Dear Mr. Zhang,

let me first apologize for the fact that my decision on your manuscript took quite a while. As you know, we have two very much contrasting recommendations. Reviewer 2 is in general very positive and recommended minor revision mainly to clarify the presentation of the proposed methodology for the reader.

Reviewer 1 was rather critical, ranked your work as “purely” diagnostic statistical exercise, without providing insights on the underlying reasons that lead to long term memory in hydrological systems, and he/she claimed your evaluation does not provide any methodological advancement. While missed to provide any reference supporting the last point in his formal review, he/she provided a long list of literature sources to support this statement, in response to your response. Unfortunately, particularly the second comment of Reviewer 1 is not very constructive, and rather unspecific, in fact it reads in many parts as like a manifest in cognitive science. Most importantly, he/she did not specify which part of your approach has been already presented in which of the studies she/he referred to.

As I know both reviewers personally well and consider them as very much competent to judge your work, I decided to thoroughly and carefully review your manuscript to make up my mind in an as much as possible independent manner. As your manuscript is technically demanding, this took a little while. After this effort I am fully convinced that your work is very valuable for the field of hydrology, and yet I think needs moderate revisions before it can be accepted.
Within this process I encourage you to address the recommendations of Reviewer 2 as outlined in your response. While Reviewer 1 did, although she/he recommended major revisions, did not come up with a single major point that can be addressed, I leave it to you whether you consult a selection of the literature sources he/she provided or not.

Finally, although I am not an expert in time series analysis, I wonder about the following points:
In spatial statistics/ geostatistics it is quite common to estimate the spatial covariance in a data set which is irregularly sampled in space by means of the semi-variogram. This implies to pool data into irregularly spaced lag classes and to fit the best suited theoretical variogram function, which of course might be also a power law. It is also standard to fill gaps between the sampling locations by interpolations methods that preserve the covariance structure for instance by means of ordinary kriging or external drift kriging, which may account for a drift in the expectation values (see next comment). I wounder whether the same procedure is not applicable to irregularly sampled time series, both to estimate the autocorrelation function and to fill gaps in a manner that preserves the autocorrelation?

The term water quality data seem a little imprecise. Do you refer to concentrations of solutes in stream flow (C) or to total loads (Q*C) in stream flow. Only the latter reflects mass conservation, and concentration data might exhibit quite a bit of pseudo-dynamics and pseudo seasonality due to simple dilution effects and seasonality in discharge (as you pointed out). In this context there is there is also quite a bit of discussion in the geostatistical literature whether data sets which include an external drift (a deterministic dependence of their mean on an external variable such as air temperature and or rainfall and topographic elevation) or in your case a flow dependence of concentration shall be de-trended before estimating the covariance or not. I personally think it is necessary to remove a drive to avoid mixing of deterministic and stochastic variability – and there is evidence that a variogram analysis without the removal of a trend leads to a positive bias in the range and the sill of the variogram (e.g. Zimmermann et al. 2008).
The definition of delta t average seems inconsistent with example 2 in line 199.
Please flip the numbering of figure 1 and 2.

Best regards,

Erwin Zehe

References:
Zimmermann, B., Zehe, E., Hartmann, N. K., and Elsenbeer, H.: Analyzing spatial data: An assessment of assumptions, new methods, and uncertainty using soil hydraulic data, Water Resources Research, 44, W1040810.1029/2007wr006604, 2008.

Dear Dr. Zhang,

I am delighted to inform you that the reviewer recommended publication of your work after a very minor technical correction. I guess this will be quickly addressed.

Best regards,

Erwin Zehe