1 Introduction

Soil salinization is a major environmental and ecological concern to sustainability of agro-ecosystems, especially in arid agricultural areas with shallow water table depth (Foley et al. 2005; Singh 2015; Sun et al. 2019; Wichelns and Oster 2006). Complicated hydrogeological conditions and anthropogenic activities (e.g., soil characteristics, crop types, and irrigation schedules) in agricultural areas increase spatiotemporal variability of soil salinity (Daliakopoulos et al. 2016; Ren et al. 2016; Sylla et al. 1995). Due to the high spatiotemporal variability, it is difficult to effectively monitor, accurately estimate, and reliably predict spatiotemporal distribution of soil salinity for agricultural management (Corwin et al. 2006; Ding and Yu 2014; Hajrasuliha et al. 1980).

There have many studies focusing on using geostatistical methods to investigating the spatial and/or temporal variability of soil salinity at the field scale (Douaik et al. 2005, 2007; Li et al. 2013; Panagopoulos et al. 2006; Scudiero et al. 2017; Sylla et al. 1995; Utset et al. 1998). Sylla et al. (1995) studied spatial variability of soil salinity and its major impact factors at three study sites with areas ranging from 4 to 14.4 ha. Panagopoulos et al. (2006) analyzed spatial variation of soil salinity at an experimental block (0.22 ha) and its effects on lettuce production. Douaik et al. (2005) investigated spatiotemporal variability of soil salinity within soil depth of 0—0.4 m at a site of 25 ha in Great Hungarian Plain of Hungary. Zheng et al. (2009) assessed spatiotemporal changes of soil salinity using monitoring data in a drip-irrigated field at a 54-ha cotton field located in Xinjiang, China. Gasch et al. (2015) evaluated soil electrical conductivity spatiotemporal dynamic using data sets collected in a 37-ha farm located near Pullman, Washington, USA. These studies concern spatiotemporal variability of soil salinity at sites of small areas.

At the regional scale, attentions were paid to study not only spatiotemporal variability of soil salinity but its relation with environmental factors (Abd-Elgawad et al. 2013; Bilgili 2013; Elprince 2013; Hajrasuliha et al. 1980; Hamzehpour et al. 2013; Juan et al. 2011; Navarro-Pedreño et al. 2007; Shahabi et al. 2016; Walter et al. 2001; Wang et al. 2018; Wu et al. 2014; Zare-Mehrjardi et al. 2010; Zhou et al. 2010). Walter et al. (2001) studied the spatial pattern of salinity in top soils (0–0.2 m in depth) in an area of 38,000 ha in the Chelif Valley, Algeria. Zare-Mehrjardi et al. (2010) mapped the spatial distribution of topsoil salinity, and investigated its relations with vegetation types. Wang et al. (2018) discussed spatial distribution of salt content in the top soils and its response to land use changes in an inland river watershed of China. Due to the difficulty of intensive soil sampling at the regional scale, the abovementioned studies only used the topsoil salinity data. This however is inadequate for assessing salinity variability, since land managements and agricultural activities affect salinity of both top soils and deep soils (Akramkhanov et al. 2011). Therefore, it is necessary to investigate spatiotemporal patterns of both top and deep soils for understanding soil salinity trends at the regional scales. This is one of the motivations of this study.

The soil salinity spatial pattern and mean is the major information reflecting the degree of soil salinization (Florinsky et al. 2002; Wang et al. 2017), which requires a large number of soil samples of different sites and times due to its highly spatial and temporal variability (Hajrasuliha et al. 1980). Then, sampling schemes which can reduce the sample number to represent different soil salinity levels over space are necessary. Temporal stability analysis is an effective method to characterize time-invariant associations between spatial locations and classical statistical parametric values. It can be used to identify the sampling locations to represent the spatial mean of the study area (Brocca et al. 2009; Douaik et al. 2006; Gao et al. 2013a; Hu et al. 2011; Jacobs et al. 2010; Penna et al. 2013; Vachaud et al. 1985; Vanderlinden et al. 2012). Scientific literatures showed that the concept of temporal stability analysis has been widely used to characterize the temporal stability of spatial patterns of soil moisture in different land usage types (grassland, farmlands, forest lands and agro-forest ecosystems) from field to watershed scales (Gao et al. 2013a; Guber et al. 2008; Hu et al. 2011, 2010; Lin 2006; Vachaud et al. 1985). The mean relative difference (MRD) method is one of most popular methods used for temporal stability analysis, in which the location with MRD closed to zero or with minimum standard deviation of relative difference (SDRD) is taken as representative location. The characteristics of MRD and SDRD may the key factors to impact the effectiveness of the method to find the representative locations. It was found that some locations can represent the mean water content at any time with MRD ranging from − 0.07 to 0.07 in an agricultural land of Sevilla in Spain (Vachaud et al. 1985). The method was successfully used to find the representative locations in four catchments with the MRD range from − 0.41 to 0.54 and with the largest SDRD of 0.30 (Grayson and Western 1998). Liu and Shao (2014) reported that the method can estimate the soil water storage well with representative locations when the maximum SDRD less than 0.12. Mohanty and Skaggs (2001) found that MRD of soil moisture can range from − 0.70 to 1.40, and SDRD from 0.12 to 1.00, while cautions should be paid in some areas with large range of MRD and SDRD values.

Comparing to the abundant study of temporal stability of soil moisture, knowledge on temporal stability of soil salt was limited to field scales with fewer studies reported. Castrignanò et al. (1994) evaluated the variability and temporal stability of soil salinity in a field with 2.8 ha within the depth of 0.6 m and found that the spatial mean of soil salinity can be represented by limited locations. Douaik et al. (2006) reported that a reliable average soil salinity can be obtained by observing the soil salinity of two locations in a 25-ha field within the depth of 0.4 m. Xing et al. (2015) studied the temporal stability of root zone soil salinity in an experiment plot with 12.5 m × 10 m and confirmed that temporal stability representative locations can be selected as long-term soil salt monitoring points in this field. Current studies on temporal stability of soil salinity focused on field scale, where relative smaller variations of soil salinity level were found with MRD values ranging from − 0.75 to 1.11 (Douaik et al. 2006; Xing et al. 2015), which help to obtain acceptable spatial mean of soil salinity by representative locations (Xing et al. 2015). However, the temporal stability analysis would be challenged in a larger scale, where owns much larger MRD and SDRD of soil salinity.

In this study, a 2-year field experiment was carried out to characterize the temporal and spatial variability of soil salinity in a relatively large irrigation area (> 80 km2). Soil samples were collected 4 times before and after the crop growing season of 2017–2018, and there were 68 sampling sites for each time. Soil samples were collected from the top soil to the depth of 1.8 m or until the water table depth if it was shallower than 1.8 m with the interval of 0.2 m. The spatial variability of soil salinity at different depth from the top soil to 1.8 m were estimated by the geostatistical analysis. The temporal stability analysis was used to estimate and to predict the spatial mean of soil salt in the entire area, while it was found being difficult to select reasonable representative locations due to the large range of MRD and SDRD. Then, the improved temporal stability analysis was proposed to overcome shortcomings of temporal stability analysis on soil salinity, in which the soil samples were divided into several groups and the mean soil salinity of each group was estimated with representative locations by using temporal stability analysis. A monitoring network for this area was then recommended to evaluate the long-term evolution characteristics of soil salinity by comprehensively considering the results of spatiotemporal variability and the improved temporal stability analysis.

2 Material and methods

2.1 Study area and field measurements

The study area, the Longsheng irrigation district, is located in the central region of the Hetao Irrigation District in the west of Inner Mongolia Autonomous Region, China (Fig. 1). Its area is 82 km2, 15.5 km long measured in the southwest-northeast direction and 8.0 km wide in northwest-southeast direction. Based on the weather data obtained from the Linhe Weather Station adjacent to the study area, the cumulative precipitation was 100.5 mm in 2017 and 176.2 mm in 2018. These two years were selected to represent the dry and wet years, respectively, according to a hydrological frequency analysis using precipitation data from 1981 to 2018. During the crop growing season from May to September, the cumulative precipitation was 53.1 mm in 2017 and 156.6 mm in 2018. Measurements of soil salinity were carried out 4 times during early May and late September of 2017 and 2018, and these measurement times were denoted as Y1705, Y1709, Y1805, and Y1809. For each measurement time, 68 sampling locations were designed as shown in Fig. 1, and observations were replicated two times at each sampling location. Soil samples were collected from the top soil to the depth of 1.8 m or until the water table depth if it was shallower than 1.8 m with the interval of 0.2 m. There were a total of 4582 soil samples collected during the experiment for measuring the soil salinity. Soil salinity was determined from measurements of electrical conductivity (EC) of leaching liquid mixed with 1 (soil sample):5 (water) ratio with electrical conductivity meter (DDSJ-308F, China) (Ding and Yu 2014; Visconti et al. 2010).

Fig. 1
figure 1

Locations of the Longsheng irrigation district, and soil salinity samples in the study area

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2.2 Geostatistical analysis

The spatial variability and correlations of soil salinity are quantified by using the empirical semivariogram defined as (Webster and Oliver 2007; Hu et al. 2010)

$$\gamma (h)=\frac{1}{2N(h)}\sum_{i=1}^{N(h)}{[Z({x}_{i}+h)-Z({x}_{i})]}^{2},$$
(1)

where γ(h) is the semivariogram; h is the lag distance; N(h) is the number of pairs (xi, xi + h); Z(xi) and Z(xi + h) are values of soil salinity at positions xi and xi + h.

Three semivariogram models (i.e., spherical, exponential, and Gaussian models) have been employed to fit the empirical semivariograms, and the models are defined as follows (Zhang 2005):

$$\gamma (h)=\left\{\begin{array}{c}0\begin{array}{cccc}\begin{array}{ccc}\begin{array}{cc}\begin{array}{cc}& \end{array}& \end{array}& & \end{array}& & & h=0\end{array}\\ {C}_{0}+{C}_{1}(\frac{3h}{2a}-\frac{{h}^{3}}{2{a}^{3}})\begin{array}{cc}& 0<h\le a\end{array}\\ {C}_{0}+{C}_{1}\begin{array}{ccc}\begin{array}{ccc}& & \end{array}& \begin{array}{cc}& \end{array}& h>a\end{array}\end{array},\right.$$
(2)
$$\gamma (h)=\left\{\begin{array}{c}0\begin{array}{cccc}& & & \begin{array}{ccc}& & \begin{array}{cc}& h=0\end{array}\end{array}\end{array}\\ {C}_{0}+{C}_{1}(1-{e}^{-\frac{h}{a}})\begin{array}{ccc}& & h>0\end{array}\end{array},\right.$$
(3)
$$\gamma (h)=\left\{\begin{array}{c}0\begin{array}{cccc}& & & \begin{array}{ccc}& & \begin{array}{cc}& h=0\end{array}\end{array}\end{array}\\ {C}_{0}+{C}_{1}(1-{e}^{-\frac{{h}^{2}}{{a}^{2}}})\begin{array}{ccc}& & h>0\end{array}\end{array},\right.$$
(4)

where C0 is the nugget variance, C1 is the structured variance, and a is the correlation length. The correlation length is related to range R, which is a, 3a, and 1.732a for the spherical, exponential, and Gaussian models, respectively. The coefficient of determination (R2) and residual sums of squares (RSS) were used to assess the fitness of different semivariogram models. Models with the highest R2 and lowest RSS were taken as the fitted semivariogram models (Li et al. 2020).

The nugget variance (C0), sill variance (C0 + C1), and range R are the three geostatistical parameters in theoretical semivariogram models. The degree of spatial dependence (GD), which is the ratio between the nugget variance and the sill variance, was used to characterize the spatial dependency of soil salinity. GD < 0.25 indicates a strong spatial dependency, while GD > 0.75 a weak spatial dependency, otherwise a moderate spatial dependency (Li et al. 2020). The range R was used to judge the spatial autocorrelation scale of random variables.

Ordinary kriging was used to estimate the values at unsampled locations, and “leave-one-out” cross-validation was conducted on the kriging analysis (Ruybal et al. 2019). The measured and predicted soil salinity were compared for goodness of fit to assess the kriging model.

2.3 Temporal stability analysis

The MRD method was employed to study the temporal stability of soil salinity. The relative difference (RDi,j) of the sampling time j at the sampling location i for a given depth with respect to the spatial mean soil salinity (Sj) is defined as (Vachaud et al. 1985),

$$R{D}_{i,j}=\frac{{S}_{i,j}-\overline{{S }_{j}}}{\overline{{S }_{j}}},$$
(5)
$$\overline{{S }_{j}}=\frac{1}{n}\sum_{i=1}^{n}{S}_{i,j},$$
(6)

where Si,j is the soil salinity at the location i of the sampling time j, and n is the number of sampling locations. The temporal mean relative difference MRDi and the standard deviation of RDi,j at the location i (SDRDi) over time are calculated as (Penna et al. 2013),

$$MR{D}_{i}=\frac{1}{m}\sum_{j=1}^{m}R{D}_{i,j},$$
(7)
$$SDR{D}_{i}=\sqrt{{\sum }_{j=1}^{m}\frac{{(R{D}_{i,j}-MR{D}_{i})}^{2}}{m-1}},$$
(8)

where m is the total number of sampling times. MRDi measures the bias between the observation values at the sampling location i and the spatial mean observation value over a certain period, and SDRDi quantifies accuracy of the bias measurement (Gao et al. 2013b). In our study, the sampling location with the minimum SDRDi was selected as the representative location (Brocca et al. 2009).

Rearranging Eq. (5), the spatial mean soil salinity can be expressed as

$${\overline{S} }_{j}=\frac{{S}_{i,}{}_{j}}{1+R{D}_{i,j}},$$
(9)

The offset (RDi,j) between the representative location and the mean value can be equal to MRDi, and the spatial mean can be estimated as (Grayson and Western 1998; Hu et al. 2010; Heathman et al. 2012; Gao et al. 2013a),

$${S}_{mean,j}=\frac{{S}_{RL,}{}_{j}}{1+MR{D}_{RL}},$$
(10)

where Smean,j is the spatial mean of soil salinity of the sampling time j, SRL,j is the soil salinity of representative locations, and MRDRL is the temporal MRD of representative locations with the smallest SDRD.

2.4 Improved temporal stability analysis of soil salinity

Temporal stability analysis can provide accurate results with relatively smaller MRD ranging from − 0.50 to 0.60 and most maximum SDRD value being smaller than 0.50 (Brocca et al. 2009; Vanderlinden et al. 2012). Since MRD and SDRD of soil salinity are much larger at this study area (shown in Sect. 3.3), the improved temporal stability analysis of soil salinity was developed to reduce MRD and SDRD, the procedures of which are shown in Fig. 2. The MRD method is first used to calculate MRDi of each sampling location. Then, all sampling locations are divided into several groups according to the ranked MRDi. The MRD method is used to calculate the MRDi,p and SDRDi,p (where p means the p-th group and i is the sampling location) of the sampling locations in each group. The reasonability of MRDi,p and SDRDi,p in each dividing group is then evaluated, and the evaluation criteria are discussed in Sect. 3.5. The sampling location with the minimum SDRDi,p in p-th group is selected as the representative location, and then the spatial mean soil salinity of each group is calculated by using Eq. (10).

Fig. 2
figure 2

Flowchart of the improved temporal stability analysis. MRDi is the temporal mean relative difference at the sampling location i; MRDi,p is the MRD at the sampling location i in the p-th group; and SDRDi,p is the standard deviation of relative difference (RD) at the sampling location i in the p-th group

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2.5 Accuracy indictors

The mean relative error (MRE), the root mean square error (RMSE), and the determination coefficient (R2) were used to evaluate the misfit between the observed and predicted soil salinity, which are defined as follows (Ren et al. 2016):

$$MRE=\frac{1}{k}\sum_{i=1}^{k}\frac{{P}_{i}-{O}_{i}}{{O}_{i}}\times 100\%,$$
(11)
$$RMSE=\sqrt{\frac{1}{k}\sum_{i=1}^{k}{({P}_{i}-{O}_{i})}^{2},}$$
(12)
$${R}^{2}={\left[\frac{\sum_{i=1}^{k}({O}_{i}-\overline{O })({P}_{i}-\overline{P })}{{\left[\sum_{i=1}^{k}{({O}_{i}-\overline{O })}^{2}\right]}^{0.5}{\left[\sum_{i=1}^{k}{({P}_{i}-\overline{P })}^{2}\right]}^{0.5}}\right]}^{2},$$
(13)

where k is the total number of observations; Pi and Oi are the predicted and observed values (i = 1, 2, …, n);‾O and‾P are the mean observations and predictions.

3 Results and discussion

3.1 Summary statistics of soil salinity

Summary statistics of soil salinity at various soil layers at the 4 sampling times are listed in Table 1. Generally speaking, the maximum values are about one order of magnitude larger than the minimum values, and the spatial variability of soil salinity is high with the coefficients of variation (CV) ranging from 0.43 to1.14. According to Warrick and Nielsen (1980), 0.1 ≤ CV ≤ 1.0 indicates moderate variability, and CV > 1.0 strong variability.

Table 1 Summary statistics of soil salinity at the 4 sampling times
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The spatial mean of soil salinity of the 4 sampling times at various depths is presented in Fig. 3. Although the soil salinity within the topsoil was distinctly impacted by upper boundary conditions (e.g., irrigation, precipitation), the soil salinity within the depth of 0–0.6 m (the root zone) in September was larger than that in May, the values of which were 0.32 dS/m, 0.34 dS/m, 0.29 dS/m, and 0.30 dS/m in Y1705, Y1709, Y1805, and Y1809. Heavy precipitation can help to leach soil salt out effectively, which can be found in Fig. 3 that the soil salinity within the depth of 0–0.6 m in Y1709 was larger than that in Y1809. And the soil salinity within the depth of 0.6–1.8 m was smaller in September than in May, the values of which were 0.30 dS/m, 0.27 dS/m, 0.31 dS/m, and 0.28 dS/m in Y1705, Y1709, Y1805, and Y1809. During the crop growing season from May to September, soil salts mainly move upwards from the deep soil layer (within the depth of 0.6–1.8 m) to the root zone caused by the shallow groundwater table depth and strong evapotranspiration. This is the major reason to result in the smaller soil salinity in the deep soil layer in September than that in May. All these demonstrate that the soil salinity has obvious seasonal variation characteristics although the upper boundary conditions are inconsistent in 2017 and 2018.

Fig. 3
figure 3

The soil salinity means of different soil layers at 4 sampling times

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3.2 Spatiotemporal pattern of soil salinity

The spatial pattern of soil salinity at different soil layers was analyzed by the semivariogram models, which are listed in Table 2. And experimental and theoretical semivariogram of soil salinity for various soil depths in Y1805 are plotted in Fig. 4. It can be found that the spherical, exponential, and Gaussian models can fit the empirical semivariograms well, with most values of R2 greater than 0.70 and most RSS smaller than 0.003. The degree of spatial dependence of soil salinity ranged from 0.07% to 49.85% with most smaller than 25%, which shows strong spatial dependency in the study area. The degree of spatial dependence at the end of the crop growing season (Y1709 and Y1809) were obviously greater than that at the beginning of growing season (Y1705 and Y1805). The average R values within the depth of 0–0.6 m were 1448 m, 1535 m, and 1703 m in Y1705, Y1709, and Y1805. The R value of soil salinity within the depth of 0–0.6 m was more than 6180 m in Y1809, which was evidently larger than those in other sampling times. It may be caused by the precipitation event happening before the sampling time that increases the spatial homogeneity of root zone soil salt. The range R values in 0.6–1.8 m were greater at the end of crop growing season (Y1709 and Y1809) than that at the beginning of crop growing season (Y1705 and Y1805). It is consistent with the law that the soil salinity with larger spatial mean own stronger variability (Table 1). Regardless of the maximum and minimum values, the average R values of 0.6–0.8 m, 0.8–1.0 m, 1.0–1.2 m, 1.2 m–1.4 m, 1.4–1.6 m, and 1.6–1.8 m were 4965 m, 8585 m, 6915 m, 4525 m, 4920 m, and 3200 m. It means that the sampling interval of soil salinity of 0–0.6 m should be smaller than 1448 m, and 0.6–1.8 m can be 3200 m when using R as a reference for determining sampling locations.

Table 2 The semivariogram models and prediction accuracy of soil salinity at the 4 sampling times
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Fig.4
figure 4

Experimental (circles) and theoretical (lines) semivariogram of soil salinity for various soil depths in Y1805

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As shown in Table 2, the spatial structure characteristics of soil salinity were different at the 4 sampling times, which are highly influenced by natural and human factors. It also implies that it is not reliable to obtain the spatial structure characteristics of soil salinity by results of single sampling time, while results of multi sampling times are needed to figure out the spatial structure characteristics of soil salinity for determining the appropriate sampling locations.

Based on the semivariograms analysis, the spatial distribution of soil salinity at different soil layers at the 4 sampling times was estimated using the ordinary kriging method (Zhang 2005), and results of “leave-one-out” cross-validation are listed in Table 2. Figure 5 shows the spatial distribution of soil salinity of different soil layers in Y1805. The distribution of high and low values of soil salinity in different soil layers are highly related. The location and size of patches with same color of each layer within the depth of 0–0.6 m were almost identical, and very similar distribution patterns were found in each layer within the depth of 0.6–1.8 m, which indicate that the soil salinity is closely related to each other in different depths. The soil salinity spatial distributions within the depths of 0–0.6 m (the root zone) and 0.6–1.2 m at the 4 sampling times are shown in Fig. 6. The soil salinity in the eastern and northeast part of the study area was always higher than that in the north and south parts. Very small changes of spatial distribution pattern were found with time. These show that the spatial patterns of soil salinity are relatively stable in time. The spatiotemporal pattern of soil salinity in this study area demonstrates that it is not necessary to monitor soil salinity of deep layer due to similar spatial pattern of different soil layers being found, and monitoring frequency can also be decreased due to its temporal stability.

Fig. 5
figure 5

The spatial distribution of soil salinity of different soil layers in Y1805

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Fig. 6
figure 6

The soil salinity spatial distribution of root zone (within the depth of 0–0.6 m) and 0.6–1.2 m layer at the 4 sampling times

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3.3 Estimating the soil salinity means with temporal stability analysis

Considering that soil salinity data within the depth of 1.2–1.8 m at some sampling locations were missing due to shallow water table in early May, only the soil salinity data within the depth of 0–1.2 m was used for temporal stability analysis. The MRD and SDRD of soil salinity are shown in Fig. 7. The variation ranges of MRD of soil salinity at the soil layers of 0–0.2 m, 0.2–0.4 m, 0.4–0.6 m, 0.6–0.8 m, 0.8–1.0 m, and 1.0–1.2 m were − 0.54–2.91, − 0.53–1.90, − 0.63–1.87, − 0.63–1.61, − 0.70–1.49, and − 0.63–1.86, respectively. The corresponding SDRD of soil salinity at different soil layers were 0.06–2.78, 0.04–1.34, 0.03–1.44, 0.03–1.44, 0.04–1.34, and 0.02–1.03. The sample location in each soil layer with the minimum SDRD was chosen as the representative location to predict the mean soil salinity. The predicted and measured soil salinity for the 4 sampling times are showed in Fig. 8a. However, the MRE values were − 6.47 to 7.2%, RMSE values 0.02 to 0.03 dS/m, and R2 values 0.33 to 0.84, which show that it is difficult to estimate the spatial mean of soil salinity by the temporal stability analysis.

Fig. 7
figure 7

The mean relative difference (MRD) and standard deviation of relative difference (SDRD) of soil salinity, and the S38, S45, S5, S64, S39, and S44 are representative locations with the minimum SDRD

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Fig. 8
figure 8

The measured and predicted mean soil salinity of each soil layer within the depth of 0–1.2 m by the temporal stability analysis and improved temporal stability analysis, and the line is 1:1

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The reason causing the unsatisfactory predictions is attributed to the strong variability of soil salinity. The MRD of soil salinity in this study area are much larger than MRD of soil water content with most ranging from − 0.5 to 0.6 (Brocca et al. 2009), and also larger than MRD of soil salinity in field scale ranging from − 0.75 to 1.11 (Douaik et al. 2006). It demonstrates that larger variation of soil salinity is found in the study area. In addition, the SDRD of soil salinity are also much larger than those of soil water content with maximum values smaller than 0.50 (Brocca et al. 2009), and also larger than that of soil salinity in field scales ranging from 0.14 to 0.53 (Douaik et al. 2006). It can also be found that the SDRD of soil salinity became larger with the increase of MRD as shown in Fig. 9a. The changes of soil salinity are highly related to its value (Sun et al. 2019), and thus the temporal stability analysis can provide accurate results when the sample location with the minimum SDRD value and meanwhile owning the MRD close to 0 existed. However, in this area, the sample location with the MRD close to 0 owning to relatively large SDRD, and the sample location with the minimum SDRD owning to relatively large negative MRD as shown in Fig. 9a. Therefore, the temporal stability analysis should be improved in this area for more accurate prediction of spatial mean of soil salinity.

Fig. 9
figure 9

The relationship between mean relative difference (MRD) and standard deviation of relative difference (SDRD) of soil salinity for a temporal stability analysis and b improved temporal stability analysis. Solid dots are results of representative locations with the minimum SDRD

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3.4 Estimating the spatial mean soil salinity with the improved temporal stability analysis

The 62 sampling locations were divided into 7 groups according to ranked MRD from small to large as shown in Fig. 7, and each of the first 6 groups have 9 sampling locations, and the 7-th group has 8 sampling locations. The data of 62 sampling locations while not 68 sampling locations were used for temporal stability analysis since there were 6 sampling locations not be collected due to irrigation events at all sampling times. The MRD and SDRD values in each group calculated by the temporal stability analysis are shown in Fig. 10. The MRD ranged from − 0.41 to 0.67, and most were between − 0.20 and 0.20. It can be found that the improved temporal stability analysis reduced variation of soil salinity in each group greatly. Similarly, the SDRD in each group with improved temporal stability analysis were also decreased greatly with most of them smaller than 0.5. The relationship between SDRD and MRD with improved temporal stability analysis is shown in Fig. 9b. The representative locations with minimum SDRD were also the ones whose MRD were close to 0, which implies that more reasonable representative locations for soil salinity are obtained by the improved temporal stability analysis. The representative location of each group with the minimum SDRD at different soil layers is listed in Table 3. The representative locations in different soil layer were different, which indicates that it is difficult to find a location to estimate the average soil salinity at different soil layers simultaneously. This is consistent with the temporal stability analysis of soil water content reported in literatures (Gao et al. 2013a; Guber et al. 2008; Heathman et al. 2012; Hu et al. 2010). The predicted and measured mean soil salinities at the 4 sampling times are shown in Fig. 8b. The MRE values were − 2.72 to 1.61%, RMSE values 0.04 to 0.05 dS/m, and R2 values larger than 0.90, which demonstrate the good performance of improved temporal stability analysis in predicting soil salinity means. As a summary, it is important to decrease the MRD and SDRD of soil salinity to improve the effectiveness of temporal stability analysis. It would be an effective way to divide the sampling locations into several groups to find the representative locations in areas with strong variability of soil salinity.

Fig. 10
figure 10

The mean relative difference (MRD) and standard deviation of relative difference (SDRD) of soil salinity at different soil layers in each group. G1–G7 are groups for improved temporal stability, and the S28, S51, …, S9 are the representative locations in each group, respectively

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Table 3 Representative locations and its mean relative difference (MRD) at different soil layers of each group obtained by the improved temporal stability analysis
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3.5 Discussion for dividing the sampling locations into groups using the improved temporal stability analysis

To investigate the impact of dividing the sampling locations into groups when using the improved temporal stability analysis for soil salinity prediction, six schemes by dividing the 62 sampling locations into 1, 3, 5, 7, 9, and 11 groups were carried out. It should be noted that the results corresponding to one group is the same as those of the temporal stability analysis discussed in Sect. 3.3. The predicted and measured soil salinity and the evaluation indictors for the 4 sampling times under the six group schemes are shown in Fig. 8. It can be found that predicted soil salinity under different group numbers ranging from 3 to 11 are significantly improved comparing to temporal stability analysis. The MRE of soil salinity with 3 to 11 groups ranged from − 2.72 to 1.75%, RMSE from 0.02 to 0.08 dS/m, and R2 from 0.84 to 0.98 with most R2 values larger than 0.90. These results indicate that dividing sampling locations into more groups can obtain more accurate range of soil salinity as shown in Fig. 8. However, increasing the group number cannot further improve the prediction results when considering the almost identical evaluation indicators of predicted soil salinity as shown in Fig. 8b–f.

The changes of MRD and SDRD of soil salinity under the six group schemes are shown in Fig. 11 a and b. The range of MRD decreased with increasing of the group number. The range of SDRD decreased obviously when the group number increased from 1 to 7, and then remained unchanged when the group number was greater than 7. Thus, it is recommended that dividing the sampling locations into 7 groups for the study area is suitable. When using the temporal stability analysis, the MRD and SDRD values under different group scheme should be evaluated to determine the group number.

Fig. 11
figure 11

The mean relative difference (MRD) and standard deviation of relative difference (SDRD) of soil salinity with different groups of sampling locations

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3.6 Long-term soil salinity sampling locations

The key to effective and efficient long-term soil salinity monitoring is to establish an effective monitoring network with minimal cost to obtain the major soil salt data (Baalousha 2010), which can be used to evaluate long-term evolution characteristics of soil salinity in time and space. Because the spatial pattern of soil salinity at different soil layers in depth of 1.2–1.8 m is similar to that of 0.6–1.2 m, sampling depth in this area was determined to be 0–1.2 m. There were 7 representative locations in every layer, and totally there were 26 representative locations as shown in Table 3. In addition, to have even distribution of the sampling locations, another 6 sampling locations, i.e., S8, S16, S19, S30, S34, and S42, were added. The sampling locations in monitoring network are shown in Fig. 12, including 32 locations.

Fig. 12
figure 12

The sampling locations for long-term soil salinity monitoring

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As listed in Table 4, the semivariogram models and parameters of root zone (within the depth of 0–0.6 m) and 0.6–1.2 m layer soil salinity obtained by the 32 sampling locations were close to that determined for all sampling locations. The distribution of root zone soil salinity determined by the 32 sampling locations is shown in Fig. 13a–d, which shows a pattern similar to that obtained by using all sampling locations as shown in Fig. 6a–d. The area of different root zone soil salinity determined by the 32 sampling locations and all sampling locations are shown in Fig. 14a–d, with the MRE ranging from − 20.78 to 2.36%, and most R2 more than 0.75. The above results indicate that the spatial distribution of root zone soil salinity can be determined by the representative sampling locations. For 0.6–1.2 m soil layer, the spatial distribution of soil salinity in Y1705, Y1709, and Y1805 determined by the 32 sampling locations (Fig. 13e–g) were also close to that obtained by all sampling locations (Fig. 6e–g). The MRE between area of different soil salinity determined by the 32 sampling locations and all sampling locations in Y1705, Y1709, and Y1805 ranged from − 23.67 to 13.70%, and R2 from 0.46 to 0.88. Only relatively poor results were found for the area with soil salinity being smaller than 0.21 dS/m in Y1809, which would be caused by sparse points. In general, the spatial distribution of soil salinity determined by the 32 representative sampling locations are acceptable in the study area.

Table 4 The semivariogram models and parameters of root zone (within the depth of 0–0.6 m) and 0.6–1.2 m layer soil salinity for all sampling locations and 32 representative sampling locations
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Fig. 13
figure 13

The spatial distribution of root zone (within the depth of 0–0.6 m) and 0.6–1.2 m layer soil salinity determined by sampling locations for long-term soil salinity monitoring at the 4 sampling times

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Fig. 14
figure 14

The area of different soil salinity determined by 32 representative sampling locations and all sampling locations

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4 Conclusions

In this study, a 2-year field experiment was carried out to characterize the temporal and spatial variability of soil salinity in a large irrigation area in northern China. The temporal stability analysis was improved to estimate and predict the spatial mean of soil salt in this area. A monitoring network for this area was then recommended to evaluate the long-term evolution characteristics of soil salinity by comprehensively considering the results of spatiotemporal variability and the improved temporal stability analysis. The major conclusions were drawn as follows:

1. Regional averaged soil salinity dynamics have obvious seasonal variation characteristics. The spatial dependency of soil salinity is strong in study area. The spatial distribution of soil salinity is similar among different soil layers and relatively stable in time.

2. It is difficult to use temporal stability analysis for estimating the spatial mean of soil salinity due to the strong variability of soil salinity with larger range of MRD and SDRD.

3. Dividing the sampling locations into several groups can decrease the range of MRD and SDRD in each group, and can significantly improve the prediction accuracy of soil salinity.

4. When using temporal stability analysis, the MRD and SDRD values under different group schemes should be evaluated to determine the group number. It should be required that the representative sampling location with minimum SDRD owns the MRD close to 0 in each group.

5. The number of sampling locations to evaluate long-term evolution characteristics of soil salinity in time and space is 32 for the study area, which are comprehensively considered by the results of spatiotemporal variability and the improved temporal stability analysis.