Introduction
Each beam measures the frequency shift of the echo of the transmitted signal, and the corresponding velocity is found by using the Doppler shift. Remember that any particle motion perpendicular to the beam will not affect the Doppler shift, so the velocity component from the Doppler shift says something about the radial velocity along one beam path. One beam is required for each velocity component, so for measuring horizontal and vertical components of velocity, data from a minimum of three beams are required. Nortek current meters have three or four slanted beams that measures one velocity component each. The beams are tilted either 20 or 25 degrees from the vertical (refer to the data sheet for specific instrument details), and depending on the instrument type the beams will be measuring velocity at three or four different locations due to this divergent design (see Figure 1). To achieve horizontal or vertical velocity components, we rely on measurements from all three or four beams, and therefore measurements from three or four separate locations. We therefore have to assume that water moved in the same direction and with the same speed at each of the individual locations covered by each beam. This horizontal homogeneity is one of the key assumptions we do when measuring ocean currents with Nortek instruments. This is an accepted requirement, as currents vary little in the horizontal plane in most areas.
Some of our instruments also have a center transducer with a vertical beam. This can have several applications, depending on the instrument type. Please refer to the instrument data sheet for further information:
- Since the beam is vertical it can not give any information about horizontal velocity, but it can be used to obtain a direct measure of the vertical motion. This is only available on the Signature instruments, and requires the Burst license.
- The vertical beam is most often used as an altimeter to measure the distance to either the air-water interface or ice. For AWACs this is the only use for the centered fourth beam. For Signature instruments this requires the Wave measurement license.
The raw data collected from the instrument is the mentioned radial velocities measured by each beam. By assuming horizontal homogeneity these velocities can be converted to more applicable coordinate systems using information about the geometry of the instrument head and sensor data gathered by the instrument. Each instrument has its own unique transformation matrix, based on the transducer orientation. This matrix can be found in the data structures for the interested user. The matrix is used when transforming the along beam velocities to instrument-referenced coordinates XYZ. In the following sections each of the three available coordinate systems are explained.
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 2). All raw velocity measurements are initially taken in beam coordinate system initially, and then converted to either XYZ or ENU. Since the transducers are fixed, the beam directions and hence the direction of the beam axes depend on the orientation of the instrument head.
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 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. In the XY-plane, currents flowing in the Y-direction is reported as a direction of 0° and the X-direction is reported as the direction of 90°. These current directions should not be confused with the reported heading, which will give the orientation of the instrument itself. To make use of the XYZ coordinate system knowledge about the instrument orientation, either from the heading value or from external sensors is necessary.
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 points towards magnetic East, the second axis points towards magnetic North and the last 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 points towards the sea surface (for a submerged upward facing instrument). Just like a compass, currents flowing towards North is reported as 0° and towards 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.
Vertical velocities
Instruments with four slanted beams will provide two independent vertical velocities: Z1 and Z2 (XYZ coordinates) and Up1 and Up2 (ENU coordinates). Z1 and Up1 is associated with beam 1 & 3 and Z2 and Up2 is associated with beam 2 & 4.
The two independent estimates of vertical velocity are useful for assessing data quality. Their difference indicates how homogeneous the velocity field is within the horizontal layer. Ideally, Z1 and Z2 should match closely, but small differences are expected since they are derived from different beam sets. Significant discrepancies, however, should prompt further quality control, as they may indicate issues such as instrument tilt, mounting problems, beam obstruction, or beam failure.
Note that some instruments may include a fifth (center) beam capable of directly measuring vertical velocity. This measurement is provided in BEAM coordinates only, but is aligned with the Z1 and Z2 direction.
Affect of tilt on coordinate transformation
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. Figure 2 illustrates the affect of tilt, on the individual velocities components during the coordinate system.
For more information about how a tilted instrument can affect your data, please refer to the tilt correction chapter.
Figure 2: The Z axis is in reference to the instrument head and changes with tilt. The Up-axis is relative to the Earth and is not affected by tilt.
Manual coordinate transformation
If you are curious about manually transforming the coordinate system of your dataset, please refer to the article relevant to your instrument type below:
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