Evaluating the impacts of environmental factors on soil moisture temporal dynamics at different time scales

Soil moisture displays complex spatiotemporal patterns across scales, making it important to disentangle the impacts of environmental factors on soil moisture temporal dynamics at different time scales. This study evaluated the factors affecting soil moisture dynamics at different time scales using long-term soil moisture data obtained from Nebraska and Utah. The empirical mode decomposition method was employed to decompose soil moisture time series into different temporal components with several intrinsic mode functions (IMFs) and one residual component. Results showed that the percent variance contribution (PVC) of IMFs to the total soil moisture temporal variance tended to increase for the IMFs with longer time periods. It indicated that the long-term soil moisture variations in study regions were mainly determined by low-temporal frequency signals related to seasonal climate and vegetation variations. Besides, the PVCs at shortand medium-temporal ranges were positively correlated with climate dryness, while negatively at longer temporal ranges. Moreover, the results suggested that the impact of climate on soil moisture dynamics at different time scales might vary across different climate zones, while soil effect was comparatively less in both regions. It provides additional insights into understanding soil moisture temporal dynamics in regions with contrasting climatic conditions. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/wcc.2020.011 om http://iwaponline.com/jwcc/article-pdf/12/2/420/865738/jwc0120420.pdf 1 Qi Chai Tiejun Wang (corresponding author) Chongli Di Institute of Surface-Earth System Science, Tianjin University, Weijin Road 92, Tianjin 300072, China E-mail: tiejun.wang@tju.edu.cn Tiejun Wang Chongli Di Tianjin Key Laboratory of Earth Critical Zone Science and Sustainable Development in Bohai Rim, Tianjin University, Weijin Road 92, Tianjin 300072, China


INTRODUCTION
Soil moisture plays a pivotal role in understanding earth system dynamics and decision-making processes, e.g., from the global hydrological and energy cycles to agricultural management and drought assessment (Gerten et al. ; McColl et al. ). Meanwhile, soil moisture is also a key state variable that links a range of land surface and subsurface hydrological processes from catchment to global scales, such as evapotranspiration, surface runoff, infiltration, and groundwater recharge (Western et  The spatiotemporal variability in soil moisture can be affected by different environmental factors at varying spatiotemporal scales. For instance, depending on the spatial scale of interest, the factors that affect soil moisture spatial variability may vary noticeably, including factors at local scales and meteorological forcings at regional scales (Seneviratne et al. ). Specifically, soil moisture spatial variability at field scales is primarily linked to local factors, including soil, vegetation, and topography (Grayson &  were also marked variations in the factors affecting soil moisture temporal dynamics. This might be partly due to the fact that the mechanisms governing soil moisture processes vary with regions of contrasting environmental conditions. As such, further investigation is still warranted to explore the factors that affect soil moisture temporal dynamics across scales. The primary purpose of this study was to examine the impacts of external factors on soil moisture dynamics at different time scales. To this end, long-term daily soil moisture data were first obtained from the Nebraska Mesonet (NM) and Soil Climate Analysis Network (SCAN), which are located in the continental United States. The empirical mode decomposition (EMD) method was then utilized to decompose soil moisture time series obtained from the NM and SCAN stations into different components with varying temporal scales. Finally, meteorological (e.g., precipitation -P and potential evapotranspiration -ET p ) and soil textural (e.g., sand and clay fractions) data were compiled for the NM and SCAN sites, and used to assess their impacts on soil moisture dynamics at different time scales.

Descriptions of study sites and data
Soil moisture data analyzed in this study were retrieved from the NM and SCAN networks (Figure 1)   Specifically, the EMD method decomposes a data sequence x(t) into a set of intrinsic mode functions (IMFs; i.e., c j (t) with j ¼ 1, 2, …, M, where t is time and M is the number of the IMFs). Each IMF represents the temporal variation in x(t) at a distinct time scale. The remainder of the decomposition is summarized by a residual term r(t), which indicates the overall trend in x(t). Finally, x(t) can be mathematically written as: To compute IMFs, an automatic algorithm was adopted in this study, which is based on a sifting process (Huang et al. ) and needs to satisfy the following two constraints: (1) each IMF has the same number of extrema and zero-crossing points (or the numbers between extrema and zero-crossing points differ by one at most), and (2) each IMF has symmetric envelopes defined by local maxima and minima (i.e., the mean value of the envelopes obtained by fitting local maxima and minima is zero). The detailed computation procedures of IMFs are given as follows: (a) Identify local maxima and minima from x(t).
(c) Compute the average value of the envelopes (i.e., .

(e) Test h(t):
if h(t) satisfies the aforementioned two conditions, an IMF is obtained (i.e., IMF ¼ h(t)), and steps (a)-(d) are then repeated to obtain the next IMF by setting and repeat steps (a)-(d) until an IMF is found.
In practice, the above procedures are generally repeated multiple times before some stopping criteria are met to exit the iterations. In Huang et al. (), Equation (2) was chosen as the stopping criteria: where SD is computed from two consecutive sifting processes (i.e., h j(kÀ1) (t) and h jk (t)) during the (k À 1)th and kth iterations, respectively, for finding the jth IMF, and T   in these regions. In particular, the PVCs at short-and medium-temporal ranges were negatively correlated with P and positively correlated with ET P , while opposite correlations existed between PVC and P and ET P at longtemporal ranges in Utah. In addition, the correlations between PVC and P and ET P strengthened when the temporal scales became longer, further demonstrating the importance of climatic conditions in controlling long-term soil moisture temporal variability as discussed above.
The results shown in Table 2 suggested that high frequencies of soil moisture temporal variability (e.g., the IMFs within short-and medium-temporal ranges as defined in this study) became increasingly important in controlling the overall soil moisture temporal variability as the climate grew drier. As a result, positive correlations emerged between PVC and MDI and ET P = P, the latter of which is a widely used metric for quantitatively characterizing climate dryness. One of the possible explanations for the negative correlation between the PVC and climate dryness at long-temporal ranges is that the occurrence of rainfall is less frequent at sites with lower P and soil moisture temporal dynamics are thus more influenced by sporadic rainfall events with short-term signals. Therefore, due to a higher impact of sporadic rainfall events on soil moisture temporal dynamics, high frequencies of the IMFs tended to contribute more to the total soil moisture temporal variability.
Although the correlations between the PVC and climatic factors were not statistically significant for different IMF groups at the NM sites, the patterns observed in Utah appeared to be still valid in Nebraska. To further illustrate the relationships of the PVC with climatic factors, the relationship between the PVC and ET P = P is plotted in Figure 5 for both NM and SCAN networks, which shows weak positive correlations between the PVC and ET P = P within short-and medium-temporal ranges while there was a weak negative correlation within long-temporal ranges for the NM sites. Nevertheless, the weakened relationship between the PVC and ET P = P might be partly due to the wetter climatic conditions in Nebraska, indicating that the impact of climate dryness on soil moisture dynamics at different time scales might vary in regions with different climatic conditions. Therefore, further investigation is still warranted to examine soil moisture data from different climate zones. This finding suggested that the impact of climate on soil moisture temporal dynamics might vary across climate zones, which warrants further investigation on the impact of climate on soil moisture temporal dynamics within different climate zones.