Adjoint-based parameter estimation for the spatially explicit model of large pelagics (with application to skipjack tuna).

Transcription

1 Inna Senina 1, John Sibert 1 and Patrick Lehodey 2 Adjoint-based parameter estimation for the spatially explicit model of large pelagics (with application to skipjack tuna). 1 Pelagic Fisheries Research Program, JIMAR, UH, Honolulu, USA 2 Marine Ecosystems Modeling and Monitoring by Satellites, CLS, Toulouse, France.

2 Model structure Tuna habitats Parameters to be estimated General scheme of the model with optimization approach Physical environment Biological input Fishing data NPZD Chlorophyll 3-layer data: Temperature (GCM), currents (GCM) Oxygen (Levitus) Six forage components: epi-pelagic Migrant and non-migrant meso-pelagic Migrant,non-migrant and highly migratory bathypelagic Pole-and-line: tropical and sub-tropical gears Purse seine: WCPO associated and unassociated fleets WCPO associated and unassociated fleets TADR tuna model Eqns for 0-3 month old juveniles: spawning, foraging, passive transport, survival, mortality, cannibalism Eqns for 1-16 quarter old adults: recruitment, foraging, migrations, ageing, natural and fishing mortality Optimization: Preliminary sensitivity analysis Constructing cost function according to data distribution minimization, parameter estimation and errors. Predictions Tuna spatial distributions, catches and length frequencies time series Estimates of model parameters Management applications I. Senina, J. Sibert, P. Lehodey

3 Model structure Tuna habitats Parameters to be estimated Tuna habitat description 3 types of habitats: Spawning habitat: SST, product of primary production ( food ), forage biomasses ( predators ) Juvenile habitat: SST, biomass of adults tuna ( cannibals ) Movement (feeding) habitat: forage biomass (epipelagic, mesopelagic, bathypelagic, migrant mesopelagic, migrant bathypelagic and highly migratory bathypelagic species), temperature and oxygen concentration at 3 layers (0-100m, m and >400m). Seasonality effect at high latitudes feeding habitat is computed as spawning habitat (obeying continuity of habitat distribution) Food requirement index index influencing the mortality rate of young tuna mostly imposing starvation penalty on their natural mortality rate. I. Senina, J. Sibert, P. Lehodey

4 Model structure Tuna habitats Parameters to be estimated Adult s habitat definition and migrations as a response to environmental heterogeneity Habitat parameters: (1) optimal temperature for spawning; (2) tolerance interval for spawning temperature; (3) optimal temperature for foraging/migrations; (4) tolerance interval for foraging temperature; (5) slope coefficient (response on food abundance); (6) critical concentration of oxygen; (7) slope coefficients in sigmoid function. Temperature functions for different ages Oxygen functions Movement parameters: (8) maximal diffusion coefficient; (9) slope coefficient in dependence on habitat index γ; (10) taxis coefficient χ; habitat quality month 9 months 3 years slope coef. = -2.5 slope coef. = -25 diffusion coefficient γ=0.5, γ=0.1, γ=0.1, Δ Δ Δ H = 0 H = 0 H = 1 δx temperature O2 concentration movement habitat I. Senina, J. Sibert, P. Lehodey

5 Model structure Tuna habitats Parameters to be estimated Movement habitat II 120E 155W 70W 30N 30N S 30N 30S 30N S 30S 120E 155W 70W I. Senina, J. Sibert, P. Lehodey

6 Model structure Tuna habitats Parameters to be estimated Natural and fishing mortality (11) maximal predation mortality; (12) slope coefficient in predation mortality function; (13) maximal senescence mortality; (14) slope coefficient in senescence mortality; (15) threshold age for senescence; (16) variability with habitat index; (17-22) target size for fleet, lˆ ; (23-28) fish size range, σ; (29-34) right asymptote, ρ; (35-40) catchability coefficients; mortality coefficient threshold age for senescence selectivity coefficient Asymmetric Gaussian: ^= l 60 σ=15 ρ=0.6 ^ l = 55 σ=20 ρ=0.8 o ^ l = 60 σ=10 ρ=1 ^ l = 55 σ=30 ρ= age (month) fork length (cm) I. Senina, J. Sibert, P. Lehodey

7 Data and simulation set-up Maximal likelihood approach Adjoint method keynotes Model domain 99 E 163 E 133 W 69 W 44 N N 1 16 N N 11 S 11 S 38 S 38 S 99 E 163 E 133 W 69 W I. Senina, J. Sibert, P. Lehodey

8 Data and simulation set-up Maximal likelihood approach Adjoint method keynotes Catch data ( ) Sub-tropical pole-and-line WCPO purse seine associated EPO purse seine associated Tropical pole-and-line WCPO purse seine unassociated EPO purse seine associated I. Senina, J. Sibert, P. Lehodey

9 Data and simulation set-up Maximal likelihood approach Adjoint method keynotes Length frequencies data ( ) LF data available for 7 regions I. Senina, J. Sibert, P. Lehodey

10 Data and simulation set-up Maximal likelihood approach Adjoint method keynotes Objective function Model predictions C K f, a f, i, j a, i, j pred pred i, j r t, f, i, j = q f Et, f, i, j s f, awa N a, i, jδxδy, Qt, f, a, r = K a= 1 f, a E f, i, j N a, i, jδxδ a= 1 i, j r The task of finding the optimal parameterization of the numerical model by fitting its prediction to observations consists in maximizing the likelihood function (or commonly, minimizing negative loglikelihood). Catch likelihood: LF likelihood: Boundary penalties. obs ( θ C ) ln L = C C ln C + ln( Γ( C t, L LF = t, f, a, r 1 2σ t 2 f f obs pr ( Q Q ) 2 t, f, a, r obs pred t, f t, f t f t f t, f, a, r Quasi-Newton minimization method being used requires evaluation of the gradient of cost function with respect to control parameters pred t, f s E N ΔxΔy y obs f + 1)) I. Senina, J. Sibert, P. Lehodey

11 Data and simulation set-up Maximal likelihood approach Adjoint method keynotes Adjoint method keynotes Adjoint method consists in constructing the reverse model in order to compute derivatives of objective function derivatives with respect to model parameters: L L αl =,.., θ1 θ n Efficacy of the adjoint method is determined by: exact evaluation of derivatives low computational cost, which does not depend on the dimension of the parametric space One of the methods of verification of adjoint model is comparison of exact derivatives with first order finite difference approximation: L θ k L ( θ k + εδθk ) L εδθ k ( θk ), k = 1..n I. Senina, J. Sibert, P. Lehodey

12 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments Pre-optimization Preliminary sensitivity analysis Based on gradient of model predictions function Based on the change of likelihood relative to the parameter bounds exclusion of non-observable parameters from optimization Create appropriate initial conditions (climatology spin-up) using optimization approach Validation of the model approach on another data set and with simplified model Application to tagging data for skipjack I. Senina, J. Sibert, P. Lehodey

13 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments Application to tag recaptures data months I. Senina, J. Sibert, P. Lehodey

14 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments A list of calibrated model parameters with their estimated optimal values and uncertainties (experiment ) θ N Description 0 * St.dev. θ θ θ θ uncertainty β P β S 1 slope coefficient in predation mortality 0 Relative uncertainty slope coefficient in senescence mortality σ γ 3 standard deviation in temperature function slope coefficient in oxygen function V max 5 maximal sustainable speed c 6 coefficient of diffusion variability q 1 q 2 q 3 ŝ 0 d 1 d 2 ŝ 2 d 3 ŝ 3 7 catchability for PLTRO fishery catchability for WPSASS fishery catchability for WPSUNA fishery target fish length, PLSUB fleet e-5 11 selectivity slope coefficient, PLTRO fleet select. width of Gaussian, WPSASS fleet target fish length, WPSASS fleet e-5 14 selectivity slope coefficient, PLSUB fleet target fish length, WPSUNA fleet I. Senina, J. Sibert, P. Lehodey

15 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments The correlation coefficients between optimal parameters (experiment ) I. Senina, J. Sibert, P. Lehodey

16 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments Predicted with estimated parameters and observed catch data I. Senina, J. Sibert, P. Lehodey

17 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments Twin experiments (simulation ) I. Senina, J. Sibert, P. Lehodey

18 Projections and management applications Results and further plans Projections? Need environmental data forecast (based on parameter estimated for ) Possible management applications: Reduction of fishing effort (for chosen fisheries) Area closures Estimate of the impact of fishing I. Senina, J. Sibert, P. Lehodey

19 Projections and management applications Results and further plans Results and further plans The efficient computational tool developed for estimating model parameters, that allows to improve fit of the model predictions to observations; Optimization experiments showed that such an explicit spatial model is able to adequately predict spatial distribution of catch with small number of control parameters; Improvements in the model made as a result of optimization experiments: Topographic indices, preventing tuna dispersal to shallow regions (with usually high habitat index); Removing variability of mortality of adults, adding starvation penalty on mortality of young tuna Adding Beverton-Holt stock-recruitment relationship. Still need improvement: Model predictions for EPO fisheries data Upcoming work: Publishing current results; Parameter estimation in the tuna-forage coupled model; Application of parameter estimation to other tuna species (bigeye and yellowfin) Projections based on different management scenarios. Thank you I. Senina, J. Sibert, P. Lehodey

20 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments Spatial correlations between predicted and observed catch and number of data points I. Senina, J. Sibert, P. Lehodey

21 Pre-optimization steps Application to tagging data Results of function minimization Twin experiments and MULTIFUN-CL predicted population biomasses I. Senina, J. Sibert, P. Lehodey