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Frontiers of Earth Science

ISSN 2095-0195

ISSN 2095-0209(Online)

CN 11-5982/P

Postal Subscription Code 80-963

2018 Impact Factor: 1.205

Front Earth Sci    2013, Vol. 7 Issue (3) : 341-350    https://doi.org/10.1007/s11707-013-0378-7
RESEARCH ARTICLE
Improving energetics in an ideal baroclinic instability case with a Physical Conserving Fidelity model
Qi ZHONG1(), Qing ZHONG2, Ziniu XIAO1
1. China Meteorological Administration Training Centre, Beijing 100081, China; 2. Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 100029, China
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Abstract

To improve the energetics in the life cycle of an ideal baroclinic instability case, we develop a Physical Conserving Fidelity model (F-model), and we compare the simulations from the F-model to those of the traditional global spectral semi-implicit model (control model). The results for spectral kinetic energy and its budget indicate different performances at smaller scales in the two models. A two-way energy flow emerges in the generation and rapid growth stage of the baroclinic disturbance in the F-model. However, only a downscale mechanism dominates in the control model. In the F-model, the meso- and smaller scales are energized initially, and then an active upscale nonlinear cascade occurs. Thus, disturbances at prior scales are forced by both downscale and upscale energy cascades and by conversion from potential energy. An analysis of the eddy kinetic energy budget also shows remarkable enhancement of the energy conversion rate in the F-model. As a result, characteristics of the ideal baroclinic wave are greatly improved in the F-model, in terms of both intensity and time of formation.

Keywords energy conversion      energy cascade      ideal baroclinic instability      high order total energy conservation      time-split scheme     
Corresponding Author(s): ZHONG Qi,Email:zhongq@cma.gov.cn   
Issue Date: 05 September 2013
 Cite this article:   
Qi ZHONG,Qing ZHONG,Ziniu XIAO. Improving energetics in an ideal baroclinic instability case with a Physical Conserving Fidelity model[J]. Front Earth Sci, 2013, 7(3): 341-350.
 URL:  
https://academic.hep.com.cn/fesci/EN/10.1007/s11707-013-0378-7
https://academic.hep.com.cn/fesci/EN/Y2013/V7/I3/341
Fig.1  Evolution of the baroclinic wave from day 4 until day 10: surface pressure. (Abscissa presents longitude and ordinate presents latitude.). The left column is the control model, and the right column is the F-model.
Fig.2  Evolution of the baroclinic wave from day 4 until day 10: temperature at 850 hPa. (Abscissa presents longitude and ordinate presents latitude). The left column is the control model, and the right column is the F-model.
Fig.3  Vorticity norms as a function of time; (a) vorticity and (b) vorticity gradient for the F-Model (solid) and the Control model (dot-dash).
Fig.4  Upper panel: spectral-time distribution of kinetic energy for the (a) Control model and (c) F-model. Bottom panel: spectral-time distribution of the time difference of kinetic energy for the (b) Control model and (d) F-model.
Fig.5  Terms of kinetic energy total horizontal wavenumber for the 850 hPa layer. The shaded regions represent negative values. The upper panel shows (1/E)dE/dt forced by advection term for (a) the control model and (b) the F-model. The bottom panel shows (1/Ek)dEk/dt forced by for (c) the control model and (d) the F-model.
Fig.6  The vertical distribution of budget terms of eddy kinetic energy at the beginning of rapid development of the baroclinic wave (6 day in the F-model and 8 day in the control model). Unit: J·m·d. The upper panel shows a comparison of the F-model and the control model; the bottom panel shows the results of the control model.
1 Bierdel L, Friederichs P, Bentzien S (2012). Spatial kinetic energy spectra in the convection-permitting limited-area NWP model COSMO-DE. Meteorologische Zeitschrift , 21(3): 245–258
2 Bourke W (1974). A multi-level spectral model. I. Formulation and hemispheric integrations. Mon Weather Rev , 102(10): 687–701
3 Charney J G (1947). The dynamics of long waves in a baroclinic westerly current. J Meteorol , 4(5): 135–163
4 Collins W D, Rasch, P J, Boville B A (2004). Description of the NCAR Community Atmosphere Model (CAM3.0). NCAR/TN-464+STR. NCAR Technical Note
5 Eady E T (1949). Long waves and cyclone waves. Tellus , 1(3): 33–52
6 Giraldo F X, Rosmond T E (2004). A scalable spectral element Eulerian atmospheric model (SEEAM) for NWP: dynamical core tests. Mon Weather Rev , 132(1): 133–153
7 Hoskins B J, Simmons A J (1975). A multi-layer spectral model and the semi-implicit method. Q J R Meteorol Soc , 101(3): 637–655
8 Jablonowski C, Williamson D L (2006). A baroclinic instability test case for atmospheric model dynamical cores. Q J R Meteorol Soc , 132(10): 2943–2975
9 Ji L R, Chen J B, Zhang D M (1990).A Global Spectral Model Including Diabatic Physical Processes and Its Preliminary Forecast Experiment. Collected Paper on Medium-Range Numerical Weather Forecast Research (II) . Beijing: China Meteorological Press, 27–40 (in Chinese)
10 Koshyk J N, Hamilton K (2001). The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere-stratosphere-mesosphere GCM. J Atmos Sci , 58(4): 299–348
11 Lauritzen P H, Jablonowski C, Taylor M A, Nair R D (2010). Rotated versions of the Jablonowski steady-state and Baroclinic wave test cases: a dynamical core intercomparison. J Adv Model Earth Syst , 2(15):1–34
12 Leith C E, Kraichnan R H (1972). Predictability of turbulent flows. J Atmos Sci , 29(6): 1041–1052
13 Lorenz E N (1963). Deterministic non-periodic flow. J Atmos Sci , 20(2): 130–141
14 Ngan K, Eperon G E (2012). Middle atmosphere predictability in a numerical weather prediction model: revisiting the inverse error cascade. Q J R Meteorol Soc , 138(666): 1366–1378
15 Polvani L M, Scott R K, Thomas S J (2004). Numerically converged solutions of the global primitive equations for testing the dynamical cores at atmospheric GCMs. Mon Weather Rev , 132(11): 2539–2552
16 Shields C A, Bailey D A, Danabasoglu G, Jochum M, Kiehl J T, Levis S, Park S (2012). The Low-Resolution CCSM4. J Clim , 25(12): 3993–4014
17 Skamarock W C (2004). Evaluating mesoscale NWP models using kinetic energy spectra. Mon Weather Rev , 132(12): 3019–3032
18 Skamarock W C, Klemp J B, Duda M G, Fowler L D, Park S H, Ringler T D (2012). A multiscale nonhydrostatic atmospheric model using centroidal voronoi tesselations and C-Grid staggering. Mon Weather Rev , 140(9): 3090–3105
19 Smagorinsky J, Manabe S, Holloway J L Jr (1965). Numerical results from a nine-level general circulation model of the atmosphere. Mon Weather Rev , 93(12): 727–767
20 Talbot C E,Bou-Zeid, Smith J(2012). Nested mesoscale large-eddy simulations with WRF: performance in real test cases. J Hydrometeorol , 13(5): 1421–1441
21 Ullrich P A, Jablonowski C (2012b). MCore: a non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods. J Comput Phys , 231(15): 5078–5108
22 Ullrich P, Jablonowski C (2012a). Operator-split runge-kutta-rosenbrock methods for nonhydrostatic atmospheric models. Mon Weather Rev , 140(4): 1257–1284
23 Vallgren A, Deusebio E, Lindborg E (2011). Possible explanation of the atmospheric kinetic and potential energy spectra. Phys Rev Lett , 107(26): 268501-1-268501-4
24 Williamson D L, Olson J G, Jablonowski z(2009). Two dynamical core formulation flaws exposed by a baroclinic instability test case. Mon Weather Rev , 137(2): 790–796
25 Zhang D M, Li J L, Ji L R (1995). A global spectral model and test of its performace. Adv Atmos Sci , 12(1): 67–78
26 Zhong Q (1992). Theory of perfect square conservative scheme and its preliminary application. CAS/JSC Working Group of Numerical Experiment. 1992 Report No.8. Publication of World Meteorology Organization . Washington DC, USA: 3–26
27 Zhong Q (1993). An inverse compensation formulation principle of long effective fidelity scheme of evolution problems and its preliminary applications. Chin Sci Bull , 38(13): 1101–1107
28 Zhong Q (1999). The formulation of fidelity schemes of physical conservation laws and improvements on a traditional spectral model of baroclinic primitive equations for numerical predictions. Acta Meteorologica Sinica , 13(2): 225–248
29 Zhong Q, Chen J T, Sun Z L (2002). Elimination of computational systemaic errors and improvements of weather and climate system models. Adv Atmos Sci , 19(6): 1103–1112
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