Application of multivariate empirical mode decomposition for revealing scale-and season-specific time stability of soil water storage

• Dominant scales were smaller in shallower depths than those in deeper depths.
• Time stability increased with scale and was the strongest at dominant scales.
• Influence of depth on time stability was related to scale and sampling season.
• MEMD combined with rank correlation can reveal scale specific time stability.

Spatial patterns of soil water storage (SWS), the total amount of water stored in soil at a given depth interval, tend to be similar if we measure at different times. This is characterized as time stability and can be used to optimize sampling design. The objective of this study was to examine the scale- and season-specific time stability of SWS spatial patterns at seven depth intervals (at every 20 cm down to 140 cm) in a hummocky landscape. Soil water content was measured 20 times using time domain reflectometry and a neutron probe along a transect of 128 points over a four-year period and converted to SWS by multiplying by the depth intervals. Multivariate empirical mode decomposition (MEMD) was used to decompose the spatial series of SWS into six or seven (depending on depth) components known as intrinsic mode functions (IMFs). Each IMF represents a specific scale of SWS. Spearman's rank correlation coefficients between IMFs from different measurement dates were used to characterize the time stability of SWS at different scales. The variance of each IMF and its ratio to the variance of the original SWS series was calculated. The dominant scale, which has the maximum ratio of variance to the original variances, was 104–128 m (IMF5) for the depth intervals of 0–20 cm to 60–80 cm and 315–412 m (IMF7) for the depth intervals of 80–100 cm to 120–140 cm. Time stability gradually increased with spatial scales and was the strongest at the dominant scale. At any scale, time stability was the strongest within the same season and the weakest between different seasons. This study indicates that MEMD combined with Spearman's rank correlation analysis has great potential for revealing the scale specific time stability of SWS.