PUV

This method was perhaps the first approach used for measuring directional and non-directional wave properties from below the surface. It dates back to the 1970’s and because of its modest requirements for instrumentation and processing, it is still in use to this day. The name itself is a description of the method as it is an abbreviation of the three quantities measured: pressure, and the two horizontal components of the wave’s orbital velocity, U and V. These measurements are made at the instrument’s deployment depth (Figure 1) and because they are co-located at the same point, this is referred to as a triplet measurement. Nortek instruments that are commonly used for wave measurements using the PUV method is the Aquadopp, the Aquadopp Profiler and the Vector.

The PUV method is unique in that it is able to accurately estimate wave height, period, and wave direction without a direct measurement of the surface by the use of inferred estimates. This is possible because both the dynamic pressure and orbital velocities are driven by the surface waves, as described in the Subsurface wave properties chapter. The signals associated with these properties attenuate exponentially with depth. The dynamic pressure measurement provides a means of estimating all of the non-directional wave parameters, while the combined P, U, and V measurements allow for estimating the directional wave parameters. The exact behavior of the attenuation has to do largely with the depth of the water and the wavelength:

• As we move down in the water column the signal is increasingly attenuated.
• As the wave length decreases (shorter period and higher frequency) the signal again experiences increasing attenuation.

In other words, waves become more difficult to estimate when they are measured from great depths or are short in period. This means we are both depth and frequency limited when measuring waves. 

PUV Processing

The process by which we arrive at wave estimates from the energy distribution requires special attention. Since the wave estimates resulting from the PUV processing method are based on the wave energy distribution, and not a direct measure of the free surface, they are considered inferred estimates. Fourier transforms are used to separate the signals into different frequency bands so that it can determine the direction separately for each band. This means that if you have a long-period swell coming from one direction, and a shorter period coming from another, you can tell the direction for each of them separately. The main assumption for standard PUV wave measurements is that waves at a given frequency come from one primary direction.

The processing steps are relatively simple and are composed of the following steps:

1. First perform the transformation on the time series (e.g. Pressure, Velocity) from the time domain to the frequency domain using a standard FFT (Fast Fourier Transform). 
2. Calculate the Auto and Cross Spectra for the pressure and two velocities. 
3. Apply the transfer functions to the Auto Spectra to arrive at the Power Spectra for the free surface (see Additional Reading). 
4. Apply quality control to the spectra (Determine a cutoff frequency and extrapolate). 
5. Estimate the wave statistics for height and period using moments calculations. 
6. Calculate the Fourier arguments which will ultimately be used for the directional estimates

Correction for Background Currents

In case of strong background currents, the measured waves may be affected by a Doppler shift. That is, when currents are directed against the waves, the waves are compressed. When the currents travel in the same direction, the waves are elongated. The resulting spectra will see the peak energy shift slightly to lower or higher frequencies. It is not just the magnitude of the currents that is essential but also the direction. Currents flowing in a direction perpendicular to the wave direction will have no effect on the waves.

The degree to which the Doppler shift modifies the surface waves depends on the current speed relative to the wave propagation speed. This means that slow propagating (short period) waves are the most affected by currents. Measurements that infer the surface waves from either orbital velocity or pressure measurements require special attention regarding background currents. This is because the transfer function used for inferring the surface waves is wavenumber dependent, and it is the wavenumber that is modified by the background currents. The wavenumber solution must take into account the mean current and direction relative to the wave direction. The post-processing method that relies on the wavenumber solution is the PUV method, and it is the one which is most sensitive to the effects of currents. The correction for background currents is done in post-processing software when necessary. Conversely, Acoustic surface tracking (AST) is a direct measure of the surface waves and therefore its response is unaffected by background currents.

Limitations

Understanding the frequency limitations and characteristics of the waves that are to be captured is critical to determining the instrument's depth and ultimately successful data collection. Therefore we aim to achieve a 'Target Depth', which is a deployment depth at which we capture as much of the wave spectrum as possible with the greatest amount of accuracy. The accuracy of the solution improves as the more of the wind wave band (waves with periods of 0.5-30 seconds) is covered. Incomplete or insufficient coverage of the wind wave band can result in underestimation of wave height and missing peaks in the spectrum.

To simplify deployment conditions and optimize data quality, Nortek recommends the following limitations when using the PUV method:

1. Deployment depths that are shallow (less than 10–15 meters)
2. Waves that are long (approximately periods of 4 seconds or longer).

Although these limitations do not encompass the entire wave band, they have been tested to provide consistent data. The limitation of only measuring long waves (swell) is the one that should raise a warning flag for those who are interested in the complete description of the wave environment. For high end users the table below shows the limitations of the minimum measurable waves with regards to depth, frequency, and height. This table is meant to be used as a guideline and the conditions at the deployment site greatly influence the necessary deployment depth, wave frequency and height.