Open Access
Table 1
Names, symbols, and definitions of group metrics and the various indices, intermediary equations, and scattering quantities used to calculate them.
| Symbol | Name (and unit) | Definition or Algorithm | |
|---|---|---|---|
| L | Length (m) | Maximum distance between all points in ƍ2D | |
| W | Width (m) | Greatest horizontal distance perpendicular to group length in the ƟL+90° direction | |
| H | Height (m) | zmax(i) − zmin(i) | |
| R | Roundness | L/W | |
| V | Volume (m3) | ƞ3D | |
| Group metrics | SA | Surface Area (m2) |
 for all k3D
|
| Sp | Spread (m−1) | SA/V | |
| d | Density (fish/m3) |
|
|
| d(BL) | Density (fish/BL3) | d/(BL3) | |
| D | Depth (m) |
|
|
| DB | 1Distance above Bottom (m) | Bottom depth − D | |
| IHh | Horizontal Internal Heterogeneity (m) |
 /L |
|
| IHv | Vertical Internal Heterogeneity (m) |
|
|
| R | Range from the ship (m) |
|
|
| HD | Horizontal distance from the ship (m) |
|
|
| n | Total number of measurements within a group | ||
| i | Each measurement within a group | ||
| Indices | k | Number of indices defining ƍ | |
| a | One of 2 measurements in ƍ2D used to define L | ||
| b | One of 2 measurements in ƍ2D used to define L | ||
| p | Total number of pings | ||
| f | Number of triangle facets | ||
| v1,v2,v3 | The vertices of each triangle facet | ||
| x,y | Horizontal position (m,m) | Universal Transverse Mercator (UTM) coordinate position of the Sv measurement | |
| Positional | Z | Depth position (m) | Depth of the Sv measurement |
| Intermediaries | sx,sy | Ship position (m,m) | UTM coordinate position of the vessel |
| Sx, Sy | Mean ship position (m,m) |
|
|
| Cx, Cy, Cz | Density dependent center of gravity (m,m,m) |
|
|
| ƍ | Convex hull |
|
|
| ƍ2D | 2D convex hull | The smallest 2D convex polygon that contains every one of the n data points (x 1,y 1….xn ,yn ) within the group | |
| Geometrical Intermediaries | ƍ3D | 3D convex hull | The smallest 3D convex volume that contains every one of the n data points (x 1,y 1,z 1….xn ,yn ,zn ) within the group |
| εi | Convex hull coefficient/ weight such that the coefficients are non-negative and sum to one | ||
| ƟL | arctan (|xa – xb | / |ya – yb |) | ||
| f | Number of triangle facets | ||
| v1,v2,v3 | The vertices of each triangle facet | ||
| sv | 2Volume backscattering coefficient (m−1) | 10 * Svc/10 | |
| Scattering quantities | FL | 3Fish length (m) | Mean for k length |
| BL | The number of body lengths per meter (m−1) | 1/FL | |
| TS | 4Target strength (dB re 1 m2) | TS = 20 * log(FL) − 66 | |
| σ bs | 2Backscattering cross section (m2) | 10 * TS/10 | |
4TS to FLcm model for walleye pollock from Foote and Traynor (1988).
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