On the sensitivity of field reconstruction and prediction using 1 Empirical Orthogonal Functions derived from gappy data

4 Empirical Orthogonal Function (EOF) Analysis is commonly used in the climate sciences 5 and elsewhere to describe, reconstruct, and predict highly dimensional data fields. When 6 data contain a high percentage of missing values (i.e. “gappy”), alternate approaches must 7 be used in order to correctly derive EOFs. The aims of this paper are to assess the accuracy 8 of several EOF approaches in the reconstruction and prediction of gappy data fields, using 9 the Galapagos Archipelago as a case study example. EOF approaches included least-squares 10 estimation via a covariance matrix decomposition (LSEOF), “Data Interpolating Empiri11 cal Orthogonal Functions” (DINEOF), and a novel approach called “Recursively-Subtracted 12 Empirical Orthogonal Functions” (RSEOF). Model-derived data of historical surface Chloro13 phyll a concentrations and sea surface temperature, combined with a mask of gaps from 14 historical remote sensing estimates, allowed for the creation of “true” and “observed” fields 15 by which to gauge the performance of EOF approaches. Only DINEOF and RSEOF were 16 found to be appropriate for gappy data reconstruction and prediction. DINEOF proved to be 17 the superior approach in terms of accuracy, especially for noisy data with a high estimation 18 error, although RSEOF may be preferred for larger data fields due to its relatively faster 19 computation time. 20