Lo et al : Modeling performance of an airborne lidar survey system for anchovy 



269 



and a threshold-to-noise ratio, TNR = 

 (T-S,;\/o. Then Pidetection )= 1 -(tKTNR - 

 SNR) for signals following normal distri- 

 bution with mean SNR and variance 1 

 when fish are present, and Pifalse alarm ) - 

 1 - 0{TNR) for signals following normal 

 distribution with mean = and variance = 

 1 when no fish are present. 

 The maximum detection depth, z 



" ' max' 



was defined as the depth at which the 

 detection probability is 0.5, i.e. the SNR, 

 is equal to the TNR because of the sharp 

 drop in detection probability from 1 to 

 with depth (Fig. 2). 



TNR = SNR^ = SNRf^e^-^""'. 



(5) 



We could rearrange the terms in Equation 

 5 and calculate that 



2a 



In 



TNR 

 SNR,, 



(6) 



« 



We investigated the degree that maxi- 

 mum detection depth for schools is affected 

 by the setting of the false-alarm rate by 

 calculating z^^^^ as a function of the false- 

 alarm probabilities and determining the 

 value of TNR to be used in Equation 6. The 

 detection probability {Pidetection)) can be 

 approximated by unity for depths above this z,,,^^^. 

 and by zero for depths below it (Fig. 2). That is 



Pidetection ) = 1 for SNRz>TNR or z < 2,„„, 

 = otherwise. 



Laser power and penetration depth 



To get an idea of the ranges of depths that might be 

 available to the lidar for a reasonable cost, we calcu- 

 lated the maximum penetration depth (■?,„„^.) with a 

 lidar model that was developed to perform engineer- 

 ing trade-offs quickly and easily. Input parameters 

 and lidar components can be changed easily by the 

 user, and the computer program automatically cal- 

 culates all of the affected quantities. Plots can be 

 quickly generated within the program to allow the 

 results to be immediately viewed. The lidar system 

 was assumed to be similar to that currently used by 

 NOAA (Churnside et al., 1997). Actual parameters 

 are presented in Table 3. 



Only laser power effects were considered. Clearly, 

 other factors were also important. These included 

 receiver telescope diameter, detector sensitivity, back- 

 ground light conditions, fish species, density, etc. 



20 30 



Depth (m) 



Figure 2 



Detection probability as a function of depth for a lidar system with a 

 false-alarm probability of 0.01 operating in water with an attenuation 

 coefficient of 0.1/m. Curves are labeled by the value of the signal-to- 



However, a full investigation of the effects of all 

 pertinent parameters was beyond the scope of our 

 study. The effects of some of these parameters, how- 

 ever, could be estimated. Doubling the receiver tele- 

 scope area, detector sensitivity, or fish density, for 

 example, is equivalent to doubling the laser power, 

 and we could have considered an equivalent laser 

 energy that included differences in these parameters. 

 Because of the assumptions used in our calculations, 

 our calculations should be taken as representative 

 and are not necessarily precise. 



Because of the interference with the surface, it 

 was difficult to actually calculate SNRq. Instead, we 

 noted that 



SNR^^ = SNR^exp(2az), 



(7) 



where z = any arbitrary depth; and 



SNR, = the signal-to-noise ratio at that depth. 



The calculations were done with a fish school deep 

 enough so that surface effects (e.g. specular reflec- 

 tions of the tail of the laser pulse) did not contribute 

 to the received signal from the school. Equation 7 

 does not hold for fish within about 1 m of the surface, 



