Uncertainties in Estimates of Reynolds Stress and TKE Production Rate Using the ADCP Variance Method

Abstract

The use of acoustic Doppler current profilers (ADCPs) to measure turbulent parameters via the variance method involves uncertainties due to instrument noise and flow-related errors in measurement. For weak flows, the uncertainty in Reynolds stress measurements arises mainly from instrument noise and is proportional to the square of the velocity standard deviation, while the uncertainty in the corresponding estimates of the rate of production of turbulent kinetic energy (TKE) is proportional to the cube of the velocity standard deviation. For stronger flows, the principal determining parameter is the number of individual independent velocity measurements over which the variance is calculated. These results are validated by detailed analyses of two datasets from an RD Instruments 1.2-MHz Workhorse ADCP, using a ping rate of 2 Hz with ensemble averaging at 0.5 Hz, and a ping rate of 10 Hz with ensemble averaging at 1 Hz, respectively. While increasing ping rate generally reduces the effects of instrument noise, it will not alleviate the influence of flow-related noise once the sampling interval is less than the autocovariance time scale of the turbulence. Using the fast ping rate, the uncertainty in the Reynolds stress due to instrument noise is reduced by a factor of more than 3 to ϳ0.02 Pa; in higher energy environments there is a reduction in the uncertainty of about 30%. The observational and theoretical estimates for the reduction in the uncertainty using the fast ping rate are in good agreement.

A Comparison of Methods for Estimating Reynolds Stress from ADCP Measurements in Wavy Environments

“…(3) (Stacey et al 1999a;Williams and Simpson 2004). This result is then adjusted by an additional parameter, on the order of 1-4, to correct for the autocorrelation of the time series (Williams and Simpson 2004). However, following Rosman et al (2008), the correlation correction was not implemented in the present study and thus the uncertainty estimates for the AF method shown represent a lower bound.…”

“…(3) (Stacey et al 1999a;Williams and Simpson 2004). This result is then adjusted by an additional parameter, on the order of 1-4, to correct for the autocorrelation of the time series (Williams and Simpson 2004).…”

“…Recent studies (Williams and Simpson 2004;Nidzieko et al 2006) have shown that the lower noise floors possible using T-RDI's mode 12 sampling lead to improved stress estimates using the variance method, in comparison to mode 1 sampling. Additionally, ADCP velocities from smaller bin sizes will be more noisy compared to larger bins, although the effect is somewhat less than the noise differences between mode 1 and mode 12 sampling.…”

“…Using the variance method, vertical profiles of Reynolds stresses have been successfully estimated from bursts of high-frequency (1-2-Hz sample rate) along-beam velocities (Stacey et al 1999a,b;Rippeth et al 2003;Williams and Simpson 2004;Nidzieko et al 2006;Lu and Lueck 1999;Rippeth et al 2002Rippeth et al , 2003, allowing detailed work on momentum transfer and turbulence in tidal channels, rivers, and estuaries. However, in most coastal ocean environments surface gravity waves dominate the energy spectrum, as orbital velocities are orders of magnitude larger than those of turbulent eddies.…”

Error and uncertainty in estimates of Reynolds stress using ADCP in an energetic ocean state

“…Finally, in section 2.3, a method for calculating the variance of the estimates directly from the data is presented using the work of Williams and Simpson [26]. The conclusion is that the ADCP can provide approximate estimates of the Reynolds stess when there is minimal beam tilt, or when the wave-induced velocities are not energetic.…”