Don't have much idea about it but i do understand that lots of water vapor mixing takes place at tropopause. This mixing affects Monsoon too.......

Hope this case study may be useful to you: http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493%281976%29104%3C0756%3ATRBETT%3E2.0.CO%3B2

Thanks.... Do you know some recent research paper about tropopause height.

Dr Tim Ball wrote this article a while ago which discusses tropopause height

http://drtimball.com/2012/static-climate-models-in-a-virtually-unknown-dynamic-atmosphere/

The zonal and vertical modulation of Kelvin waves by the background flow may help explain the origin of the very cold air over the western tropical Pacific, which is known to cause freeze-drying of tropospheric air en route to the stratosphere.

http://journals.ametsoc.org/doi/abs/10.1175/2007JAS2466.1

Rossby waves in the northern hemisphere due to orographic effects propagate up to the tropopause. These Rossby waves can ‘break’ leading to ‘Sudden Stratospheric Warming’ events which can temporarily halt or even reverse the polar vortex.

http://www.atmos.umd.edu/~seminar/past_files/misc/Norton1994.pdf

and do not forget critical role that is played by deep tropical convection in delivering water vapor to high altitudes in the troposphere - to the extent that DTC may be increasing (a project I am working on) as a result of SST increases, the water vapor content is increasing (this statement can be somewhat supported by data) which might result in the change of scale height or physical height of the 500 mb geopotential surface (and I said might ...)

The tropopause is connected to water vapour in several ways, some of which are far from fully understood but water vapour both influences and is influenced by the tropopause:

The height of the tropopause is connected to the temperature structure of the troposphere. In the tropics, this is closely related to the amount of deep convection which releases latent heat in the upper troposphere as water vapour condenses. This link results in the radiative-convective equilibrium model of the tropical atmosphere: http://www.gfdl.noaa.gov/bibliography/related_files/sm6701.pdf

Above the convection zone, air continues to rise slowly through the tropical tropopause and much of the water vapour is then freeze dried out due to the very low temperatures. Fluctuations in tropical tropopause temperature thereby cause variations in water vapour concentration entering the stratosphere and give rise to the tropical 'tape recorder' effect: http://onlinelibrary.wiley.com/doi/10.1029/95JD03422/abstract

The consequences of the height increase could be dramatic even in France: Hail like hell.

On the 4th of july, in Brigueil Correze (16) in France, was shelled by hailstones the size of "tennis balls" or "oranges". From witnesses it was hell and the mayor who was shell shocked said it was just like a war zone after bombing. It destroyed roofs, cars, even security glass. From records this phenomenon has never been witnesses before.

http://www.meteo-paris.com/actualites/forts-orages-avec-grele-et-rafales-ce-debut-juillet-02-juillet-2018.html

In the range of foolish remedy to protect crops against hailstones, for about two decades french farmers have been shooting rockets in the sky loaded with silver salts to reduce their size. The escalation of such interventions is futile on a large scale, does worse than good, and accelerates pollution and the climate disruption.

Is there any current research on measuring or simulating the evolution of concentration of vapor pressure with respect to global warming?

The CYGNUS satellite recently launched by NASA is able to eventually make these measurements over tropical waters. The same concern exists there it terms of deep tropical convection, accelerated water vapor transport, and increasingly large thunderstorm complexes. There are models on the moist convection water budget (see K. Emanuel) and there soon may be some actual measurements to better constrain these models.

I add the same problem.

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I downloaded your article on Consumerism. Thank you for sharing

Indeed, It is a large cause of the global warming.

Is there any rough model that just simulate an average water vapor thickness and density distribution in the atmosphere with regards to the increase of temperature due to solar radiation and human activities (evaporation, energy, radiation heat and microwaves) around the globe without taking into account local effects (microclimates)?

Short answer for now

First one needs to establish that atmospheric water vapor content, in fact, is increasing. While there is some evidence for this, this is a difficult measure. More on this later when I find the time

At what altitude these large 150mm>> 17mm hailstones may have formed?

What mechanism of nucleation and growth may apply? I suppose that there have been some over supercooling at much much higher altitude than that the common freezing point line utilized in some current models. (see enclosed picture) for small hails.

What kinetic of growth and melting could have applied?