The Research On The Kinetic Energy Spectrum Of Semi-lmplicit Semi-Lagrangian Dynamical Core

The dissipation in the dynamical framework of numerical model has significant impact on the performance of the numerical model, and the kinetic energy spectrum (KES) is a direct measure of the dissipation in the dynamical core of numerical model. Using KES to evaluate numerical model is a non-traditional effective method. There are more and more applications of using KES to evaluate numerical model around the world. But, the systematical work on the KES of meso-scale regional model is little, and the work of using KES to evaluate the Semi-Implicit Semi-Lagrangian (SISL) regional grid model is rare, particularly in China. The past work primarily forcus on the impact of numerical dissipation and spatial resolution on the KES, but the work of the evolvement of the KES during the SPINUP process is litte, especially there is almost non work on the impack of timestep on the KES. The major objective of this paper is to investigate the characteristic and behavior of the SISL dynamical core using KES.Using the KES calculate method and spectral filter based on 2D-DCT algorithm, this paper calculates and investigates the KES of GRAPES model by a lot of numerical competitive experiments in the following aspects: the impact of timestep on the KES, the relationship between spectral characteristic of the impact of timestep on the KES and the mesoscale and smaller structure in physical space, the impact of timestep on the KES without physical procedure, the impact of spatial resolution on the KES, the relationship between spectral characteristic of the impact of spatial resolution on the KES and the mesoscale and smaller structure in physical space, the evolvement of the KES during SPINUP process, the relationship between spectral characteristic of the evolvement of the KES during SPINUP process and the generation, development and die of mesoscale and smaller structure in physical space during SPINUP process, the comparison between the KES derived from GRAPES model and that derived from WRF model, and the characteristic of the KES derived from GRAPES global medium-range model. Finally, we draw the following fundamental conclusions:A lot of results from observational analysis showed that the atmospheric KES in the free troposphere and lower stratosphere possess a wavenumber dependence of k ?3 for large scale, and a transition to a dependence of k ?5/3 in mesoscale and smaller scales. We found that GRAPES model can reproduce the characteristic of the atmospheric KES very well, including the transition to k ?5/3 dependence in mesoscale and smaller scales.The impact of timestep on the KES shows that GRAPES model has a largest effective timestep. When the timestep is smaller than the largest effective timestep, the KES decays as the timestep increases. When the timestep is larger than the largest effective timestep, the KES unphysical builds up as the timestep increases. Furthermore, the impact of timestep on the KES without physical process shows that when the timestep is smaller than the largest effective timestep, the KES does not decay as the timestep increases and when the timestep is larger than the largest effective timestep, the KES unphysical builds up as the timestep increases. The comparison the impact of timestep on the KES derived from the model had physical procedure and that derived from the model had non physical procedure shows that the decay of the KES is primarily due to the error of physical parameter procedure when timestep increases, while the unphysical build up of the KES is caused by the SISL dynamical core. Finally, we get the illustration of the KES varies as timestep and the relationship between the largest effective timestep and the spatial resolution.The impact of spatial resolution on the KES shows that the KES decays significantly at the wavelength about 5 x . Obviously, the KES decaying at this truncate wavelength is caused by the dissipation implicit in the SISL dynamical core. So, we define the wavelength 5 x as the highest effective resolution of GRAPES model. Summarily, on one hand, when the timestep is smaller than the largest effective timestep, as the spatial resolution increases, the KES extents to mesoscale and smaller and closes to the Lindborg reference curve gradually, but the KES in large scale keep close to the Lindborg reference curve. On the other hand, when the timestep is larger than the largest effective timestep, even the spatial resolution can resolve the mesoscale and smaller, but the KES already appears unphysical builds up, the model can not properly even unphysically generate, develop and die mesoscale and smaller system, so the error in the KES in mesoscale and smaller become large. This error will grow and upscale cascade to large scale, that is, the error in mesoscale and smaller will contaminate large scale, destroys the resolvable large scale system and results in large error in the KES in large scale.The evolvement of the KES during SPINUP process shows that: When the timestep is small, the KES develops gradually, especially in mesoscale and smaller, the KES close to the Lindborg reference curve as SPINUP time increases; in general, the KES develops fully at about 9 ~12 hour which indicates that the SPINUP time is about 9 ~12 hours. When the timestep is large, even SPINUP time approach 12 hour, the KES has not develop properly, especially in mesoscale and smaller, the KES deviates from the Lindborg reference curve very much, indicates that the model lack of kinetic energy in mesoscale and small significantly.Furthermore, using the meso-scale horizontal wind derived from spectral filter, this paper systematically analyses the relationship between the impact of timestep, spatial resolution and SPINUP process on the KES and the mesoscale and smaller structure in physical space. Its is found that the more the KES close the real atmosphereic KES, the better meso scale amd smaller structure is reproduced, reversely the worse meso scale amd smaller structure is reproduced. The relationship indicates the characteristics in spectral space and in physical space are consistent.In addition, the comparison of the KES between GRAPES and WRF shows that both are fundamentaly consistent, and the highest effective resolution of GRAPES model is about 5 x , while that of WRF model is about 5 x ( ARM ) ~ 7 x ( NMM ); that is, there is no distinct difference between Semi-Lagrangian and Eulerian dynamical core in term of KES. And the KES derived from GRAPES global medium-range model shows that it can reproduce the dependence of k ?3 for large scale very well, but can not reproduce the dependence of k ?3 in mesoscale.In summary, using KES to evaluate numerical model is a non-traditional effective method. But, the systematical work on the KES of meso-scale regional model is little, and the work of using KES to evaluate the SISL regional grid model is rare, particularly in China. This paper investigated the KES derived from the GRAPES model which based on SISL scheme and achieved the conclusions such as the largest effective timestep, the highest effective resolution, and the impact of timestep, spactial resolution, physical procedure and SPINUP process on the KES. These conclusions have innovation and important applied value and scientific significance, provide a scientific guide to research, improve and apply the GRAPES model, and also have scientific significance on the research on high resolution multiscale unified model, on the probability of numerical model, and on the maintain mechanic of the k ?5/3 distribution of the atmospheric KES in meso scale and smaller, on the meso-scale energy transfer and transport mechanic, on the dynamic drives the meso-scale system, on improving the understanding of dynamical process of meso-scale atmosphere.