Abstract: A wave action density has been derived from a linearized Boussinesq system for inertia gravity waves by use of WKBJ method. The characteristics of the evolution of the waves have been investigted based on the principle of the conservation of the wave action density defined in this paper. The results showed that the developing waves are characterized by the decrease of the horizontal wave length L and the increase of the vertical wave length D. Once the horizontal wave length L has been reduced to a value less than a critical wave length Lc the wave tends to break down and convectve activity may be excited as a result of the breakdown of the waves. The environment conditions favoring the development of the waves are also the conditions favoring the break down of waves and the occurence of convective activity. The effect of the environment condition(varying stratification) on the development of the inertia gravity waves has been discussed in relation to the spatial scale changes of the waves.