KRM models predict backscatter as a function of fish length, acoustic frequency, fish aspect (i.e. tilt), and have been expanded to include fish roll. The user chooses the range for a variable of interest and then the model calculates backscatter for each cylinder in the body, in the swimbladder, and adds backscatter from the two body parts coherently. The swimbladder is the main contributor to the total backscatter. Depending on acoustic frequency, the fish body may increase or decrease total backscatter because of constructive and destructive interference between the body and swimbladder.
To illustrate KRM model output, reduced scattering length (a dimensionless amplitude measure) of a Lake Whitefish (Coregonus hoyi) is plotted as a function of fish length, acoustic frequency, and fish aspect (i.e. tilt). Reduced scattering length (RSL) is converted to target strength (TS, units decibels) by:
where L is fish caudal or standard length (in meters).
It is important to note that echo amplitude does not monotonically increase with increased fish length. This is a different pattern than that predicted by statistical models used to relate fish length to empirical measures of target strength (e.g. Foote or Love equations). Predicted backscatter from the fish body varies more than that from the swimbladder. As a result, different sized fish are predicted to reflect the same amount of sound, or alternatively, target strengths from the same fish may be the same or different at different frequencies or angles. Target strength measurements at a single frequency are not guaranteed to reliably indicate fish size. Among swimbladdered fish, maximum target strength typically occurs within 5 to 10 degrees when the fish is tilted head down. This aligns the dorsal surface of the swimbladder parallel to the incident wave front (and the transducer face).
|Clay, C.S. and J.K. Horne. 1994. Acoustic models of fish: the Atlantic|
|cod (Gadus morhua). The Journal of the Acoustical Society of America 96: 1661-1668.|
|Horne, J.K. and C.S. Clay. 1998. Sonar systems and aquatic organisms:|
|matching equipment and model parameters. Canadian Journal of Fisheries and Aquatic Sciences 55: 1296-1306.|