Thank your for taking the time to review the manuscript and give critical feedback.

Below, we reproduce your comments/suggestion in bold font, followed by our response in non-bold font. Italicized text indicates proposed additional material that will be inserted into the revised manuscript.

While the mathematical rigor is a strength, early sections could benefit from briefly reinforcing why these inconsistencies in risk matrices matter for public safety and policy credibility. Consider simplifying the initial explanation of “forecast directive” and “warning directive” for non-technical readers.

Thanks for this suggestion. We will add a couple of extra sentences in the manuscript to help orientate the reader with the "forecast directive" terminology. When the term "forecast directive" is forecast introduced (L25), we will give the following simple example:

     For example, a forecast directive for a warning service for damaging wind gusts might be "Issue a warning if and only if the probability of a wind gust exceeding 90 km/h is at least 10%".

We will also elaborate why directives are important by inserting an additional sentence after the existing sentence starting at L43:

    When warning decision process lacks adequate definition, two forecasters with identical probabilistic assessments of the hazard could issue two different warning levels. This may lead to warning messages that fluctuate unnecessarily, compromising both public safety and service credibility.

The distinction from the UK Met Office (UKMO) and other operational frameworks is clear, but it might help to include a side-by-side visual comparison in an appendix or supplementary material (if possible).

We think implementing this suggestion will be helpful for the reader. We have prepared a side-by-side visual comparison which fits naturally in Section 2.2 as a new figure. The text of Section 2.2 will also be updated to reference this visual comparison.

The method for deriving weights from stakeholder input (e.g., community consultation on false alarm vs. miss costs) is strong. However, a brief reflection on the subjectivity and variability in such consultations would add depth.

We believe that such discussion on this is beyond the scope of the current work. However, we will include a brief sentence at the end of Section 3.1 to note that the development of our framework motivates further research:

    Although the process for determining weights in this fictitious flood example was presented straightforwardly, this framework motivates further research into developing best practices for eliciting thresholds and weights through stakeholder consultation.

Although the framework is hazard-agnostic, a discussion on how it could scale or adapt to multi-hazard interactions (e.g., flood + wind) would strengthen its applicability. That being said, it would be helpful to shed light on this framework toward earthquake hazards as they are growing in frequency (if possible).

We will include the following comment near the end of Section 2.1 on the applicability of the framework to a generic index, which may account for multi-hazard interactions:

     More generally, the framework could be applied to an index, which itself represents complex multi-hazard interactions. An example of such an index is the Fire Behaviour Index (FBI) used in the Australian Fire Danger Ratings System (AFDRS), which combines weather and fuel state information to determine the severity of fire behaviour.

Although the framework is applicable to earthquake hazards, we believe it is not appropriate to discuss this in detail, as earthquakes lie outside the authors' area of expertise.

The use of distinct matrices for LONG-, MID-, and SHORT-range phases is excellent. It would be helpful to mention how this could be dynamically updated as new ensemble data arrives.

How the arrival of new ensemble data impacts the warning issue process will depend on the way each warning service is designed. Going into such details is beyond the scope of this manuscript but could be explored using concrete warning service examples in a follow-up paper. Nonetheless, we note here that there are at least two factors at play. One is where the lead time phases are a function of the onset to severe phenomena, and new ensemble data shifts the time of onset sufficiently to change the phase. The other is where new ensemble data leads to a re-evaluation of the likelihood and/or severity of the phenomena, which may prompt an update of the warning based on pre-defined amendment criteria for the warning service.

Thank you for reading the manuscript and your positive review

Thank you for reading the manuscript and your positive review