We thank the referee for useful comments. We have addressed them all in
the revised version. The changes to the manuscript are marked in blue.

> 1) A linear stability analysis similar to that in Kemel et al (2013) may be
> carried out to understand why in the current stratification, the fastest
> growing mode is of a much smaller horizontal wavelength compared to the
> previous isothermal case. It should be clarified whether the initial
> stratification (shown in Figure 1) is an equilibrium solution (radiative
> equilibrium and hydrostatic equilibrium) of the mean-field equations (this
> is not made clear in the paper), and how this stratification and the
> established profiles of the effective magnetic pressure shown in Figure 7
> affect the growth rates of the instability and the dominant modes. Such
> analysis may help to understand why NEMPI is much harder to excite in the
> present case and why the modes excited are of smaller horizontal scales.

We have now clarified explicitly that Fig.1 shows the hydrostatic
equilibrium solution obtained by solving the equations in only one
dimension. Performing a detailed linear stability analysis
is not easy for a model with general optically thin and thick radiative
transfer. However, to get closer to the answer, we have now solved
intermediate models where we consider an optically thick model with a
boundary condition at the location that corresponds to the tau=1 surface.
This models shows structures near the surface, but they still have a
small horizontal scale. We explain this difference by the fact that in the
optically thin model there is high entropy material in the upper layers
that gets pulled down by NEMPI and counteracts NEMPI in the top layers,
whereas in the optically thick model, this layer is absent. Next, we present
an isentropic model with otherwise the same properties to demonstrate that
buoyancy effects are enhanced when entropy evolution is included. This
is related to continued entropy loss of descending structures in models
with radiation (compressed structures head adiabatically and lose entropy
by radiation). This occurs on small diffusive length scales.

We return to this new and surprising interpretation in the conclusions,
where we also explain why this will be different in a model where
convection is included.

> 2) Previous DNS simulations by Kemel et al. (2013) with an isothermal
> layer, and the DNS and mean-field simulations of Losada et al.(2014) in a
> polytropic layer are 3D. Here the mean-field simulations are 2D. How the
> limitation of the 2D Cartesian geometry might have affected the results and
> the growth of the instability should be discussed.

Simulations by Losada et al. (2012) have shown moderate differences in
the excitation conditions, but less so in the typical length scales that
are being excited. One might expect even smaller structures in 2-D than
in 3-D. We have therefore not pursued this extension of our models,
but have instead added a reference to this earlier work.

> 3) In the introduction: "On the other hand, radiation also leads to the
> equilibration of temperature differences between neighboring fluid
> elements and reduces therefore all buoyancy effects, ….. This has
> potentially detrimental effects on the instability that need to be
> assessed". This seems contradicting the results to be explained in this
> study, since previous isothermal models, which correspond to the extreme
> case where temperature variations are all removed, are showing stronger
> NEMPI than the present case.

We agree with the referee, and this realization contributed now to our
revised interpretation presented at the end of the paper in our new
Section 4.

> 4) In the second to last paragraph of section 3.3: “For large values of k,
> turbulent diffusive damping, which scales quadratically with k, becomes
> dominant. Thus, the instability is unable to develop large length scales.”
> The second sentence seems contradicting the first. It is not clear.

Again, we agree with the referee that this was a wrong interpretation which
has now been removed from the paper.