Dudhia, J.: A Multi-layer Soil Temperature Model for MM5, The Sixth PSU/NCAR Mesoscale Model Users' Workshop, Boulder, Colorado, USA, 22–24 July 1996, 49–50,
https://www.researchgate.net/publication/259865197_A_Multi-layer_Soil_Temperature_Model_for_MM5, (last access: 25 August 2025), 1996.
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res.-Oceans, 99, 10143–10162, https://doi.org/10.1029/94JC00572, 1994.
Evensen, G.: The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynam., 53, 343–367, https://doi.org/10.1007/s10236-003-0036-9, 2003.
Han, J. and Pan, H.-L.: Sensitivity of Hurricane Intensity Forecast to Convective Momentum Transport Parameterization, Mon. Weather Rev., 134, 664, https://doi.org/10.1175/mwr3090.1, 2006.
Han, J. and Pan, H.-L.: Revision of Convection and Vertical Diffusion Schemes in the NCEP Global Forecast System, Weather Forecast., 26, 520–533, https://doi.org/10.1175/WAF-D-10-05038.1, 2011.
Hong, S.-Y., Dudhia, J., and Chen, S.-H.: A Revised Approach to Ice Microphysical Processes for the Bulk Parametrisation of Clouds and Precipitation, Mon. Weather Rev., 132, 103–120, https://doi.org/10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2, 2004.
Huang, L., Gianinazzi, L., Yu, Y., Dueben, P. D., and Hoefler, T.: DiffDA: a Diffusion model for weather-scale Data Assimilation, arXiv [preprint] https://doi.org/10.48550/arXiv.2401.05932, 2024.
Iacono, M. J., Delamere, J. S., Mlawer, E. J., Shephard, M. W., Clough, S. A., and Collins, W. D.: Radiative forcing by long-lived greenhouse gases: Calculations with th
e AER radiative transfer models, J. Geophys. Res.-Atmos., 113, https://doi.org/10.1029/2008JD009944, 2008.
Inverarity, G. W., Tennant, W. J., Anton, L., Bowler, N. E., Clayton, A. M., Jardak, M., Lorenc, A. C., Rawlins, F., Thompson, S. A., Thurlow, M. S., Walters, D. N., and Wlasak, M. A.: Met Office MOGREPS-G initialisation using an ensemble of hybrid four-dimensional ensemble variational (En-4DEnVar) data assimilations, Q. J. Roy. Meteor. Soc., 149, 1138–1164, https://doi.org/10.1002/qj.4431, 2023.
Keller, J. D. and Potthast, R.: AI-based data assimilation: Learning the functional of analysis estimation, arXiv [preprint], https://doi.org/10.48550/arXiv.2406.00390, 2024.
Li, H. R., Ding, W. Y., Xue, J. S., Chen, Z. T., and Gao, Y. D.: A Study on the Application of Fy-2e Cloud Drift Wind Height Reassignment in Numerical Forecast of Typhoon Chanthu (1003) Track, J. Trop. Meteorol., 21, 34–42, https://doi.org/10.16555/j.1006-8775.2015.01.004, 2015.
Li, J., Tian, Q., Shen, Z., Xu, Y., Yan, Z., Li, M., Zhu, C., Xue, J., Lin, Z., Yang, Y., and Zeng, L.: Fidelity of global tropical cyclone activity in a new reanalysis dataset (CRA40), Meteorol. Appl., 31, https://doi.org/10.1002/met.70009, 2024.
Li, N., Zhang, S., and He, J.: Data Assimilation using MWHTS Onboard FY-3C Satellite for Typhoon Case, IGARSS 2022 – 2022 IEEE International Geoscience and Remote Sensing Symposium, https://doi.org/10.1109/igarss.2019.8898363, 2019.
Lin, X., Feng, Y., Jian, Y., Xu, D., Huang, J., Chen, H., and Zhang, B.: Nowcasting of a Warm-Sector Rainfall Event in Southern China With the TRAMS Model: Sensitivity to Different Radar Reflectivity Retrieval Methods and Incremental Updating Strategies, Earth Space Sci., 12, https://doi.org/10.1029/2024ea003724, 2025.
Liu, K. and Xu, D.: TRAMS 3.0 Model and SVD-3DEnVar Data Assimilation Framework Source Code, Science Data Bank [code], https://doi.org/10.57760/sciencedb.30837, 2025a.
Liu, K. and Xu, D.: TRAMS: SVD-3DEnVar Simulations, Observation Data, and Plotting Scripts, Science Data Bank [data set], https://doi.org/10.57760/sciencedb.28464, 2025b.
Lorenc, A. and Jardak, M.: A comparison of hybrid variational data assimilation methods for global NWP, Q. J. Roy. Meteor. Soc., 144, https://doi.org/10.1002/qj.3401, 2018.
Lorenc, A. C.: The potential of the ensemble Kalman filter for NWP – a comparison with 4D-Var, Q. J. Roy. Meteor. Soc., 129, 3183–3203, https://doi.org/10.1256/qj.02.132, 2003.
Lu, X. and Wang, X.: Simultaneous Multiscale 4DEnVar With Scale Dependent Localization (SDL) in Hurricane Analysis and Forecast System (HAFS), J. Geophys. Res.-Atmos., 129, https://doi.org/10.1029/2023jd040550, 2024.
Lu, X., Yu, H., Ying, M., Zhao, B., Zhang, S., Lin, L., Bai, L., and Wan, R.: Western North Pacific Tropical Cyclone Database Created by the China Meteorological Administration, Adv. Atmos. Sci., 38, 690–699, https://doi.org/10.1007/s00376-020-0211-7, 2021.
Miyoshi, T. and Yamane, S.: Local Ensemble Transform Kalman Filtering with an AGCM at a T159/L48 Resolution, Mon. Weather Rev., 135, 3841–3861, https://doi.org/10.1175/2007MWR1873.1, 2007.
Qiu, C. and Chou, J.: Four-dimensional data assimilation method based on SVD: Theoretical aspect, Theor. Appl. Climatol., 83, 51–57, https://doi.org/10.1007/s00704-005-0162-z, 2005.
Qiu, C., Shao, A., Xu, Q., and Wei, L.: Fitting model fields to observations by using singular value decomposition: An ensemble-based 4DVar approach, J. Geophys. Res.-Atmos., 112, https://doi.org/10.1029/2006jd007994, 2007.
Shao, A., Xi, S., Qiu, C., and Xu, Q.: A hybrid space approach for ensemble-based 4-D variational data assimilation, J. Geophys. Res.-Atmos., 114, https://doi.org/10.1029/2009jd012032, 2009.
Thiruvengadam, P. and Wang, X.: A comparison of En4DVar and 4DEnVar in convective-scale supercell data assimilation: A study of the 8 May 2003 Oklahoma City tornadic supercell, Q. J. Roy. Meteor. Soc., 152, e70071, https://doi.org/10.1002/qj.70071, 2025.
Tian, X. and Feng, X.: A non-linear least squares enhanced POD-4DVar algorithm for data assimilation, Tellus A, 67, 25340, https://doi.org/10.3402/tellusa.v67.25340, 2015.
Tian, X., Xie, Z., and Dai, A.: An ensemble-based explicit four-dimensional variational assimilation method, J. Geophys. Res.-Atmos., 113, https://doi.org/10.1029/2008JD010358, 2008.
Tian, X. J., Xie, Z. H., and Sun, Q.: A POD-based ensemble four-dimensional variational assimilation method, Tellus A, 63, 805–816, https://doi.org/10.1111/j.1600-0870.2011.00529.x, 2011.
Wang, B., Liu, J., Wang, S., Cheng, W., Juan, L., Liu, C., Xiao, Q., and Kuo, Y.-H.: An economical approach to four-dimensional variational data assimilation, Adv. Atmos. Sci., 27, 715–727, https://doi.org/10.1007/s00376-009-9122-3, 2010.
Wang, X., Barker, D. M., Snyder, C., and Hamill, T. M.: A Hybrid ETKF–3DVAR Data Assimilation Scheme for the WRF Model. Part I: Observing System Simulation Experiment, Mon. Weather Rev., 136, 5116–5131, https://doi.org/10.1175/2008MWR2444.1, 2008.
Wang, X., Parrish, D., Kleist, D., and Whitaker, J.: GSI 3DVar-Based Ensemble–Variational Hybrid Data Assimilation for NCEP Global Forecast System: Single-Resolution Experiments, Mon. Weather Rev., 141, 4098–4117, https://doi.org/10.1175/mwr-d-12-00141.1, 2013.
Wang, Y. and Wu, C. C.: Current understanding of tropical cyclone structure and intensity changes – a review, Meteorol. Atmos. Phys., 87, 257–278, https://doi.org/10.1007/s00703-003-0055-6, 2004.
Wang, Y., Chen, H., He, J., Chen, Y., and Min, J.: The Potential Benefits of Assimilating Future CubeSat-Constellation Microwave Radiances on Regional NWP for Typhoon and Heavy Rainfall With a Rapid-Update Convection-Permitting 4DEnVar, J. Geophys. Res.-Atmos., 130, https://doi.org/10.1029/2024jd041746, 2025.
Weng, Y. and Zhang, F.: Assimilating Airborne Doppler Radar Observations with an Ensemble Kalman Filter for Convection-Permitting Hurricane Initialization and Prediction: Katrina (2005), Mon. Weather Rev., 140, 841–859, https://doi.org/10.1175/2011MWR3602.1, 2012.
Wu, C.-C., Chou, K.-H., Lin, P.-H., Aberson, S. D., Peng, M. S., and Nakazawa, T.: The Impact of Dropwindsonde Data on Typhoon Track Forecasts in DOTSTAR, Weather Forecast., 22, 1157–1176, https://doi.org/10.1175/2007WAF2006062.1, 2007.
Xiang, Y., Jin, W., Dong, H., Weyn, J., Bai, M., Fang, Z., Zhao, P., Sun, H., Thambiratnam, K., Zhang, Q., and Huang, X.: ADAF: An Artificial Intelligence Data Assimilation Framework for Weather Forecasting, J. Adv. Model. Earth Sy., 17, https://doi.org/10.1029/2024ms004839, 2025.
Xiao, X., Lu, Q., Lv, X., and Shen, W.: Assimilation of FY-4A GIIRS radiance observations in the forecast of Typhoon Bavi, Front. Earth Sci., 10, https://doi.org/10.3389/feart.2022.1033474, 2023.
Xie, Y., Koch, S., McGinley, J., Albers, S., Bieringer, P. E., Wolfson, M., and Chan, M.: A Space-Time Multiscale Analysis System: A Sequential Variational Analysis Approach, Mon. Weather Rev., 139, 1224–1240, https://doi.org/10.1175/2010mwr3338.1, 2011.
Xu, D., Shao, A., and Qiu, C.: Assimilation of Doppler Radar Velocity Observations with SVD-En3DVar Method. Part II – Real Data Experiments, Chinese Journal of Atmospheric Sciences, 35, 818–832, https://doi.org/10.3878/j.issn.1006-9895.2011.05.03, 2011a.
Xu, D., Shao, A., and Qiu, C.: Assimilation of Doppler Radar Velocity Observations with SVD-En3DVar Method. Part I – Simulated Data Experiments, Chinese Journal of Atmospheric Sciences, 35, 753–766, https://doi.org/10.3878/j.issn.1006-9895.2011.04.14, 2011b.
Xu, D., Shao, A., and Qiu, C.: Doppler radar data assimilation with a local SVD-En3DVar method, Acta Meteorol. Sin., 26, 717–734, https://doi.org/10.1007/s13351-012-0604-3, 2012.
Xu, D., Chen, Z., Zhang, Y., Dai, G., Zhong, S., Zhang, B., Chen, D., Wu, N., Wu, K., and Li, H.: Updates in TRAMS 3.0 model version and its verification on typhoon forecast, Meteorological Monthly, 46, 1474–1484, https://doi.org/10.7519/j.issn.1000-0526.2020.11.008, 2020 (in Chinese).
Xu, D., Lu, Z., Leung, J. C.-H., Zhao, D., Li, Y., Shi, Y., Chen, B., Nie, G., Wu, N., Tian, X., Yang, Y., Zhang, S., and Zhang, B.: AI models still lag behind traditional numerical models in predicting sudden-turning typhoons, Sci. Bull., 70, 2705–2708, https://doi.org/10.1016/j.scib.2025.06.010, 2025a.
Xu, X., Sun, X., Han, W., Zhong, X., Chen, L., Gao, Z., and Li, H.: FuXi-DA: a generalized deep learning data assimilation framework for assimilating satellite observations, NPJ Clim. Atmos. Sci., 8, 156, https://doi.org/10.1038/s41612-025-01039-3, 2025b.
Yang, X., Carcione, V., Nunziata, F., Portabella, M., and Migliaccio, M.: Assimilation of SAR-Derived Sea Surface Winds Into Typhoon Forecast Model, IGARSS 2022 – 2022 IEEE International Geoscience and Remote Sensing Symposium, https://doi.org/10.1109/igarss.2018.8518842, 2018.
Ying, M., Zhang, W., Yu, H., Lu, X., Feng, J., Fan, Y., Zhu, Y., and Chen, D.: An Overview of the China Meteorological Administration Tropical Cyclone Database, J. Atmos. Ocean. Tech., 31, 287–301, https://doi.org/10.1175/JTECH-D-12-00119.1, 2014.
Zafarmomen, N., Alizadeh, H., Bayat, M., Ehtiat, M., and Moradkhani, H.: Assimilation of Sentinel-Based Leaf Area Index for Modeling Surface-Ground Water Interactions in Irrigation Districts, Water Resour. Res., 60, https://doi.org/10.1029/2023wr036080, 2024.
Zhang, H. and Tian, X.: A Multigrid Nonlinear Least Squares Four-Dimensional Variational Data Assimilation Scheme With the Advanced Research Weather Research and Forecasting Model, J. Geophys. Res.-Atmos., 123, 5116–5129, https://doi.org/10.1029/2017JD027529, 2018.
Zhang, L., Qiu, C., and Zhang, S.: Experiments on the 4D-variation with ensemble convariances, Acta Meteorol. Sin., 1124–1132, https://doi.org/10.11676/qxxb2009.108, 2009.
Zhang, M., Zhang, L., Zhang, B., Guan, J., and You, W.: Assimilation of MWHS and MWTS radiance data from the FY-3A satellite with the POD-3DEnVar method for forecasting heavy rainfall, Atmos. Res., 219, 95–105, https://doi.org/10.1016/j.atmosres.2018.12.023, 2019.
Zhang, M., Zhang, L., Zhang, B., Guan, J., You, W., and Yu, P.: Preliminary evaluation of all-sky radiance assimilation scheme with POD-3DEnVar method, Atmos. Res., 275, 106198, https://doi.org/10.1016/j.atmosres.2022.106198, 2022a.
Zhang, S., Tian, X., Han, X., Zhang, M., Zhang, H., and Mao, H.: Improvement of PM
2.5 forecast over China by the joint adjustment of initial conditions and emissions with the NLS-4DVar method, Atmos. Environ., 271, https://doi.org/10.1016/j.atmosenv.2021.118896, 2022b.
Zhang, S., Leung, J. C.-H., Xu, D., Wang, L., Chen, Y., Huang, Y., Ma, S., Tian, W., and Zhang, B.: Multivariate Adjustment in the IAU-Based Tropical Cyclone Initialization Scheme in the TRAMS Model, Adv. Atmos. Sci., 43, 436–450, https://doi.org/10.1007/s00376-025-4444-3, 2026.
Zhang, X., Xu, D., Liu, R., and Shen, F.: Impacts of FY-4A AGRI Radiance Data Assimilation on the Forecast of the Super Typhoon “In-Fa” (2021), Remote Sens., https://doi.org/10.3390/rs14194718, 2022c.
