Robust Estimations of Current Velocities with Four-Beam Broadband ADCPs

An extended explanation of the hypothesis and equations traditionally used to transform between fourbeam ADCP radial beam velocities and current velocity components is presented. This explanation includes a dissertation about the meaning of the RD Instrument error velocity and a description of the standard beamto-current components transformation as a least squares solution. Afterward, the variance–covariance matrix associated with the least squares solution is found. Then, a robust solution for transforming radial beam velocities into current components is derived under the formality of a weighted least squares approach. The associated variance–covariance matrix is also formulated and theoretically proves that the modulus of its elements will be generally lower than the corresponding modulus of the variance–covariance matrix associated with the standard least squares solution. Finally, a comparison between the results obtained using the standard least squares solution and the results of the weighted least squares method, using a high-resolution ADCP dataset, is presented. The results show that, in this case, the weighted least squares solution provides variance estimations that are 4% lower over the entire record period (8 days) and 7% lower during a shorter, more energetic period (12 h).

[1]  I. Yasuda,et al.  Meridional transport of North Pacific Intermediate Water across 37°N based on an objective analysis of lowered acoustic Doppler current profiler data , 2004 .

[2]  Ann E. Gargett,et al.  Observing Turbulence with a Modified Acoustic Doppler Current Profiler , 1994 .

[3]  Reynolds Stresses and Secondary Circulation in a Stratified Rotating Shear Flow , 2002 .

[4]  Teresa K. Chereskin,et al.  Modeling the Performance of an Acoustic Doppler Current Profiler , 1993 .

[5]  F. F. Pérèz,et al.  Large and mesoscale variability of the water masses and the deep chlorophyll maximum in the Azores Front , 2003 .

[6]  Youyu Lu,et al.  Using a Broadband ADCP in a Tidal Channel. Part II: Turbulence , 1999 .

[7]  R. Lhermitte,et al.  Open-Channel Flow and Turbulence Measurement by High-Resolution Doppler Sonar , 1994 .

[8]  Bill Hughes,et al.  Acoustic Doppler Current Profiler Wave Sentry buoy , 2009, OCEANS 2009.

[9]  David Hurther,et al.  A Correction Method for Turbulence Measurements with a 3D Acoustic Doppler Velocity Profiler , 2001 .

[10]  J. Simpson,et al.  Uncertainties in Estimates of Reynolds Stress and TKE Production Rate Using the ADCP Variance Method , 2004 .

[11]  Roger Lhermitte,et al.  Pulse-to-Pulse Coherent Doppler Sonar Signal Processing Techniques , 1984 .

[12]  Hans van Haren,et al.  Estimates of sea level, waves and winds from a bottom-mounted ADCP in a shelf sea , 2001 .

[13]  Blair H. Brumley,et al.  Performance of a broad-band acoustic Doppler current profiler , 1991 .

[14]  Sea surface conditions remotely sensed by upward-looking ADCPs , 1995 .

[15]  P. R. Bevington,et al.  Data Reduction and Error Analysis for the Physical Sciences , 1969 .

[16]  A. Lohrmann,et al.  High Resolution Measurements of Turbulence, Velocity and Stress Using a Pulse-to-Pulse Coherent Sonar , 1990 .

[17]  R. Guza,et al.  Observations of turbulence in the surf zone , 1994 .

[18]  Stephen G. Monismith,et al.  Observations of Turbulence in a Partially Stratified Estuary , 1999 .

[19]  J. Simpson,et al.  Reynolds Stress and Turbulent Energy Production in a Tidal Channel , 2002 .

[20]  S. Bacon,et al.  Transports across the 2002 Greenland-Portugal Ovide section and comparison with 1997. , 2007 .

[21]  Martin Visbeck,et al.  Deep Velocity Profiling with Self-contained ADCPs , 1993 .

[22]  C. Wunsch.  The Ocean Circulation Inverse Problem , 1996 .

[23]  Martin Visbeck,et al.  Deep Velocity Profiling Using Lowered Acoustic Doppler Current Profilers: Bottom Track and Inverse Solutions* , 2002 .

[24]  A. L. New,et al.  Factors affecting the quality of shipboard acoustic Doppler current profiler data , 1992 .

[25]  Robert Pinkel,et al.  Repeat-Sequence Coding for Improved Precision of Doppler Sonar and Sodar , 1992 .

[26]  E. Firing,et al.  A Direct Comparison of Two RDI Shipboard ADCPs: A 75-kHz Ocean Surveyor and a 150-kHz Narrow Band , 2003 .

[27]  A. Haghighat,et al.  Performance of A 3 MCNP™ for Calculation of 3-D Neutron Flux Distribution in a BWR Core Shroud , 2001 .

[28]  An Improvement in the Calculation of ADCP Velocities , 2002 .

[29]  The accuracy of acoustic vertical velocity measurements: instrument biases and the effect of Zooplankton migration , 2005 .

[30]  Youyu Lu,et al.  Using a Broadband ADCP in a Tidal Channel. Part I: Mean Flow and Shear , 1999 .

[31]  J. Hamilton,et al.  Mooring Vibration as a Source of Current Meter Error and Its Correction , 1997 .

[32]  T. Joyce,et al.  Zonal circulation in the NW Atlantic and Caribbean from a meridional World Ocean Circulation experiment hydrographic section at 66°W , 2001 .