Thank you very much for your Review. Below are the replies to the comments raised.

Comment 1) The annual cycle is removed by filtering out the annual frequencies. However, the analogs themselves are chosen from candidates with a calendar date within a temporal window centered on the target. I wonder whether the filtering of the annual cycle is really necessary, since all analogs candidates are located in the same 'season' as the target. I do not think the filtering is damaging, but in my view it is not necessary. Perhaps the authors may like to add a couple of sentences to inform the reader

Reply 1) The reviewer notes that the subtraction of the annual cycle may not be necessary since anyway a seasonal window is specified. We will add information on that. Note, first, that this only concerns temperature (pressure is not deseasonalized). Basically, the subtraction of the annual cycle increases the size of the analog pool. This arguably does not matter for most cases, but it does for extremes, as for this extreme winter 1788/89.



Comment 2) Background state in the EnKF. The background state is chose as the best analog. I also wonder whether this is consistent with the calculation of the covariance matrix using all n-nearest neighbour analogs. It seems to me more logical to choose either the average of all n-analogs or possibly the member of the analog ensemble with median distance. Again, perhaps the auhors may want to comment on this

Reply 2) We prefer to work with one analog as this is physically consistent, while an average of analogs is not necessarily physically consistent. Of course, we could choose all n closest analogs as background and update them using the covariance matrix of n analogs and then do the ensemble mean (which again might not be physically consistent). We will discuss this in the revised manuscript.



Comment 3) The Kalman filter set-up is generally used to combine two independent estimations, for instance one from a model run and one from a noisy observation. Both need to be independent for the method to be statistically sound. Here, however, both estimations are not independent: one is the best analog, which uses the observations, and the second is the observation itself. Thus, the separation is not clean, if I am not mistaken.

I would not be very picky here, since the authors test their results with independent observations and the method, pragmatically, indeed works: the EnSK is able to improve the analog-based estimation. However, the more theory-inclined reader may frown upon this dependency. The authors may again want to include a warning or a comment.

Reply 3) The reviewer is correct that the background uses the observations; it is basically an interpolation of observations. However, the target day (and surrounding) is excluded from the pool of analogs, so we never assimilate observations from the same date. We will add a sentence to be more clear on that.

 

Comment 4) ' The RMSE also shows an improvement from 3.4 to 2.7 °C, as does the mean bias from 0.67 to -0.13'

Reply 4) Thanks the unit is °C. We will add that.

Thanks for the review of our paper. We will follow the advice and restructure, re-write, and shorten the paper. The main focus clearly is on the reconstruction itself, as indicated in the title. The current paper has arguably too many aims, and we will revise the paper along your second suggestion (“It could be a paper on a new weather-field reconstruction method combining analogues and EnKF, with a thorough validation using subsampled modern reconstructions, then a case-study on 1788/9”). In particular, the analysis of other cold winters will be dropped (Sect. 2.7 and 3.2.3).

The submitted paper has a long, sub-structured “Results” Section but no “Discussion” section. We will use a “Discussion” to better structure the paper. This section will cover uncertainty and limitations (currently Section 2.6 in the “Methods”), it will compare results with the (few) existing daily products, and it will compare the winter 1788/9 with literature on other winters, without doing own analyses (parts of what is now 2.7). The literature analysis of the winter 1788/9 (currently Section 3.2.1) will be removed from the Results section. In much condensed form it will appear in the Introduction, while some aspects will then be taken up again in the “Discussion”. The data collection part is not the focus and will be further condensed (although it is already very brief).

In all, we think that these indicated changes will lead to a restructured paper that emphasises the main results – the feasibility of daily reconstructions of pressure and temperature over Europe back to the 18^th century. A more detailed reply will follow.

As outlined in our first reply, we have a clear idea of how to restructure the paper (which was judged as "well written" by reviewer 1). We will revise the paper according to our reply. Below are additional replies to minor comments.



Comment: "Please be careful of terminology when describing the method, I'm still not quite sure if 'post-processing' and EnKF mean the same thing, or whether either of them is included in ARM."

Reply:  We will better define our terminology. Our approach goes back to Pfister et al. (2019), where we applied EnKF to update temperature and quantile mapping to debias precipitation data and used "post-processing" as a summary term for both methods. Here we apply EnKF to both variables, temperature and pressure, so there is no need for this terminology except consistency with Pfister. We will explain that. 



Comment: "They might end up with more than one paper"

Reply: The entire study was already split into two papers, of which this is the second. I think we can safely keep it as one paper by dropping the additional analyses of other cold episodes as well as restructuring and shortening as indicated in our first Reply.



Comment: "I'd like to see it successfully published."

Thanks!