International audienceModel drift in the Labrador Sea in eddy permitting model simulations is examined using a series of configurations based on the NEMO numerical framework. There are two phases of the drift that we can identify, beginning with an initial rapid 3-year period, associated with the adjustment of the model from its initial conditions followed by an extended model drift/adjustment that continued for at least another decade. The drift controlled the model salinity in the Labrador Sea, over-riding the variability. Thus, during this initial period, similar behavior was observed between the inter-annually forced experiments as with perpetual year forcing. The results also did not depend on whether the configuration was global, or regional North Atlantic Ocean. The inclusion of an explicit sea-ice component did not seem to have a significant impact on the interior drift. Clear cut evidence for the drift having an advective nature was shown, based on two separate currents/flow regimes. We find, as expected, the representation of freshwater in the sub-polar gyre's boundary currents important. But this study also points out another, equally important process and pathway: the input of high salinity mode water from the subtropical North Atlantic. The advective regime is dependent on the details of the model, such as the representation of the freshwater transport in the model's East Greenland Current being very sensitive to the strength of the local sea surface salinity restoring (and the underlying field that the model is being restored to)

Principal component analysis (PCA) has been generalized to complex principal component analysis (CPCA), which has been widely applied to complex-valued data, 2-dimensional vector fields, and complexified real data through the Hilbert transform. Nonlinear PCA (NLPCA) can also be performed using auto-associative feed-forward neural network (NN) models, which allows the extraction of nonlinear features in the data set. This paper introduces a nonlinear complex PCA (NLCPCA) method, which allows nonlinear feature extraction and dimension reduction in complex-valued data sets. The NLCPCA uses the architecture of the NLPCA network, but with complex variables (including complex weight and bias parameters). The application of NLCPCA on test problems confirms its ability to extract nonlinear features missed by the CPCA. For similar number of model parameters, the NLCPCA captures more variance of a data set than the alternative real approach (i.e. replacing each complex variable by 2 real variables and applying NLPCA). The NLCPCA is also used to perform nonlinear Hilbert PCA (NLHPCA) on complexified real data. The NLHPCA applied to the tropical Pacific sea surface temperatures extracts the El Niño-Southern Oscillation signal better than the linear Hilbert PCA.

Abstract.Complex principal component analysis (CPCA) is a useful linear method for dimensionality reduction of data sets characterized by propagating patterns, where the CPCA modes are linear functions of the complex principal component (CPC), consisting of an amplitude and a phase. The use of non-linear methods, such as the neural-network based circular non-linear principal component analysis (NLPCA.cir) and the recently developed non-linear complex principal component analysis (NLCPCA), may provide a more accurate description of data in case the lower-dimensional structure is non-linear. NLPCA.cir extracts non-linear phase information without amplitude variability, while NLCPCA is capable of extracting both. NLCPCA can thus be viewed as a non-linear generalization of CPCA. In this article, NLCPCA is applied to bathymetry data from the sandy barred beaches at Egmond aan Zee (Netherlands), the Hasaki coast (Japan) and Duck (North Carolina, USA) to examine how effective this new method is in comparison to CPCA and NLPCA.cir in representing propagating phenomena. At Duck, the underlying low-dimensional data structure is found to have linear phase and amplitude variability only and, accordingly, CPCA performs as well as NLCPCA. At Egmond, the reduced data structure contains non-linear spatial patterns (asymmetric bar/trough shapes) without much temporal amplitude variability and, consequently, is about equally well modelled by NLCPCA and NLPCA.cir. Finally, at Hasaki, the data structure displays not only non-linear spatial variability but also considerably temporal amplitude variability, and NLCPCA outperforms both CPCA and NLPCA.cir. Because it is difficult to know the structure of data in advance as to which one of the three models should be used, the generalized NLCPCA model can be used in each situation.

Complex principal component analysis (CPCA) is a linear multivariate technique commonly applied to complex variables or 2‐dimensional vector fields such as winds or currents. A new nonlinear CPCA (NLCPCA) method has been developed via complex‐valued neural networks. NLCPCA is applied to the tropical Pacific wind field to study the interannual variability. Compared to the CPCA mode 1, the NLCPCA mode 1 is found to explain more variance and reveal the asymmetry in the wind anomalies between El Niño and La Niña states.