|Also there are a number of interesting scientific results in the manuscript, their presentation is not ideal at the moment. Please consider my points below.|
Study objectives: I think the focus the authors lay on their pet statistical methods somewhat distracts from the interesting science they do. Currently, at many points of the manuscript, especially in the opening sections, one gets the impression that main aim of the authors is to advertise GCSs, rather than presenting novel scientific results. I suggest to rewrite the article by asking the scientific questions first and to develop the methodology purely as a means to answer these questions. This would mainly entail a slight reorganization of the manuscript, particularly in the introduction and section 1.2. This would also be a much better way to demonstrate the power of the methods.
In contrast with reviewer #1, I have no problem with the use of the term ‘covariance structures’. I think the term is sufficiently well defined to not cause confusion.
The manuscript is currently wordy and somewhat meanders in the argumentation. This is currently the greatest weakness and distracts from the scientific results and arguments. I believe there is ample opportunity for streamlining and consolidation. Example are the outline of the objectives in line 56 and then again in section 1.2 (line 159), the description of the GCS method, scattered over introduction, methodology. The site description is also lengthy and detailed, and the authors could cut material that is not directly relevant to the purpose of the study.
Momentum and d*v^2
I was a bit confused by the square in the momentum calculation (line 437) and later noted that reviewer #1 of the previous round had commented likewise. There, the authors replied: “Note that in classical physics momentum is defined as the product of mass and velocity squared.” – This is actually untrue; in classical physics momentum is linear in velocity, while kinetic energy is proportional to its square. Since, as the authors state in the mentioned reply, the overall patterns do not seem to change when using v instead of v^2, they could just relabel for energy. Also, by using d*v^2 (or d*v), variations in width are neglected. For a quantity directly analogous to momentum or energy, width would need to be taken into account, and this would make a lot of sense in a paper concerned with reach-scale width variations.
A note on style: The authors frequently use the formulation ‘this study seeks’, ‘…is concerned’ or similar. In my mind, studies do not seek anything, they are in general rather inactive… I think a study can ‘show’ something, but it is the scientists who seek.
56 and following: here, the authors give (parts of) the study objectives, to which they also dedicate an entire section later on (line 159), but also individual sentences elsewhere (e.g., line 190). This should be consolidated.
76 …river reach exhibits…
78 Knowledge of spatial patterns…
197 the term ‘cross product’ has a well-defined meaning in vector algebra and might be misleading here.
204 misplaced hyphen between sentences
210 Full stop missing after ‘flow’
402 Full stop missing after ‘flow’
437 momentum is linear in velocity (vector quantity). What about variations in width?
463 double full stop after ‘pathway’
473 It is not quite clear what the authors mean by ‘standardized’, or how standardization was achieved – maybe they could include the appropriate equations.
477 The spectral analysis has not been described at this point and the statement here takes the reader a little by surprise.
504 What was the purpose of visual assessment and what criteria were applied?
769 either ‘…both narrow and deep and wide and shallow geometries…’ or ‘…both a narrow and deep and a wide and shallow geometry…’