We hypothesize that abundance of fish schools can be modeled by summing backscatter from individuals within an aggregation. To test this hypothesis, densities of Namibian pilchard schools are modeled in combination with volume backscatter measurements obtained using a sector scanning sonar. A commercial purse seiner caught six of the schools that were surveyed to provide a measurement of absolute biomass.
Below is an echosounder's view of a pilchard school that was observed in the Benguela Current off the coast of Namibia in southern Africa.
Echosounder's
view  pilchard school 


Incorporating behavior in school density calculations uses tilt and roll distributions in calculations of effective target strength. To accurately reflect movement and behavior of fish schools we include movement, school geometry, and orientation angle distributions in density calculations.

We can model effective backscattering crosssections of fish aggregations if we make some assumptions about tilt and roll distributions. Length frequencies are obtained from catch data and mean volume backscattering measurements are obtained from sector scanning sonar. The equation listed above can be rearranged and solved for packing density.
Horizontal
Plane 
Vertical
Plane 
These schematics show the sector scanning sonar's perspective of a fish school. The beam width of the sonar is 40^{o} in the horizontal plane and 10^{o} in the vertical plane. Snapshots of the school geometry can be taken with every pass of the beam.
Preliminary results of two snapshots from three different schools are presented as examples. The first density measure is that estimated using the KRM model with tilt and roll distributions. The second density measure is that estimated using geometry and backscatter measurements from echosounder data and traditional target strength  length relationships.
School 









A1 
337.8 
5.980 
2.9 
0.0355 
1.1 
56.4 
0.68 
7.3 

A2 
370.8 
239.6 
2.9 
0.0373 
1.2 
68.2 
9.5 
7.3 

D1 
352.0 
28.02 
4.9 
0.0498 
0.67 
68.3 
13.9 
17.4 

D2 
528.1 
196.9 
4.0 
0.0604 
0.75 
67.5 
8.99 
17.4 

E1 
900.3 
305.1 
6.0 
0.1937 
0.88 
67.5 
18.07 
4.3 

E2 
892.2 
122.1 
6.0 
0.2402 
0.65 
67.9 
27.7 
4.3 
The two density measures do not exactly match but we are encouraged with the preliminary results. This is a work in progress, additional results will be posted in the future.
Relevant Publications
Horne, J.K. and J.M. Jech. Incorporating behavior in target strength predictions of  
fish schools. ICES FAST working group manuscript. 