Confidence Limits for Friction Velocity Determined from Turbulence Profiles in Coastal Waters

William R. Crawford Institute of Ocean Sciences, Department of Fisheries and Oceans, Sidney, British Columbia, Canada

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Richard K. Dewey College of Oceanography, Oregon State University, Corvallis, Oregon

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Abstract

It is possible to determine the friction velocity u* at the ocean bottom in coastal waters by measuring a profile of the local rate of turbulent dissipation. A single profile of dissipation gives one computation of u*. The statistical distribution of u* measured in this way is examined to determine the confidence limits one can expect from multiple profiles in a short time. Observations in late spring and summer at two sites in waters on the continental shelf of British Columbia, Canada, indicate that values of u* follow a weakly lognormal distribution with a variance σ2 of 0.1, a value sufficiently small that normal rather than lognormal analysis may be applied. The application of this analysis to these particular data indicates that u* can be determined to within ±20% with 95% confidence with 11 samples of u*.

It is shown that a commonly used method of plotting the cumulative lognormal distribution on probability paper introduces a bias with sample sizes of 10, and also causes the tails of the distributions to curve even for sample sizes of 100 and 1000. A method is presented to remove this bias and curvature.

Abstract

It is possible to determine the friction velocity u* at the ocean bottom in coastal waters by measuring a profile of the local rate of turbulent dissipation. A single profile of dissipation gives one computation of u*. The statistical distribution of u* measured in this way is examined to determine the confidence limits one can expect from multiple profiles in a short time. Observations in late spring and summer at two sites in waters on the continental shelf of British Columbia, Canada, indicate that values of u* follow a weakly lognormal distribution with a variance σ2 of 0.1, a value sufficiently small that normal rather than lognormal analysis may be applied. The application of this analysis to these particular data indicates that u* can be determined to within ±20% with 95% confidence with 11 samples of u*.

It is shown that a commonly used method of plotting the cumulative lognormal distribution on probability paper introduces a bias with sample sizes of 10, and also causes the tails of the distributions to curve even for sample sizes of 100 and 1000. A method is presented to remove this bias and curvature.

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