Principles of Operation:
Pressure Sensor Performance

Contents

1. Data
2. Equations for noise level and uncertainty
3. How Vectors and Aquadopps sample pressure
4. What do the specifications mean?

All Nortek products with pressure sensors use the same silicone piezoresistive pressure sensor. The biggest advantage of this sensor over older sensors (i.e. strain gauges) is their low noise level. Pressure sensor specifications can be confusing and misleading -- the purpose of this page is to clarify what these specifications mean and how you can use them. It will also describe how pressure is measured in these instruments and what your choices are so that you can achieve the best results with them.

1. Data  

Figure 1 shows spectra from two different measurements using the same Vector Velocimeter, which has a pressure sensor with a range of 0-200 m. One site was a tidal channel in which the primary fluctuations were caused by turbulence. The other site was a shallow site (8 m deep) that was dominated by surface waves at frequencies below 0.3 Hz and by turbulence above 0.5 Hz. The instrument was sampled at 16 Hz in the tidal channel and 32 Hz in the waves.

Figure 1. Pressure spectra from two different sites, both using the same Vector Velocimeter. The horizontal black line is at 3x10^-7 m²/Hz.

Both measurements bottom out at a noise level near 3 x 10^-7 m²/Hz. For the 16 Hz tidal channel measurement, this corresponds to a single-sample uncertainty of around 1.5 mm, and an uncertainty for a 1-s average of around 0.4 mm (see below). If the wave spectrum bottoms out at 3 x 10^-7 m²/Hz as well (we do not see enough of the flat part of the spectrum to be sure), then its single-estimate uncertainty would be around 2 mm. Another data set from a lake with very weak flow produced a noise level of 1.3 x 10^-6, using 4 Hz sampling - -this corresponds to a single-estimate uncertainty of 1.7 mm.

Combined, these results tell us that the single-estimate uncertainty in a 200 m pressure sensor is around 1.5-2 mm.

2. Equations for noise level and uncertainty  

Many sensors produce white noise in absence of signal. The measurable signal is the part of the signal spectrum that rises above the noise level. Given the noise level, the following equation tells you the single-sample uncertainty:

STD(p) = (ns/2)^1/2

where STD(p) is the standard deviation, or single-estimate uncertainty, of the pressure p, n is the spectral noise level, and s is the sample rate. If each sample is independent of the next (which is true if the noise spectrum is white), then averaging multiple samples reduces the uncertainty according to:

STD(p|_n) = STD(p)/n^1/2

where p|_n is p obtained by averaging n samples.

3. How Vectors and Aquadopps sample pressure  

Vectors sample pressure each time they report a velocity, and Aquadopps & Aquadopp Profilers sample pressure once each second. For a Vector, this means that rapidly-sampled velocity will produce more independent pressure estimates in a given interval, which in turn lowers the noise level. For example, if sampling once each second produces an uncertainty of 2 mm, averaging 16 estimates each second reduces the uncertainty by a factor of four, to 0.5 mm.

Vectors and Aquadopps record pressure with 24-bit numbers. With a standard resolution of 1 mm, the maximum pressure is greater than 16 km. For 200 m pressure sensors, digitizing with a resolution of 1 mm adds insignificant uncertainty. This is because the uncertainty (standard deviation) associated with 1 mm resolution is around 0.3 mm, which is far smaller than the 1.5 mm single-estimate uncertainty of a 200 m pressure sensor.

Pressure sensors with smaller ranges could benefit from finer resolution. For example, a 50 m pressure sensor should have a single-measurement uncertainty of around .4-.5 mm. At this level, the 0.3 mm discretization uncertainty begins to be significant. The implication is that pressure sensors in the range 10-50 m will benefit from using a resolution of 0.1 mm. This is possible today, but you must have the factory set the resolution to 0.1 mm at the time of manufacture. Then you will have to divide your pressure readings by 10 to obtain the pressure in meters. For existing systems, we can also provide a modified head configuration file, which you can download, to implement 0.1 mm pressure resolution.

Pressure sensors with smaller ranges should produce correspondingly lower noise levels. The pressure sensor's single-sample uncertainty should be proportional to the pressure range. This means that the single-sample pressure uncertainty of a 10 m pressure sensor will be less than 0.1 mm.

4. What do the specifications mean?  

There are three specifications that matter (numbers in parentheses are our specifications). These are:

• Long-term uncertainty or drift (0.25%)
• Resolution (1 mm standard; 0.1 mm optional)
• Single-sample uncertainty (0.001% of full-scale)

Long-term uncertainty matters primarily if you want to estimate tidal levels and changes in sea level. If these measurements are important to you, however, you must account for changes in atmospheric pressure as well. Because atmospheric pressure fluctuations are larger than typical long-term drifts, reducing the drift adds little to overall data quality. The long-term drift in Nortek's pressure sensor is predominantly caused by changes in temperature.

Resolution and single-sample uncertainty are important when you are observing rapid fluctuations, particularly waves. Keeping in mind that the discretization uncertainty associated with a given resolution is about 1/3 of the resolution, the parameter that counts is the larger of the single-sample uncertainty and the discretization uncertainty. For 200 m sensors, the single-sample uncertainty dominates. For shallow sensors, the resolution dominates unless you use a resolution of 0.1 mm. When you are measuring waves, the 0.25% long-term drift is unimportant.