Correcting for the effect of daylight in abundance estimation of juvenile haddock (Melanogrammus aeglefinus) in the North Sea: an application of kriging with external drift

Kriging with external drift allows for the estimation of a spatial variable when this is driven by an external parameter, through a response function only known up to constants. This is advantageous when the effect of the parameter exists or is postulated but is not known precisely. A postulated day/night effect on catch rates in trawl survey data can be accounted for even when the day and night levels are poorly known. Similarly, the effect of time of day on catch rates can be accounted for supposing, for instance, that it varies as a cosine but with unknown coefficients. The methods are illustrated on catches of age 1 to 3 haddock in the North Sea from the first quarter International Bottom Trawl Survey (IBTS) 1983–1997, where daylight effects exist without being precisely known. A cross-validation on data values is used to measure the improvement of the methods over Ordinary Kriging. It reveals excessive variations in the parameters of individual annual variograms. Using a generic variogram appears an improvement, though not changing the global abundance. The results of kriging with external drift are compared to Ordinary Kriging, IBTS standard indices and the assessment made by the International Council for the Exploration of the Seas (ICES), in terms of global abundance and mortality coefficients. The level of agreement with the ICES assessment was similar for the abundance indices obtained by the different methods. This indicates that the IBTS standard indices are remarkably robust against sampling irregularities. Nonetheless, External Drift Kriging resulted in higher indices than the IBTS standard ones, notably for the 1-group. External Drift Kriging is capable of compensating successfully for daylight effects and provides a valuable tool for the calculation of survey-based abundance indices.