Prior to the start of EISCAT_3D radar observations, this paper shows how the accuracy of the ionospheric potential reconstruction changes by varying the beam pattern of the EISCAT_3D radar. It deserves publication with some minor modifications, as this is a very important toolkit needed when designing experiments according to the scientific objectives of each user.

Minor revisions:

Figures 4g-i: The scatter plots are used to show that the accuracy of the estimation results is good, but information on where the residuals are small is lost if only the scatter plots are used. It is therefore recommended that the scatterplot is replaced or added to a two-dimensional heatmap displaying the residuals of the estimates for GEMINI.

Equation (6): Definition of "N" should be added. 

Equation (10): It is suggested that a more detailed explanation of formula conversions be added, in addition to citing references, to make it easier for the reader to understand.

Line 173: It is helpful for readers to add more detailed explanation about B.2.4 of Lehtinen et al. (2014).

Line 201–202: Why were uncertainties estimated by this study underestimated relative to those of GUISDAP above ~300-km altitudes? Are assumptions used in GUISDAP desirable compared to e3doubt?

Line 314: The abbreviation "SECS" should be added after "spherical elementary current system".

Line 331: "Madelaire et al. (2023)" should be "(Madelaire et al., 2023)".

Line 345: "(Reistad et al., 2024)" should be "Reistad et al. (2024)".

This paper presents a software toolkit (“e3doubt”) that allows to estimate the uncertainty of plasma parameter measurements with the upcoming EISCAT_3D incoherent scatter radar system. Since phased-array incoherent scatter radars like EISCAT_3D can be run in a large variety of measurement settings to accommodate different spatial and temporal resolutions, such a toolkit will allow conducting individual observing system simulation experiments (OSSEs) for specific processes. The low computational requirements and its applicability for ionosphere scientists who are not ISR experts make e3doubt a clear improvement over existing software.

The underlying equations (e.g., radar equation, incoherent scatter spectrum, noise levels) are well described, and the applied assumptions and simplifications are clearly stated. Two experiment examples are presented to demonstrate the developed toolkit. The uncertainties estimated with e3doubt for a 1-hour measurement window with the existing EISCAT UHF are compared to uncertainty estimates given by the ISR analysis software GUISDAP. It is shown that the e3doubt uncertainty estimate is very close to the GUISDAP estimate, though both are considerably lower than the actual variability of the plasma parameters.

There are some minor concerns regarding the provided guidelines in Section 4. If this section is to be seen as a general manual for e3doubt, a more distinguished identification of the single steps should be provided during the examples in Section 5. Additionally, I think it would be beneficial if the examples in Section 5 were more focused on how e3doubt can help with the decision-making process when designing E3D experiments. Other open questions remain about the underestimation of parameter uncertainties in the topside ionosphere (Figure 2) and a more detailed discussion of the simplifying assumptions that are employed to allow for the low computational overhead in comparison with Swoboda et al., 2017.

Overall, the paper is well-written and addresses an important issue. The comments below mostly address the discussion and presentation of the provided examples. I therefore see the paper to be suitable for publication after minor revisions.

Minor comments:

Guidelines in Section 5 examples

Section 4 introduces a set of guidelines for designing E3D experiments to study specific processes with the help of e3doubt. I think this is an excellent approach, but the demonstration in Section 5 is somewhat incomprehensible. In Section 5.1, steps 1-3 of the proposed guidelines are described in detail, but step 4 is neglected, though it is the crucial part of the whole process. The selection of the beam pattern shown in Figure 3 appears to be somewhat arbitrary. Why was this beam pattern selected? How does the sampling in 5 km intervals translate to bit length? Why was an integration time of 7.5s chosen (see also in the next comment)? It would be helpful if step 4 of the guidelines were discussed similarly as the first three steps. Maybe a comparison of two (reasonable) experiment setups and their impact on the resulting errors would be helpful. In Section 5.2, a similar step-by-step explanation should be added.

Integration time

In line 302, you state that the integration time per beam for the chosen experiment mode is 7.5 s. This is significantly shorter than the common integration times for the classical EISCAT systems (~1 min, sometimes 30s). Does EISCAT_3D generally allow for lower integration times (e.g., due to higher antenna gain, transmission power)? Please add a short clarification for readers who are familiar with the classical EISCAT systems but not the upcoming E3D.

Pre-defined set-ups (Common Programmes)

As mentioned already above, the selection of the beam patterns in Section 5 (except for the one taken from Reistad et al.) appears to be somewhat arbitrary. Does e3doubt contain a pre-defined set of beam patterns, and if yes, how (by what criteria) are they selected? Making the experiment design process more accessible is, from my point of view, the key point of the paper, and hence, should be explained rather than just stated. Once E3D Common Programmes have been designed and selected, will they be made available as predefined setups in e3doubt?

Differences between e3doubt and GUISDAP uncertainties

In Figure 2 e-h, it can be seen that in the topside ionosphere, the e3doubt uncertainty estimates are lower than the GUISDAP estimates for all plasma parameters. Can this trend be pinned to a specific assumption made in Section 2? Also, there is an interesting spike in the e3doubt uncertainty estimate for electron density around the F2 peak. I am aware that such features cannot always be explained in detail, but I would like to see the discussion of Figure 2 e-h in lines 191-198 extended.

Discussion of assumptions for low computational demand

One of the key improvements of the presented toolkit is its low computational demands and accessibility to non-radar experts. Hence, the discussion in lines 383-386 is rather short and could be extended. Why is it ok to make these assumptions, and what are the possible consequences on the uncertainty estimate? Especially, the assumptions of a Gaussian beam pattern and pulse shape (l. 106) and a Gaussian electron density profile (l. 114f) for the self-noise calculation are not straightforward to me and should be discussed in more detail.

Technical comments:

• Line 1 (and later): “phased-array” and “phased array” should be used consistently (I think no hyphen is more common, but both are acceptable)
• Line 5: “the the”
• Line 11: Technically, the mean molecular mass also affects the spectrum. As stated later in the paper, 30.5u is usually assumed, which is a fair estimate. I leave it to the authors if they want to add the mean molecular mass to this list
• Line 16: The duty cycle is not discussed later in the paper (e.g., in Section 4 together with bit length and range resolution).
• Figure 1c: The field strength values are cut off at the edge of the figure
• Line 197f: the ACF covariance matrix Σ_l is not labeled as such in Section 2. Is it equivalent to Σ_m?
• Line 402 and Equation A1: “the kth species”. From Equation A1, I would think the labelling of ion species is j?