Use of a disjunctive kriging to model areas of high pelagic fish density in acoustic fisheries surveys

Abstract

Resume Schooling fish may aggrcgate in vcry high dcnsitics covering very small areas. Thus the probability of hitting such high-density spots during a large-scalc sampling is vcry low. Thc sampling fluctuations of the tail of the histogram are thought to be very significant. The stock biomass cstimate and its precision rely greatly on how prcciscly thc tail of the histogram can be sampled. In order to acquire clcmcnts for improving survey designs and abundance estimators WC study hcrc thc relation in space that thc high valucs have with the other values. A disjunctive kriging approach is used. Differcnt quantiles of the histogram arc codcd by indicators. The spatial structure of each indicator and its spatial covariation with the others are studied by computing cxpcrimcntal indicator variograms and cross-variograms. Such analysis is applied to dissect finely the spatial structure of a Norwegian herring stock sampled acoustically. It is shown that when going from low-density arcas to high-density ones, intcrmediate values are not necessarily crossed. Thus a particular disjunctive kriging modcl with no transition in space is wcll adaptcd to the herring data. The model is based on the regressions of each indicator on the one immediately below it. In the modcl one can cstimatc the probability for the fish density to trespass a given cut-off at a given location when knowing that the density trcspasscs lowcr cut-offs at surrounding points. It is shown on the data that the high densities are structured and show small aggregations. Then it is shown that having trespasscd a certain cut-off, i.e. inside the corresponding areas in space, the high-density aggregations can be considered to be positioned independently from the other values. These areas, where the structuring of the high values is not correlated to the structuring of the other values, are mapped using the fittcd disjunctive kriging model. The implications for survey designing of the existence of such areas and of their geometry are discussed. AIso discussed is the possibility of stratifying the data in spatially uncorrelated boxes when deriving the biomass estimate and its precision, on the basis of an observed spatial non-correlation property between the spatial distribution of different quantiles.