Patchy distribution fields: sampling distance unit and reconstruction adequacy

A mathematical model (Kriging) was used to examine the effects of choosing various units of sampling distance 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 parallel transects along which a unit of sampling distance is set. Conformity of the reconstructed fields to those originally generated was evaluated by calculating their correlations. If a priori information on patch orientation is available, the optimal ratios of the distance between transects and the sampling distance unit to the corresponding autocorrelation radius for the field have been determined, ensuring the required match between the reconstructed field and its original. The experiments with a certain unit of sampling distance confirm that a posteriori determination of patch orientation allows reconstruction of the best field attainable on the basis of the data from the survey conducted. In cases of field movement, the criterion for choosing a survey direction is based on the relationship between the dimension of moving patches in the direction of movement and that of the surveyed area; the criterion remains valid when a unit of sampling distance is set along transects.