Dear Christopher Chagumaira,

please revise your manuscript according to your discussions with the two referees. In the discussion, you've already made some suggestions for your edits, of which I am convinced that they will further improve your paper. I'm looking forward to the revised version!

Best regards,
Kirsten

Dear Authors,

Referee 1 has made following statement:
"I am satisfied with most responses to my comments to the original manuscript but there are still a few that remain (line numbers refer to the ATC version of the revision):

(L39, Eq. 1) I maintain that the lower case z should be an upper case Z. Here, the random function model is invoked and the kriging variance refers to the variance of the kriging prediction error Z(x_0)-Z~(x_0). I am surprised that authors (in particular the last author) maintain their earlier view that it should be E[{z(x_0)-Z~(x_0)}^2]. Authors refer to Webster and Oliver (2007) to support their claim, but please check Eq. 8.2 in their book, which clearly writes E[{Z(x_0)-Z~(x_0)}^2], as it should be. Note that in case of E[{z(x_0)-Z~(x_0)}^2] we have that z(x_0) is a deterministic constant and so we effectively get the variance of Z~(x_0), which is very different from the variance of Z(x_0)-Z~(x_0). For example, suppose x_0 is a measurement location. In that case we would get Z~(x_0)=Z(x_o) and hence E[{Z(x_0)-Z~(x_0)}^2]=0, while E[{z(x_0)-Z~(x_0)}^2]=Var(Z(x_0)). In line 155 it should be z~(x_0) instead of Z~(x_0), because here you refer to the cross-validation prediction errors, which are deterministic values, not random variables.

I maintain that authors should in Poster 3 better have presented the kriging standard deviation instead of the kriging variance. From their response I now understand that the kriging variance is that of the log-transformed selenium content, while the kriging prediction is the back-transformed (hence median) selenium content. This explains the extremely low values. Now I wonder, does it make sense to present a kriging prediction map of the back-transformed variable and a kriging variance map of the transformed variable? How can we ever expect users to make sense of that and grasp the uncertainty? Note that the spatial pattern of the variance map is strongly influenced by whether it is done for the log-transformed or back-transformed variable. Authors justify showing a kriging variance map of the log-transformed selenium because “we cannot back-transform” the variance. Well, why not use Eq. 8.40 in the Webster and Oliver book? Admittedly this refers to simple kriging, which is not the same as ordinary kriging, but the difference will be small. All in all quite unsatisfactory how uncertainty was communicated in Poster 3: not only authors show the kriging variance instead of the kriging standard deviation, but they also mix up log-transformed and back-transformed variables. As before, I am not requesting that the questionnaires are redone, but authors should mention the weaknesses of their approach in the Discussion. The text that they now include in the revision (L148-L150, L429-431), is a good step in this direction, but they might add that they could have done better."

Please consider these suggestions for minor revisions.

Best regards,
Kirsten

Thank you for choosing Geoscience Communication for your research and for engaging so thoroughly in the peer review process. I am delighted to be able to accept your manuscript for publication.

Many Thanks,
Sam Illingworth
(Chief Executive Editor of Geoscience Communication)