Improved methods to calculate depth-resolved velocities from glider-mounted ADCPs

Ocean gliders are autonomous underwater vehicles typically used to sample spatial variations in scalar variables (e.g., temperature, salinity, and bio-optical water properties) along transects. More recently, gliders have been equipped with ADCPs for measuring current profiles along transects. Accurate measurement of velocity profiles from a moving platform requires knowledge of the platform motion over the earth. Determination of glider motion over the earth relies on glider GPS positions available only at times of glider surfacing. Glider surfacing intervals typically range from 10´s of minutes to hours, precluding accurate instantaneous knowledge of glider motion. This is a major challenge for measuring velocity profiles from ocean gliders. One approach for determining vertical velocity profiles from glider-mounted ADCPs relies on estimating depth-integrated currents averaged between glider surfacings. Once estimated, vertically averaged velocity can be combined with horizontal glider velocities relative to the water to obtain depth-resolved velocities using methods of Visbeck (2001) and Todd et al. (2011). The vertically averaged velocity is calculated from the distance the glider strays from its projected position during the time between surfacings. This distance is computed as the difference between the dead-reckoned surfacing location and the actual surfacing location as measured by GPS. There are numerous methods for computing the dead-reckoned position of glider surfacings, but these have not been evaluated to determine which best predicts surfacing locations. Here, three methods for calculating vertically averaged horizontal current velocities from gliders are evaluated. Two Slocum Coastal G1 gliders (manufactured by Teledyne Webb Research), each with an upward looking 1 MHz ADCP (manufactured by Teledyne RD Instruments), were deployed off the California coast during the summer of 2012. The gliders flew 500 m square patterns around a bottom-mounted, upwa- d-looking 600 kHz ADCP (manufactured by Teledyne RD Instruments) moored at a depth of 26 m. The moored ADCP data are key to evaluating methods for computing vertically averaged velocity from gliders and ultimately assessing depth-resolved current velocities obtained from glider-mounted ADCPs. The first method calculates the glider´s horizontal velocity using pitch and vertical velocity. Vertical velocity is calculated by taking the derivative of pressure with respect to time. It is often assumed that the flight path is in the direction of the glider´s long axis and α, the angle of attack or the angle between the glider´s path through the water and its long axis, is zero. This assumption can result in errors of 2.5 cm s^-1 (Merckelbach et al. 2001) which are on the order of 10% of the horizontal velocity. Previous studies have estimated angle of attack (e.g. Sherman et al. 2001) using model results for internally-mounted ADCPs on Spray gliders. The gliders in this study carried externally-mounted ADCPs, so errors may also result from extra drag and non-zero values of α. The value of α is found by maximizing the r2 of vertically averaged velocities found by this method with vertically averaged velocities from the mooring. The second method directly measures currents using the ADCPs mounted on the gliders. Water velocity relative to the glider is obtained from the ADCP bin nearest the glider which is 1m long and begins 1.2 m from the glider. This velocity is calculated on glider upcasts and downcasts in east-north-up (ENU) coordinates. Velocities in ENU coordinates are derived from software provided with the ADCP. The third method uses velocities measured along the ADCP beams in so-called beam coordinates. Directly measured velocity can then be used (see Todd et al. 2011) from the component of the ADCP beams oriented in the direction parallel to the glider´s long axis - this can be 2 or 3 beams depending on the transducer head on