This is an interesting paper that describes a statistical method for estimating vertical profiles of refractivity (N) biases (REFB) in radio occultation (RO) observations. The paper shows that the REFB is related to the local spectral width (LSW) and the temperature and specific humidity in the lower troposphere. While the correlation of REFB with these parameters is already known (Sokolovskiy, 2010; Gorbunov et al. 2015; Sjoberg et al. 2023), the paper is a useful contribution and should be published subject to major revisions.

The paper provides a good review of relevant research and the figures are of high quality. It is fairly well written, but is repetitive, speculative, and confusing in places. I have suggested a number of editorial changes that improve the text and reduce some of the unnecessary speculative and repetitive verbiage, resulting in a shorter, more readable paper. The detailed edits are too numerous to include in this review, so I transmitted them directly to the authors as an edited Word file.

Estimation of the observed refractivity bias is difficult because the true refractivity (Truth) is unknown. Here the reference Truth is taken as the refractivity from ERA5. However, ERA5 is not Truth; it may also be biased. The use of ERA5 as the Truth assumes that the ERA5 biases are small compared to the RO biases, and this is probably a good assumption. This issue is mentioned in the paper, but only at the end in the Conclusions section. It should be mentioned earlier when the bias with respect to ERA5 is defined (in Section 2.1).

The potential use of this statistical technique to estimate the likelihood and magnitude of refractivity biases in individual RO observations for data assimilation (DA) could be mentioned after line 108. However, most global model assimilate bending angles (BA) rather than refractivity. Did the authors try their statistical model to estimate BA biases? If so, they could summarize what they found. If not, this could be a topic for further study.

A key part of this paper is the regression model for REFB vs. LSW or T and q. It is not clear how the two regression equations for LSW and for T and q were obtained. Why is Eq. (5) a quadratic in LSW and not some other relationship (e.g. linear, cubic, or higher order)? Why is Eq. (7) quadratic in Q (normalized specific humidity) plus the product of normalized Q and T? What other polynomials were tested? Presumably some of the process in selecting the optimum polynomial is described in lines 181-188, but additional detail would be useful.

In Section 2.3 the authors say that they derived the statistical models using the data for five different subsets of the data and chose the ones with the best fits as their model. I am not an expert in statistics, but why not use the entire sample of data for their statistical model? The “best” model for one subset may not be the “best” model overall? And if more subsets (e.g. 10) were chosen, a different “best” model would be obtained. This issue should be discussed.

Specific comments

1. Line 123: Fig. 1 is labeled profile density, but it is actually profile counts. The label should be changed.
2. Line 128: The issue with possible biases in the reference (ERA5) should be mentioned here.
3. Sometimes N-REFB is used and other times REFB is used. Please be consistent. Since you are only discussing refractivity biases, I suggest using just REFB. When referring specifically the negative biases, I suggest saying “negative REFB.”
4. 5 caption: I suggest emphasizing that the REFB, LSW, q and T in Fig. 5 are all averages over the lowest 1.5 km MSL. Add to the caption: “The values of REFB, LSW, specific humidity and temperature are averages over the lowest 1.5 km MSL of the atmosphere.” And in line 251 write “the averaged value of REFB below 1.5 km”
5. 6 caption: “Vertical cross section of refractivity bias over the ocean as a function of height and average values over the lowest 1.5 km of (a) LSW/2, (c) specific humidity and (e) temperature over land……….
6. Lines 131-173 (Section 2.2)

This section contains some incorrect or misleading statements and is unnecessary for this paper. For example, in Lines 144-146: “Normal” is not well defined; nonspherically symmetric conditions are common. Spherically symmetric means no horizontal variation of refractivity on a constant level surface, either small-scale turbulent variations in T and q or larger-scale horizontal gradients of T and q. In line 146, a large vertical gradient of refractivity does not necessarily imply nonspherical symmetry, which depends on horizontal variations of N not vertical gradients.

I suggest a much shorter simplified summary that refers to more complete discussions of the causes of negative refractivity biases. Here is an example:

“Negative refractivity biases can arise in the atmosphere from multiple causes, as summarized by Feng et al. (2020) and Wang et al. (2020). A common cause (but not the only one) of negative biases in the lower troposphere is ducting or superrefraction (Sokolovskiy 2003; Ao et al. 2003). When the vertical gradient of refractivity ∂N/∂z exceeds a critical value of -157 N units per km, ducting occurs and rays are trapped inside the ducting layer. This leads to a negative bias in N and there are an infinite set of bending angle profiles that correspond to the observed refractivity profile.”

1. Line 175: Why not use LSW as a predictor instead of LSW/2? The correlations should be the same.
2. Line 194—what 1D-Var algorithm was used? The original CDAAC wetPrf or the new CDAAC wetPf2 (Wee et al. 2023)? Or some other one?
3. Lines 255-257: there is no direct relationship between large vertical gradients of N and nonspherical symmetry, which is caused by horizontal variations in N. Large horizontal variations in N and corresponding large LSW may occur with small vertical gradients of N. I suggest deleting the two sentences in lines 255-257; the previous sentence is sufficient.
4. 8: Which is land and which is ocean in Fig. 8? The caption should provide more details, i.e. explain the dots, explain the surface (is it a fit to the dots?)
5. Lines 311-312 and Fig. 9: Why aren’t the “Real REFB” the same for the training and testing data? Is this a sampling issue?

Please see the attachment.