3 Forward Projections

Each operating model has 100 independent simulations with stochastic samples of the log-normally distributed recruitment deviations, the observation error for the indices of abundance, and the catches in the initial projection years (see below).

The projection period covers 2022–2057, with 4 quarterly time steps per year.

3.1 Management Cycle and Data Lag

The MSE assumes that the first TAC generated by the CMPs will apply in 2028, with a 3-year management cycle and a 2-year data lag.

This means that the TAC for 2028 is calculated in 2027 using data up to 2025, and the TAC is then updated every 3 years (Table 3.1).

The TAC is set for each calendar year and applies to the total catch of all fleets. Within each year, the TAC is split among the quarters in proportion to the seasonal distribution of the catch over the last 5 historical years.

Table 3.1: The management interval and data lag used in the North Pacific swordfish MSE.

Implementation Year	Calculation Year	Management Year?	TAC decision	DataYear used
2028	2027	Yes	Calculated in 2027, implemented 2028	2025
2029	2028	No	Carries forward 2028’s TAC	—
2030	2029	No	Carries forward 2028’s TAC	—
2031	2030	Yes	Calculated in 2030, implemented 2031	2028
2032	2031	No	Carries forward 2031’s TAC	—
2033	2032	No	Carries forward 2031’s TAC	—
2034	2033	Yes	Calculated in 2033, implemented 2034	2031

3.2 Initial Projection Years

The historical period of the OMs ends in 2021, the terminal year of the assessment. Because the first TAC generated by the CMPs will apply in 2028, the first 6 years of the projection period (2022–2027) are an extension of the historical period rather than years managed by the CMPs.

The catches in these interim years combine reported catches, where they are available, with assumed catches based on the recent catches of each fleet (all in t):

Reported catches are available for F3_US_WCNPO_LL_shallow_late and F9_US_WCNPO_LL_deep in 2022–2025, and for F19_WCPFC in 2022–2024.

The catches of F3 and F9 are reported in numbers of fish and are converted to biomass with the mean weight of the catch of each fleet in the last five assessment years.
Assumed catches are used for all other fleets and years, including all fleets in 2026–2027 and F19_WCPFC in 2025.

For each fleet, the catch is drawn from a lognormal distribution with the mean and coefficient of variation (CV) of the fleet’s catch over its last five years with catch data, truncated at the maximum catch over its last ten years. These catches are the historical catches of the OM (the catch biomass estimated in the corresponding SS3 run, which the OM reproduces) followed by any reported catches, so for most fleets they are the catches in 2017–2021.

The catches of the individual fleets are then combined into the total catch in each year (Table 3.2).

Table 3.2: The mean, CV, and maximum of the total catch (t, all fleets) in the initial projection years for the base case OM. The total catch combines reported catches (fixed) and assumed catches (random) of the individual fleets.

Year	Mean	CV	Max
2022	11,128	0.056	13,925
2023	10,935	0.057	13,732
2024	10,479	0.060	13,275
2025	10,945	0.063	16,215
2026	10,744	0.065	16,437
2027	10,744	0.065	16,437

Note on Assumed Data

As shown in Table 3.1, the 2028 TAC is calculated in 2027 using data up to 2025. The simulated catch and index data for 2022–2025 are therefore used by the CMPs to calculate the 2028 TAC.

When the real data for these years become available, they can replace the simulated values without requiring any change to the MSE framework (although the CMPs may need to be re-tuned; see Section 5.7).

3.3 Recruitment Deviations

Recruitment deviations are generated as autocorrelated, bias-corrected log-normal deviates around the stock-recruit relationship. For a given simulation, the (log-scale) deviation in year \(y\) is calculated as:

\[ \varepsilon_y \sim \text{TruncNormal}(\mu, \sigma_R,\ \pm 3\sigma_R) \]

\[ x_y = \rho\, x_{y-1} + \varepsilon_y \sqrt{1-\rho^2} \]

\[ \text{RecDev}_y = \exp(x_y) \]

where \(\sigma_R\) is the recruitment deviation standard deviation, \(\rho\) is the lag-1 autocorrelation, and \(\mu = -0.5\sigma_R^2(1-\rho)/\sqrt{1-\rho^2}\) is a bias-correction term so that \(E[\text{RecDev}_y] = 1\) on the natural scale. Deviations are truncated at \(\pm 3\sigma_R\) (on the log scale).

\(\sigma_R\) and \(\rho\) are calculated for each OM from its historical recruitment deviations, estimated in the corresponding SS3 run, where \(\sigma_R\) is the standard deviation and \(\rho\) the lag-1 autocorrelation of the log recruitment deviations (Table 3.3).

Only the years in which the recruitment deviations are informed by the data are used (1996–2020), because the deviations in the early and final years are shrunk toward zero and would underestimate the variability.

The resulting \(\sigma_R\) (0.17 in the base case) is lower than the value assumed in the assessment (0.42), so the projected recruitment is less variable than the assessment’s prior assumption.

Table 3.3: The standard deviation (\(\sigma_R\)) and lag-1 autocorrelation (\(\rho\)) of the recruitment deviations used in the projections for each OM, calculated from the historical recruitment deviations estimated in the corresponding SS3 run, and the \(\sigma_R\) assumed in the assessment.

OM	Years	\(\sigma_R\)	\(\rho\)	Assessment \(\sigma_R\)
00: Base Case	1996–2020	0.17	0.35	0.42
01: M 10% lower	1996–2020	0.17	0.35	0.42
02: M 10% higher	1996–2020	0.17	0.34	0.42
04: Steepness 0.81	1996–2020	0.17	0.36	0.42
07: Growth from Sun et al. (2002)	1996–2020	0.18	0.34	0.42
08: L50 10% higher	1996–2020	0.17	0.35	0.42
09: L50 10% lower	1996–2020	0.17	0.35	0.42

3.4 Observation Error for Simulated Data

The data used by the CMPs (catches and CPUE indices) are simulated from the OM with multiplicative observation error.

For catch, the observation error is conditioned on the historical fit between the OM catch and the catch data. The catch in the OMs matches the catch data closely (Section 2.1), so the catch data provided to the CMPs match the catches in the OM.

For the CPUE indices, the observation error is conditioned on the residuals between the observed index and the corresponding vulnerable abundance in the OM, including the lag-1 autocorrelation of the residuals. The index observation error in the projection period follows the same truncated, autocorrelated log-normal process described above for the recruitment deviations, continuing from the last historical residual. All indices are assumed to be proportional to vulnerable abundance (i.e., no hyperstability or hyperdepletion).

Indices are simulated in the projection period only if they have data at the end of the historical period. Table 3.4 shows the standard deviation and lag-1 autocorrelation of the observation error for these indices in the base case OM. The conditioned values vary among the OMs, since each OM is conditioned on its own historical fit.

Table 3.4: Conditioned CPUE index observation error for the Base Case OM showing the SD of the log-scale residuals and the lag-1 autocorrelation for the indices that are simulated in the projection period.

Index	SD (log-scale)	Lag-1 AC
S2_JPN_WCNPO_OSDWCOLL_late_Area1	0.184	0.600
S4_JPN_WCNPO_OSDWLL_late_Area2	0.163	0.325
S5_TWN_WCNPO_DWLL_late	0.328	0.617
S6_US_WCNPO_LL_deep	0.245	-0.144
S8_US_WCNPO_LL_shallow_late	0.195	0.620