| 半隐式半拉格朗日动力框架的动能谱分析 |
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| 引用本文： | 郑永骏,金之雁,陈德辉.半隐式半拉格朗日动力框架的动能谱分析[J].气象学报,2008,66(2):143-157. |
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| 作者姓名： | 郑永骏 金之雁 陈德辉 |
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| 作者单位： | 中国气象科学研究院灾害天气国家重点实验室,北京,100081 |
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| 基金项目： | 国家自然科学基金
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国家科技部支撑项目
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国家重点基础研究发展计划(973计划) |
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| 摘 要： | 大量的观测事实表明自由大气动能谱与波数之间满足如下关系:在大尺度区域满足E∝k-3关系,过渡到中尺度区域表现为E∝k-5/3关系.数值模式动能谱是测量模式动力框架的耗散的直接度量,而耗散对模式的性能有着重要影响,因此动能谱是研究和评估模式动力框架的非常规的有效方法.文中使用基于半隐式半拉格朗日动力框架的全球/区域一体化模式GRAPES进行数值模拟试验,然后计算GRAPES模式的动能谱并与实际观测得到的大气动能谱比较,得到GRAPES模式能够很好地复制出实际大气动能谱的分布特征,包括从大尺度区域的E∝k-3关系向中尺度的E∝k-5/3关系的过渡特征.并且发现GRAPES模式存在最大有效时间步长,当时间步长小于最大有效时间步长时,模式动能谱随时间步长增大而逐渐衰减;当时间步长大于最大有效时间步长时,模式动能谱随时间步长增大而虚假增长.同时通过与实际大气动能谱比较,发现模式动能谱在5Δx波长附近开始明显衰减,因此将5Δx波长定义为GRAPES模式的最高有效分辨尺度;当空间分辨率提高与时间步长等相协调时,中小尺度模式动能谱向中小尺度延伸而更接近实际大气动能谱;当空间分辨率提高与时间步长等不相协调时,中小尺度模式动能谱存在较大误差,相应的大尺度模式动能谱亦存在较大误差.此外,时间步长对模式spin up过程有着重要的影响,较小时间步长时,spin up过程能够很好发展出合理的动能谱结构,在物理空间上表现为模式能够在spin up时间内生成和发展出合理的中小尺度系统;而较大时间步长时,spin up过程很难发展出合理的动能谱结构,在物理空间上表现为模式未能在spin up时间内生成和发展出合理的中小尺度系统.最后,GRAPES模式动能谱与WRF模式动能谱具有一致性,GRAPES全球中期模式能够完美地模拟出大尺度的E∝k-3动能谱特征.综上所述,本文通过研究GRAPES模式动力框架的动能谱得到了一些有意义的结果,为进一步研究、完善、优化和应用模式提供了科学的指导,可见动能谱是评估模式动力框架的有效方法.
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| 关 键 词： | 动能谱 GRAPES模式 半拉格朗日动力框架 最高有效分辨尺度 最大有效时间步长 中小尺度 Spinup Kinetic energy spectrum GRAPES model Semi-Lagrangian dynamic framework Highest effective resolution scale Maximum effective time-step Small-meso scale Spin-up |
| 收稿时间： | 9/6/2006 12:00:00 AM |
| 修稿时间： | 2006年9月6日 |
Kinetic energy spectrum analysis in a semi implicit semi Lagrangian dynamical framework |
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| ZHENG Yongjun,JIN Zhiyan,CHEN Dehui.Kinetic energy spectrum analysis in a semi implicit semi Lagrangian dynamical framework[J].Acta Meteorologica Sinica,2008,66(2):143-157. |
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| Authors: | ZHENG Yongjun JIN Zhiyan CHEN Dehui |
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| Abstract: | A large number of observational analyses have shown that the atmospheric kinetic energy spectrum in the free troposphere and lower stratosphere possesses a wavenumber dependence of k-3 for large scale systems, and a transition to a k-5/3 dependence for small- meso scale systems. The kinetic energy spectrum derived from a numerical model is a direct measure of the dissipation in the dynamical framework of the numerical model, and the dissipation has significant impact on the performance of the numerical model, so using kinetic energy spectrum to evaluate the numerical model is a non-traditional effective method. The global/regional unified model GRAPES, based on a Semi-implicit Semi-Lagrangian dynamical framework, is evaluated by verifying the simulated kinetic energy spectrum against the atmospheric kinetic energy spectrum derived from the actual atmospheric observations. It is found that the GRAPES model is able to reproduce the observed atmospheric kinetic energy spectrum, including the transition to k-5/3 dependence in the small-meso scale. Meanwhile, there exists a maximum effective time-step, when the time-step is smaller/larger than the maximum effective time-step, the simulated kinetic energy spectrum gradually decays/unphysically grows as the time-step increases. And compared with the observational atmospheric kinetic energy spectrum, the simulated kinetic energy spectrum decays rapidly at the wavelength of about 5Δx, so we define the 5Δx wavelength as the highest effective resolution of the GRAPES model. Also, when the increasing of spatial resolution is coordinated with the time-step and other factors such as physical parameterization processes, the simulated kinetic energy spectrum in the small-meso scale approaches closely the observed atmospheric kinetic energy spectrum, otherwise, the simulated kinetic energy spectrum in the small-meso scale has larger errors, and correspondingly its kinetic energy spectrum in the large scale also has larger errors. In addition, the time-step has significant impact on the spin-up process, when a smaller time-step is used, the model can develop well the reasonable kinetic energy spectral structure in the spectral space and can generate and develop reasonable small-meso scale systems in the physical space during the spin-up period, while a larger time-step is used, the opposite is true. Finally, it is found that the kinetic energy spectra derived from GRAPES and WRF are consistent each other, and the global medium-range model GRAPES can simulate perfectly the characteristic of E∝k-3 for the large scale kinetic energy spectrum. In summary, this investigation on the simulated kinetic energy spectrum of the GRAPES model reveals several meaningful results, which provide a scientific guidance for further research, improvement and application of the GRAPES model, and also demonstrates the effectiveness of kinetic energy spectrum in evaluating numerical models. |
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| Keywords: | Kinetic energy spectrum GRAPES model Semi-Lagrangian dynamic framework Highest effective resolution scale Maximum effective time-step Small-meso scale Spin-up |
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