Toward Estimating the Variance in Acoustic Surveys Based on Sampling Design
Magnar Aksland
DOI: 10.4236/ojms.2011.11001   PDF    HTML     4,007 Downloads   11,289 Views  


This paper develops a sampling method to estimate the integral of a function of the area with a strategy to cover the area with parallel lines of observation. This sampling strategy is special in that lines very close to each other are selected much more seldom than under a uniformly random design for the positions of the parallel lines. It is also special in that the positions of some of the lines are deterministic. Two different variance estimators are derived and investigated by sampling different man made signal functions. They show different properties in that the estimator that estimate the biggest variance gives an error interval that, in some situations, may be more than ten times the error interval computed from the other estimator. It is also obvious that the second estimator underestimates the variance. The author has not succeeded to derive an expression for the expectation of this estimator. This work is motivated towards finding the variance of acoustic abundance estimates.

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Aksland, M. (2011) Toward Estimating the Variance in Acoustic Surveys Based on Sampling Design. Open Journal of Marine Science, 1, 1-17. doi: 10.4236/ojms.2011.11001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Stevens D. L. and Olsen A. R. Spatially Balanced Sampling of Natural Resources. Journal of the Americal Statistical Association 99, No. 465, 2004, 262-278.
[2] D. N. MacLennan. Acoustical measurement of fish abundance. J. Acoust. Soc. Am.; vol. 87(1): 1990, 1-15.
[3] Craig R. E. Re-definition of sonar theory in terms of energy. In: Selected papers of the ICES/FAO Symposium on fisheries acoustics. FAO Fish. Rep; (300), 1983, 331 p.
[4] Aksland M. Acoustic abundance estimation of the spawning component of the local herring stock in Lindaaspollene, western Norway. FiskDir. Skr.Ser. HavUnders. 1983, 297-334.
[5] Aksland M. Estimating numbers of pelagic fish by echo integration. J. Cons. int. Explor. Mer. 43, 1986, 7-25.
[6] Aksland M. An alternative echo-integrating method. ICES Journal of Marine Science 62, 2005, 226-235.
[7] Aksland M. Applying an alternative method of echo-integration. ICES Journal of Marine Science 63, 2006, 1438-1452.
[8] Zhao X. and Ona E. Estimation and compensation models for the shadowing effect in dense fish aggregations. ICES Journal of Marine Science 60, 2003, 155-163.
[9] Aksland M. Analysing Estimators in the Alternative Echo Integrator Method. The Open Ocean Engineering Journal 3, 2010, 116-128.
[10] Foote K. G., and Stefánson G. Definition of the problem of estimating fish abundance over an area from acoustic line-transect measurements of density. ICES Journal of Marine Science 50, 1993, 369-381.
[11] Matheron G. Principles of geostatistics. Economic Geology 58, 1963, 1246-1266.
[12] Krige D. G. A statistical approach to some mine valuations and allied problems at the Witwatersrand. Master's thesis of the University of Witwatersrand. 1951.
[13] Rivoirard J. Simmonds K. G., Foote P., Fernandes and N. Bez. Geostatistics for estimating fish stock abundance Blackwell Science, Osney Mead, Oxford, 2000, 206 pp.
[14] Cassel C. M., S?rndal C. E. and Wretman J. H. Foundations of Inference in Survey Sampling. John Wiley & Sons, 1977.
[15] Thompson, S. K. Sampling, 2nd edn. John Wiley and Sons, New York, 2002.
[16] Thompson, S. K., and Seber, G. A. F. Adaptive Sampling. John Wiley and Sons, New York, 1996.
[17] Harbitz A., Ona E. and Pennington M. The use of an adaptive acoustic-survey design to estimate the abundance of highly skewed fish populations. ICES Journal of Marine Science 66, 2009, 1-6.
[18] Conners M. E. and Schwager S. J. The use of adaptive cluster sampling for hydroacoustic surveys. ICES Journal of Marine Science 59, 2002, 1314–1325.
[19] McQuinn I. H., Simard Y., Stroud W. F., Beaulieu J. L., and Walsh S. J. An adaptive, integrated “acoustic-trawl” survey design for Atlantic cod (Gadus morhua) with estimation of the acoustic and trawl dead zones. ICES Journal of Marine Science 62, 2005, 93-106.
[20] Matern B. Sample Survey Problems. Bulletin of the International Statistical Institute Vol. XLII, Book 1, 1969, 143-154.
[21] Des Raj. SAMPLING THEORY. McGraw-Hill Publishing Company LTD, 1968.
[22] Tillé Y. Some remarks on unequal probability designs without replacement. Annales D’économie et de Statistique No 44, 1996, 177-189.

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