Regarding the differences in moist lapse rates I do remember seeing simpler, but less accurate formulas for estimating the moist adiabats. Is that what you're talking about Jeff D.? I ask because I believe that Earl Barker's skew-t moist adiabats are slightly steeper than I see elsewhere and I think this may lead to slightly higher CAPE values as compared to other sounding sites. I wonder if he is using a moist lapse rate equation that is slightly different?

Also, there are a couple of different ways of selecting the parcel for the MUCAPE calculation as well. You can brute force it by walking up the sounding and performing the CAPE calculation for every parcel and then select the one with the maximum value. Or, what RAOB does is immediately select the parcel level with the highest wet bulb temperature and just use that. Obviously, that is significantly more computationally efficient, but I wonder if it is at the expense of missing a more unstable parcel in strange (and not very likely) scenarios. Maybe John Shewchuk can comment more about this if he sees this post.

Anyway, the main takeaway (for me anyway) is that CAPE calculations can be very nuanced so making comparisons of the values obtained between different programs or even different versions of the same program need to done with at least some understanding of the potential issues.
 
Regarding the differences in moist lapse rates I do remember seeing simpler, but less accurate formulas for estimating the moist adiabats. Is that what you're talking about Jeff D.? I ask because I believe that Earl Barker's skew-t moist adiabats are slightly steeper than I see elsewhere and I think this may lead to slightly higher CAPE values as compared to other sounding sites. I wonder if he is using a moist lapse rate equation that is slightly different?

Also, there are a couple of different ways of selecting the parcel for the MUCAPE calculation as well. You can brute force it by walking up the sounding and performing the CAPE calculation for every parcel and then select the one with the maximum value. Or, what RAOB does is immediately select the parcel level with the highest wet bulb temperature and just use that. Obviously, that is significantly more computationally efficient, but I wonder if it is at the expense of missing a more unstable parcel in strange (and not very likely) scenarios. Maybe John Shewchuk can comment more about this if he sees this post.

Anyway, the main takeaway (for me anyway) is that CAPE calculations can be very nuanced so making comparisons of the values obtained between different programs or even different versions of the same program need to done with at least some understanding of the potential issues.

@Jeff Snyder brought this up first, but it reminded me there are several ways to calculate a parcel path. I found three formulas in the AMS Glossary alone:
The latter two are actually identical except for the inclusion of condensed water in the reversible lapse rate equation. However, within these formulas, there are "constants" that are not truly constant. These include the latent heat of vaporization and the heat capacities, both of which have slight dependencies on temperature. Also, at a certain point, the phase change process is going to shift more towards deposition (forming ice crystals) rather than condensation (forming liquid water drops) at colder temperatures, so at some point you'd have to switch over to (Lv + Lf) rather than just Lv, or more likely some weighted combination of the two (as both condensation and deposition may occur simultaneously).

An additional method I have tried in the past is simple conservation of theta-e. Tends not to work well in the unsaturated portion of the path, though.

It's my understanding that MUCAPE is typically calculated using the parcel with the highest theta-e in the lowest few hundred mb. This is done because it represents the parcel with the rightmost path on the skew-T, which should generally result in the largest CAPE value of any parcel in the column. However, I have also envisioned situations (perhaps involving multiple elevated capping inversions) in which a parcel other than the one with the highest equivalent potential temperature may actually result in larger CAPE. However I have not yet confirmed such a case.
 
Have you looked at the Davenport sounding from 2008-08-05 00Z? I think that had more cape than the ILX one IIRC. Might have been the special RAOB earlier in the day, though. Either way, that was the first date that popped into my head, with mesoanalysis showing 8000+ MLCAPE over IA
 
June 28, 2012 is another day that comes to mind for me. I can't find the observed soundings for that day on SPC, however I remember mesoanalysis showing ~8000 J/KG of MLCAPE over SE Iowa/WC Illinois. Of course the next morning the infamous Ohio Valley/East Coast derecho would get going in Northern Illinois on the northern edge of this air-mass, as is often typical. This is the 00z mesoanalysis plot that evening, like I said I can't find the sounding, so if anyone had one for Davenport, that might be interesting to look at :)
363b7bba4dec170b40b30646ab0aadf9.gif
 
The problem with many sounding/skewt products is the lack of detail regarding CAPE calculation methods and criteria. With RAOB you have complete control over all CAPE processing options. Regardless of which CAPE criteria is used, and for greatest accuracy, RAOB calculates CAPE values at 1 mb pressure intervals, summing up all values throughout the sounding profile. This video shows all of RAOB's CAPE processing options >
 
My RAOB Program does calculate MUCAPE by selecting the level with the highest theta-w (wetbulb potential temperature). However, I just added a new option to the RAOB 6.9 program. This option calculates CAPE at 1 mb intervals for the entire lower 300 mb layer (or whatever base layer you identify) and picks the level with the highest CAPE value. But, this method is very time consuming -- taking 2 to 3 extra seconds for an average PC.
 
My RAOB Program does calculate MUCAPE by selecting the level with the highest theta-w (wetbulb potential temperature). However, I just added a new option to the RAOB 6.9 program. This option calculates CAPE at 1 mb intervals for the entire lower 300 mb layer (or whatever base layer you identify) and picks the level with the highest CAPE value. But, this method is very time consuming -- taking 2 to 3 extra seconds for an average PC.

Interesting. Now perform an experiment - how often does the parcel with the largest CAPE match the parcel with the highest theta-w? Is there a characteristic shape in such soundings? I have a suspicion it is possible and that it involves multiple inversions above the PBL.
 
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