274 



Fishery Bulletin 98(2) 



100 150 



Swath width (m) 



200 



1600 



Figure 4 



Simulated encounter probability of anchovy schools in Los Angeles Bight (Table 2) 

 for 16,000. 32.000, and 80,000 schools. The swath width ranged from 1 m to 1600 m. 

 The multiplier for mean and standard deviation of the log of diameter of school 

 group and the log of school density in a school group are given in parentheses. 

 Values for populations with multiplier (1.5,1.5), similar to populations with mul- 

 tiplier ( 1.0,1.01, are not shown. 



ing features of these results. The 

 first is that when a critical depth 

 is reached, the detection proba- 

 bility drops abruptly from nearly 

 unity to nearly zero over a narrow, 

 5-10 m span of depth. Because of 

 this sharp transition, we defined 

 a maximum detection depth '^,„„^1 

 as the depth at which the detec- 

 tion probability is 0.5. The depth 

 2,„„^ depends logarithmically on 

 signal level because of the expo- 

 nential attenuation of the signal 

 with depth. Thus, each order-of- 

 magnitude increase in signal level 

 (illustrated in Fig. 2) provides an 

 increase in 2„j^^ of just over 10 m in 

 depth. Ten meters is just about 1 

 lidar attenuation depth, defined as 

 l/a(Eq. 6). We can rewrite Equa- 

 tion 6 as z,„„^ = \n(SNR^/TNR) x 

 0.5/a. Therefore, if the attenua- 

 tion coefficient ( a) is different from 

 0.1/m, the value used in our study, 

 these z^^^ depth values scale lin- 

 early with lidar attenuation depth 

 ( 1/a). 

 To examine the sensitivity of z,,,^,^. (Eq. 6) 

 to TNR and thus the false alarm probabil- 

 ity (Eq. 6), we used the same values of the 

 surface signal-to-noise ratio as those used 

 in Figure 2. This calculation indicated that 

 the maximum detection depth (2,„oj) was 

 relatively insensitive to changes in false- 

 alarm probabilities. Decreasing the false 

 alarm rate by a factor 10 from 0.01 to 

 0.001 would only increase the maximum 

 detection depth by a few meters (Fig. 6). 

 Thus, a fairly low rate of false alarms 

 for a system could be selected without 

 seriously degrading the detection perfor- 

 mance. It also implied that we could select 

 a nominal threshold level and obtain a 

 simple expression for the maximum detec- 

 tion depth. A value of TNR - 3 results in a 

 false-alarm probability of just above 0.1%. 

 Therefore, according to Equation 6, 2„,„^ is 

 determined by 



2a 



In 



SNR, 



(19) 



We then considered the depth in the water 

 colum at which schools can be detected by 



