The limitations of the PUV method, particularly related to water depth and measurable wave periods, motivated the development of alternative techniques for wave measurements. One such approach uses current profilers to measure orbital velocities closer to the surface, where the wave-induced velocities are less attenuated by depth.
This configuration enables the use of array-based processing methods, of which the Maximum Likelihood Method (MLM) is the most widely applied. MLM has been shown to provide robust estimates of the directional wave spectrum.
By measuring velocities higher in the water column, the method significantly extends the usable depth range. In practice, this results in an approximate doubling of performance: the deployment depth can be doubled, or equivalently, the shortest resolvable wave period can be reduced by half.
However, this approach introduces additional complexity. Unlike the PUV method, which relies on co-located (triplet) measurements, MLM is based on an array of spatially separated measurement cells (Figure 1). This requires more advanced processing techniques to combine the information from multiple depths into a consistent estimate of the wave field.
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Array Method Concept When measuring waves with an ADCP the instrument measures currents in the BEAM coordinate system. This means that the orbital velocity measurements are projected collinearly with the beam. This is why when an array method is used in wave processing, the sinusoidal time series of the velocity from one beam is slightly out of phase and with a different amplitude than the other beams. The phase difference is a result of the time lag as the wave passes through the array of velocity measurement cells below the free surface. The amplitude difference is attributed to how much of the wave's direction is in line with the projection of the orbital velocity in line with the beam. This concept is demonstrated in Figure 1. |
To measure orbital velocities, Nortek instruments use one cell, known as the wave velocity cell (see Wave velocity cell for more details).
In Nortek instruments, MLM is typically not used on its own, but combined with AST measurements in the MLMST time-series method.
MLMST
The MLMST is a version of the array method, adapted for surface tracking measurements instead of pressure measurements. Wave orbital velocity measurements are still made close to the surface like in the MLM solution, but instead of the dynamic pressure, the AST option is utilized to estimate the nondirectional spectrum. It is important to note that array solutions in wave processing is only an adequate solution for a bottom-mounted instrument that is not rotating.
Limitations
Even though the introduction of AST enabled wave measurements at greater depths compared to pressure-only measurements, depth still limits the minimum wavelength that can be resolved. We distinguish between a directional and a non-directional frequency limit, where the non-directional limit is lower than the directional one. Both of these limitations should be considered when deploying an instrument for wave measurements and are described in detail below.
Non-directional limitations (AST footprint)
The ability to estimate wave parameters using AST is limited by the size of the surface area covered by the AST beam, referred to as the AST footprint. The footprint size is determined by the beam width and the distance between the instrument and the sea surface, and increases with both wider beam angles and greater distance to the surface.
The non-directional cutoff frequency (limit of the shortest measurable wave) is affected by the size of the footprint. As a rule, we follow a Nyquist-like reasoning; the frequency limit associated with the footprint is when half the wavelength is on the order of the diameter of the footprint (Equation 1). This clearly is the absolute shortest measurable wave, because shorter waves will have several crests and/or troughs within the AST footprint (Figure 1).
| \(\lambda_{non-directional\ minimum} = 2 \times AST\ Footprint \) | (1) |
\(AST\ Footprint = 2 \times tan(\frac{\theta}{2}) \times D\) |
(2) |
Where \(\lambda_{non-directional\ minimum}\) is the minimum resolvable wave length for non-directional parameters, \(\theta\) is the total opening angle of the AST beam and \(D\) is the deployment depth of the instrument. The beam width for a specific instrument can be found in the technical specifications.
Wave theory gives us the equation to relate the wave length found in Equation 1 to wave period (Equation 3)
| \( \lambda = \frac{gT^{2}}{2\pi} \) | (3) |
Where \( \lambda \) is wave length, \(g\) is the acceleration of gravity, and \(T\) is the wave period
Directional limitations
When using array methods to estimate wave direction, the shortest resolvable wavelengths are limited by the horizontal separation between measurement cells in the projected array. This separation depends on the beam geometry and the deployment depth, and increases with depth (Equation 4).
As the separation distance increases, so does the minimum wavelength that can be resolved directionally. A common rule of thumb is that waves must have a wavelength at least twice the separation distance to be resolved unambiguously. Shorter wavelengths lead to spatial aliasing, introducing a Nyquist-type limit beyond which wave direction cannot be determined.
| \(\lambda_{directional\ minimum} = 2 \times D_{velocity\ cell} \times tan(\alpha) \) | (4) |
Where \(\lambda_{directional\ minimum}\) is the minimum resolvable wave length for directional parameters, \(\alpha\) is angle of the slanted beam from the vertical and \(D_{velocity\ cell}\) is the distance from the instrument head to the location of the wave velocity cell. The angle of the slanted transducers for a specific instrument can be found in the general arrangement drawings.
Sampling limitations
In addition to instrument geometry, the sampling scheme can limit the shortest resolvable wavelength through temporal aliasing and sampling frequency. For further details, see Sampling and measurement principles.
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