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

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.     

Patchy distribution fields: a zigzag survey design and reconstruction adequacy

A mathematical model was used to examine the effects of a zigzagsurvey design 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 set of transects forming a zigzag. Adequacyof the reconstructed fields to those originally generated was evaluated by calculating their correlations (r). A prioriinformation on the autocorrelation radius for the field in thedirection of a survey (R) allows optimization of survey design and the algorithm of data analysis. A patchy field can be reconstructed properly (r > 0.80) if the distance between transects D < (1.0–1.5)R. If a priori information onthe field is not available, the autocorrelation radius should bedetermined when reconstructing the field, i.e. a posteriori. In cases of field movement, the criterion for choosing a survey direction is based on the relationship betweenthe dimension of moving patches in the direction of movement andthat of the surveyed area. The results obtained indicate that, for a fixed transect spacing, zigzag pattern allow less adequatereconstruction of an original distribution field (in cases of both immovable and movable fields) than corresponding parallel pattern.     

Patchy distribution fields: sampling distance unit of a zigzag survey and reconstruction adequacy

A mathematical model was used to examine the effects of choosingvarious units of sampling distance of a zigzag survey on the adequacy of reconstructing patchy distribution fields. The modelsimulates fish or plankton patches (or gaps) of different shapesand spatial orientations, and an acoustic survey by zigzag or parallel transects along which a unit of sampling distance is set. Adequacy of the reconstructed fields to those originally generated is evaluated by calculating their correlations (r). A priori information on the autocorrelation radii for the field in the directions of the survey (R_s) and perpendiculardirection (R_p) allows optimisation of the survey design andthe algorithm of data analysis. A field can be reconstructed properly (r² > 0.70) if the distance between transects D < (1.0–1.5)R_s and the unit of sampling distance d < (1.0–1.5)R_p. A posteriori determination of patchorientation allows reconstruction of the best field attainable onthe basis of the survey data. In cases of field movement, if thedimension of patches in the direction of movement exceeds that ofa surveyed area, a survey in the opposite direction gives bestresults; in contrast, if the dimension of moving patches is smaller than that of a surveyed area, it is reasonable to carryout a survey in the same direction. The criterion remains validwhen a survey is carried out by zigzag transects and a unit ofsampling distance is set along them. The results obtained indicate that, for a fixed transect spacing and a given number of sampling points on each full transect, zigzag pattern allowsless adequate reconstruction of an original distribution field (in cases of both immovable and movable fields) than corresponding parallel pattern.