564 



Fishery Bulletin 101(3) 



Laser spots on seafloor 



Figure 4 



Schematic representation of the relationship between the camera lens, image plane, and laser spots on 

 the seafloor. 



Di = D' cos 0, and // = D' sin 

 H D'sine 



A=- 



tan 6 + 



tan e + 



(2) 

 (3) 



In Equation 3, estimation of D^ requires the height of 

 the camera above the seafloor (H); however, the need for 

 a direct measurement of H can be eliminated by using 

 camera parameters that provide an independent estimate 

 ofDMFig. 4). 



Figure 4 shows the relationships between the camera 

 lens, image plane, and laser spots, where d is a constant 

 representing the distance from the focal point to the image 

 plane, and c is a constant representing the distance from 

 the camera lens to the image plane (note that c may be 

 positive or negative). 



Note that both d and c are specific to the video display 

 monitor employed, W, 0, and « are fixed, and w is observed. 



Therefore, 



W 



D' = D-d-c. ■dndD = d 



w 



D' = il\—-\\-( 



(4) 



(5) 



Underwater tests were conducted and the constants c and 

 d were estimated for Delta s video camera and laser set-up 

 by following the procedures of Davis and Tusting (1991). 

 The distance traveled (T) for each area-swept trapezoid 

 (from the center of the image to the lower edge of camera 

 field of view), then, is 



T=a-D, = D' 



cos 



180 



sin 6 



1 180 



tani 1 e + 



180l T 



(6) 



Appendix II: Derivation of the trawl-survey 

 habitat-bias estimator, and the trawl-survey 

 habitat-bias effect size-index (t/^,) 



To estimate the trawl survey habitat bias, we contrasted 

 1 ) the traditional abundance estimator, which does not dis- 

 criminate between fish density differences in trawlable and 

 untrawlable habitats (habitat-biased), with 2) an unbiased 

 abundance estimator that explicitly allows for density dif- 

 ferences between trawlable and untrawlable habitats. 



Let D, = the true density in the trawlable habitat; 

 A, = the area of trawlable habitat; 

 D = the true density in the trawlable habitat; 

 A = the area of untrawlable habitat; 



A = the total area = A^ + A„; 



A^ = total abundance; and 



A = the difference in true densities = D^-D^. 



Then, for the unbiased estimator. 



Ar = D,A, + £>„Ar 



and for the biased estimator, 



N = D^ = D,A, + D,A^. 



The habitat bias, then, is the difference of the two estima- 

 tors, or 



Bias = (D/i, + D/iJ - 



(1) 



The total error in the abundance estimator is a function 

 of both the bias and the variance ¥(/),) of the fish density 

 estimator 



MSE = Bias'^ -t- (A2)V(D,), 



(2) 



