Decomposing velocity measurements

The quality-controlled velocities are first detrended before being further analysed to determine mean flow past the sensor and surface wave statistics. These quantities are necessary for later choosing the appropriate inertial subrange model for spectral fitting.

Methods for detrending

There is no exact definition for what consists of a "trend", nor any set algorithm for identifying the trend. The following techniques can be used for detrending :

1. Linear trend removal
2. Low-pass linear filters (e.g., butterworth filter)
3. Empirical modal decomposition

The first two methods presume the original time series is stationary and linear, while the third is adaptive and applicable to nonlinear and non-stationary timeseries.

Measured velocities at 4 Hz from an Acoustic-Doppler Velocimeters have been detrended using three different techniques. Empirical modal decomposition (EMD) , linear trend, and a 2nd order low-pass Butterworth filter. A cut-off period of 10 min was targeted by both the filter and EMD

Long continuous sampling

Info needs simplifying after convening as a subgroup Different techniques dependent on whether measurements were collected continuously or in long bursts (define here).

Short burst sampling

A short burst is typically at most 2-3x the expected largest turbulence length scales. As a rule of thumb, turbulence estimates from the inertial subrange of velocity rely on 5 to 15 min long-segments. ``` Act of segmenting is effectively a form of filtering

• Linear trend removal
• Empirical mode decomposition (nonlinear and/or non-stationary signal)

Notes

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