Tilt compensation

There seems to be some confusion out there about how current profilers correct for the influence of instrument tilt.  Here is a short description of the problem and how it is approached in the Nortek current profilers.

1) In all current profilers, the velocity is measured in fixed cells along each acoustic beam.  The length of each cell ("cell size") is defined as a time interval multiplied by the speed of sound which is then projected onto the vertical axis.  For example: If we speak of a cell of 1 m, this refers to the the projection along the vertical axis.  The corresponding length of the cell along the acoustic beam is 1/cos 25.

Imagine a 2D system with two 25-degree beams oriented 180 degrees apart.  If the system is tilted by 10 degrees, one beam will have an angle of 15 degrees relative to the vertical and the other will have an angle of 35 degrees.  

The velocity measured along beam 1 and beam will not be the same since the tilt is different.  Furthermore, the cells along beam 1 and 2 do not correspond to the same distance above the bottom.  For example, the data coming from beam 1 in cell 18 may correspond to the same vertical level as what comes in from beam 2 in cell 19.

If we start out with a current profile with significant shear (blue), a tilt of 10 degrees would give the along-beam current profiles shown in this figure:

Beam velocity

For each of the beam velocities, the curve is referenced a fixed vertical axis.

Once we have calculated the beam velocities, the current profiler will transform the data to ZX coordinates (2D system).  This transform will generate velocities in a orthogonal coordinate system that is fixed to the instrument.  In our example, the coordinate system is tilted 10 degrees relative to the vertical. Practically speaking, the horizontal velocity will then be quite close to correct velocity coordinates while the vertical velocity is typically too large.  

The next step is to correct for the tilted coordinate system. In this step, we convert the XY data to East and Up data, where East means that the conversion also normally includes the compass heading and Up means along the gravitation axis.  The data in this figure shows the result from these two transforms:

EastUp

Please note that these transforms corrects for tilt (and compass) in the sense that the final coordinate system is aligned with the gravitational axis (and the magnetic north pole).  However, the data are not automatically corrected for the vertical mapping of the cells and for this reason there will be residual errors in the current profile: 

Error

The residual error can be characterized:
- Smearing of shear.  The shear layer will look thicker than it really is.  The mid-point will also be slightly off.
- Apparent vertical velocities.  In areas of shear, there will appear to be a vertical velocity that is in fact an artifact of the processing.

It is possible to remap the velocity cells for each beam and thereby minimize the residual error.  However, this is not done in the Nortek instruments for the simple reason that the mapping is non-linear.  A failed tilt sensor (for example, one that shows 45 degrees instead of 0 degrees) can potentially destroy most of the current data in a deployment, which made us very cautious about automatic remapping.  Instead,  we have included the remapping as processing options in the softwares "Storm" and "Surge" - which incidentally also includes the option of reprocessing data with only two valid beams.  Reprocessing with this software will ensure that the shear data are as accurate as possible.  The best solution, however , is to make sure the instrument is level during deployment.  Tilt degrades data in ways that are not always recoverable, such as increasing the thickness of the surface sidelobe layer and in some case reducing the effective range of your instrument. As usual, the very best strategy is to get it right in the first place. 

Best regards,

Atle Lohrmann