In this work we present the first parameterizations of the global occurrence rate and chemical influence of Blue Jets, a type of Transient Luminous Event (TLE) taking place in the stratospheric region above thunderclouds. These parameterizations are directly coupled with five different lightning parameterizations implemented in the Whole Atmosphere Community Climate Model (WACCM4). We have obtained a maximum Blue Jet global occurrence rate of about 0.9 BJ per minute. The geographical occurrence of Blue Jets is closely related to the chosen lightning parameterization. Some previously developed local chemical models of Blue Jets predicted an important influence onto the stratospheric concentration of N$_2$O, NO$_x$ and O$_3$. We have used these results together with our global implementations of Blue Jets in WACCM4 to estimate their global chemical influence in the atmosphere. According to our results, Blue Jets can inject about 3.8 Tg N$_2$O-N yr$^{-1}$ and 0.07 Tg NO-N yr$^{-1}$ near the stratosphere, where N$_2$O-N and NO-N stand for the mass of nitrogen atoms in N$_2$O and NO molecules, respectively. These production rates of N$_2$O and NO$_x$ could have a direct impact on, for example, the acidity of rainwater or the greenhouse effect. We have found that Blue Jets could also slightly contribute to the depletion of stratospheric ozone. In particular, we have estimated that the maximum difference in the concentration of O$_3$ at 30 km of altitude between simulations with and without Blue Jets can be about -5 \% in Equatorial and Polar regions.
