General comments:

This study focuses on the sub-seasonal predictability of heat waves over Europe using the ECMWF model. The variable studied here is 'heat wave days,' which refers to the number of 5-day periods whose average temperature exceeds the 90th percentile of the climatological distribution. This approach highlights certain performances beyond week 2, particularly for the most intense and prolonged episodes, and mostly over the eastern half of the continent.

In general, the scientific question addressed and the method to answer it are entirely relevant and sound. Among other interesting results, I find particularly original and smart the evaluation of the capacity of the model to predict the life cycle of heat waves, taking into account the relative time of forecast issuance and heatwave initiation. However, in my view three aspects need to be revised or further elaborated before the manuscript can be accepted. These points, detailed below, concern first the structure of the manuscript which requires improvements, then the case of the summer of 2010 which needs to be further discussed, and also some missing specifications in the description of the method.

Specific comments

1- Paper organization:

I find the organization of the manuscript rather clumsy, in particular the discussion part that dwells into strategies of adaptation to heat, thereby repeating or elaborating some elements of the introduction. Additionally, it sometimes go quite far (too far!) into details when it comes to adaptation and preparedness measures, keeping in mind that the core of the paper is an evaluation of heat wave forecast skill.

The conclusion reads like a shorter repetition of the discussion. 

Finally, the part of the discussion providing avenues for enhancing heat wave forecast skill (hence more aligned with the main work of this paper) refers very vaguely to “additional bias techniques” and cites  a list of (sub-)seasonal forecast predictors without indicating in which manner they could contribute to refine the heat wave forecasts.  

2- Impact of the summer of 2010 in eastern Europe / western Russia:

That summer was characterized by a particularly long lasting heat wave over that region, and this is well reflected in your manuscript. Yet, that summer of 2010 seems to ‘contaminate’ your results and conclusions  : it is particularly obvious when comparing your fig. 4g with 4i (and 4j with 4l), keeping fig. 2a in mind. Without that particular summer of 2010, most of the skill over Europe is gone in weeks 3 and 4.

Could you elaborate on this, and discuss the significance of your results considering the huge weight of that event ?

3- Method: 

 L.115-117: It is not very clear if your take the lead time into account when computing the 90th𝑇𝐸𝐶5𝑑  .  For example, when computing this value for, say, July 1st : do you compute one single value by pooling together all the hindcast members that include the sequence July 1st- July 5th (regardless of the start date) ? Or instead, do you compute different percentile values according to the lead time (i.e. one value if July 1st is part of week 1, another one if it is part of week 2 etc.) ?

From my understanding, the former strategy allows a larger statistical sample to compute percentiles, but on the other hand, there is a potential impact of lead-time dependency. The latter one seems more accurate from this point of view but then of course the sample size is smaller. I guess the “lead time dependent climatology” indicated on l.125 refers to this strategy.

Additionally, you should specify the range of start dates used in the method. I believe this would help understand how you computed percentiles for the very first days of June in particular. In other words, did you include hindcasts initialized in early May, to ensure a homogeneous sample size throughout all summer days ? Or did you only consider the first days of June as part of ‘‘week 1” lead time)?

Could you clarify (and potentially discuss) these method points in the manuscript ? Maybe include a schematic or a table if needed. 

Technical corrections:

L.179 “by change” => “by chance” (?)

L.196 Do you mean “how early a heat wave becomes…” or “how early heat wave days become” ?

L.248-250 : OK, but this sounds more like a rephrasing of what precedes than a new information.

1. 271-273: Nice result for week 3 but it would be fair to remind that the sample size of week 3 forecasts with p>0.5 is probably very small, considering Figure 3a.  So I think this result should be considered with a pinch of salt.

Figure 1: I would recommend to display the 4 ECMWF maps as “bias wrt. ERA5”, ie plotting the difference “ECMWF minus ERA5”. The associated comment L. 213 would be more convincing.

1. 268 and elsewhere : Choose between “Figure 3(b)” or Figure “3b” (even better: remove one of them) and choose also between “Fig.” and “Figure” . 

Non-existing “Figure 3d” shows on L. 272. Better remove it, since it seems quite obvious that you keep commenting Figure 3b here.

1. 294: Typo (?) . I was expecting : “Eastern Europe (summer 2010)“

L.319-326: Ok but this part is very unpleasant to read. Please rephrase by not repeating the exact same sentence 4 times !

1. 406: heat-health action plans (2 typos)