[Feature]: Add standard errors for area-specific quantities

[e-perl-NOAA]

Describe the solution you would like.

From Brett Crisafulli in Western Australia

"As recommended by Andre, it would be great in SS3 if it were able to output standard errors for area-specific time series for biomass and fishing mortality. We hope that this would not be a difficult change to make and be something of value to other users."

Describe alternatives you have considered

NA

Statistical validity, if applicable

No response

Describe if this is needed for a management application

No response

Additional context

No response

[Rick-Methot-NOAA]

This is feasible, but will take a moderate amount of work.
The sdreport quantities are created here:

ss3-source-code/SS_param.tpl

Lines 622 to 632 in 9b3fcf9

	!!// SS_Label_Info_5.2 #Create sdreport vectors
	sdreport_vector SSB_std(1,N_STD_Yr);
	sdreport_vector recr_std(1,N_STD_Yr);
	sdreport_vector SPR_std(1,N_STD_Yr_Ofish);
	sdreport_vector F_std(1,N_STD_Yr_F);
	sdreport_vector depletion(1,N_STD_Yr_Dep);
	sdreport_vector Mgmt_quant(1,N_STD_Mgmt_Quant)
	sdreport_vector Extra_Std(1,Extra_Std_N) // includes many subvectors created in SS_readcontrol
	sdreport_vector Svy_sdreport_est(1,Svy_N_sdreport)

So each that became area-specific would be *nareas longer such that the areas would be end-to-end in each vector and appropriate quantity labels would be created.

Propose to do only SSB and F.
SSB by area (and morph) already exists as: SSB_pop_gp(styr-3,YrMax,1,pop,1,N_GP)

F will be harder.
Z by area exists for all "g":
Z_rate(styr-3*nseas,k,1,pop,1,gmorph,0,nages)
and is already output

natM also, but only main morphs, not the platoons:
4darray natM(styr-3nseas,k,0,pop,1,N_GPgender*N_settle_timings,0,nages)

we also have:
ivector GP3(1,gmorph) // index for main genderGPatsettlement

So, a new way to show F is
F(t,p,g,a) = Z_rate(t,p,g,a) - natM(t,p,GP3(g),a)

That should be added to ther report file, but first verify whether or not predM is already in natM; it certainly is in Z_rate.

Open to ideas as to how to summarize across morph and age to get each area's F statistic. it gets messy quickly!

[e-perl-NOAA]

We would like for Andre @puntae to work on this.

[puntae]

Err OK. You want me to extend SS to allow users to specify they want area-specific SE? I agree with Rick that area-specific F would be messy