Kinetic energy spectrum analysis in a semiimplicit semi Lagrangian dynamical framework

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 5Δ x, 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.