We greatly appreciate your  very valuable comments. These are very helpful in guiding the improvement of our manuscript. A point-by-point response to the comments is provided below. We hope this could address the issues..

## Specific comments



- L148-149: It seems that the labels for Exp. 1 and Exp. 2 are mistakenly swapped. In addition, it's not clear what the CTL case is. My guess is that it's a single member free run without data assimilation, but the authors may consider adding some description for each case as well as the idea of the twin-experiment setup so that readers unfamiliar with the experiment can understand.

Reply: Thanks for your comments. Now, the two labels have been swapped back to the correct positions. Moreover, to make the definition clear, descriptions of each case and basic idea of the twin-experiment setup have been added  in line 150-152 as "The CTRL is derived from a single free run, which mirrors the True in all aspects, except for a 60-hour delay in its starting time. The ENS, comprising 40 ensemble members, is generated by introducing an initial perturbation to the CTRL. According to the ENS, the DA twin experiments are implemented by assimilating observations using different localization radii."



- "3.1 Subsection (as Heading 2)" seems like unfinished writing.

Reply: Thanks for your comments. "3.1 Subsection (as Heading 2)" has been corrected to "Description of PDAF"



- L185: "in in"

Reply: Thanks for your comments. "in in" has been corrected to "in"



- The teletype (monospace) font should be applied for routine names.

Reply: Thanks for your comments. We rechecked the content, and the font of all routine names has been changed to 'consolas', including the main text and figures. 



- L373: How can the RMSE of ENS be lower than that of the true state? In addition, the expression "single control run" seems odd. Perhaps the authors mean "single member control run"? 

Reply: Thanks for your comments. In line 373, "and the true state" has been changed to "compared to the true state". Furthermore,  the odd expression "single control run" has been changed to "control run" to make the context consistent. As the currently added description in line 150-152, the control run is defined as a single run, actually the same meaning with "single member control run". 



- L377: "Smaller and large" -> "Smaller and larger" ?

Reply: Thanks for your comments.  In order to avoid mistake and ambiguity, "Smaller and large" has been changed to "Compared to ANA4, either smaller or larger"



- L381: "in Fig. 3" --> "in Fig. 4" ?

Reply: Thanks for your comments. Corrected.



- L387: "Figure 3b and 3c" --> "Figure 4b and 4c" ?

Reply: Thanks for your comments. Corrected. in addition, the label (a),(b),...,(f) have been added to the subfigures.



- L400: Can we expect that the selection of 4dx is a good choice for realistic cases? Or is the optimal selection case by case?

Reply: Thanks for your comments. Actually, the optimal selection is case by case. As we noted in line 405-407, "It is important to emphasize that the experiments conducted based on different localization radii serve as fundamental demonstrations of the functionality of the DA program, with in-depth analysis not being the primary focus of this study." Even in the same case, different assimilation observation (i.e. U or V) may have different optimal selection. To avoid misleading, we added a clarification in line 407 as "In addition, the optimal selection is case dependent." 

See attachment please.