C2: L 132-133: The assumption is made that T_s,eff is approximately independent of frequency. Is this really justified given the different penetration depths (as alluded to elsewhere in the paper)?

R2: The discussion in the paper regarding changing penetration depths with frequency is most significant for those parameters which impact the scattering properties of the snowpack (correlation length, density, and layer thickness), and generally see greater variability. Although we do not expect temperature to have a strong direct effect on emissivity, we highlight the non-isothermal nature of a snowpack when simulating emissivity, whereby it is possible to use Eq. 3 to avoid using an average snowpack temperature. For the purpose of the observation emissivity retrieval, it is necessary to use effective temperature calculated for the channels centred on gaseous absorption lines, as discussed in the paper (line 130).

With the channels available on MARSS and ISMAR we are able to use the published method of Harlow (2009) to retrieve the effective surface temperature at 118 and 183 GHz. Emissivities at 89, 157 and 183 GHz (MARSS) are then calculated using the 183 GHz temperature, and those at 118 and 243 GHz (ISMAR) using the 118 GHz temperature. Based on differences between the 118 and 183 GHz effective temperatures, we expect a maximum error in the effective temperature assumption to be of the order of ± 3K, similar to the average variability in temperature observed in the snow pits of 2.9K. The corresponding error in emissivity is of the order of 0.01, which when added in quadrature to the observation error estimates, increases the emissivity uncertainty from 0.01 to 0.014 at 89 GHz, and from 0.02 to 0.022 at 243 GHz. However, we would not expect these small differences in emissivity error to have a significant impact on the SCEM-UA retrievals, and given the computational expense, we do not feel there would be significant benefit from re-running the retrievals to include these errors.

We will add a note to the methods in Sect. 2.2 (line 141), to acknowledge this: “These errors do not include uncertainty due to frequency-dependent changes in Ts,eff , which would have the greatest impact at 89 GHz, increasing uncertainty by a maximum of 0.004. This corresponds to a maximum error in Ts,eff of ± 3K, based on differences between 118 and 183 GHz Ts,eff , and average variability in observed snowpack temperature of 2.9K. This is not expected to have a significant impact on the SCEM-UA retrievals.”

We will also add the following sentence to line 133 to further describe the observed emissivity retrieval: “To ensure consistent viewing geometry, Ts,eff at 183 GHz is used to calculate e for the MARSS channels (89, 157 and 183 GHz), and Ts,eff at 118 GHz to calculate e for the ISMAR channels (118 and 243 GHz).”

This comment also highlighted a typographic error in Eq. 3, where simulated upwelling was denoted using Tb, which was not consistent with the text (Tbsmrt). This will be updated in the revised manuscript to consistently use Tbsmrt.

C3: L168-169/Table 1: Strictly, the table gives correlation length, thickness and density, rather than SSA, thickness, density and temperature. The conversion of SSA to correlation length is only introduced later in the paper which might be confusing to some readers. Correlation length is probably indeed the better quantity to show in the table, so I suggest introducing the conversion earlier.

R3: We acknowledge there is a mismatch between the contents of Table 1 and the text at Line 168/169. This table was intended to summarise the parameter ranges used in the retrievals, rather than summarising all the snow pit observations.

In the revised manuscript we therefore suggest moving the table to Sect. 2.6.2, which discusses the use of parameter ranges of correlation length, layer thickness and density in the SCEM-UA retrievals, and occurs after the conversion of SSA to correlation length has been introduced.

C4: Sections 2.2., 3: The use of cluster mean emissivity spectra (rather than individual spectra) seems an important choice which I feel should be motivated better, including a discussion of the implications. It has important implications on the results and their interpretation:

R4: Firstly, this comment has highlighted that the text and Fig. 3 caption are incorrect, as the observed spectra used in the retrievals were cluster centroids, rather than cluster means.

The manuscript will be updated to refer to cluster centroids in the Fig. 3 caption, and in the text.

C4 a: Presumably, it means that the RMSE & MAE shown in table 3 and elsewhere are based on 5 values (ie the 5 frequencies considered). It would be worth making this clear in the text – it’s not a very large sample to calculate statistics from. Using individual spectra would increase the sample size and produce presumably more informative statistics.

R4 a: We agree that calculating the statistics, particularly RMSE, using only the five frequency values is a limited statistical analysis. As Table 3 was primarily intended to quantify the simulation-observation difference from Fig. 5, with the in-text discussion focussing on the overlap between the standard deviation of the simulated spectra and the observation error, we suggest that MAE is the more relevant value, and given the limitations of calculating the RMSE in this way, we propose removing RMSE from Table 3 altogether.

We will update the manuscript to remove RMSE from Table 3 and the text, and instead focus on MAE and the in-text discussion of Fig. 5.

We discuss the suggestion of running the retrieval for individual spectra in response to part 2 of this comment (R4 b).

C4 b: The cluster means are necessarily smoother in frequency than some of the individual spectra shown in Fig. 3. I would expect that less structure makes it easier to find a parameter set that is able to model the spectra. So I suspect the RMSE values are a little optimistic as a result of using the cluster means as observations? An alternative would be to try and fit the individual spectra and calculate RMSEs from these results, still keeping the clustering to separate different regimes (with different demands on the modelling). This would increase the sample size and, provided RMSEs are similar, it would strengthen the finding that SMRT is capable of modelling very diverse spectra.

R4 b: As mentioned in the initial response to this comment (R4), the observed spectra were cluster centroids rather than cluster means. As the cluster centroids are taken from an observed spectrum, they preserve the shape of that spectrum, as opposed to the smoothing that would result from a cluster mean. We hope this addresses concerns around how easily the retrieval was able to model the spectra.

Both parts of this comments suggest running the retrieval for individual spectra, however, the decision to cluster the observations and use cluster centres to represent observations, was made to reduce the computational cost of running the retrieval for thousands of spectra. We determined that the clustering method allowed us to represent the variability observed, while using the cluster centres preserves the different shapes of the observed spectra. Although we agree running the analysis for a greater number of observations would strengthen the statistics, we would not expect to see large differences in the retrieved parameters between similar observed spectra in a cluster group.

C5: Section 3: The snowpack parameter retrievals exhibit considerable differences at least for some clusters. I wonder whether these differences are backed up by the snowpack measurements. For instance, the snowpack measurements could be grouped into the 8 clusters based on the aircraft data that is most appropriate in terms of location and timing. Based on this grouping, is there a tendency for larger/smaller thickness or correlation length measurements in line with the retrieved values? I appreciate that the limited number of the pit-measurements and the heterogeneity may prevent such an analysis from being meaningful, but I would nevertheless be interested if this has been considered or attempted.

R5: We agree that this is an interesting comparison to make, and in response to this comment we attempted an analysis where each pit was assigned a cluster according to its nearest aircraft observation. Some similarities could be seen between the snow pit parameters and those retrieved by SCEM-UA, such as wind slab thickness of pits near clusters 0 and 3 being shallower than those near clusters 5 and 7, as was also seen in the retrieved parameters. However, as suggested in the comment, the limited number of pits meant that not all clusters were represented by the pit locations, and some clusters were only represented by 1 or 2 pits. It is therefore not possible to draw any meaningful comparisons using the pit data.

 References:

Harlow, R. C.: Millimeter microwave emissivities and effective temperatures of snow-covered surfaces: Evidence for lambertian surface scattering, IEEE. T. Geosci. Remote., 47, 1957–1970, https://doi.org/10.1109/TGRS.2008.2011893, 2009

Sandells, M., Rutter, N., Wivell, K., Essery, R., Fox, S., Harlow, C., Picard, G., Roy, A., Royer, A., and Toose, P.: Simulation of Arctic snow microwave emission in surface-sensitive atmosphere channels, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-696, 2023