Idealized Experiments for Optimizing Model Parameters Using a 4D-Variational Method in an Intermediate Coupled Model of ENSO
Tóm tắt
Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational (4D-Var) data assimilation system was developed for an intermediate coupled model (ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer (Te), which is empirically and explicitly related to sea level (SL) variation. The strength of the thermocline effect on SST (referred to simply as “the thermocline effect”) is represented by an introduced parameter, αTe. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Var data assimilation system implemented in the ICM are also discussed.
Tài liệu tham khảo
Ballester, J., D. Petrova, S. Bordoni, B. Cash, M. García-Díez, and X. Rodó, 2016: Sensitivity of El Niño intensity and timing to preceding subsurface heat magnitude. Scientific Reports, 6, 36344, https://doi.org/10.1038/srep36344.
Bjerknes, J., 1966: A possible response of the atmospheric Hadley circulation to equatorial anomalies of ocean temperature. Tellus, 18, 820–829, https://doi.org/10.1111/j.2153-3490.1966.tb00303.x.
Chen, D., M. A. Cane, A. Kaplan, S. E. Zebiak, and D. Huang., 2004: Predictability of El Niño over the past 148 years. Nature, 428, 733–736, https://doi.org/10.1038/nature02439.
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., 120, 1367–1387, https://doi.org/10.1002/qj.49712051912.
Dommenget, D., and D. Stammer, 2004: Assessing ENSO simulations and predictions using adjoint ocean state estimation. J. Climate, 17, 4301–4315, https://doi.org/10.1175/3211.1.
Gao, C., and R.-H. Zhang, 2017: The roles of atmospheric wind and entrained water temperature (Te) in the second-year cooling of the 2010-12 La Niña event. Climate Dyn., 48, 597–617, https://doi.org/10.1007/s00382-016-3097-4.
Gao, C., X. R. Wu, and R.-H. Zhang, 2016: Testing a fourdimensional variational data assimilation method using an im-proved intermediate coupled model for ENSO analysis and prediction. Adv. Atmos. Sci., 33(7), 875–888, https://doi.org/10.1007/s00376-016-5249-1.
Huang, R. H., R. H. Zhang, and B. L. Yan, 2001: Dynamical effect of the zonal wind anomalies over the tropical western pacific on ENSO cycles. Science in China Series D: Earth Sciences, 44, 1089–1098, https://doi.org/10.1007/BF02906865.
Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 342 pp.
Liu, D. C., and J. Nocedal, 1989: On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45, 503–528, https://doi.org/10.1007/BF01589116.
Liu, Y., and H.-L. Ren, 2017: Improving ENSO prediction in CFSv2 with an analogue-based correction method. International Journal of Climatology, 37(15), https://doi.org/10.1002/joc.5142.
Liu, Y., Z. Liu, S. Zhang, R. Jacob, F. Lu, X. Rong, and S. Wu., 2014: Ensemble-based parameter estimation in a coupled general circulation model. J. Climate, 27, 7151–7162, https://doi.org/10.1175/JCLI-D-13-00406.1.
Lu, J. X., and W. W. Hsieh, 1998: On determining initial conditions and parameters in a simple coupled atmosphere–ocean model by adjoint data assimilation. Tellus A, 50, 534–544, https://doi.org/10.3402/tellusa.v50i4.14531.
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., W. S. Duan, and C. J. Wang, 2002: The predictability problems in numerical weather and climate prediction. Adv. Atmos. Sci., 19, 191–204, https://doi.org/10.1007/s00376-002-0016-x.
Mu, M., W. Duan, Q. Wang, and R. Zhang, 2010: An extension of conditional nonlinear optimal perturbation approach and its applications. Nonlinear Processes in Geophysics, 17, 211–220, https://doi.org/10.5194/npg-17-211-2010.
Peng, S.-Q., and L. Xie, 2006: Effect of determining initial conditions by four-dimensional variational data assimilation on storm surge forecasting. Ocean Modelling, 14, 1–18, https://doi.org/10.1016/j.ocemod.2006.03.005.
Peng, S. Q., Y. N. Li, and L. Xie, 2013: Adjusting the wind stress drag coefficient in storm surge forecasting using an adjoint technique. J. Atmos. Oceanic Technol., 30, 590–608, https://doi.org/10.1175/JTECH-D-12-00034.1.
Ren, H.-L., Y. Liu, F.-F. Jin, Y. P. Yan, and X. W. Liu, 2014: Application of the analogue-based correction of errors method in ENSO prediction. Atmospheric and Oceanic Science Letters, 7, 157–161, https://doi.org/10.3878/j.issn.1674-2834.13.0080.
Tao, L.-J., R.-H. Zhang, and C. Gao, 2017: Initial error-induced optimal perturbations in ENSO predictions, as derived from an intermediate coupled model. Adv. Atmos. Sci., 34, 791–803, https://doi.org/10.1007/s00376-017-6266-4.
Wang, B., X. L. Zou, and J. Zhu, 2000: Data assimilation and its applications. Proceedings of the National Academy of Sciences of the United States of America, 97(21), 11 143–11 144, https://doi.org/10.1073/pnas.97.21.11143.
Wu, X. R., S. Q. Zhang, Z. Y. Liu, A. Rosati, T. L. Delworth, and Y. Liu, 2012: Impact of geographic-dependent parameter optimization on climate estimation and prediction: Simulation with an intermediate coupled model. Mon. Wea. Rev., 140, 3956–3971, https://doi.org/10.1175/MWR-D-11-00298.1.
Wu, X. R., G. J, Han, S. Q. Zhang, and Z. Y. Liu, 2016: A study of the impact of parameter optimization on ENSO predictability with an intermediate coupled model. Climate Dyn., 46, 711–727, https://doi.org/10.1007/s00382-015-2608-z.
Xie, S.-P., C. Deser, G. A. Vecchi, J. Ma, H. Y. Teng, and A. T. Wittenberg, 2010: Global warming pattern formation: Sea surface temperature and rainfall. J. Climate, 23, 966–986, https://doi.org/10.1175/2009JCLI3329.1.
Zebiak, S. E., and M. A. Cane, 1987: A model El Niño-southern oscillation. Mon. Wea. Rev., 115, 2262–2278, https://doi.org/10.1175/1520-0493(1987)115<2262:AMENO>2.0.CO;2.
Zhang, R.-H., and C. Gao, 2016a: Role of subsurface entrainment temperature (Te) in the onset of El Niño events, as represented in an intermediate coupled model. Climate Dyn., 46, 1417–1435, https://doi.org/10.1007/s00382-015-2655-5.
Zhang, R.-H., and C. Gao, 2016b: The IOCAS intermediate coupled model (IOCAS ICM) and its real-time predictions of the 2015-2016 El Niño event. Science Bulletin, 61, 1061–1070, https://doi.org/10.1007/s11434-016-1064-4.
Zhang, R.-H., S. E. Zebiak, R. Kleeman, and N. Keenlyside, 2003: A new intermediate coupled model for El Niño simulation and prediction. Geophys. Res. Lett., 30, 2012, https://doi.org/0.1029/2003GL018010.
Zhang, R.-H., R. Kleeman, S. E. Zebiak, N. Keenlyside, and S. Raynaud, 2005a: An empirical parameterization of subsurface entrainment temperature for improved SST anomaly simulations in an intermediate ocean model. J. Climate, 18, 350–371, https://doi.org/10.1175/JCLI-3271.1.
Zhang, R.-H., F. Zheng, J. Zhu, and Z. G. Wang, 2013: A successful real-time forecast of the 2010-11 La Niña event. Scientific Reports, 3, 1108, https://doi.org/10.1038/srep01108.
Zhang, S., M. J. Harrison, A. T. Wittenberg, A. Rosati, J. L. Anderson, and V. Balaji, 2005b: Initialization of an ENSO forecast system using a parallelized ensemble filter. Mon. Wea. Rev., 133, 3176–3201, https://doi.org/10.1175/MWR3024.1.
Zhang, X. F., S. Q. Zhang, Z. Y. Liu, X. R. Wu, and G. J. Han, 2015: Parameter optimization in an intermediate coupled climate model with biased physics. J. Climate, 28, 1227–1247, https://doi.org/10.1175/JCLI-D-14-00348.1.
Zheng, F., J. Zhu, R.-H. Zhang, and G. Q. Zhou, 2006: Ensemble hindcasts of SST anomalies in the tropical Pacific using an intermediate coupled model. Geophys. Res. Lett., 33, L19604, https://doi.org/10.1029/2006GL026994.
Zheng, F., J. Zhu, H. Wang, and R.-H. Zhang, 2009: Ensemble hindcasts of ENSO events over the past 120 years using a large number of ensembles. Adv. Atmos. Sci., 26, 359–372, https://doi.org/10.1007/s00376-009-0359-7.