Review in file

Review of “Large Uncertainty in Observed Meridional Stream Function Tropical Expansion”

This paper analyzes various “tropical width” metrics from the ERA5 reanalysis ensemble members to assess the “data-driven” uncertainties in the various metrics. As a wide range of widening estimates have been published over the past decade and a half or so, it is very helpful for the community to have a better understanding of the uncertainties in these estimates. The authors use of the ERA5 ensemble members is to be commended, as this available data has heretofore been highly under-utilized. It is encouraging to see the demonstration that, in some cases, the increased observational system in recent decades has led to a smaller spread of tropical width estimates. However, this paper contains numerous over-interpretations of the results presented and fails to compare the spread due to data uncertainty with the much larger spread due to interannual variability. When placed in the proper context, the results of this paper represent an interesting finding regarding relative uncertainty in tropical width metrics and changes over time, but the results are highly oversold as currently written.

Most critically, the authors have not made the very obvious comparison between their “data-driven uncertainty” and the uncertainty one gets in the tropical width trends due simply to interannual variability. The authors do use a “normalized intermember STD” in Sect 3.3 (e.g., Fig. 4), and the limited info available from this suggests that data-related uncertainty is actually not that large relative to interannual variability. E.g., The normalized STD near the HC edges at 500 hPa in Fig. 4 are ~6%, which means that the spread in ensemble members is only 6% of the year-to-year variability in the streamfunction.

More importantly than showing this normalized STD for a field like the meridional streamfunction is showing what it means for the mean HC edge position and trends therein. From what I can glean from Figs. 1 and 2, the spread in SF edge trends is ~0.05° decade^-1 for the annual mean. Comparing to studies that have looked at multiple reanalyses (e.g., Fig. 4 of Davis and Rosenlof, 2012), SF edge trends span well over 1° decade^-1 among different reanalyses, and their uncertainties (for a single reanalysis, due to interannual variability) are ~0.5° decade^-1. If this were the only information available, I would say it shows that data-driven uncertainty is in fact not a substantial contributor to our understanding of historical tropical widening trends. The authors need to make a much more convincing argument as to why data-related uncertainty is substantial in the contexts of all of the other uncertainties related to different reanalyses, metrics, and interannual/natural variability.

Some more minor points are as follows:

Line 15: “data-driven uncertainty” – I don’t agree that the ensemble member spread in tropical edge latitudes (or their trends) can simply be interpreted as “data-driven uncertainty” and meaningfully compared across metrics. The atmosphere may be very smooth/laminar/‘predictable’ in some places and much less so in others. For metrics based on fields that are ‘predictable’, one could easily get the same tropical width (or tropical width trend) among ensemble members even in an area with no data. Conversely, in highly chaotic/noisy/unpredictable regions, one might get a large spread in width/trend values even with relatively high quality/dense data to constrain the reanalysis. Ultimately, the only way to truly get at whether the differences in ensemble spread are “data-driven” vs. “atmosphere-driven” would be to compare the spread in an ensemble of free-running simulations to the spread in a (data-constrained) reanalysis. Without doing this, all you can say is that one metric is noisier than another. But one doesn’t even really need reanalysis ensembles to demonstrate that, it has been shown before in a number of papers that have presented tropical width trends.

Line 17-18 “to date no study has quantified and compared the uncertainty in different HC metrics”. This is simply incorrect. Numerous studies have both quantified and compared uncertainty in different HC metrics.

Line 79: “several ensemble members” Just state how many there are.

Lines 105 - 106: Please provide a reference describing the ensemble data assimilation.

Lines 106 – 108: Please provide more details on the differences between the full ERA5 reanalysis and the ensemble version, as this is highly relevant to the interpretation of all of the results in this paper. For example, do both versions assimilate the same data? How different are the resolutions? Also, as all previous studies have used the full ERA5 reanalysis, it is critically important to also include the metrics and trends here for reference. Without doing this, we don’t know whether there is some kind of bias in the lower resolution ensemble version of the reanalysis, or whether to expect that the results in this paper actually apply to the full reanalysis.

Line 110 – 112: Given that ERA5 resolution is ~30km (I’m not sure what the ensemble version is), reducing the data to 1 degree for your analysis seems like a really bad choice. Especially when you are trying to infer extremely small changes ~ 0.1 degree per decade. Some consideration needs to be paid to whether or not this degradation of the reanalysis resolution impacts your analysis.

Line 111: “conservational” -> conservative

Line 119: Please provide link/reference/version information for the python TropD code you are using.

Line 126: “… poleward of the minimum … equatorward of the maximum … “ this is correct for the NH but not the SH edge. Please clarify or make the language more general to apply to both hemispheres.

Line 134: I believe Solomon et al. 2016 was the first to show this, and should be cited here in addition to Davis and Birner.

Solomon, A, L M Polvani, D W Waugh, and S M Davis. “Contrasting Upper and Lower Atmospheric Metrics of Tropical Expansion in the Southern Hemisphere.” Geophysical Research 2016. https://doi.org/10.1002/2016GL070917.

Line 143-144: “[PSL is] …poorly correlated to P-E”. From Waugh et al. 2018, the correlation between PSL (they call it SLP) and P-E is 0.32 in the NH and 0.69 in the SH. I would not call this correlation poor in the SH. Also, PSL is correlated with UAS in the SH with 0.98, so they are virtually interchangeable with one another. The authors should do a better job of making this distinction.

Line 153: “intermember average” (and many other points in the paper) - It is much more common to refer to this type of average as an ensemble average. I suggest changing this terminology throughout the paper.

Line 165-166 and Figure 1: I don’t understand the need to do some kind of fit to 9 data points here, why not just show a simple histogram of the data? If the authors have a compelling reason to use these ‘kernels’, they should explain clearly, and also briefly explain Scott’s rule.

Line 177 (and possibly elsewhere in paper): “low” -> “small” The word low is appropriate for heights, not quantities.

Lines 176-179: This sentence doesn’t make sense. The authors state that the trends are a substantial downward revision but then that they are similar to Grise et al. It’s not clear what the authors are trying to say here.

Line 189-190: This goes to my point about “data-driven uncertainty” being a misnomer for describing the spread among reanalysis ensemble members. The authors state that over the SH, SF-based expansion is more robust (i.e., less uncertain). However, we know that reanalyses are less constrained by data in the SH. The fact that the “data-driven uncertainty” is smaller in the SH suggests that other factors are at play such as a stronger forced signal (e.g., due to ozone depletion) or less noise.

Figure 3: It is very hard to tell the difference in color between the UAS and PSL curves. Please consider using different colors.

Line 226: Are the reanalysis ensemble members really created by perturbing the model parameters?! Maybe the authors mean initial conditions here and not model physics, which is what I think of when I hear the word “model parameters”. This is really important information for the reader to understand, as it has direct bearing on how the spread of the ensemble members is interpreted.

Fig 6b: Is “SF uncertainty” just the ensemble STD of the SF in the vicinity of the edge (+- 2 deg) at 500 hPa? Or is it the ensemble average of the standard deviation within +-2 deg of the edge computed from each member? The caption doesn’t specifically state what the statistic is, so this discussion is hard to evaluate.