Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data

Abstract

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 spatiotemporal datasets and decompose the information efficiently. Principal Component Analysis (PCA), also known as Empirical Orthogonal Functions (EOF) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this work, 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) and 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 non-seasonal 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 inter-annual component of SM is shown to be highly correlated with El Niño 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 a working source code of the presented method for the interested reader in https://github.com/DiegoBueso/ROCK-PCA.

Kernel methods and their derivatives: Concept and perspectives for the earth system sciences

“…The most common applications in Earth system sciences are anomaly and target detection [ 65 ], the estimation of biogeochemical or biophysical parameters [ 66 – 68 ], dimensionality reduction [ 15 , 69 , 70 ], and the estimation of data interdependence [ 31 ]. However, so far multivariate spatio-temporal data problems have received comparable little attention [ 71 , 72 ], and in particular regarding the use of the derivatives of kernel methods [ 25 , 26 ]. This is surprising, given the high-dimensional nature of most spatio-temporal dynamics in most sub-domains of the Earth system, e.g.…”

Autocorrelation Metrics to Estimate Soil Moisture Persistence From Satellite Time Series: Application to Semiarid Regions

“…Nonetheless, differences are minor, and the combination of measurements from the two orbits has been adopted in a variety of studies to maximize data coverage (e.g. [51], [52]). Likewise, we averaged SMOS ascending and descending orbits into daily estimates and show results for the SMOS combined product only.…”

Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems

“…It consists in finding the rotation that maximizes the sum of the squared correlations between the original variables and the rotated PCs. While rotated PCAs have often been used in climate science (Mestas-Nuñez and Enfield 1999; Lian and Chen 2012; Chen et al 2017), they have rarely been applied in a complex domain such as the Fourier domain, and, in these rare examples (Wallace and Dickinson 1972;Bloomfield and Davis 1994;Bueso et al 2020), only using the varimax or promax criteria, which ignore the phase information and the spatial structure of the eigenvectors.…”