General comments

The authors present a comparative study on sorption isotherms for ammonium in soils. The manuscript is well-structured and written in a concise style. I see sound scientific work all over, with some minor issues to methodological aspects. But I am sure this could be sorted out...

Specific comments

15 'conventional' I suggest to be a bit more precise at this point

26 many references of NH3 emissions from plants not from soil

29-31 I suggest to delete this motivation for sampling natural soils. The sorption mechanism (or the physico-chemistry) of soils with N fertilization, and probably  higher NH4 and NH3 concentrations, is exactly the same as for natural soils. The same sorption isotherms are applied...

43 '... soil sample able to participate ...' I suggest to rewrite

110 'RSE' I strongly suggest to compute the Akaike information criterion (AIC) or the Baysian information criterion (BIC) instead of RSE for model identification. AIC relates the model error to the number of parameters. 

112 parameters of non-linear functions usually do not average well, and usually using the geometric mean is better than using the arithmetic mean

117 please justify the selection of min, max and some mean value instead of a random sample. And a higher number than just 3 samples in the test data set would actually be required

119-120 points 'i.' and 'ii.'; do you intend to test the potential of CEC to predict sorption?! That's a good idea anyways, but it would be nice to mention it already in the introduction as a goal.

138 pooling is theoretically the more appropriate procedure

148 'individual' instead of 'individually'?

150 For the figure caption I suggest to replace 'standardizing the y-axis' with 'normalized'

Table 2 Use either 'SE' or 'Standard error' in the column headers for consistency; I guess the number of parameters stated for Langmuir is wrong, this is also =2; For Freundlich I would move 'Smax*0.052...' one column to the right?!

161 would be nice to have a sort of pedotransfer function to estimate Smax or other sorption parameters from CEC. I think even the small data set present in this study could be used for an initial test ...

162 well, there are differences in the model errors, however for field conditions, e.g in the context of agroecosystem models, it actually does not matter much. Simply because the sorption if NH4 is very, very high. And it does not really matter that much how high Smax is as long as the sorption at low concentrations near zero is estimated well. And in that range of concentrations I assume the four isotherms provide very similar results. Something that should probably be picked up in the discussion.

167 'an additional parameter' this is where the AIC is helpful...

155-160 I think this paragraph would benefit from additional references to literature

figure 2 I think the label of the y-axis is wrong. This probably is the non-normalized sorbed NH4 concentration, otherwise it should also vary around values <1 ...

190-194 I am not sure I understand the idea behind Eqs. 9 to 13. Eq. 7 could be rearranged to C=((mNH4-S)*p)/w and S can be computed from any of the isotherm equations given in Table 1. OK, then you need two equations, but this is easy to compute. For me it is particularly difficult to understand the assumption wC/p=0. You basically neglect the liquid phase concentration of NH4, and this is basically not required. It just makes your estimate of C worse.

196 yes, that 0.57-1.5% is probably the ratio of C/S, and just a consequence of neglecting the liquid phase NH4 concentration

226 replace 'more sound' with 'mechanistic'?

251-252 please remove the phrase '; and more research ... of both approaches.'

253-255 please delete or relate to any of your results

264 how much better?  % ... 

In Section 2.2.2. Adsorption curve characterization (Line 85), if I understand correctly, an indirect method used to quantify adsorbed ammonium and amount remaining in solution based on the displaced Na+, Mg2+, Ca2+ and K+ ions measured in solution. Could not the ammonium remaining in solution been measured directly and then used to determine adsorbed amount by subtraction, perhaps to confirm with the indirect measurements of other cations? Do the authors believe that the indirect measurement is more reliable than direct for some reason?