This study primarily seeks to examine sensitivities in convection-resolving numerical simulations of tropopause-overshooting convection and cross-tropopause transport to the choice of turbulence parameterization. A secondary focus is on sensitivity to the use of single- or double-moment microphysics parameterization. The model used is ICON and one of the turbulence parameterizations tested is the new 2TE scheme. Given the recency of the 2TE scheme and the need to more broadly evaluate it, I find the work to be timely and of interest to the upper troposphere lower stratosphere community. The study is focused and comprised of expected analyses based on similar approaches taken in prior studies. I found the graphics to be mostly well constructed. My comments are largely minor in nature and directed toward analysis design choices or explanation, but I anticipate the amount of work to address them being closer to major revision. 

General Comments:

1. There are a few places where the text lacks direction/completion and fails to make a point that I could follow. Examples include Lines 41-47, 234-239, . These elements should be revised for clarity.

2.  The analysis would benefit from a more thorough evaluation of overshooting using approaches with differing strengths & weaknesses. Namely, the use of the water vapor - longwave IR brightness temperature difference (BTD) for diagnosing overshooting is a bit underwhelming as it has been shown to poorly isolate convective overshoots (e.g., Bedka et al 2012; http://dx.doi.org/10.1175/JAMC-D-11-0131.1). While I appreciate the need to have an observation-based evaluation tool for the model, some alternative approaches could be explored and included, such as the temperature difference between the longwave brightness temperature and tropopause temperature.

3. The diagnosis of cross-tropopause transport could benefit from a few changes. First, it is stated that a cold-point tropopause definition is used, but such a choice is commonly problematic in the extratropics because it often leads to a biased tropopause identification. Figure 12 helped alleviate my concerns somewhat, but I would recommend an alternative choice such as a smoothed lapse-rate tropopause definition be used instead. In any case, diagnosing the tropopause and overshooting in a model simulation can be challenging because the tropopause is poorly defined in a convective core, such that a broader environmental reference tropopause height (e.g., a spatial average or median) may need to be used for reliable assessment. Second, only ice mass above the tropopause is considered for diagnosing cross-tropopause transport. Because the partitioning of water between the vapor and condensed phase can be quite sensitive to the choice of microphysics parameterization and mixing frequency, I would argue that both ice and water vapor distributions should be evaluated in Section 3.3. This could be done, for example, by examining total water instead (i.e., the sum of vapor and condensed mass) and differencing the result from the pre-convective tropopause-relative total water profile (which is likely all vapor).

4. It is not stated what type of CAPE is computed for Figure 10. I am surprised that the differences in vertical velocity amongst the simulations were small compared to the CAPE diagnosed. Thus, I am curious if what is shown is surface-based CAPE rather than most unstable CAPE. Thus, it would benefit the evaluation if both surface-based and most-unstable CAPE were evaluated to best appreciate the differences in the simulations and their sensitivity to turbulence parameterization. 

Specific Comments:

Line 6: insert ":" after "parameterizations" 

Line 8: Recommend changing "schemes" to "parameterizations" for consistency

Line 102: it is stated that a sponge layer spans 12.5 -- 20 km. Is this true? If so, I'd be very concerned about dynamics being unphysically dampened throughout the UTLS layer reached by the overshooting convection. Most prior studies performing similar simulations include a sponge layer in the top ~5 km of the model, well removed from layers impacted by the convection.

Figure 4, 6, & 7: it is impossible to know which lines correspond to the single-moment (SM) and double-moment (DM) simulations with the included key. Either the key should be updated or the caption should comprehensively describe the association. 

Line 293: "updrafts strenght" should be "updraft strength"

Review contained in supplement PDF.