# 9. SOURCES OF ERROR IN THE ESTIMATES

## 9.1 Systematic/Random Errors

Statistical considerations play a role in connection with physical measurements since the latter involve an error, or inaccuracy caused by small systematic and/or random disturbances which cannot be completely eliminated. Thus, measurements of quantities such as length, pressure, voltage and temperature (factors of great concern to the acoustician), involve errors caused by the nature of the physical measurement. This is because the person who performs the measurement, the instrument used, and the system to be measured, are all affected by small unpredictable disturbances. It is to be expected that a process involving an acoustic system as the 'measuring instrument' has potential sources and causes of errors because the actual quantification of fish echoes is achieved through remote-sensing, and the physical quantity to be measured is related to a mobile, living thing. As a result, the error of measurement, or error of observation, associated with acoustic measurement and the subsequent estimates of biomass are factors of prime interest to the research worker.

Acoustic samples taken during measurement of fish stock density, and consequently, statistics derived from these samples, are subject to the two kinds of errors implied above, ie systematic errors (biases) and random errors. Both kinds of error may enter into the selection of the observations and into the values (eg integrator readings) of the observations.

Systematic errors are those that cause a bias. Acoustic measurements are often affected by a number of biases that can be either additive, or may combine so as to cancel one another. In this connection it is important to note that statistical formulae for standard error and test of significance, cannot be applied to provide an estimate of the direction or magnitude of systematic errors in the selection of acoustic samples. Systematic errors associated with acoustic surveys can often be detected and corrected by an overall logical examination of the measurement/estimation process, a fact underlining the great importance of training and the field experience necessary to attain the desired level of proficiency in this field.

Contrary to the systematic errors, the random errors are related to probabilistic considerations, this is the reason why they are often referred to as statistical errors. The level and instantaneous direction of these errors (variations showing no reproducible pattern) cannot generally be predicted and hence they cannot be avoided or eliminated. However, their effect can be understood on the basis of a theory of statistical errors first developed by Gauss and Laplace. Since then a huge volume of statistical literature has come into existence, providing in-depth analysis of random errors. Thus, to familiarize himself with the related formulae and parameters involved such as arithmetic mean, standard deviation, variance, coefficient of variance and the confidence limits about the mean, the reader is referred to the recommended literature on the subject. Finally, as an important conclusion from the above, it should be noted that while random errors govern precision, the accuracy is governed by systematic errors.

## 9.2 Equipment Operational Errors

Experience over the past 12 years or so, since acoustic equipment became a quantitative tool in fisheries research, has demonstrated that extreme care is required in operating the equipment (scientific sounders and integrators) to avoid unnecessary errors in the fish abundance estimate. To monitor and correct operational errors, or better still, to take preventative measures to avoid their occurrence, requires skill only properly learned through experience. However, a prior knowledge of the nature of these errors is helpful in putting the problems into perspective. The following subsections summarize the problems involved and explain how corrections can be made.

### 9.2.1 Bottom Pulse Failure

When the echo-sounder fails to produce a bottom pulse for each sounding (ping), there will be no integrator bottom stop function; thus the bottom echo will be integrated as a false fish echo. This only happens if the lower depth limit of a selected integration interval is set below the actual sounding depth, and when the 'Bottom Stop' control is in the 'ON' position.

This kind of error is commonly observed under the following conditions:

1. very uneven (rugged) rocky or coral bottom
2. extremely steep sloping bottom
3. bad sea conditions (vessel rolling and pitching)
4. exceptionally 'soft' bottom sediment.

A typical situation is illustrated in Figure 78 alongside, which is largely self-explanatory.

Figure 78.

It will be readily understood that errors of this kind can reach major proportions if not kept under reasonable control by the equipment operator. Such a control can be exercised in two ways. Firstly, the operator should maintain the 'Discriminator' control in a relatively high position (6-8). This improves the response of the system and increases the chance of reliably generating the bottom pulse function. Secondly, if this does not minimize the problem sufficiently, change to a manual control of the integration interval lower limit, regularly operating the 'Interval' thumb-wheel selector. In the latter case, a problem arises when the fish concentration of interest is located on, or close to the sea-bed, when it may be difficult to follow the contour of the latter. Also the thumb wheel switching creates 'spikes' (explained in the following section) that cause false integration. As the reader will gather from the above, minimizing the described error, can only be learned through field experience.

### 9.2.2 Layer Selector Spike

This particular error is caused by an undesirable side-effect in the thumb-wheel selector of the QM echo-integrator, which, when rotated, generates an electrical spike and this is picked up by the integration circuits. A false fish echo integration results which appears on the integram in much the same way as the bottom echo shown in Figure 78. Apparently the only way for the integrator operator to avoid this problem when using the standard QM, is to manually time the actual rotation, so as to let it occur when the rotating EK recorder stylus is not in contact with the recording paper. This effectively ensures that the integrator is 'OFF'. The problem can be cured and other improvements made to the QM integrator which increase the dynamic range and reduce drift.

### 9.2.3 School Generated Bottom Stop Pulse

While the two errors explained above (9.2.1 and 2) result in apparent false fish echo integration, and hence positive bias, the School Generated Bottom Pulse Error (hereafter SGBPE) always brings about negative bias due to blocking of the fish echo integration. In principle, this kind of error occurs because the EK echo-sounder is sometimes unable to make a physical distinction between a fish school and a seabed; it can only distinguish between low and high echo levels. Consequently, when the sounder is operated in a white-line mode and detects a very dense fish school exhibiting similar target strength to that of a seabed (say, TS = 20 dB), the 'sharp', strong echo returned from that school will be indistinguishable from a seabed echo. A 'bottom pulse' will be generated, resulting in complete blocking of integration until the next transmission takes place. For a better illustration of the problem, consider Figure 79, which shows (a) the theoretical recording of a very dense pelagic school on the echo-sounder recorder, (b) the corresponding graphic integrator output (integram), and (c) the geometric cross-section of the school that has been effectively blocked from echo-integration during the survey vessel's traverse time.

As seen in the corresponding realistic pictures, the SGBPE error can be severe. In practical survey work involving densely packed school concentrations (eg Anchovy schools off Peru, Horse-mackerel in the Black Sea, Turkey, or Sardine schools in the Moroccan waters) it can be of crucial importance. In fact, many survey operations have turned out heavily biased data due to inadequate control of such errors, and on some occasions, a considerable amount of data has had to be discarded.

The SGBPE error cannot be fully controlled in difficult conditions, but it is within a skilled operator's ability to keep it within acceptable bounds. To achieve such control, the following guidelines are important:

a. The operator must exercise due awareness as to the type of fish concentrations he is surveying and also check that both echo-sounder and integrator gain controls are in low positions to avoid saturation in the equipment. In practice, this means that when the overall performance of the EK (SL + SRT) is high, say, 30 dB, its gain control would be in position -20 dB. The QM integrator gain could be in the 10 dB position, or possibly as high as 20 dB, if the red saturation warning light does not indicate the need for a lower setting. In the case of a relatively low overall performance the EK gain can usually remain in 0 dB position with the QM set at 10 dB gain.

b. When gain controls are operated as above, the 'Discriminator' control usually needs to be kept in a relatively high position to ensure a steady white line recording, or, in other words, an effective prevention of bottom layer integration. Hence, there are contradictory requirements, namely, that whilst a high setting of the discriminator control helps to avoid undesired bottom echo integration, it also invites a school generated bottom stop pulse and the subsequent SGBPE. When a reasonable compromise cannot be found for the control settings, the only solution is to manually control the integration intervals. In cases when integration blocking has already occurred, a crude correction can be made using the following procedure. Assume that a survey vessel is sailing at 10 knots, the echo-sounder is operated at a rate of 96 ping/min. and the paper speed is 25 mm/min. Integration is made over one nautical mile as the standard distance unit, corresponding to 6 min. sailing time at the given speed. Then the total number of pings per distance unit Nt = 576 and the corresponding recorder paper advance between successive one-mile log marks lp = 150 mm.

Figure 79.

From Figure 79 we can define l0 as the observed length in millimetres of the school cross-section which is not integrated, indicated by the length of the white band at the top of the school trace. Mp = the maximum observed deflection (mm) for the individual pings prior to (or after) blocking. From the above, the total number of non-integrated 'lost' pings (Np) can be calculated from the relationship

Np = (Nt lo/lp)

Assuming that lo = 4.7 mm, Np = 576 x (4.7/150) = 18 pings.

Knowing Np and assuming that Mp is representative of the 'lost' mean ping integrals from the school cross-section, the total correction, or lost integrator school reading Mc, can be calculated from

Mc = Mp x Np

Hence, for Mp = 4.5 mm the correction, Mc = 4.5 x 18 = 81 mm.

### 9.2.4 Secondary Echo Interference

This form of echo interference is a special problem. For the present purpose it is defined as echoes received in one transmit/receive period which were initiated by the previous transmission. It occurs, both in marine surveys conducted in shelf seas, and in those carried out on large lakes. The magnitude of the positive bias error introduced by this effect depends on the relative depths of the fish distribution, the bottom and its reflecting strength, plus the overall performance of the echo-sounder as well as the depth range on which it is operated.

For an example of this problem, assume that an echo-sounder is being operated on a range of 0 - 125 m, ie a pulse rate Pr of 96 pings/minute. This means that the time between the start of each transmission is

Tt = 60/Pr = 60/96 = 0.625 seconds.

During this time interval a transmitted pulse can travel a total distance in the water of

d = speed x time

Hence, for this time interval and using 1500 m/s as the approximate speed of acoustic waves one obtains

d = 1500 x 0.63 = 937 metres

ie an indicated (true) depth of 937/2 = 468 metres.

Taking this distance as the actual depth and considering the echo-sounder pulse train P1, P2, P3, P4,........ Pn (96 pulses per minute), it will be realized that the penultimate pulse, say P3, will return its detected bottom echo at the same time P4 is being transmitted. More generally, if the bottom depth varies in range from d1 = 468 m to d2 = 468 + 125 = 593 m, the second bottom echo can theoretically interfere with any other echo occurring in the basic range interval 0 - 125 m. The echogram (a), corresponds to a situation where the bottom depth has theoretically varied from 593 (point 1) to approximately 470 m (2). As indicated, the bottom trace appears strongly at the end of the 125 m scale and then gradually weakens until it usually fades out at, say 20 m range. This is due to the effects of the Time Varied Gain (TVG) function of the receiver. If the bottom depth had been a constant 520 m, the penultimate bottom echo trace would have been recorded as a relatively faint bottom at a constant depth of 50 m on the 125 m scale. Figure 80(b) illustrates the theoretical contribution to the integrator output of the unwanted bottom echo, resulting in an error reading of D M = M2 - M1.

Figure 80 depicts the problem and shows the principal error introduced into the integrator observation (M).

The only measures the equipment operator can take to minimize such problems is to change the sounding rate, (depth range), and possibly the integration interval(s) according to the distribution of the fish surveyed. Further ways of dealing with the problem may be learned at sea.

### 9.2.5 Instrument Drift

One of the problems associated with the operation of the QM echo-integrator quickly encountered by the user, is the so-called 'drift problem'. This is caused by inherent limitations of the analogue circuits involved. Its symptoms are observed as variations in the integrator output (mm deflections) when no echo-signal is present, ie when there should be no deviation of the QM recorder stylus from its zero position over a given time interval or distance, eg one nautical mile. The level of drift is generally affected by ambient conditions (temperature and humidity) and it may appear as a negative, or a positively sloped graph on the recorder. The slope coefficient may remain fairly constant over long periods of time, but it sometimes has a tendency to cyclic variation with time, eg diurnal variations.

A pictorial presentation of the drift problem is presented in Figure 81(a-e). Whilst illustrations (a-d) are self-explanatory of the drift characteristic, illustration (e) is intended to show the relationship between an observed integrator reading M0, the mm deviation caused by the drift Md and the mm component of the fish echo Mc which contributed to the observed reading. Given these, we can define the relative drift error Ed as the ratio (Md/Mo) or, in more general terms, the error in percentage can be expressed as follows:

Figure 81.

From this formula it can be inferred that, when large, dense, fish concentrations are being measured (Mo......Md), the drift error is likely to be insignificant, where in low-density situations (Mo~Md), the error caused by the drift can be of major magnitude.

Knowing the nature of, and what generally governs the level of the drift error, the reader may ask what can be done to exercise control over it. The answer to that question is two-sided; firstly, the service, or acoustic engineer responsible for the survey equipment must make due effort to ensure that all relevant circuits of the system are adjusted for optimum performance. Secondly, it is the role of the operator (and the data analyst) to carefully monitor the drift 'behaviour' during a survey exercise, and thus be able to separate the Md component from the observed integrator values, to permit a reasonable post correction of these data. For digital integrators this is not necessary.

### 9.2.6 Attentuation by Bubbles

Attentuation of acoustic waves, due to wind induced bubbles in the upper layers of the sea, is a problem which can affect both hull-mounted and towed transducers. Recently, investigations have been made by Novarini and Bruno (1982) into the influence that such attenuation may have on echo-integration surveys. Their study covered frequencies of 8-60 kHz and wind speeds up to 30 knots, providing evidence that attenuation due to this effect starts at a lower wind force and is of greater magnitude than hitherto reported for shallow transducers.

Many surveys are carried out in weather conditions up to wind force 7 on the Beaufort Scale (35 knots). In order to maximise the efficiency of a survey, the ship must be run at the fastest speed possible for the prevailing conditions. It is also important to maintain the accuracy of the results to the greatest possible extent, thus any legitimate correction available should be applied.

Figure 82 is drawn from Novarini and Bruno's equation 9. It shows a rapidly rising attenuation, 6 dB per 7 knot increase in wind speed at 38 and 120 kHz when the transducer is only 1 m deep.

The rate of change of attenuation is 9 dB per 7 knot when the transducer is at 5 m depth but there is less than 0.3 dB loss until the wind reaches 23 knots. It should be pointed out that the authors only claim validity for their formula in the frequency range 8 kHz £ f £ 60 kHz and over the wind speeds of 6 to 30 knots. Nevertheless the results at 120 kHz are not dissimilar to those published by Dalen and Lovik (1981) although the latter authors include bubbles other than those from wind generated sources.

The authors of these papers point out that users of high-frequency echo-sounders should especially be aware of this possible source of serious error.

This is another case where the use of a towed transducer could be beneficial.

## 9.3 Noise

A simple definition of noise states that it is the cause of any unwanted power output from the receiver amplifier, regardless of the source. Note the emphasis on the word unwanted. Noise can arise from electrical sources, or from the sea state, but by definition any target, or targets, not being sought give rise to noise. Naval forces seeking submarines may regard schools of fish as noise, scientists surveying for schools of fish might consider the signals from plankton as noise. What we want to avoid is the recording of any form of signal which might give a false estimate of the particular type of biomass we are seeking.

With experience a paper record can be used to interpret signals sufficiently well to differentiate between electrical, or acoustic noise which is not synchronised to the display and, sometimes, the signals from small organisms. It is evident from section 9.7.7 that for some sizes of organism at certain depths, the acoustic echoes are magnified considerably.

To function correctly, acoustic systems must have high sensitivity, ie the receiving transducer and the amplifier must respond to very small echoes. This makes them prone to interference from quite low levels of acoustic and electrical noise generated on or near the ship. Noise is rarely confined to one frequency, or even to a narrow band of frequencies, it tends to be spread widely, but its effect on system performance is limited to the amount of noise power occurring within the operating bandwidth of the echo-sounder transducer and receiver amplifier. The effect of a high level of noise on a pulse is shown in Figure 83 below.

Figure 83.

### 9.3.1 Biological Noise

Biological noise as a subject forms a part of a wider study of marine organisms which covers both their acoustic production and detection abilities. A brief review of the subject (by Tavolga) is presented in Underwater Acoustics, Albers (1967), Volume 2, but a more detailed review can be found in Tavolga (1965). In the context of the present manual, which deals with the practical application of acoustics to the estimation of aquatic biomass, we are concerned with the implications of two noise categories; these are:

a. intense noise; for example that emitted by a school of porpoises which produce a strong noise trace on the echo-sounder recorder and causes biased readings on the integrator.

b. the stridulatory noise (rubbing and rasping) such as that produced by crabs, shrimps or lobsters which, in special circumstances, may give rise to an error in integrator observations and/or introduce confusion in the interpretation of echograms.

The latter category (b) may not be of immediate concern in acoustic survey work, but it is sufficiently significant to make the reader aware of possible implications. According to Tavolga (1965), the individual clicks of snapping shrimps are quite powerful and at a distance of one metre may attain an intensity of over 150 dB//1 m Pa.

The ambient noise level produced by a concentration of shrimps can reach levels of up to 140 dB//1 m Pa. In the case of the warm-blooded mammals (toothed whales) such as porpoises, dolphins, pilot whales, etc, they emit high-pitched whistles, or squeals, whose pitch varies from about 1,000 to 10,000 Hz, (some dolphins go higher than 200 kHz). The large baleen whales that feed upon plankton by filtering water through their mouths are known to produce a variety of sounds of a harmonic type, most of which have fundamental frequencies below 400 Hz.

From these few examples it will be clear that an aquatic survey environment is not acoustically quiet and that noises of biological origin can sometimes play a role in acoustic measurement errors.

### 9.3.2 Electrical Noise

This may be generated by electrical machines, in which case it could be conducted to the echo-sounder directly through the wiring, or, it may be reradiated as electromagnetic waves and be picked up on the transducer/amplifier wiring at the most sensitive parts of the system. Cables carrying power, or, control signals, which are routed close to the transducer wiring may easily induce voltages of a few microvolts into the latter. It is essential therefore, to separate the transducer cable from any others as far as possible, and, to ensure that the screening and earthing arrangements specified by the echo-sounder manufacturer are scrupulously observed.

Noise entering via the power line may be related to the mains frequency. To check this, connect one of the vertical channels of the oscilloscope to the calibrated output of the echo-sounder. Set the oscilloscope trigger selector to 'mains' and select a sweep speed of 10 ms/cm. Turn up the vertical sensitivity so that the noise is clearly displayed. If it is related to the mains frequency the noise will stay in position on the oscilloscope screen. However, many frequencies may be present, so that the trace shows random movements and an estimate of the peak amplitude of these should be made.

To prevent excessive noise affecting the sounder it is necessary to locate the source and eliminate it. Identification of noise sources can be time consuming and requires much patience. The usual method of working is to first switch off as much of the machinery as possible, then reconnect one after another, the different motors, compressors, inverters, etc until the source, or sources are found. Each of these noise sources will have to be repaired, if faulty, or electrically suppressed. If the noise is from the vessel's generator it might be identified by changing over if there are two or more auxiliary engines or, if shore power is available, this might be used for a comparison.

Installation of noise suppressors on generators or their regulators is a job for a qualified electrician and should never be attempted by a non-specialised person. Voltage regulators are easily damaged if noise suppressors are not properly installed. If in doubt, contact the manufacturer of the actual generator for advice.

Some of the noise on the power line may be suppressed at the input to the sounder or within the unit itself. It is the high frequency noise, from rotating machinery, or solid-state switches such as thyristors, which interferes with echo-sounding. Often a filter at the mains input will suppress this noise. Such filters can be purchased but it is important to be certain that they have an adequate current carrying capacity before having them installed.

The total noise measured at the calibrated output of the receiver, is due to all noise at the input, plus the actual noise generated within the amplifier itself. For practical operating purposes the total noise is significant, but it is important to be able to separate the noise of the amplifier from electrical noise picked up on wiring, and from acoustic noise arriving via the transducer.

Measurement of the EK series receiver self noise can be made as follows

Step 1 Connect a high impedance voltmeter (vacuum tube, or transistor voltmeter) to the calibrated output of the echo-sounder.

Step 2 Set the echo-sounder controls as follows:

 TVG and Gain : one of the two 0dB positions Bandwidth : narrow Test/operate : test (no signal to test input) Output power : 1/1

Step 3 Stop transmitting trigger

: for EK and EK-R set phased range selector to ext.
: for EK-S set basic range selector to 0.
disconnect transmitter trigger. (cable No. 6 at 11000 recorder main terminal).

Step 4 Switch echo-sounder on, the voltmeter indicates the self-noise. Note result.

Step 5 Change to wide bandwidth, note voltmeter deflection. Normal values below:

 Frequency Typical Noise Levels, Calibrated output Narrow Bandwidth Wide Bandwidth 12 kHz -61 dB/V 0.9 mV -55 dB/V 1.8 mV 18 -59 1.12 -53 2.2 38 -59 1.12 -50 3.2 50 -59 1.12 -49 3.5 120 -54 2.0 -48 4.0

There is no point in trying to make other measurements unless the receiver amplifier noise level is normal. If it is too high, try to find out if the noise is produced by the echo-sounder, or if it enters from outside. The following measurements may help to indicate the source.

Whilst observing the voltmeter, change the power output selector from 1/1 to 1/10 and then to ext. transmitter. If the noise level drops immediately the power selector is changed from 1/1 to 1/10, then to ext. transmitter, the noise is probably electrical, originating outside the echo-sounder, perhaps entering via the mains cable, or, induced into the transducer leads. If the noise level drops slowly after changing from 1/1 to 1/10 power, the transmitter itself is probably the source. Noise is most commonly generated in this unit by the output stage, where one or more transistors may have developed a leakage.

### 9.3.4 Acoustic Noise

Sources of noise arise from natural causes within the sea itself, or at its boundaries. They may also arise through the movement of the ship through the water, or, from the means of propulsion. Noise due to natural causes alone is not under the control of man so it must be measured and then tolerated. It is due to rain on the surface of the sea, from waves, from the interaction of water currents with seabed material and also from thermal molecular activity at the higher frequencies. Noise from natural causes is usually regarded as ambient noise ie (all encompassing) but it is by no means constant.

The noise output from an echo-sounder may be measured at any instant of time, but many sources of noise are dynamic and the resultant levels may change quickly. Probably the most important example of this is the increasing sea-state noise as the wind force gets higher; the effect of this is to produce bursts of noise as the interaction of ship and waves becomes more violent. An associated effect is loss of signal because of aeration at the face of a hull mounted transducer. Clearly, the direction in which the ship is travelling and its speed relative to the wind and swell can make a significant difference to the level of noise and loss of signals. However, it is the high transient level of noise resulting from weather and related sea conditions which initially causes a reduction in ships survey speed, often delaying the progress of the survey until the noise level drops (if a more favourable course is not feasible).

An effect which is not well known is that found in coastal zones where there is a high rate of tidal flow. Wideband noise (certainly up to 300 kHz) is generated by the action of fast-flowing water over sand ridges, evidently causing sand particles to go into suspension where their frequent collisions generate noise. This is often evident as a 'plume' trace above the seabed echo, extending almost to the surface, but not always appearing to connect to the seabed. The noise disappears completely when the tidal flow rate drops as the direction is about to change, so for a period of nearly two hours it may not be in evidence. Minimum spectrum levels at the seabed, measured at 30 kHz and 100 kHz off the east coast of Britain were 93 dB/1m Pa/1 Hz and 85 dB/1m Pa/1 Hz respectively (Harden Jones and Mitson, 1982).

At the lowest level is thermal noise which can be detected in very quiet conditions down to about 20 kHz, but it is normally only of importance above 100 kHz, see Figure 35. Knowing the temperature of the water, the bandwidth of the receiver and the radiation resistance of the transducer, it is possible to calculate the voltage VRT at the transducer terminals which is due to thermal noise.

VRT = (4ktB RR)1/2 (79)

where

VRT = Vrms due to thermal noise
k = Boltzmanns constant 1.37x 10-23
t = temperature, 271 + °C
B = bandwidth in Hz

Example: A transducer with a bandwith of 10 kHz, operating at a temperature of 10°C and having a radiation resistance of 800 ohms, will have a thermal noise voltage of 0.35 m V produced across its terminals, that is -129 dB/V. If the amplifier increases this by say, 60 dB, the output noise will equal 60-129, or -69 dB/V ie Antilog -69/20 = 350 m V, or 0.35 mV. The same answer is obtained if we say that 60 dB voltage gain is 103 times, for 0.35 x 10-6 x 103 = 0.35 mV, or 350 m V.

### 9.3.5 Ship Noise

When wideband measurements are made of ship radiated noise, they normally show a high intensity at frequencies of a few hundred Hz, dropping steadily as frequency increases. The measurements are rarely extended above 10 kHz, so for acoustic survey purposes it is necessary to take the noise level at the output of each echo-sounder. The main sources of ship noise are machinery, propeller and flow.

Machinery noise may arise from high levels of vibration transferred through the hull into the water. The amount of acoustic energy at echo-sounder frequencies is generally low, but up to 50 kHz it may form a measurable background noise. In calm weather conditions it can set the effective threshold of the survey equipment although in most vessels this is due to the propeller noise.

When noise measurements are made at the output of the echo-sounder at various ship speeds and the results are plotted on a graph, with noise voltage on the vertical scale and speed on the horizontal, the voltage against speed is usually an almost horizontal line for slow speeds. This is probably due to machinery with perhaps a small amount from the echo-sounder amplifier. Then suddenly an almost vertical line appears; this is due to the onset of propeller cavitation. As a physical phenomenon, cavitation evidently causes the formation of bubbles by negative pressure, literally a tearing apart of the water, and the sudden collapse of the bubbles causes noise over a wide band of frequencies. Cavitation occurs at the tips, or on the edges of the propeller blades.

Damage to the blades in the form of quite small cuts can cause a considerable increase in noise at echo-sounder frequencies. It is therefore important to ensure that any rough or jagged surfaces, or edges are removed from the propeller and that all surfaces are smooth and polished after dry-docking. A well-designed propeller should not cavitate at the lower speeds, but if it does it is often possible for experts to treat the leading edges of the blades, or the tips, to prevent cavitation noise from unduly restricting survey speeds.

By the nature of their operation, controllable pitch (CP) propellers are a source of variable noise level and when measurements are made on vessels so equipped, it is necessary to repeat them for several pitch settings.

When towing a trawl the noise level is greatly increased and allowance must be made for this in a systematic way, by using the results taken with particular nets and at known towing speeds to set the increase in threshold at which the equipment is integrating. Because we are used to looking at pictures of sections through a transducer beam it is easy to forget that it is actually three-dimensional and that there are sidelobe responses which may look directly at the propeller.

Example: The seventh sidelobe of a 30 kHz transducer had its line-of-sight through the position of the propeller, with a range between the transducer and the propellor of 66 m. The response of the sidelobe was -24 dB relative to the main beam which had a sensitivity of -184 dB/V/1 m Pa. Thus the sidelobe sensitivity was -208 dB/V/1 m Pa with a directivity index of 15 dB. Noise level at 30 kHz referred to a position 1 m from the propeller = 125 dB/1 m Pa/m in a 2 kHz band at a ship speed of 9 knots.

Propagation loss = 20 log66 = 36.4 dB and
VRT(noise) = 125 + (-208) - 36.4 + 15 = -104.4 dB/V which is antilog -104.4/20 = 6 m V

Because the noise level due to the propeller may change suddenly during operational service it should be checked, recorded and graphed at regular intervals.

Flow noise is largely a matter of the transducer siting and the manner in which the installation is completed. If there are projections or cavities along the hull in front of the transducer they will often generate speed dependent noise. Rough edges near the transducer face due to welding, or the sides of a housing not faired sufficiently carefully to the hull can also be responsible for high noise levels.

### 9.3.6 Miscellaneous Sources

Acoustic interference occurs when different instruments operate on the same frequency but it is rare for this to cause any problems when the beams are directed vertically downwards as for echo-sounding. Two equipments on the same vessel, operating at the same time are likely to interfere seriously with one another and even if they are synchronised no quantitative measurements will be possible. Despite considerable frequency separation of the systems, mutual interference results because of the wide range of frequencies present in a pulse.

Acoustic noise measurements at sea need to be recorded in detail because there are so many variables such as weather and depth. For these measurements the depth of water should be no less than 20 m, but if possible it should be deeper and the sea calm. Depth is important because noise is reflected from the seabed, and this causes problems the extent of which depends on the level of ship noise radiated towards the seabed. Noise levels in shallow water and under bad sea conditions are also important, so the opportunity should be taken to measure these when conditions are suitable.

Normal measurement procedure begins with the engines stopped, except for auxiliaries supplying power. After initial measurements with the ship in this state, the main engine/s is started and the measurements repeated but without the propeller turning. Results of these static measurements should be recorded in a suitable table which will also be sufficient to take those following. Next the propeller/s is engaged and the ship taken through its speed range at intervals of 2 knots, the noise level being recorded at each interval once the ship has actually reached the called-for speed. Finally the vessel is run up to full speed and the propeller is stopped. Whilst still at full forward speed the flow noise, sometimes called 'speed noise', is measured at various intervals as the speed drops.

Towed transducers need a similar procedure to be applied, although the effects of machinery noise will normally be less. It is often necessary to try the body with various lengths of cable let out in order to achieve the best position with respect to low noise pick-up.

Graphs of noise measurement against ships speed are best illustrated on log/log paper as in Figure 84. If the sensitivity of the transducer is known, plus its bandwidth, or that of the receiver amplifier, it is possible to calculate the acoustic spectrum level SPL at the transducer face from measurements of noise voltage. SPL is the noise power for one cycle (Hz) of energy and is expressed in dB/1 m Pa/1 Hz. This information is a useful reference against the SPL of ambient noise likely to be encountered at various sea-states. An oscilloscope or sensitive voltmeter can be used, but readings must be converted to rms and an allowance made for any gain in the system between the transducer terminals and the point from where the measurements are taken.

Figure 84.

## 9.4 Coverage Errors

Acoustic surveys are based on the premise that if a ship makes a track across a given area of sea surface, the acoustic signals received from its scientific echo-sounder represent a true proportion of the biomass in that area.

There are times and situations when the spatial coverage of a given area is adequate, but for various other reasons the depth coverage of the water column is restricted. The next section discusses the inherent limitation of echo-sounders in the detection and estimation of fish close to the boundaries of sea surface, bottom and shore.

### 9.4.1 Near Surface Layer

Excepting when both are perfectly flat, the surface and bottom act differently as reflectors of acoustic waves. Often the water surface is moving in a random manner, thus reflecting significant amounts of acoustic energy in different directions with respect to the transducer. Therefore it is difficult to use the water surface as a reliable reference, either in terms of its distance from the transducer, or in the stability of the signal amplitude obtained from its echo. This means that in addition to the 'dead-zone' (section 9.4.3) there is a volume of water where uncertainty exists due to wave motion and this is difficult to define.

For practical purposes of fish detection it seems likely that the greater the agitation of the water near the surface, the less chance there is of significant quantities of fish being within the volume of uncertainty. As a rough guide it might be reasonable to assume that no fish will be detected within a distance from the surface of twice the wave-height, plus half the pulse length. Another factor, associated with wave action, is the production of bubbles which may persist for long periods in the surface region. Bubbles have the effect of introducing extra attenuation in the acoustic path, so reducing the efficiency of detection, see Section 9.2.6. When surveying for fish close to the surface a towed transducer must be used to look upwards. It is then the ventral surface of fish which is insonified by the acoustic beam instead of the dorsal surface; in some species this may mean a lower target strength.

### 9.4.2 Near Bottom Zone

The first factor to be established when considering errors due to the lack of coverage near the bottom is the closest point to the bottom at which detection/estimation of fish is possible. The distance of this point above the bottom is half the physical length of the transmitted pulse ct, where c is the speed of acoustic waves in the water medium and t is the time duration of the pulse. A graph of detection height on the axis of the beam above the sea bottom, in relation to pulse duration is shown in Figure 85.

Figure 85.

The reason why this distance is half the pulse length is illustrated in Figure 18, where the lower of the two objects x-y (representing fish) may be considered as the sea bottom for the purpose of explanation. When the distance between the fish and the bottom is equal to half the pulse length, it is evident that, as the rear of the pulse leaves the fish, but is still moving towards the bottom, its echo starts moving toward the transducer. However, the leading edge of the pulse (or wavefront) has already been to the bottom and its echo has travelled by half the pulse length, also back towards the transducer. Therefore, at the instant we are considering, the front edge of the bottom echo is level with the rear edge of the transmitted pulse at the position the rear edge of the fish echo has just left. If the fish is any closer to the bottom than half the pulse length, the rear edge of the pulse would not have left the fish before the wavefront of the bottom echo arrived back at the fish position. The fish and the bottom echoes would therefore be merged.

A half pulse length is the theoretical distance for the discrimination between objects/targets, but in practice it may be greater because pulses are rarely perfect, taking a finite time to rise and decay. Instead of simply assuming a value of ct /2 from nominal figures for the speed of acoustic waves and the manufacturer's pulse duration it is instructive and sometimes important to measure these factors.

The speed of acoustic waves can be obtained from Figure 8, if the water temperature and salinity are known. This speed should then be multiplied by the measured time duration of the transmitter pulse, from the point where it first reaches 10% of maximum pulse amplitude to where it has decayed to the 10% level. Speed is in metres/second and time in seconds, eg c = 1495 m/s and if t = 0.5 x 10-3 seconds, so ct /2 = 1495 x 0.5 x 10-3/2 = 0.374 metres.

If the speed and time measurements cannot be made, c should be assumed to be 1500 m/s, t taken from the manufacturer's data and the product of the two divided by 1.5 instead of 2 to allow for an imperfect shape.

Of course these figures for minimum distance refer only to the axis of the beam and, because of the spherically shaped wavefront of the pulse, the distances off axis are much greater, see Figure 86.

Figure 86.

The minimum distance (height), at which fish can be detected, for beam angles relative to the axis and for given transmitter pulse lengths, can be calculated from

h = d(1 - cosq /2) + ct /2

where

h = height in metres
d = total depth of water from transducer face to sea bottom
q = full beam angle of transducer at half power points
ct /2 = half pulse length.

Because detection ceases at ct /2 on the axis, all other detection along the wavefront ceases at the same time, thus the total volume where fish cannot be detected, the dead zone, may be considerable, Mitson (1982).

The volume of the 'dead-zone' when related to a conical beam, comprises the frustrum of a cone minus the cap of a sphere. In terms of the depth of water from transducer to bottom (d), beam angle q and the pulse length ct it can be expressed as

Volume of dead zone = Volume of frustrum - Volume of cap

Vfrustrum = 0.268 (d - ct /2)((1 - sinq /2)/tanq /2) + ct /2 (2d tan q /2)2 + 2((d - ct /2) sinq /2)2 + (2d tanq /2)(2[d - ct /2]sinq /2) (83)

Vcap = p /3[(d - ct /2)((1-sinq /2)/tanq /2)]2 [3(d - ct /2)-(d-ct /2)((1-sinq /2)/tanq /2)] (84)

The volume given above for the dead zone relates to one transmission only, whereas in normal survey operation a succession of transmissions occur as the vessel moves along its course. Depending on the beam angle, the speed of the vessel and the depth of water, these transmissions may overlap, especially near the sea bed. These factors therefore, cause some variability in the effective sampled volume of the region where the pulse approaches the height ct /2 above sea bed. But, whatever the beam angle, the depth of water, or the rate of transmission, the distance of ct /2 above the sea bed marks a definite boundary under which no sampling is possible at all.

Figure 87.

For each km2 of survey area, the total volume of water near the sea bed which cannot be sampled is 106ct /2 (m3) shown in Figure 87 for pulse durations of 0 to 1.2 ms. This clearly emphasises the need for the shortest possible pulse duration in order to minimise this zone which could be designated the definite dead zone (DDZ).

In certain circumstances it may be important to consider the volume of the beam as the pulse approaches the bottom, especially if the near bottom sample is important. The acoustic pulse increases in volume as it progresses in depth, but it reduces sharply as the half pulse length height above the seabed is approached. Whilst the transmitted pulse contained in a conical beam is travelling through the sea, clear of any boundaries, its volume is contained within a spherical shell of common solid angle between the ranges d2 to d1 where d1 - d2 is equal to the pulse length ct.

This volume can be calculated from

V1 = (2p /3)(1 - cosq /2)(d13 - d23) (85)

where

V1 = the volume of the range shell in m3
d1 = depth from transducer to the pulse wavefront (m)
d2 = depth from transducer to the rear of the pulse (m)
q /2 = half angle of the beam in degrees, to the half power level

At the point where the wavefront is one pulse length above the seabed, the volume in which detection can be made is reduced to

V2 = (p /3)(1 - cosq /2)(d13 - d23) (86)

where the units have the same dimensions as above.

As the wavefront travels through the last half pulse length to reach the distance ct /2 above the seabed, the volume diminishes to the cap of a sphere, which finally reduces to zero at the height of ct /2. For this situation the 'cap' is on the axis of the beam and the minimum useful volume for sampling purposes might be considered as that occurring when the height of arc of the cap is slightly greater than the dorsivental height of a single fish on the beam axis.

Volume of the cap of a sphere, V3 (m3).

V3 = ((p h12)/3) [3 d1 - h1] (87)

where

h1 = height of the arc (m)
d1 = depth of water from transducer to the bottom of the arc (m).

The simple treatment given above when studied in conjunction with the Figures should be sufficient for the organiser of an acoustic survey to make an analysis of the volumes of water he is able to sample and those which he is not.

### 9.4.3 Inaccessible Fish Distribution

Section 9.4.1/2 discussed the situations when the coverage is limited by the pulse length of the echo-sounder and the roughness of sea surface or bottom. A more difficult situation to assess and make allowance for, is when a proportion of the fish population moves into water so shallow, that the combination of draught of the vessel, the minimum distance from the transducer, and the depth restriction of ct /2 leave little, or no water to be surveyed.

In such circumstances a little inshore vessel is needed, preferably with a quiet engine, to carry a suitably small calibrated echo-sounder and tow a transducer as close to the surface as possible. The Simrad EY-M, plus a tape recorder, is suitable for this purpose although it works at 70 kHz and care must be taken in relating the results to higher or lower frequencies. Results can be processed through a QM integrator by means of the interface described by Larsen (1983).

## 9.5 Vessel Avoidance (variability with depth of fish)

It is necessary for the survey operator to be aware of fish behaviour in relation to the survey vessel for this may cause an incorrect estimate of the stock to be made. Fish react to both acoustic and visual stimulii, but the degree of reaction varies with species, season, time of day (probably related to feeding), intensity of the disturbing source and the acoustic frequency band. Some pelagic fish are known to move from areas where the large number of vessels must be producing considerable amounts of low frequency noise.

There are two effects to be considered. Fish moving out of the path of the vessel completely and fish swimming downwards, but remaining in the path of the acoustic beam. If fish move out of the path, the situation is serious, so what can be done? It is rarely possible to modify the vessel so as to reduce the noise level significantly. The measures necessary to decouple the low frequency noise produced by diesel engines are very costly, even if introduced during the building of the vessel. It may be possible to find periods when the particular species is less sensitive to noise, for there is evidence to show considerable variability with time of day and season.

Recordings have been made showing that it is not only fish concentrations very close to the surface which are affected by a ships presence or the noise it generates. Concentrations of adult herring, under the path of the vessel, extending from about 10 m below the surface down to 40 m, have completely disappeared, but quickly returned again after its passage, Olsen (1979). The fact that fish were densely packed from top to bottom of the school may have led to the 'scare' reaction passing quickly through it. It is possible that the noise intensity from the particular vessel was very high, thus causing such an extreme reaction through the water column, but noise level data on this vessel are not available.

To guard against the possibility of survey results being affected by this type of behaviour in relation to his vessel, the acoustic survey operator is advised to make observations whenever possible which may assist him in determining the extent of the problem, or even if it exists at all. Occasionally visual observations can be made, but can be misleading because fish very close to the surface and in the path of the vessel will move aside. A horizontally directed sonar beam may provide useful clues by showing the general distribution of fish in the area which can be related to the quantities being recorded by the echo-sounder.

Sometimes it is possible to observe the rapid descent of fish under a vessel if a wide beam transducer is in use. Normally a fish at constant depth relative to the transducer will produce an inverted 'V' shaped trace if the axis of the beam crosses it, but, a quick descent will appear as a sloping line on the paper record. This type of movement produces a change in the orientation of the fish with respect to the acoustic beam, hence its effective target strength changes, almost certainly becoming lower. If such behaviour is widespread amongst the fish population being investigated, then the overall stock estimate will be biassed low. Avoidance behaviour is likely to be more prevalent in shallow waters because the vessel noise does not die away quickly, but reverberates between surface and bottom.

The use of towed transducers may be a good solution under some conditions, if they can be towed well clear of the ship and are not likely to be visible to the fish being surveyed. They also have other advantages, see Sections 9.3.4, 9.3.5, 9.6.1.

## 9.6 Other Errors

There are other possible sources of error to be considered. The first two relate to operational matters and the last two to the biomass being surveyed.

### 9.6.1 Motion Induced Errors

Conditions for acoustic survey are most satisfactory when the transducer beam axis remains approximately perpendicular (at an angle of 90°) to the sea bottom, or oscillates slightly around this position.

It is difficult to quantify the exact effects of roll and pitch motions of a vessel in relation to the schools of fish it is surveying - the greater the amplitude of motion and the narrower the beam, the more significant the error becomes. Stanton (1982) has studied the problem and his paper is recommended to those using hull-mounted transducers.

When the rate and amplitude of motion is high and the fish are fairly deep a transmission made at one instant of time may occur at the extreme roll of the vessel and by the time that echoes start to return, the transducer may be 'looking' in another direction. This effect is significant when narrow beam transducers are used in a vessel which has a high rate of movement in pitch or roll. Consider a maximum roll amplitude of ±15°, at a rate of 5°/s for a vessel fitted with a transducer having a full beam angle of 15°. It is clear that at either extreme of the roll, the transducer beam will be 'looking' away from the vertical, and near bottom detection will be affected because of the rapid changes in range as the beam swings. There will be a reduction in echo amplitude due to the outer edges of the beam (low intensity/sensitivity) being at the shortest range to the bottom. Both of these effects give rise to a 'ragged' bottom echo, making it difficult for any automatic 'bottom stop' or 'bottom lock' to function efficiently, or for fish to be discriminated from the bottom echoes. There would not be a complete loss of signal for the angle of beam and the rate and angle of motion, given above at practical ranges for fish detection, due to the effect of motion alone. Acoustic waves travel at about 1500 m/s, so if we assume a maximum range/depth of 375 m, the time for a pulse to travel to that range and an echo to travel back, would be 0.5 s. During this time the beam would have moved 2.5°, not sufficient to cause a serious loss of signal.

Because many species of fish have directional scattering characteristics, where the main 'lobe' of the response is not necessarily perpendicular to the length axis of the fish's body there may be an effect when the transducer is 'viewing' these responses as its angle changes due to motion. Directional effects of fish target strength response greatly increase at higher frequencies and a fish of 40 cm length at 38 kHz might have a response 5° wide, which at 120 kHz would be reduced to about 1.5°. Possibly the random angles of maximum fish response and transducer motion tend to give insignificant errors.

### 9.6.2 Acoustic Beam Overlap

The amount of overlap will vary according to the beamwidth in the fore-aft plane, the rate at which transmissions are being made, the speed of the vessel and the depth interval at which integration is taking place. Each of these parameters has to be taken into account in the calculations.

A problem which is difficult to quantify arises when the density of fish in schools is such that those in the lower levels of the school are in the 'shadow' of the top layers. As a result the acoustic echo signals may not be proportional to fish density, the normal premise for echo-integration. This effect has been studied theoretically and using practical data by Ertugrul and Smith (1982). Other useful references are Røttingen (1976), Foote (1978, 1978a, 1978b), and Lytle and Maxwell (1982).

### 9.6.4 Resonance of Organisms

Air bubbles appear within biological organisms over a wide size range, from fish larvae to the swimbladders of adult fish, and they have been studied in relation to resonance. When an acoustic wave strikes a bubble, the latter responds to the compressions and rarefactions of the wave. At resonance the frequency of the wave and size of the bubble interact in such a way that the bubble compressions and rarefactions are a maximum, ie its oscillations are at their greatest. Thus a maximum of energy is extracted from the acoustic wave. Some of the energy is scattered in all directions by the pulsating bubble, the remainder being changed to other forms of energy such as heat.

Various effects prevent swimbladders from acting as ideal resonators, the most important being the viscous damping due to the surrounding flesh and tissue. A detailed description of the physical process is beyond the scope of this manual but it must be realised that the phenomenon of resonance can be of considerable importance in fisheries acoustics, for it can give rise to an enhanced target strength.

There are two components of resonance to be considered.

1. Frequency: which depends on the size of the swimbladder, and the depth of the fish, Figure 88.

2. The 'Q': This factor determines the increase in back-scattered energy over that due to the geometric cross section of the target. 'Q' is the reciprocal of the damping factor, which represents the sum of the effects limiting the oscillation.

At resonance an ideal bubble would have a ratio of acoustic cross-section to geometric-cross-section of 4Q2. Measurements on large fish, such as cod and saithe have shown Q to be about 2.5, but it is possible that smaller organisms may have higher Q's for the damping factor was thought to be due principally to shear losses within the tissue of the swimbladder wall. Even with a Q = 2.5 the ratio of acoustic cross-section to geometric cross-section is increased by 25 times (14 dB). The effect of this is shown in Figure 89 where the target strength of one organism 5 mm in length is seen to increase by this amount and 100 organisms of the same size could evidently reach a TS of -24 dB, comparable to a very large fish. A layer of such organisms at about 40 m depth might give a significant result on the echo-integrator used at 38 kHz. Because of enhanced TS of such organisms it may be difficult to discriminate between densely aggregated resonant targets and densely schooled non-resonant fish.