The paper presents an interesting dataset about the field measurement of fallout pyroclastic deposits thickness in the peri-volcanic areas of Campania region (Italy). Moreover, the authors discuss a relevant problem that can be solved using the dataset and statistical models, that is the spatial thickness estimation using statistical methods. In particular, the combination of different statistical and geological methods is proposed and alternative combination schemes are compared.

Overall, I find the work clear and the paper to be well written. I found the idea discussed in the paper very interesting, and the statistical procedures proposed for thickness estimation are adequate for dealing with the problem at hand.

However the description of the dataset is not well organized yet in my view. I think more effort should be devoted presenting relevant information about the data adopted for the analysis. Thus my main suggestion is to improve Section 4 of the manuscript. I do not think all the figures included in the current version of the paper are relevant, and a better selection of the most interesting ones should be considered.

Another minor comment is about Table 7. Consider to replace “constant” with “test statistics” or simply “statistics”.

Some references seem to be incomplete. Be sure all references have volumes, issue and pages. Include the doi for all the papers if possible.

The manuscript of Ebrahimi et al. deals with the application of statistical tools for reconstructing the original thickness of pyroclastic deposits on mountain slopes. Examples are provided from Campania region, downwind of the main Neapolitan volcanoes.

In my opinion the manuscript presents some important flaws that need to be fixed before consideration for publication. The first one is the lack of adequate volcanological terminology and referencing, which make it the reading sometimes very hard to understand and to be correctly placed in current state of the art of the volcanological literature. The second critical point is the absence of any discussion about the uncertainty associated to input data. Some of the methods described in the text (SPT, coring, etc) have associated large errors related to the method itself, which can significantly alter the measured thickness of the pyroclastic deposit. In some cases the bias introduced by measurement method can be comparable with reduction to the original thickness by erosion. It is not clear how the interceding of paleosoils is treated when measures are acquired using penetrometric tests. 

The uncertainty of results is even more important if we consider that the original thickness is derived from published isopach maps, which are the results of approximation and interpolation themselves.

Line 101: The somma Vesuvius summit caldera is the result of the 4 main Pinion eruption of the volcano. The AD 79 is only the last one (Cioni et al., 1999; Santacroce et al., 2008). I wonder which eruption is 18 AD. The references cited are not appropriate, because of the mess of publications regarding the eruptive activity of SV.

Line 103: The term "large explosively index" has no meaning. Please use more appropriate terminology

Line 104: the activity of Phlegran Fields did not initiate with the CI(see Orsi et al., 1996; Di Vito et al., 2008)

I wonder why you introduced Ischia and Roccamonfina volcanoes if you do not use their deposits in the manuscript.

The volcanic history of Phlegrean Fields may be shortened and better described

The same for the SV eruptive history. Please, cite also the large amount of newer literature available fr most of the cited eruptions

Minor points:

Line 44: please provide more references. The cited authors are not the first that noted the thickness decrease with distance, which is a common sense in volcanology

Line 102: Phlegrean Fields are not a volcanic field but a caldera

Line 129: I wonder what means "under 80 km from the eruptive vent"

Line 130: please rephrase. It has not meaning as it is 

Table 3: Taurano is not a Phlegran Fields eruption (Di Vito et al., 2008)