Technical Note No. 98/1 - At What Depth Should DOBIE be Deployed?

Technical Note No. 98/1 - At What Depth Should DOBIE be Deployed?

To answer the question, we need to explain what DOBIE actually measures and how waves exert pressure at depth.

DOBIE measures pressure. In still water, the pressure experienced at depth is composed of two parts: hydrostatic pressure, which is due to the weight of the overlying water and which is proportional to the height of the water column above the observer, and atmospheric pressure, which is due to the weight of the atmosphere. When waves are passing overhead, there is also a fluctuating pressure associated with the rising and falling of the water being driven by the waves. However, the fluctuating pressure is not exactly hydrostatic, meaning that it is not exactly proportional to the changing height of the water column above the observer.

The fluctuations in pressure due to the waves actually decrease in amplitude with depth below the mean water level, and the rate of decrease with depth depends on the wave period. Thus, pressure fluctuations under long-period waves can be readily felt, and measured, at depth, but pressure fluctuations under short-period waves may not actually penetrate to the same depth. Real waves are always irregular, which means that the wave train is made up of many component waves spanning a range of periods and heights. In that case, the fluctuating pressure at depth is also made up of many components, the long-period components being less attenuated than the short-period components.

DOBIE measures the pressure due to the overlying weight of water and atmosphere and due to the waves passing overhead. In order to convert the pressure sensed at depth by DOBIE into wave statistics, the data may have to be transformed "back up to the surface", and that transformation will have to account for the way the different pressure components of the wave train decay with depth below the mean water level. Here is how DOBIE deals with the problem:

  • Imagine an irregular wave train with a certain characteristic wave period (it may be the "mean spectral period" or the "zero downcrossing period", or the "peak spectral period" - it does not matter for the purposes of this discussion). As you move down through the water column to the seabed, the higher frequency (i.e. shorter period) components of the wave train become more and more attenuated, and the characteristic period therefore appears to become longer and longer. Thus, the characteristic period appears to change (increase) with depth in the water column at which the measurement is made. DOBIE reports the wave period as it sees it: it does not attempt to make corrections for attenuation of the various components of the irregular wave train. Thus, the wave period reported by DOBIE when deployed at one level in the water column many be different to the wave period reported at another level under the same wave train. The main reason that DOBIE works this way is to encourage the user to deploy DOBIE at the level in the water column where information is required. Thus, if you are interested in the period of surface waves, you should deploy DOBIE near the surface. If you are interested in the period of orbital motions at the seabed, then deploy DOBIE near the bed. In that way, you are guaranteed reliable and relevant information, because you do not have to rely on a scheme - which can easily "blow up" - to correct for the effects of attenuation.
  • There are many different ways to report wave height - significant, root-mean-square, average, for example - but they are all meaningful only at the surface. Thus, in this case DOBIE does correct the raw pressure data for the effects of attenuation (i.e. it amplifies the raw pressure data) and computes wave height from the corrected data. Thus, the wave height reported by DOBIE applies to the wave train at the surface, regardless of the depth at which DOBIE is deployed. The correction scheme that DOBIE uses to estimate wave height is quite robust - meaning that it will nearly always give "reasonable" results, assuming that there is enough information to work from in the first place - because it depends on the average properties of the pressure spectrum, not the details of the pressure spectrum as some schemes do. The latter schemes will be more accurate in some circumstances, but they will also produce wildly erroneous results more often, too.
  • Associated with the pressure fluctuations under waves are orbital motions, which drive sediment transport and disturb benthic habitats, among other things. Orbital motions decay with depth below the mean water level in exactly the same way that pressure fluctuations do: the higher frequency components are attenuated faster than the lower frequency components. Thus, below the water surface, "wave height" becomes meaningless as a measure of wave activity - the amplitude of the orbital motions is what counts. DOBIE reports the characteristic orbital speed at the seabed, because that is where most interest is focused. If DOBIE happens to be deployed on the seabed, then the estimate of orbital speed at the bed will be very accurate because pressure fluctuations and orbital motions are directly linked to each other at the same level. If DOBIE is deployed above the seabed then the pressure fluctuations must be mathematically attenuated to estimate orbital speed at the bed, not amplified as was the case with wave height. This means that the estimation can never go too far wrong, as both the mathematical attenuation and the actual orbital motions tend towards zero anyway. This makes the estimate of orbital speed at the bed very robust. In effect, what you see is what you get: if the pressure fluctuations are very small, then so too are the orbital motions at that same level and lower, and it does not matter what is happening up at the surface.
  • The central difficulty in transforming a pressure signal back up to the surface is distinguishing between the "real" pressure signal and the inherent noise of the sensor which, if it were transformed, could result in erroneous (and often huge) estimates of wave height.

To help interpret the data, DOBIE reports a statistic called "penetration", which is defined as:

where

is mean water depth,
is depth of DOBIE below mean water level and
is the wavenumber (reciprocal of wavelength) based on the mean spectral period and the mean water depth.

Penetration is an approximate indicator of how much the pressure signal has been attenuated between the surface and the level of the DOBIE. For instance, if the penetration is 0.15, then something like 15% of the surface pressure-fluctuation signal has penetrated to the level of the DOBIE. In effect, the pressure signal is multiplied by the reciprocal of the penetration to "transform the pressure data back up to surface". If penetration is very small (say, less than 0.05) then chances are most of the signal is really just sensor noise. When the noise is multiplied by 1/0.05 then huge (and erroneous!) wave heights result, which is why DOBIE applies its "real-world plausibility checks" to the wave statistics (explained in another Technical Note). If the real-world checks are not failed but the penetration is still very low, then use the wave height only with caution.

The figure shows how penetration varies with wave period (T) and water depth. As a rule of thumb, sensor noise will begin to mask the real signal when penetration gets as low as 0.01 to 0.05.

With that background information we can now explain how the answer to the question "at what depth should DOBIE be deployed?" depends on what it is you want to measure.

  1. If you are interested in wave height and period at the surface. In this case, you need to deploy DOBIE as near to the surface as possible so that it senses, as closely as possible, "unattenuated" pressure. In that way, you are relying as little as possible on the attenuation correction to "invent" information needed for the estimation of wave height. Wave period reported by DOBIE will be close to the wave period at the surface. You can use the figure above to estimate the greatest depth you should go to: guess a likely wave period (around 2 -5 seconds for estuaries; 6 - 16 seconds for open coast) and then read off the graph the water depth where penetration drops below 0.01 to 0.05. Do not deploy greater than that depth.
  2. If you are interested in wave activity at depth. In this case, simply deploy DOBIE at or near the depth you are interested in. DOBIE will still attempt to estimate wave height at the surface, but may fail from time to time when signal noise overwhelms the weak, attenuated pressure signal sensed by DOBIE at depth. However, that same weak pressure signal can always be used to calculate orbital motions in the vicinity of DOBIE and lower. If the pressure fluctuations are too weak for DOBIE to measure then the orbital motions at that depth and deeper are too weak to be significant anyway.

Under no circumstances deploy DOBIE below the maximum rated depth, beyond which the pressure sensor will be permanently damaged. Refer to your DOBIE specifications.

If you want to use your own scheme for correcting for the effects of attenuation, then run Task 4/1, which stores the spectrum of raw pressure and the mean water depth, make the correction, and compute your own wave statistics.

MOG
June, 1998