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 (R n ) and Soil Heat Flux (G), so that R n – G – H – LE = Closure Error. R n – 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.

The “young” Henk de Bruin and Oscar Hartogensis, by a Beaver Pond in Logan Canyon, Utah, Inset: R.Allen by the Great Wall, 2011 and Henk on Univ. Idaho National Science Foundation Flux Tower near Island Park, ID,2010. Photo by R.Allen, Univ. Idaho

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. The Energy Balance Closure Blues R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012 P. 1 of 4

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. 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. 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. 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. The Energy Balance Closure Blues -- Continued R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012 P. 2 of 4

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. The Energy Balance Closure Blues -- Continued R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012 P. 3 of 4

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, The Energy Balance Closure Blues -- Continued R.Allen and H.deBruin Jan. 2011, rev. April 2011, June 2012 P. 4 of 4 Rock and Roll for the End: 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.‘.