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



275 



a single lidar pulse and computed, using 

 Equation 16, the proportion offish schools 

 that could be detected for anchovy (Fig. 

 3). During the daytime, and at a depth 

 of 30 m, 97*7^ of 10-cm anchovy would be 

 detected (p„izK when a=0.1/m). Moreover, 

 one can also compute a signal-to-noise 

 ratio from the packing density(.v): SNR, 

 = Av exp{-2(xz) for a fish length of 10 cm 

 and compare it to the threshold target- 

 to-noise ratio iTNR) of 3. At the surface, 

 SNRq was 11,480 for 10-cm anchovy and 

 ^max = 41-24 m. At a depth of 30 m, SNR.^^ 

 (a=0.1) was 28.5, which was above TNR = 

 3, indicating that most of the schools in the 

 upper 30 m could be detected. The detec- 

 tion probability for anchovy was unity 

 over the upper 30 m (Fig. 3), which was 

 consistent with the results we obtained 

 from Equation 16 (Fig. 3). 



For the schools at night, we used a very 

 low packing density (0.53 anchovy/m'^). 

 The signal-to-noise ratio at the surface 

 (SNRq) for such diffuse schools was 53, 

 substantially above a TNR of 3, and 2,^^^. = 

 14 m. At 20 m, the SNR.-,,^ for anchovy 

 schools declined to 0.97 with a probability 

 of detection of only 13%. At 30 m, the 

 detectability of anchovy was less than l^c. 



Overall vulnerability of schools to lidar 

 detection in the vertical plane 



We estimated the cumulated proportion of schools of 

 anchovy that might be detected by a lidar assuming 

 constant day and night vertical distributions. As the 

 first step in the discussion that follows, we focused 

 on the two components used to make the estimate: 

 1) the average vertical distributions of schools of 

 anchovy during the day and the night (Fig. 3; Eq. 

 13); and 2) the depth-specific probability of detecting 

 a school, which was discussed in the previous sec- 

 tion (Eq. 16). These two components were combined 

 to obtain the final estimates . 



The probability of detecting a school during the 

 day declined from about 1 at the surface to 0.50 at 

 40 m and approached zero at 60 m (a=0.1, Eq. 16; 

 Fig. 3). Because of the lower packing density of the 

 school, the depth-specific probability of detecting a 

 school was much lower at night (with the detection 

 probability dropping from 1 at the surface to 0.10 

 at 20 m and zero at 30 m). Thus, even the very dif- 

 fuse nighttime aggi'egations of anchovy (0.53 fish/m'^) 

 observed by Aoki and Inagaki ( 1988) could be distin- 

 guished from background noise. That shallow night- 



time schools can readily be detected by an airborne 

 lidar despite their low packing density means that 

 during the night lidar surveys are feasible. 



By combining the detection probabilities with the 

 vertical distributions (Eq. 17), we could calculate the 

 proportion of anchovy schools that could be detected 

 (9) by the lidar (Fig. 7). This calculation indicated that 

 a lidar survey at night would be more accurate than 

 one during the day because the cumulated proportion 

 of schools detected during the night was 60*^ in the 

 upper 20 m, whereas during the day. it was 409^ in the 

 upper 20 m. Thus, despite the higher packing density 

 in the day (115 fish/m^) which permitted detection 

 down to about 50 m, schools were detected more often 

 at night. This feature was due to the difference in verti- 

 cal distributions between night and day. 



Up to this point we have discussed only cases in 

 which the lidar attenuation coefficient, a, equals 

 0.1/m, a typical value for the coastal waters of 

 southern California. To illustrate the effect of water 

 clarity, we varied a from 0.05 to 0.6, where the 

 attenuation coefficient for the most turbid coastal 

 water was 0.52. Generally, the proportion of anchovy 

 schools detected (g) declines rapidly with increasing 

 a, although detection also depends on the design 



