Numeric modeling of a pelagic longline based on minimum potential energy principle

Abstract

Fishing parameters(such as the shooting speed of mainline,vessel speed,time interval between two hooks,numbers of hooks between two floats) can be adjusted to deploy the hooks to water layers that are preferred by target species,such as tuna.As a result,the catch rate of the target species can be increased and the catch of bycatch species(e.g.,loggerhead turtles,Caretta caretta;blue sharks,Prionace glauca;silky sharks,Car-charhinus falciformis) can be reduced.Together,these actions improve fishing efficiency and help maintain bio-logical diversity.To better understand the relationship between these factors and the fishing depth of longline gear,we developed a numeric model of the behavior of a pelagic longline.We conducted surveys on board Chinese large scale tuna longliners in the Indian Ocean between September 2008 and January 2009.During the surveys,the vessels targeted bigeye tuna(Thunnus obesus)but also caught yellowfin tuna(Thunnus albacares),swordfish(Xiphias gladius),albacore(Thunnus alalunga) and billfishes(Istiophoridae).The hook depths(188 hooks) were measured using temperature depth recorders(TDRs) and the three dimensional current was measured at a range of depths at 24 sites using an acoustic doppler current profiler(ADCP).We developed a three-dimensional numerical longline model(3DNLM) using finite element analysis and the minimum potential energy principle method.We used Matrix Laboratory(MATLAB) software to program and conduct the numerical calculations.The three di-mensional current data were assigned to seven,50 m depth intervals(e.g.,0–50,50–100,or 300–350 m).The co-ordinates of all the nodes of the longline(including the float lines,mainline,and branch lines) were calculated by inputting three-dimensional current profile data,fishing gear parameters(the diameter of the mainline and branch line,the total weight of the branch line and the bait in the water,the density of the mainline and branch line,the elastic modulus of the mainline,the length of the branch line,and the length of the float rope),operating parame-ters(vessel speed,line shooter speed,and the time interval between two hooks) into the numerical model.The model then outputs the shape of the longline under water and the depth of each hook.We verified the model output using experimental data.The model was able to accurately depict the three-dimensional shape and hook depths of the pelagic longline.There was no significant difference between the hook depth measured by TDR and the model estimate of hook depth(P=0.220.05).The average difference between two methods was 12.03 m(range: 0.02–40.36 m,S2=100.30,S=10.01,n=188).The underwater shape of the main line was represented by a wave-shaped curve.The shape was related to the force of the branch line.This load was concentrated at the re-spective node of the main line and made the depth of this node deeper.The main line between two nodes may have floated somewhat because of lift generated by sea currents,especially upwelling currents.The model estimates of the three-dimensional shape and the hook depths were influenced by the value of the drag coefficient(CN90).CN90 was defined as the drag coefficient associated with water flow plumb to the cylinder.The value of the drag coeffi-cient(CN90) was determined based on the Reynolds number(Re) of the study object.