Hi Class,

You will see on your handout that I have a variable ZU (shown on the handout in the definitions for the moisture and potential temperature profiles).  A student pointed out that "ZU" does not appear in Fovell's notes.

Really, "ZU" is just "Z", but it is specifically the height of the U-levels.  I do this because our grid will be staggered (see Fig. 9.1).  The U-levels are those on which U, as well as all of the scalars (including potential temperature and mixing ratio) are carried.  I like to call the variable ZU because the W-points are at different heights.  (So, yes, I also define ZW in my model, although the usefulness of this will not become apparent until much later in the semester, so it's not necessary to do it now).

I hope this helps!

Best,
Matt

*************************************************************************
Hi Class,

A student asked:

>  Would it be possible to obtain some C values that you got
> in your calculation for CAPE?

And, another student asked:

>
> I'm wrapping up model task 2 here and am getting a
> capesum of about 3109 J/kg, which is ~31 fewer J/kg than you
> got. Just wanted to check with you to see if that's
> "close enough" and could be attributed to round
> off (I guess I'm only losing 1 or 2 J/kg per level) or
> if you think I might have done something wrong.  I know you
> can't really tell without looking at my program whether
> I've done something wrong, but I figure you can tell me
> if that's within normal range of error.

First off, here are some sample values:

Initial parcel potential temperature: 300.52 K
Initial parcel vapor mixing ratio: 14.8 g/kg
Initial parcel height:  0.35 km
  z    Parcel PT Parcel Qv     Diff
(km)     (K)     (g/kg)       (K)
1.05     303.09    13.79      1.35 phi= 1.920 c=.00099 CAPE=  30.51
1.75     307.23    12.24      3.89 phi= 1.623 c=.00155 CAPE= 117.85
2.45     311.20    10.78      6.07 phi= 1.478 c=.00145 CAPE= 253.45
3.15     315.19     9.36      8.12 phi= 1.317 c=.00142 CAPE= 433.75

Second off... folks, every year, people ask me if their values are "close
enough".  The answer is, unless you are within machine precision (i.e. all but
the very last digit are the same), then our calculations are not identical.
My final CAPE value is 3140.418, so I will accept 3140.417 or 3140.419.  But,
sorry, computers do not produce errors of 1% via rounding!

I am willing to allow for the possibility that my code is incorrect, but this
is the 4th time I've taught this class, and I am pretty darn sure the CAPE
calcs are right.  So, unless everybody in the class comes up with numbers that
are identical to one another *and* different from mine, then the short answer
is:

* your values should be identical to mine *

Even if your CAPE value is a paltry 1 J/kg off from mine, then something is
*still* incorrect.  Some things to check if you're close but not exact include
the virtual temperature correction and also how you handle the final level
where the parcel kicks over from being positively buoyant to negatively
buoyant.  One more thing to check: make sure that your initial parcel
values are set to the actual grid-point values at k=2 (don't hardwire/type in
rounded-off values or this *will* cause rounding error).  It's best not
to hardwire the parcel values because, in the future, you may want to start
with a different parcel!


I hope this helps!

Best,
Matt

************************************************************************