An Overview of the Dynamic Framework in Earth-System Model and Its Well-Posedness

Abstract

The well-posedness of the dynamic framework in earth-system model (ESM for short) is a common issue in earth sciences and mathematics. In this paper, the authors first introduce the research history and fundamental roles of the well-posedness of the dynamic framework in the ESM, emphasizing the three core components of ESM, i.e., the atmospheric general circulation model (AGCM for short), land-surface model (LSM for short) and oceanic general circulation model (OGCM for short) and their couplings. Then, some research advances made by their own research group are outlined. Finally, future research prospects are discussed.

Keywords

Earth-System model / Dynamic framework / Well-posedness

References

[1] Zeng Q C, Lin Z H. Recent progress on the earth system dynamical model and its numerical simulations. Advances in Earth Science, 2010, 25(1): 1-6 (in Chinese)

[2] Wang B, Zhou T J, Yu Y Q A perspective on earth system model development. Acta Meteorologien Sinica, 2008, 66(6): 857-869 (in Chinese)

[3] Wang H J, Zhu J, Pu Y F. The earth system simulation. SCIENTIA SINICA Physica, Mechanica & Astronomica, 2014, 44(10): 1116-1126 in Chinese)

[4] Zeng Q C. Mathematical and Physical Foundations of Numerical Weather Prediction, 1979, Beijing: Science Press (in Chinese)

[5] Zeng, Q. C., Some Numerical Ocean-atmosphere Coupling Models, Proceedings of the First International Symposium on Integrated Global Ocean Monitoring, Tallin, 1983.

[6] Liang, X. Z., Design and Climate Simulation of IAP GCM, Doctoral Dissertation, Institute of Atmospheric Physics, Chinese Academy of Sciences, 1986 (in chinese).

[7] Zeng Q C, Zhang X H. Available energy-conserving schemes for primitive equations of spherical baroclinic atmosphere. Chinese Journal of Atmospheric Sciences, 1987, 11(27): 121-142 (in Chinese)

[8] Zeng, Q. C., Zhang, X. H., Liang, X. Z., et al., Documention of IAP two-level atmospheric general circulation model, TRO44.DOE/ER/60341-H1, 1989.

[9] Zhang X H. Dynamical framework of IAP Nine-level atmospheric general circulation model. Advances in Atmospheric Sciences, 1990, 7(1): 66-77

[10] Zeng Q C, Yuan C G, Wang W Q Experiments in numerical extraseasonal prediction of climate anomalies. Chinese Journal of Atmospheric Sciences, 1990, 14(1): 10-25 (in Chinese)

[11] Bi, S. Q., Climate simulation efficacy of IAP nine-level atmospheric general circulation model, Doctoral Dissertation, Institute of Atmospheric Physics, Chinese Academy of Sciences, 1993 (in chinese).

[12] Liang X Z. Descripton of a nine-level grid point atmospheric general circulation model. Advances in Atmospheric Sciences, 1996, 13(3): 269-298

[13] Zuo R T, Zhang M, Zhang D L Designing and climatic numerical modeling of 21-level AGCM (IAP AGCM-III) part I dynamical framework. Chinese Journal of Atmospheric Sciences, 2004, 28(5): 659-674 (in Chinese)

[14] Lin Z H, Wang H J, Zhou G Q Recent advances in dynamical extra-seasonal to annual climate prediction at IAP/CAS. Advances in Atmospheric Sciences, 2004, 21(3): 456-466

[15] Zhang M, Zuo R T, Zeng Q C. IAP Nine-level Atmospheric General Circulation Model, 2007, Beijing: China Meteorological Press (in chinese)

[16] Zhang X H, Liang X Z. A numerical world ocean general circulation model. Advances in Atmospheric Sciences, 1989, 6(1): 44-61

[17] Zhang R H, Endoh M. A free surface general circulation model for the tropical Pacific Ocean. Journal of Geophysical Research, 1992, 97: 11237-11255

[18] Zhang R H. A free surface Tropical Pacific circulation model and its applications. Science in China (Series B), 1995, 25(2): 204 (in chinese)

[19] Zeng Q C, Lin Z H, Zhou G Q. Dynamical Extraseasonal Climate Prediction System IAP DCP-II. Chinese Journal of Atmospheric Sciences, 2003, 27(3): 289-303 Beijing

[20] Lin Z H, Li X, Zhao Y An improved short-term climate prediction system and its application to the extraseasonal prediction of rainfall anomaly in China for 1998. Climatic and Environment Research, 1998, 3(4): 339-348 (in Chinese)

[21] Lin Z H, Li X, Zhou G Q Extra seasonal prediction of summer rainfall anomaly over China with improved IAPPS SCA. Chinese Journal of Atmospheric Sciences, 1999, 23(4): 351-366 (in Chinese)

[22] Lin Z H, Zhao Y, Zhou G Q Prediction of Summer Climate Anomaly over China for 1999 and Its Verification. Climatic and Environment Research, 2000, 5(2): 97-108 (in Chinese)

[23] Lin Z H, Zhao Y, Zhou G Q Numerical prediction of summer precipitation anomalies over China in 2000. Progress in Natural Science: Materials International, 2002, 12(7): 771-774 (in Chinese)

[24] Zeng Q C, Zhou G Q, Pu Y F Research on the earth system dynamic model and some related numerical simulations. Chinese Journal of Atmospheric Sciences, 2008, 32(4): 653-690 (in Chinese)

[25] Zhang H, Zhang M H, Jin J B Description and climate simulation performance of CAS-ESM version 2. Journal of Advances in Modeling Earth Systems, 2020, 12(12): e2020MS002210

[26] Lions J L, Temam R, Wang S H. New formulations of the primitive equations of atmosphere and applications. Nonlinearity, 1992, 5(2): 237-288

[27] Lions J L, Temam R, Wang S H. Odean J. Models of the coupled atmosphere and ocean (CAO I & CAO II). Computational Mechanics Advance, 1993, Amsterdam: Elsevier 5-54 1

[28] Lions J L, Temam R, Wang S H. Mathematical theory for the coupled atmosphere-ocean models (CAO III). Journal de Mathématiques Pures et Appliquées, 1995, 74(2): 105-163

[29] Zeng Q C. A Mathematic Model of Climate Dynamics Suitable for Modern Mathematical Analysis. Chinese Journal of Atmospheric Sciences, 1998, 22(4): 408-417 (in Chinese)

[30] Wu Y H, Mu M, Zeng Q C Weak solutions to a model ofclimate dynamics. Nonlinear Analysis: Real World Applications, 2001, 2(4): 507-521

[31] Zeng, Q. C. and Mu, M., On the design of compact and internally consistent model of climate system dynamics, An invited lecture presented at the 1st International Symposium of CAS-TWAS-WMO Forum on Physico-Mathematical Problems Related to Climate Modelling and Prediction, Beijing, 2001.

[32] Huang H Y, Guo B L. The Existence of Weak Solutions and the Trajectory Attractors to the Model of Climate Dynamics. Acta Mathematica Scientia, 2007, 27A(6): 1098-1110 (in Chinese)

[33] Guillén-González F, Masmoudi N, Rodríguez-Bellido M. Anisotropic estimates and strong solutions for the primitive equations. Differential And Integral Equations, 2001, 14(11): 1381-1408

[34] Temam R, Ziane M. Some mathematical problems in geophysical fluid dynamics. Handbook of Mathematical Fluid Dynamics, 2004, Amsterdam: North Holland Publishing Company 535-657 III

[35] Cao C S, Titi E S. Global well-posedness of the three-dimensional viscous primitive equations of large-scale ocean and atmospheredynamics. Annals of Mathematics, 2007, 166: 245-267

[36] Guo B L, Huang D W. Existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics. Journal of Mathematical Physics, 2006, 47(8): 237-254

[37] Guo B L, Huang D W. On the 3D viscous primitive equations of the large-scale atmosphere. Acta Mathematica Scientia, 2009, 29(04): 846-866

[38] Guo B L, Huang D W. Existence of the universal attractor for the 3-D viscous primitive equations of large-scale moist atmosphere. Journal of Differential Equations, 2011, 251(3): 457-491

[39] Cao C S, Titi E S. Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity. Archive for Rational Mechanics and Analysis, 2014, 214(1): 35-76

[40] Cao C S, Titi E S. Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. Journal of Differential Equations, 2014, 257(11): 4108-4132

[41] Cao C S, Titi E S. Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. Communications on Pure and Applied Mathematics, 2016, 69(8): 1492-1531

[42] Hittmeir S, Klein R, Li J K Global well-posednessed for the primitive equations coupled to nonlinear moisture dynamics with phase changes. Nonlinearity, 2020, 33(7): 3206-3236

[43] Huang A, Kukavica I, Zelati C The primitive equations of the atmosphere in presence of vapor saturation. Nonlinearity, 2014, 28(3): 625-668

[44] Zelati C, Temam R. The atmosphere equation of water vapor with saturation. Bollettino dell’Unione Matematica Italiana, 2012, 5: 309-336

[45] Zelati C, Fremond M, Temam R The equation of the atmosphere with humidity and saturation: Uniqueness and physical bounds. Physical D, 2013, 264: 49-65

[46] Lian R X, Zeng Q C, Jin J B. Stability of weak solutions to climate dynamics model with effects of topography and non-constant external force. SCIENCE CHINA Earth Sciences, 2018, 61(1): 47-59

[47] Lian R X, Zeng Q C. Existence of a strong solution and trajectory attractor for a climate dynamics model with topography effects. Journal of Mathematical Analysis and Applications, 2018, 458(1): 628-675

[48] Lian R X, Ma J Q. Existence of a strong solution to moist atmospheric equations with the effects of topography. Boundary Value Problems, 2020, 2020(1): 1-34

[49] Ma J Q, Lian R X, Zeng Q C. Local well-posedness of strong solution to a climate dynamic model with phase transformation of water vapor. Journal of Mathematical Physics, 2022, 63(5): 051504

[50] Jin J B, Zeng Q C, Wu L Formulation of a new ocean salinity boundary condition and impact on the simulated climate of an oceanic general circulation model. SCIENCE CHINA Earth Sciences, 2017, 60(3): 491-500

[51] Zhang Y L, Zhang B R, Lian R X. The Existence of Global Weak Solutions to Ocean Dynamics Equations with New Salinity Boundary Condition. Journal of LanZhou University of Arts And Science, 2021, 35(1): 7-13 (in Chinese)

[52] Lian R X, Zhang Y L, Huang L. The stability of global weak solutions to the ocean dynamics equations with topography effects. Journal of Henan Normal University, 2021, 49(03): 18-26 (in Chinese)

[53] Zhang B R, Lian R X. The well-posedness analysis of weak solution to moist atmospheric equations with stochastic external forces. Journal of Xiamen University, 2022, 61(2): 174-181 (in Chinese)