# Southern Ocean GasEx Blog

## (Cor)relation for Air-Sea fluxes

Posted by sogasex on April 8, 2008

By Alejandro Cifuentes, University of Connecticut

Let me introduce you to my good friend the correlation function (whom you may already know well) and its relevance in the air-sea flux calculations (momentum, energy and mass). The correlation function is a powerful statistical tool, specifically in the analysis of time series measurements. The combination of the time averaged measurement of a normally distributed random series coupled with the correlation function can ultimately define the behavior of the series. As we try to understand and interpret nature’s behavior we are typically given the response of a suite of physical variables that are arranged in time (i.e., wind velocity, temperature, relative humidity, pressure, CO2 concentrations, etc.). Ultimately the correlation function becomes a consistent statistical approach for digesting the data and supplying a physical interpretation.

So consider the fluctuating time series of wind velocities, applying the correlation function will tell us about the momentum exchange. The energy flux (vertical transfer) transported as sensible heat can be described by the correlation function applied to the vertical wind velocity fluctuation and temperature fluctuation. Ultimately, the mass flux (vertical transport) is determined as the correlation between the fluctuation of a compound (i.e. CO2) and the vertical wind velocity fluctuation. This method evolved into what is now known as Direct Covariance (a.k.a. the Eddy Correlation) Method, recently introduced to me (just six months ago) by my advisor Dr. James Edson as I stepped into his domains of the Air-Sea interaction. The whole process has become increasingly familiar with time, especially the power of the correlation function which has yet even more to offer. Based on it, a spectral analysis of the series via Fourier transform can be developed and more information can be squeezed out of our precious time series. This describes very roughly the use and the power of the correlation function in the flux calculations and the concept behind the Eddy Correlation Method. For details on the procedure and hardware required on this process I recommend checking Ludo’s recipe posted on the blog: “Shake and Bake” … baby!

The correlation function is not to be confused with the relation function for the fluxes; the relation concept might escape the realm of statistics, but is no less fascinating. Remember, four cooks in the kitchen…the relation function here is defined as any interaction (you can read correlation too!) between us, the cooks (a.k.a. the CO2 flux team). Before February 22nd, I didn’t know Chris Zappa (or Dr. Zap, an evil doctor with unholy snoring powers, but with great advice regarding work), Ludovic nor Byron. Through time, the domain of our relation function has grown in both appreciation and complexity. Ludo and I have worked in tandem during much the SOGasEx campaign. As you might expect, a good relation developed. Our electronics were no exception; they too felt the power of the relation function. Our Data Acquisition Systems (DAS) began to mimic one another. Without fail, if Ludo’s DAS crashed, mine would follow (a stochastic process? I think not!). The Licors 7500 adopted the same tendency. In the end, a good relation function was able to do the trick, for the sake of the experiment but mainly for the sake of the fluxes.

So you can imagine we went through on the Brown for nearly two months time: discussions, arguments, chats, advice, guidance, laughs, dancing, a lot of singing and some more laughter. One certainty: all the variables helped to achieve our overall success.

PS: Kate, thank you once more for your help editing.

Below is a look to our highly Entropic Data Acquisition Systems.

GASEX-DAS I: Not to be deceived, high entropy levels got nothing to do with disorder or chaos!

DAS II: Ludo’s system, maybe reaching its own “Heat Death” …

Air-Sea Interaction: It’s happening, can you see it? … Look at those fluxes!

1. ### Gailynne Bouretsaid

Dr. Cifuentes,
I am preparing the annual report for NASA’s Airborne Science Program, which includes a write-up about the SoGASEX mission. I found this blog while searching for interesting images to include in the layout. I wonder if I may ask for a high-rez copy of the photo of the ocean and sky that you’ve used in your blog (captioned as “Air-Sea Interaction”). I would be happy to credit the image to you or whoever the photographer was who took the photo.
Many thanks,
Gailynne Bouret

2. ### Alejandro Cifuentes-Lorenzensaid

Dear Gailyne,

Thank you for your interest, first of all am just a PhD student at the moment so no Dr needed !. Just send me your email and I will be happy to send you the image. I hope you get the resolution that you look for, I just took it with digital camara.

Cheers !

ACL