Quality control of ε estimates (QA2)

1. Use the coefficient [math]\displaystyle{ a_0 }[/math] (the intercept of the regression) to estimate the noise of the velocity observations and compare to the expected value based on the instrument settings.
2. Data segments for which the regression coefficient a₁ (see previous step) is negative yield an imaginary [math]\displaystyle{ \varepsilon }[/math] value, which should be rejected
3. Data segments for which the regression coefficient a₀ (see previous step) is negative (implying a negative noise floor) are likely to be invalid and are typically rejected
4. Examine the consistency of [math]\displaystyle{ \varepsilon }[/math] between bins (if evaluated) and between beams as an indication of estimate reliability - the geometric mean between beams is frequently used as the representative value
5. Evaluate the impact of varying r_max values (within the anticipated inertial range) on [math]\displaystyle{ \varepsilon }[/math]; an increase in [math]\displaystyle{ \varepsilon }[/math] with increasing r_max is likely to indicate that v’ retains a non-turbulent contribution to the velocity difference between bins
6. The goodness of fit (R²) for the regression provides a basic indication of the quality of the fit
7. A better indication of the quality of the fit is usually provided by looking at the ratio of the estimated [math]\displaystyle{ \varepsilon }[/math] value to that based on the 95%-ile confidence interval estimate of the a₁ regression coefficient e.g. reject values where the ratio exceeds a specified threshold
8. Examine the distribution of [math]\displaystyle{ \varepsilon }[/math] estimates - in most situations, this would be expected to be log-normal
9. Comparison of observed values with nominal values based on established boundary-forced scalings may also be informative and help to identify observation or processing issues

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