The Spatial Scale Dependence of The Hurst Coefficient in Global Annual Precipitation Data, and Its Role in Characterising Regional Precipitation Deficits within a Naturally Changing Climate
Round 1
Reviewer 1 Report
This interesting manuscript explores the theoretical basis and analyses spatial scale dependence of long-term persistence (LTP) of precipitation using a global gridded annual precipitation data set and discharge for two large river basins (the Colorado and Mississippi). Evidence of Hurst (H) scaling is found in 5 out of 11 regions, and somewhat confounded by competing forces at the scale of Asia. These results are likely sensitive to the choice of region locations, areas and shapes analysed as well as dependent on the rules for box inclusion within selected domains. Such critical methodological points need to be unpacked. The discussion should also focus more on the new evidence presented, and better reflect contemporary practices in water planning for both natural climate variability and anthropogenic climate change. The wider discussion offers some perspectives that are valid but stray somewhat from the core material. Hence, the authors should concentrate more on how their own study might be strengthened to improve the robustness of findings, not least by referring to well-known patterns of global modes of hydro-climatic variability when selecting domains and basins that are most likely to exhibit LTP. On this basis, publication is recommended subject to the following modest revisions, minor corrections and clarifications.
Major comments
[1] The rationale behind the choice of the pre-defined regions and two rivers needs to be explained since their size and location with respect to major modes of climate variability likely shape the outcome of the scale-dependency analysis of LTP. This is especially important for the Asia box which encompasses various regional climate forcings that are then ‘blended’ at the larger scales (as subsequently acknowledged in section 3.2). For instance, when searching for LTP, the Sahel region would have been a good candidate given well-known shifts in the multi-decadal rainfall regime. Furthermore, existing studies showing zones of precipitation forcing by multi-decadal variations in the PDO and AMO, and multi-annual variations in ENSO, would have been a better starting point and thereby avoid places with counteracting signals. See for example: McGregor (2017) ‘Hydroclimatology, modes of climatic variability and stream flow, lake and groundwater level variability: A progress report’.
[2] Please explain exactly how the different areas were generated at each scale. For instance, are boxes allowed to overlap and/or required to fall entirely within the confines of each regional/ catchment boundary?
[3] Justify the choice of the two rivers analysed, given that there are possibly better alternatives. For example, the Murray-Darling might have been selected given the highly persistent Federation (~1895-1902), World War II (1937-1945), and Millennium (1997-2010) droughts. Ditto for the Amazon.
[4] The Discussion should concede that the results are likely sensitive to the domain shapes, sizes and locations assessed.
[5] The Discussion of links between droughts and anthropogenic climate change should stress that the findings within the present manuscript are based entirely on historic data up to the year 2013 [L457-L458, L482]. The limited ability of GCMs to capture modes of climate variability is widely recognised, but the issues around, for instance, the East African paradox are more nuanced than implied here. The assertion that ‘the main physical risk of precipitation deficits is coming from LTP’ (L458) may be valid historically and in the short-term. However, anthropogenic forcing of droughts is expected to intensify with rising concentrations of greenhouse gases and will interplay with natural modes yielding complex patterns of change in space and time, overlain by human adaptations. It is too simplistic to say otherwise.
[6] The Discussion of inappropriate trend analyses and hypothesis testing holds true but overlooks some more considered hydrological literature with testing of multiple working hypotheses. See for example: Merz et al. (2012) ‘More efforts and scientific rigour are needed to attribute trends in flood time series’; Harrigan et al. (2014) ‘Attribution of detected changes in streamflow using multiple working hypotheses’; Mallucci et al. (2019) ‘Detection and attribution of hydrological changes in a large Alpine river basin’.
[7] It is unsurprising that ‘O’Connell et al. [under review] did not find any significant correlations between average annual regional precipitation and the NAO for the eight LTP regions listed in Table 3’. Analysis at the annual scale is too coarse and likely blends opposing signals at seasonal/sub-seasonal scales. There is a considerable body of literature that clearly demonstrates profound forcing of regional precipitation by NAO at these scales. Stochastic weather generators that are conditioned by low-frequency modes such as NAO (and others) are an effective way of combining statistical and quasi-physical modelling approaches. The narrative should be amended to reflect these points.
[8] The Discussion (L514-L531 and L577-L581) should better reflect current practices. These sentences over-simplify the present state of the art where anthropogenic climate change with natural climate variability are considered in water resource plans. For instance, water companies in England are now required to test resilience of their plans to a 500-year drought with and without climate change. Please either omit this material or better articulate current practice.
[9] The Discussion (L532-L561) makes some valid points but deviates somewhat from the new analyses and evidence presented in the manuscript. This paragraph could be omitted to improve conciseness/focus.
[10] The Conclusions highlight evidence of an increase of H with the scale of averaging in 5 out 11 climatic regions assessed. This is roughly what would be expected by chance. The lower H value at the scale of Asia is rightly accepted as an expression of blended modes of climate variability. The authors should sign-post better criteria for defining the size, location and shapes of domains for future analysis.
Minor corrections and clarifications
[Line 40] Typo ‘unknown [to] Hurst and others’.
L47 Please elaborate the ‘aggregation process performed by the river network’.
L62 Define the term ‘crossing properties’ for the benefit of a wider readership.
L71-82 Presumably annual precipitation totals were used. Why were only 11 out of the 19 regions analysed?
L226 Now it seems that 19 regions were analysed. Which is correct?
L235 Again, please clarify whether 8, 11, or 19 regions were analysed.
L248 Define ‘40dd scale’.
L279 Typo ‘Estimate[s]’.
L286 Justify the choice of 5 years for the deficit periods.
Figures 9 and 11. Redraw with years shown on the horizontal axis.
L358 Reword ‘[persistent] rainfall deficits’.
Figure 12. Could be omitted as this duplicates the information in Table 5.
L412 Add ENSO and PDO to the list – globally the two most influential modes.
L435-L436 Syntax ‘shows that there some regions encountered’.
L449 and L608 Typo ‘global war[m]ing’.
L572 The GPCC data set used here ends in 2013 so neglects nearly a decade of information since. Please suggest some more up to date alternatives, perhaps including global re-analyses.
L608 No attribution analyses were performed in this study so please simply state: ‘No evidence has been found to show that there has been any increase in precipitation deficits in recent decades.’
L609-L611 Reword as ‘Historic precipitation deficits are a consequence of natural climatic variability/the level of LTP, so Hurst Coefficient and HK stochastic simulations may be used to test water system resilience to a wide range of conditions beyond those seen in observational records’. Other tools are needed to examine resilience to future climate conditions.
Author Response
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Author Response.pdf
Reviewer 2 Report
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Comments for author File: Comments.pdf
Author Response
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Reviewer 3 Report
Review of “Long-term persistence, precipitation deficits and changing climate, with implications for risk assessment in sustainable water resources management”
O’Connell, O’Donnell, and Koutsoyiannis
The paper presents an interesting development of the theoretical background to the Hurst-Kolmogorov framework for long-term persistence in a time series that is aggregated in space and time. Section 2 is very well written and presents a good analysis leading up to an interesting result in Equation 17. The paper will be suitable for publication once the following major structural issues have been addressed:
The Introduction has a very superficial motivation for why the specific analyses were carried out (Line 57 – 65) and I found myself wondering about how the results that are presented in Section 3.2 to 3.4 relate to either the conclusions or the introduction.
This is especially an issue for all of Section 3.4, but particularly Lines 301 – 336, which I found to be difficult to follow and largely superfluous to the main theme of the paper. There is no motivation for why the analysis of the crossing properties of precipitation deficits was carried out and how this analysis contributes to the conclusions of the paper.
Both of the Sections 4.5 are problematic for me since they include material that is only loosely related to the preceding analysis. In my view it would be better to either have this rather free-ranging discussion/opinion either up front in the Introduction as a motivation for the research, or preferably as a second paper that includes an analysis of the ability of GCM data to reproduce a time series of mean areal annual rainfall with an appropriate H exponent.
A paper that is based on the theoretical development in Section 2 with supporting analysis from Sections 3.1 and 3.2 would make a very interesting paper that deals with the more technical aspects of long-term persistence.
I missed a discussion on Table 2 where the H estimates based on stream flow are significantly higher that those for rainfall. Some comments about the reasons for this difference would add value to the paper. Does this mean that the areas like South Africa and Australia that have low H exponents for rainfall could also have significant long-term persistence in streamflow? See Vervoort et al (2021) for an example of an analysis of Australian data.
Vervoort, RW, Dolk, MM, van Ogtrop, FF. Climate change and other trends in streamflow observations in Australian forested catchments since 1970. Hydrological Processes. 2021; 35:e13999. https://doi.org/10.1002/hyp.13999
Alan Seed
Author Response
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Author Response File: Author Response.pdf
Reviewer 4 Report
Enda O 'Connell et al. 's paper entitled " Long-term persistence, precipitation deficits and changing climate, with implications for risk assessment in sustainable water resources management " discusses the important role of HK theory and the Hurst Coefficient in risk assessment of precipitation deficit, as well as the shortcomings of GCM prediction, and provides some suggestions for sustainable water resources management. The Angle of topic selection is novel, of course, within the scope of the journal.
In this paper, the authors collected precipitation grid datasets from 11 locations in Antarctica and Asia. This paper analyzes Monte Carlo simulation of theoretical scale dependence of H，the spatial scale dependence of the H for the average annual precipitation, LTP in catchment boundary box precipitation and rivers flows and the crossing properties of precipitation deficits. The results show that the Hirst Coefficient increases with the spatial scale of regional mean annual precipitation, and the LTP of mean precipitation is consistent with the LTP of annual discharge in some large basins. Further analysis of the cross characteristics of precipitation deficit in LTP region shows that the Hurst coefficient can be used as a simple description of the risk of severe precipitation deficit, which makes up for the shortcoming that GCM prediction may not accurately capture the long-term natural variability of climate. The results can provide a basis for sustainable water resources management and risk assessment of precipitation deficit. However, further revisions are required before the recommendations can be published.
1. Major comments.
(1) The title of the paper is " Long-term persistence, precipitation deficits and changing climate, with implications for risk assessment in sustainable water resources management ", but the conclusion of the paper is that the precipitation deficit is the result of changing natural climate, and the Hurst coefficient can be used as a concise description of the risk of severe precipitation deficit. I suggest that the title of the paper be modified to make its content more appropriate.
(2) Some contents that are not closely related to the research purpose of the article can be appropriately simplified. For example, lines from 541 to 560 in section 4.5 introduce the private sector water resource management method of 2030WRG, which is not relevant to the core content of the article and can be appropriately simplified.
2. Specific comments
(1) P6, the subtitle in line 173 is "2.5.2 Generalization", which should be "2.5.4" according to the context order.
（2）Some drawings are not standardized, such as Figure 9-11.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Thank you for a thorough and clear explanation of revisions made in the wake of the first round of reviews. Some important caveats and possibilities for further research are now included. Major points and minor edits have been addressed satisfactorily, or otherwise rebutted.
However, it is a shame that ENSO still does not get a mention anywhere in the paper despite being the leading mode of global climate variability. The justification given is that ENSO results in antipersistence which is a very interesting point in itself. Please do incorporate a sentence or two to this effect, with supporting reference(s) for completeness. This is all the more pertinent given that PDO (which is now mentioned) interplays with ENSO either amplifying or damping regional rainfall signatures depending on their respective phase synchroneity. Such multi-mode interactions further confound detection of linear, univariate correlations with LTP.
Author Response
Response to Reviewer
The Authors are pleased that the Reviewer is happy with the thorough and clear explanation of the revisions made in response to the first round of reviews.
To address the Reviewer’s request that the connection between ENSO and anti-persistence should be explained, we have inserted, in section 3.2, a Climacogram for the whole of Australia, and explanatory text (highlighted in RED), which shows that, while ENSO results in anti-persistence at short time scales, LTP emerges at longer time scales, reflecting, inter alia, the influence of the PDO. We hope that this is satisfactory.
We have also done a careful proof-read.
