Review of “Reduced non-Gaussianity by 30-second rapid update in convective-scale numerical weather prediction ” by J. Ruiz et al..

General comments: The manuscript investigated the degree of non-Gaussianity of forecast error distributions and how it is affected by the DA update frequency and observation number. This article used 1000 ensembles, but the generation of ensembles is not very clear. The introduction of the KLD method is not clear. Some words are not rigorous. This paper theoretically provides evidence that increasing the update frequency and the observations can improve the accuracy of assimilation in convective-scale. I think this manuscript can be considered for publication if these concerns could be addressed:

Specific comments: 

1. The generation of ensembles need to be described in detail, because it is very important for this article and the ensemble DA method.
2. The introduction of KLD should containhow to operate in this article? What should be noted? So that readers can repeat your experiment
3. Is the solution of KLD grid point by grid ? Using the assimilated ensembles to statistics?
4. Please give the formula of relative KLD difference.
5. Please explain "closest" quantitatively.
6. The higher the update frequency, will it break the balance between physical variables? How to understand and explain.
7. This paper used the super-observations. What is the relationship between observation scale and grid scale matching and more observations?
8. This article needs polishing.

Review of “Reduced non-Gaussianity by 30-second rapid update in convective-scale numerical weather prediction ” by J. Ruiz et al..

General comments:

This paper has investigated how the DA frequencies affect non-Gaussianity using a high resolution NWP model with LETKF method for data assimilation. DA experiments with different frequencies are conducted using real observations. They have some findings about the non-Gaussianity in data assimilation, which are quite new and interesting. They have used a high resolution DA system with very high DA frequencies to support their conclusions. And they have analyzed the results comprehensively. The manuscript is overall well-written. I am in support of publishing this manuscript after minor revision.

Specific comments:

1. This work measures the non-Gaussianity (by KLD) of the analysis fields. They found that increasing the assimilation frequency up to 30 seconds and assimilating more observations can reduce KLD. This conclusion can be expected easily. As acknowledged, EnKF and LETKF are sub-optimal when the forecast error are non-Gaussian, and the non-Gaussianity of the forecast error grows during model integration. If the DA frequency is higher, the non-Gaussianity of the forecast will be smaller due to shorter integration period, therefore the EnKF will be more effective.

   However, they didn’t show the KLD of the prior error distribution. If they can compare the posterior KLD with prior KLD with different DA frequencies, they can better illustrate the “reduced non-Gaussianity by 30-second rapid update” in the title.

2. Page 5, lines 110-125 and figure 2. Compared with the rest of this article, the readability of this paragraph is poor. They have shown too much information in figure 2, such that they need to use parentheses constantly to indicate the subplots and features (shades or contours) in figure 2. And there are also some problems with the order of expression in this paragraph, therefore the readers have to look at the subplots back and forth. I suggest splitting the paragraph from line 116 or 117.

3. Figure 2e-h, they use shades to show KLD for W, while use blue contours for KLD for T and red contours for ensemble spread. This is very odd. In my opinion, use contours of different colors to show KLD for different variables seems more reasonable.

4. Figure 2a-h, the location of the maximum KLD for vertical velocity is shown by blue circles. I think the circle is too large and its color is inappropriate. I cannot clearly see whether the ensemble spread maxima are slightly out of phase with respect to the KLD maxima. What about a black x or plus sign?

5. Line 114 and line 117. The authors have shown that “KLD is reduced more from 5MIN to 2MIN than from 1MIN to 30SEC” and “The ensemble spread for W is reduced significantly from 5MIN to 2MIN”. I think this is also associated with the nonlinearity of this model. Could it possible that the non-Gaussianity of prior distribution grows fastest during the freerun between 2min to 5min?

6. Since increasing the analysis update frequency from 5 minutes to 2 minutes has most significant impact upon non-Gaussianity. So can we say it is a optimal strategy considering the trade-off between cost and efficiency?

General comments:

This study focuses on investigating the impacts of DA update frequency and observation number on the non-Gaussianity of model simulation error, in a case of strong convection. Results shown in the manuscript show that the non-Gaussianity of error can be reduced by increasing the DA frequency and number of observations, which could possibly improve the performance of EnKF. While the results are impressive, there are several problems the authors may need to address before the manuscript is published. I hereby recommend a major revision.

Specific comments:

1. Model configuration: The authors did not provide enough information about the model’s configurations. In line 59, the model used in this study has a horizontal resolution of 1 km, 50 vertical sigma levels, and a size of 180 km by 180 km (Fig. 1a). I wonder what the range and resolution of the vertical sigma levels are defined. According to my knowledge, models with higher horizontal resolutions should also have higher vertical resolutions. The number of vertical levels of the model introduced in this study is probably too coarse for 1km-scale simulations. (also see specific comment 2)
2. According to the paper, better results of radar data assimilation were obtained with vertical localization scale of 2 km and horizontal localization of 4 km (Line 70 – 73). In this sense, a 1:2 ratio of the horizontal to vertical resolutions of the model could give more reliable simulation results. i.e., If, in this study, the model’s horizontal resolution if set as 1 km, then the vertical resolution could be set as around 500 m.
3. The authors mentioned that the non-Gaussianity reduced by 40% when assimilation window length shortened from 5 minutes to 30 seconds. What are the main benefits from the reduction? The authors claimed that this could improve the performance of the EnKF, without showing any evidence. It might be better by simply showing the error of precipitation output simulated in different experiments.
4. 2e–h: The authors marked the location of the maximum KLD for vertical velocity at the lower troposphere in Fig. 2f, but middle troposphere in Figs. 2e, 2g and 2h even though a maximum KLD center is not obvious in Figs. 2g and 2h. If the authors intended to emphasize the improvement of KLD in the middle troposphere, they should consider the KLD in the middle troposphere in all cases.
5. 5b and 5h: The main highlight of this figure (which is also that of the manuscript) is improvement in the KLD with higher DA frequency. However, Fig. 5 also shows obvious increase in the KLD of specific humidity in the 30SEC experiment, in both the raining and non-raining cases. And, it seems that the authors did not make any discussion on these results. While there are great improvements in KLD of most grid points, especially that of vertical velocity when the authors focus on convective-scale simulation, why is the same improvement not obtained for specific humidity? Are errors generated from the more frequent DA update?
6. Line 67: “… Climate Forecast System Reanalysis Saha et al. (2010)” à “… Climate Forecast System Reanalysis (Saha et al., 2010)”
7. Line 99 and Eq.(1): “where P(x) and Q(x) are two . . . “ à should be “where p(x) and q(x) are two . . .”?
8. Lines 140–141: Wrong use of “so that”.
9. Lines 144: “raining” and “non-raining” grid points sound better than “rain” and “non-rain” grid points to me.