Patchy Distribution Fields: Sampling Distance Unit of a Spiral Survey and Reconstruction Adequacy

Abstract

A mathematical model is used to examine the effects of choosing various units of sampling distance of a spiral acoustic survey on the adequacy of reconstructing patchy distribution fields. The model simulates fish or plankton patches (or gaps) of different shapes and spatial orientations, and an acoustic survey by a spiral of Archimedes along which a unit of sampling distance is set. For comparison, surveys are imitated by parallel transects along which the same unit of sampling distance is set. Adequacy of the reconstructed fields to those originally generated is evaluated by calculating their correlations (r). In the case of a spiral survey, the mathematical experiments conducted show that an immovable field can be reconstructed properly (r(2) > 0.70) if the ratio of the units of sampling distance to the autocorrelation radius for the field averaged in various directions d/R(av) < 1.0-1.5. Regarding immovable fields, the spiral surveys ensure, practically speaking, the same adequacy of the field reconstruction as do surveys by parallel transects with the same unit of sampling distance. In regard to movable fields, a comparison of the results of spiral surveys with those of surveys by parallel transects indicates that the former may ensure even higher adequacy of the field reconstruction than do the latter, provided that the units of sampling distances in these surveys are equal to each other.