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Convective overshooting tops reach above the normally horizontal flat layer of the convective system, a layer that should coincide with the tropopause. If we have such an overshooting top, does this mean we actually have the cloud reaching into the stratosphere, or does it mean that the convective system locally pushes the tropopause upward, while the convection is still limited to the (temporarily extended) troposphere? Both alternatives are given as unsourced answers to this identical Yahoo! Answers question, so I would like to see a referenced answer that specifically addresses the distinction between "air parcel reaches stratosphere" or "air parcel pushes tropopause upward".

(Note that this is not merely a matter of terminology, but should affect troposphere-stratosphere interaction in general)

Overshooting top
Source: NOAA

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    $\begingroup$ Is this somewhat of a definitional problem? I mean, the troposphere is the level at which the upward cooling gradient ceases, and the air is almost completely dry. Well if it's got cloud in it, it's not dry. The wikipedia tropopause article discusses overshooting tops, and provides a reference (that my library doesn't contain, so I can't really be of more help, sorry). $\endgroup$ – naught101 Apr 17 '14 at 8:07
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    $\begingroup$ @naught101 I guess what it distinguishes from a definitional problem is: what happens next?. Do particles transported upward along with the updraft then transfer horizontally into the stratosphere, or do will they rather be advected along the (locally extended?) tropopause, remaining in the troposhere? Maybe that is a different question, though. $\endgroup$ – gerrit Apr 17 '14 at 14:03
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This is an interesting question and I feel the best answer is "a little bit of both". Consider your picture without the overshooting top and just the anvil. The tropopause is clearly defined as the anvil spreads out horizontally against the static stability of the stratosphere.

Now let us consider a single parcel in the updraft, accelerating upward due to CAPE and hitting the tropopause with significant vertical momentum. This parcel is full of tropospheric air but makes an excursion into the stratosphere until the negative buoyancy it experiences reduces its vertical velocity to 0 (the top of the overshooting top) and then continues to accelerate downward to eventually oscillate about its equilibrium level (level of neutral buoyancy). For this single parcel I would argue that it is in the stratosphere.

Now consider all of the updraft parcels doing this. They are all transporting tropospheric air upward into the stratosphere -- inside that cloud it is all tropospheric air and toward the edges it is a mix of tropospheric and stratospheric air due to entrainment. The tropospheric air transported upward that mixes with the stratospheric air will reduce the static stability locally and may eventually modify the temperature gradient such that you consider the tropopause lifted.

I may run a simulation later with many grid levels around the tropopause and see what a model has to say. I'll edit with my results.

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