7 replies to this topic

[Roger Edwards]

EJSSM Forum comments are welcome on this manuscript.

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Abstract

This study establishes a U. S. climatology of potentially severe convective environments for the 30-y period 1980–2009 from the North American Regional Reanalysis. Variability of environments supporting significant severe weather is examined for four active severe-weather regions in the U. S. Regional comparisons illustrate potentially significant-severe environments varied greatly both spatially and temporally over the 30-y period of record. The spatial and temporal distributions of significant severe-weather environments and reports are subjectively examined for comparison purposes. While one has to be cautious when linking environments and reports, average calculated significant severe-weather environments show similarities to the annual cycle of significant severe-weather reports. Additionally, mean center analysis indicates that there is no significant shift in the average position of these environments during the period of record.

[Chuck Doswell]

The proposed C-index clearly is not able to limit the apparently favorable environments of southern TX, which evidently are dominated by high CAPE values, combined with high values of CIN (when considering strong caps to represent large, positive CIN). This likely is the result of inadequate vertical resolution in the reanalysis data to represent CIN reasonably accurately. The inability of the C-index to deal with the discrepancy between the frequency of favorable environments and the actual occurrence of severe weather in southern TX is a reason to reconsider the suitability of the C-index as a measure of how favorable for severe weather the environment is. Since the C-Index formula is essentially arbitrary, rather than one that has some physical basis, I see no reason to consider the proposed C-index as anything more than a preliminary attempt at the proposed goal of this work (i.e., to "[establish] a U. S. climatology of severe convective environments"). It's not a dismal failure, but it's not a particularly notable success.

[Victor Gensini]

This likely is the result of inadequate vertical resolution in the reanalysis data to represent CIN reasonably accurately.

Dr. Doswell,

This is certainly one possibility that we put forth with a preliminary investigation into reanalysis "proxy" soundings and observed soundings at KBRO. See Fig. 9 in the manuscript. I would also like to point out that studies from Brooks et al. (2003) didn't even attempt to use CIN as a discriminator of such environments. It would be interesting to see your review of that particular manuscript...

Since the C-Index formula is essentially arbitrary, rather than one that has some physical basis, I see no reason to consider the proposed C-index as anything more than a preliminary attempt at the proposed goal of this work

This is rather misleading. You are essentially stating that all common composite indices are arbitrary and have no physical basis. The C-index is based upon a statistical threshold in which adequate CAPE and deep-shear are present (three of the four ingredients needed for a supercell; as large CAPE implies adequate moisture). An increase in CAPE (with other variables remaining constant) equates to a theoretical increase in updraft velocity. This is not arbitrary, rather based upon physical principles. The argument you present would eliminate all indices from such an analysis. I understand your argument surrounding arbitrary indices, but most are a combination of both physical and an arbitrary statistical component.

In addition, I feel that the index used herein is more at the mercy of the vertical resolution of the reanalysis dataset used surrounding CIN, rather than the failures you note.

[Chuck Doswell]

I would also like to point out that studies from Brooks et al. (2003) didn't even attempt to use CIN as a discriminator of such environments. It would be interesting to see your review of that particular manuscript...

There's a reason for not considering CIN as a discriminator ... I'm not speaking for Harold and his collaborators but I know they believed the vertical resolution of the reanalysis was inadequate to depict it properly. It was understood that an inaccurate diagnosis of CIN was an issue that would make its use problematic.

My review of that manuscript, if I were to create it, would be mostly positive. Their use of discrimination analysis to develop "discrimination planes" is on a much stronger foundation than the C-index (see below).

This is rather misleading. You are essentially stating that all common composite indices are arbitrary and have no physical basis. The C-index is based upon a statistical threshold in which adequate CAPE and deep-shear are present (three of the four ingredients needed for a supercell; as large CAPE implies adequate moisture). An increase in CAPE (with other variables remaining constant) equates to a theoretical increase in updraft velocity. This is not arbitrary, rather based upon physical principles. The argument you present would eliminate all indices from such an analysis. I understand your argument surrounding arbitrary indices, but most are a combination of both physical and an arbitrary statistical component.

In addition, I feel that the index used herein is more at the mercy of the vertical resolution of the reanalysis dataset used surrounding CIN, rather than the failures you note.

I'm not about to repeat my arguments about my stance regarding indices - see the paper by Dave Schultz and myself. I disagree that most indices are what you say they are. Most indices are arbitrary formulae that have little if any physical basis.

CAPE is an "index" that does indeed have at least some physical basis, although my concerns about indices specifically include the combination of moisture and instability into a single parameter rather than considering the moisture and instability ingredients separately. I maintain that your formulaic combination of ingredients into the C-Index has no physical basis whatsoever. What statistical analysis underlies its formulation? The discrimination planes in Brooks et al. (2003) do use discriminant analysis to define them, very much unlike your C-Index. I don't know what the geographical distribution of CIN looks like, but it's at least possible that although the CIN values from the NARR are likely underestimating the strength of the capping, the spatial distribution of CIN (or perhaps the CIN in relation to the CAPE) would suggest stronger capping in south TX when CAPES are high there, and an index that put more weight on that CIN might not reproduce the evident mismatch between the frequency of "favorable environments" in south TX and the frequency of actual severe weather reports there. Because your formula has no physical basis, it leaves open the possibility that a different formula might be an improvement. Given this logical possibility, how does one go about selecting which formula (out of the very large number of possibilities) to use?

[Victor Gensini]

My review of that manuscript, if I were to create it, would be mostly positive. Their use of discrimination analysis to develop "discrimination planes" is on a much stronger foundation than the C-index (see below).

...I maintain that your formulaic combination of ingredients into the C-Index has no physical basis whatsoever. What statistical analysis underlies its formulation? The discrimination planes in Brooks et al. (2003) do use discriminant analysis to define them, very much unlike your C-Index.

Do you realize that the "C-index" you are referring to (and the basis for the analysis in this manuscript) is derived from Brooks et al. (2003)? Please see our manuscript for clarification regarding this. We termed it the "proxy" C-index due to the use of CIN (this has *no* impact on the discrimination plane described by B03) and the difference in calculation. CAPE*0-6BWD >=20,000 is quantitatively similar to the formula used by B03. Please reference the reply and response to Harold (Reviewer 'B') for more information on this.

Basically, the discrimination analysis used in B03 was the basis for this research.

[Chuck Doswell]

Do you realize that the "C-index" you are referring to (and the basis for the analysis in this manuscript) is derived from Brooks et al. (2003)? Please see our manuscript for clarification regarding this. We termed it the "proxy" C-index due to the use of CIN (this has *no* impact on the discrimination plane described by B03) and the difference in calculation. CAPE*0-6BWD >=20,000 is quantitatively similar to the formula used by B03. Please reference the reply and response to Harold (Reviewer 'B') for more information on this.

Basically, the discrimination analysis used in B03 was the basis for this research.

Precisely in what way was the C-Index "derived" from the discrimination analysis of Brooks et al. (2003)? Can you show me the math connecting the two formulas? It may have been "inspired" by their work, but "derived" is not an appropriate description of the process unless you can demonstrate their mathematical relationship. Showing quantitative "similarity" is not the equivalent of a proper derivation.

[Victor Gensini]

Precisely in what way was the C-Index "derived" from the discrimination analysis of Brooks et al. (2003)? Can you show me the math connecting the two formulas? It may have been "inspired" by their work, but "derived" is not an appropriate description of the process unless you can demonstrate their mathematical relationship. Showing quantitative "similarity" is not the equivalent of a proper derivation.

You are correct. Derivation was a poor word choice. However, you initially asked, "What statistical analysis underlies its formulation?"

That would be the discrimination planes discussed by B03. You are making it sound like their formula and the one used in this manuscript are two completely different entities. They are *not*. In fact, the B03 line is generally lower than BWD6*CAPE=20,000. Until CAPE >~4800, the B03 line is below 20,000. For example, for CAPE of 1000, the B03 line is at BWD6=11.1, instead of 20. Thus, the straight 20K line is actually a conservative estimate of the discrimination plane described by B03. Results from B03 also portrayed an overestimation of events in S Texas...

I've plotted out the graphs of the discriminate equation from B03 and the "C Index" used in our manuscript (see below). As you can see, BWD6*CAPE=20,000 is much more conservative in portraying a significant severe environment. If anything, we certainly missed some of those low-CAPE high-Shear events (as discussed in the manuscript). Consider environment A. This environment would be non-severe using both methods. Event B would be considered a sig-severe environment by B03, but not by our manuscript, and environment C would be considered sig-severe in both studies.

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[Chuck Doswell]

Sorry for the long delay in my response ...

I'm simply pointing out that there is no mathematical or physical "connection" between the two. They may have some resemblance to one another but the process by which each was "derived" differs considerably between the two.