Catch in weight

The catch in weight $Y$ is $$Y_{y,f} = \sum_a C_{y,a,f} w_{y,a}.$$

Mean size

The mean length of the catch $\bar{L}_{y,f}$ is $$\bar{L}_{y,f} = \dfrac{\sum_{\ell} L_{\ell} C_{y,\ell,f}}{\sum_{\ell} C_{y,\ell,f}},$$ where $L_\ell$ is the midpoint of the length bin $\ell$.

The mean weight of the catch $\bar{w}_{y,f}$ is $$\bar{w}_{y,f} = \dfrac{\sum_a C_{y,a,f}w_{y,a}}{\sum_a C_{y,a,f}},$$

Survey

If the $s^{\textrm{th}}$ survey is biomass-based, then the survey value $I_{y,s}$ is calculated as $$I_{y,s} = q_s \sum_a v_{y,a,s} N_{y,a} w_{y,a},$$ where $q$ is the scaling coefficient and $s$ indexes survey.

If the survey is abundance-based, then $$I_{y,s} = q_s \sum_a v_{y,a,s} N_{y,a} .$$

The proportion-at-age vulnerable to the survey is $$p_{y,a,s} = \dfrac{v_{a,s}N_{y,a}}{\sum_a v_{a,s}N_{y,a}}.$$

The proportion-at-length vulnerable to the survey is $$p_{y,\ell,s} = \dfrac{\sum_a v_{a,s} N_{y,a} P(\ell|a)}{\sum_{\ell} \sum_a v_{a,s} N_{y,a} P(\ell|a)}.$$