The split beam echo sounder
Echosounder and sonar basics and Echo data analysis
WAVELENGTH VERSUS TARGETS PHYSICAL AND ACOUSTICAL SIZE ................................13
History
1490 Leonardo da Vinci described that one could hear noise from a ship by putting a tube into the water.
1827 Colladon an Sturm measured the sound speed in water. Lake Genfer,
Switzerland
1914..1918 First world ware. Stereo listening for submarines. Two pipes one from the front of the boat and one from the aft.
1929 Kimura showed that echo sounders could detect fish in a pond. Forward detection. 200kHz modulated by 1 kHz
1935 Sund published echograms of Cod and showed that Cod was confined to a
10 m thick layer close to the bottom. 16kHz echosounder
1965 Dragsund and Olsen Echo integration , abundance estimation
Split beam, multibeam, echo counting, trace counting......
Transducers
Figure 1.Typical beam pattern Simrad ES120-7c (120kHz 7x7 deg composit) Right
Simulation of ES120 4x10(120kHz 4 times 10 deg elliptical transducer.
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
0.1
0.08
0.06
0.04
-0.1
-0.05
50 50
73 73
40 50 50 40
82 40 40 82
40 73 50 50 73 40
50 73 100 100 73 50
73 73 100 100 73 73
73 82 100 100 100 100 82 73
73 100 100 100 100 100 100 73
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
73 100 100 100 100 100 100 73
73 82 100 100 100 100 82 73
73 73 100 100 73 73
50 73 100 100 73 50
40 73 50 50 73 40
82 40 40 82
40 50 50 40
73 73
50 50
0 0.05
0.1
Figure 2. Simrad ES120 4x10 deg transducer.
The transducer consist of a set of elements that convert electric vibrations into mechanical vibrations. Elements can be based on piezoelectric, magnetostrictive, or modern composite materials or build up by moving coil devices.
The beam pattern is formed by the positions of the individual elements and by the
intensity weights given to each individual element as seen in Figure 2
Distance between the elements is in order of a wavelength. For a 120 kHz transducer the wavelength is λ=c/f = 1500/120000= 1.25cm
1.1. Split beam transducer
The most common scientific echo sounders today is probably the split beam echo sounders. (Earlier single and dual beam) The split beam echosounder transmits a short pulse with all elements and starts listen with four groups of elements. The geometrical displacement of the listening elements makes it possible to detect the position of the target within the beam. The position is important both to compensate the echo intensity according to the beam pattern and to estimate target position and movements.
0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
50 50
73 73
40 50 50 40
82 40 40 82
40 73 50 50 73 40
50 73 100 100 73 50
73 73 100 100 73 73
73 82 100 100 100 100 82 73
73 100 100 100 100 100 100 73
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
73 100 100 100 100 100 100 73
73 82 100 100 100 100 82 73
73 73 100 100 73 73
50 73 100 100 73 50
40 73 50 50 73 40
82 40 40 82
40 50 50 40
73 73
50 50 -0.1
-0.1
-0.05
0 0.05
0.1
Figure 3. For splitbeam listening mode the elements are divided into four groups.
1.2. Sonars versus echo sounders
SONAR means SOund NAvigation and Ranging. The people working with echo sounders needed a nicer name to be able to compete with the people working with radars.
The distinction between an echosounder and a sonar are not well defined. If we take a simple single beam echosounder and point it in various directions, we have a sonar. A horizontally aligned split-beam echosounder is now and then referred to as a SONAR.
The trend is that a sonar is a multi beam device that creates a radar like picture of the waters surrounding the ship while single dual and split beam devices generating traditional echograms are referred to as echo sounders.
Figure 4. Left: Typical presentation of data from an omni sonar. Right: Echogram from a split beam echosounder passing above a trawl (Marc Schmidt (Ge))
1.3. Multi beam systems
There exists a variety systems using a large number of beams. The beams, the most sophisticated multi beam systems are the acoustic imaging systems which generates pictures or movies similar to visual underwater videos. Examples are the underwater camera from Reson i Denmark and the Didson camera which will be demonstrated later in this course.
Figure 5. Transducer arrays
The scanning array transmits a wide pulse with its centre element. In listening mode, all elements are applied to form a tin beam sweeping the pulse volume. In this way it is possible to locate more than one target position within the same pulse volume which is not possible with the split beam principle. On the other hand, the array can only determine the angular position in one domain.
Figure 6. Acoustic camera beam matrix and Semi sphere sonars with beams pointing in all directions directions.
While the arrays only determine the targets angular position in one domain, a matrix of transducer elements can steer the beam in all directions. This allows the system to form a sort of 3D picture of the targets in the water.
1.4. Multi frequency and wide band
A new trend today is to equip vessels with an echosounder with many overlapping transducers operating on different frequencies. An example is the new Norwegian research vessel G.O.Sars using 6 frequencies. The idea is that different species reflects different wavelengths in different ways. Mackerel seems to reflect high frequency better than herring who reflects lower frequencies better than the mackerel. This increases the possibility of classifying targets. (Ref human color view)
Figure 7. The research vessel G.O.Sars has 6 matched split beam echo sounders with differnt frequencies.
The split beam echo sounder
Hardware
Software
Amp echogram
Amp-detector
Gain
Phase-detector
SED echogram
SED
Tracking
Figure 8.Main components in a split beam echosounder system.
Sonar equations
1.1. Three assumptions
Single targets are a point source.
Waves hitting the target are plane waves
Sound spread out in a spherical manner.
1.2. Quick look at Target Strength and volume reflection
TS describe the size of a single target by means of its reflection area or acoustic area. The unit is m
2
This area is frequently presented in logarithmic terms as Target Strength or TS.
Although having an associated acoustic area, single targets are regarded as point sources when observed from the echosounder. Hence, the sonar equation used to estimate single targets is frequently referred to as the point source model.
Sv describes the reflection properties of the water. The unit is m
2
/m
3
. The concentration of e.g plankton in the water will influence on the reflection properties. Clean water reflects little sound while polluted water or water with a lot of silt has higher reflections.
Clearly a bunch of fish will increase the reflection too. Since Sv is supposed to be the
reflection property from any point in the water, while the echosounder only measure the reflection from some liter of water at a time, we must normalize the numbers coming from the echosounder upon the involved volume of water.
For TS and SV we can write...
The echosounder produce the sound SL or Source level. The sound intensity is reduced due to transmission loss TL before it hits the target having the Target Strength (TS) or the volume of water V reflecting Sv. Then the sound is reflected back to the transducer loosing as much energy as on the way to the transducer. Hence, we must subtract TL once more before we can find the Echo Level (EL) produced by the fish at the transducer surface. We set up the equation
SL
SL
TL
TL
TS
Sv
V
TL
TL
EL
EL
Which we can solve with respect to TS or Sv to find
TS
Sv
EL
EL
2 TL
2 TL
SL
SL
V
1.3. More details about the elements in the two Sonar equations
1.4.1. The Source Level SL or the transmitted power
Whether we express the sonar equations in terms of intensity or power does not actually matter as long as Power = Intensity * Area.
We let the echosounder transmit the power Pt. Because the power is transmitted in one particular direction we multiply the power with the gain G. Hence the transmitted power is
Eq. 1 tx
p
T g or TX
10log( p
T g )
1.4.2. Transmission loss
The waves spread out in a spherical manner. At the range R from the transducer, the area of this spherical surface has become A=4πR 2
. This means that the intensity at any point on this sphere has been “thinned” out to I = 1/4πR 2
This thinning is called the geometrical transmission loss. In addition to the geometrical loss, a propagating sound wave will interact with the water and parts of the energy will convert into chemical energy and heat.
This loss is named alpha (α). Alpha increases with frequency and salinity. For 120 kHz and sea water alpha is about 38dB/km while it is only about 4 for clean fresh water. It is
mainly MgSO
4
and Bor and not NaCl the causes the loss of energy. Together the geometrical spreading and alpha forms the transmission loss tl.
Eq. 2 tl
4
R
2
10
R or TL(dB)
20log(4
R)
R One way trans mission loss
The power hitting the target is found from the incident intensity and the area hit by this intensity.
Eq. 3 P i
I i
Assuming that the target re-radiates all the power in all directions, we can find an expression for the targets scattering cross section area σ
S
by equating the incident and the radiated power.
Eq. 4
P i
I i
P s
S
I s
A ( R
1 m )
S
I s
I i
4
The subscript s indicates that the sound is scatter in all direction. Seen from the target, the echo sounder looks like a point in the horizon. To find the scattered intensity at a point we must divide the scattered intensity by the total area of the sphere surrounding the target. At one meter from the target, the surface area of this surrounding sphere is
A=4π1 2 =4π. Intensity passing through this sphere goes in all direction. To find the amount of intensity scattered in one direction, namely back to the transducer, we divide the total intensity by the area of the sphere. This gives the back scattered intensity I bs
= I s
/4π. The cross section area observed by the transducer will be 1/4π part of the total scattering area.
Eq. 5
bs
4
s
I s or TS
I i
10log
4
s
For the above theory to be correct, we have assumed that the distance between the transducer and the target is sufficiently large so that the waves hitting the target are approximately plane waves. At this range the target looks like a point.
The power reradiated by the target area propagates back to the transducer which gives us
a second transmission loss tl. The power p
R
received by the transducer is now found by multiplying the transducer area with the returned intensity.
Eq. 6 ra
2 g
TS
4
Receiving area of the transduce r.
(m
2
)
Where λ is the wave length and g the gain due to the transducers directivity properties.
The received power is found by
Eq. 7 P
R
tx
1/tl
bs
1/tl
ra or
Eq. 8
P
R
p
T g
TS
1
4
R
2
P
R
p
T g
TS
1
4
R
2
10
1
R
1
4
R
2
10
1
R
sv
v
1
4
R
2
1
10
R
2 g
4
TS
10
1
R
2 g
TS
4
) : point spreading model
) : volume reflection model where the involved symbols have been defined earlier.
1.4. Finishing the Sv ( volume reverberation)
As stated earlier, the only difference between Sv and TS is that Sv measures the reflection properties of a unit of water rather than the area of a target. Hence, we have to find the volume that causes the reflection. The water that the echosounder see is the water covered by the transmitted pulse. This volume is named the pulse volume or the shell volume. It depends on the transducers opening angle and it increases with the distance from the transducer.
The opening angle is traditionally named Psi (ψ) and measured in ste-radians. Ste-radians is the probably more known from astronomy where it is used to denote the part of the hemisphere that a planet covers, independent of the distance to that planet. The actual area of the planet is found by multiplying ψ with the squared range.
For the echo sounder we can think of the beam as being 1 inside ψ and 0 outside the beam. Integrating the true beam pattern and the equivalent beam gives the same result.
ψ
Equivalent beam
True beam
Pulse volume at range R
R h= cτ/2
R
A= ψR
2
R
Figure 9. Left True and equivalent beam, Right: Consept of the of pulse volume. V=A*h
R=range, c=soundspeed, τ=transmitted pulse duration,
Exchanging the volume v with the expression for volume gives
P
R
p
T g
TS
1
4
R
2
10
1
R
sv
R
2 c
2
1
4
R
2
10
1
R
2 g
TS
4
) : volume reverberat ion
We can now solve for sv and organize the equation to recognize the initial elements in the sonar equation.
SL EL 2TL sv
p
T
1 g
TS
P
R
2 g
TS
4
4
R
V
2
2
10
R
R
2
1 c
2
) : volume reverberat ion
If we now separate variable and constant elements we find
Eq. 9
Sv
10 log( Pt )
40 log( R )
TS
10 log( Pt )
40 log( R )
2
R
20 log( R )
C
1
) : volume
2
R
C
2
) : volume reverberat ion reverberat ion
Eq. 10
Sv
10 log(
TS
10 log(
Pt )
Pt )
20 log(
40 log(
R )
R )
2
R
2
R
C
1
) volume
C
2
) : Point reverberat ion source
It is these equations that are applied in many echo sounders such as Simrads EY500 and
EK60.
1.4.3. TVG
We recognize the term 20log(R) and 40log(R) in the equations and know that the number
20 is a mixture of geometric spreading loss and the range from the pulse volume. In old analog echo sounders this part of the equation was implemented in hardware controlling the receiver amplifier. Since the gain was controlled so that it increased with range and since range is a function of time R= ct/2 these amplifiers was named time variable gain or
TVG. Still we find the name 20log TVG and 40logTVG in as names for the volume reverberation and point source equation.
Near field and far field
The distance between the transducer centre and the outer element defines together with the wavelength defines the transducers near field. It is important to know the transducers near field because here the intensity varies unpredictable and disable our possibilities for exact target sizing.
Intensity
Transit zone
Transmission loss due to geometrical spreading
Range
Nearfield
Farfield
Fresnel zone
Figure 10. Near and far field
Fraunhofer
d = Rc + λ/2 r
Range R
Rc
R cancel transducer
Figure 11.The geometry of the transducer cause the nearfield. r =separation between center and outer transducer element. Rc=distance from trancduscer senter and the range of total canceling. d=distance from outer element to the canceling point.
We can use simple triangular quadrates to calculate Rc (c=cance) d
2 r
2
Rc
2
Rc
2 d
2 r
2
Rc
2
Rc
2
Rc
2
Rc
Rc
2
r
2
2
2
Rc
2
Rc
2
2 Rc
2
2
4
r
2
r
2
Rc
2
Rc
2
Rc
r
2
4
2 Rc
2
2
4
r
2
Eq. 11
R c
r
2
,where we have omitted the last part because it is so small. If we assume a transducer with radius 0.2 m and 120kHz we will find
1500 m / s
120 kHz
R c
r
2
0 .
00125 m
0 .
2
2
0 .
00125
3 .
2 m
Wavelength versus targets physical and acoustical size
If we start with a very small target relative to the wavelength we will find that the actual cross-section area is much larger than the acoustic area. If we than slowly increase the physical size there will be a period where the acoustic size increases very quickly until it reaches the same size as the physical size. We will then enter a period of oscillation between physical and acoustical size until the acoustic size stabilize. (Rayleight 1945)
σ/πr 2
1
2πr/λ =kr
1
Figure 12. Raileight scatter.
For a 120 kHz transducer with a wavelength of 1.25cm we find that the maximum acoustic size of a spherical target has a radius of 1.8mm and that we are in the safe zone for targets of 18mm.
Calibration
Echo sounders have to be calibrated in order to produce accurate estimates. There are many ways to calibrate an echosounder. The simplest is to place a target with known acoustic size in the center of the beam and adjust the gain until the echosounder reproduce the expected value. I addition to the gain, offset angles and angel sensitivity can be calibrated. This is done by placing the standard target at different positions in the beam and let a computer algorithm fit the measured positions to the beam shape and from that estimate the calibration figures.
Some considerations
Calibration should be carried out in open clean water.
Salinity and temperature must be estimated and applied to the echosounder
The size of the standard target must fit the echo sounder frequency. It should have a size that match one of the peaks in the Raileight scatter.
The target should be cleaned by soap and not touched by bear hands
The target should be acclimatized.
Pre-analysis
1.5. Single echo detection:
1.5.1. Echo length detector,
1.5.2. Crossfilter detector
1.6. Bottom detection: Algorithm based , Image analysis based
1.7. Heave correction
1.8. Filtering
1.9. Noise reduction
Analysis
1.10. Tracking
Multiple target tracking MTT
Observations
SED
Association Track support
Resulting
Tracks
Gating
Prediction
The track support decides about birth and death of a track
Prediction looks into the future and decide where to place the gate. Prediction can be based on variations on Kalman filtering, regressions, weighted mean etc
The gate decides what echo to consider and the association defines what echo belongs to what track when more than one track competes for an echo and when more than one each competes for a track.
Gap
Result a Result b Result c Result d
Figure 13. Two tracks under formation competing for one and the same echo. Four out of many possible associations.
1.10.1. Ping gate
Ping gate defines the gate size in the ping domain. The future is well known in post processing. Hence we can test echoes that will occur well into the future. It might happen that an echo found two or more pings into the future is better suited than the closest echo found in the next ping. As an example the echo in the next ping may be a noise-based echo with a TS very different from the TS in the already combined echoes. If the next echo in time has a TS value similar to the rest of the track, this might be a better echo to combine even if a missing detection will occur. Applying high values on association in time and TS may cause the tracker to skip the nearest echo in time in favor of the next echo.
1 2 3 4 5 6 7
Ping
Gate e
Observations
Estimates
Range
Figure 14. Gating and echo-association including the time domain may result in rejection of the echo (marked e) when a better-suited echo is located at a later time. This can result in a smoother or more correct track, but at the cost of an increased number of missing detections.
1.11. Abundance estimation methods
The echo sounder measure the power received by the transducer. Integrating this power over time gives the energy. Alternatively, we can find the volume back scattering coefficient backscattering coefficient (sv=σ v
) from the sonar power equation. Knowing sv and the target strength from each individual fish a volume of water enable us to estimate the fish density. To find the target strength distribution, one can apply catch data together with empirical knowledge of the TS versus fish length relationship, or one can apply in-
situ target strength measurements. The latter involves single echo detection or single echo detection and tracking. Applying tracked fish rather than the individual echoes can reduce variability in the distribution.
The fish density can be found in many ways
sv / ts scaling (ts dist. found from insitu SED or tracked targets)
sv / ts scaling (ts dist found from catch data or exitu tracked fish)
Mean ping (ts detections and volume of the beam)
Sailed distance (tracked fish and navigation data)
1.11.1. Abundance estimation based on sv / ts scaling
Density per volume or surface
Bodholt 1990a describes this method. The volume density number of fish per unit volume of water.
A
f / m
2
V
f / m
3
defines the
define the number of fish per unit area of the surface. For the latter, the fish in question are found in the water column below the unit area of the sea surface.
Eq. 12
f / m
2
Ru
Rl
f / m
3
dR
If we assume constant density in the layer we can write:
Eq. 13 f
/ m
2
f / m
3
(
R l
R u
)
An example of 8 known fish
In the case where all fish have equal and known scattering coefficient (σ s
= ts), and where we observe the unit volume back scattering coefficient (σ v
= sv) we can write
Eq. 14 sv
f
/ m
3
ts
As an example, assume that we have 5 fish with ts
1
and 3 fish with ts
2
. The contribution to sv from the two sizeclasses will be
Eq. 15 sv
1 sv
2
f
f
/
/ m
3 m
3
1
2
ts
1 ts
2
5
8
3
8 f
f
/
/ m
3 m
3
ts
1 ts
2
n
1
N n
2
N f
/ f
m
/
3 ts
1 m
3
ts
2
Summing the two equations gives
Eq. 16 sv
1 sv
sv
2 f / m
N
3 n i
N
f
n
1 ts
1
/
m
3
n
2
ts
1 ts
2
n
2
N f /
N f m
3
/
m
3
k
K
1 n k ts
2 f
/ m
3
sv ts k
1
N k
K
1 n k ts k
Where N is the total number of fish, K is the number of size classes (here K=2) , k indicates the k th
size class and n k
the number of fish in size class k. We don’t know the number of fish, but if we assume that each size class are detected equally well within the analyzed layer, then the ratio between the number of single echo detections in a size class to all single echo detections will be equal to the ratio between the number of fish in the same size class to the total number of fish. Hence, we can substitute the number of fish with single echo detections.
Scaling the total fish density by the ratios n k
/N where n k
is the number of detections in size class k and N the total number of detections gives the density for the individual size classes.
Eq. 17
f / m
3 k
f / m
3
n k
N
Applying tracked fish
To reduce variability in the size distribution, we can track the fish. The number of tracked fish gives N and n k
while the average sv and ts are obtained from the individual single echo detections from the applied tracks.
1.11.2. Abundance estimation based on echo counting
Single echo detections as source
Kieser and Mulligan (1984 ) describes this method. With the singe echo detections (SED) per ping method, f/m
3
is found by calculating the mean number of single echo detections per ping, dividing by the volume of the beam and multiplying with the height of the beam.
Eq. 18
N
P
V
Where N is the number of fish detections, ρ=f/m x
the number of fish per unit volume or area. P is the number of ping and V the sound covered water volume.
As an example, assume 5 fish in size class 1 and 3 fish in size class 2 obseved in one ping and with a beam with the volume V=10m
3.
f /
3 m
SED
All
All
P
N
V
8
10
f /
3 m
SED 1
1
P n
1
V
T
n
2
N
8
10
5
8
5
10
Eq. 19
f f /
/ m 3
SED
2
3 m
SED
2
All
f
/
P n
2
V
3 m
SED 1
T f
/ n
2
8
N
3 m
SED
10
2
3
8
All k
1
3
10
P n k
V
P
N
V
Where All indicates all size classes, k the individual size classes, N the total number of singfle echo detections, and n k
the number of single echo detections in one size class.
The above equation gives the number of fish per volume that have been resolved as single echo detections. If the density increases, the number of detections will increase until the echoes starts to overlap. With further increase in the density, the single echo detector will fail and the number of detections will be reduced. Hence, the single echo density estimate will only be correct intil overlapp occure. Higher densities can still be estimated by scaling the result with the ratio between the total and the single volume reverberation integral as showed below.
Eq. 20 f
/ m
3
Tot k
f / m
3
SED k
s v
TOT sv
SED
Fish per area is found by exchanging the volume for the surface area covered by the beam in the above equations.
Applying tracked fish
We can apply tracked fish as well. We then find the total number of single echo detections from tracks and divide them by the beam volume and the number of ping in the analyzed region. This gives the total density. The size distribution is based on the average TS from each tracked fish. This distribution will have less variance than the distribution of the untracked detections. Finding nj and N from the tracked distribution enable us to calculate fish density for each size class and obtain a more accurate density distribution than with the non tracked distribution.
1.11.3. Abundance estimation based on trace counting
Kieser and Mulligan (1984 ) describes this method. The method can only be applied when
fish has been tracked and stored in a fish basket. The operator can select vertical or horizontal survey and weather the transducer was mounted with its athwart ship axis in the ship's sailing direction or in the ships athwart direction.
Sonar5-Pro stores navigation information in a separate file distinguished from the echogram file name by the extension *.nav. This file contains registrations of the boat position along each transect. Sonar5-Pro sum up the total sailed distance from the individual detections and divide by the number of transmitted pings. A Wedge is then calculated for each ping. The volume of each wedge is summed to find the total volume along the analyzed transect. In this way the software can allow for changes in the volume due to changes in the bottom or a variable layer (See section Layers in chapter 4).
f /
3 m tracks k
i
P
2
P
1 n k i
P
2
1
P
1
V i , i
1
Eq. 21 f / m 3 tracks
All
k
K
1
f / m 3 tracks
k
“All” indicates all size classes. n k
is the number of tracks in size class k. P
1
and P
2
are the investigated ping interval and V i, i+1
the investigated volume between ping i and i+1. V is calculated from the beam geometry and the sailed distance.
Area density is found by exchanging volume for the surface area covered by the submerged beam in the equation above.
1.11.4. Abundance estimation based on catch data or ex-situ tracked fish
While the other methods compare single echo detections or tracks found within the analyzed region in the echogram, this method simply applies tracks from everywhere.
Hence, the tracks may come from tracked fish in the file, from other files, or be generated from catch data. This enables the operator to track and save fish with a representative size distribution once for all. Independent on where the tracks came from, the tracks are applied to establish the size distribution. The size distribution is applied for scaling the average sv or sa to obtain the abundance.
The formulas are identical to the formulas applied by the sv / ts scaling method with the exception that ts are taken from a generalized size distribution and not only from detections within the analyzed region.
When do I use the catch tracks method?
This method is common in vertical ocean applications. It has advantages when single echo detections are unreliable. As an example, consider a huge herring school. Within the
school, the fish density is too high to give reliable single echo detections. Outside the school bigger predators will produce reliable single echoes, but with higher TS than the herring. Using in situ estimates based on detections from the school or from the surrounding of the school will not result in reliable abundance estimates. Then estimation based on catch date is a better approach then the in situ sv / ts scaling method.
When do I not use catch tracks method!
Since the average ts are obtained from catch data or from tracks obtained totally or partly outside the analyzed region, it is possible to obtain more energy in the single echo detections than in the echo integral (sv). Assume that tracks have been tracked and stored from all part of a lake to establish a reliable size distribution. If one then analyzes a part of the lake containing only small fish, these fish will produce an average sv with less energy than the average TS obtained from all fish in the lake. The result will of course be erroneous. The reason is that the catch tracks method only work when the established size distribution is representative for the analyzed region.
Interpretation
1.12. Biomass estimation
When we know the number of fish in each size class, it can be tempting to try to estimat the weight or biomass. This is done by means of regressions. First the relation between
TS and length are developed such Loves equation TS = a*log
10
(L) + c. This has to be done for each species and each sound frequency. Similar empirical equations are developed for conversion between length and weight. Knowing the number of fish in each size class per surface are enables us to estimate the number of tons or kilos.
1.13. Survey planning and density maps
When we want to survey a large lake or see, we need to do some planning. We have limited resources and time and we need sufficient coverage to get statistical significant data. Our aim is to come up with a reliable fish density map.
ρ
D,
ρ
ρ
ρ
ρ
Ai
Area of cell i
EDSU
Figure 15. A part of the see divided in sampling rectangles with area Ai. The boat passes each rectang onc. A passage is named EDSU or elementary distance sampling unit. The sum of all EDSU gives the Active distance D.
Distance actively pinging
If we have allocated a vessel and a crew for a week, we can estimate the possible distance that we can monitor by subtracting the total available time T and the unused time U.
Unused time is the time spent on loading the vessel, traveling to the site and traveling between transects etc. We multiply this time with the boats survey speed to get the active distance D. We may also include a ratio (P) of the day if it is not possible to ping 24 hour a day.
Eq. 22 D
( T
U ) Pv
Sampling intensity in individual cell Si can be defined as
Eq. 23 Si
Ai / EDSU
Precession of the density estimates depend on the transect spacing
Coefficient of variability (Cv) in the abundance estimation depends upon the degree of coverage defined as
Eq. 24 dc
A / D (Aglen 1983,1989 )
CV should be at least 0.25 or greater which means that dc should be equal to 4 or more.
