measurement uncertainty
What is the instrument measurement uncertainty, or error, for the velocity in each bin of an ADP profile? In particular, I'm using the HR-ADP with 3cm bins, averaging over 10 minutes, and I'm doing an error analysis, so I need to know the instrument uncertainty.
Thanks!
Jeremy
Thanks!
Jeremy
Dear Jeremy
Your question is difficult to answer, mostly because we have not really done the work required to give a quantitative response. The other problem is that this forum is absolutely no good for equations!
In contrast to narrowband system, broadband systems such as the HR-NDP have the potential to have a very low velocity standard deviation. The value is given by these two equations:
Sigma (phase shift) = f(correlation)
Sigma (v) = Sigma (phase shift)/pulse separation
where Sigma is meant to signify standard deviation of the noise. In other words, the uncertainty in the phase shift estimate - which is what we calculate when we process for Doppler shift - is a function of the correlation. The relation is strong - having correlation close to 1 (100%) makes a huge difference relative to data where the correlation is 0.5 (50%).
The second equation says that the standard deviation of the velocity scales with the pulse separation. In other words, the longer the pulse separation (which also defines the ambiguity velocity), the smaller the standard devation.
As you may see, this is actually a pretty long story and I don't know what the fast and hard numbers are. What we do around here in order to estimate the noise is that we take the time series data and calculate the frequency spectrum. The high frequency part of the spectrum sometimes turn out to be flat and thereby constitutes the upper band for the (white) noise spectrum. Integrate the energy in the box bound by the white noise and you have an estimate of the noise variance. If you do not find the flat line near the high frequency range in the spectrum, the noise level is too low to play a part in your data.
Best regards,
Atle Lohrmann
PS Sorry about the incredibly slow answer..
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Your question is difficult to answer, mostly because we have not really done the work required to give a quantitative response. The other problem is that this forum is absolutely no good for equations!
In contrast to narrowband system, broadband systems such as the HR-NDP have the potential to have a very low velocity standard deviation. The value is given by these two equations:
Sigma (phase shift) = f(correlation)
Sigma (v) = Sigma (phase shift)/pulse separation
where Sigma is meant to signify standard deviation of the noise. In other words, the uncertainty in the phase shift estimate - which is what we calculate when we process for Doppler shift - is a function of the correlation. The relation is strong - having correlation close to 1 (100%) makes a huge difference relative to data where the correlation is 0.5 (50%).
The second equation says that the standard deviation of the velocity scales with the pulse separation. In other words, the longer the pulse separation (which also defines the ambiguity velocity), the smaller the standard devation.
As you may see, this is actually a pretty long story and I don't know what the fast and hard numbers are. What we do around here in order to estimate the noise is that we take the time series data and calculate the frequency spectrum. The high frequency part of the spectrum sometimes turn out to be flat and thereby constitutes the upper band for the (white) noise spectrum. Integrate the energy in the box bound by the white noise and you have an estimate of the noise variance. If you do not find the flat line near the high frequency range in the spectrum, the noise level is too low to play a part in your data.
Best regards,
Atle Lohrmann
PS Sorry about the incredibly slow answer..
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