This work stands apart from its neighbors: there is almost no one nearby, the closest neighbor is at a distance of 0.53, and only one out of eight works touches on space telescopes and exoplanet atmospheres. Around it lie studies of deserts, weather on lone planets, bacteria in soil pores, liquid boundaries, AI weather models, molecular motion, and underground structures. This article takes a different path: it takes global satellite data on soil moisture and applies a new decomposition method to uncover hidden patterns.
The authors construct the ROCK PCA method. First, they apply the Hilbert transform to soil moisture time series, obtaining complex data. Then they move from the covariance matrix to the Gram matrix, reducing computational complexity from quadratic to linear in the number of pixels. This allows direct introduction of a kernel, specifically a complex RBF kernel with parameter σ. Finally, they apply oblique promax rotation, which finds physically interpretable components by optimizing the varimax criterion. The method is validated on a toy example with a known function, then applied to SMOS data.
The first four components explain 98.2% of the total variance: PC1 accounts for 70.6%, PC2 for 13.5%, PC3 for 10.2%, and PC4 for 4.3%. PC1 shows the annual cycle with a period of 12 months and a global spatial distribution. PC2 and PC4 are resonances of the annual cycle with periods of 6 and 4 months, linked to oscillations of the intertropical convergence zone and seasonal transitions. PC3 has a non-seasonal oscillation with a period of about 4.5 years, which falls within the range of El Niño anomalies (3 to 7 years). The Spearman correlation between PC3 and the ENSO4 index reaches 0.8 with a p-value less than 10⁻¹⁶. The spatial correlation map reveals wet and dry patterns: increased moisture in eastern Europe, southeastern South America, and the southern United States, and decreased moisture along the eastern coast of Australia, northern South America, and the northern Gulf of Guinea.
Unlike neighboring works that use standard methods or models for specific regions, this article offers a fast nonlinear method that separates spatial and temporal components and makes them physically interpretable. This is the first test of such an approach on global soil moisture data. The method can be applied to any spatial-temporal remote sensing data.
The method can be extended to other satellite products, such as sea surface temperature or vegetation indices. It may also enable the study of finer nonlinear interactions and teleconnections. Applying it to longer time series, once data spanning decades accumulate, is also promising.
The method is useful for climatology, hydrology, agrometeorology, and drought monitoring. It allows a better understanding of global moisture patterns and their connection to climate phenomena.
Apply the method to data from other satellite missions, such as SMAP, and compare results. Investigate the connection of the identified modes with other climate indices, such as the Pacific Decadal Oscillation.
For Earth sciences, the question of nonlinear interactions between ocean, atmosphere, and land remains open. This method offers a tool for detecting such connections in observational data, which could help understand the mechanisms of teleconnections.
The observation period includes the 2015–2016 El Niño event, which was nicknamed 'Godzilla' due to its strength.