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                                 toplankton) and the higher levels of the food web (e.g., fish, many marine mammals, seabirds, pinnipeds) (Croll and Tershy, 1998; Lang et al., 2005).
Why is counting fish important?
To properly manage a fishery and sustain fish popula- tions, accurate knowledge of the standing stock is necessary. Historically (and presently in some cases), net tows are con- ducted to collect fish which are measured (and their gender identified) to produce year-class (or cohort) data. By con- ducting multiple tows at multiple sites and times, fishery sci- entists can estimate how many adult and juvenile fish are present in an ecosystem and predict how many will be there over the next few years. Similarly, net tows are also used to measure the abundance and distribution of zooplankton species in many areas. In some cases, zooplankton are com- mercially fished; whereas in other areas, ecologists are inter- ested in knowing how many and what kind of animals are present to study and model the marine ecosystem.
One limitation of using net or trawl collected data is that most marine ecosystems are very large (100s–10,000s) of km2 and nets sample a very, very small fraction of that environ- ment. The smaller the area that is surveyed, the more uncer- tainty there will be in estimates of fish abundance and distri- bution. Since most marine ecosystems are already a very dif- ficult place to accurately sample due to their size and dynam- ic nature, sampling systems that can increase the volume of water surveyed to produce population estimates are needed. Optical systems, such as underwater cameras, are also used to survey fish and zooplankton stocks; however, they suffer from the same limitations as net sampling in that the volume surveyed by these methods is very small compared to the overall ecosystem (Benfield et al., 1996).
Active acoustic methods allow scientists to sample a much larger volume of water than either net or optical meth- ods. In a few seconds, a typical scientific echosounder can collect data from a volume of water that is comparable to typ- ical net tows (~ 1000 m3). In addition, the acoustic data has a very fine vertical resolution of approximately a meter or smaller. If acoustic echosounders are used during a ship- based survey, they allow for continuous measurements of the scattering below the vessel. How deep the acoustic systems “hear” is dependent on their frequency but most systems used for surveys cover at least several hundred meters in depth. These systems “ping” every few seconds so the hori- zontal resolution of these data is on the order of 1–10s of meters depending on ship speed. These fishery systems have even been used in non-fishery survey situations where the increased sampling abilities provided information regarding the Gulf of Mexico Deepwater Horizon Oil spill (Weber et al., 2011).
While these are substantial advantages compared to other ways of measuring marine life, acoustic systems have a major disadvantage best summarized by the quote on a tee shirt from a bioacoustics course I took in graduate school. “We only measure voltage and time.”
Converting voltage (pressure) and time information into something that is biologically-meaningful (such as an esti-
 mate of fish abundance for the survey area) can be incredibly difficult and sometimes impossible. So a primary challenge in our field is to transform the acoustic information to bio- logical data. The errors and uncertainties in this conversion process are dependent on many things: the acoustic systems used, the survey methods, and the number, behavior, fitness; and type of fish, zooplankton, or other scatterers that are present.
The inverse problem
This conversion process is called the “inverse problem” and is best explained using a simple example. Acoustic sur- veys collect volume backscatter strength (Sv) data which is a measure of how much acoustic energy was scattered back to the transmitter on the ship in a volume of water. If we assume that all the scatterers in this volume of water are identical and the target strength (TS) of a single organism is known, we can use the difference to calculate the number (N) of these targets that are in the volume of water. For a more detailed explana- tion of this see: Beamish, 1971; Foote and Stanton, 2000; or Warren and Wiebe, 2008.
If a scientific echosounder is properly calibrated (Foote et al., 1987), accurate volume backscatter data can be collect- ed. The target strength value of a scatterer can be measured (either in situ or in a laboratory), predicted using physics- based scattering models (Anderson, 1950; Stanton et al., 1993; Stanton et al., 1998b; Stanton and Chu, 2000; Demer and Conti, 2005; Conti and Demer, 2006), or found in the lit- erature (Amakasu and Furusawa, 2006; Benoit-Bird et al., 2008). If these two values are known, then numerical density (# of animals per volume) can be calculated. Unfortunately, there are often numerous complications that occur which transform this simple equation into a much more complex equation. If multiple types of scatterers such as different species or size classes, non-biological scatterers such as bub- bles, suspended sediments, or turbulence (Woods, 1977; Stanton et al., 1994b) are present in a given volume, then there are multiple contributors to the measured scattering and the equation no longer has a unique solution (i.e., you can’t determine if the measured scattering is due to a single strong scatterer or multiple weaker scatterers) (Stepnowski and Moszynski, 2000).
There are several ways this equation can be constrained. Ground-truthing of acoustic data via net, video, or literature data is a necessity and can determine what potential scatter- ing types and size classes are present in the region (Sameoto et al., 1993; Greene et al., 1998; Kasatkina et al., 2004; Wiebe et al., 1996; Wiebe et al., 1997; Ressler et al., 2012). Physical oceanographic data can also be used to determine if some non-biological sources are important and need to be consid- ered (Goodman, 1990; Seim, 1999; Seim et al., 1995). The “forward problem” uses ground-truthing data to provide information on the number and type of scatterers present which are combined with target strength models to produce an estimate of expected acoustic scattering. If there is good agreement with the expected and measured backscatter data, then the solutions to the inverse problem are likely to be more accurate. However this assumes that there are not
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