It is a wide discussion. Generally speaking, trends in the upper atmosphere are mostly negative, except in the mesopause/lower thermosphere region.

Concerning troposphere, global warming should rise the tropopause. Why? Well, you know that a major controversy exists about whether upper tropospheric satellite data has shown warming. It’s difficult to measure the effects due to the fact that measurement combines upper troposphere, which is likely warming, with lower stratosphere, which is likely cooling. Then, with the increasing of global warming, stratosphere is cooling, due to increased thermal emission by CO2 there. There are also changes in the lapse rate, due to the increase of moisture content and this will imply more heating aloft.

At the end there is an increase of tropopause height which likely influences the position of the jet stream and the strength and scale of storms in extratropics and tropics.

It is a wide discussion. Generally speaking, trends in the upper atmosphere are mostly negative, except in the mesopause/lower thermosphere region.

Concerning troposphere, global warming should rise the tropopause. Why? Well, you know that a major controversy exists about whether upper tropospheric satellite data has shown warming. It’s difficult to measure the effects due to the fact that measurement combines upper troposphere, which is likely warming, with lower stratosphere, which is likely cooling. Then, with the increasing of global warming, stratosphere is cooling, due to increased thermal emission by CO2 there. There are also changes in the lapse rate, due to the increase of moisture content and this will imply more heating aloft.

At the end there is an increase of tropopause height which likely influences the position of the jet stream and the strength and scale of storms in extratropics and tropics.

Raffaele is correct :- carbon dioxide warms the surface and the troposphere, and the warming increases with height in the tropics so that it maximizes in the upper tropical troposphere.  However, it simultaneously cools the stratosphere and mesosphere.  There is obviously then a point in between with no warming or cooling and this occurs near the tropopause.  This warming of the lower atmosphere and cooling of the stratosphere and mesosphere can be explained by radiative arguments, as carbon dioxide is a net emitter of long wave radiation at higher altitudes.  The cooling increases with height and is around a degree or so per decade at the stratopause - much faster then the warming rate below.

Note though that this is not true of all greenhouse gases and CFCs for example warm the whole depth of the atmosphere as they absorb/emit at different wavelengths. 

I would recommend the basic climate change book by John Houghton which contains an explanation of these effects.  You should also try working through the 2 layer model of the atmosphere, assuming blackbody radiation and ozone heating  in the upper layer to represent the stratosphere and this basic result can be derived analytically.

Best regards

Adam

Observations are different from simulations. Modeling, and the theory also, indicates an increased warming with height in the tropics, with the largest warming in the upper troposphere, but this has not been observed from sounding and satellite even if the observations have been adjusted for inhomogeneities and other biases. In mainland China, we found that the warming in middle and upper troposphere over the period 1961-2004 is much smaller than that in the surface based on sounding observations regardless of the usage of inhomogeneity-adjusted data. It is my opinion that the issue of the inconsistence between observations and simulations is still to be settled.

There is an early online release of a paper by Cook and Vizy arguing that "the surface temperature of the Sahara Desert has increased at a rate that is 2-4 times greater than that of the tropical mean temperature over the 34-year time period." http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00230.1?af=R

This seems to me to be further evidence that the models are incorrectly predicting that the upper troposphere will warm as a result of AGW.

One possible link between climate change (e.g. Globle warming) and upper-air temperatures is the large scale circulation variability (e.g. Blocking, NAO, AO, IPO... ...). Most of them are deep  convective processes which can infulence the upper-air temperatures. And the decadal and inter-decadal variabilities of the large scale circulation can be affected by globle warming or other climate change. I guess there may exist a correlation between climate change and upper-air temperature through large scale circulation processes. 

I think we can't ignore the influence a "thinner" ozone layer might have in the modified temperature gradients due to climate change. A warming trend from the extra  UV radiation might affect all other gradients.