Technical Note: Higher-order statistical moments and a procedure that detects potentially anomalous years as two alternative methods describing alterations in continuous environmental data

Arismendi, I.; Johnson, S. L.; Dunham, J. B.

doi:https://doi.org/10.5194/hess-19-1169-2015

Articles | Volume 19, issue 3

https://doi.org/10.5194/hess-19-1169-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/hess-19-1169-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 19, issue 3

Technical note

|

02 Mar 2015

Technical note |

| 02 Mar 2015

Technical Note: Higher-order statistical moments and a procedure that detects potentially anomalous years as two alternative methods describing alterations in continuous environmental data

I. Arismendi, S. L. Johnson, and J. B. Dunham

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Final revised paper (published on 02 Mar 2015)
Supplement to the final revised paper
Preprint (discussion started on 13 May 2014)
Supplement to the preprint

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC C2495: 'Peer-Review Comments for hess-2014-142', Anonymous Referee #1, 15 Jul 2014
- AC C4543: 'Responses Reviewer 1', Ivan Arismendi, 19 Oct 2014
RC C3703: 'Peer-Review of HESS-2014-142', Anonymous Referee #2, 10 Sep 2014
- AC C4548: 'Responses Reviewer 2', Ivan Arismendi, 19 Oct 2014

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (04 Nov 2014) by Stacey Archfield

AR by Ivan Arismendi on behalf of the Authors (04 Nov 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (07 Nov 2014) by Stacey Archfield

RR by Anonymous Referee #2 (20 Nov 2014)

Suggestions for revision or reasons for rejection

Arismendi et al. have provided a significant revision on their original manuscript. Pending some minor revisions of the methodology and minor clarifications, I feel that this manuscript merits publication. They present tools to assess the distributional shifts of continuous climate variables and to identify potentially anomalous years. In the interest of a targeted response, I have provided line-by-line comments and suggestions. I am confident, that upon additional revision, Arismendi et al. will have provided a good contribution to the analysis of environmental phenomena.

Throughout: The authors refer to ‘higher statistical moments’ and ‘lower statistical moments’. Please consider revising to ‘higher-order statistical moments’ and ‘lower-order statistical moments’ throughout the manuscript. The point is not that the statistical moment is higher (a mean of 5 is higher than a mean of 3), but rather that the order of the moment is higher (a mean is a first-order moment, while a standard deviation is a second-order moment). Though not an exhaustive list, examples occur at lines 1, 28, 65, 72, 74, 96, 121, 125, 133, 226, etc.

Throughout: Central tendency statistics are not meant to capture characteristics of the variation. Furthermore, the paper discusses the shortcomings of statistics of central tendency and dispersion; this is not reflected in the current abstract or manuscript. I would suggest revising the first clause of line 25 to read “Statistics of central tendency and dispersion may not capture relevant or desires characteristics of the distribution of continuous…” This is also reflected in lines 47-50, line 331 and elsewhere.

Throughout: I am uncomfortable with the term ‘outlier-detection’. As mentioned below, this technique will always identify 5% of the years as outliers. The term outlier carries a negative connotation, but all this method is doing is identifying years in the tails of the distribution. The authors proposed changing ‘outlier’ to ‘anomalous’ in the revised manuscript, but this completed, as can be seen throughout the manuscript and in the title. While I would argue that anomalous carries a similar connotation, I cannot think of a better term; perhaps something like ‘potentially anomalous’. In any case, please consider modulating the use of the terms ‘outlier’ or ‘anomalous’.

Line 27-8: The author claims to present two methods that identify long-term changes. This suggests, along with comments in lines 62, 282-3, and elsewhere, that the outlier detection technique is capable of identifying distributional shifts. The identification of an extreme year, as this method will do for 5% of all years regardless, does not imply distributional shifts. Instead, it merely indicates a particularly extreme event. Instead, as the authors observe in lines 100-3, the outlier-detection methods merely identifies years that may prove interesting upon further investigation. The manuscript should be revised to clarify this point: outlier-detection does not imply distributional shifts.

Line 47-50: This sentence states that most traditional statistical approaches are based on the detection of location changes. This implies that tests of variability or other parameters are not common. Considering that there are many tests of variability, the widely-used ANOVA test, for example, I do not think that this statement is accurate. I agree with the second clause, namely that testing locations over-simplifies the problem, but I do not think that the authors should dismiss the testing of higher-order statistics so quickly. Please revise or provide a citation that supports the claim.

Line 62-6: In the previous paragraph, the authors observe the limited value of central tendency metrics. Here they jump to a discussion of skewness and kurtosis without any discussion of the value of dispersion metrics (IQR, range, standard deviation).

Line 65: Revise ‘the shape of stream temperature empirical distributions’ to read ‘shape of the empirical distribution of stream temperature’.

Line 100-1: Insert ‘an’ between ‘Using’ and ‘outlier’. Remove the hanging parenthesis after technique. The revision should read: ‘Using an outlier detection technique, we…’

Lines 116-7: The authors state that a stream was classified as regulated if reservoirs existed prior to 1978. Does this imply that an unregulated stream could have a reservoir on it that has been operational since 1980? The degree of abstraction allowable in the unregulated class is unclear. Please clarify the definitions of regulated and unregulated.

Line 117-8: Add commas between ‘and’ and ‘for’ in line 117 and between ‘below)’ and ‘we’ in line 118. More importantly, how much of the record was interpolated: days, months, years?

Lines 133-4: This first sentence, as it reads now, suggests that parametric statistics assumed normality. This is not the case. Parametric analysis implies a distributional assumption, not an assumption of normality. I believe the authors intend to point out that common estimators of skewness and kurtosis are unbiased only for normal distributions. Please revise this sentence accordingly.

Line 134: Remove the phrase ‘In reality, however,’. The reality of the previous statement does not contradict the reality of this statement. Please revise the transition. Something like ‘Still,’ or ‘Regardless,’.

Lines 159-63: The authors cite the missing values as a motivation for the subsequent formulae. Weren’t these records already completed, per lines 117-8? Please explain.

Line 192: Strike the phrase ‘A rule of thumb, (‘ to begin the sentence ‘Clarke (1993) suggests…’

Line 219: Revise ‘occurred’ to ‘occurring’.

Line 224: Include the word ‘Possible’ to start this sentence. Because there is no way to reliably test the changes in skewness or kurtosis, it is inaccurate to trust changes explicitly.

Line 263: Add a comma and append an ‘s’ to ‘season’. The revision should read ‘regimes, showing which seasons were’.

Line 264: Revise the beginning of this sentence to read ‘The use of higher-order moments could help improve…”

Line 264-6: This claim is not substantiated by the text. How do higher-order moments of temperature incorporate site-specific characteristics? Please clarify this statement and provide additional support or remove it.

Line 278: Strike the word ‘spatially’ to read ‘…sites located close…’

Line 279: Add a comma between ‘years’ and ‘suggesting’ to read ‘…anomalous years, suggesting that…’

Line 306-11: This is a very important statement and should not be appended to the tail of the discussion. This is a limitation of the methodology. As such, it should be mentioned in the methods section and discussed in tandem with the relevant results. The interconnectedness of moments significantly alters the readers’ interpretation of the results presented in lines 224-66.

Line 311-6: As with the previous observation, this is an extremely important claim. Again, it is a limitation of the methodology and should be mentioned when the method is introduced. The ‘outlier-detection’ method will always identify 5% of the years as ‘outliers’. This limitation affects the interpretation of the results and should be included in the discussion.

Lines 335-7: The authors have not shown the power of looking at the entire empirical distribution. Instead they have presented the merits of looking at both the empirical distributions and multiple moments. Please add the phrase ‘and multiple moments’ to read ‘By examining the whole empirical distribution and multiple moments, we can …’

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ED: Reconsider after major revisions (08 Dec 2014) by Stacey Archfield

I thank the authors for addressing the initial review comments thoughtfully and thoroughly. As noted by all of the reviews, the manuscript is also very well written. I agree with the review comments that this manuscript will provide a useful technical note to aid in the detection of change in environmental phenomena. Approaches and techniques to identify these shifts are critical to the future of hydrology research and I commend the authors for taking on such a difficult yet highly important topic.

Because the manuscript had been recommended for major revision, I sent the manuscript to one of the previous reviewers for comment on the revised manuscript. While I believe the current revision addresses many of the previous reviewers’ comments, I ask the authors to consider and revise the manuscript in response to the additional review comments.

I also had the opportunity to carefully look over the revised version of the manuscript and have some additional comments noted below. I hope the authors do not find these comments too onerous to address and I look forward to the revised manuscript.

1. Please provide additional description of the N-MDS procedure. This is not a common statistical technique applied to hydrologic problems. Please add 2-3 more sentences about this method and, if possible, include an example or equations so that a reader can gain a basic understanding of this technique.

2. Clarify the time series used. In line 183, it is stated that “365 days of daily minimum stream temperature” were used. Does this mean you had sub-daily temperature data from which the daily minimum was obtained? Describe in more detail how the data were broken up and standardized by season. Was this a result of the technique or did you make this classification prior to applying the technique (this was particularly confusing in lines 216-223).

3. Consider another naming convention rather than “unregulated site2” (line 230). Maybe a shorter abbreviation or site name?

4. How does your approach take into account sample size when identifying a shift? Can the method determine with some confidence that observed shifts are simply not due to chance versus a true shift?

5. In lines 303-306, you state that you used longer time periods to remove the effects of serial dependence. But if the time resolution of those longer periods were still on the order of days, using longer sequences would not result in less serial correlation. Aggregating to seasonal or annual series would, however. Could you clarify your statements here?

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AR by Ivan Arismendi on behalf of the Authors (20 Jan 2015) Author's response Manuscript

ED: Publish as is (03 Feb 2015) by Stacey Archfield

Short summary

We present tools to assess shifts in the distributional properties of continuous environmental variables and to identify potentially anomalous years. We demonstrate the utility of these tools using stream temperature as an illustrative example. We were able to examine seasonal and annual responses to climate and other human-related influences. These tools will be useful to characterize how regimes of continuous phenomena have changed in the past, or may respond in the future.