Hydroacoustic Assessment Of Fish Stocks In The Gulf Of Nicoya, Costa Rica

The Gulf of Nicoya, Costa Rica is a relatively shallow, tidallyinfluenced estuary that supports a substantial artisanal fishery on various stocks, primarily corvinas. Little is known about the population size or productivity of these stocks. Hydroacoustic techniques have been successfully applied to fish population estimation in many circumstances. However, application to the Gulf of Nicoya stocks faces a double consideration: economic considerations force a relatively simple, cost effective approach, but the environment, including the species and size composition is complex. We approached the problem of the complex biological composition with Clay's deconvolution technique. This approach allowed us to obtain substantial information about the acoustic size characteristics and density of the fishes with a relatively simple, single-beam echo sounder. We implemented the deconvolution analysis, along with standard echo integration techniques, using the BioSonics ESP acoustic signal processing system. This PC-based system combines portability with substantial processing power and storage capability. The deconvolution technique provides the necessary scaling factor for echo integration, so that absolute population estimates can be made. INTRODUCTION The Gulf of Nicoya covers about 1530 square kilometers and is the largest of the Pacific Ocean gulfs of Costa Rica. The inner or northern half of the Gulf is more shallow than the outer parts, with typical depths of 4 to 20 meters. About 50% of the production of fish and invertebrates in Costa Rica comes from the Gulf of Nicoya [l]. Artisanal fisheries contribute to the majority of landings. The dominant group of the 100 species of commercial fishes is the Sciaenidae, consisting of 31 species. About 30% of the Gulf's production is represented by three sciaenids, the corvina species Cvnoscion albus (corvina reina), Cvnoscion sauambinnis (corvina aguada) and Micropogonias ah innis (corvina agria). Until now knowledge about the abundance of fishes in the Gulf of Nicoya came from fisheries landing statistics and some scientific trawl sampling. Using semi-balloon trawls, Leon [2] found that, in the inner Gulf, a non-commercial sciaenid dominated catches, followed by sea catfish, then engraulids and clupeids. From a later survey, Bartels et al. [31 published a similar finding except that engraulids and clupeids were less important. During September 1987, we began a survey of the inner Gulf of Nicoya using hydroacoustic equipment consisting of a singlebeam echo sounder. Groundtruthing by net sampling was limited, but a rapport with fishermen was established to sample catches aboard vessels and to work in proximity to their fishing gear. Early in 1988, we designed and built a midwater trawl in order that groundtruthing could proceed unhindered, and we conducted another survey in the inner Gulf, August and September 1988. We have begun to analyze this most recent data with deconvolution analysis [4,5], along with echo integration techniques. Preliminary results suggest that previous studies have undersampled smaller size fishes. METHODS The basis for the mobile hydroacoustic sampling design was a stratified random sample of parallel transects. Tidal currents are swift in the inner Gulf of Nicoya, and so for ease of navigation, transects were run parallel to current direction, and consisted of about three nautical miles in length. i n this paper, we apply the deconvolution technique to data from two of these transects. Deconvolution of Fish Signals A beam from an echosounder is like a flashlight which is strongest on the center axis and weaker at the edges. Simplistically, voltages received from the same size fish farther from the acoustic axis are, on average, smaller than from those on the axis. In order to compare all of the voltages, one needs to remove this beam pattern effect. Clay [4] presented an outline of a inverse technique, a deconvolution procedure, which removes the beam pattern effect from fish echo signals. Earlier, Clay and Medwin [6] showed that fish echoes were a convolution of the beam probability density function (PDF) and the on-axis voltages. Stanton and Clay [5] also described the deconvolution procedure and included a minimum density estimator when fish targets are too dense to use a deconvolution procedure successfully [7]. The inverse problem has been long recognized. In 1877 Lord Rayleigh suggested that it would be possible to determine the density distribution of a string from knowledge of its vibrations [8]. In 1966, Kac posed this problem again in a famous paper "Can one hear the shape of a drum?" . Robinson [8] and his proteges developed an inverse or deconvolution approach for seismic exploration, removing the effect of various strata overlying an oil field. Clay's deconvolution method gives the distribution of on-axis voltages, which can provide estimates of backscattering cross sections as well as density estimates. To promote an understanding of the inversion process of deconvolution, the convolution of two signals follows. A simple example, given in Twomey's [9] text, is that of running means, taken three at a time. Samples from the signals are taken at discrete intervals; a similar process has been applied to the convolution and deconvolution of fish echo signals. There are two sets of data to consider in the running mean example. One set is the data to be smoothed, available at positive and negative integer intervals. The other set (responsible for the running mean procedure) is centered at the origin, with amplitude 1/3 at -1,O and 1, and 0 amplitude elsewhere. First, reflect the data set responsible for the smoothing procedure about the origin. Since it is centered on the origin, the reflection does not change this signal. Multiply one data set by the other at corresponding integer locations. The running mean at 0 is then the sum of the multiplications. Shifting the rectangular 113 amplitude signal (the data set responsible for the running mean procedure) one integer to the right or positive side of the other signal, multiplying and summing, gives the mean at 1. Shifting in the other direction gives the mean at -1. Shifting twice gives the mean at 2 and -2, and so on. Now the inverse problem could be the following in this example. Given the set of running means, and the process and signal (1/3 amplitude signal) which formed them, find the original data set. (if you didn't throw away the end data points, of the original set of data, this is possible by recursive division). Deconvolution has been performed by polynomial division of ztransforms of the fish echoes by the z-transforms of the beam PDF [4,5]. This result comes from discrete linear system theory 1039 [lo], the approach used in the running mean example above. In order to follow the deconvolution procedure into its goals of density and backscattering cross section estimates, the theory will be presented. If all fish were on-axis, after correcting for spreading and absorption losses they would create a voltage PDF, fs(s). However, the fish are not all on-axis, and so the collected data possess a Pdf, fv(v) where V is measured in volts. If the beam pattern PDF is fB(b) then the cumulative density function, Fv(v), was shown by Clay and Medwin [6] to be 1 v /b Fv(v) = I fJb) db I fs(s) ds 0 0 The maximum value of b is 1 (on axis) and the maximum of S for any b is v/b. The derivative of Fv(v) with respect to v is the PDF This becomes the convolution integral [ l l ] after a change of variables b = e-x O