Meet the challenge of predictability desert - a machine learning model that outperforms conventional global subseasonal forecast models - Supplementary Notes

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Supplementary Notes detail how the FuXi-S2S machine learning subseasonal forecasting system improves predictability by introducing flow-dependent perturbations into hidden features. Experiments compare Perlin-noise-only initialization versus fixed and flow-dependent perturbation strategies, producing 42-day forecasts and assessing skill against a baseline FuXi-S2S configuration. Results include TCC and RMSE evaluations across regions and variables, plus energy-spectrum analyses showing how the models’ ensemble mean and members align with ERA5 benchmarks over increasing lead times.

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Supplementary Notes

Effectiveness of flow-dependent perturbations

Deterministic forecast metrics comparison

Energy spectra analysis across forecast lead times

arXiv:2312.09926v2 [[physics. ao-ph](physics. ao-ph) ] 5 Jul 2024 Supplementary Information: Meet the challenge of predictability desert: a machine learning model that outperforms conventional global subseasonal forecast models Lei Chen 1,2†, Xiaohui Zhong 1†, Hao Li 1*†, Jie Wu3†, Bo Lu3,4*, Deliang Chen5 , Shang-Ping Xie6 , Libo Wu7,8,9 , Qingchen Chao3 , Chensen Lin 1 , Zixin Hu 1 and Yuan Qi2,1* 1 Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China. 2 Shanghai Academy of Artificial Intelligence for Science, Shanghai, 200232, China. 3 China Meteorological Administration Key Laboratory for Climate Prediction Studies, National Climate Center, Beijing, 100081, China. 4 Xiong’an Institute of Meteorological Artificial Intelligence, Xiong’an, China. 5 University of Gothenburg, Sweden. 6 Scripps Institution of Oceanography, University of California San Diego, USA. 7 School of Data Science, Fudan University, Shanghai, 200433, China. 8 Institute for Big Data, Fudan University, Shanghai, 200433, China. 9 MOE Laboratory for National Development and Intelligent Governance, Fudan University, Shanghai, 200433, China. *Corresponding author(s). E-mail(s): lihao [lh@fudan.edu.cn](lh@fudan.edu.cn) ; [bolu@cma.gov.cn](bolu@cma.gov.cn) ; [qiyuan@fudan.edu.cn](qiyuan@fudan.edu.cn) ; Contributing authors: [cltpys@163.com](cltpys@163.com) ; [x7zhong@gmail.com](x7zhong@gmail.com) ; [wujie@cma.gov.com](wujie@cma.gov.com) ; [deliang@gvc.gu.se](deliang@gvc.gu.se) ; [sxie@ucsd.edu](sxie@ucsd.edu) ; 2 FuXi-S2S [wulibo@fudan.edu.cn](wulibo@fudan.edu.cn) ; [chaoqc@cma.gov.cn](chaoqc@cma.gov.cn) ; [linchensen@fudan.edu.cn](linchensen@fudan.edu.cn) ; [huzixin@fudan.edu.cn](huzixin@fudan.edu.cn) ; †These authors contributed equally to this work. Contents of this file Supplementary Notes 1 to 8 Supplementary Figures 1 to 16 Supplementary Table 1 Supplementary Notes 1 Effectiveness of flow-dependent perturbations This section discusses the effect of incorporating the flow-dependent perturbations into the model’s hidden features to enhance performance in subseasonal forecasts. We conducted experiments using FuXi-S2S models which exclusively employ Perlin noise in the initial conditions or combine Perlin noise in the initial conditions with fixed perturbations added into the hidden features, to generate 42-day forecasts. Subsequently we evaluate their performance in comparison with the original FuXi-S2S model. Supplementary Figure 1 presents a comparison of the globally-averaged and latitude-weighted TCC for TP. This analysis encompasses all testing data from the period spanning from 2017 to 2021 . The FuXi-S2S model, which incorporates flow-dependent perturbations into its hidden features, consistently exhibits considerably improved forecast performance in comparison to the FuXi-S2S model that incorporates fixed Gaussian noise into the hidden features, across all forecast lead times. Furthermore, the introduction of flowdependent perturbations has extended the FuXi-S2S model’s skillful MJO prediction from 22 days to 36 days. 2 Deterministic forecast metrics comparison Supplementary Figure 3 presents a comparison of latitude-weighted TCC between FuXi-S2S and ECMWF S2S. It examines TP, T2M, Z500, and OLR across four geographical regions: in the extra-tropics (90°S - 30°S and 30°N- 90°N), in the tropics (30°S-30°N), over land, and over the ocean. Within the extra-tropical regions, FuXi-S2S consistently exhibits superior performance compared to ECMWF S2S for all four variables. In tropical regions, FuXi-S2S outperforms ECMWF S2S for TP and OLR, while achieving comparable accuracy in T2M and Z500 . Over land areas, FuXi-S2S demonstrates consistently higher TCC values for TP, Z500, and OLR. FuXi-S2S 3 Supplementary Figure 4 presents a comparison of the globally-averaged and latitude-weighted root mean square error (RMSE) of the ensemble mean between ECMWF S

FAQs

What is the main purpose of the supplementary notes?

They investigate how flow-dependent perturbations added to the FuXi-S2S model’s hidden features improve subseasonal forecast performance and skill duration.

How do the notes evaluate forecast effectiveness?

They compare metrics such as TCC and RMSE between FuXi-S2S variants and ECMWF S2S across multiple variables, regions, and forecast lead times.

What do the energy-spectrum results indicate about model behavior over longer lead times?

At longer wavelengths, selected ensemble members from FuXi-S2S and ECMWF S2S better align with ERA5, while at shorter wavelengths FuXi-S2S shows a gradual reduction in energy, implying smoother forecasts at smaller scales.

Aug 4, 2026

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