About the Cell statistic operator

The Cell statistic and the Cell statistic [Single targets] operators accept Sv data or single target data and output cell samples that are set to a selected cell statistic. The grid for the cell is specified under the Grid page of the operator. The available Cell statistics are: Mean, Minimum, Maximum, Median, Percentile and Number of samples/targets. Cell statistics can be used to mask original data. This combination of processes can offer information-rich visualizations, based on qualitative calculations, and enable innovative analysis insights into your data. The Cell statistic operator is licensed with the Advanced Operators module.

Note: Samples that are excluded or thresholded affect the calculation of cell statistics.

Cell statistic settings
Cell statistic algorithms
Examples of use
Future enhancements

Proxy for fish density

Top left: Raw Sv data.

Bottom left: Cell statistic (Mean Sv) on raw Sv data.

Top right: Cell statistic (Mean TS) on single target data.

Bottom right: Fish per cubic meter, restricted to the cells where the mean Sv is <-64dB.

Dataflow for a Proxy for fish density (Sv - TS = 10 log ρ)

Dataflow object name	Operator	Description
Single target - split beam (method 2) 1	Single target - split beam (method 2)	Applies single target detection - split beam (method 2). Uses TS and angular position operands. Grid applied. Result Detect single targets.
Cell statistic [single targets] 1	Cell statistic	Operand 1 is the Single target - split beam (method 2) 1. Operand 2 is the Sv variable (to match ping geometry). Cell statistic is Mean. Result Cells display mean TS with Sv ping geometry.
Mask 1	Mask	Operand 1 is Cell statistic [single targets] 1. Operand 2 is Data range bitmap 1 (mask). Masked values are set to no data. Result Mean TS > -70 dB are set to no data. Leaves TS mean < -70 dB.
Cell statistic 2	Cell statistic	Input operand is the Sv raw variable (grid pre-applied). Cell statistic is Mean of Sv. Result Cells display mean Sv.
Data range bitmap 1	Data range bitmap	Input operand is Cell statistic 2 (for Sv). -1000.00 < True < -70.00, otherwise set to False. Result A bitmap mask based on Sv mean.
Minus 1	Minus	Operand 1 is Cell statistic 2. Operand 2 is Mask 1. Calculates Cell statistic 2 - Mask 1. Result Sv - TS = 10 log ρ, where ρ is fish density.
dB to linear 1	dB to linear	Input operand 1 is Minus 1. Converts dB to linear values. Result Proxy for fish density in linear units.

TS calibration with a Calibration sphere

The Cell Statistic operator can provide visual guidance whilst calculating TS calibration with a calibration sphere and tuning the single target detection of the sphere.

Calculating the number of fish per acoustic sampling volume

When calculating biomass it is important to evaluate the density of organisms in the water column: if the density is too high it is not possible to obtain reliable in situ TS values. The calculation of the number of fish per acoustic sampling volume (Nv), sometimes known as the Sawada index, and the ratio for multiple echoes (M) give you a confidence limit for TS estimation.

It is generally accepted that if a sampling volume has Nv < 0.1, then the hydroacoustic data can be included in in situ calculations (see Parker-Stetter et al. 2009). Sawada et al 1993, in their small study of Walleye Pollock, report that estimated TS was accurate when M is less that 70% and Nv is less than 0.04.

M, Nv

Sawada indices

Where:

M is the ratio of multiple echoes when measuring a single target.

Nei is
the fish density output by the echo integrator.

This can be expressed as Sv_mean - TS_mean. See Proxy for fish density.

Nei is also know the quantity n as used by Sawada et al.

Note: Sawada (1993) uses a TS-fish length relationship from trawl data to estimate TS_mean. This may not be suitable in the case where you have no trawl data or the case where there is more than one species present. It is possible to use an iterative approach by calculating the TS_mean of cells. The iterative approach can be seen as circular, given that the calculated TS_mean is used to calculate an index for the appropriateness of the TS estimate.

Nec is
the fish density from single target detection.

This can be expressed as Echo density = Number of single targets/Beam_volume_sum of single targets.

Echo density is output by the Cell statistic (single targets) operator.

Nec is also known as the quantity ns as used by Sawada et al.

Nv is
the fish number in the reverberation volume where TS is estimated.

c is the speed of sound in water (m/s).

τ is the effective pulse width (seconds).

Ψ is
the equivalent beam angle. The linear form is used in the equation for Nv.

Note: Ψ dB re 1 steradian = 10log(ψ)

r is range in meters (of the reverberation volume).

An example of the use of the density indices

Sv

Raw variables for Sv, TS and angular position. Large schools of fish, single fish.

Potential single targets in the water column

Single target split beam detection (method 2) using TS and angular position.

Fish density (linear)

Sv(mean) dB - TS(mean) dB = 10 log ρ
where ρ is fish density. Sv(mean) and TS(mean) are output by a Cell statistic operator.

Nv

Formula operator output for the Nv equation.

M

Formula operator output for the M equation. M may be evaluated using other operators.

Masked targets with density index criteria

Density criteria M < 0.70 And Nv < 0.04 mask the single targets outside schools variable. The density index criteria may be evaluated using the Formula operator or with other operators such as Data range bitmap and AND.

Example dataflow

This example uses an the TS_mean of a cell to evaluate density indices.

Extended_Sawada

Dataflow object name	Operator	Description
Raw variables Sv, TS angular position	N/A	Apply grids, Set up Analysis exclusions.
Pre-processing Sv samples in the water column	Processed data	Sv raw variable. Analysis exclusions set to no data. Result Gridded echogram with Sv samples in water column.
TS samples in the water column	Processed data	TS raw variable. Analysis exclusions set to no data. Result Gridded echogram with TS samples in water column.
Single targets in water column	Single target detection split beam method 2	TS samples outside schools Angular position raw pings T1 Result Detected single targets in water column and outside of schools.

Note: Echoview's suite of operators can offer a number of ways to achieve a desired result. Pre-processing steps and later processing steps are shaped by the nature of the data and your analysis intentions. Generally, a greater the number of operators in a virtual chain means a greater calculation time.

Density criteria

Dataflow object name	Operator	Description
Density criteria Cell statistic Sv mean	Cell statistic	Sv samples outside schools, Statistic = Mean. Set fill empty cells with mean of surrounding cells. Result Cells with samples set to Sv mean of input operand cells.
Cell statistic [Single targets] TS mean	Cell statistic [Single targets]	TS samples outside schools, geometry provided by angular position variable. Statistic = Mean. Set fill empty cells with mean of surrounding cells. Result Cells with samples set to TS mean of input operand cells.
Cell statistic [Single targets] Echo density	Cell statistic [Single targets]	TS samples outside schools, geometry provided by angular position variable. Statistic = Echo density. Set fill empty cells with mean of surrounding cells. Result Cells with samples set to Echo density of input operand cells.
Sv(mean) - TS(mean) dB	Minus	Cell statistic Sv mean. Cell statistic [Single targets] TS mean. Result Sv(mean) dB - TS(mean) dB = 10 log ρ, where ρ is fish density.
fish density (linear)	dB to linear	Sv(mean) - TS(mean) dB. Result Cells that display Fish density in fish per cubic meter, for samples in the water column but outside of schools.
Formula M	Formula	Fish density (linear), Cell statistic [Single targets] Echo density. Result Cells that display values for M.
Formula Nv	Formula	c, τ, Ψ from Calibration page of Variable Properties dialog box. The linear form of equivalent beam angle is used. Nei is represented by V1 which is set to the fish density (linear) variable and r comes from V1. Result Cells that display values for Nv.
Formula Nv < 0.04 and M < 0.70 criteria	Formula	V1 represents Formula Nv. V2 represents Formula M. Criteria from Sawada et al. f(p,s) = (V1<0.04) and (V2<0.7) Result Boolean result that satisfies f(p,s).
Mask Single targets outside schools	Mask	Single targets outside school masked with Formula Nv < 0.04 and M < 0.70 criteria. Result Detected single targets that satisfy the density criteria Nv < 0.04 and M < 0.70.

Future enhancements

Other cell statistics could facilitate other types of analysis. Please contact support@echoview.com if you'd like to work with new statistics in this area.

M	is	the ratio of multiple echoes when measuring a single target.
Nei	is	the fish density output by the echo integrator. This can be expressed as Sv_mean - TS_mean. See Proxy for fish density. Nei is also know the quantity n as used by Sawada et al. Note: Sawada (1993) uses a TS-fish length relationship from trawl data to estimate TS_mean. This may not be suitable in the case where you have no trawl data or the case where there is more than one species present. It is possible to use an iterative approach by calculating the TS_mean of cells. The iterative approach can be seen as circular, given that the calculated TS_mean is used to calculate an index for the appropriateness of the TS estimate.
Nec	is	the fish density from single target detection. This can be expressed as Echo density = Number of single targets/Beam_volume_sum of single targets. Echo density is output by the Cell statistic (single targets) operator. Nec is also known as the quantity ns as used by Sawada et al.
Nv	is	the fish number in the reverberation volume where TS is estimated.
c	is	the speed of sound in water (m/s).
τ	is	the effective pulse width (seconds).
Ψ	is	the equivalent beam angle. The linear form is used in the equation for Nv. Note: Ψ dB re 1 steradian = 10log(ψ)
r	is	range in meters (of the reverberation volume).

About the Cell statistic operator

Proxy for fish density

Dataflow for a Proxy for fish density (Sv - TS = 10 log ρ)

Result

Result

Result

Result

Result

Result

Result

TS calibration with a Calibration sphere

Calculating the number of fish per acoustic sampling volume

M, Nv

An example of the use of the density indices

Sv

Potential single targets in the water column

Fish density (linear)

Nv

M

Masked targets with density index criteria

Example dataflow

Raw variables

Pre-processing

Result

Result

Result

Density criteria

Density criteria

Result

Result

Result

Result

Result

Result

Result

Result

Result

Future enhancements

See also