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Fishery Bulletin 103(2) 



candidate point [j, t(i)] 



with inherited 



temperature cost 



ATQ, t(i)] 



enumerate all 



possible Arcs between 



consecutive search 



areas 



arc D.t(l) >[k.t(l+1>] 



whose cost is a 



function of distance 



and temperature costs 



candidate point [k,t(h 

 with inherited 

 temperature cost 

 AT|j,t(i+1)] 



11] 



End 



Figure 3 



Enumerating and costing arcs. An arc is defined as the arc between any two candidate points 

 of adjacent search areas. The cost of an arc depends upon the temperature cost, AT, of the two 

 candidate points of the arc. It is also depends upon the swimming speed required to travel 

 the distance of the arc. 



The cost of the arc between candidate point j and can- 

 didate point k is 



arccost({j,t(i)}->{k,Hi + l)}) = {AT(j,t(i)) + AT(k(t,i + l)) + 



DistFactorl - 



velocity 



where velocity = the maximum sustained swimming 

 speed of the fish; and 

 DistFactor = a factor that scales the cost of swim- 

 ming at a given speed in relation to 

 the sum of the temperature costs of 

 the two candidate points. 



Values for the DistFactor and Velocity are determined 

 by the user. The rationale for such cost is that the best 

 track should include an assessment of variations in 

 swimming velocity as well as the costs of temperature. If 

 swimming speed is judged to be an insignificant cost or 

 too difficult to quantify, the DistFactor can be set to 0. If 

 a land barrier lies between the pair of candidate points, 

 the distance to swim around the barrier is calculated and 

 included in the cost of the arc. In this study an interme- 



diate value (5000 out of 9999) was assigned for the Dist- 

 Factor, and this value was constant for all evaluations. 



Step 5: Calculating the best track Finally, the algorithm 

 calculates the sum of the arc costs for each track: 



Cost of tract = £ g£, arccost({j,t(i)}- > {k,t(i + l)}). 



The costs for all possible tracks are then ranked, and 

 the track(s) with the lowest cost(s) is then saved and 

 available for display (Fig. 4). The track is saved in a 

 table of the PSAT Tracker database; the table contains 

 records of the latitude, longitude, time, and surface 

 temperature of the candidate points that comprise the 

 track, as well as records of surface temperature from 

 the satellite imagery at regular intervals along the arcs 

 between candidate points. Depending on the length of 

 the time series, this process analyzes tens of thousands 

 to hundreds of thousands of tracks and thus is the most 

 time-consuming step of the algorithm. 



Analyzing position data from PSAT Tracker 



Location estimates provided by PSAT Tracker were 

 subjected to spatial analysis to describe the move- 



