Detection of Compound and Seesaw Hydrometeorological Extremes in New Zealand: A Copula-Based Approach

Bennet, Morgan J.; Kingston, Daniel G.; Cullen, Nicolas J.

doi:https://doi.org/10.5194/egusphere-2025-3592

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https://doi.org/10.5194/egusphere-2025-3592

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04 Sep 2025

| 04 Sep 2025

Status: this preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).

Detection of Compound and Seesaw Hydrometeorological Extremes in New Zealand: A Copula-Based Approach

Morgan J. Bennet, Daniel G. Kingston, and Nicolas J. Cullen

Abstract. Compound hot and dry and dry-to-wet seesaw events are hydrometeorological extremes that involve the propagation of water deficits through the hydrological cycle, driven by multiple interactions between precipitation, temperature and soil moisture. Here we demonstrate new understanding of such events gained by directly modelling these interactions using copulas rather than treating each variable separately. New Zealand makes for a useful case study, owing to the occurrence of relatively high-magnitude extremes across strong hydroclimatic gradients. Standardised indices are constructed for soil moisture, temperature and precipitation using ERA5-Land for 1950–2021. A conventional bivariate copula model is used to capture the joint variation between precipitation and soil moisture indices for seesaw events, with a more novel trivariate (vine) copula for modelling all three indices during compound events. Differences in compound event detection are strongest in eastern regions, where evapotranspiration is more important for dry phase development. The copula approach reveals more frequent/extreme occurrence of compound events compared to coincident extremes in separate variables: for a 1-in-100-year vine copula event the equivalent magnitude coincident soil moisture and temperature extreme is a 141-year event (171-year for the coincident precipitation-temperature event). Large differences in seesaw event detection also occur in the east: compared to a 1-in-100-year bivariate copula event the equivalent soil moisture extreme is less frequent (126 years) but the precipitation extreme more frequent (65 years). These results highlight the advances that a copula approach can provide in terms of better understanding the magnitude-frequency characteristics of compound and seesaw events, as well as their drivers – critically important for managing the impacts of these events, especially in the context of climate change.

Received: 11 Aug 2025 – Discussion started: 04 Sep 2025

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Morgan J. Bennet, Daniel G. Kingston, and Nicolas J. Cullen

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RC1:
'Comment on egusphere-2025-3592', Anonymous Referee #1, 02 Oct 2025 reply
Bennet et al. compare different approaches to detect compound and seesaw events across New Zealand, particularly focusing on the potential value of using multivariate copula-based approaches. They recommend using multivariate indices (incl. soil moisture metrics) for assessing compound hot-dry events, whereas the selection of indices for seesaw events may depend on the hydrological domain (i.e., drought type or dry phase) investigated. The manuscript is a valuable contribution to research on compound events and is for the most part well written. Nevertheless, it would benefit from some corrections outlined below, which the authors may want to consider. Overall, I would recommend publication subject to major revisions.

General comments
In the Introduction, it would be helpful if the authors placed more emphasis on describing the specific knowledge gap they are addressing and the objectives they want to meet. Specifically, the description of the objectives in the last paragraph of the Introduction is somewhat unclear and would benefit from clear structuring, e.g., by using numbering (1), (2), ... to indicate the specific objective.

In the last paragraph of the Discussion, the authors briefly discuss the topic of selecting the indicators for hot-dry and seesaw event detection. As also shown in the Results, detection of hot-dry events is more sensitive to the indicators used compared to seesaw events, where no approach is somewhat superior to another. It would be beneficial if the authors would discuss more in detail the reasons for this discrepancy, possibly also in terms of the different copula indices (SMI and SBI) used for the two event types.

The Discussion partly reads like an introduction (especially section 4.1) or like a summary of the results (e.g., lines 506-512). In this regard, the Discussion may be shortened and more specifically focus on discussing the objectives outlined in the Introduction (see also first comment).

Although the authors briefly mention the role of evapotranspiration in the Discussion section 4.2, a more thorough discussion on how seasonality in evapotranspiration influences the indices investigated (related to both compound and seesaw events) would be valuable.

Minor comments
Line 62: This sentence may rather fit into the paragraph talking about copulas (Line 50 and following)
Line 79: “new insights” is a somewhat vague formulation and may be replaced with a more specific objective (see also first general comment)
Line 107: It would be helpful for the reader if the authors would provide the equations for the respective calculated indices
Line 159: When describing the Standardised Multivariate Index (SMI), it may be beneficial to shortly repeat the original variables (precipitation, …) contained in the copula data which are then represented by the index
Line 193: The description of the averaging process at each grid cell is partly unclear (“taking the mean” of what exactly?) and a more thorough explanation would be valuable
Line 206: The authors may provide a short explanation of why 14 days were chosen as a threshold length for the compound event duration
Line 260: Here, the authors may briefly mention variations of the run theory metrics between the North and South Island (in terms of the coincident SSMI and STI approach), as is also displayed in Figure 3b and 3e
Line 363: “longer transition time” compared to which approaches? It becomes clear from Figure 8, but it would be beneficial to shortly mention the two other approaches in this sentence
Line 423: This sentence is rather long and may be split
Line 506: This paragraph may be moved to the Results section
Line 548: The authors may consider renaming this section “Summary and conclusions”, as the text up until line 572 reads like a summary
Line 581: This sentence is rather long and may be split

Technical points
The figures would benefit from increasing the font sizes on the x- and y-axis and legends, particularly figures 2, 3, 6, 7

For an overview, a table with the indices (and their abbreviations) used and the respective approaches applied would be helpful for the reader

Please ensure that headings follow a consecutive order (e.g., 2.5.2 appears two times) and do not repeat themselves (e.g., 2.3.1 Preliminary work on Vine Copula Structure and 2.3.2 Preliminary work on Vine Copula Structure)

In the Supplement, the authors may provide a reference list for the sources they cite, even if they already appear in the original manuscript’s reference list

For better coherence, it would be helpful to not repeat content in the Supplement that has already been written in the manuscript (and vice versa); this particularly relates to the Data and Methods sections. In general, I would recommend to shorten the sections describing the methods and refer the reader to the Supplement for more in-depth information, e.g., on the preliminary work conducted (sections 2.3.1 and 2.3.2)

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Citation: https://doi.org/10.5194/egusphere-2025-3592-RC1

Morgan J. Bennet, Daniel G. Kingston, and Nicolas J. Cullen

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https://doi.org/10.5194/egusphere-2025-3592-supplement

Morgan J. Bennet, Daniel G. Kingston, and Nicolas J. Cullen

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Short summary

The temperature, precipitation and soil moisture drivers of extreme hot-dry compound events and rapid dry-to-wet seesaw events are modelled for New Zealand using tri- and bi-variate copulas (respectively), as well as a more conventional approach of analysing each variable separately. Copula-based direct modelling of the joint variation between these variables reveals that the conventional approach leads predominantly to the underestimation of return periods for these extreme events.


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