All Nortek instruments define the direction of measured current velocities using three primary coordinate systems:
- Beam coordinate system
- Cartesian coordinate system (XYZ)
- East-North-Up coordinate system (ENU)
Beam coordinate system
In beam coordinates, each beam makes up one axis, and velocities are measured as vectors in the direction of the transducer beams. A positive velocity measurement is directed in the same direction as the beam points. The transducers/beams are numbered, and the axes are named according to the numbering (as shown in Figure 1). All raw velocity measurements are taken in beam coordinate system initially and then converted to either XYZ or ENU. Since the transducers are fixed relative to the instrument, the beam directions, and hence the direction of the beam axes, depend on the orientation of the instrument head. This implies that a shift in tilt and/or heading will change their direction.
Figure 1: Beam coordinates on a Signature instrument.
Cartesian coordinate system (XYZ)
The Cartesian coordinate system is defined by an origin point and three perpendicular axes X, Y, and Z. On most Nortek instruments, the X-axis is in the same direction as beam 1. However, the X-axis does not have the same angle as the Beam 1-axis, rather it points orthogonal to the instruments with positive direction defined outwards. The Y-axis follows the same convention. The XY-plane is also orthogonal to the instrument, which means that the Z-axis points straight upwards when the instrument is looking up and straight downwards when the instrument is looking down. Two independent vertical estimates (Z1 and Z2) are provided from instruments with four slanted beams, where Z1 and Z2 are associated with beam 1 & 3 and beam 2 & 4 respectively. The axis directions can be found using the right-hand rule with the first (index) finger pointing in the positive X-direction, the second (middle) finger in the positive Y-direction, and the thumb in the positive Z-direction. It is important to note that the XYZ coordinates are in reference to the instrument head so the measured velocity directions are dependent on the instrument orientation. Changes in tilt and heading will thus shift the axes' direction. In the XY-plane, Y is reported as a direction of 0° and X is reported as a direction of 90°.
Figure 2: XYZ coordinates on a Signature instrument.
East-North-Up coordinate system (ENU)
ENU stands for "East", "North" and "Up" and similarly to the Cartesian coordinate system is also defined by three perpendicular axes. The first axis (x-axis) points towards magnetic East, the second axis (y-axis) points towards magnetic North, and the last (z-axis) points vertically upwards orthogonal to the East-North plane. As with the XYZ coordinates, the right-hand rule can be used to find the axis directions, with the index finger indicating East, the middle finger as North, and the thumb representing Up-direction. This coordinate system is relative to the earth's magnetic field and not the instrument head like the others, meaning that measured velocity directions do not depend on instrument orientation. The directions East and North will always be towards magnetic East and magnetic North, while Up will always point toward the sea surface (for a submerged upward-facing instrument). Instruments with four slanted beams will provide two independent Up estimates, where Up1 is associated with beams 1 & 3 and Up2 is associated with beams 2 & 4.
Built-in compass and tilt sensors make the determination of this coordinate system possible. Although tilt corrections are made during the ENU velocity conversion, these corrections are separate from the optional corrections made when remapping cells using the "remove tilt effects" or "bin mapping" feature in Nortek software. Additionally, just like a compass, North is reported as 0° and East as 90°. It is important to note that only the slanted beams can be represented in ENU coordinates. If collecting current data from the vertical center beam, this will always be given in BEAM coordinates.
Figure 3: ENU coordinates on a Signature instrument.
Note: The Z-axis and Up-axis may seem very similar, and they are similar in the way that they both measure velocities along the same vertical line when an instrument is level. However, the difference between them becomes very clear with tilt, as described here: What is the difference between Z and Up?