Time-Lagged Correlation between Soil Moisture and Intra-Annual Dynamics of Vegetation on the Mongolian Plateau

: Soil moisture is a reliable water resource for plant growth in arid and semi-arid regions. Characterizing the interaction between soil moisture and vegetation is important for assessing the sustainability of terrestrial ecosystems. This study explores the spatiotemporal characteristics of four soil moisture layers (layer 1: 0–7 cm, layer 2: 7–28 cm, layer 3: 28–100 cm, and layer 4: 100–289 cm) and the time-lagged correlation with the normalized difference vegetation index (NDVI) for different vegetation types on an intra-annual scale on the Mongolian Plateau (MP). The most signiﬁcant results indicated that: (1) the four layers of soil moisture can be roughly divided into rapid change (layers 1 and 2), active (layer 3), and stable (layer 4) layers. The soil moisture content in the different vegetation regions was forest > grassland > desert vegetation. (2) The soil moisture in layer 1 showed the strongest positive correlation with NDVI in the whole area; meanwhile, the soil moisture of layers 2 and 3 showed the strongest negative correlation with the NDVI mainly in grassland and desert, and layer 4 showed the strongest negative correlation with the NDVI in the forest. (3) Mutual responses of NDVI and deep layer soil moisture required a longer time compared with the shallow layer. In the annual time scale, the NDVI was affected by the change in soil moisture in most of the study area, except for coniferous forest and desert vegetation regions. (4) Under the different stages of vegetation change, the soil moisture changes advance than NDVI about 3 months during the greening stage, while the NDVI changes advance than soil moisture by 0.5 months during the browning stage. Regardless of the stage, changes in soil moisture are initiated from the shallow layer and advance to the deep layer. The results of this study provide deep insight into the relationship between soil moisture and vegetation in arid and semi-arid regions.


Introduction
Soil moisture is an important driver of the productivity and sustainability of terrestrial ecosystems [1,2], and a limiting factor for plant transpiration and photosynthesis, which determines the vegetation type and structure during ecological construction, particularly in arid and semiarid regions [3]. At the same time, vegetation in an ecosystem controls the soil moisture distribution pattern [4], and affects soil moisture to varying degrees in two opposing aspects through the ecological functions of water storage and conservation, and the absorption and consumption of soil moisture [5,6]. Plant biological processes also affect soil moisture content [7,8]. Different plant species cause different rainfall-runoff and evaporation, thereby inducing spatial distribution of soil moisture at various depths and different hydraulic properties [9,10]. Generally, we hope to discover the time-lagged correlation between soil moisture and vegetation, e.g. the correlation at the various soil depths, under the different vegetation types, and in different growth stages of vegetation, at different stages of vegetation changes across the MP. The results of this study contribute to the sustainable management of terrestrial ecosystems in the MP and other similar regions.

Study Area
The study area ranged over the Mongolian Plateau (MP) (87°43′-126°04′E and 37°22′-53°20′N), covering the entire Mongolian People's Republic and the Inner Mongolia Autonomous Region of China, with an area of 2.74 × 10 6 km 2 [30] and an elevation of 85-4203 m ( Figure 1). This region is the largest arid/semi-arid plateau in the Northern Hemisphere, and obvious zonality is produced by the distribution of hydrothermal conditions, which is prompted by the differences in the geographical location and underlying surface [34]. The regional mean annual precipitation is approximately 300-400 mm, which decreases from north to south and east to west. The MP's mean temperature is between −1.7 and 5.6 °C, and is characterized by a large temperature difference between day and night, abundant sunlight, strong ultraviolet radiation, gales, and fast weather changes [35,36].
The ecosystem is mainly composed of grassland (70%) [37], with relatively small areas of forests in the north and northeast, shrubs in the south and southeast, farmland and sparse vegetation in the Gobi desert, and sandy areas in the southwest, which form an important and unique geographical landscape of Eurasia [30]. Therefore, we divided the vegetation into three primary types namely, I: forest, II: grassland, and III: desert vegetation, and further classified them into secondary types namely I-1, coniferous forest; I-2, broad-leaved forest; II-1, forest steppe; II-2, typical steppe; II-3, desert steppe [38]. The MP serves as an important and ideal region for research on the response of arid and semi-arid ecosystems to global climate change [39].

Data Sources
The monthly average soil moisture data were acquired from the fifth and latest global climate reanalysis datasets (ERA5  The ecosystem is mainly composed of grassland (70%) [37], with relatively small areas of forests in the north and northeast, shrubs in the south and southeast, farmland and sparse vegetation in the Gobi desert, and sandy areas in the southwest, which form an important and unique geographical landscape of Eurasia [30]. Therefore, we divided the vegetation into three primary types namely, I: forest, II: grassland, and III: desert vegetation, and further classified them into secondary types namely I-1, coniferous forest; I-2, broad-leaved forest; II-1, forest steppe; II-2, typical steppe; II-3, desert steppe [38]. The MP serves as an important and ideal region for research on the response of arid and semi-arid ecosystems to global climate change [39].

Data Sources
The monthly average soil moisture data were acquired from the fifth and latest global climate reanalysis datasets (ERA5 improved with several modifications, representing a decade of research and development in modeling and data assimilation. The ERA soil moisture dataset was validated against the available data from multiple sources, and the use of this dataset for testing model simulations on daily to seasonal time scales has been confirmed [40,41]. In this study, we used the ERA5 soil moisture data from 1982 to 2015, and the depths of the four soil layers ranged from 0 to 7, 7-28, 28-100, and 100-289 cm, respectively. To calculate the correlation between soil moisture and vegetation, we used the resample tool of the raster processing module in ArcGIS10.5, which is consistent with the spatial resolutions of soil moisture and NDVI. In order to improve the spatial resolution of the data, the soil moisture data were resampled to 8 km using the bilinear resampling mode selected in this study. The bilinear calculates the value of each pixel by averaging (weighted for distance) the values of the surrounding four pixels, which is suitable for continuous data.
Precipitation and evaporation data were obtained from the ERA5 dataset. The Global Inventor Modeling and Mapping Studies (GIMMS) NDVI3g data  were used to explore the time-lagged correlation with soil moisture. The NDVI dataset was obtained from the GIMMS group of the US National Oceanic and Atmospheric Administration's Advanced Very High-Resolution Radiometer (AVHRR). The dataset had a spatial resolution of 8 × 8 km and a temporal resolution of 15 days [42]. It has been shown to be more accurate for monitoring vegetation activity and phenological changes [43].

Data Smoothing and Up-Sampling
The multi-year averages for the 15-day NDVI and monthly soil moisture data were calculated. The resolution of the time series data of the NDVI and soil moisture at intraannual stages must be unified, for which the monthly soil moisture data were up-sampled to a 15-day temporal resolution. First, the Whittaker smoother was used [44], followed by Fourier interpolation to increase the sampling of the soil moisture data [45]. Then, the original monthly-scale time-series data were transformed to the frequency domain, and the sampling points (filling the blank values) were expanded in the frequency domain series. Finally, inverse Fourier transformation was used to increase the sampling to a 15-day time scale (1-24 periods).

Time-Lagged Correlation Analysis
In this study, based on the 15-day soil moisture and NDVI data, the maximum correlation coefficient, and the lag time between the two were calculated using time-lagged correlation analysis [45]: (1) First, the correlation coefficients between NDVI and soil moisture were calculated for different time lags as follows: where r k (x,y) refers to the series of correlation coefficients between the NDVI and soil moisture under time lag k, x i and y i are the series of soil moisture and NDVI, respectively; n is the length of the series; and k is the time lag (k = 0, ±1, ±2, . . . ), where k ≤ n/4. As the correlation analysis used 15-day interval data at an annual scale (n = 24), the maximum value of k was 6 (6 × 15 = 90 days). (2) Next, the maximum values of the correlation coefficients for each time lag were calculated as follows: where r 1 is the maximum value of the correlation coefficient between the NDVI and soil moisture under time lag k 1 ; r 2 is the minimum value of the correlation coefficient between the NDVI and soil moisture under time lag k 2 , and R and K refer to the extremum value and time lag of the cross-correlation between the NDVI and soil moisture, respectively. Within this, k > 0 indicates that the soil moisture change affects the NDVI variation; k < 0 indicates that the NDVI change affects soil moisture variations; and k = 0 indicates synchronous intra-annual changes in soil moisture and NDVI.

Defining the Different Stages of Vegetation Change
To identify the relationship between the soil moisture and NDVI at different stages of vegetation change, the phenological nodes of the vegetation were further extracted. Firstly, a curve was fitted for the cumulative NDVI based on a regression logistic model, which was first proposed by Zhang et al. [46].
where y(t) is the cumulative NDVI at day t, d is the initial background NDVI value, and c is the difference between the maximum and minimum cumulative NDVI values. Therefore, c + d is the maximum cumulative NDVI, while a and b are the fitting parameters [47]. According to the fitting curve, the greening stage of the vegetation was from January to August (Figure 2a) while the browning stage was from August to December (Figure 2b).   Next, according to the curvature curve [46,47] and curvature extremum [48] of the cumulative NDVI logistic fitted curve method, the maximum (SOS_K) and minimum (1 + z) 4 + (bcz) 2 1.5 (6) where z = e a+bt α is the angle (in radians) of the unit tangent vector at time t along a differentiable curve, and s is the unit length of the simulated NDVI curve. Finally, the rate of curvature change (RCC) method [49] was used to define the corresponding times for the maximum curvature change rate during the greening stage as the start of the growing season (SOS_RCC) and the minimum curvature change rate during the browning stage at the end of the growing season (EOS_RCC).
where a, b, c, and z represent the same values as in Equations (5) and (6). is relatively large, accounting for 37% and 18%, respectively. In general, the soil moisture content increased with increasing depth. The soil moisture contents in layers 1 and 2 were relatively lower than those in layers 3 and 4. In the horizontal distribution, the soil moisture decreased from east to west and from north to south in each layer. The spatial heterogeneity was obvious, which was consistent with the distribution of different vegetation types in the MP. Among them, the soil moisture content was highest in vegetation type I, which was higher than 0.3 m 3 /m 3 , followed by the soil moisture content in the II vegetation type area, which was approximately 0.2-0.3 m 3 /m 3 in II-1 vegetation type, 0.1-0.3 m 3 /m 3 in II-2 vegetation type, and less than 0.2 m 3 /m 3 in II-3 vegetation type. The soil moisture content in the III vegetation type was the lowest, with a content of less than 0.1 m 3 /m 3 . The order of the soil moisture contents at different depths for the different vegetation types was I > II (II-1 > II-2 > II-3) > III.

Temporal Distribution of the Soil Moisture at Various Depth
Data smoothing and up-sampling methods were used to process the soil moisture data on a daily scale. Figure 4 shows the variations in soil moisture over an average period between 1982 and 2015 at various depths in intra-annual at daily scale across the MP. The uniformity and stability of the soil moisture increased with depth, which is the soil moisture volatility at layers 1, 2, and 3, and the stability in layer 4 was obvious.

Temporal Distribution of the Soil Moisture at Various Depth
Data smoothing and up-sampling methods were used to process the soil moisture data on a daily scale. Figure 4 shows the variations in soil moisture over an average period between 1982 and 2015 at various depths in intra-annual at daily scale across the MP. The uniformity and stability of the soil moisture increased with depth, which is the soil moisture volatility at layers 1, 2, and 3, and the stability in layer 4 was obvious.

Spatial Characteristics of the Time-Lagged Correlation between NDVI and Soil Moisture
The extremum correlation coefficient and lag time between NDVI and soil moisture at various depths in different vegetation types are shown in Figure 5. Regarding the timelagged correlation between the soil moisture and NDVI in layer 1 (Figure 5a-1,a-2), the extremum correlation coefficient was positively correlated with the lag time according to the spatial distribution. When the extremum correlation coefficient was positive, the lag time was positive; otherwise, it was negative. For layer 1, the positive correlation between NDVI and soil moisture accounted for 86% of the area. The NDVI was affected by soil moisture and accounted for 64% (1< k < 3), mainly distributed in the II-1 and II-2 vegetation regions. The synchronization between the changes in the soil moisture and NDVI accounted for 22% (k = 0), mainly distributed in vegetation areas II-3 and III. The negative correlation between the NDVI and soil moisture was 14% (-3 < k < -1), mainly distributed in vegetation region I. For layer 2, the positive correlation between the NDVI and soil moisture was 45%, and the negative correlation was 55% (Figure 5b-1,b-2). The NDVI was affected by soil moisture, accounting for 45% (1< k < 2) and was mainly distributed in the I and II-1 vegetation regions. In comparison, the NDVI change the soil moisture area, occupying 55% of the study area, and the lag time was comparatively longer (−6 < k < −4), and was mainly distributed in the II-2, II-3, and III vegetation types. For layer 3, the negative correlation between the NDVI and soil moisture accounted for 78%, while 22% of the area showed a positive correlation (Figure 5c-1,c-2). The area of soil moisture affecting the NDVI change accounted for 69%. Among them, the NDVI lag change than soil moisture was 1-3 months for the II-2 and II-3 vegetation types and 0.5 month in the I type. The area in which the NDVI change affected the soil moisture accounted for 26%, with a comparatively longer lag time (−4 < k < −2), mainly distributed in vegetation types II-1 and III. In addition, the area in which the changes in the soil moisture and NDVI were synchronized accounted for 5% (k = 0). For layer 4, the areas of positive and negative correlations between the NDVI and soil moisture accounted for 59% and 41%, respectively (Figure 5d-1,d-2). Among them, the area of NDVI affected by the soil moisture was mainly distributed in I-2 and II vegetation types, and the lag times in I-2 and II vegetation types were k

Spatial Characteristics of the Time-Lagged Correlation between NDVI and Soil Moisture
The extremum correlation coefficient and lag time between NDVI and soil moisture at various depths in different vegetation types are shown in Figure 5. Regarding the timelagged correlation between the soil moisture and NDVI in layer 1 ( Figure 5(a-1,a-2)), the extremum correlation coefficient was positively correlated with the lag time according to the spatial distribution. When the extremum correlation coefficient was positive, the lag time was positive; otherwise, it was negative. For layer 1, the positive correlation between NDVI and soil moisture accounted for 86% of the area. The NDVI was affected by soil moisture and accounted for 64% (1< k < 3), mainly distributed in the II-1 and II-2 vegetation regions. The synchronization between the changes in the soil moisture and NDVI accounted for 22% (k = 0), mainly distributed in vegetation areas II-3 and III. The negative correlation between the NDVI and soil moisture was 14% (-3 < k < -1), mainly distributed in vegetation region I. For layer 2, the positive correlation between the NDVI and soil moisture was 45%, and the negative correlation was 55% ( Figure 5(b-1,b-2)). The NDVI was affected by soil moisture, accounting for 45% (1< k < 2) and was mainly distributed in the I and II-1 vegetation regions. In comparison, the NDVI change the soil moisture area, occupying 55% of the study area, and the lag time was comparatively longer (−6 < k < −4), and was mainly distributed in the II-2, II-3, and III vegetation types. For layer 3, the negative correlation between the NDVI and soil moisture accounted for 78%, while 22% of the area showed a positive correlation ( Figure 5(c-1,c-2)). The area of soil moisture affecting the NDVI change accounted for 69%. Among them, the NDVI lag change than soil moisture was 1-3 months for the II-2 and II-3 vegetation types and 0.5 month in the I type. The area in which the NDVI change affected the soil moisture accounted for 26%, with a comparatively longer lag time (−4 < k < −2), mainly distributed in vegetation types II-1 and III. In addition, the area in which the changes in the soil moisture and NDVI were synchronized accounted for 5% (k = 0). For layer 4, the areas of positive and negative correlations between the NDVI and soil moisture accounted for 59% and 41%, respectively ( Figure 5(d-1,d-2)). Among them, the area of NDVI affected by the soil moisture was mainly distributed in I-2 and II vegetation types, and the lag times in I-2 and II vegetation types were k = 6 and 1 < k < 4, respectively. The area of soil moisture affected by NDVI was mainly distributed in vegetation types I-1 and III, and the lag time k = −6. The time-lagged correlation between the NDVI and soil moisture at various depths was different on an intra-annual scale in the different ecological regions of the MP. Therefore, in this study, different vegetation cover types were used to analyze the interrelationship between NDVI and soil moisture at various depths.
Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 19 = 6 and 1< k < 4, respectively. The area of soil moisture affected by NDVI was mainly distributed in vegetation types I-1 and III, and the lag time k = −6. The time-lagged correlation between the NDVI and soil moisture at various depths was different on an intraannual scale in the different ecological regions of the MP. Therefore, in this study, different vegetation cover types were used to analyze the interrelationship between NDVI and soil moisture at various depths.  Furthermore, we used the different vegetation types on the MP to calculate the mean value of the extremum correlation coefficient and time lag between the soil moisture at various depths and NDVI (Figure 6a). The NDVI and layer 1 soil moisture were positively correlated in all vegetation types; the extremum correlation coefficient in II-2 and II-3 vegetation types was the highest, followed by the I, II-2, and III regions, respectively. There was a positive correlation between layer 2 soil moisture and NDVI in regions I and II-1, and the extremum correlation coefficient was high, with a negative correlation in the II-2, II-3, and III regions, but the extremum correlation coefficient was low. There was a negative correlation between layer 3 soil moisture and NDVI, and the extremum correlation coefficient in region II was the highest, followed by regions III, I-2, and I-1. The correlation between layer 4 soil moisture and NDVI was negative in regions I and II-1, and in I-2 had the highest correlation, while the II-2, II-3, and III regions had a positive correlation, and the extremum correlation coefficient was low.
etation types was the highest, followed by the I, II-2, and III regions, respectively. There was a positive correlation between layer 2 soil moisture and NDVI in regions I and II-1, and the extremum correlation coefficient was high, with a negative correlation in the II-2, II-3, and III regions, but the extremum correlation coefficient was low. There was a negative correlation between layer 3 soil moisture and NDVI, and the extremum correlation coefficient in region II was the highest, followed by regions III, I-2, and I-1. The correlation between layer 4 soil moisture and NDVI was negative in regions I and II-1, and in I-2 had the highest correlation, while the II-2, II-3, and III regions had a positive correlation, and the extremum correlation coefficient was low.
The time lag between NDVI and soil moisture at various depths is shown in Figure  6b. Soil moisture changes in layers 1 and 2 affect the NDVI (k = 1-2) in regions I and II, and layer 1 soil moisture synchronous changes with NDVI in III. Layer 2 soil moisture was affected by the NDVI changes in regions II-2, II-3, and III, while soil moisture change lag was longer than NDVI in II-2 and II-3 (k = −5) and shorter in III (k = −2). Layer 3 soil moisture change affected the NDVI in regions I, II-1, and II-3, and NDVI changes lag time was shorter (k = 1-3). The NDVI change affected the soil moisture in regions II-2 and III; among them, the soil moisture change lag time was shorter in II-2 (k = −1) and longer in III (k = −5). Layer 4 soil moisture change affected the NDVI in I-2 and II regions, and NDVI changes lag time was longer (k = 3-5). The NDVI change affected the soil moisture in the I-1 and III regions, while the soil moisture change lag time was longer (k = −5).  The time lag between NDVI and soil moisture at various depths is shown in Figure 6b. Soil moisture changes in layers 1 and 2 affect the NDVI (k = 1-2) in regions I and II, and layer 1 soil moisture synchronous changes with NDVI in III. Layer 2 soil moisture was affected by the NDVI changes in regions II-2, II-3, and III, while soil moisture change lag was longer than NDVI in II-2 and II-3 (k = −5) and shorter in III (k = −2). Layer 3 soil moisture change affected the NDVI in regions I, II-1, and II-3, and NDVI changes lag time was shorter (k = 1-3). The NDVI change affected the soil moisture in regions II-2 and III; among them, the soil moisture change lag time was shorter in II-2 (k = −1) and longer in III (k = −5). Layer 4 soil moisture change affected the NDVI in I-2 and II regions, and NDVI changes lag time was longer (k = 3-5). The NDVI change affected the soil moisture in the I-1 and III regions, while the soil moisture change lag time was longer (k = −5).

Variations Trend of NDVI and Soil Moisture at Different Stages of Vegetation Change
The maximum change curvature of NDVI and soil moisture at different stages of vegetation change was obtained using the logistic fitted curve method. The NDVI continued to increase during the vegetation greening stage (Figure 7a). Corresponding to the start of the growing season (SOS_RCC) on around day 90, the layer 1 soil moisture curve showed the highest decrease curvature (layer 1_-k), while the layer 2 soil moisture curve showed the highest decrease curvature (layer 2_-k) on day 110. As the NDVI changed to the highest increased curvature (SOS_k/NDVI_k) on day 115, layer 1 soil moisture presented the lowest valley in the year, while the layer 3 soil moisture change curve presented the highest decrease curvature (layer 3_-k). With the continuous increase in NDVI, the soil moisture declined rapidly in layer 3, and showed an upward trend in layers 1 and 2. The soil moisture in layers 1 and 2 showed the highest upward curvature on day 152 (layer 1_k) and day 162 (layer 2_k), respectively. The corresponding soil moisture in layer 3 decreased to its lowest value on day 165, and then showed an upward trend. On day 200, with the soil moisture rapidly increasing in layer 3 (layer 3_k), the soil moisture of layer 4 also showed an obvious upward trend. At the same time, the soil moisture in layer 1 had the highest value of the year. The curvature of the soil moisture change curve in layer 4 was smaller during the entire vegetation greening stage.
The NDVI continued to decrease during the vegetation browning stage (Figure 7b). With the rapid decline of NDVI, the soil moisture change curve of layer 3 showed the highest decrease in curvature (layer 3_-k) on day 250. On day 260, the highest decreasing curvature of the soil moisture change curve of layer 1 (layer 1_-k) was observed, which corresponded to the highest decreasing curvature of the NDVI curve (NDVI_-k). The highest decreased curvature of the soil moisture change curve of layer 2 was observed on day 270 (layer 2_-k). Subsequently, the soil moisture in layer 3 increased rapidly after day 275. The change curve of soil moisture in layer 3 showed the highest increasing curvature (layer 3_k), and the soil moisture in layer 4 showed a downward trend corresponding to the end of the growing season (EOS_RCC).

Variations Trend of NDVI and Soil Moisture at Different Stages of Vegetation Change
The maximum change curvature of NDVI and soil moisture at different stages of vegetation change was obtained using the logistic fitted curve method. The NDVI continued to increase during the vegetation greening stage (Figure 7a). Corresponding to the start of the growing season (SOS_RCC) on around day 90, the layer 1 soil moisture curve showed the highest decrease curvature (layer 1_-k), while the layer 2 soil moisture curve showed the highest decrease curvature (layer 2_-k) on day 110. As the NDVI changed to the highest increased curvature (SOS_k/NDVI_k) on day 115, layer 1 soil moisture presented the lowest valley in the year, while the layer 3 soil moisture change curve presented the highest decrease curvature (layer 3_-k). With the continuous increase in NDVI, the soil moisture declined rapidly in layer 3, and showed an upward trend in layers 1 and 2. The soil moisture in layers 1 and 2 showed the highest upward curvature on day 152 (layer 1_k) and day 162 (layer 2_k), respectively. The corresponding soil moisture in layer 3 decreased to its lowest value on day 165, and then showed an upward trend. On day 200, with the soil moisture rapidly increasing in layer 3 (layer 3_k), the soil moisture of layer 4 also showed an obvious upward trend. At the same time, the soil moisture in layer 1 had the highest value of the year. The curvature of the soil moisture change curve in layer 4 was smaller during the entire vegetation greening stage.
The NDVI continued to decrease during the vegetation browning stage (Figure 7b). With the rapid decline of NDVI, the soil moisture change curve of layer 3 showed the highest decrease in curvature (layer 3_-k) on day 250. On day 260, the highest decreasing curvature of the soil moisture change curve of layer 1 (layer 1_-k) was observed, which corresponded to the highest decreasing curvature of the NDVI curve (NDVI_-k). The highest decreased curvature of the soil moisture change curve of layer 2 was observed on day 270 (layer 2_-k). Subsequently, the soil moisture in layer 3 increased rapidly after day 275. The change curve of soil moisture in layer 3 showed the highest increasing curvature (layer 3_k), and the soil moisture in layer 4 showed a downward trend corresponding to the end of the growing season (EOS_RCC).

Time-Lagged Correlation between the NDVI and Soil Moisture at Different Stage of Vegetation Changes
In this study, we investigated the time lag between the changes in the NDVI and soil moisture at various depths in different stages of vegetation changes using the statistics of the pixel number proportion (Figure 8). In the greening stage, the soil moisture in layer 1, 2, 3 changes advance than NDVI about 3 months (k = −6). However, there were differences in the relationship between the NDVI and soil moisture at various depths in the different vegetation types during the browning stage. The change of layer 1 soil moisture lagged than NDVI by 0.5-1 months (k = 1, 2) in I and II regions, and 3 months (k = 6) in III region. The change of layer 2 soil moisture lagged NDVI by 0.5 month (k = 1), except for regions II-2 and III. The changes in the NDVI and soil moisture were synchronized (k = 0) in region II-2, while the NDVI changes were lagged 2 months (k = −4) with those of the soil moisture in region III. The changes in the NDVI and soil moisture at layer 3 differed between the individual vegetation types. The changes in the NDVI lagged behind the soil moisture by 1 month (k = −2) in region I-1, and changes advance about 0.5 month (k = 1) and 2.5 months (k = 5) in I-2, III regions and II region, respectively. The NDVI changes advanced soil moisture at layer 4 in the greening stage, while the NDVI lagged behind the soil moisture changes in the browning stage. However, the changes in the NDVI and soil moisture in layer 4 were obviously synchronized in region III.

Time-Lagged Correlation between the NDVI and Soil Moisture at Different Stage of Vegetation Changes
In this study, we investigated the time lag between the changes in the NDVI and soil moisture at various depths in different stages of vegetation changes using the statistics of the pixel number proportion (Figure 8). In the greening stage, the soil moisture in layer 1, 2, 3 changes advance than NDVI about 3 months (k = −6). However, there were differences in the relationship between the NDVI and soil moisture at various depths in the different vegetation types during the browning stage. The change of layer 1 soil moisture lagged than NDVI by 0.5-1 months (k = 1, 2) in I and II regions, and 3 months (k = 6) in III region. The change of layer 2 soil moisture lagged NDVI by 0.5 month (k = 1), except for regions II-2 and III. The changes in the NDVI and soil moisture were synchronized (k = 0) in region II-2, while the NDVI changes were lagged 2 months (k = −4) with those of the soil moisture in region III. The changes in the NDVI and soil moisture at layer 3 differed between the individual vegetation types. The changes in the NDVI lagged behind the soil moisture by 1 month (k = −2) in region I-1, and changes advance about 0.5 month (k = 1) and 2.5 months (k = 5) in I-2, III regions and II region, respectively. The NDVI changes advanced soil moisture at layer 4 in the greening stage, while the NDVI lagged behind the soil moisture changes in the browning stage. However, the changes in the NDVI and soil moisture in layer 4 were obviously synchronized in region III. Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 19

Spatiotemporal Characteristics of the Soil Moisture in MP
On the vertical scale, according to the four-layer soil moisture distribution of intraannual, the soil moisture can be roughly divided into the rapid change (layers 1 and 2), active (layer 3), and stable (layer 4) layers [50]. Across the MP, the uniformity and stability of the soil moisture increased with depth. Similar results were found by Zhao et al. in the Loess Plateau, China [51]. To further illustrate the relationship between the soil moisture at various depths and precipitation/evaporation according to the different vegetation types, a partial correlation analysis was performed (Figure 9) due to the susceptibility of soil moisture to rainfall, vegetation transpiration, and soil evaporation [52,53]. It was found that the precipitation and evaporation correlation with soil moisture decreased with increasing depth. Among them, there was a positive correlation with the soil moisture in layer 1 and layer 2, and the correlation coefficient was higher in layer 1 than layer 2. The negative correlation with soil moisture in layer 3 and layer 4, and the correlation coefficient was higher in layer 3 than layer 4. The above results agree with previous studies that the immediate effects of external factors on soil moisture are weakened by soil depth, thus ensuring that the soil moisture in deeper layers is less disrupted [54][55][56].
On the horizontal scale, the correlation coefficient between the precipitation/ evaporation and soil moisture in layers 1 and 2 was higher than in layers 3 and 4 in region I. The deep rooting pattern of trees, unlike other plants, allows for the movement of water from deep to shallow soil horizons [9]. This specific water pumping property, known as hydraulic lifting [57,58], can have an important ecological role in terms of water redistribution in soils [59]. We found significant differences in the relationship between precipitation and soil moisture in the different forest types. The I-1 region is mainly distributed in

Spatiotemporal Characteristics of the Soil Moisture in MP
On the vertical scale, according to the four-layer soil moisture distribution of intraannual, the soil moisture can be roughly divided into the rapid change (layers 1 and 2), active (layer 3), and stable (layer 4) layers [50]. Across the MP, the uniformity and stability of the soil moisture increased with depth. Similar results were found by Zhao et al. in the Loess Plateau, China [51]. To further illustrate the relationship between the soil moisture at various depths and precipitation/evaporation according to the different vegetation types, a partial correlation analysis was performed (Figure 9) due to the susceptibility of soil moisture to rainfall, vegetation transpiration, and soil evaporation [52,53]. It was found that the precipitation and evaporation correlation with soil moisture decreased with increasing depth. Among them, there was a positive correlation with the soil moisture in layer 1 and layer 2, and the correlation coefficient was higher in layer 1 than layer 2. The negative correlation with soil moisture in layer 3 and layer 4, and the correlation coefficient was higher in layer 3 than layer 4. The above results agree with previous studies that the immediate effects of external factors on soil moisture are weakened by soil depth, thus ensuring that the soil moisture in deeper layers is less disrupted [54][55][56].
On the horizontal scale, the correlation coefficient between the precipitation/ evaporation and soil moisture in layers 1 and 2 was higher than in layers 3 and 4 in region I. The deep rooting pattern of trees, unlike other plants, allows for the movement of water from deep to shallow soil horizons [9]. This specific water pumping property, known as hydraulic lifting [57,58], can have an important ecological role in terms of water redistribution in soils [59]. We found significant differences in the relationship between precipitation and soil moisture in the different forest types. The I-1 region is mainly distributed in high latitudes, where the temperature is relatively low, little evaporation and less precipitation.
At the same soil type, the root system of I-2 is deeper and more developed, and can infiltrate the water into the deep soil layer following precipitation, therefore, the soil moisture of this area is easily disturbed by precipitation and highly correlated with precipitation compared with the I-1 region [60].
In the II-2 region, the negative correlation coefficient between precipitation/ evaporation and layer 3 soil moisture is higher than that of other layers, primarily due to the same period of the hydrothermal and growing season in the study area [49]. The results indicated that the soil moisture in layer 3 was the most important water source during plant growth in the II-2 region. However, the correlation between soil moisture and evaporation was higher than that with precipitation in regions II-3 and III. Evaporation is highly sensitive to variations in soil moisture in arid and semi-arid regions [61].
On the temporal scale, the soil moisture content was higher from June to October, which shows the regularity of soil water consumption in late spring and early summer, soil water accumulation in late summer and early autumn, and soil water consumption in late autumn and early winter, which is consistent with previous findings [62,63].
(a) (b) Figure 9. Partial correlation coefficient between the precipitation (a), evaporation (b), and soil moisture at various depths for different vegetation types.

Relationship between the Soil Moisture and NDVI in MP
The analysis of the time-lagged correlation between the NDVI and soil moisture at various depths showed significant differences in the interaction characteristics of different ecological communities. The strongest positive correlation between the NDVI and soil moisture was in layer 1, which was mainly attributed to the simultaneous effects of precipitation and water fixation by vegetation. Conversely, the strongest negative correlation between the NDVI and soil moisture in the forest was in layer 4, while that for grassland and desert vegetation was in layer 3. This was attributed to the widely penetrating roots of desert and grassland vegetation within the 0-70 cm soil layer [64], and the forest roots deeper than 100 cm [65] on the MP (Figure 10). We also found that the correlation between two different forest types was different in the same soil layer, mainly due to the different root distribution depths of the two forest types. Since previous studies have shown that coinciding with rooting patterns, the soil water content at 50 and 70 cm depth remains low in the I-1, where coarse roots are found in deeper soil horizons, more water is directed deeper in the II-2 [60]. Mutual responses of NDVI and soil moisture in the deep layer required a longer time compared with the shallow layer. This is mainly due to the small change in deep layer soil moisture, which makes the vegetation insensitive to changes. In the annual time scale, the NDVI is affected by the change of soil moisture in most areas of the study area, except for I-1 and III regions. This results due to the less precipitation and low groundwater level in I-1 and III regions, thereby these regions are rarely disturbed by external factors. Studies have shown that the soil moisture "memory" increases with In the II-2 region, the negative correlation coefficient between precipitation/ evaporation and layer 3 soil moisture is higher than that of other layers, primarily due to the same period of the hydrothermal and growing season in the study area [49]. The results indicated that the soil moisture in layer 3 was the most important water source during plant growth in the II-2 region. However, the correlation between soil moisture and evaporation was higher than that with precipitation in regions II-3 and III. Evaporation is highly sensitive to variations in soil moisture in arid and semi-arid regions [61].
On the temporal scale, the soil moisture content was higher from June to October, which shows the regularity of soil water consumption in late spring and early summer, soil water accumulation in late summer and early autumn, and soil water consumption in late autumn and early winter, which is consistent with previous findings [62,63].

Relationship between the Soil Moisture and NDVI in MP
The analysis of the time-lagged correlation between the NDVI and soil moisture at various depths showed significant differences in the interaction characteristics of different ecological communities. The strongest positive correlation between the NDVI and soil moisture was in layer 1, which was mainly attributed to the simultaneous effects of precipitation and water fixation by vegetation. Conversely, the strongest negative correlation between the NDVI and soil moisture in the forest was in layer 4, while that for grassland and desert vegetation was in layer 3. This was attributed to the widely penetrating roots of desert and grassland vegetation within the 0-70 cm soil layer [64], and the forest roots deeper than 100 cm [65] on the MP (Figure 10). We also found that the correlation between two different forest types was different in the same soil layer, mainly due to the different root distribution depths of the two forest types. Since previous studies have shown that coinciding with rooting patterns, the soil water content at 50 and 70 cm depth remains low in the I-1, where coarse roots are found in deeper soil horizons, more water is directed deeper in the II-2 [60]. Mutual responses of NDVI and soil moisture in the deep layer required a longer time compared with the shallow layer. This is mainly due to the small change in deep layer soil moisture, which makes the vegetation insensitive to changes. In the annual time scale, the NDVI is affected by the change of soil moisture in most areas of the study area, except for I-1 and III regions. This results due to the less precipitation and low groundwater level in I-1 and III regions, thereby these regions are rarely disturbed by external factors. Studies have shown that the soil moisture "memory" increases with depth that in the top 1 m layer being 2.5 months in northern China [66], so the deeper layer's soil moisture is not sensitive to changes in NDVI.
albedo and Bowen ratio, precipitation and water fixation by the dense vegetation [13,14]. At the start of the browning stage, the soil moisture in layers 1 and 2 began to decline a few days earlier than the NDVI. When the browning rate reached its highest point, the soil moisture simultaneously increased in layer 3 and decreased in layer 4. Due to the weakened water fixation effect and larger evaporation during autumn, which leads to the rapid loss of soil moisture in the shallow layers, the soil moisture in layer 4 moves to the upper layers for evaporation [68]. We also found that the changes in soil moisture at each level during the browning stage were less dynamic and decreased at a constant rate in comparison with that during the greening stage. This is mainly because the speed of soil thawing in spring is greater than the speed of freezing in autumn [69].

Conclusions
In this study, we investigated the spatiotemporal characteristics of soil moisture at various depths and the time-lagged correlation between with NDVI according to the different stages of vegetation changes in different vegetation types on the MP. We found that the uniformity and stability of soil moisture increased with depth, indicating the fine soil moisture conditions of the deepest layer. According to the four layers, soil moisture However, the correlation between the NDVI and soil moisture at various depths in different vegetation types is associated with the root length and water consumption intensity during the different stages of vegetation changes [45]. For example, at the start of the growing season (SOS_RCC), on day 90, the soil moisture in layers 1 and 2 began to decline, indicating that vegetation growth requires water absorption, which mainly comes from the shallow soil layers. When the vegetation growth reached the highest rate (SOS_K), on day 115, the soil moisture in layers 1 and 2 reached the minimum value during the year, while that in layer 3 began to decline rapidly. This shows that vegetation requires significant water consumption during the rapid growth stage, and when the soil moisture supply of layers 1 and 2 becomes insufficient, water is absorbed from the soil moisture of layer 3 [67]. To a certain extent, the soil moisture also began to increase with vegetation growth, which indicates that the increase in vegetation changed the surface albedo and Bowen ratio, precipitation and water fixation by the dense vegetation [13,14]. At the start of the browning stage, the soil moisture in layers 1 and 2 began to decline a few days earlier than the NDVI. When the browning rate reached its highest point, the soil moisture simultaneously increased in layer 3 and decreased in layer 4. Due to the weakened water fixation effect and larger evaporation during autumn, which leads to the rapid loss of soil moisture in the shallow layers, the soil moisture in layer 4 moves to the upper layers for evaporation [68]. We also found that the changes in soil moisture at each level during the browning stage were less dynamic and decreased at a constant rate in comparison with that during the greening stage. This is mainly because the speed of soil thawing in spring is greater than the speed of freezing in autumn [69].

Conclusions
In this study, we investigated the spatiotemporal characteristics of soil moisture at various depths and the time-lagged correlation between with NDVI according to the different stages of vegetation changes in different vegetation types on the MP. We found that the uniformity and stability of soil moisture increased with depth, indicating the fine soil moisture conditions of the deepest layer. According to the four layers, soil moisture change characteristics can be roughly divided into the rapid change layers (layer 1 and 2), active layer (layer 3) and stable layer (layer 4). The soil moisture content increased with the value of NDVI, which indicated that the vegetation is one of the important controlling factors of the soil moisture spatial distribution.
The extremum correlation between the soil moisture at various depths and NDVI showed that the strongest positive correlation between with NDVI and soil moisture at layer 1 in all vegetation types and has the highest correlation coefficient in desert steppe region. Except for the coniferous forest region, the negative correlation between with NDVI and soil moisture at layer 3 in the study area, especially the highest correlation in typical steppe region. The soil moisture at layer 4 has a higher negative correlation between NDVI in forests than other vegetation types, and in particular the highest in boreal-leaved forest. These results indicate that the length of plant roots determines the different correlations between with NDVI and different layers soil moisture.
Mutual responses NDVI and soil moisture in the deep layer required a longer time than the shallow layer. In the annual time scale, the NDVI is affected by the change of soil moisture in most areas of the study area, except for coniferous forest and desert vegetation regions. In different stages of vegetation change, the soil moisture changes advance NDVI about 3 months in the greening stage, while the NDVI changes advance soil moisture by 0.5 months in the browning stage. Regardless of which stage of vegetation changes, the changes of soil moisture start from the shallow layer, then to deep layer. In addition, the peak and valley values of soil moisture changes intra-annually are very consistent with the vegetation phenology period and, therefore, the annual changes in the soil moisture can be used as an important basis for the extraction of the phenological features of vegetation.
Author Contributions: L.N., conceptualization, methodology, writing-original draft; J.Z., conceptualization, supervision; R.N., writing-review and editing; Y.B., software. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the International (Regional) Cooperation and Exchange Programs, grant number 41961144019.