Vectrino noise not white

Dear Sir/Madam,

In order to investigate the noise level of a Nortek Vectrino that I am using, I set up an experiment where I seeded a bucket of stationary water and recorded a 5 minute time series at 200Hz using a downward facing probe. I expected the resulting spectrum of the noise to be white as stated in other posts on the forum (http://www.nortek-bv.nl/en/knowledge-center/forum/velocimeters/30181035#724744946). However the spectrum resembled something closer to pink noise - see attached figure. I have repeated the test at both 200Hz and 32Hz sampling (output) frequency, and the same result is observed.

Therefore I cannot find a noise floor as I cannot assume the noise is white. This makes it difficult to account for the noise in the method suggested in the forum post http://www.nortek-as.com/en/knowledge-center/forum/velocimeters/206041974.

Do you have any thoughts why this noise is not white, or any alternative methods of correcting for noise that do not make this assumption?

Regards,

Sam

Hi Sam, What you've plotted is technically the velocity spectrum. It's a combination of the noise spectrum and velocity spectrum for each component. There needs to be a little more work before obtaining just the noise spectrum. There are velocities in the bucket for several reasons, one of which is acoustic streaming. I would estimate the noise floor of the instrument as 10^-7 for the horizontal components and 10^-8 for the vertical component from your plot (looking at the very tail end of the spectrum). Everything in between is a combination of signal and noise, and as you can see, the noise floor of the instrument is really low. To apply any noise correction, you'll want to estimate the noise spectrum or variance under the operating conditions for data collection. So, a bucket test to get a single noise spectrum won't work unfortunately. I'm not too familiar with the C. Marcelo method (I know the paper, but haven't read it closely in a while and never implemented their correction) so I can't comment further on that. I'd recommend taking a look at this paper: Hurther, D., & Lemmin, U. (2001). A correction method for turbulence measurements with a 3D acoustic Doppler velocity profiler. Journal Of Atmospheric And Oceanic Technology, 18(3), 446–458. As it discusses a simple method to estimate noise from an instrument like the Vectrino. Ultimately, any of these methods just winds up being some type of Optimal Filter on the spectrum. The assumption of Gaussian white noise for a Vectrino is pretty reasonable as well. If it wasn't we'd all be in a lot of trouble. P.J.

Hi P.J.

Do you have a better citation for the C. Marcelo method or an algorithm to follow?

I used the Hurther/Lemmin method for my dissertation when I could, and just approximated the noise spectrum by averaging over the frequency range (or wavenumber range depending on what kind of data I was looking at) where noise was dominant when I couldn't (which was most of the time since I was looking at Vector or HR Profiler data). See this paper for a simple demonstration: http://www.nortek-as.com/lib/bibliography/internal-wave-generation-in-lakes-with-very-slow (last two or three figures I think). This is just an Optimal Filter (at least in my fairly limited understanding of that term, check this webpage for a better description: http://www.dspguide.com/ch17/3.htm). Nick Scott who I think is at Arette Associates currently uses this method quite extensively as well. There's a section in the Numerical Recipe books on it as well if you prefer. I'll try to read through the C. Marcelo paper soon and see if I can make sense of it. I think fundamentally it's doing something similar since the noise doesn't really change, just the method of estimating it. P.J.

Also, sorry the formatting on these is so odd. I changed a setting recently and now paragraph breaks need to be hardcoded or something.

Just read through parts of the C. Marcelo paper today at lunch. The discussion is a little different, but the same assumptions are underlying it, namely the noise spectrum is dominated by what we call Doppler noise, its spectrum is white, and we can obtain an estimate of the noise spectrum a few different ways.

Here's the Numerical Recipes chapter on Optimal Filtering which discusses all of this from a more signal processing perspective:

http://www.it.uom.gr/teaching/linearalgebra/NumericalRecipiesInC/c13-3.pdf