An ensemble modelling approach for spatiotemporally explicit estimation of fish distributions using data assimilation

Abstract

This article presents a novel method for estimating large scale spatiotemporal distribution patterns of fish populations modelled at the individual level. A single realization of an individual-based model calibrated on historic data has weak predictive capacity, given the underlying uncertainties faced when modelling a relatively small cluster of individuals operating in a high dimensional spatial plane. By incorporating real-time data sources to update these models, we can improve their predictive capacity. When correcting estimates from a large population of individuals, we don’t have access to information about individual histories, such as information derived from tagging data. We propose mapping individuals to derived density matrices, which can be corrected using conventional data sources which describe a mass of individuals e.g. catch data. An ensemble of derived states are used as forecast inputs to an assimilation procedure, that calculates an analysis state matrix of the same form. An individuals’ position and biomass values are updated based on the analysis values. To assess the effect of corrections, we setup a simulation experiment to explore the impact the number of measurement points has on the updated spatiotemporal distribution. The measurement points were sampled from derived states of a twin model that resembles the original model. The output of the twin model serves as the true distribution. With an increasing number of measurement points the centre of mass of the modelled distribution converges on the true distribution and the two distributions increase in overlap. Additionally, the absolute error between model and true values decreases. This estimation method, applied to individual-based models and coupled with real-time fisheries data, can improve spatially explicit estimates of fish distributions.