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



271 



From this expression, we ob- 

 tained the scattering coefficient 

 and the backscatter coefficient for 

 each of the Jerlov water types. 

 The beam attenuation coefficient 

 is given by 



C 



a + 



(11) 



The hdar attenuation coefficient 

 lies somewhere between the dif- 

 fuse attenuation coefficient and 

 the beam attenuation coefficient in 

 such a wa}' that it depends on the 

 beam divergence of the Hdar and 

 on the spot size of the laser at the 

 surface. The details of this depen- 

 dence are not completely under- 

 stood, and therefore we made what 

 we hoped were reasonable esti- 

 mates. Following Feigels and Kopi- 

 levich (1994), we estimated the 

 divergence angle effect for a beam 

 of negligible size by assuming that 

 photons scattered at angles greater than the lidar 

 divergence angle 0/2 are lost. We then applied a cor- 

 rection to this value for the finite size of the spot at 

 the surface based on a curve fitted to the results of 

 Gordon ( 1982). The final result was an estimate for 

 the lidar attenuation coefficient given by 



o 



CD 



Figure 3 



Vertical distribution and probability of detection (Eq. 16) by lidar of anchovy 

 during day (open symbols) and night (solid symbols). The mean depth of anchovy 

 schools was 38.98 m during the day and 11.64 m during the night (Eq. 13). 



a 



KD+27tbexp{-0.8c<ph)\^^sm{e}de, (12) 

 J b 



where h = the height of the lidar above the surface. 



The results were fairly sensitive to this parameter; a 

 factor of 2 in a is equivalent to a factor of 2 in depth 

 penetration. The values used in our study were con- 

 sistent with observations in the Southern Califor- 

 nia Bight, and are representative of what can be 

 expected. However, more work is needed before accu- 

 rate predictions of detection probability can be made 

 for a specific water mass based on measurements of 

 the optical properties. Direct measurements of a can 

 provide better detection predictions and can also be 

 used to refine this relationship. 



Vertical distribution and packing 

 density of fish schools 



The vertical distributions of schools below the sur- 

 face, their packing density, and fish size are critical 

 biological properties affecting detection of schools 



with a lidar. Two vertical distributions of anchovy 

 fish schools were used in our analyses. One repre- 

 sented an average distribution of anchovy schools 

 during the day and the other, average distribution 

 of anchovy schools during the night (Fig. 3). The 

 da.ytime vertical distribution fitted the average of 

 the cumulative proportion of fish schools during the 

 May 1997 and September 1997 surveys of Holliday 

 and Larson (1979), who used the acoustic reflection 

 from the bottom as a better way to probe the upper 

 10-20 m than that afforded by conventional acoustic 

 methods. The nighttime vertical distribution curve 

 fitted the cumulative proportions of newly spawned 

 anchovy eggs from two California sites (Pommeranz 

 and Moser, 1987) and anchovy schools from three 

 anchoveta acoustic surveys in Peru (Castillo Valder- 

 rama, 1995). The depth of early-stage anchovy eggs 

 may indicate school depth because anchovy spawn 

 during the night. Vertical distributions during the 

 daytime and nighttime were fitted to an exponential 

 distribution function: 



Fiz) =p{Z <z)= 1 -exp(-2/A), 



(13) 



where Fiz) = the proportion of fish schools in the 

 upper z meter depth; and 

 A = the mean depth of the fish schools. 



Direct measurements of school packing density 

 (numbers of fish/m'^) for anchovy were taken from 

 the literature (Table 4). Graves (1977) deployed a 



