This work builds on the previously reported LUT-COBRA algorithm (Theys et al., 2022) for volcanic SO2 plume height retrievals, by applying it to the UV2 measurements from TROPOMI. Through theoretical calculations and sensitivity tests, the authors demonstrated that the TROPOMI UV2 measurements at shorter wavelengths (~305 nm) can provide better accuracy for SO2 layer height than UV3 measurements. The authors also described the implementation of the LUT-COBRA algorithm with the TROPOMI UV2 band, and compared the retrieved plume heights with those from the operational TROPOMI SO2 height algorithm (based on a machine learning technique) as well as those from infrared (IASI) and microwave limb (MLS) sensors. Overall, this is a well-written paper, and the topic should be of interest to the atmospheric science and remote sensing communities. While the technique has been previously described, the application to TROPOMI UV2 clearly shows improvement in the retrieved SO2 heights. The paper can be further improved by addressing some technical points (see specific, mostly minor comments below) and I’d recommend minor revisions before the paper can be accepted for publication in AMT.

Specific comments:

Lines 140-142: In Jacobian calculations, the authors used LIDORT (instead of VLIDORT) and did not explicitly consider aerosols or rotational Raman scattering. Can the authors comment on the uncertainties in the retrieved SO2 plume heights associated with these factors?

Lines 149-150 and Table 3: the interpolation error for Jacobians at relatively large SO2 VCDs can be quite substantial especially at short wavelengths – can the authors comment on the selected SO2 VCD nodes in the LUTs?

Figure 5: is the apparent increase in error for SO2 LH > 25 km due to the coarse resolution of LH nodes in the LUT?

Figure 6 and lines 239-240: some of the error sources are not completely independent (e.g., T prof. and Air prof., O3 prof. and O3 VCD). Not sure if quadrature summation is justified here.

Section 4.1: The construction of the weighted O3 profiles was done to reduce the size of the LUTs, right? How does this affect O3 profile related errors?

Lines 315-318: what is the typical number of eigen vectors used in equation 9? Is this done for all spectra (or just those with ill-conditioned covariance matrix)?

Table 4 and section 4.2: all examples given here appear to be under relatively small or moderate SZAs. Can the authors present some results for higher SZAs, where the O3 profile effect could be more significant?

Figure 8: there appears to be a general tendency of pixels with lower VCDs to have lower plume heights. Is there an explanation for this?

Figure 10c: the BD2 retrievals appear to be quite noisy for the eastern branch of the plume – how confident are the authors in the retrieved heights here?

Figures 11 and 14: it is a bit difficult to directly compare IASI with TROPOMI using these maps. The profile plots (Figures 12 and 15) are more informative for these two cases.

The authors presented an improved SO₂ layer height and vertical column densities retrieval algorithm for TROPOMI’s second spectral band (BD2) demonstrated stronger SO₂ absorption sensitivity than the traditional (BD3) approach and plume height estimates consistent with independent IASI and MLS measurements The paper was organized in three sections, introduction of TROPOMI and SO₂ retrieval methodology, theoretical bases of LUT-COBRA and sensitivity tests, and showing main results for various examples of volcanic. Because my background is in atmospheric science and I work on modeling, my comments mainly focus on the results and their comparison with satellite observations (Section 4.2).

General comment:

1. Throughout the analysis of the SO₂ height retrievals from BD2 and BD3 over eruption cases, it is observed that SO₂ heights are generally lower in BD2 than in BD3 for common pixels. It seems the authors implicitly explain that BD2 reduces over-sensitivity to noise and brings the retrievals closer to IASI and MLS. I might be missing this somewhere in the manuscript, but a clearer explanation of the higher values of the BD3 values would be helpful. Do these cause artificially inflated heights in BD3?

2. With the improved sensitivity of BD2, could the authors comment on whether the retrievals provide any insights even indirectly in the vertical extent or thickness of the volcanic plume from the lower to the upper layers?  

3. In the conclusion, the authors mention that the operational product fails to reproduce SO₂ heights at the tropical tropopause level, and that the reason for this remains unclear. With respect to temperature inversion and ozone gradients in the tropical tropopause layer, it would be useful if authors could comment on whether these factors might help explain that failure to reproduce SO₂ heights at this level.