This folder contains work related to the gear models used in the TNC fishing gear study.
From the methodology document, the key formula for computing gear losses is:
\[ L_{g,s} = \frac{F_{g,s}}{\chi_g}\cdot \left(a_{g,s} + l_{g,s} + d_{g,s}\right ) \]
where \(F_{g,s}\) is total catch (reported plus unreported plus discards) for gear of type g in a given segment s, \(\chi_g\) is the capture rate for gear type g (amount of catch for a unit of gear operation), and a, l and d represent the mass of gear that is abandoned, lost, and discarded for each gear operation unit.
This formluation leaves a little bit out because it does not localize exactly where the mass of the gear is defined. This is nominally defined in the gear unit \(\ \mathbf{\mu}_g\), but that cancels out in the formulation, and so that means the mass of the gear has to be folded into the capture rate. Capture rate becomes a definition of “mass of fish caught per mass of gear per unit of operation”, and then a, l, and d can be pure loss fractions.
Let’s try out how this works. Let’s say the mass of a characterized longline rig is 2,254 kg and includes 1,729 branchlines. And let’s say that during an 8-hour soak, 85% of hooks get hooked (C+U+D) with an average weight of 30 kg. That’s a catch of 1729 * 0.85 * 30 = 44090 kg.
MM’s loss rate is 375 kg per 200 sets (leaving out abandoned and discarded). That’s 1.875 kg per set– almost nothing! That means the parameter l is 1.875 / 2254 = 0.00083.
Meanwhile, the F for those 200 sets is 8.82e6. We have \(\frac{F}{\chi}\cdot l = 375\) which means \(\ \chi = \frac{F\cdot l}{375} = 19.52\) kg/kg/set. That’s 44090/2254.
So reformulating the methodology, \(\chi\) is mass of catch per mass of gear per unspecified unit of operation, and a, l, and d are the fractional loss of that mass of gear over the same unspecified unit of operation.
| Parameter | Dimension | Meaning |
|---|---|---|
| m | kg | Mass of a characterized unit of gear |
| T | operation unit | characterized unit of operation (set, hour, etc) |
| \(\hat{\chi}\) | kg/op unit | Modified capture: total mass of catch per T |
| \(\chi\) | 1/op unit | Nominal Capture Rate; \(\hat{\chi}/m\) |
| a | fraction | Dimensionless abandonment fraction per T |
| l | fraction | Dimensionless loss fraction per T |
| d | fraction | Dimensionless discard fraction per T |
| \(p_a\) | plastic fraction | Fraction of a that is plastic |
| \(p_l\) | plastic fraction | Fraction of l that is plastic |
| \(p_d\) | plastic fraction | Fraction of d that is plastic |
Gear Loss Equation:
\[ \bar{L}_g = \frac{L_{g,s}}{F_{g,s}} = m_g\cdot \frac{ a_g\cdot p_{a,g} + l_g\cdot p_{l,g} + d_g\cdot p_{d,g}}{\hat{\chi}_g} \]
Required parameters for gear g include m, T, \(\hat{\chi}\), a, l, d, \(p_a\), \(p_l\), \(p_d\).
Compute \(\bar{L}_g\) for each gear type.
Multiply \(\bar{L}_g\) by \(F_{g,s}\) for each segment to determine the gear loss per segment.