| Birgin, E. G., J. E. Martínez, and M. Raydan, 2001: Algorithm 813: SPG—software for convex-constrained optimization. ACM Transactions on Mathematical Software, 27, 340−349, https://doi.org/10.1145/502800.502803. |
| Bishop, C. H., B. J. Etherton, and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420−436, https://doi.org/10.1175/1520-0493(2001)129<0420:ASWTET>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. |
| Cardinali, C., R. Buizza, G. Kelly, M. Shapiro, and J.-N. Thépaut, 2007: The value of observations. III: Influence of weather regimes on targeting. Quart. J. Roy. Meteor. Soc., 133, 1833−1842, https://doi.org/10.1002/qj.148. |
| Chen, B.-Y., 2011: Observation system experiments for typhoon nida (2004) using the CNOP method and DOTSTAR data. Atmos. Ocean. Sci. Let., 4, 118−123, https://doi.org/10.1080/16742834.2011.11446914. |
| Chen, Y. F., and G. Gao, 2010: An analysis to losses caused by meteorological disasters in China during 1989−2008. Meteorological Monthly, 36, 76−80, https://doi.org/10.7519/j.issn.1000-0526.2010.2.011. (in Chinese with English abstract |
| 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. |
| Doyle, J. D., C. A. Reynolds, and C. Amerault, 2019: Adjoint sensitivity analysis of high-impact extratropical cyclones. Mon. Wea. Rev., 147, 4511−4532, https://doi.org/10.1175/MWR-D-19-0055.1. |
| Ehrendorfer, M., and R. M. Errico, 1995: Mesoscale predictability and the spectrum of optimal perturbations. J. Atmos. Sci., 52, 3475−3500, https://doi.org/10.1175/1520-0469(1995)052<3475:MPATSO>2.0.CO;2. |
| 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. |
| Grell, G. A., J. Dudhia, and D. R. Stauffer, 1995: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 121 pp. |
| Hakim, G. J., and R. D. Torn, 2008: Ensemble synoptic analysis. Meteor. Monogr., 33, 147−162, https://doi.org/10.1175/0065-9401-33.55.147. |
| Hamill, T. M., and C. Snyder, 2002: Using improved background-error covariances from an ensemble Kalman filter for adaptive observations. Mon. Wea. Rev., 130, 1552−1572, https://doi.org/10.1175/1520-0493(2002)130<1552:UIBECF>2.0.CO;2. |
| Hoskins, B. J., and P. J. Valdes, 1990: On the existence of storm-tracks. J. Atmos. Sci., 47, 1854−1864, https://doi.org/10.1175/1520-0469(1990)047<1854:OTEOST>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. |
| Huang, L., and Z. Y. Meng, 2014: Quality of the target area for metrics with different nonlinearities in a mesoscale convective system. Mon. Wea. Rev., 142, 2379−2397, https://doi.org/10.1175/MWR-D-13-00244.1. |
| Joseph, S., and Coauthors, 2015: North Indian heavy rainfall event during June 2013: Diagnostics and extended range prediction. Climate Dyn., 44, 2049−2065, https://doi.org/10.1007/s00382-014-2291-5. |
| Jung, B.-J., and H. M. Kim, 2009: Moist adjoint-based forecast sensitivities for a heavy snowfall event over the Korean Peninsula on 4-5 March 2004. J. Geophys. Res., 114, D15104, https://doi.org/10.1029/2008JD011370. |
| Kim, H. M., S.-M. Kim, and B.-J. Jung, 2011: Real-Time adaptive observation guidance using singular vectors for typhoon Jangmi (200815) in T-PARC 2008. Wea. Forecasting, 26, 634−649, https://doi.org/10.1175/WAF-D-10-05013.1. |
| Li, X. S., Y. L. Luo, and Z. Y. Guan, 2014: The persistent heavy rainfall over southern China in June 2010: Evolution of synoptic systems and the effects of the Tibetan Plateau heating. Journal of Meteorological Research, 28, 540−560, https://doi.org/10.1007/s13351-014-3284-3. |
| Li, X. Z., W. Zhou, Y. Q. Chen, and D. Chen, 2016: Detecting the origins of moisture over southeast China: Seasonal variation and heavy rainfall. Adv. Atmos. Sci., 33, 319−329, https://doi.org/10.1007/s00376-015-4197-5. |
| Liu, J. Y., and Z.-M. Tan, 2009: Mesoscale predictability of mei-yu heavy rainfall. Adv. Atmos. Sci., 26, 438−450, https://doi.org/10.1007/s00376-009-0438-9. |
| Liu, J. Y., Z. M. Tan, and S. N. Gu, 2011: Flow-dependent mesoscale predictability of Meiyu heavy rainfall. Chinese Journal of Atmospheric Sciences, 35, 912−926, https://doi.org/10.3878/j.issn.1006-9895.2011.05.11. (in Chinese with English abstract |
| Liu, S.-Y., Y.-G. Zheng, and Z.-Y. Tao, 2003: The analysis of the relationship between pulse of LLJ and heavy rain using wind profiler data. Journal of Tropical Meteorology, 9, 158−163, https://doi.org/10.3969/j.issn.1006-8775.2003.02.006. |
| Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130−141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2. |
| Lynch, S. L., and R. S. Schumacher, 2014: Ensemble-based analysis of the May 2010 extreme rainfall in Tennessee and Kentucky. Mon. Wea. Rev., 142, 222−239, https://doi.org/10.1175/MWR-D-13-00020.1. |
| Mahfouf, J.-F., and B. Bilodeau, 2007: Adjoint sensitivity of surface precipitation to initial conditions. Mon. Wea. Rev., 135, 2879−2896, https://doi.org/10.1175/MWR3439.1. |
| Meng, X. F., Y. G. Sun, Sarina, H. M. Yuan, and Hasi, 2013: Correlation between eastward developing of Hetao cyclone and the severe rainstorm in Beijing on 21 July 2012. Meteorological Monthly, 39, 1542−1549, https://doi.org/10.7519/j.issn.1000-0526.2013.12.002. (in Chinese with English abstract |
| 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. |
| Montani, A., A. J. Thorpe, R. Buizza, and P. Undén, 1999: Forecast skill of the ECMWF model using targeted observations during FASTEX. Quat. J. Roy. Meteor. Soc., 125, 3219−3240, https://doi.org/10.1002/qj.49712556106. |
| Mu, M., and W. S. Duan, 2003: A new approach to studying ENSO predictability: Conditional nonlinear optimal perturbation. Chinese Science Bulletin, 48, 1045−1047, https://doi.org/10.1007/BF03184224. |
| Mu, M., H.-L. Wang, and F.-F. Zhou, 2007: A preliminary application of conditional nonlinear optimal perturbation to adaptive observation. Chinese Journal of Atmospheric Sciences, 31, 1102−1112, https://doi.org/10.3878/j.issn.1006-9895.2007.06.06. (in Chinese with English abstract |
| Ni, Y. Q., X. J. Zhou, R. H. Zhang, P. Y. Wang, and Q. J. Yi, 2006: Experiments and studies for heavy rainfall in southern China. Journal of Applied Meteorological Science, 17, 690−704, https://doi.org/10.3969/j.issn.1001-7313.2006.06.007. (in Chinese with English abstract |
| 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. |
| Qi, L. B., and J. Xu, 2018: Rethink on short range forecast of the 9 July severe rainstorm in northern Henan. Meteorological Monthly, 44, 1−14, https://doi.org/10.7519/j.issn.1000-0526.2018.01.001. (in Chinese with English abstract |
| Reynolds, C. A., and T. E. Rosmond, 2003: Nonlinear growth of singular-vector-based perturbations. Quart. J. Roy. Meteor. Soc., 129, 3059−3078, https://doi.org/10.1256/qj.02.193. |
| Reynolds, C. A., J. D. Doyle, F. M. Ralph, and R. Demirdjian, 2019: Adjoint sensitivity of North Pacific atmospheric river forecasts. Mon. Wea. Rev., 147, 1871−1897, https://doi.org/10.1175/MWR-D-18-0347.1. |
| Schumacher, R. S., 2011: Ensemble-based analysis of factors leading to the development of a multiday warm-season heavy rain event. Mon. Wea. Rev., 139, 3016−3035, https://doi.org/10.1175/MWR-D-10-05022.1. |
| Sippel, J. A., and F. Q. Zhang, 2010: Factors affecting the predictability of hurricane Humberto (2007). J. Atmos. Sci., 67, 1759−1778, https://doi.org/10.1175/2010JAS3172.1. |
| Sun, J. H., Y. C. Zhang, R. X. Liu, S. M. Fu, and F. Y. Tian, 2019: A review of research on warm-sector heavy rainfall in China. Adv. Atmos. Sci., 36, 1299−1307, https://doi.org/10.1007/s00376-019-9021-1. |
| Wang, C.-C., J. C.-S. Hsu, G. T.-J. Chen, and D.-I. Lee, 2014a: A study of two propagating heavy-rainfall episodes near Taiwan during SoWMEX/TiMREX IOP-8 in June 2008. Part II: Sensitivity tests on the roles of synoptic conditions and topographic effects. Mon. Wea. Rev., 142, 2644−2664, https://doi.org/10.1175/MWR-D-13-00330.1. |
| Wang, J. Y., C. G. Cui, X. F. Wang, and W. J. Cui, 2014b: Analysis on water vapor transport and budget of the severe torrential rain over Beijing region on 21 July 2012. Meteorological Monthly, 40, 133−145, https://doi.org/10.7519/j.issn.1000-0526.2014.02.001. (in Chinese with English abstract |
| Wang, Q., and M. Mu, 2017: Application of conditional nonlinear optimal perturbation to target observations for high-impact ocean-atmospheric environmental events. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. III), S. K. Park and L. Xu, Eds., Springer International Publishing, 513-526, https://doi.org/10.1007/978-3-319-43415-5_23. |
| Xu, J., Y. Chen, J. Sun, S. Yang, Z. Zong, T. Chen, C. Fang, and J. Sheng, 2012: Observation analysis of Beijing extreme flooding event 21 July 2012. Weather Forecast Review, 4, 9−19. (in Chinese) |
| Yu, H. Z., and Z. Y. Meng, 2016: Key synoptic-scale features influencing the high-impact heavy rainfall in Beijing, China, on 21 July 2012. Tellus A: Dynamic Meteorology and Oceanography, 68, 31045, https://doi.org/10.3402/tellusa.v68.31045. |
| Yu, H. Z., H. L. Wang, Z. Y. Meng, M. Mu, X.-Y. Huang, and X. Zhang, 2017: A WRF-based tool for forecast sensitivity to the initial perturbation: The conditional nonlinear optimal perturbations versus the first singular vector method and comparison to MM5. J. Atmos. Oceanic Technol., 34, 187−206, https://doi.org/10.1175/JTECH-D-15-0183.1. |
| Zhang, F., C. Snyder, and R. Rotunno, 2002: Mesoscale predictability of the "surprise" snowstorm of 24–25 January 2000. Mon. Wea. Rev., 130, 1617−1632, https://doi.org/10.1175/1520-0493(2002)130<1617:MPOTSS>2.0.CO;2. |
| Zhang, F., C. Snyder, and R. Rotunno, 2003: Effects of moist convection on mesoscale predictability. J. Atmos. Sci., 60, 1173−1185, https://doi.org/10.1175/1520-0469(2003)060<1173:EOMCOM>2.0.CO;2. |
| Zhang, F. Q., A. M. Odins, and J. W. Nielsen-Gammon, 2006: Mesoscale predictability of an extreme warm-season precipitation event. Wea. Forecasting, 21, 149−166, https://doi.org/10.1175/WAF909.1. |
| Zhang, G. C., 2006: Prevention and mitigation of the meteorological disasters-The world meteorological day, 2006. Meteorological Monthly, 32, 3−5, https://doi.org/10.7519/j.issn.1000-0526.2006.03.001. (in Chinese with English abstract |
| Zhang, M. R., and Z. Y. Meng, 2018: Impact of synoptic-scale factors on rainfall forecast in different stages of a persistent heavy rainfall event in South China. J. Geophy. Res., 123, 3574−3593, https://doi.org/10.1002/2017JD028155. |
| Zhang, X. B., Y. L. Luo, Q. L. Wan, W. Y. Ding, and J. X. Sun, 2016a: Impact of assimilating wind profiling radar observations on convection-permitting quantitative precipitation forecasts during SCMREX. Wea. Forecasting, 31, 1271−1292, https://doi.org/10.1175/WAF-D-15-0156.1. |
| Zhang, Y. J., F. Q. Zhang, D. J. Stensrud, and Z. Y. Meng, 2016b: Intrinsic predictability of the 20 May 2013 tornadic thunderstorm event in Oklahoma at storm scales. Mon. Wea. Rev., 144, 1273−1298, https://doi.org/10.1175/MWR-D-15-0105.1. |
| Zhou, F. F., and H. Zhang, 2014: Study of the schemes based on CNOP method to identify sensitive areas for typhoon targeted observations. Chinese Journal of Atmospheric Sciences, 38, 261−272, https://doi.org/10.3878/j.issn.1006-9895.2013.13129. (in Chinese with English abstract |
| Zhu, B. L., W. T. Lin, and Y. Zhang, 2009: Impacts of initial perturbations on prediction of a heavy rain in South China. Chinese Journal of Atmospheric Sciences, 33, 1333−1347, https://doi.org/10.3878/j.issn.1006-9895.2009.06.18. (in Chinese with English abstract |
| Zhu, H. F., D. Y. Wang, Z. Y. Guan, Y. Liu, and Y. F. Fu, 2007: Effects of different initial fields on GRAPES numerical prediction. Journal of Meteorological Research, 21, 496−506. |
| Zou, X. L., F. Vandenberghe, M. Pondeca, and Y.-H. Kuo, 1997: Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN2435+STR, 110 pp. |