Characterizing scale-specific environmental factors affecting soil organic carbon along two landscape transects
Soil organic carbon (SOC) is one of the most important soil properties affecting many other soil and environmental properties and processes. In order to understand and manage SOC effectively, it is important to identify the scale-specific main factors affecting SOC distributions, which in this study occurred in a watershed on the Loess Plateau. Two transects were selected that passed along the upper slopes on each side of the main gully of the Liudaogou watershed. Transect 1 (3411-m length) had 27 sampling sites at 131-m intervals; transect 2 (3597 m length) had 30 sampling sites at 124-m intervals. The two transects were chosen in order to compare landscape patterns of differing complexity that were in close proximity, which reduced the effects of factors that would be caused by different locations. The landscape of transect 1 was more complex due to the greater diversity in cultivation. Multivariate empirical mode decomposition (MEMD) decomposed the total variation in SOC and five selected environmental factors into four intrinsic mode functions (IMFs) and a residual according to the scale of occurrence. Scale-specific correlation analysis was used to identify significant relationships between SOC and the environmental factors. The dominant scales were those that were the largest contributors to the total SOC variance; for transect 1, this was the IMF 1 (scale of 403 m), whereas for transect 2, it was the medium scale of the IMF 2 (scale of 688 m). For both transects, vegetation properties (vegetation cover and aboveground biomass) were the main factors affecting SOC distributions at their respective dominant scales. At each scale, the main effective factors could be identified although at the larger scales, their contributions to the overall variance were almost negligible. The distributions of SOC and the factors affecting it were found to be scale dependent. The results of this study highlighted the suitability of the MEMD method in revealing the main scale-specific factors that affect SOC distributions, which is necessary in understanding and managing this important soil property.
Multivariate empirical mode decomposition
Despite empirical mode decomposition (EMD) becoming a de facto standard for time-frequency analysis of nonlinear and non-stationary signals, its multivariate extensions are only emerging; yet, they are a prerequisite for direct multichannel data analysis. An important step in this direction is the computation of the local mean, as the concept of local extrema is not well defined for multivariate signals. To this end, we propose to use real-valued projections along multiple directions on hyperspheres (n-spheres) in order to calculate the envelopes and the local mean of multivariate signals, leading to multivariate extension of EMD. To generate a suitable set of direction vectors, unit hyperspheres (n-spheres) are sampled based on both uniform angular sampling methods and quasi-Monte Carlo-based low-discrepancy sequences. The potential of the proposed algorithm to find common oscillatory modes within multivariate data is demonstrated by simulations performed on both hexavariate synthetic and real-world human motion signals.
Yeats, Eliot, Pound and the Politics of Poetry: Richest to the Richest
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