General comments:

This paper presents a detailed description of the methodology in the preparation of the boundary conditions for PGW simulations, provided in the companion software PGW4ERA5. As the authors have said, the PGW approach offers several benefits, so it will be attractive not only for climatologists but also for the groups who are not familiar with atmospheric dynamics and have interest in impact assessment of future climate change in a certain field. The proposed software and this description paper must support such groups.

This paper basically includes sufficient information as a description paper of PGW4ERA5. This paper is also worthy in that the several specific considerations when preparing boundary conditions for PGW simulations are described based on the authors’ knowledge and results of sensitivity experiments. On the other hand, there are somewhat insufficient points in terms of discussing how appropriate it is to create boundary conditions for PGW experiments. Whether those insufficient points should be included or not may be a matter of opinion. However, since this paper is expected to be useful to readers who want to know the specific procedures of the PGW method, and not just a description paper, it is suggested the authors revise the manuscript following the comments below prior to publication.

Specific comments:

[1]

The method presented in this paper to create the lateral boundary data for a PGW experiment is one of several options; the procedure in this paper uses ERA data on the original (hybrid) coordinate as a base climate and the changes in geopotential at the reference level obtained from pressure level GCM data. On the other hand, the simplest and easiest option may be the case of using pressure level data both for reanalysis (base climate) and GCM (climate change) data. In this case, one can simply add Δφ given from the GCM to the reanalysis data without pressure adjustment. The impacts on the RCM (PGW) results of using reanalysis data on pressure level instead of the original ERA-coordinate as a base climate should be mentioned, because many RCM users usually use pressure level data for boundary conditions.

The boundary conditions are further converted to the RCM coordinate for calculation because the coordinate of a GCM or reanalysis providing boundary conditions usually differs from that of the RCM. At that time, the bias in pressure adjustment generated in the conversion procedure to the RCM coordinate will be more significant in the case of using pressure level data than the original coordinate data. Therefore, it is also important to evaluate the magnitude of the bias and to indicate the authors' opinion on the use of pressure level data for base climate.

[2] Sec. 2.6 (L. 246): How do you determine the convergence of iterations? Please describe the definition of convergence determination.

[3] L.267-271 and Figure 4

How were "errors in the integration of φ'_ref and in the adjusted surface pressure" obtained? Please describe more in detail. For example, does it mean that the error in Δφ_ref in Figure 4 is Δφ'_ref^N - Δφ_ref^GCM? Note that, Δφ'_ref^N = φ'_ref^N - φ_ref and N is the number of n when iteration is converged, and Δφ_ref^GCM is climate change of φ at the reference level obtained from GCM. However, the iteration should be performed until Δφ'_ref^N agrees with Δφ_ref^GCM, as described in L.229-231. Why are there large differences as shown in Figure 4? Alternatively, does Figure 4 show the results of the difference between Δφ^GCM recalculated by Eq. (7) using only AMON/EMON data and Δφ directly provided in the AMON/EMON data, which is calculated using the native grid data? Either way, a more careful description is needed.

[4] Section 4.3

There are other ways to treat humidity changes in PGW methods; for example, there is the idea of not considering the change in RH (as introduced in Sec. 4.5.2 of Adachi and Tomita, (2020)). It is better to mention those other methods. In addition, when the temperature is below 0°C (upper atmospheric level), there are two definitions of RH. It is possible that the definitions may differ between the reanalysis data and a GCM. In such cases, simply summing them is undesirable.

Technical corrections:

[1] L.50-54: What is described here is correct, however, this explanation may lead readers to misunderstand that this paper focuses on the preservation of the hydrostatic balance when converting from the driving reanalysis/PGW coordinate (i.e., boundary conditions) to the RCM coordinate, for instance, HIST_ERA to HIST_LBC or PGW_ERA to PGW_LBC in Figure 2. In fact, the paper explains how to maintain the hydrostatic balance when adding the climate change Δ in the GCM coordinate system to the base climate (i.e., reanalysis data), although the concept is the same in either case. In other words, the treatment of hydrostatic balance when converting boundary conditions with the driving reanalysis/PGW coordinate to the RCM coordinate depends on a used RCM's internal procedure.

[2] L.70: “Figures 1 and 6” --- “Figure 1 and Figures 6e and f, respectively” will be better.

[3] L.93-95: While it may be difficult to refer to all the studies using the PGW method, it is suggested to cite several pioneering studies. For example, there are studies that investigated changes in precipitation (Sato et al., 2007; Kawase et al., 2009), temperature changes (Adachi et al., 2012), and snow changes (Hara et al., 2008).

• Sato et al., 2007, Journal of Hydrology, https://doi.org/10.1016/j.jhydrol.2006.07.023
• Kawase et al., 2009, JGR, https://doi.org/10.1029/2009JD011803
• Adachi et al., 2012, JAMC, https://doi.org/10.1175/JAMC-D-11-0137.1
• Hara et al., 2008, Hydrological Research Letter, https://doi.org/10.3178/hrl.2.61

[4] L.115-122: The difference between “Complete GCM output” and “CFDAY data” is not clear. Both data have the same category on a temporal resolution, i.e., daily, and a spatial resolution, i.e., the original/native (GCM) grid.

[5] L.161-162: Please add a reference related to “nonlinear heuristic procedures”, if possible.

[6] L.202-204: If my understanding is correct, the description here is not accurate. Δ in the GCM coordinate system is interpolated to the ERA grid to add it to ERA reanalysis, and then the merged data (Δ+ERA) is regridded from the ERA grid to the coordinate of the target RCM.

[7] L.252: It would be better to add “Eq.(7)” such as “(see Subsection 2.5 and Eq. (7))”

[8] L.266: Does it mean “on the native vertical grid of the GCM”?

[9] Caption of Figure 4: What is the P_s in the caption? Does it mean P_sfc?

[10] L.322: The definition of EKE would be better moved to L.291, where EKE first appears.

The pseudo-global warming (PGW) approach, pioneered by Schar et al (1996), has been widely used in the regional climate modeling community as an alternative to the traditional GCM-based dynamical downscaling strategy. This manuscript presents an overview of the methodology and provides a detailed description of the forcing construction for PGW simulations in the case of the COSMO-CLM regional climate model (RCM) and ERA5 reanalysis. The pressure adjustment is particularly highlighted to maintain the important physical and dynamical balances in large-scale motions, such as the hydrostatic balance, the thermal wind balance, and the geostrophic balance. The methodology is validated by comparing against the standard GCM-RCM simulation and a set of sensitivity tests. Along with the development of a Python-based software package (i.e., PGW4ERA5), this work will greatly facilitate the preparation and implementation of PGW-type simulations and further promote the application of the PGW approach in the regional climate modeling community. I have a few comments for the authors' consideration and clarification.

1. The authors focus on the construction of the three-dimensional fields which are required for deriving the lateral boundary conditions for PGW simulations, but completely ignore the discussion on the construction of lower boundary conditions such as sea surface temperature, sea ice, sea level pressure etc. As well as the text, the workflow in Figure 2 needs revisions to include the missed information of lower boundary conditions.

2. The proposed procedures for PGW simulations are specifically designed for the COSMO-CLM model, but are generally applicable to other RCMs. Nevertheless, some adjustments may be necessary when the software package is applied to other models because of different initialization and input data processing strategy. For example, in the case of the WRF model surface pressure is computed using the input sea level pressure and geopotential at pressure levels by the standard initialization module, and the computed surface pressure and input temperature fields are then used to reconstruct the geopotential using the hydrostatic equation. In this particular case, perhaps the pressure adjustment is only required for surface pressure.

3. As far as I'm aware, outside Europe the 38-pressure-level ERA5 data are most commonly used, instead of the native model level data; the latter is much larger and its downloading is time-consuming.

4. English editing is needed to correct grammatical errors.