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affect the transmission of energy and momentum, the winter westerly jet and summer easterly jet in
the upper middle atmosphere are obviously strengthened. Non-orographic gravity waves not only
affect the zonal circulation, but also meridional circulation. It is important to maintain the
temperature structure of the middle atmosphere due to the meridional circulation caused by the non-
orographic gravity waves, especially in the polar regions, because the solar sunshine in the winter is
disappeared, which leads to the decrease of the radiation heating in the polar regions, and the
dynamic heating caused by the meridional circulation is particularly important. Non-orographic
gravity waves caused by convective forcing have important effect on the generation and development
of tropical weather systems at low latitudes, such as Typhoons and Inter-tropical Convergence Zone.
Above all, an accurate and effective non-orographic gravity wave parameterization scheme is
introduced into the global numerical weather prediction operational model, it may improve the
simulation of the momentum transmission and Eliassen-Palm (E-P) flux adjustment caused by the
non-orographic gravity waves, and then improve the prediction of temperature and wind field in the
middle atmosphere. It has important research and operational value to improve the prediction
performance of the numerical weather prediction model.
2. Study on non-orographic gravity wave parametrization scheme
Non-orographic gravity waves are forced by dynamical motions such as convection, frontogenesis,
and jet stream activity. The formational mechanism of non-orographic gravity waves is more
complex. Because of the strong impact on the large scale circulation, so the non-orographic gravity
waves have become one of the parametrization physical processes in model which can't be ignored.
1964, Leovy [5] tried to study the effect of non-orographic gravity waves on the zonal average
circulation of the middle atmosphere by using constant Rayleigh friction and Newton cooling
coefficients, called the Rayleigh friction scheme. This method has serious systematic deviation in the
simulation of the middle atmosphere. The tropical circulation has an unrealistic tendency towards
radiation balance and cannot simulate the inter-annually variability of the tropical stratospheric
circulation. Most obviously, it can’t accurately describe the QBO and SAO.
1981, Lindzen [6] developed the first gravity wave parameterization scheme based on single wave
assumption. He regarded gravity waves as single disturbance that propagates energy upward in the
slow-changing background wind, but they don’t interact with each other. An analytic solution can be
obtained by using the dispersion relation WKB approximation. This scheme was first applied in a
middle atmosphere model [7, 8]. Numerical simulation results showed that the scheme was better
than the Rayleigh friction scheme, and it was possible to simulate the zonal wind overturning of the
middle atmosphere by using discrete spectrum to the waves with different phase speeds that was
unrealizable to Rayleigh friction scheme. In addition, this scheme can simulate the influence of the
non-orographic gravity waves generated by air flow on terrain, then reduces the systematic easterly
deviation of the zonal wind in the winter hemisphere, and contributes to perfect the simulation of the
troposphere jet.
1996, Warner et al [9] regarded the original non-orographic gravity waves of the tropopause or
low stratosphere as an upward propagating "launch" spectrum. Warner used 1D spectral equations to
study the propagation of gravity waves, the critical-level filtering and some nonlinear diffusion
mechanisms were used to solve the wave breakdown caused by the increase of amplitude as a
consequence of increasing height and decreasing density, and then he used the wave breakdown and
other nonlinear processes to disperse the conservation propagation of the waves. Finally, he used the
spectral saturation criterion to constrain the scheme, and the WM96 parameterization scheme of non-
orographic gravity waves was obtained. The WM96 scheme used a framework that includes non-
hydrostatic and rotational wave dynamics, thus the dispersion relation of gravity waves was more
reality. The scheme considered the seasonal variation in the energy function of launch spectrum, so
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