Modelling non-stationary flood frequency in England and Wales using physical covariates
Abstract. Non-stationary methods of flood frequency analysis are widespread in research but rarely implemented by practitioners who manage flood risk. One reason for this may be that research papers on non-stationary statistical models tend to focus on model fitting rather than extracting the sort of results needed by designers and decision makers. It can be difficult to extract useful results from non-stationary models that include stochastic covariates for which the value in any future year is unknown. Examples of such covariates include rainfall, temperature or indices of fluctuations of atmospheric pressure.
We explore the motivation for including such covariates, whether on their own or in addition to a covariate based on time. We set out a method for expressing the results of non-stationary models, and their uncertainty, as an integrated flow estimate, which removes the dependence on a particular value of the covariates. This can be defined either for a particular year or over a longer period of time. The methods are illustrated by application to a set of 375 river gauges across England and Wales. We find annual rainfall to be a useful covariate at many gauges, sometimes in conjunction with a time-based covariate.
For estimating flood frequency in future conditions, we advocate exploring hybrid approaches that combine the best attributes of non-stationary statistical models and simulation models that can represent the impacts of changes in climate and river catchments.
Duncan S. Faulkner et al.
Duncan S. Faulkner et al.
Duncan S. Faulkner et al.
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Thank you for the opportunity to review Faulkner et al. Modelling non-stationary flood frequency in England and Wales using physical covariates
The central problem the manuscript seeks to address (that of extracting decision-useful outputs from non-stationary flood frequency analysis) is compelling problem and I agree with the authors that this issue is often overlooked in the academic literature. The fact that one of the authors is from the Environment Agency of the UK shows that this work is recognized by the appropriate government agency.
That being said, this manuscript is essentially a rewrite of a technical report on the topic of non-stationary flood frequency submitted to the Environment Agency (Faulkner et al., 2020; which is extensively referenced in the manuscript). I did not do an extensive/exhaustive comparison, yet it is clear that some portions of the manuscript are directly copy-paste (or nearly so; e.g., compare lines 81-105 of the manuscript to pgs. 34-35 of the report, lines 119-125 of the manuscript to pgs. 36-37 of the report, Figure 3 of the manuscript to Figure G-9 of the report, and Table 2 of the manuscript to Table 4.7 of the report). I state this (without any judgement) for the purpose of bringing it to the attention of the editor.
Apart from what is noted in the previous paragraph, the science presented in this paper is incremental. Essentially, this is a case study applying non-stationary frequency analysis to flood events in England and Wales. The primary advancement, that of an “integrated flow estimate” which allows for representing the non-stationary results in a decision-centric way, is essentially an integration of the non-stationary flood frequency estimate over the domain space of the covariates. I think this advancement, while incremental, is useful and should be made know to the academic/practitioner world.
However, it seems it has already been proposed by Eastoe & Tawn (2009). If improvements are needed (lines 127-129), then perhaps this additional paper is justified; but, what were the weaknesses? (They are not mentioned) and does this paper address those weaknesses? Here was a missed opportunity to further justify the significance of this paper.
Also, the results associated with this “integrated flow estimate” are fairly minimal (Figures 5 and 6; lines 297 – 322; nothing at all in the discussion and conclusion). Since this is the stated main point of the manuscript, more is needed. You could walk through a hypothetical example of how a decision-maker or engineer might use Figure 5. You could answer questions such as (and I am sure you can think of additional ones to enrich this portion of the manuscript): What is the implication of a 7x ratio of non-stationary to stationary? Which AEPs are used by UK regulatory standards (and how that does affect the interpretation of these results)? What about the case where the ratio was 0.54 (should we disregard the non-stationary model in that case and use the stationary model since it is more conservative)?
Which brings me to the issue that the discussion and conclusion seem disconnected from rest of paper. They read more like a literature review which is found at the beginning of a work, rather than a reflection on what was done. I do not disagree with what is noted in the discussion and conclusion, but it is not in the right place in the manuscript and is not connected with what was shown in the results. Consequently, the reader misses out on a discussion on the actual results that were presented (e.g., answers to the various questions posed in the previous paragraph).
Some minor comments
Line 79: To my knowledge, I do not think that Francois et al. 2019 use/reference the East Atlantic pattern (East Atlantic is not found when I do a search). Please double check and correct the reference. As a recent review paper on this topic, Francois et al. 2019 is relevant and should probably be referenced in this manuscript, but referenced correctly.
Line 82: AMAX is not defined.
Lines 94 – 105: I am not sure that this discussion of Reason 2 for choosing physically-based covariates correctly captures the intent of many of the authors I have read, and the approach as best implemented. The intent of a physically-based covariate to is represent mathematically some physical driving mechanism of floods, whether oceanic, atmospheric, or land based. The confusion of correlation for causation will only happen when an analyst somewhat blindly applies this method: that is, coming up with a suite of possible covariates and trying as many possible and choosing the one with the best correlation. As written, I think this section is somewhat misleading (as if it is the fault of the method, when really this is an error in application of the method).
Line 119: The flood frequency estimate is time-dependent regardless of the covariates – either directly dependent on time or implicitly dependent on time via a physical covariate. Wording could be improved here.
Line 198: Why were the models just limited to two covariates? In particular, why weren’t the two physically based covariates used in one model – are they too strongly correlated? Need to justify this choice. Based on skimming the report, I suspect your answer might be that it was too many models... perhaps; but the model with the two physical covariates seems important enough to test regardless of the issue of computation.
Line 219: Why include the GLO if the results are not analyzed? My suggestion is to remove it from the paper, or justify its inclusion (and include results).
Figure 6: They y-axis scale is confusing. Is it a log-scale? If so please note in the caption. More labels would also be helpful.
Appendix B: Why is this included? It is just a suggestion, without any testing or analysis or use in the manuscript. I suggest to remove it or to more fully incorporated in the manuscript.