On the apparent "imbalance" term in the turbulent kinetic energy budget

A synthetic dataset is used to show that apparent variations between different stability classes in the mean drag coefficient, C-D10n, to wind speed relationship can be explained by random errors in determining the friction velocity u(*). Where the latter has been obtained by the inertial dissipation method, the variations in C-D10n have previously been ascribed to an imbalance between production and dissipation in the turbulent kinetic energy budget. It follows that the application of "imbalance corrections" when calculating u(*) is incorrect and will cause a positive bias in C-D10n, by about 10(-4). With no imbalance correction. random errors in u(*) result in scatter in the C-D10n values, but for most wind speeds, there is no mean bias. However, in light winds under unstable conditions random errors in u(*) act to positively bias the calculated C-D10n values. This is because the stability related effects are nonlinear and also because for some records for which C-D10n would be decreased, the iteration scheme does not converge. The threshold wind speed is typically 7 m s(-1), less for cleaner datasets. The biased C-D10n values can be avoided by using a u(*) value calculated from a mean C-D10n-U-10n relationship to determine the stability. The choice of the particular relationship is not critical. Recalculating previously published C-D10n values without imbalance correction, but with anemometer response correction, results in a decrease of C-D10n but only by about 0.05 x 10(-3). In addition to removing a previous cause of scatter and uncertainty in inertial dissipation data, the results suggest that spurious stability effects and low windspeed biases may be present in C-D10n estimates obtained by other methods.