This paper described a dynamic framework for atmospheric spectral model. In order to improve pressure gradient force and gradients of surface pressure and temperature,a reference stratified atmospheric temperature and a reference surface pressure were introduced into the governing equations. The vertical profile of the reference atmospheric temperature approximately represents that of the US middle-latitude standard atmosphere within the troposphere and stratosphere. The reference surface pressure is a function of surface terrain geopotential and close to surface pressure observation. The prognostic variables for temperature and the surface pressure are replaced by their perturbations from the reference atmospheric temperature or the reference surface pressure, respectively. The numerical algorithms of the explicit time difference scheme for vorticity and the semi-implicit time difference scheme for divergence, perturbation temperature, and perturbation surface pressure equation were given in details.

In order to evaluate its advantage to the commonly used dynamic framework for atmospheric spectral model, the modified numerical algorithm was utilized in the Community Atmospheric Model version 3 (CAM3) in the National Center for Atmospheric research (NCAR) and replaced the spectral Eulerian dynamical core but retained all the model physics. The simulations with the forcing of 1970-2000 observed monthly mean sea surface temperature and sea-ice concentration data by CAM3 and its dynamic-modified model named as CAM3D at T42 resolution were done. The CAM3 and CAM3D simulated climates averaged for the last 30 years run of 1971-2000 were analyzed and compared with the ERA-40 reanalyses for the same period. The statistical significance for the difference between CAM3 and CAM3D is tested. The results showed that there was an obvious improvement, especially in middle-latitude tropospheric temperature, wind, and moisture and during the first 10-year of run. The improvement in the vicinity of the Tibetan Plateau which is one of major orographic obstacles is also tested. The use of the modified dynamical scheme could reduce the biases of their climate simulations.