Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data

Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we propose a nonlinear PCA method to deal with spatio-temporal Earth system data. The proposed method, called rotated complex kernel PCA (ROCK-PCA for short), works in reproducing kernel Hilbert spaces to account for nonlinear processes, operates in the complex kernel domain to account for both space and time features, and adds an extra rotation for improved flexibility. The result is an explicitly resolved spatio-temporal decomposition of the Earth data cube. The method is unsupervised and computationally very efficient. We illustrate its ability to uncover spatio-temporal patterns using synthetic experiments and real data. Results of the decomposition of three essential climate variables are shown: satellite-based global gross primary productivity (GPP), soil moisture (SM), and reanalysis sea surface temperature (SST) data. The ROCK-PCA method allows identifying their annual and seasonal oscillations, as well as their nonseasonal trends and spatial variability patterns. The main modes of variability of GPP and SM match expected distributions of land-cover and eco-hydrological zones, respectively; the interannual component of SM is shown to be highly correlated with El Nino Southern Oscillation (ENSO) phenomenon; and the SST annual oscillation is perfectly uncoupled in magnitude and phase from the global warming trend and ENSO anomalies, as well as from their mutual interactions. We provide the working source code of the presented method for the interested reader in https://github.com/DiegoBueso/ROCK-PCA.