# Principles of Operation:1. Doppler Velocity Measurement

Contents

This section briefly describes some of the underlying principles that control the operation and application of the Aquadopp Current Meter, Aquadopp Current Profiler, EasyQ and EasyV. All of these are monostatic Dopplers, which means that they use a single transducer to transmit and receive.

To keep this primer simple and consistent, where the following uses the name Aquadopp by itself, you can understand that it can as easily apply to the Aquadopp Current Meter, the Aquadopp Current Profiler, the EasyQ or the EasyV. Information that applies to a specific instrument will use the instrument's full name.

## 1. Doppler Effect

You hear the Doppler effect whenever a train passes by - the change in pitch you hear tells you how fast the train is moving. The Aquadopp uses the Doppler effect to measure current velocity by transmitting a short pulse of sound, listening to its echo and measuring the change in pitch or frequency of the echo.

There are many ways to measure the Doppler effect, each with its own advantages and drawbacks. Nortek implements a narrowband autocovariance method because it has been established as robust, reliable and accurate.

Sound does not reflect from the water itself, but rather from particles suspended in the water. These particles are typically zooplankton, suspended sediment or small bubbles. Bubbles cause trouble at far lower acoustic frequencies, but they look like any other scatterer at the Aquadopp's frequency (2 MHz). Long experience with Doppler current sensors tells us that the small particles the Aquadopp sees move on average at the same speed as the water - the velocity it measures is the velocity of the water.

## 2. Doppler Beams and Measurement Cells

Doppler current sensors use large transducers (relative to the wavelength of the sound) to obtain narrow acoustic beams. The Aquadopp's beams have a beamwidth of 1.7° (2 MHz) or 3.4° (1 MHz) . Narrow beams are essential for obtaining good data.

Each beam measures velocity parallel to the beam and does not sense the velocity perpendicular to the beam at all. The Aquadopp senses the full 3D velocity with three beams, all pointed in different directions. The Aquadopp measures horizontal velocity with two horizontal, orthogonal beams, and the vertical component with the beam slanted up (or down) at 45°. If you assume the flow is uniform across the three beams, simple trigonometry is sufficient to compute the vertical velocity.

A single measurement cell is shaped like a triangle, as shown in Figure 1 for an Aquadopp Current Meter. The trianglar shape means that it is more sensitive to currents in the middle of the cell than at either end. The maximum extent of the cell is double the length of the transmit pulse. Even though the cell in Figure 1 extends 150 cm, the nominal cell size is 75 cm because the cell is most sensitive to currents in the middle 75 cm. Figure 1. Measurement cell location for an Aquadopp Current Meter.

The Aquadopp Current Profiler and the EasyQ use multiple cells, each of which overlaps its neighbor. Because the transmit pulse and measurement cell sizes are commonly the same size, the cells look like a series of overlapping triangles as shown in the top of Figure 2. If the cell interval is larger than the transmit pulse, the center of the cell flattens, as shown at the bottom of Figure 2. Using a short transmit pulse for a long cell has several consequences. The first is that it produces cells that are more uniformly weighted. Long transmit pulses produce cells weighted more strongly close to the instrument. Shortening the pulse evens out the response across the cell. The second consequence is that a shorter transmit pulse increases the measurement uncertanty. For longer cells, this is of little consequence, but it could be a factor for small cells. The third consequence is that cells can be centered closer to the profiler. This difference is apparent in Figure 2. Figure 2. (top) A series of cells where the separation between adjacent cells is equal to the length of the transmit pulse. (bottom) A series of cells where the transmit pulse is shorter than the cell separation.

The first cell is centered at a distance equal to:

center of first cell = blank + (cell size + transmit size)/2

A current profiler usually looks up toward the surface or down toward the bottom. Figure 3 shows a series of cells above a profiler. The distance from the transducer to the first cell is the blank Figure 3. A series of cells above a current profiler. The number of cells is limited only by the profiling range of the instrument.

## 3. Sound Speed Correction

An Aquadopp measures distance indirectly by computing the time it takes for sound to go out and back. It uses the speed of sound to convert time to distance. It obtains the speed of sound by assuming a nominal salinity and computing the sound speed based on the measured temperature. The process works relatively well because sound speed is more sensitive to temperature than it is to salinity.

If you must correct velocity data for sound speed, use the following equation:

Vcorrected = Vold (SSnew/SSold)

where V is velocity and SS is sound speed.

## 4. Attitude Correction

Moorings often allow Aquadopps to tilt and rotate freely. It measures its tilt and heading and uses this information to correct the data to true earth coordinates. Because the compass uses energy, the Aquadopp reads heading only as often as it need to. In moorings that move around a lot, you can set the instrument to read the compass more often.

## 5. Flow Disturbance

The Aquadopp Current Meter's beam geometry is one of its innovative features. While a current profiler must slant its beams vertically to obtain a profile, an Aquadopp Current Meter is free to keep its beams horizontal. This gives the you more freedom to design your mooring to minimize disturbance caused by the mooring itself. Self-disturbance of flow is a chief source of data contamination with traditional current meters.

Nortek's AquaFin optimizes the Aquadopp's ability to measure without flow disturbance while simplifying inline deployment. The AquaFin shackles inline and swivels the Aquadopp so that its beams always face into undisturbed flow. The Aquadopp's compass has no trouble compensating for the heading changes. The Aquafin works equally well for the Aquadopp Current Meter and Current Profiler.

If you simply attach the Aquadopp directly to a rope or cable, you can position the center of the measurement cell further away from the instrument. A rule of thumb is to position the cell away from disturbing objects by a distance that is at least 10 times as great as the size of the object. For most mooring situations, you can easily move an Aquadopp's cells more than 10 times the dimension of either the Aquadopp or the mooring structure.

If you place an Aquadopp on a pier or piling to the side of the flow you are measuring, flow disturbance will not generally be such a problem. The worst disturbance occurs when your measurement volume is in the wake of the disturbance.

If you have unusual situations, you can select one of the many non-standard transducers that have already been designed for these instruments, or you can have Nortek design a transducer specifically for your requirement.

## 6. Boundaries

In open waters, boundaries are not a concern, but if you want to use an Aquadopp near the bottom or surface, you should consider the boundaries as you design your experiment. Figure 4 illustrates a simple problem that can occur when you use an Aquadopp near the water surface. Deploying upside down with the beams touching the bottom leads to a similar problem. Figure 4 Be careful with an Aquadopp Current Meters beam 3 in shallow-water and near-surface applications.

There are several different ways to improve the situation:

• Change the orientation. For example, turn a near-surface Aquadopp upside down.
• Use XYZ coordinates instead of ENU and coordinate transform your data later. You could use this approach when the water level changes a lot, and ignore the vertical velocity when the surface interferes with beam 3. This approach works only if your system is fixed in place and not allowed to move while measurements are taken.
• Use a custom transducer designed to obtain good data specifically for your application.

## 7. Boundaries and Sidelobes

Profilers looking up or down typically lose data near the surface or bottom. This loss is caused by contamination of the near-surface data by sidelobe echoes. The acoustic beams focus most of the energy in the center of the beams, but a small amount leaks out in other directions. Because sound reflects much better from the water surface than it does from the water, the small signals that travel straight to the surface can produce sufficient echo to contaminate the signal from the water. Figure 5 illustrates how this works. If the distance to the surface is A, then contamination of the current measurements begin at the same distance A along the slanted beams. In Figure 5, the top two cells are contaminated. The following is an approximate equation for near-surface contamination:

Rmax = A cos(angle) - Cell

where Rmax is the range for good data, angle is the angle of the beam relative to vertical, and Cell is the sell size. To be conservative, you could choose to subtract two depth cells instead of one. Figure 5. The geometry of profiler sidelobe interference.

## 8. Horizontal Profiling in Shallow Channels

The EasyQ and EasyV profile horizontally, sometimes over distances that are large compared with the water depth. The ratio of channel width to depth is called the aspect ratio.This works only because acoustic beams are narrow. Figure 6 illustrates a horizontally-oriented beam. Dashed lines represent side-lobes going up to the surface or bottom, touching at locations A and B. The echoes from the bottom (location B) will generally be more likely to contaminate the data than the echoes from the surface. There are several reasons for this:

• The surface is smoother than the bottom. Grazing reflections from the surface produce little backscatter, but even a smooth bottom can have irregularities and rocks that reflect sound.
• The bottom does not move, so echoes from the bottom bias velocities toward zero. In contrast, the surface moves at approximately the same speed as the water just below it. Figure 6. The geometry of profiling long distances in shallow water.

The ability to profile long distances depends on a variety of factors, including the following:

• Beam width
• Signal strength from the water vs. from the surface or bttom
• Stratification

Aquadopp beam widths are 1.7° (2 MHz) and 3.4° (1 MHz). You will generally profile further when there is a lot of material in the water, but the concentrations of suspended material vary with time. Stratification is a problem near the ocean and in slow-moving water heated at the surface. Stratification can force even the narrowest beams to curve down to the bottom. Depending on these factors, one can expect to profile over aspect ratios of 10-50.

## 9. Velocity Uncertainty

Doppler velocity measurements are averages of many velocity estimates (called pings). The uncertainty of each ping is dominated by the short-term error. We reduce the measurement uncertainty by averaging together many pings. There is a limit to how much you can reduce your uncertainty. We call this limit the long-term bias. The long-term bias depends on internal signal processing, especially filters, and by your beam geometry. The long-term bias in the Aquadopp is typically a fraction of 1 cm/s.

The instrument's software predicts errors based on the short-term error of a single ping and the number of pings averaged together. The short term error of a single ping depends on the size of the transmit pulse and the measurement volume, and it depends on the beam geometry. Beams parallel to the dominant flow will have smaller short-term errors than beams at a steep angle relative to the flow. Averaging multiple pings reduces errors according to the formula: where the Greek letter sigma represents the standard deviation and n is the number of pings you average together. Note that the software predicts only the instrumental error. In many situations, the environment itself dominates the short-term error. This is true near a wavy surface and in turbulent flow such as boundary layers and rivers. In situations like this, your data collection strategy should take into account the nature and the time scales of the environmental fluctuations. Here are two examples:

• Waves. A good rule of thumb to follow when measuring mean velocities in the presence of waves is that you should sample velocity at roughly ¼ the interval of the dominant wave period, and you should sample through 6-10 wave cycles. If your peak wave velocities tend to be around 5 or 6 s, then sampling at a 1-s interval for a minute would make sense. In this case, you could reduce the measurement load to a relatively small fraction (say 4 or 8%).
• Turbulent flow. A rough rule of thumb in boundary layers is that the rms turbulent velocity is 10% of the mean velocity. If, for example, your mean velocity is 1 m/s, you could estimate turbulent fluctuations to be 10 cm/s. Obtaining 1 cm/s rms uncertainty would require at least 100 pings.

## 10. Maximum Range to the Measurement Cell

Aquadopp software sets a default blanking distance, but you can adjust the range out further. Figure 7 shows how signal strength varies with range, based on the sonar equation. Signal strength varies with transmit power, backscatter strength and distance. If you know the signal strength at a give power level and a given range, you can use the figure to predict the signal strength you would have at a different power level and range.

If you keep the same power level and change the range, follow the curve closest to the value you started with. If you change the power level, move up or down one curve for each power level (the curves are 6 dB apart).

The noise floor is typically found at around 25 counts. Because of the way we compute the signal strength, you can actually obtain good data at signal strengths a few dB below the noise floor. This means the noise floor gives you a conservative cutoff for good data. Figure 7. Measurement range vs. signal strength at 2 MHz. The "+" symbols show actual data from a river at power level 2. 