The Energy Balance Closure Blues
Rick Allen
University of Idaho
and
Henk de Bruin
Wageningen University (ret.)
The Energy Balance Closure Blues
Background: Energy Balance Closure is a concept used with Eddy
Covariance Systems to Determine if the Flux Measurements of Sensible
Heat Flux (H) and Evaporation (LE) have values sufficient to explain all
of the ‘Available Energy’, represented by Net Radiation (Rn) and Soil
Heat Flux (G), so that
Rn – G – H – LE = Closure Error.
One hopes that Closure Error is ~ 0, but it often tends to be positive,
even after much work. Out of frustration, Allen and deBruin wrote the
following lyrics, to be set to a blues tune.
In 2012, Allen suggested adding ‘Rock and Roll’ stanzas to the end in
‘celebration’ of a multilinear regression method that can determine
closure if error is mostly systematic, plus the appreciation that often,
the primary culprit in closure error may be the innocuous G.
Photo by R.Allen, Univ. Idaho
The “young” Henk de Bruin and Oscar Hartogensis, by a Beaver Pond
in Logan Canyon, Utah, 1999. Inset: R.Allen by the Great Wall, 2011 and Henk
on Univ. Idaho National Science Foundation Flux Tower near Island Park, ID,2010.
The Energy Balance Closure Blues
R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012
In the time of good ol' Bowen
Life was smooth and easy goin’
‘cuz energy, per definition,
Was conserved and always known.
But now has come eddy covariance
with all these twists and corrections too,
And today I'm singing
these energy balance closure blues.
I thought I really had something
when I could measure every eddy,
See all the ups and downs
with my sonic shiny and ready.
But I found not so simple,
and the mathematics, they gave little clue.
And today I'm still singing
these energy balance closure blues.
I love the sonic temperature.
and the vertical velocity, too.
Together they should correlate
to show the flux on cue.
but I compare against available
energy
that I think is holding true,
And today I'm always singing
these energy balance closure blues.
You talk about frequency response
and sensor separation too.
To use Webb, Pearman and Leuning,
Yes, all these things I do.
But even with idealization of eddies,
I still don’t have such good news,
and today I'm still singing
these energy balance closure blues.
P. 1 of 4
The Energy Balance Closure Blues -- Continued
R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012
I don't trust those radiometers
and those little plates stuck in the ground
I know I am just a dreamin'
to think those apply all around.
Please tell me how to integrate
these measures I pick 'n choose,
'cuz today I'm still singing
these energy balance blues.
I chased after that new scintillometer
that can see miles through eddies true,
I've used higher order closure
and better friction velocity too.
and still I am troubled
not knowing what is really true.
and today I'm still a singing
these energy balance closure blues.
You say 70% closure ain't bad
Well I tell you my dog can do as well
in guessing where the energy is.
It can't be that hard to tell.
I don't know what truth is anymore
and I need a new set of rules,
'cuz today I‘m a singing
these energy balance closure blues.
People talk about angle of attack error,
and how that pulls w and H on down
Well if that is true, and it means one
more correction,
then do we still wear such a big frown?
Why don't we just admit that there is so
much to know
That father physics and mother nature
have deemed it to be so.
P. 2 of 4
The Energy Balance Closure Blues -- Continued
R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012
Some day I will close that balance.
I'll have all the components tight in place.
That same day my baby will come back,
and she'll punch me in the face,
and tell me that only in my dreams can it close,
and this, everybody knows.
and that every day I'll still be singing
these energy balance closure blues.
P. 3 of 4
The Energy Balance Closure Blues -- Continued
R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012
Rock and Roll for the End:
Out of pure desperation and a little
cleverness too,
I pulled out the regression code to see
what it could do.
I stubbornly placed trusted H to the left
of that equality
and everything else to the right, to find
fidelity.
The squares of numbers flew and some
coefficients, they climbed,
and when the numerical smoke had
settled,
I nearly lost my mind.
Here, was Mr. G, the quiet flux to the
ground,
waving a coefficient of 2 and more, and
so proudly to be found,
to be of so much significance and power
to solve so much error
and here all this time, we were looking
only to the air.
So now I am much more happy, and no
longer singing so much blues,
and have shifted to Rock n‘ Roll to
conclude that it really is all true:
that some hard hitting regression, while
not so very profound,
can sometimes sort things out and reduce
those things that so confound,
It can take us to a place where we finally
sing and muse:
‘I no longer have to sing
those energy balance closure blues.‘
.
P. 4 of 4