气象学报
氣象學報
기상학보
ACTA METEOROLOGICA SINICA
2008年
2期
143-157
,共15页
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
動能譜%GRAPES模式%半拉格朗日動力框架%最高有效分辨呎度%最大有效時間步長%中小呎度%Spinup
동능보%GRAPES모식%반랍격랑일동력광가%최고유효분변척도%최대유효시간보장%중소척도%Spinup
Kinetic energy spectrum%GRAPES model%Semi-Lagrangian dynamic framework%Highest effective resolution scale%Maximum effective time-step%Small-meso scale%Spin-up
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.
大量的觀測事實錶明自由大氣動能譜與波數之間滿足如下關繫:在大呎度區域滿足E∝k-3關繫,過渡到中呎度區域錶現為E∝k-5/3關繫.數值模式動能譜是測量模式動力框架的耗散的直接度量,而耗散對模式的性能有著重要影響,因此動能譜是研究和評估模式動力框架的非常規的有效方法.文中使用基于半隱式半拉格朗日動力框架的全毬/區域一體化模式GRAPES進行數值模擬試驗,然後計算GRAPES模式的動能譜併與實際觀測得到的大氣動能譜比較,得到GRAPES模式能夠很好地複製齣實際大氣動能譜的分佈特徵,包括從大呎度區域的E∝k-3關繫嚮中呎度的E∝k-5/3關繫的過渡特徵.併且髮現GRAPES模式存在最大有效時間步長,噹時間步長小于最大有效時間步長時,模式動能譜隨時間步長增大而逐漸衰減;噹時間步長大于最大有效時間步長時,模式動能譜隨時間步長增大而虛假增長.同時通過與實際大氣動能譜比較,髮現模式動能譜在5Δx波長附近開始明顯衰減,因此將5Δx波長定義為GRAPES模式的最高有效分辨呎度;噹空間分辨率提高與時間步長等相協調時,中小呎度模式動能譜嚮中小呎度延伸而更接近實際大氣動能譜;噹空間分辨率提高與時間步長等不相協調時,中小呎度模式動能譜存在較大誤差,相應的大呎度模式動能譜亦存在較大誤差.此外,時間步長對模式spin up過程有著重要的影響,較小時間步長時,spin up過程能夠很好髮展齣閤理的動能譜結構,在物理空間上錶現為模式能夠在spin up時間內生成和髮展齣閤理的中小呎度繫統;而較大時間步長時,spin up過程很難髮展齣閤理的動能譜結構,在物理空間上錶現為模式未能在spin up時間內生成和髮展齣閤理的中小呎度繫統.最後,GRAPES模式動能譜與WRF模式動能譜具有一緻性,GRAPES全毬中期模式能夠完美地模擬齣大呎度的E∝k-3動能譜特徵.綜上所述,本文通過研究GRAPES模式動力框架的動能譜得到瞭一些有意義的結果,為進一步研究、完善、優化和應用模式提供瞭科學的指導,可見動能譜是評估模式動力框架的有效方法.
대량적관측사실표명자유대기동능보여파수지간만족여하관계:재대척도구역만족E∝k-3관계,과도도중척도구역표현위E∝k-5/3관계.수치모식동능보시측량모식동력광가적모산적직접도량,이모산대모식적성능유착중요영향,인차동능보시연구화평고모식동력광가적비상규적유효방법.문중사용기우반은식반랍격랑일동력광가적전구/구역일체화모식GRAPES진행수치모의시험,연후계산GRAPES모식적동능보병여실제관측득도적대기동능보비교,득도GRAPES모식능구흔호지복제출실제대기동능보적분포특정,포괄종대척도구역적E∝k-3관계향중척도적E∝k-5/3관계적과도특정.병차발현GRAPES모식존재최대유효시간보장,당시간보장소우최대유효시간보장시,모식동능보수시간보장증대이축점쇠감;당시간보장대우최대유효시간보장시,모식동능보수시간보장증대이허가증장.동시통과여실제대기동능보비교,발현모식동능보재5Δx파장부근개시명현쇠감,인차장5Δx파장정의위GRAPES모식적최고유효분변척도;당공간분변솔제고여시간보장등상협조시,중소척도모식동능보향중소척도연신이경접근실제대기동능보;당공간분변솔제고여시간보장등불상협조시,중소척도모식동능보존재교대오차,상응적대척도모식동능보역존재교대오차.차외,시간보장대모식spin up과정유착중요적영향,교소시간보장시,spin up과정능구흔호발전출합리적동능보결구,재물리공간상표현위모식능구재spin up시간내생성화발전출합리적중소척도계통;이교대시간보장시,spin up과정흔난발전출합리적동능보결구,재물리공간상표현위모식미능재spin up시간내생성화발전출합리적중소척도계통.최후,GRAPES모식동능보여WRF모식동능보구유일치성,GRAPES전구중기모식능구완미지모의출대척도적E∝k-3동능보특정.종상소술,본문통과연구GRAPES모식동력광가적동능보득도료일사유의의적결과,위진일보연구、완선、우화화응용모식제공료과학적지도,가견동능보시평고모식동력광가적유효방법.
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.
