We would like to express gratitude to anonymous referee no. 1 for reviewing the preprint and their contribution to quality control. Their comments are highly appreciated and of great value to improve the scientific value of the paper.

Line 24 – the references to models that explicitly use Bz as a parameter is incomplete, I suggest to add “for example” to the brackets with references.

Thank you for pointing that out, “e.g.” was added to the citations.

Line 42 – I suggest discarding the sentence about Sh98 model starting in this line and continue the text.

The sentence is removed for a better overall flow.

Line 125 – The formula uses only the Earth orbital motion, but the aberration depends on the perpendicular solar wind components. Its true that analysis in Safrankova et al. (2002) revealed that the application of propagated values of perpendicular components does not improve the prediction significantly and the authors argue that the main reason is probably the uncertainty in propagation of these component. However, Nemecek et al. (2020) have shown that there is a systematic deflection of the solar wind from the radial direction in the fast wind and application of this finding can further improve the prediction. This point would be discussed.

Thank you for this interesting comment. We added some sentences starting in line 126 and 129 discussing the remark. The paragraph reads as follows:

“Equation 4 is a simplification of the exact formula ψ=arctan(v_⊥/v_x), where v_⊥=v_y+v_E. Since the v_x component dominates the solar wind direction, v_x≈v can be assumed safely. The v_y component however is often not small compared to v_E, especially not in the fast solar wind where the flow deflection has a median value of 18 km s^-1 (Nemecek et al., 2020a). Including the v_y component would increase the absolute aberration by almost two degrees which especially effects the position of the MPCs on the nightside. In the subsolar region, the aberration of the position is neglected since the effect is smaller and the absolute value of the magnetopause distance, which is unchanged by the aberration correction, is more important for our model than the exact position of the MPC. By rotating coordinate sensitive parameters, such as the position and the IMF, by ψ around the z-axis, the system is transformed into aberrated GSE (AGSE) coordinates. Again, the transformation is done for each MPC separately with its respective aberration angle. Derived quantities (like the clock and cone angles, the zenith angle, etc.) are then recomputed in AGSE format. A comparison of the AGSE IMF components derived with this method to those obtained when the aberration includes the v_y component (see above) shows discrepancies of only a few tenths of a nanotesla. We argue that that the uncertainty in the IMF data is larger than this deviation and therefore use the simplified equation for the aberration. Including v_y could be considered in future studies to account for the aforementioned effects more precisely.”

Lines 254 and 255 – I would suggest to rephrase the sentence, because the quantities like n_estimator or learning_rate  are specific for the software used and they are not necessarily clear for readers that are not familiar with ML techniques.

We have added an explanation that specifies what the hyperparameter names mean in a more general setting, not exclusive to the used software. The sentence reads:

“All but three hyperparameters of the XGB model are kept at their default values. The adjusted hyperparameters are the number of trees in the random forest (n_estimators = 1000), the depth, i.e. number of decisions, of each tree (max_depth = 6), and the contribution of each tree, which also influences how conservative the model is and how it generalizes (learning_rate = 0.05).”

Line 329 – The authors probably have in mind “spatial coverage”

That is right, the typo is corrected.

References:

Němeček, Z; Ďurovcová, T; Šafránková, J; Richardson, JD; Šimůnek, J; Stevens, ML, (Non)radial Solar Wind Propagation through the Heliosphere, Astrophys. J. Lett., 897 (2): Art. No. L39, 2020.

Safrankova, J; Nemecek, Z; Dusik, S; Prech, L; Sibeck, DG; Borodkova, NN, The magnetopause shape and location: a comparison of the Interball and Geotail observations with models, Ann. Geophys., 20 (3): 301–309, 2002.

We would like to express gratitude to anonymous referee no. 2 for reviewing the preprint and their contribution to quality control. Their comments are highly appreciated and of great value to improve the scientific value of the paper.

The manuscript refers to a second-order polynomial representation of the subsolar standoff distance but does not provide its explicit formula. I think that including a mathematical expression for the second-order polynomial model would greatly enhance accessibility and allow other researchers to readily implement the model.

Thank you for the comment, we included the formula for the non-reduced polynomial model as equation (B1). r₀ is given in units of R_E, parameters are without units since they are expected to be scaled as explained in the text before they are used in the formula. Table B1 has been removed since the added written out formula provides the same information and the table would be redundant. Appendix B has been renamed as well since it now contains the model equation.