Evaluating the uncertainty of abundance estimates from acoustic surveys using geostatistical simulations

Geostatistical simulations, which can reproduce the spatial variability of a variable, are particularly helpful in estimating the uncertainty associated with the combination of different sources of variability. Acoustic surveys offer an example of such complex situations, where different data (e.g. acoustic backscatter, fish length, and fish age) must be combined to estimate abundance and its associated uncertainty. In this paper, the uncertainty of Scottish herring acoustic-survey estimates is investigated using these techniques. A specific multivariate, geostatistical model is used to describe the structural relationships, which includes highly skewed distributions of the acoustic-backscatter data and incorporates relationships between depth, mean length, and proportions-at-age. Conditional simulations, i.e. geostatistical simulations that honour the data values known at the data points, are used to generate multiple realizations of acoustic backscatter, mean length, and proportions-at-age. These are combined to produce multiple realizations of herring density over the sampled domain. Multiple realizations of total abundance and abundance-at-age are then provided. The uncertainty is assessed using basic statistics to track the significant variations of these values over the period 1989-2005. Higher coefficients of variation (CVs) are found on average for extreme ages (ages 1, 2i, 8, and 9+); otherwise, CVs are mostly around 12% for abundance-at-age and around 10% for total abundance.