Abstract
A new forecasting system—the System of Multigrid Nonlinear Least-squares Four-dimensional Variational (NLS-4DVar) Data Assimilation for Numerical Weather Prediction (SNAP)—was established by building upon the multigrid NLS-4DVar data assimilation scheme, the operational Gridpoint Statistical Interpolation (GSI)-based data-processing and observation operators, and the widely used Weather Research and Forecasting numerical model. Drawing upon lessons learned from the superiority of the operational GSI analysis system, for its various observation operators and the ability to assimilate multiple-source observations, SNAP adopts GSI-based data-processing and observation operator modules to compute the observation innovations. The multigrid NLS-4DVar assimilation framework is used for the analysis, which can adequately correct errors from large to small scales and accelerate iteration solutions. The analysis variables are model state variables, rather than the control variables adopted in the conventional 4DVar system. Currently, we have achieved the assimilation of conventional observations, and we will continue to improve the assimilation of radar and satellite observations in the future. SNAP was evaluated by case evaluation experiments and one-week cycling assimilation experiments. In the case evaluation experiments, two six-hour time windows were established for assimilation experiments and precipitation forecasts were verified against hourly precipitation observations from more than 2400 national observation sites. This showed that SNAP can absorb observations and improve the initial field, thereby improving the precipitation forecast. In the one-week cycling assimilation experiments, six-hourly assimilation cycles were run in one week. SNAP produced slightly lower forecast RMSEs than the GSI 4DEnVar (Four-dimensional Ensemble Variational) as a whole and the threat scores of precipitation forecasts initialized from the analysis of SNAP were higher than those obtained from the analysis of GSI 4DEnVar.
摘要
本文基于WRF数值预报模式(亦可被任意全球或区域模式替代)、多重网格同化框架构建了多重网格NLS-4DVar资料同化系统SNAP(System of Multigrid NLS-4DVar Data Assimilation for Numerical Weather Prediction)。SNAP系统采用业务化的NCEP/GSI分析系统的观测资料质量控制与观测算子模块,用以计算同化模块所需要的模拟观测等;SNAP同化系统采用多重网格NLS-4DVar同化框架可从大尺度到小尺度顺序修订误差、加速迭代;同时,NLS-4DVar方法利用高斯—牛顿显式迭代、可有效应对预报模式和观测算子的高度非线性;SNAP中快速局地化方案的使用,进一步地提高了同化效率;不同于一般变分同化系统所采用的控制变量方式,SNAP的同化变量为模式变量。本文设计了真实个例和一周的循环同化常规资料试验来评估SNAP同化系统。真实个例试验结果表明:相比较实况,SNAP系统通过同化常规观测资料,强降水的强度和位置均得到较好改善。初始场分析增量的结果与降水预报结果有很好的一致性。降水分量级TS评分的结果也表面SNAP同化系统可以有效吸收观测信息、改进初始场,进而改进降水预报。一周的循环同化试验对比了SNAP和GSI 4DEnVar的同化性能,结果表明,整体而言,相比较GSI 4DEnVar,SNAP的预报均方根误差(RMSE)略有减小;降水预报的ETS评分结果也表明SNAP可以更好的改进降水预报。
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–2903, https://doi.org/10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.
Benjamin, S. G., and Coauthors, 2004: An hourly assimilation-forecast cycle: The RUC. Mon. Wea. Rev., 132, 495–518, https://doi.org/10.1175/1520-0493(2004)132<0495:AHACTR>2.0.CO;2.
Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The rapid refresh. Mon. Wea. Rev., 144, 1669–1694, https://doi.org/10.1175/MWR-D-15-0242.1.
Briggs, W., V. E. Henson, and S. F. McCormic, 2000: A Multigrid Tutorial. 2nd ed., SIAM, 95–109.
Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010a: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments. Mon. Wea. Rev., 138, 1550–1566, https://doi.org/10.1175/2009MWR3157.1.
Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010b: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations. Mon. Wea. Rev., 138, 1567–1586, https://doi.org/10.1175/2009MWR3158.1.
Chen, F., and J. Dudhia, 2001: Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569–585, https://doi.org/10.1155/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.
Chen, S. H., and W. Y. Sun, 2002: A one-dimensional time dependent cloud model. J. Meteor. Soc. Japan, 80, 99–118, https://doi.org/10.2151/jmsj.80.99.
Clayton, A. M., A. C. Lorenc, and D. M. Barker, 2013: Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office. Quart. J. Roy. Meteor. Soc., 132, 1445–1461, https://doi.org/10.1002/qj.2054.
Courtier, P., J. N. Thépaut, and A. Hollingsworth, 1994: A strategy for operational implementation of 4D-Var, using an incremental approach. Quart. J. Roy. Meteor. Soc., 118, 1367–1387, https://doi.org/10.1002/qj.49712051912.
Dennis, J. E., and R. B. Schnabel, 1996: Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics). SIAM, 378 pp.
Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 3077–3107, https://doi.org/10.1175/1520-0469(1989)046<3077:NSO-COD>2.0.CO;2.
Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99(C5), 10 143–10 162, https://doi.org/10.1029/94JC00572.
Evensen, G., 2003: The Ensemble Kalman Filter: Theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–367, https://doi.org/10.1007/s10236-003-0036-9.
Evensen, G., 2007: Data Assimilation-The Ensemble Kalman Filter. Springer, 157–176.
Gauthier, P., M. Tanguay, S. Laroche, S. Pellerin, and J. Morneau, 2007: Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada. Mon. Wea. Rev., 135, 2339–2364, https://doi.org/10.1175/MWR3394.1.
Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev., 118, 2905–2919, https://doi.org/10.1175/115201049312000(128<2905:AHEKFV>2.0.CO;2.
Hamill, T. M., J. S. Whitaker, and C. Snyder, 2001: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129, 2776–2790, https://doi.org/10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.
Hong, S. Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 13, 2318–2341, https://doi.org/10.1175/MWR3199.1.
Houtekamer, P. L., and H. L. Mitchell, 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131, 3269–3289, https://doi.org/10.1256/qj.05.135.
Houtekamer, P. L., and H. L. Mitchell, 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 114, 796–811, https://doi.org/10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2.
Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner, M. Charron, L. Spacek, and B. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133, 604–620, https://doi.org/10.1175/MWR-2864.1.
Hu, M., and Coauthors, 2018: Grid-point Statistical Interpolation (GSI) User’s Guide Version 3.7. Developmental Testbed Center. Available from http://www.dtcenter.org/com-GSI/users/docs/index.php.
Hunt, B. R., Kostelich, E. J., Ott, E., Szunyogh, I., 2007: Efficient data assimilation for spatio temporal chaos: A local ensemble transform Kalman filter. Physica D, 230(1–2), 112–126, https://doi.org/10.1016/j.physd.2006.11.008.
Kleist, D. T., D. F. Parrish, J. C. Derber, R. Treadon, W. S. Wu, and S. Lord, 2009: Introduction of the GSI into the NCEP global data assimilation system. Wea. Forecasting, 24, 1691–1705, https://doi.org/10.1175/2009WAF2222201.1.
Kuhl, D. D., T. E. Rosmond, C. H. Bishop, J. McLay, and N. L. Baker, 2013: Comparison of hybrid ensemble/4DVar and 4DVar within the NAVDAS-AR data assimilation framework. Mon. Wea. Rev., 141, 2740–2758, https://doi.org/10.1175/MWR-D-12-00182.1.
Lewis, J. M., and J. C. Derber, 1985: The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus A: Dynamic Meteorology and Oceanography, 37, 309–322, https://doi.org/10.3402/tellusa.v37i4.11675.
Li, W., Y. F. Xie, S. M. Deng, and Q. Wang, 2010: Application of the multigrid method to the two-dimensional doppler radar radial velocity data assimilation. J. Atmos. Oceanic Technol., 27(2), 319–332, https://doi.org/10.1175/2009JTECHA1271.1.
Li, Z. J., Y. Chao, J. C. McWilliams, and K. Ide, 2008: A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System: Implementation and basic experiments. J. Geophy. Res., 113, C05002, https://doi.org/10.1029/2006JC004042.
Li, Z. J., Y. Chao, J. D. Farrara, and J. C. McWilliams, 2013: Impacts of distinct observations during the 2009 Prince William Sound field experiment: A data assimilation study. Cont. Shelf Res., 63, S209–S222, https://doi.org/10.1016/j.csr.2012.06.018.
Liao, J., and Coauthors, 2018: Pre-process and data selection for assimilation of conventional observations in the CMA global atmospheric reanalysis. Advances in Meteorological Science and Technology, 8(1), 133–142, https://doi.org/10.3969/j.issn.2095-1973.2018.01.018.
Lin, Y. L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteorol., 22, 1065–1092, https://doi.org/10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.
Lorenc, A. C., 2003a: Modelling of error covariances by 4D-Var data assimilation. Quart. J. Roy. Meteor. Soc., 129, 3167–3182, https://doi.org/10.1256/qj.02.131.
Lorenc, A. C., 2003b: The potential of the ensemble Kalman filter for NWP—A comparison with 4D-VAR. Quart. J. Roy. Meteor. Soc., 129, 3183–3203, https://doi.org/10.1566/qj.02.132.
Lorenc, A. C., 2013: Recommended nomenclature for EnVar data assimilation methods. Research Activities in Atmospheric and Oceanic Modelling, WGNE. [Available from http://www.wcrp-climate.org/WGNE/BlueBook/2013/individual-articles/01_Lorenc_Andrew_EnVar_nomenclature.pdf]
Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102(D14), 16 663–16 682, https://doi.org/10.1029/97JD00237.
Pan, Y. J., K. F. Zhu, M. Xue, X. G. Wang, M. Hu, S. G. Benjamin, S. S. Weygandt, and J. S. Whitaker, 2014: A GSI-based coupled EnSRF-En3DVar hybrid data assimilation system for the operational rapid refresh model: Tests at a reduced resolution. Mon. Wea. Rev., 102, 3756–3780, https://doi.org/10.1175/MWR-D-13-00242.1.
Pan, Y. J., M. Xue, K. F. Zhu, and M. J. Wang, 2018: A prototype regional GSI-based EnKF-variational hybrid data assimilation system for the Rapid Refresh forecasting system: Dual-resolution implementation and testing results. Adv. Atmos. Sci., 35(5), 518–530, https://doi.org/10.1007/s00376-017-7108-0.
Qiu, C. J., A. M. Shao, Q. Xu, and L. Wei, 2007: Fitting model fields to observations by using singular value decomposition: An ensemble-based 4DVar approach. J. Geophy. Res., 110, D11105, https://doi.org/10.1029/2006JD007994.
Rabier F., and Coauthors, 2000: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics. Quart. J. Roy. Meteor. Soc., 026, 1143–1170, https://doi.org/10.1022/qj.49712656415.
Rosmond, T., and L. Xu, 2006: Development of NAVDAS-AR: Non-linear formulation and outer loop tests. Tellus A: Dynamic Meteorology and Oceanography, 58, 45–58, https://doi.org/10.1111/j.1600-0870.2006.00148.x.
Rutledge, S. A., and P. V. Hobbs, 1984: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: A diagnostic modeling study of precipitation development in narrow cold-frontal rainbands. J. Atmos. Sci., 20, 2949–2972, https://doi.org/10.1175/1520-0469(1984)041<2949:TMAMSA>2.0.CO;2.
Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 3465–3485, https://doi.org/10.1016/j.jcp.2007.01.037.
Tian, X. J., and Z. H. Xie, 2012: Implementations of a square-root ensemble analysis and a hybrid, localization into the POD-based ensemble 4DVar. Tellus A: Dynamic Meteorology and Oceanography, 21, 18375, https://doi.org/10.3402/tellusa.v64i0.18375.
Tian, X. J., and X. B. Feng, 2015: A non-linear least squares enhanced POD-4DVar algorithm for data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 22, 25340, https://doi.org/10.3402/tellusa.v67.25340.
Tian, X. J., and H. Q. Zhang, 2019: A big data-driven nonlinear least squares four - dimensional variational data assimilation method: Theoretical formulation and conceptual evaluation. Earth and Space Science, 6, 1430–1439, https://doi.org/10.1029/2019EA000735.
Tian, X. J., Z. H. Xie, and A. G. Dai, 2008: An ensemble-based explicit four-dimensional variational assimilation method. J. Geophy. Res., 113, D21124, https://doi.org/10.1029/2008JD010358.
Tian, X. J., Z. H. Xie, and Q. Sun, 2011: A POD-based ensemble four- dimensional variational assimilation method. Tellus A: Dynamic Meteorology and Oceanography, 23, 805–816, https://doi.org/10.1111/j.1600-0870.2011.00529.x.
Tian, X. J., H. Q. Zhang, X. B. Feng, and Y. F. Xie, 2018: Nonlinear least squares En4DVar to 4DEnVar methods for data assimilation: Formulation, analysis, and preliminary evaluation. Mon. Wea. Rev., 112, 77–93, https://doi.org/10.1175/MWR-D-17-0050.1.
Wang, B., J. J. Liu, S. D. Wang, W. Cheng, L. Juan, C. S. Liu, Q. N. Xiao, and Y. H. Kuo, 2010: An economical approach to four-dimensional variational data assimilation. Adv. Atmos. Sci., 02, 715–727, https://doi.org/10.1007/s00376-009-9122-3.
Wu, W. S., R. J. Purser, and D. F. Parrish, 2002: Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev., 131, 2905–2916, https://doi.org/10.1175/1520-0493(2002)130<2905:TDVAWS>2.0.CO;2.
Xie, Y. F., S. E. Koch, J. A. McGinley, S. Albers, and N. Wang, 2005: A sequential variational analysis approach for mesoscale data assimilation. Preprints, 21st Conf. on Weather Analysis and Forecasting/17th Conf. on Numerical Weather Prediction, Washington, DC, Amer. Meteor. Soc.
Xie, Y., S. Koch, J. McGinley, S. Albers, P. E. Bieringer, M. Wolfson, and M. Chan, 2011: A space-time multiscale analysis system: A sequential variational analysis approach. Mon. Wea. Rev., 139, 1224–1240, https://doi.org/10.1175/2010MWR3338.1.
Xu, Q., 1996: Generalized adjoint for physical processes with parameterized discontinuities. Part I: Basic issues and heuristic examples. J. Atmos. Sci., 53(8), 1123–1142, https://doi.org/10.1175/1520-0469(1996)053<1123:GAFPPW>2.0.CO;2.
Zhang, F. Q., Y. H. Weng, J. A. Sippel, Z. Y. Meng, and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 132, 2105–2125, https://doi.org/10.1175/2009MWR2645.1.
Zhang, H. Q., and X. J. Tian, 2018a: An efficient local correlation matrix decomposition approach for the localization implementation of ensemble-based assimilation methods. J. Geophy. Res., 103, 3556–3573, https://doi.org/10.1002/2017JD027999.
Zhang, H. Q., and X. J. Tian, 2018b: A multigrid nonlinear least squares four-dimensional variational data assimilation scheme with the advanced research weather research and forecasting model. J. Geophy. Res., 103, 5116–5129, https://doi.org/10.1029/2017JD027529.
Zhang, H. Q., 2019: Improvement and application of nonlinear least squares ensemble four-dimensional variational assimilation method. PhD dissertation, Institute of Atmospheric Physics, Chinese Academy of Sciences, 136–139. (in Chinese)
Zhang, M., and F. Q. Zhang, 2012: E4DVar: Coupling an ensemble Kalman filter with four-dimensional variational data assimilation in a limited-area weather prediction model. Mon. Wea. Rev., 140, 587–600, https://doi.org/10.1175/MWRD-11-00023.1.
Zhu, K. F., Y. J. Pan, M. Xue, X. G. Wang, J. S. Whitaker, S. G. Benjamin, S. S. Weygandt, and M. Hu, 2013: A regional GSI-based ensemble Kalman filter data assimilation system for the rapid refresh configuration: Testing at reduced resolution. Mon. Wea. Rev., 111, 4118–4139, https://doi.org/10.1175/MWR-D-13-00039.1.
Acknowledgements
This work was partially supported by the National Key Research and Development Program of China (Grant No. 2016YFA0600203), the National Natural Science Foundation of China (Grant No. 41575100), the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDY-SSW-DQC012) and the CMA Special Public Welfare Research Fund (Grant No. GYHY201506002). We would like to thank the two anonymous reviewers for their critical comments and suggestions, which helped to improve the manuscript greatly.
Author information
Authors and Affiliations
Corresponding author
Additional information
Article Highlights
• The establishment of SNAP builds upon the multigrid NLS-4DVar assimilation scheme, the GSI-based observation operators, and the WRF model.
• The multigrid NLS-4DVar framework with fast localization corrects multiscale errors and accelerates iteration solutions.
• By assimilating conventional observations, the performance of SNAP is slightly better than that of GSI 4DEnVar.
Electronic Supplementary Material
376_2020_9252_MOESM1_ESM.pdf
System of Multigrid Nonlinear Least-squares Four-dimensional Variational Data Assimilation for Numerical Weather Prediction (SNAP): System Formulation and Preliminary Evaluation
Rights and permissions
About this article
Cite this article
Zhang, H., Tian, X., Cheng, W. et al. System of Multigrid Nonlinear Least-squares Four-dimensional Variational Data Assimilation for Numerical Weather Prediction (SNAP): System Formulation and Preliminary Evaluation. Adv. Atmos. Sci. 37, 1267–1284 (2020). https://doi.org/10.1007/s00376-020-9252-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00376-020-9252-1