Update annF and Fstd

_f_mortality.tex

@@ -56,38 +56,44 @@ \subsection{Fishing Mortality in Stock Synthesis}
 In the benchmark section of the code, SS3 searches for an $F$mult to achieve various management reference points (often referred to as benchmarks). In this search, SS3 calculates a benchmark $F$ as  $F_{ben,f}' = F\text{mult} * \text{rel}F_f$, then calculates equilibrium yield and spawning biomass per recruit (SPR). SS3 searches for the $F$mult that satisfies the search conditions, first for user-specified SPR, then for user-specified spawning biomass at a management target (B\textsubscript{TGT} or $F_{0.1}$), then for MSY. The resultant benchmark quantities are reported in the derived quantities, but $F$mult and $F_{ben,f}'$ are only reported in the Forecast\_report.sso file. SS3 stores the benchmark $F$mult values so that user can invoke them for the forecast.
 
 \myparagraph{Annual $F$}
-The $\text{ann}F$ is a single annual value across all fleets and areas according to F\_report\_units, which is specified by users in the starter file. If there are many fleets, across several areas and with very different selectivity patterns, $\text{ann}F$ can have a complicated relationship to apical $F$. The F\_report\_units specification in the starter.ss file, see example line below, allows user to calculate it using $F'$ directly, use exploitation rate, or be derived from $Z$-at-age.
+The annual\_$F$, also seen to as ann$F$ in the Report file, is a single annual value across all fleets and areas. If there are many fleets, across several areas and with very different selectivity patterns, ann$F$ can have a complicated relationship to apical $F$.
 
-Example $F$ reporting unit specification in the starter.ss file:
+The ann$F$ is calculated for each year of the estimated time series and of the forecast. Additionally, an ann$F$ is calculated in the benchmark calculations to provide equilibrium values that have the same units as ann$F$ from the time series. In versions previous to v.3.30.15, it was labeled inaccurately as $F$std in the output, not ann$F$. For example, in the Management Quantities section of derived quantities prior to v.3.30.15, there is a quantity labeled Fstd\_Btgt. This is more accurately labeled as the ann$F$ associated with the biomass target, ann\_F\_Btgt, in v.3.30.15.
 
+\myparagraph{$F$std}
+$F$std is a single annual value based on ann$F$ according to the F\_std\_reporting\_units specified in the starter.ss file. The F\_std\_reporting\_units specification allows user to calculate it using $F'$ directly, use exploitation rate, or be derived from $Z$-at-age.
+
+% While F is a simple concept in a biomass dynamics model with a single fishing fleet, the concept of "F" as a single number is very incomplete when there are multiple fleets, some with length-based and/or dome-shaped selectivity. In SS3, the F multiplier is multiplied first by fleet-specific relative F's to get the F for each fleet, then that fleet-specific F is multiplied by the age-selectivity to get F at age. Depending on the choice of selectivity pattern, these age-specific F's may or may not peak at 1.0 and can even exceed 1.0 in some circumstances. The realized F-at-age for each fleet is (F multiplier) * (relative F) * (age-selectivity). You can see the results in the F\_AT\_AGE section of the Report file. 
+
+% While F multiplier is always done as just described, the user has various options for the reporting of the realized F. These are in starter.ss and described in the manual.
+
+$F$std reporting unit specification in the starter.ss file:
 \begin{center}
 	\begin{longtable}{p{2cm} p{12cm}}
 		\hline
-		5 & \# F\_report\_units:\Tstrut\\
+		5 & \# F\_std\_reporting\_units:\Tstrut\\
 		  & 0 = skip; \\
 		  & 1 = exploitation(Bio); \\
 		  & 2 = exploitation(Num); \\ 
-		  & 3 = sum(Frates); \\
-		  & 4 = true F for range of ages; \\
-		  & 5 = unweighted avg. F for range of ages. \Bstrut\\
+		  & 3 = sum(Apical\_F's); \\
+		  & 4 = mean F for range of ages (numbers weighted); \\
+		  & 5 = unweighted mean F for range of ages. \Bstrut\\
 		\hline
 		3 7 & \# min and max age over which average F will be calculated \Tstrut\Bstrut\\
 		\hline
 	\end{longtable}
 \end{center}
 
-For options 4 and 5 of F\_report\_units, the $F$ is calculated as $Z-M$ where $Z$ is calculated as $ln(N_{t+1,a+1}/N_{t,a})$, thus $Z$ subsumes the effect of $F$.
-
-The ann$F$ is calculated for each year of the estimated time series and of the forecast. Additionally, an ann$F$ is calculated in the benchmark calculations to provide equilibrium values that have the same units as ann$F$ from the time series. In versions previous to v.3.30.15, it was labeled inaccurately as $F$std in the output, not ann$F$. For example, in the Management Quantities section of derived quantities prior to v.3.30.15, there is a quantity labeled Fstd\_Btgt. This is more accurately labeled as the annual $F$ associated with the biomass target, ann\_F\_Btgt, in v.3.30.15.
+For options 4 and 5 of F\_std\_reporting\_units, the $F$ is calculated as $Z-M$ where $Z$ is calculated as $ln(N_{t+1,a+1}/N_{t,a})$, thus $Z$ subsumes the effect of $F$.
 
-\myparagraph{$F$std}
-$F$std is a single annual value based on ann$F$ and the relationship to ann$F$ is specified by F\_report\_basis in the starter.ss file. The benchmark ann$F$ may be used to rescale the time series of ann$F$s to become a time series of standardized values representing the intensity of fishing, $F$std. The report basis is selected in the starter file as:
+The $F$std reporting units and the relationship of $F$std to ann$F$ are specified in the starter.ss file as F\_std\_reporting\_units and F\_std\_scaling respectively. The F\_std\_scaling specification allows users, for example, to rescale the time series of ann$F$s by the benchmark ann$F$ to become a time series of standardized values representing the intensity of fishing, $F$std.
 
+$F$std scaling is selected in the starter file as:
 \begin{center}
 	\begin{longtable}{p{2cm} p{12cm}}
 		%\multicolumn{2}{l}{The starter file line:}\\
 		\hline
-		0 & \# F\_report\_basis: \Tstrut\\
+		0 & \# F\_std\_scaling: \Tstrut\\
 		& 0 = raw F report; \\
 		& 1 = F / F\textsubscript{SPR}; \\ 
 		& 2 = F / F\textsubscript{MSY}; \\