Empirical Orthogonal Maps (EOM) and Principal Spatial Patterns: Illustration for Octopus Distribution Off Mauritania Over the Period 1987–2017

Abstract

Analysis of spatiotemporal observations often leads to decomposition of the problem into a spatial part multiplied by a temporal part (factorization). Principal component analyses produce factors that are temporally uncorrelated but that remain spatially correlated, leading to incomplete factorization. Min–max autocorrelation factors developed many years ago are adapted here to ecological applications, leading to empirical orthogonal maps (EOMs). EOMs owe their name to the fact that they are indeed an enhancement of empirical orthogonal functions which extract the spatial patterns that explain most of the variability of a set of spatiotemporal observations indexed by time. Application on a time series of 61 scientific monitoring surveys targeting octopus distribution off the Mauritanian coast indicates that ten basic maps are sufficient to recover 68% of the total variability, and that the first two EOMs explain 38.4% of this variability. This manuscript clarifies the concept of orthogonality between factors in a spatial context. This provides the conditions for using Euclidean distance between spatial distributions, which in turn supports the reduction of a large set of spatial distributions into a small subset of basic spatial distributions explaining most of the variability within the set of input maps.