Review on Developments and Improvements in Vertical Coordinates for Numerical Prediction Models

  • Rui CHENG ,
  • Rucong YU ,
  • Youping XU ,
  • Jing HUANG ,
  • Xiaojing SHEN
Expand
  • 1. State Key Laboratory of Geo-Information Engineering,Xi’an 710054,Shaanxi,China
    2. Chinese Meteorological Administration,Beijing 100081,China
    3. Beijing Institute of Applied Meteorology,Beijing 100029,China

Received date: 2022-10-08

  Revised date: 2023-05-06

  Online published: 2024-01-11

Abstract

As we know, the atmosphere is mainly characterized by its baroclinicity and stratification.The vertical coordinate is crucial for the description of 3D atmospheric motion and thermal-dynamic condition of the static atmosphere.Furthermore, the vertical coordinate is foundation of numerical prediction model construction.Different atmospheric dynamic cores, such as height, pressure and potential temperature-based frames are usually established depending on different vertical coordinate modes.The development of vertical coordinates always contributes to major version update and considerable upgrade of the numerical prediction model.In this paper, we briefly review the history of vertical coordinates for the numerical model.Then, we mainly demonstrate the design art for hybrid vertical coordinates in some operational non-hydrostatic models at home and abroad.Additionally, this paper presents some suggestions on how to select model vertical resolution and prediction variables vertical distribution style.Finally, the progress on arrangement and application of the vertical coordinate for numerical prediction models is summarized and its development tendency is also illustrated.

Cite this article

Rui CHENG , Rucong YU , Youping XU , Jing HUANG , Xiaojing SHEN . Review on Developments and Improvements in Vertical Coordinates for Numerical Prediction Models[J]. Plateau Meteorology, 2024 , 43(1) : 16 -27 . DOI: 10.7522/j.issn.1000-0534.2023.00042

References

null
Aligo E A Gallus W A J Segal M2009.On the impact of WRF model vertical grid resolution on midwest summer rainfall forecasts[J].Weather and Forecasting24(2): 575-594.DOI: https: //doi.org/10.1175/2008WAF2007101.1 .
null
Arakawa A Moorthi S1988.Baroclinic instability in vertically discrete systems[J].Journal of the Atmospheric Science45(11): 1688-1708.
null
Charney J G Phillips N A1953.Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flows [J].Journal of Atmospheric Sciences10(2): 71-99.
null
Chen X Natalia A Bram V L, et al, 2013.A control-volume model of the compressible Euler equations with a vertical Lagrangian coordinate[J].Monthly Weather Review 141(7): 2526-2544.
null
Corby G A Gilchrist A Newson R L1972.A general circulation model of the atmosphere suitable for long period integrations[J].Quarterly Journal of the Royal Meteorological Society98(418): 809-832.
null
Dudhia J1993.A nonhydrostatic version of the Penn state-NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front[J].Monthly Weather Review121(5): 1493-1513.DOI: 10.1175/1520-0493(1993)121<1493: ANVOTP>2.0.CO; 2 .
null
Egger J1972.Incorporation of steep mountains into numerical forecasting models[J].Tellus, 24: 324-335.
null
Eliassen A1949.The Quasi-Static equations of motion with pressure as independent variable[J].Geofysiske Publikasjoner17(3): 1-44.
null
Erdun H1997.Two-dimensional atmospheric flow modelling by using Schwarz-Christoffel transformation over complex topography[D].Istanbul: Istanbul Technical University.
null
Gal-Chen T Somerville R1975.On the use of a coordinate transformation for the solution of the Navier-Stokes Equations[J].Journal of Computational Physics17(2): 209-228.
null
Gallus W A J R Ran?i? M1996.A non-hydrostatic version of the NMC’s regional eta model[J].Quarterly Journal of the Royal Meteorological Society, 122: 495-513.
null
Gallus W A Joseph J R Klemp B2000.Behavior of flow over step orography[J].Monthly Weather Review, 128: 1153-1164.
null
Gentry M S Lackmann G M2009.Sensitivity of simulated tropical cyclone structure and intensity to horizontal resolution[J].Monthly Weather Review138(3): 688-704.DOI: 1175/2009MWR2976.1 .
null
Ishida J2007.Development of a hybrid terrain-following vertical coordinate for JMA non-hydrostatic model[J].Monthly Weather Review, 134: 1266-1298.
null
Janjic Z I Gerrity J P Nickovic S2001.An alternative approach to nonhydrostatic modeling[J].Monthly Weather Review129(5): 1164-1178.DOI: 1175/1520-0493(2001)129<1164: AAATNM>2.0.CO; 2 .
null
Janjic Z I Black T L Rogers E, et al, 2003.The NCEP nonhydrostatic meso model (NMM) and first experiences with its applications[C].EGS/EGU/AGU Joint Assembly, Nice, France, 6-11 April.
null
Kasahara A Washington W M1967.Ncar global general circulation model of the atmosphere[J].Monthly Weather Review95(7): 389-402.DOI: 1175/1520-0493(1967)095<0389: NGGCMO>2.3.CO; 2 .
null
Klemp J B2011.A terrain-following coordinate with smoothed coordinate surfaces[J].Monthly Weather Review139(7): 2163-2169.DOI: 10.1175/MWR-D-10-05046.1 .
null
Laprise R1992.The euler equations of motion with hydrostatic pressure as an independent variable[J].Monthly Weather Review120(1): 197-207.DOI: 10.1175/1520-0493(1992)120<0197: TEEOMW>2.0.CO; 2 .
null
Li C Chen D H Li X L, et al, 2015.Effects of terrain-following vertical coordinates on high-resolution NWP simulations[J].Journal of Meteorological Research29(3): 432-445.DOI: 10.1007/s13351-015-4212-x .
null
Lindzen R S Fox-Robinovitz M S1989.Consistent vertical and horizontal resolution[J].Monthly Weather Review117(11): 2575-2583.DOI: 10.1175/1520-0493(1989)117<2575: CVAHR>2.0.CO; 2 .
null
Lin S J Rusty B Chen J H, et al, 2016.A brief overview of the FV3 dynamical core[DB/OL].DOI: https: //www.weather.gov/media/sti/nggps/20160127_FV3_overview_discription.pdf .
null
Mesinger F1984.A blocking technique for representation of mountains in atmospheric models[J].44: 195-202.
null
Mesinger F1988.The step-mountain coordinate: model description and performance for cases of alpine lee cyclogenesis and for a case of an Appalachian redevelopment[J].Monthly Weather Review, 116: 1493-1518.DOI: 10.1175/1520-0493(1988)116<1493: TSMCMD>2.0.CO; 2 .
null
Mesinger F Chou S C Gomes J, et al, 2012.An upgraded version of the Eta model[J].Meteorology and Atmospheric Physics, 116: 63-79.
null
Mesinger F Veljovic K2017.Eta vs.sigma: review of past results, Gallus-Klemp test, and large-scale wind skill in ensemble experiments[J].Meteorology and Atmospheric Physics, 129: 573-593.DOI: 10.1007/s00703-016-0496-3 .
null
Park S H Joseph B K Kim J H2019.Hybrid mass coordinate in WRF-ARW and its impact on upper-level turbulence forecasting[J].Monthly Weather Review, 147: 971-985.
null
Pecnick M J Keyser D1989.The effect of spatial resolution on the simulation of upper tropospheric frontgenesis using a sigma-coordinate primitive equation model[J].Meteorology and Atmospheric Physics, 40: 137-149.
null
Persson P O G Warner T T1991.Model generation of spurious gravity waves due to inconsistency of the vertical and horizontal resolution[J].Monthly Weather Review119(4): 917-935.
null
Phillips N A1957.A coordinate system having some special advantages for numerical forecasting[J].Journal of the Atmospheric Sciences, 14: 184-185.
null
Pielke R A1984.Parameterization-averaged subgrid scale fluxes-sciencedirect[J].Mesoscale Meteorological Modeling, 128-186.
null
Li Y Y Wang B Wang D, et al, 2014.An orthogonal terrain-following coordinate and its preliminary tests using 2-D idealized advection experiments[J].Geoscientific Model Development, 7: 1767-1778.
null
Richardson L F1922.Weather prediction by numerical process[M].London: Cambridge University Press, 236.
null
Ruti P M Di R D Gualdi S2006.Impact of increased vertical resolution on simulation of tropical climate[J].Theoretical and Applied Climatology85(1-2): 61-80.
null
Sangster W F1960.A method of representing the horizontal pressure force without reduction of station pressures to sea level[J].Journal of the Atmospheric Sciences, 17: 166-176.
null
Schar C Leuenberger D Fuhrer O, et al, 2002.A new terrain-following vertical coordinate formulation for atmospheric prediction models[J].Monthly Weather Review, 130: 2459-2480.
null
Smagorinsky J Strickler R F Sangster W E, et al, 1967.Prediction experiments with a general circulation model[M].Paper presented at Dynamics of Large Scale Atmospheric Processes, Moscow, USSR, 70-134.
null
Steppeler J2002.Nonhydrostatic atmospheric modeling using a z-coordinate representation[J].Monthly Weather Review, 130: 2143-2149.
null
Steppeler J Park S H Dobler A2013.Forecasts covering one month using a cut-cell model[J].Geoscientific Model Development, 6: 875-882.
null
Skamarock W C Klemp J B Dudhia J, et al, 2005.A description of the advanced research WRF version 2[R].Boulder, Colorado: National Center for Atmospheric Research.
null
Untch A Hortal M2004.A finite-element scheme for the vertical discretizatdis of the semi-lagrangian version of the ECMWF forecast model[J].Quarterly Journal of the Royal Meteorological Society, 130: 1505-1530.
null
Walko R L Tremback C J Hertenstein R F A1995.The regional atmospheric modeling system, version 3b, user’s guide[R].Fort Collins, CO: ASTER Division, Mission Research Corporation.
null
Wang Y Q2007.A multiply nested, movable mesh, fully compressible, nonhydrostatic tropical cyclone model—TCM4: model description and development of asymmetries without explicit asymmetric forcing [J].Meteorology and Atmospheric Physics, 97: 93-116.DOI: 10.1007/s00703-006-0246-z .
null
Westerhuis S Fuhrer O2021.A locally smoothed terrain-following vertical coordinate to improve the simulation of fog and low stratus in numerical weather prediction models[J].Journal of Advances in Modeling Earth Systems, 13: e2020MS002437.
null
Xue M Droegemeier K K Wong V2000.The advanced regional prediction system (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction mode1.Part I: model dynamics and verification[J].Meteorology and Atmospheric Physics, 75: 161-193.
null
Xue M Droegemeier K K Wong V, et al, 1995.Advanced regional prediction system (ARPS) version 4.0 user’s guide[R].Oklahoma: Center for Analysis and Prediction of Storms.
null
Yang J H Song J Q Wu J P, et al, 2015.A high-order vertical discretization method for a semi-implicit mass-based non-hydrostatic kernel[J].Quarterly Journal of the Royal Meteorological Society141(692): 2880-2885.
null
Zhang D L Wang X X2003.Dependence of hurricane intensity and structures on vertical resolution and time-up size[J].Advances in Atmospheric Sciences, 20: 711-725.
null
陈得圆, 王磊, 李谢辉, 等, 2022.四川盆地西部一次典型连续夜雨的数值模拟[J].高原气象41(1): 216-225.DOI: 10.7522/j.issn.1000-0534.2019.00109.Chen D Y
null
Wang L Li X H, et al, 2022.Numerical simulation of a typical continuous night rain processin the western Sichuan Basin[J].Plateau Meteorology41(1): 216-225.DOI: 10.7522/j.issn.1000-0534.2019.00109 .
null
陈豫英, 苏洋, 杨银, 等, 2021.贺兰山东麓极端暴雨的中尺度特征[J].高原气象40(1): 47-60.DOI: 10.7522/j.issn.1000-0534.2020.00012.Chen Y Y
null
Su Y Yang Y, et al, 2021.The mesoscale characteristics of extreme rainstorm in the eastern region of Helan Mountain[J].Plateau Meteorology40(1): 47-60.DOI: 10.7522/j.issn.1000-0534.2020.00012 .
null
程锐, 宇如聪, 徐幼平, 等, 2018.非静力 AREM 设计及其数值模拟, Part I: 非静力框架设计[J].大气科学42(6): 1286-1296.
null
Cheng R Yu R C Xu Y P, et al, 2018.Design of non-hydrostatic AREM model and its numerical simulation.Part I: design of non-hydrostatic dynamic core[J].Chinese Journal of Atmospheric Sciences(in Chinese)42(6): 1286-1296.
null
程锐, 宇如聪, 徐幼平, 等, 2019.非静力AREM设计及其数值模 拟, Part II: 数值模拟试验[J].大气科学43(1): 1-12.
null
Cheng R Yu R C Xu Y P, et al, 2019.Design of non-hydrostatic AREM model and its numerical simulation.Part II: numerical simulation experiments[J].Chinese Journal of Atmospheric Sciences(in Chinese)43(1): 1-12.
null
程锐, 宇如聪, 徐幼平, 等, 2022.一个基于Eta垂直坐标的新WRF动力框架及其数值试验[J].大气科学46(2): 237-250.
null
Cheng R Yu R C Xu Y P, et al, 2022.A new eta-coordinate-based WRF dynamic core and its numerical experiments[J]. Chinese Journal of Atmospheric Sciences(in Chinese)46(2): 237-250.
null
邓莲堂, 周嘉林, 2012.不同垂直分辨率对台风数值模拟影响的敏感性试验[J].气象与减灾研究35(1): 17-20.
null
Deng L T Zhou J L2012.A sensitivity test of different vertical resolution effect on numerical simulation of typhoon[J].Meteorology and Disaster Reduction Research35(1): 17-20.
null
何光碧, 彭俊, 屠妮妮, 2015.基于高分辨率地形数据的模式地形构造与数值试验[J].高原气象34(4): 910-922.DOI: 10.7522/j.issn.1000-0534.2014.00022.He G B
null
Peng J Tu N N2015.Terrain construction and experiment for numerical model based on high resolution terrain data[J].Plateau Meteorology34(4): 910-922.DOI: 10.7522/j.issn.1000-0534. 2014. 00022 .
null
胡江林, 王盘兴, 2007.地形跟随坐标下的中尺度模式气压梯度力计算误差分析及其改进方案[J].大气科学31(1): 109-118.
null
Hu J L Wang P X2007.The errors of pressure gradient force in high-resolution meso-scale model with terrain-following coordinate and its revised scheme[J].Chinese Journal of Atmospheric Sciences31(1): 109-118.
null
纪立人, 陈嘉滨, 张道民, 等, 2005.数值预报模式动力框架发展的若干问题综述[J].大气科学29(1): 120-130.
null
Ji L R Chen J B Zhang D M, et al, 2005.Review of some numerical aspects of the dynamic framework of NWP Model[J].Chinese Journal of Atmospheric Sciences29(1): 120-130.
null
孔祥伟, 张君霞, 杨晓军, 等, 2022.西北地区东部强降水大尺度数值模式预报空间偏差分析[J].高原气象41(5): 1109-1123.DOI: 10.7522/j.issn.1000-0534.2021.00041.Kong X W
null
Zhang J X Yang X J, et al, 2022.Spatial deviation analysis of heavy precipitation forecast of large scale numerical weather prediction in eastern northwest China[J].Plateau Meteorology41(5): 1109-1123.DOI: 10.7522/j.issn.1000-0534.2021.00041 .
null
李超, 陈德辉, 李兴良, 等, 2019.一种改进的平缓-混合地形追随坐标在GRAPES中尺度模式中的应用研究[J].气象学报77(6): 1041-1052.
null
Li C Chen D H Li X L, et al, 2019.A study on application of an improved terrain-following vertical coordinate in the GRAPES model[J].Acta Meteorologica Sinica77(6): 1041-1052.
null
李兴良, 陈德辉, 2005.非静力中尺度高分辨率模式模拟中的垂直坐标影响研究[J].气象学报63(2): 161-172.
null
Li X L Chen D H2005.Impact study of the vertical coordinate on a non-hydrostatic mesoscale high-resolution model[J].Acta Meteorologica Sinica63(2): 161-172.
null
廖洞贤, 朱艳秋, 1992.关于平流方程的水平和垂直分辨率之间的协调[J].计算物理9(S2): 5237-5258.
null
Liao D X Zhu Y Q1992.Concerning the consistent vertical and horizontal resolution for the advection equation[J].Chinese Journal of Computational Physics9(S2): 5237-5258.
null
钱永甫, 颜宏, 骆启仁, 等, 1978.一个有大地形影响的初始方程数值预报模式[J].大气科学2(2): 91-102.
null
Qian Y F Yan H Luo Q R, et al, 1978.An initial equation numerical prediction model with large topographic effects[J].Chinese Journal of Atmospheric Sciences2(2): 91-102.
null
钱永甫, 1985.一个考虑地形的五层原始方程模式[J].高原气象4(2): 1-28.
null
Qian Y F1985.A five-layer primitive equation model considering terrain[J].Plateau Meteorology4(2): 1-28.
null
钱永甫, 周天军, 1995.有地形模式中气压梯度力误差扣除法[J].高原气象14(1): 1-9.
null
Qian Y F Zhou T J1995.Modelling tests of the error subtraction scheme for the pressure gradient force in models with topography[J].Plateau Meteorology14(1): 1-9.
null
汤剑平, 赵鸣, 苏炳凯, 2006.分辨率对区域气候极端事件模拟的影响[J].气象学报64(4): 432-442.
null
Tang J P Zhao M Su B K2006.Effects of model resolution on the simulation of regionally climatic exterme events[J].Acta Meteorologica Sinica64(4): 432-442.
null
屠妮妮, 陈静, 何光碧, 2012.切比雪夫多项式在模式地形平滑中的应用研究[J].高原气象31(1): 47-56.
null
Tu N N Chen J He G B2012.Research on application of chebyshev polynomial filtering method in smooth topography of GRAPES Model[J].Plateau Meteorology31(1): 47-56.
null
薛纪善, 陈德辉, 2008.数值预报系统 GRAPES的科学设计与应用[M].北京: 科学出版社, 300-330.Xue J S, Chen D H, 2008.Scientific design and application of numerical prediction system GRAPES[M].Beijing: Science Press.
null
宇如聪, 1989.陡峭地形有限区域数值预报模式设计[J].大气科学13(2): 139-149.
null
Yu R C1989.Design of numerical prediction model for limited area of steep terrain[J].Chinese Journal of Atmospheric Sciences13(2): 139-149.
null
宇如聪, 1992.考虑陡峭地形的有限区域数值预报模式的设计及其对雅安天漏的数值预报试验[D].北京: 中国科学院大气物理研究所.YU R C, 1992.Design of a finite area numerical prediction model considering steep terrain and numerical prediction experiment for Ya 'an sky leak[D].Beijing: Institute of Atmospheric Physics, Chinese Academy of Sciences.
null
宇如聪, 1994.一个η坐标有限区域数值预报模式对1993年中国汛期降水的实时预报试验[J].大气科学18(3): 284-292.
null
Yu R C1994.A test for numerical weather prediction of real-time for China flood season precipitation in 1993 by a regional η-coordinate mode[J].Chinese Journal of Atmospheric Sciences18(3): 284-292.
null
宇如聪, 徐幼平, 2004.AREM及其对2003年汛期降水的模拟[J].气象学报62(6): 715-724.
null
Yu R C Xu Y P2004.AREM and its simulations on the daily rainfall in summer in 2003[J].Acta Meteorologica Sinica62(6): 715-724.
null
张旭, 黄伟, 陈葆德, 2015.一种新型高度地形追随坐标在GRAPES区域模式中的实现: 理想试验与比较研究[J].气象学报73(2): 331-340.
null
Zhang X Huang W Chen B D2015.Implementation of the Klemp height-based terrain-following coordinate in the GRAPES regional model: Idealized tests and inter-comparison[J].Acta Meteorologica Sinica73(2): 331-340.
null
曾庆存, 1963.大气运动的特征参数和动力学方程[J].气象学报33(4): 472-83.
null
Zeng Q C1963.Characteristic parameters and dynamic equations of atmospheric motion[J].Acta Meteorologica Sinica33(4): 472-83.
null
曾庆存, 1979.数值天气预报的数学物理基础[M].北京: 科学出版社.Zeng Q C, 1979.Mathematical physical basis of numerical weather prediction[M].Beijing: Science Press.
null
赵鸣, 方娟, 1996. P-σ混合坐标原始方程模式的改进和试验[J].高原气象15(2): 195-203.
null
Zhao M Fang J1996.The improvement and experiments of primitive equation model with mixed P-σ Coordinates[J].Plateau Meteorology15(2): 195-203.
null
赵宗慈, 罗勇, 1999.区域气候模式在东亚地区的应用研究—垂直 分辨率与侧边界对夏季季风降水影响研究[J].大气科学23(5): 522-532.
null
Zhao Z C Luo Y1999.Investigations of application for the regional climate model over east Asia[J].Chinese Journal of Atmospheric Sciences23(5): 522-532.
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