| Barkmeijer, J., R. Buizza, T. N. Palmer, K. Puri, and J.-F Mahfouf, 2001: Tropical singular vectors computed with linearized diabatic physics. Quart. J. Roy. Meteor. Soc., 127, 685−708, https://doi.org/10.1002/qj.49712757221. |
| Buizza, R., 1994: Sensitivity of optimal unstable structures. Quart. J. Roy. Meteor. Soc., 120, 429−51, https://doi.org/10.1002/qj.49712051609. |
| Buizza, R., and T. N. Palmer, 1995: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci., 52, 1434−1456, https://doi.org/10.1175/1520-0469(1995)052<1434:TSVSOT>2.0.CO;2. |
| Buizza, R., and A. Montani, 1999: Targeting observations using singular vectors. J. Atmos. Sci., 56, 2965−2985, https://doi.org/10.1175/1520-0469(1999)056<2965:TOUSV>2.0.CO;2. |
| Buizza, R., C. Cardinali, G. Kelly, and J.-N. Thépaut, 2007: The value of observations. II: The value of observations located in singular-vector-based target areas. Quart. J. Roy. Meteor. Soc., 133, 1817−1832, https://doi.org/10.1002/qj.149. |
| Buizza, R., J. Tribbia, F. Molteni, and T. Palmer, 1993: Computation of optimal unstable structures for a numerical weather prediction model. Tellus A, 45, 388−407, https://doi.org/10.3402/tellusa.v45i5.14901. |
| Coutinho, M. M., B. J. Hoskins, and R. Buizza, 2004: The influence of physical processes on extratropical singular vectors. J. Atmos. Sci., 61, 195−209, https://doi.org/10.1175/1520-0469(2004)061<0195:TIOPPO>2.0.CO;2. |
| Diaconescu, E. P., and R. Laprise, 2012: Singular vectors in atmospheric sciences: A review. Earth-Science Reviews, 113, 161−175, https://doi.org/10.1016/j.earscirev.2012.05.005. |
| ECMWF., 2017: IFS Documentation Cy43r3 Operational Implementation. Part Ⅱ: Data assimilation. ECMWF, 23−24. |
| Ehrendorfer, M., R. M. Errico, and K. D. Raeder, 1999: Singular-vector perturbation growth in a primitive equation model with moist physics. J. Atmos. Sci., 56, 1627−1648, https://doi.org/10.1175/1520-0469(1999)056<1627:SVPGIA>2.0.CO;2. |
| Hakim, G. J., 2000: Role of nonmodal growth and nonlinearity in cyclogenesis initial-value problems. J. Atmos. Sci., 57, 2951−2967, https://doi.org/10.1175/1520-0469(2000)057<2951:RONGAN>2.0.CO;2. |
| Hoskins, B. J., R. Buizza, and J. Badger, 2000: The nature of singular vector growth and structure. Quart. J. Roy. Meteor. Soc., 126, 1565−1580, https://doi.org/10.1002/qj.49712656601. |
| Hoskins, B. J., and M. M. Coutinho, 2005: Moist singular vectors and the predictability of some high impact European cyclones. Quart. J. Roy. Meteor. Soc., 131, 581−601, https://doi.org/10.1256/qj.04.48. |
| Kim, H. M., and B.-J. Jung, 2009: Influence of moist physics and norms on singular vectors for a tropical cyclone. Mon. Wea. Rev., 137, 525−543, https://doi.org/10.1175/2008MWR2739.1. |
| Leutbecher, M., and T. N. Palmer, 2008: Ensemble forecasting. J. Comput. Phys., 227, 3515−3539, https://doi.org/10.1016/j.jcp.2007.02.014. |
| Li, X. L., J. Chen, Y. Z. Liu, and Z. H. Huo, 2019: Representations of initial uncertainty and model uncertainty of GRAPES global ensemble forecasting. Journal of Nanjing Institute of Meteorology, 42, 348−359, https://doi.org/10.13878/j.cnki.dqkxxb.20190318001. (in Chinese with English abstract) |
| Li, X. L., and Y. Z. Liu, 2019: The improvement of GRAPES global extratropical singular vectors and experimental study. Acta Meteorologica Sinica, 77, 552−562, https://doi.org/10.11676/qxxb2019.020. (in Chinese with English abstract) |
| Liu, Y. Z., X. S. Shen, and X. L. Li, 2013: Research on the singular vector perturbation of the GRAPES global model based on the total energy norm. Acta Meteorological Sinica, 71, 517−526, https://doi.org/10.13209/j.0479-8023.2011.039. (in Chinese with English abstract) |
| Liu, Y. Z., L. Zhang, and Z. Y. Jin, 2017: The optimization of GRAPES global tangent linear model and Adjoint model. Journal of Applied Meteorological Science, 28, 62−71, https://doi.org/10.11898/1001-7313.20170106. (in Chinese with English abstract) |
| Liu, Y. Z., J. D. Gong, L. Zhang, and Q. Y. Chen, 2019: Influence of linearized physical processes on the GRAPES 4DVAR. Acta Meteorologica Sinica, 77, 196−209, https://doi.org/10.11676/qxxb2019.013. (in Chinese with English abstract) |
| Lorenz, E. N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus, 17, 321−333, https://doi.org/10.3402/tellusa.v17i3.9076. |
| Mahfouf, J.-F., 1999: Influence of physical processes on the tangent-linear approximation. Tellus A, 51, 147−166, https://doi.org/10.3402/tellusa.v51i2.12312. |
| Molteni, F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc., 122, 73−119, https://doi.org/10.1002/qj.49712252905. |
| Palmer, T. N., R. Gelaro, J. Barkmeijer, and R. Buizza, 1998: Singular vectors, metrics, and adaptive observations. J. Atmos. Sci., 55, 633−653, https://doi.org/10.1175/1520-0469(1998)055<0633:SVMAAO>2.0.CO;2. |
| Puri, K., J. Barkmeijer, and T. N. Palmer, 2001: Ensemble prediction of tropical cyclones using targeted diabatic singular vectors. Quart. J. Roy. Meteor. Soc., 127, 709−731, https://doi.org/10.1002/qj.49712757222. |
| Tompkins, A. M., and M. Janisková, 2004: A cloud scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc., 130, 2495−2518, https://doi.org/10.1256/qj.03.162. |
| Yamaguchi, M., T. Iriguchi, T. Nakazawa, and C.-C. Wu, 2009: An observing system experiment for typhoon Conson (2004) using a singular vector method and DOTSTAR data. Mon. Wea. Rev., 137, 2801−2816, https://doi.org/10.1175/2009MWR2683.1. |
| Zadra, A., M. Buehner, S. Laroche, and J.-F. Mahfouf, 2004: Impact of the GEM model simplified physics on extratropical singular vectors. Quart. J. Roy. Meteor. Soc., 130, 2541−2569, https://doi.org/10.1256/qj.03.208. |
| Zhang, L., and Coauthors, 2019: The operational global four-dimensional variational data assimilation system at the China Meteorological Administration. Quart. J. Roy. Meteor. Soc., 145, 1882−1896, https://doi.org/10.1002/qj.3533. |