Review of: Development of a fast radiative transfer model for ground-based microwave radiometers (ARMS-gb v1.0): Validation and Comparison to RTTOV-gb

This article presents the development and extensive validation of a new fast radiative transfer model for ground-based microwave radiometers. It is compared versus a line-by-line model and the well-established RTTOV-gb forward model. The topic is of high relevance, the model and its development are described adequately, and the corresponding validation is carried out carefully and described properly. I recommend the publication of this manuscript subject to some (minor) corrections.

Abstract: In my opinion the abstract should be easy to understand for people who have not yet read the article, and who might not be that familiar with the overall topic. Several terms like “Optical Depth in Pressure Space Scheme”, “UMBC48”, “MonoRTM” are used without saying at least very roughly what it is. It is not really clear that with bias drops and different Jacobians you mean the two biases and Jacobians of the two different vertical interpolation modes.

Line 10-11 and line 66-67: From my opinion it is difficult to say that GMR observations are the true reference here. It is reasonable to do “obs minus background” comparisons, but as you are using ERA5- profiles as input to the radiative transfer codes, and not real observations of temperature and humidity, I would not name it “true reference value”, as with simulated input profiles having certain errors it is not expected to obtain the observation as output.

Line 12-14: Also this last sentence is only understandable having read the paper before.

Line 63: typo, must be “each component”

Line 102: shouldn’t it be “transmittance in spectral channel V”?

Section 3.2: For me here the description is somewhat confusing and not really exact (especially Line 138 and line 150). The tangent linear and the adjoint model are two different things needed for four-dimensional variational data assimilation, although they are closely related. The tangent linear model linearizes the forward model to compute how small changes in the state affect the future model state. The adjoint model is the "backward" version of this process. It allows the calculation of the sensitivity of the cost function with respect to the state at previous times. Thus, in four-dimensional variational data assimilation, they work together to update the model state based on observational data, by first using the tangent linear model to compute how perturbations in the state evolve and then using the adjoint model to find how these perturbations should be adjusted to minimize the difference between the model output and the actual observations. I suggest to correct this chapter.

Line 208: Say more exactly what you mean with “bias drops”

Line 210: Grammar mistake, rewrite to: “The slight reduction of STD…”

Line 216: Please rewrite to: “The Jacobians calculated by the two interpolation modes….”

Line 254: I would rewrite the heading to “Comparison to RTTOV-gb”

Line 349: also here the term “bias drops” is not clear enough. It would be better to describe which bias is lower compared to what.

Line 366: I would recommend to start a new line after “2.59%.”

Line 386: better: “… obtained by taking the mean over the…”

The manuscript egusphere-2024-2884 by Shi et al presents the development of a fast radiative transfer model (called ARMS-gb) for simulating brightness temperatures observed by ground-based microwave radiometers (GMRs). The characteristic of the model are described, including peculiarities in training and profile interpolation. The resulting simulations are compared with simulations from a similar existing code and with real observations from two GMR instruments. Also, the use of ARMS-gb to compute Observation Minus Background (OMB) differences and monitor GMR calibration stability is shown.

As similar codes and analysis already exists, the degree of novelty is relatively small. But the manuscript does fit the scope of the journal, and I find it clear and easy to read. However, there are aspects that need to be clarified, which could possibly undermine some of the results and conclusions. 

Therefore, I could recommend publication only after addressing the following comments.

Major comments:

1) The authors miss to explain what's special about the seven profiles added to the training set and how the authors determined that this addition improved the training. They mention "moist environment" but to my knowledge the 101-level ECMWF 83 profiles do provide very humid profiles (see also minor comment on line 96).

2) Section 2.2 introduces a vertical interpolation method, which effects are then compared in Section 3.1 with those of another commonly used method. 

However, it not clear if Section 3.1 compares these two methods (called mode 1 and 2) as both implemented within ARMS-gb or if it rather compares RTTOV-gb (implementing mode 1) with ARMS-gb (implementing mode 2). 

The authors need to clarify this point, as the two situations would lead to different conclusions (see also minor comment on line 196).

3) Section 4 shows comparison between observations and simulations in clear sky, considering three cloud detection criteria. As written, criterium 3 does not seem correct, or at least does not correspond to the criterium given in the quoted references (Turner et al., 2007; Cimini et al., 2019). These two references identify cloudy conditions by setting thresholds on the standard deviation of observed BT at 31.4 GHz over a time period, while the authors states they use standard deviation of OMB. If the background simulation is constant over the 10-min period, then the results should be the same, but the authors need to clarify this point as it sounds like an unnecessary complication (see also minor comment on lines 251 and 267-268).

4) In a validation experiment, such the one described in Section 4.1, three sources are contributing: (i) the RT model, (ii) the input profiles, and (iii) the observing instrument. Figures 4 and 5 reports the results for two stations, representing relatively drier and moister environments. The two figures report very different results, although the input profiles and the simulations come from the same sources (ERA5 and ARMS-gb/RTTOV-gb, respectively). I understand the ERA5 and RT models may perform differently in different environments, but the one aspect that doesn't seem to be considered is the GMR instrument, which are of different type (Airda-HTG4 and YKW3) and independently calibrated.

Unless the absolute calibration can be validated properly at the two sites, using for example radiosonde profiles, a miscalibration of either instrument cannot be excluded. The stability of OMB does not suffice, as it only indicates a stable calibration, but does not say much about calibration accuracy (see also minor comment on lines 266-267 and 286-297).

Minor comments:

- Line 9: either "also differ" or "are also different"

- Line 18: "thermal" -> "thermodynamical"

- Line 20: "which extends" -> "which may extend"

- Line 43-45: "RTTOV-gb is trained using AMSUTRAN"; this is correct for RTTOV, but not for RTTOV-gb. Section 2.2 of Cimini et al., 2019 says: "Conversely, RTTOV-gb was trained using a later version of MPM, described by Rosenkranz (1998, hereafter R98), which is probably the most used among the ground-based microwave radiometry community. This model is continuously revised and freely available (Rosenkranz, 2017, hereafter R17), and its uncertainty has been carefully investigated (Cimini et al., 2018). Therefore, RTTOV-gb has been trained using the R17 model also (version of 17 May 2017 available at http://cetemps. aquila.infn.it/mwrnet/lblmrt_ns.html, last access: 14 November 2018). Coefficients for both the R98 and R17 models are now available within RTTOV-gb v1.0."

The authors should modify the statement with a short summary of the above and remove the corresponding sentence at line 256 (as also suggested below) and in Table 3.

- Line 96: what's special about those seven profiles?

- Line 102: what's "channel spectral V"? I guess it is channel bandwidth? Also, I guess Eq.4 is discretised as a sum; the authors should also state what spectral resolution they used to compute the sum.

- Line 120: "dense" -> "denser"

- Line 172: N was previously used to indicate the number of channels. I'd suggest to change letter to avoid confusion.

- Line 175: As above: the integral is computed as a sum, and the adopted spectral resolution should be stated.

- Line 191: either "two vertical interpolations are required" or "vertical interpolation is required twice"

- Line 196: it is not clear if the two modes are applied both tho ARMS-gb or rather mode 1 is used with RTTOV-gb and mode 2 with ARMS-gb. The two situations would lead to different conclusions.

- Line 251: not sure if there is a typo, but otherwise criterium (3) does not correspond to that used by Turner et al., 2007 or Cimini et al., 2019. It's the 10-min std of observed Tb at 31 GHz to be checked against the 0.2 K threshold, not the OMB.

- Line 253: As stated at line 71, ARMS-gb is limited to clear-sky simulations. As such, it is not clear why the threshold for cloud water content is set to 100g/m2 and not to 0 g/m2. Is cloud water provided in input at all to either ARMS-gb or RTTOV-gb?

- Line 256: Please, remove "It accounts gaseous absorption by ODPS which is trained by AMSUTRAN (Turner et al., 2019)" and refer to Cimini et al., 2019 for the absorption model. Same in Table 3.

- Lines 261-264: The altitude above sea level and the surrounding orography of the two sites should also be reported, as these may have an effect on the simulated BTs (e.g., if orography is complex, bilinear interpolation may be misleading).

- Lines 266-267: The stability of OMB indicates that the calibration may be stable, but does not say much about calibration accuracy. 

- Lines 267-268: This seems to hint that std of simulated BTs are used for cloud detection (see previous comment to line 251), which I think is wrong or at least does not correspond to the screening used by Turner et al., 2007 and Cimini et al., 2019. 

- Lines 286-297: The results in Figure 5 are very different from those in Figure 4. If the analysis is correct, one would expect similar results, for example at channels 1, 2 and 3 of HATPRO (or Airda-HTG4), which are very close to channels 1, 3 and 4 of MP3000A (or YKW3). This may be due to uncertainties in ERA5, as the authors seem to suggest, but also to GMR instrument mis-calibration. This cannot be excluded, unless a proper calibration evaluation can be performed using, e.g., radiosonde profiles.

- Line 347: "HATRPO" is mispelled.

- Lines 371-372: Accuracy may be improved also updating spectroscopy to the newest developments. This is likely the case at 50-54 GHz, i.e. HATPRO channels 8-9-10, as shown in Figures 7-8 of Larosa et al., 2024 (https://doi.org/10.5194/gmd-17-2053-2024). To my knowledge, those spectroscopy improvements are not implemented in MonoRTM.