndiscuss the precipitation forecast performance comparisons using IMERG as the\nreference dataset. The references suggested by the reviewer also been added.\nWe have also added lines 505-510 in “Discussion” section to highlight the potential for\nimproved FuXi precipitation forecasts when trained and evaluated against more\naccurate observational datasets such as IMERG.\nAdditionally, the “Data Availability Statement” section (lines 548-459) has been\nupdated to include information on accessing the IMERG dataset.\n7. I still don’t understand the reasoning behind using overlapping DA windows. Why\nwas this design choice made? Can you articulate the motivation behind this design\nchoice in the paper? Also, I would recommend explicitly stating in the\nsupplementary information that some observations are used more than once, if that\nis the case.\nResponse:\nThank you for your valuable comment. We have now explicitly clarified the use of\noverlapping DA windows in Section 1.2, lines 94-101 of the Supplementary\nInformation. The choice of an 8-hour window is based on practical considerations\nrelated to deep learning implementation. Specifically, the number 8 was chosen because\nit is a power of two, which aligns well with the computational architecture of GPUs.\nUsing dimensions that are powers of two allows for more efficient memory usage and\ncomputational performance, due to the way parallel processing is handled by GPUs.\n8. Supplementary Info line 538: “a small perturbation at a single grid point.” If I\nunderstand correctly, this is inaccurate, since the perturbation is in fact over\nseveral grid points, correct?\nResponse:\nThanks for highlighting this issue, we removed the word “at a single grid point”.\n9. Captions of supp figs 18-22 and related description: May want to clarify that these\nare differences of RMSEs, as opposed to RMS differences, and define the direction\nof the difference. It would be helpful to add the description of what red vs blue\nmeans in the figure captions as well.\nResponse:\nAs suggested by the reviewer, we have revised the captions of the original\nSupplementary Figures 18–23 (renumbered as Supplementary Figures 15–20)\naccordingly.\nReferences:\nSlivinski, Laura C., et al. \"Assimilating observed surface pressure into ML weather\nprediction models.\" Geophysical Research Letters 52.6 (2025): e2024GL114396.\nHuffman, George J., et al. \"Improving the global precipitation record: GPCP version\n2.1.\" Geophysical Research Letters 36.17 (2009).\nKirschbaum, D.B.; Huffman, G.; Adler, R.F.; Braun, S.; Garrett, K.; Jones, E.;\nMcNally, A.; Skofronick-Jackson, G.; Stocker, E.; Wu, H.; et al. NASA’s Remotely\nSensed Precipitation: A Reservoir for Applications Users. Bull. Am. Meteorol. Soc.\n2017, 98, 1169–1184.\nLavers, D.A., Simmons, A., Vamborg, F. & Rodwell, M.J. (2022) An evaluation of\nERA5 precipitation for climate monitoring. Quarterly Journal of the Royal\nMeteorological Society, 148(748) 3124–3137. Available\nfrom: https://doi.org/10.1002/qj.4351\nReply to Reviewer #2\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #2 (Remarks to the Author):\nI wish to thank the Authors for their detailed responses and the time and effort devoted\nto run the additional experiments and produce the new diagnostics.\nUnfortunately, I am still not convinced that the manuscript is ready for publication.\nMy main concern, among others, was that Fuxi-DA produces analyses that when used\nto initialise a forecast model generate forecasts that have ~2 days lower skill than those\ninitialised with ERA5 initial conditions. To put things into perspective, a 2-day forecast\nskill drop is what we would see in a state of the art NWP DA system if all satellite\nobservations were withheld. Bear in mind that satellite observations constitute ~95%\nof all assimilated observations in current operational NWP.\nThe Authors have two answers to this: 1) This is comparable to the state of the art in\nML-driven DA, citing Allen et al. 2025 (https://www.nature.com/articles/s41586-025-\n08897-0); 2) The amount of observations assimilated by Fuxi-DA is smaller than that\nused in ERA5, especially considering the absence of conventional observations.\nMy perspective is that even though results of Allen et al., 2025, were not particularly\nconvincing, results presented here do not show a significant improvement on those.\nMy suggestion to the Authors is to further develop their system by suitably extending\nthe range of observations used, and only at that point it would be clearer whether end-\nto-end ML DA is a serious candidate for operational/reanalysis DA.\nResponse:\nWe sincerely appreciate the reviewer’s thoughtful and constructive comments. To\nprovide a broader perspective on the differences among various analyses, we have\nincluded, for the Reviewer’s interest, the RMSE of HRES-fc0 and 36-hour ECMWF\nHRES forecasts evaluated against ERA5, using a format similar to that of Extended\ndata Fig. 2. As expected, for U, V, Z, and T, FuXi Weather analyses do not perform as\nwell as HRES-fc0, primarily due to the significantly smaller number of observations\nused. Specifically, FuXi Weather relies on data from five microwave instruments,\nwhereas ECMWF HRES incorporates observations from approximately ninety satellite\ninstruments. However, for relative humidity, particularly at 850 hPa, FuXi Weather\nanalyses are nearly as accurate as the RMSE between HRES-fc0 and ERA5. Overall,\nFuXi Weather analyses achieve performance comparable to that of 36-hour ECMWF\nHRES forecasts, and for variables such as relative humidity, FuXi Weather analyses\ndemonstrate notably higher accuracy.\nWe have not added this additional figure in the manuscript, as in the rest of the paper,\nECMWF HRES forecasts are evaluated against HRES-fc0, and we do not feel that the\n0 lead time analysis error is the primary point of our study. We certainly agree with the\nreviewer that reducing this error is a desirable goal for the DA component of the system.\nHowever, for this stage the early time error, while carefully documented, is not the\nprimary focus. We hope we can convince the reviewer of the value of demonstrating an\nend-to-end system that yields competitive medium and long lead forecasts even without\nusing all available data.\nWe believe this paper is already comprehensive, demonstrating a machine learning–\nbased system capable of cycling data assimilation and forecasting, marking a significant\ndevelopment in its own right. We welcome the opportunity to include additional\nobservations in future studies, where more extensive results can be presented and\ndiscussed relative to the current baseline.\nReply to Reviewer #3\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #3 (Remarks to the Author):\nSummary:\nThe authors revised their paper in response to three reviews. The clarity of the paper\nhas greatly improved but I still feel that it needs several corrections and changes\nbefore publication.\nComments:\n• Abstract: ECMWF would claim that they are running an all-grid, all-sky/surface,\nallchannel forecasting system, which Fuxi is actually benefiting from because ERA-5\nsupplies the training data. ECMWF’s exclude selected observations because of too\nlarge uncertainties due to cloud/precipitation/surface contamination. However, the fact\nthat Fuxi includes all radiometer channels in their training (in a rather unqualified\nmanner) does not mean that all channels contribute useful information in all situations.\nFuxi ould have to mimic ECMWF’s observation screening to understand whether the\nmore aggressive approach is beneficial or not.\nResponse:\nWe appreciate the reviewer’s comment regarding whether all satellite data from all\nchannels provide useful information. We have removed the claim in the “Abstract”\nthat FuXi is the first system to achieve all-grid, all-surface, all-channel, and all-sky DA.\n• Section 3.2 and Fig. 3: Fuxi seems to outperform ECMWF mostly for days 6 and\nbeyond for the important variables, namely geopotential height, temperature and wind.\nThe more general statements on Fuxi outperforming ECMWF in the Abstract should\ntherefore be more specific. I really appreciate the addition on analysis and forecast\nactivity that was also requested by Reviewer no. 2. However, when looking at Fuxi’s\nforecast activity, even after its enhancement, it is still substantially lower than that of\nECMWF. This happens to coincide with the forecast range where Fuxi appears to be\nbetter. A sound conclusion could be that Fuxi only beats ECMWF forecasts at forecast\nranges where it is quieter and will therefore produce better RMSEs.\nThe claims on performance in both Abstract and Discussion need to be very clear on\nthis.\nResponse:\nFollowing the reviewer’s suggestion, we have revised the statement in the Abstract to\nclarify that “FuXi Weather consistently outperforms ECMWF HRES in observation-\nsparse regions beyond day one”. Additionally, in the “Discussion” (lines 492-494), we\nhave included a statement highlighting that FuXi outperforms ECMWF HRES in global\nforecasting performance at lead times where FuXi’s forecasts exhibit greater\nsmoothness.\n• Section 3.3: I still think that verification against analyses in these areas is not very\nuseful, and that a verification against observations would carry a lot more weight!\nResponse:\nAs suggested by the reviewer, we have added Extended Data Fig.9, which evaluates\nprecipitation forecasts using IMERG instead of ERA5.\nThese findings are discussed in the revised Section 3.3 (lines 393-403), where we\ndiscuss the precipitation forecast performance comparisons using IMERG as the\nreference dataset.\n• Section 3.4: I remarked in my initial review that I appreciate single-observation\nexperiments as they are informative about the sanity of the system and the information\ncontributed by observations to analyses.\nThe choice of variable - in this case humidity - is ok, but it only shows the change of\nthe humidity analysis in response to moisture-sensitive radiance perturbations. In data\nassimilation, one would then look at the response of the wind fields because moisture\nchanges require advection. The change in winds would therefore indicate that the\nmoisture changes happen for the right reason. If this is left out, the test carries little\ninformation on the physical consistency of the system.\nThere are still two ’increments’ left in lines 416 and 425.\nI still think that Section 5.2 on Jacobians in the Supplementary Information is too long.\nThis is known information and may only require a single figure, a paragraph and\nreferences.\nResponse:\nThe choice of variable - in this case humidity - is ok, but it only shows the change of\nthe humidity analysis in response to moisture-sensitive radiance perturbations. …\nWe thank the reviewer for the valuable suggestion to include the changes in wind vector\nanalysis fields in the single observation tests. And we have added a new Supplementary\nFigure 9 in Section 5.1 of the Supplementary Information. This figure illustrates that\nthe perturbation enhances the advection of drier air into a more humid region near the\nperturbed location, consistent with the results shown in Figure 4 of the main text.\nCorresponding descriptions have been added to Section 3.4 of the main text (lines 444-\n449) to explain the newly included Supplementary Figure 9.\nThere are still two ’increments’ left in lines 416 and 425.\nWe have fixed the inaccurate use of the term “increments” (lines 432 and 441).\nI still think that Section 5.2 on Jacobians in the Supplementary Information is too long.\nAs suggested by the reviewer, we have only kept Jacobians for ATMS aboard NOAA-\n20.\n• A general conclusion from the experiments with and without backgrounds is that the\nassimilated observational data is clearly not enough to constrain the analysis\nsufficiently well. This is mentioned in the Discussion but should also finds its way into\nthe Abstract.\nResponse:\nAs suggested by the reviewer, we have revised the Abstract to include a statement\nhighlighting the value of incorporating background forecasts in data assimilation."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I appreciate the authors responses and modifications to the paper, and I think the paper is nearly ready for publication. I have only a few minor comments remaining.\n1. Lines 161-163: consider including the Slivinski et al (2025) citation here.\n2. Lines 395-396: consider replacing “indicating higher accuracy” with “relative to IMERG”.\n3. Supplement: I think the added sentences on lines 94-101 regarding the 8h window would be more natural in the DA section instead (e.g. line 348).\n4. Supplement lines 342-345: This is inconsistent with the statement that the assimilation window is 8h. These lines describe a window that is 7h long.\n5. Supplement, added Section 9: I appreciate the authors added this section. However, my previous comment was more a request for the technical details of this “direct from obs” experiment. Was a different model trained for the experiments without background fields? Does the architecture of that model differ from the one with background fields? Or was the same model used, but with fewer inputs than it was trained to take? Maybe I missed it, but it seems like these details would be useful for interpretation of the results that background fields are helpful for forecast accuracy.\n(Remarks on code availability)", "reviewer_3": "(Remarks to the Author)\n(Remarks on code availability)"}, "author_response": "3rd Review of “FuXi Weather: A data-to-forecast machine learning system for global weather”\nReply to Reviewer #1\nWe appreciate the reviewer’s meticulous review and valuable feedback. We have made\ncareful amendments to our paper, taking into account all the suggestions provided. Our\nresponses to the comments, which are quoted in italic font, are detailed below.\nReviewer #1 (Remarks to the Author):\nThe authors did a lot of work clarifying parts of the manuscript based on reviewer\nsuggestions, which I appreciate. I have a few remaining comments. I appreciate the\nauthors responses and modifications to the paper, and I think the paper is nearly\nready for publication. I have only a few minor comments remaining.\nComments\n1. Lines 161-163: consider including the Slivinski et al (2025) citation here.\nResponse:\nFollowing the reviewer’s suggestion, we have added Slivinski et al (2025) citation in\nline 156 of the main text.\n2. Lines 395-396: consider replacing “indicating higher accuracy” with “relative\nto IMERG”.\nResponse:\nAs suggested by the reviewer, we have revised the original lines 395-396 (now\nrenumbered as line 341) by replacing “indicating higher accuracy” with “relative to\nIMERG”.\n3. Supplement: I think the added sentences on lines 94-101 regarding the 8h window\nwould be more natural in the DA section instead (e.g. line 348).\nResponse:\nWe appreciate the reviewer’s suggestion and we have moved the added sentences\noriginally in lines 94-101 to lines 343-351 in Section 2.2 of the Supplementary\nInformation.\n4. Supplement lines 342-345: This is inconsistent with the statement that the\nassimilation window is 8h. These lines describe a window that is 7h long.\nResponse:\nThank you for your insightful comment regarding the description of the assimilation\nwindow. We acknowledge the inconsistency and have revised the text to provide a\nclearer explanation. Specifically, satellite observations at a given time (e.g., 18 UTC)\ncorrespond to measurements collected within a one-hour window centered on that\ntime, spanning from 17:30 to 18:30 UTC.\nTo enhance clarity, we have revised the relevant sentence in the Supplementary\nInformation (lines 336-339) to: “… each within an 8-hour assimilation window that\nstarts 3 hours before and ends 4 hours after the forecast initialization time, with each\nobservation representing conditions over a one-hour interval centered on the\nobservation time.”\n5. Supplement, added Section 9: I appreciate the authors added this section. However,\nmy previous comment was more a request for the technical details of this “direct\nfrom obs” experiment. Was a different model trained for the experiments without\nbackground fields? Does the architecture of that model differ from the one with\nbackground fields? Or was the same model used, but with fewer inputs than it was\ntrained to take? Maybe I missed it, but it seems like these details would be useful\nfor interpretation of the results that background fields are helpful for forecast\naccuracy.\nResponse:\nThank you for your insightful comment regarding the need for additional technical\ndetails. In the “direct from obs” experiment, we used a separately trained model that\ndoes not incorporate background fields. This model shares the same architecture as the\none used in experiments with background fields. Following the reviewer’s suggestion,\nwe have added the following clarification to lines 679-680 of the Supplementary\nInformation:\n“The two variants of FuXi-DA are trained independently but share the same model\narchitecture described in Section 2.2.”"}]

Decision letter