1 Introduction

A dried soil layer (DSL) has often been found in water-deficient regions around the world, for example, the Loess Plateau of China (Li 1983), eastern Amazonia (Jipp et al. 1998), and southern Australia (Robinson et al. 2006). A DSL is formed by long-term water shortage (evapotranspiration > precipitation) and/or excessive depletion of deep soil moisture by vegetation (Wang et al. 2009; Shangguan 2007; Chen et al. 2008). In general, a DSL has the following characteristics: (1) a soil water content (SWC) range between the permanent wilting point and the stable field capacity (SFC); (2) a well-defined location at a certain soil depth, mainly in deeper layers that may extend to 10 m; and (3) a persistent spatial and temporal distribution that cannot be reversed by rainfall infiltration in a normal year. (Li 1983; Wang et al. 2008, 2011; Li et al. 2008). A DSL could negatively affect the water cycle in soil–plant–atmosphere systems by preventing water interchanges between upper soil layers and groundwater (Chen et al. 2008) and the phenological pattern (Valdez-Hernandez et al. 2010; Lucero et al. 2000). In addition, a DSL potentially leads to soil degradation, failure of afforestation, regional vegetation die-off, and aridity in the local climatic environment (Breshears et al. 2005; García et al. 2008; Ashton and Kelliher 1996).

In general, 60% of field capacity (FC) has been considered equivalent to SFC based on the soil textures of soils found on the Loess Plateau (Chen et al. 2008; Wang et al. 2010b). A soil layer with a SWC lower than the SFC would thus be considered a DSL (Wang et al. 2010b). Four indices can be used to quantify the extent of a DSL: (1) DSL thickness (DSLT); (2) the depth where DSL begins to form (DSL forming depth, DSLFD); (3) mean SWC over the DSLT within the soil profile (i.e., soil water content within the DSL, DSL–SWC); and (4) the SFC (Wang et al. 2011).

The plant–soil–atmosphere environment is a mutually interacting system where plants (especially trees) form pathways for deep soil water transport to the atmosphere. Soil water enters the plants through their roots and is transpired and evaporates above the ground (Robinson et al. 2006; Yu et al. 2007). As an integrated response of the soil–plant system to climate change (e.g., decreasing rainfall, global warming, increasingly extreme drought events) and ill-advised land management measures (e.g., introducing exotic species, planting at too high a density), DSLs have been attracting increasing interest in recent years, including studies on DSL definition and types (Yang and Tian 2004; Li 1983; Chen et al. 2008), basic characteristics (Han et al. 1990; Yang 2001; Wang et al. 2008; Huang and Gallichand 2006), and influencing factors (Li 2001; Yang 1996; Han et al. 1990; Meiners et al. 1984). Several studies have shown that a DSL is often less severe in the order of (1) forestland > grassland > cropland; (2) vegetation-covered land > bare land; (3) steep slopes > gentle slopes; (4) hill and ridge > tableland or gully bottom; and (5) arid > semiarid > semi-humid (Han et al. 1990; Li 1983; Chen et al. 2008).

The DSLs under forestland have been identified as the worst among different land-use types (Wang et al. 2010a); thus, they have attracted more attention. Robinson et al. (2006) assessed the spatial patterns of soil water depletion by Eucalyptus in southern Australia. The authors found that eucalypt species can exploit soil water to depths of at least 8–10 m within 7 years of planting. In addition, the lateral influence of mallee belts ranged from 15 to 42 m as indicated by SWCs that were depleted to wilting point. The authors then used these data to attempt adjusting the catchment water balances that prevent groundwater recharge (due to land-use change), leading to landscape salinization. Wang et al. (2009) reported that the soil water depletion depth of planted grassland, scrubland, and forest in a semiarid area on the Loess Plateau reached 15.5, 22.4, and 21.5 m, respectively. Liu et al. (2010) quantified the extent of deep soil water recharge and soil water profile dynamics during 1987–2003. A DSL between 2 and 3 m depths would be fully recharged at least once in about 10 years for all existing cropping systems, excluding continuous alfalfa.

Wang et al. (2010b) analyzed DSL formation and development processes under planted non-native and natural vegetation in the semiarid region of the Loess Plateau. The rate of formation and DSLT depended on vegetation type and its growth year. In addition, the use of natural vegetation succession management principles would possibly reduce soil desiccation during vegetation restoration. Furthermore, the spatial variability of DSL across the complex landscape of the Plateau was investigated (Wang et al. 2010a). DSLFD and DSLT demonstrated an obvious spatial heterogeneity (which can be explained by land use, rainfall, and soil type), with ranges of 33.9 and 125 km, respectively. However, the nature of the spatial distribution of DSLs under forestland is still unknown.

The severity of the DSL, represented by DSLFD, DSLT, and DSL–SWC, is site specific. DSL characteristics and dynamic properties depend on many interrelated links among climate, soil, terrain, and vegetation (Hernández-Santana et al. 2008; Li et al. 2002; Vörösmarty and Moore 1991). However, the measurement of DSL indices in the field is expensive, time-consuming, and technically difficult. This limitation is especially true for cases investigating regional DSL distribution patterns, where the collection of deep soil samples and laboratory analysis of large numbers of samples usually limit the efficiency of related research work. Therefore, developing a model to predict DSLs is desirable. Li (1983) and Liu et al. (2010) presented a regression model for predicting DSLFD. However, equations for use in modeling other DSL indices, such as DSLT and DSL–SWC, are scarce.

In the present study, 125 typical forestlands on the Loess Plateau of China were selected. The objectives were: (1) to measure the DSL indices (DSLT and DSL–SWC) of the sample sites and related environmental factors (i.e., topographic and meteorological elements, plant and soil properties); (2) to investigate the DSL spatial distribution and its variation characteristics; (3) to identify the main factors controlling DSL distribution at a regional scale; and (4) to develop the regression models of DSLT and DSL–SWC. Understanding the spatial pattern of DSL can provide invaluable information for plant construction and layout, as well as forest management. The regression models can help ascertain the DSL level at regional scale using existing soil, plant, climate, and topographic data without DSL field measurements.

2 Materials and Methods

2.1 Study Area

Experiments were conducted across the entire Loess Plateau of China (34º–45º5′ N, 101º–114º33′ E), which covers a total area of 620,000 km2. The elevation range is 200–3,000 m above mean sea level (Fig. 1). The loess–paleosol layers of the Plateau are 30–80 m thick. The annual solar radiation ranges from 5.0 × 109 to 6.7 × 109 J m−2. The annual mean temperature is 3.6°C in the northwest and 14.3°C in the southeast. The annual evaporation is 1,400–2,000 mm (He et al. 2003; Shi and Shao 2000).

Fig. 1
figure 1

Position of the Loess Plateau in China (a) and the location of 125 sampling sites across the entire Plateau (b)

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The Loess Plateau is in the continental monsoon climate region. The annual precipitation ranges from 150 mm in the northwest to 800 mm in the southeast. The annual mean precipitation is 466 mm, 55–78% of which falls from June–September. The soils are sandy in texture in the northwest and more clayey in the southeast. We have also evaluated the vertical distribution of soil texture at four sites to a depth of 6 m at 10-cm intervals for the 0- to 200-cm soil layer, and at 20-cm intervals for the 200- to 600-cm layer in typical subregions of the Loess Plateau; results indicated that clay, silt, and sand contents within the 0–600 cm depth did not change significantly but fluctuated slightly, from which it can be inferred that soil texture within a 6-m profile is homogenous. The main geomorphic landforms are Yuan (large flat surfaces with little or no erosion), ridges, hills, and gullies (Yang and Shao 2000; Shi and Shao 2000).

To date, on the Loess Plateau, DSLs have been found under the following natural vegetation species: Quercus liaotungensis, Populus davidiana, Crategus pinnatifida Bunge, Malus kansuensis, Campylotropis macrocarpa, and Sophora viciifolia Hance. In addition, DSL has been found under the following non-native, planted species: Pinus tabulaefomis, Robinia pseudoscacia L., Salix psammophylla, and Caragana microphylla Lam. (Wang et al. 2004; Hou et al. 2000).

2.2 Soil Sampling and Measurements

2.2.1 Samples for Measuring Profile Soil Water Content

An intensive soil sampling strategy was devised, and 125 sampling sites were selected and located using a GPS receiver (5 m in precision). The sampling sites generally were in forestland (wide range of naturally grown trees and shrubs) across the entire Loess Plateau. The sampling locations on the Plateau are shown in Fig. 1.

Soil samples for measuring SWCs were collected using a soil auger (5 cm in diameter) at 10-cm increments along the soil profile to a depth of 0–600 cm. SWC (g H2O/100 g dry soil) was determined by determining mass loss during drying (oven-drying at 105°C to constant mass). The samples were collected from April 9 to November 6, 2008.

The data from soil located within the 0- to 100-cm layer were excluded to avoid the seasonal SWC variation caused by rainfall during the sampling period. Attention was focused on analyzing SWC below 100 cm depth from the surface, under such conditions, comparing soil water contents at different sites is reasonable (Li 1983; Chen et al. 2008).

2.2.2 Samples for Measuring Soil Properties

For each site, a total of 250 soil samples (125 undisturbed soil cores and 125 disturbed soil samples) were collected to determine soil properties potentially related to DSL. Undisturbed soil cores were removed from the soil surface layer (0–5 cm) and placed in metal cylinders (diameter, 5 cm; length, 5 cm). These cores were used to measure saturated hydraulic conductivity (Ks), bulk density (BD), capillary water content (CWC), and saturated soil water content (SSWC). Disturbed soil samples were collected to determine particle size distribution and soil organic carbon (SOC).

The Ks of the undisturbed soil cores was determined using a constant head method (Klute and Dirksen 1986; Wang et al. 2008). The BD was calculated from the volume–mass relationship for each core sample (Wang et al. 2008). CWC and SSWC were determined from the loss of mass during drying of soil samples that either had been allowed to wet up through capillary action alone or were saturated (oven-drying at 105°C to constant mass). The disturbed soil samples were air-dried and passed through 1- or 0.25-mm meshes. The soil particle composition of the samples that passed through the 1-mm mesh was measured by laser diffraction using a Mastersizer 2000 (Malvern Instruments, Malvern, England) (Liu et al. 2005). The SOC of the samples that passed through the 0.25-mm mesh was measured using dichromate oxidation (Nelson and Sommers 1982).

2.3 Evaluation Indices of DSL and their Calculations

In the present study, two evaluation indices of DSL (DSLT and DSL–SWC) were considered. For each sampling site, DSLT (cm) was calculated using the following equation (Wang et al. 2010b):

$$ {\text{DSLT}} = 10 \times \sum\limits_{i = 11}^{n} {S(\theta_{i} - \theta_{\text{SFC}} )} $$
(1)

where \( S(\theta_{i} - \theta_{\text{SFC}} ) = \left\{ {\begin{array}{*{20}c} {0,} & {\theta_{i} - \theta_{\text{SFC}} > 0} \\ {1,} & {\theta_{i} - \theta_{\text{SFC}} \le 0} \\ \end{array} } \right. \), (i = 11, 12, 13, …, n), n = 60; θ i is the SWC of the ith soil layer; θ SFC is the SWC at the SFC, defined as θ SFC = θ FC × 60%; and θ FC is the SWC at FC. After DSLT was calculated, the corresponding DSL–SWC could be determined by calculating the mean values of SWC with DSLT.

2.4 Determination of Factors Potentially Related to DSL

The factors (a total of 28 variables) potentially related to DSL were comprehensively considered to develop a sound equation for predicting DSL. These factors were divided into four classes as follows.

2.4.1 Topographic Factors

Topographic factors (10 in total) were collected in two ways. (1) Direct measurements were taken at each site, where the geographic coordinates (including altitude, longitude, and latitude) were determined using a GPS receiver (5 m location precision). The slope gradient and aspect were measured using a geological compass. (2) Factors were derived from a 100 m × 100 m digital elevation model (DEM, in Albers coordinates). Five topographic parameters were calculated from the DEM through ArcInfo GIS software: total curvature, profile (vertical) curvature (CV), plan (horizontal) curvature (CH), slope length (SL), and topographic wetness index (TWI).

2.4.2 Plant Factors

The vegetation condition was carefully investigated at each site. Plant species, diameter at breast height (DBH), plant height, vegetation coverage (VC), growth age, and row and column spacing were included in the study. DBH (mean value of at least 10 trees around a central sampling point within a 20 m × 20 m plot) and row and column spacings were measured with a measuring tape. Plant height, which was the mean value of at least 10 trees, and VC within the plots were estimated by visual observation against a 5-m ruler for scale. Planting density (PD) was calculated based on the value of row and column spacing as well as the number of trees. The growth age of the plants was obtained from local people who were familiar with the land-use history.

In total, five plant factors (i.e., DBH, VC, PD, growth age, and plant height) were selected as the factors potentially related to DSL.

2.4.3 Soil Parameters

Based on the measurements in Sect. 2.2.2, nine soil parameters were chosen as potentially related factors of DSL. These variables were Ks, SSWC, CWC, BD, FC, SOC, clay, silt, and sand content.

2.4.4 Meteorological Factors

Climatic conditions largely determine the amount of soil water on the Loess Plateau. However, directly measuring the meteorological factors for each site was impractical. Therefore, meteorological data (51 years, 1951–2001) were first obtained from 64 meteorological stations located on the Loess Plateau (the data were provided by the National Climatic Center of the China Meteorological Administration). Second, the mean values of the meteorological factors were calculated, and their spatial distribution maps were produced using the kriging method. Third, re-sampling in ArcInfo GIS software (version 9.2) was used to extract the meteorological factors for each sampling point from these maps. Thus, approximations of the four meteorological factors of precipitation, evaporation, temperature, and aridity (= evaporation/precipitation) were obtained for each site.

2.5 Selection Procedures of DSL Dominant Factors

After the 28 potentially related factors were obtained, four main steps were conducted to select the best representative factors of DSL variation. The regression model of DSL can then be developed with fewer input variables.

  1. 1.

    Correlation analysis. Pearson correlation analysis was used to select the related factors of DSL from the 28 potentially related factors. Only significantly correlated factors were considered in the further analyses. The factors weakly correlated with DSL were neglected.

  2. 2.

    Principal component analysis (PCA) was then performed for the significantly correlated variables. PCA is a special case of factor analysis. This analysis transforms the original set of inter-correlated variables into a new set of an equal number of independent uncorrelated variables or principal components (PCs). PCs with high eigenvalues and comprising variables with high factor loading were assumed to be the variables that best represent the system attributes. Therefore, only the PCs with eigenvalues >1.0 were taken into account. Within each PC, only the variables with highly weighted factor loading, that is, those with absolute values for factor loading within 10% of the highest value, were selected for further analysis (Mandal et al. 2008).

  3. 3.

    Correlation coefficients and correlation sums were used to reduce redundancy and rule out spurious groupings among the highly weighted variables within a particular PCA (Andrews and Carroll 2001; Lark et al. 2007). Thus, a minimum dataset (MDS) of variables that best represented DSL were compiled from each PC, including (a) the variable with the highest factor loading as the most important contributor to the PC; (b) the variable with the highest correlation sum, which is most generally related to other variables and thus best represents the group; and (c) the variable with the lowest correlation sum because of its implied relative independence from the group (Mandal et al. 2008; Webster et al. 1994). Therefore, the factors selected into the MDS were the dominant DSL factors.

  4. 4.

    Multiple linear regressions (MLR) were conducted on the selected variables using the final MDS indicators as independent variables and the DSL indices as dependent variables. Consequently, the regression models of DSLs were developed with fewer but significant factors. The 125 datasets were divided arbitrarily into two subsets: subset 1 with 100 derivation datasets and subset 2 with 25 validation datasets. Two steps were conducted to develop the model—in step I, regression models were developed from subset 1 and validated by subset 2; in step II, the 125 datasets of the Loess Plateau were used for obtaining the final models in order to make use of all the data. The accuracy of the regression models developed in the two steps was evaluated and compared by using three evaluation indices: the coefficient of determination (R 2), the root mean square error (RMSE), and the mean error (ME). Negative and positive values of ME indicated under- and over-estimation of the model for a given variable, respectively.

2.6 Statistical Analysis Software

Analyses of primary statistical parameters [including mean, standard deviation (SD), and coefficient of variation (CV)], skewness, kurtosis, PCA, MDS calculation, MLR, and analysis of variance (ANOVA) were conducted using Microsoft Excel (version 2003), SigmaPlot (version 10.0), and SPSS (version 13.0). Geostatistical analyses were performed using GS + software (version 7.05). Maps of sampling points and DSL distribution were produced using GIS software (ArcGis 9.2).

3 Results

3.1 Spatial Pattern of DSL Across the Loess Plateau

3.1.1 Basic Characteristics of DSLs

For the 0- to 600-cm SWC data collected from 125 forestlands, DSLT was calculated in accordance with Eq. 1. Theoretically, if DSLT = 0, then no DSL has formed in the soil profile. However, if DSLT > 0, then a DSL has formed and the value of DSLT represents the level of soil drying. The calculated DSLT data show that DSLs were found in 102 of 125 study sites, accounting for 82%. The other 24 sites (18%) had a good SWC throughout the soil profile (SWC > SFC), and thus no DSL formed.

For the 102 forestlands where DSLs were detected, the characteristics of DSLT and DSL–SWC were further analyzed. Basic statistical characteristics of DSL indices are presented in Table 1. The mean thickness of DSLs exceeded 300 cm (DSLT = 304 cm) at the sampling depth of 0–600 cm. The mean DSL–SWC was 7.9%, which was much lower than the FC of 18.1%. These results indicated the severity of DSL detected in most of the sampling sites.

Table 1 Statistical characteristics of dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC) for the 102 forestlands (out of 125 sample sites) where DSLs had been detected in the Loess Plateau
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3.1.2 Distribution of DSLs Across the Loess Plateau

Figure 2a shows the classified post-plots across the entire Loess Plateau, where the majority of forestlands had clearly formed DSLs. The distribution of DSLs exhibited an obvious spatial heterogeneity. The higher DSLTs (generally >300 cm) were mainly found at the center of the Plateau. On the southern and southeastern parts of the study area, the DSLTs were relatively thinner (generally <180 cm) because of the relatively high precipitation in these regions.

Fig. 2
figure 2

Spatial distribution of the thickness of dried soil layers (DSLT) and soil water content in DSL (DSL–SWC) under forestland across the entire Loess Plateau (n = 125)

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Three possible reasons can account for the occurrence of the sites with DSLT = 0 (Fig. 2a). First, the high water table can continuously supply water used by plants (A point in Fig. 2a). Second, irrigation is provided in areas along the Yellow River and within some interior areas where it is practical. This measure improves the tree wood volume or the orchard yield. Thus, farmers always keep the soil at a high water content (B point in Fig. 2a). Third, relatively high precipitation occurs in the area (C point in Fig. 2a). Moreover, scientifically based land management measures (e.g., terrace construction, conservation tillage, and appropriate planting density) may fully utilize rainfall and maintain a balance between soil water input and output. In contrast to the DSLT distribution, the DSL–SWC under forestland demonstrated an obvious decreasing trend from southeast to northwest across the Plateau (Fig. 2b).

3.1.3 Spatial Variation Structures of DSLT and DSL–SWC

Geostatistical techniques were used to quantify the specific spatial patterns and structures of DSL variations. Semivariograms were constructed from the normally distributed dataset of DSLs (Table 1), and directional variation was sought based on the anisotropy ratios. Weak directional variances were determined for DSLT and DSL–SWC based on their small anisotropy ratios (1.1 and 2.4, respectively; <2.5) (Wang et al. 2002). Hence, omnidirectional semivariograms were calculated (Fig. 3). The geostatistical model that could best fit each variogram was identified from the lowest RSS and highest R 2 values. The parameters providing a quantitative expression of spatial structure were then obtained.

Fig. 3
figure 3

Semivariograms of data (square) for dried soil layer thickness (DSLT) and mean soil water content in DSL (DSL–SWC) distributions across the entire Loess Plateau. The solid lines represent the best fit model

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Figure 3 presents the semivariograms of DSLT and DSL–SWC, and the corresponding best fit model. The shape of the experimental semivariogram of DSLT was closely matched by the exponential model (RSS = 0.493, R 2 = 0.37), whereas DSL–SWC was a spherical model (RSS = 7.28, R 2 = 0.98). Both semivariograms showed clear sills (3.05 and 20.0, respectively), indicating that the DSL data were stationary. DSL–SWC had a larger range (513 km) than DSLT (69 km), which suggests that observations would be spatially dependent for sampling points separated by less than the values of the range. The nugget ratios for DSLT and DSL–SWC were 54 and 12%, respectively, which indicated a moderate and strong spatial dependence.

In addition, the spatial autocorrelation characteristics of DSLs at different lag distances were evaluated. Moran’s I analysis was performed to derive an index that quantified the spatial autocorrelation existing between sites for DSLT and DSL–SWC. Figure 4a shows that DSLT had positive autocorrelation at distances less than 150 km, whereas beyond this distance, a very weak autocorrelation existed. In comparison, DSL–SWC showed a different autocorrelation characteristic. Figure 4b shows DSL–SWC with different ranges for positive and decreasing correlations (300 km), and negative autocorrelation at distances of more than 350 km.

Fig. 4
figure 4

Moran’s I for dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC) across the entire Loess Plateau

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3.2 Dominant Factors of DSL Variation

3.2.1 Correlation Analysis

Pearson correlation analysis showed that 9 out of 28 variables were significantly correlated with DSLT (Table 2). Positive correlations were found for slope gradient, slope aspect, CWC, FC, SSWC, and silt content (P < 0.05). A negative correlation existed for longitude, BD, and clay content (P < 0.05).

Table 2 Pearson correlation coefficients between dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC), and 28 environmental factors on the Loess Plateau. Variables that correlated significantly with DSLT or DSL-SWC were showed in bold
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Table 2 also shows that 15 out of 28 variables were significantly correlated with DSL–SWC (P < 0.01). Eight variables (i.e., FC, SSWC, SOC, VC, precipitation, temperature, and clay and silt content) were positively correlated with DSL–SWC. Seven variables were negatively correlated including latitude, altitude, BD, sand content, growth age, evaporation, and aridity. Moreover, Pearson correlation analysis also confirmed that a very weak correlation existed between DSLT and DSL–SWC (r = −0.092, P > 0.05), which can also be seen in the scatterplot for the measured data of DSLT and DSL–SWC (Fig. 5). Consequently, the significantly related factors of DSLT and DSL–SWC (9 and 15, respectively) were selected for further analysis.

Fig. 5
figure 5

Scattergram for measured data of the dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC)

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3.2.2 PCA

PCA was then used to extract the latent roots and vectors of the correlation matrix for the selected variables of DSLT and DSL–SWC. The variables uncorrelated with either DSLT or DSL–SWC were excluded from the respective PCAs (Table 2). For DSLT, PCA identified three PCs that accounted for 72% of the variance, with the first two PCs accounting for 60%. Four PCs were identified for DSL–SWC, accounting for 78% of the variance (Table 3).

Table 3 Results of the principal component analysis of 9 and 15 potential predictive variables for the dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC), respectively
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The first PC accounted for 41% of the variance for DSLT (Table 3). BD was the greatest contributor to PC1 as given by the factor loading (−0.93). SSWC and field capacity had high weighted factor loadings, that is, having absolute values within 10% of the BD factor loading (=−0.837). PC2 explained 19% of the variance, in which slope gradient was the greatest contributor (factor loading = 0.80), and slope aspect was selected as highly rated (<10% of slope gradient factor loading). For PC3, only CWC was identified as the best representative variable.

Similarly for DSL–SWC, PC1 was represented by four variables (FC, aridity, latitude, and sand content), which accounted for 46% of the variance. The weighted factors of the three other PCs were determined as altitude (PC2), VC (PC3), and evaporation (PC4) (bold typeface; Table 3).

Therefore, six variables for DSLT (BD, SSWC, FC, slope gradient, slope aspect, and CWC) and seven variables for DSL–SWC (FC, aridity, latitude, sand content, altitude, VC, and evaporation) were selected by PCA for inclusion in their respective MDSs as the most suitable to explain DSL variation at this stage.

3.2.3 MDS Compilation

For PCs containing at least two highly weighted variables, Pearson correlation coefficients and correlation sums were derived from each PC individually (Table 4). For DSLT in PC1, BD had the highest factor loading (−0.93) and correlation sum (2.747) and was therefore retained for the MDS. Although SSWC had the second correlation sum (2.721) and was considered as the best group representative, it was excluded from the MDS because of its high correlation with BD (r = −0.967, P < 0.01). FC had the lowest correlation sums (2.535) but was also selected for the MDS, as it may imply relative independence from the group. In PC2, both slope gradient and aspect were retained for the MDS because of their relatively weak correlation.

Table 4 Pearson correlation coefficient and correlation sums for highly weighted variables with high factor loading under the principal component (PC) for the dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC)
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Similarly for DSL–SWC, FC had the highest factor loading (Table 3) and the highest correlation sum (2.912). Thus, it was included in the MDS as the best representative of PC1. Aridity had the second correlation sum (2.897) and was also selected. On the other hand, latitude was excluded because it was highly correlated with aridity (r = 0.725, P < 0.01). Sand content was retained for the MDS because its correlation sum was the lowest.

Thus, the final MDS of DSLT and DSL–SWC comprised five (i.e., BD, FC, slope gradient, slope aspect, and CWC) and six (i.e., FC, aridity, sand content, altitude, VC, and evaporation) variables, respectively (underlined and bold typeface; Table 3). Consequently, these were determined as the dominant DSL factors.

3.3 Multiple Regression Models

The variables in the final MDS (selected from 28 independent variables) were used to obtain the predictive models of DSL through multiple regression methods. Regression models for DSLT and DSL–SWC, developed during step I, were tested by using the validation datasets (subset 2). The predictive capacity for DSLT and DSL–SWC models in step I was acceptable at the level of 0.05, according to the values of three evaluation indices (R 2 = 0.08 and 0.36, RMSE = 217.22 and 2.83, and ME = 64.24 and −1.46).

After validation of the regression models in step I, we repeated the whole procedure using all the 125 datasets as the development datasets (step II). The evaluation indices (R 2 = 0.13 and 0.73, RMSE = 180.75 and 1.83, and ME = 0.06 and 0.10) indicated that regression models developed from 125 datasets had a relatively superior performance than those developed from 100 datasets. Hence, we treat the models developed in step II as the final models. The final predictive models developed, as well as the F-values for each regression, are listed in Table 5. The positive or negative sign of the regression coefficients of the variables reflects its correlation (positive or negative) with DSL.

Table 5 Results of multiple regression analysis for the dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC)
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The regression model for DSLT explained 13% of the overall variability, which can be attributed to BD, FC, slope gradient, slope aspect, and CWC. These variables all significantly contributed to the model (P < 0.01). The adjusted R 2 of the DSLT prediction model was low, implying that a more complex model may be required. However, the simplicity of this model indicates the importance of its component factors for DSLT formation. For DSL–SWC (Table 5), the model accounted for 73% of the overall variability, which can be attributed to the variables in its MDS (i.e., FC, aridity, sand content, altitude, VC, and evaporation).

The models of DSLT and DSL–SWC passed the F test (P < 0.01) (Table 5). The distributions of the residuals (Fig. 6) were approximately normal, with zero means and no detectable serial correlation. These results indicated a high accuracy for predicting DSLT and DSL–SWC at the regional scale.

Fig. 6
figure 6

Normal P–P plot of multiple regression standardized residual for the dried soil layer thickness (DSLT) and soil water content in DSL (DSL–SWC)

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4 Discussion

4.1 Formation Mechanism of DSL

DSL formation depends on the soil water balance and water cycles in the ecosystem. When soil water output (e.g., evapotranspiration and drainage) increases and/or input (e.g., rainfall and irrigation) decreases, soil drying may occur. Thus, a DSL may be formed (Entekhabi and Eagleson 1991; Wang et al. 2010a, b, 2011; Entekhabi and Eagleson 1991). Soil desiccation and hence DSL formation may be a consequence of climate change and/or poor water management (Chen et al. 2008). On the other hand, the nature and extent of DSLs may serve as an indicator for evaluating soil desiccation processes and soil water status. The functional root status in the proximity of the DSL for different plant communities may also be reflected (Wang et al. 2010b).

The plant–soil environment is a mutually interacting system. During the life cycle of plants, the soil environment provides water, physical structural support, and nutrients. In turn, the plants tend to stabilize the soil structure and add metabolites and organic matter (through senescence and death) back to the soil (Hodge 2004; Bogeat-Triboulot et al. 2007). In forestland, the process of plant–root water uptake → deep soil water moves upward through the roots → water arrival in the parts of the plants above-ground → water evaporation through plant transpiration into the atmosphere is a primary mechanism of deep soil water loss (Yamanaka and Yonetani 1999).

4.2 Spatial Variability of DSL and Its Influencing Factors

DSL occurrence is a regionalized variable, showing great variability both in space and time. Based on the coefficients of variation of the DSL indices (>35%, Table 1), the DSL variation extent had moderate variability in accordance with the criteria of Nielsen and Bouma (1985), which reflected a combined influence of biotic and abiotic factors (e.g., differences in rainfall and soil texture, evapotranspiration rates, soil moisture content, and plant growth) on DSL indices at a regional scale.

DSL variability was related to micro-topographic elements (i.e., slope gradient, slope aspect) (Han et al. 1990; Li 1983; Chen et al. 2008). However, variability may be related to some large-scale factors (i.e., soil type, rainfall) across a wider range of scales (Wang et al. 2010a). DSL variation has been proved to be scale dependent. Thus, the contribution of small-scale factors to DSL variability may be masked by large-scale processes. Therefore, with increasing spatial scales, large-scale factors and processes that govern DSL variation must be taken into account.

At a regional scale, DSLs under forestland demonstrated an obvious spatial pattern. The DSL indices each had different patterns due to varying dominant factors and processes. The DSL–SWC pattern can largely be explained by the soil textures of the Plateau, which are sandier in the northwest and more clayey in the southeast (Shi and Shao 2000). Soil texture may determine its soil water holding capacity, and the spatial distribution of chemical and biological soil properties when water content is scant. However, soil texture may have negligible effects under conditions of high water availability (Rodríguez et al. 2009).

The variables relating to DSL in forestlands on the Loess Plateau could be statistically divided into four classes (Table 5): soil properties (FC, sand content, and BD), vegetation characteristics (VC), topographic elements (slope gradient, aspect, and altitude), and climatic conditions (aridity and evaporation). This classification implied that DSL is an integrated result of many factors and their interactions under the overall environment of water-deficit conditions. The importance of FC was expected since the magnitude of a DSL is a phenomenon of soil drying. Similarly, BD and sand content are important as these factors directly affect soil hydrology. Slope gradient, aspect, and altitude are often related to other slope properties, such as slope position. In turn, these slope properties are related to landscape geomorphology. This factor can directly influence soil hydrology and may also be indirectly related to rainfall patterns and the use of irrigation measurements. The conditions of both climate and plants generally dominate the water balance processes by changing the soil water inputs and outputs.

5 Conclusions

Most of the forestlands across the Loess Plateau had a dried soil layer (82%) under the overall environment of long-term water shortages combined with excessive depletion of deep soil moisture by vegetation. The thickness of DSLs generally exceeded 300 cm and the mean soil water content within the DSL was 7.9%, indicating serious soil desiccation on the Plateau.

At the regional scale, both DSLT and DSL–SWC exhibited a moderate variability based on the CV values. The values of nugget ratios for DSLT (54%) and DSL–SWC (12%) indicated a moderate and strong spatial dependence. The spatial distribution map shows that thicker DSLTs were mainly distributed around the center of the Plateau, whereas thinner DSLTs were found in the south and southeast. This difference in distribution is due to the relatively high precipitation in these areas. However, the DSL–SWC under forestland demonstrated an obvious decreasing trend from southeast to northwest across the Plateau. This trend may be largely explained by the varying soil textures of the Plateau.

The dominant factors of DSLT under forestlands were found to be BD, FC, slope gradient, slope aspect, and CWC. The DSL–SWC dominant factors were FC, aridity, sand content, altitude, VC, and evaporation. These factors were determined by correlation analysis, PCA, and MDS calculation. The predictive models of DSLT and DSL–SWC developed in the present study using multiple regressions are suitable for predicting DSLs, especially for DSL–SWC (adjusted R 2 = 73%).

Understanding the spatial variability, pattern, and dominant factors of DSLs is a pre-condition of scientifically based plant selection, location, and management in water-limited ecosystems. To prevent or alleviate or eradicate DSLs, it is necessary to reduce soil water outputs (e.g., selecting an appropriate vegetation type, planting density, and using scientifically based management methods) and to increase soil water inputs (e.g., reducing rainwater losses, irrigation). Predicting the level of DSLs at regional scale by using existing soil, plant, climate, and topographic data is an effective measure to link the response of soil–plant system to climate change and/or ill-advised land management.