Identifying representative sites to simultaneously predict hillslope surface and subsurface mean soil water contents

Catena 167 (2018) 363–372

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Identifying representative sites to simultaneously predict hillslope surface and subsurface mean soil water contents

T

⁎

Xiaoming Laia,b, Zhiwen Zhoua,b, Qing Zhua,b,c, , Kaihua Liaoa a

Key Laboratory of Watershed Geographic Sciences, Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 210008, China University of Chinese Academy of Sciences, Beijing 100049, China c Jiangsu Collaborative Innovation Center of Regional Modern Agriculture & Environmental Protection, Huaiyin Normal University, Huaian 223001, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Temporal stability analysis k-means clustering Up-scaling

Many approaches have been proposed to identify the representative sampling sites for estimating the spatial mean soil water contents. However, comparisons on these approaches have seldom been conducted to simultaneously predict the surface and subsurface mean soil water contents. In this study, five approaches were evaluated in identifying representative sites to estimate the surface and subsurface mean soil water contents on a typical hillslope in Taihu Lake Basin, China. They were temporal stability analysis (TSA), k-means clustering with environmental factors as inputs (EFs), combinations of TSA and EFs (EFs + TSA), k-means clustering with surface soil water contents as inputs (Theta), and combinations of TSA and Theta (Theta+TSA). The correlation coefficient (r) and root mean squared error (RMSE) between estimated and measured mean soil water contents were used to evaluate the accuracies during the calibration period (the first 25 dates) and validation period (the last 18 dates). Results showed the optimal number of representative sites on this hillslope was six. When > 6 representative sites were selected, the TSA had the lowest accuracies for estimating both surface and subsurface mean soil water contents during validation period (mean RMSE ≥ 0.011 m3 m−3). The Theta and Theta + TSA had better accuracies in estimating surface mean soil water contents during both calibration and validation periods (mean RMSE < 0.007 m3 m−3). However, to estimate surface and subsurface mean soil water contents simultaneously, the EFs and EFs + TSA were more promising (mean RMSE < 0.011 m3 m−3 during validation period), especially the EFs which only required one-time collection of environmental factors. These findings will be beneficial for choosing proper approach to calibrate and validate the remote sensed soil water contents.

1. Introduction In-situ monitoring and remote sensing are two most common techniques to measure soil water contents at different spatial scales (Robinson et al. 2008; Brocca et al. 2010; Zhu et al. 2012; Vereecken et al. 2014). Relative to in-situ monitoring, remote sensing technique is more promising in fast and cost-efficient measurements of surface soil water contents at large spatial scales. However, remotely sensed soil water contents require the ground-based in-situ observations at the corresponding pixel for the calibration and validation (Mohanty and Skaggs 2001; Martínez-Fernández and Ceballos 2005; Mohanty et al. 2017), which are highly costly and time-consuming (Brocca et al. 2010; Faridani et al. 2016). Therefore, identifying the representative sites of in-situ observations to predict the spatial mean soil water contents by balancing the predicting accuracy and sampling costs is of great significance in hydrological studies. Temporal stability analysis (TSA) has been commonly used to

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identify the representative sites for predicting mean soil water contents in previous studies (e.g., Grayson and Western 1998; Cosh et al. 2004; Martínez-Fernández and Ceballos 2005; Vivoni et al. 2008; Ran et al. 2017). The TSA was proposed by Vachaud et al. (1985) and defined as the time invariant associations between spatial locations and classical statistical parameters of soil water contents (e.g. spatial average or relative ranking). Traditionally, the location with the temporal mean relative difference (MRD) closest to zero or the lowest value of the standard deviation of relative difference (SDRD) was recognized as the representative site (e.g., Grayson and Western 1998; MartínezFernández and Ceballos 2005; Brocca et al. 2010). However, the performances in identifying the representative site to estimate the mean soil water contents by these two parameters were challenged in previous studies (Hu et al. 2012; Liao et al. 2017). Some other indicators, such as the index of temporal stability (ITS) (Jacobs et al. 2004), the mean absolute bias error (Hu et al., 2010), were proposed by previous studies and found have better performances in identifying the

Corresponding author at: Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 210008, China. E-mail address: [email protected] (Q. Zhu).

https://doi.org/10.1016/j.catena.2018.05.016 Received 21 October 2017; Received in revised form 15 May 2018; Accepted 16 May 2018 0341-8162/ © 2018 Elsevier B.V. All rights reserved.

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vertical directions. Therefore, new approaches should be tested to identify the representative sites to simultaneously estimate the surface and subsurface mean soil water contents. Therefore, based on the surface (10 cm) and subsurface (30 cm) insitu soil water content observations from 77 sampling sites on a hillslope, the objectives of this study were to: (i) find the optimal number of representative sites by methods of TSA, k-means clustering algorithm and the combinations of TSA and k-means clustering algorithm; (ii) evaluate the accuracies in predicting the surface mean soil water contents by multiple representative sites identified by these methods; (iii) investigate the feasibility of estimating the subsurface mean soil water contents by representative sites identified by surface soil and terrain information.

representative sites. Contradictory prediction accuracies in estimating the mean soil water contents were derived by using TSA to identify the representative site. For example, Zhao et al. (2010) and Penna et al. (2013) found that the determination coefficients between predicted and actual mean soil water contents were higher than 0.90, while Cosh et al. (2004) and Vivoni et al. (2008) summarized that the determination coefficients were below 0.85. This may be attributed to that only one representative site was generally determined in previous studies, which resulted in large uncertainty. To reduce the representative error, both in the studies by Van Arkel and Kaleita (2014), She et al. (2015) and Ran et al. (2017), multiple representative sites were identified by TSA and prediction accuracies were sensitive to the number of representative sites. To improve the prediction accuracy, representative sites were also identified by combining TSA with other prior information (e.g., soil properties, landscape heterogeneity) (Vereecken et al. 2008). For example, Zhou et al. (2007) integrated soil information into the TSA and provided more accurate representative locations for capturing mean soil water contents. Ran et al. (2017) considered the village groups as a stratification layer and applied TSA region by region to identify multiple representative sites and achieved good accuracy. Thereby, combining the TSA with the stratification of the study area based on prior information is an alternative in identifying the optimal number of representative sites and may perform better than the traditional TSA. The k-means clustering algorithm is a new approach in identifying the representative sites for predicting mean soil water contents. It is the most popular and simplest clustering method that separates the multivariate data into k clusters so that the squared error between the empirical mean of the cluster and the points in the cluster is minimized (Jain 2010). Van Arkel and Kaleita (2014) firstly applied soil properties and terrain attributes as inputs into the k-means clustering to determine the representative sites and better accuracies were achieved than TSA. Liao et al. (2017) evaluated the performances of TSA, k-means clustering and random sampling strategy in identifying representative sites, and found the k-means clustering performed better than other approaches. However, only several limited number of clusters were taken into account in these studies, thus the optimal number of representative sites could not be determined. For example, in the study by Van Arkel and Kaleita (2014), only schemes of 1, 2, 3, 4 clusters were considered, and Liao et al. (2017) only considered 2, 4, 6, 8 clusters. In addition, the combination of TSA with stratifications of the study area by the kmeans clustering to identify the representative sites has rarely be investigated in previous studies. Previous studies were mostly focused on identifying the representative sites for predicting surface mean soil water contents and subsurface mean soil water content estimation had been less addressed (e.g., Vivoni et al. 2008; Zhao et al. 2010; Mohanty et al. 2017; Liao et al. 2017). Efforts have been made to estimate subsurface soil water contents by integrating remote sensed surface soil water contents with soil hydrologic models and assimilation schemes in previous (e.g., Albergel et al. 2008; Faridani et al. 2016; González-Zamora et al. 2016). However, validation of the estimated subsurface soil water contents by in-situ measurements is still an inevitable issue (Teuling et al. 2006). Whether the representative sites identified by the surface soil and terrain information can be used to estimate the subsurface mean soil water contents have not been fully revealed. Several studies have been conducted on this issue but mixed conclusions have been received. For example, Penna et al. (2013) and Wang et al. (2013) indicated that one representative site recognized at surface soil layer was adequate to estimate the mean soil water contents at other depths. However, Gao and Shao (2012) and Heathman et al. (2012) concluded that none point was sufficient to represent the mean soil water contents for different soil layers. Previous studies were mostly relied on the surface soil water content data to identify the representative sites to simultaneously predict the surface and subsurface mean soil water contents. However, the soil water contents have high spatial variability in both horizontal and

2. Materials and methods 2.1. Study hillsope Two adjacent hillslopes which are separated by ditch and respectively covered by green tea (Camellia sinensis (L.) O. Kuntze) and moso bamboo (Phyllostachysedulis (Carr.) H. de Lehaie), were selected as the study region in the hilly area of Taihu Lake Basin, China (Fig. 1). The weather of this region belongs to the north subtropical-middle subtropical transition monsoon climate, with annual mean temperature and mean precipitation of 15.9 °C and 1157 mm, respectively. The soil type is categorized as shallow lithosols according to FAO soil classification and the parent material is quartz sandstone. Soil texture of this study region is classified as silt loam, and the thickness of soil varies from < 0.3 m at the summit slope position to about 1.0 m at the foot slope position. Detailed descriptions of this study area can be found in the study by Lai et al. (2017). 2.2. Soil water content measurement For monitoring volumetric soil water contents, access polyvinyl chloride tubes were installed at 77 sites on this hillslope (Fig. 1). A portable time-domain reflectrometry TRIME-PICO-IPH soil moisture probe (IMKO, Ettlingen, Germany) was employed to measure the soil water contents of these 77 sites on 43 dates from January 2013 to March 2016. Considering the non-saline and non-viscous soils on the study hillslope, the factory-set calibration curve was adopted to infer the volumetric soil water contents from the measured dielectric constant. However, the uncertainty of measurements could still exist, which provided by the factory was ± 0.03 m3 m−3, and provided by Cosh et al. (2016) was ± 0.05 m3 m−3. Before the campaign on each survey date, the TRIME-PICO-IPH probe was adjusted in buckets with dry and saturated beads following the standard procedure in the user manual. Soil water contents were measured at the depth interval of 0to 20-cm and 20- to 40-cm (representing the soil water contents at the depths of 10- and 30-cm, respectively). More detailed information in soil water content measurements is presented in Lai et al. (2017). 2.3. Soil properties and terrain attributes Soil samples at 0- to 20-cm and 20- to 40-cm depth intervals were collected around each soil water content access tube. After air dried, weighted, ground and sieved, these soil samples were used to determine the rock fragment contents (RFC), soil clay content (clay), silt content (silt) and sand content (sand), and the organic matter (OM) (Lai et al. 2017). In addition, the depths to bedrock (DB) of all 77 sites were also determined when installing the access tubes and taking soil samples using a hand auger. A high spatial resolution (1 m × 1 m) digital elevation model (DEM) of the study hillslope was obtained based on the 1:1000 contour map. Terrain attributes including elevation, slope, plane curvature (PLC), profile curvature (PRC), and topographic wetness index (TWI) were 364

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Fig. 1. (a) Location of the study hillslope, (b) the distributions of sampling sites on the study hillslope, and (c) the photographs from both hillslopes, the measurements of soil water contents by TDR, and the weather station.

determined from this DEM in ArcGIS 10.0 (ESRI, Redlands, CA). The terrain attributes of all 77 sampling sites were then extracted. Soil properties and terrain attributes of this hillslope are listed in Table 1.

MRDi =

1 T

T

∑ j=1

θij − θj θj

(1)

where θij is the soil water content on the j sampling day (total T sampling days) at the i site of N sampling sites on the hillslope, and θj is the arithmetic mean of soil water content on day j (j = 1 to T).

2.4. Methods of analysis 2.4.1. Temporal stability analysis The MRD and SDRD were calculated in the TSA. The MRD is defined as follows:

θj =

1 N

N

∑ θij i=1

The SDRD is calculated by: 365

(2)

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unit (BMU) to the cluster centroid. The estimated mean soil water content on day j (θj est ) was calculated using the following equation:

Table 1 Statistical summaries of soil properties, terrain attributes and the temporal mean soil water contents (θt ) on the study hillslope. SP: slope percent; TWI: topographic wetness index; PLC: plane curvature; PRC: profile curvature; DB: depth to bedrock; RFC: rock fragment content; OM: organic matter; Min: minimum; Max: maximum; SD: standard deviation. Properties

10 cm

Terrain attributes SP (%) 10.04 Elevation (m) 81.85 TWI 5.17 PLC −0.15 PRC 0.04 DB (cm) 52.55

θ t (m3 m−3)

0.46 12.63 73.62 13.75 2.12 0.18

1 T−1

SDRDi =

T

∑ ⎛⎜ j=1

Min

Max

SD

0.02 77.50 1.72 −9.80 −20.70 18.00

19.49 87.17 10.03 13.67 12.63 86.00

3.83 2.69 1.88 3.50 4.94 13.40

0.17 4.60 55.89 9.35 1.31 0.06

0.66 34.76 82.24 19.90 2.95 0.36

0.10 5.18 4.84 2.04 0.38 0.06

θij − θj

⎝

θj

Mean

Min

Max

SD

0.47 11.65 73.91 14.44 1.56 0.18

0.21 3.28 61.96 10.39 0.48 0.05

0.78 26.13 84.07 23.69 2.87 0.33

0.11 4.53 4.74 2.25 0.46 0.07

2

− MRDi ⎟⎞ ⎠

(3)

The MRD at each site quantifies the systematic bias of soil water content at a certain location with respect to the spatial mean. Locations with a near to zero MRD are considered to have small systematic biases when representing mean soil water contents. The SDRD characterizes the variance of the representativeness of the location, smaller SDRD means more temporally stable. In this study, the index of temporal stability (ITS) proposed by Jacobs et al. (2004) was adopted to identify the representative sites, which performed better than the SDRD as exposed by Liao et al. (2017) on this study hillslope:

ITSi =

MRDi 2 + SDRDi 2

(4)

The TSA was conducted on the surface soil water contents. The arithmetic mean of soil water contents of multiple representative sites with the ranked smallest ITS was used to estimate the hillslope mean soil water contents. The number of representative sites ranging from 1 to 20 was considered to recognize the optimal number of representative sites in this study as 20 representative sites were sufficient to estimate the spatial mean soil water contents on this study hillslope (Lai et al. 2017).

k

N

(6)

2.5. Evaluation criteria The temporal soil water content data on the first 25 dates (accounting for 60% of the entire observation dates) were used as the calibration dataset, and the data on the remaining 18 dates (40% of the entire dates) were applied as the validation dataset. The correlation coefficient (r) and the root mean squared error (RMSE) were used to quantify the accuracies of different approaches. In addition, the soil water contents during the validation period were further divided into dry and wet periods with a criteria of surface mean soil water content of 0.211 m3 m−3. This was used to assess prediction accuracies during dry and wet periods. Soil water contents on eight dates were determined as dry period, on the remain ten dates were recognized as wet period.

2.4.2. k-Means clustering algorithm In the k-means clustering algorithm, cluster centers are initially chosen randomly from the set of input observation vectors. An iterative approach is then employed by minimizing the objective function ξ(k) between the input vector and the centroid vector:

ξ (k ) =

∑i = 1 θBMUij × ni

where k is the number of clusters determined a priori, θBMUij is the soil water content on day j for the BMU to the centroid of the cluster i, ni is the number of sampling sites belonging to the cluster i, and N is the total number of sampling sites (N = 77). In this study, we proposed a new approach to estimate the mean soil water contents. Instead of using the BMU, the representative site of each cluster was determined by TSA. For each cluster, sampling site with the lowest ITS value was considered as the representative site of this cluster. Thus, in Eq. (6), the θBMUij was replaced by the soil water content of the representative sites with lowest ITS value on cluster i and on day j. Two kinds of input variable datasets were used in the k-means clustering algorithm. The first one contained the surface soil water contents during calibration period. The second one contained the 11 environmental factors (slope, elevation, TWI, PLC, PRC, DB, RFC, sand, silt, clay and OM). Therefore, four schemes were derived to estimate the hillslope mean soil water contents, they are: (1) denoted as “Theta”, which applied the surface soil water contents as inputs in k-means clustering to identify the representative sites; (2) denoted as “Theta + TSA”, which applied the surface soil water contents as inputs in k-means clustering to cluster the sampling sites and then used the TSA to identify the representative site on each cluster; (3) denoted as “EFs”, which applied the environmental factors as inputs in k-means clustering to identify the representative sites; (4) denoted as “EFs + TSA”, which applied the environmental factors as inputs in kmeans clustering to cluster the sampling sites and then used the TSA to identify the representative site on each cluster. Before the k-means clustering, the input variables were normalized to avoid an overweighting of higher values (Altdorff and Dietrich 2012). The number of clusters conducted on this study ranges from 1 to 20 to determine the optimal number of representative sites. The k-means clustering algorithm was realized by writing codes in MATLAB R2012a (MathWorks, Natick, MA, USA).

30 cm

Mean

Soil properties RFC (g g−1) Sand (%) Silt (%) Clay (%) OM (%)

k

θj est =

ni

∑ ∑ ‖Xij − ui ‖2 i=1 j=1

3. Results

(5)

3.1. Spatio-temporal dynamics of soil water contents

where k is the number of clusters determined a priori, ni is the number of points belonging to the cluster i, Xij is the vector of attributes of the j data object of the cluster i, ui is the mean value of the attributes for the data objects in the cluster i, and || || describes the Euclidean distance between two data objects. In this study, Hartigan and Wong's (1979) algorithm was used to run the k-means clustering. The centroid vector of each cluster was then identified by 200 times of iteration in this study, since stable results were derived after 200 times of iteration by multiple tests. Finally, the input vector with the smallest distance from each centroid corresponded to the best matching

Remarkable fluctuations of the surface (10 cm) and subsurface (30 cm) mean soil water contents (ranging from 0.090 to 0.252 m3 m−3 and from 0.112 to 0.249 m3 m−3, respectively) on the hillslope were presented during the study period (Fig. 2). The greatest surface and subsurface mean soil water contents were observed on 17 July 2015, 20 November 2015, respectively, and low mean soil water contents occurred from September 2013 to January 2014. Both the surface and subsurface mean soil water contents were significantly correlated 366

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Fig. 2. Times series of (a) surface and (b) subsurface mean soil water contents and the corresponding standard deviations, and (c) the correlation coefficients between surface and subsurface soil water contents, and (d) the rainfall.

points on the curves of correlation coefficients or RMSE vs. the number of representative sites (Figs. 4 and 5). Below the threshold, the prediction accuracies (r and RMSE of estimated and measured surface mean soil water contents) decreased remarkably with the reducing of representative site quantities. Above the threshold, additional representative sites did not obviously improve the prediction accuracies. During calibration period, the r improved from 0.973 by one representative site to 0.990 by 6 representative sites when using TSA, EFs + TSA, Theta and Theta+TSA, while the RMSE declined from 0.020 m3 m−3 to 0.006 m3 m−3. For EFs, a lower r (0.864) and larger RMSE (0.036 m3 m−3) were found when one representative site was used. During validation period, the r improved from 0.914 by one representative site to 0. 970 by 6 representative sites when using TSA, EFs + TSA, Theta and Theta + TSA, while the RMSE reduced from 0.024 m3 m−3 to 0.007 m3 m−3. For EFs, also a lower r (0.863) and larger RMSE (0.045 m3 m−3) were found when one representative site was selected. Above the threshold, the r were all above 0.990 and the RMSE were mostly below 0.010 m3 m−3 for all these approaches during calibration period, while during validation period, the r were all above 0.950 and the RMSE were mostly below 0.010 m3 m−3. Therefore, to better evaluate the performances of different approaches in estimating the hillslope mean soil water contents, boxplots of the RMSE with the number of representative sites ranging from 6 to 20 were displayed in Fig. 6. The performances of these five approaches in estimating surface mean soil water contents during calibration period were different from

(p < 0.01) with the corresponding standard deviations of the soil water content observations (r = 0.766 and r = 0.721 for surface and subsurface, respectively). Large correlation coefficients were observed between surface and subsurface soil water contents (mean: 0.740, and ranged from 0.565 to 0.871) (Fig. 2c). 3.2. Temporal stability of soil water contents The ranked MRD and the corresponding SDRD and ITS during the calibration period were varied for surface and subsurface soil water contents (Fig. 3). The MRD and SDRD for the surface soil water contents respectively ranged from −0.786 to 1.063 and from 0.051 to 0.397, and the ITS ranged from 0.101 to 1.117. Site 35 was most appropriate to estimate the surface mean soil water contents (r = 0.973 and RMSE = 0.019 m3 m−3) since it had the lowest ITS value. For subsurface soil water contents, the MRD ranged from −0.729 to 0.981 and the SDRD ranged from 0.048 to 0.363, and the ITS ranged from 0.109 to 1.047. Still site 35 had the smallest ITS, and was most appropriate to estimate the subsurface mean soil water contents (r = 0.939 and RMSE = 0.018 m3 m−3). 3.3. Accuracies in estimating surface mean soil water contents A threshold of the number of representative sites (about 6) can be observed when using different approaches during both calibration and validation periods (Fig. 4). In this study, the “threshold” is the break 367

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Fig. 3. The ranked MRD of (a) surface and (b) subsurface soil water contents during the calibration period. Vertical bars correspond to ± SDRD over time, and the solid line denotes the ITS.

Fig. 4. The changes of the prediction accuracies (r and RMSE) in estimating surface mean soil water contents during (a) calibration and (b) validation periods with the number of representative sites identified by TSA, EFs, EFs + TSA, Theta, Theta+TSA. 368

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Fig. 5. The changes of the prediction accuracies (r and RMSE) in estimating subsurface mean soil water contents during (a) calibration and (b) validation periods with the number of representative sites identified by surface soil and terrain information by TSA, EFs, EFs + TSA, Theta, Theta + TSA.

performance (mean r value of 0.993 and mean RMSE value of 0.006 m3 m−3), and followed by the EFs + TSA (mean r value of 0.992 and mean RMSE value of 0.009 m3 m−3). During validation period, EFs + TSA, Theta and Theta+TSA had similar performances, with the mean r values around 0.980 and RMSE values around 0.007 m3 m−3. However, the accuracy of Theta was greatly fluctuated with the number

that during validation period when the representative sites were above 6 (Figs. 4 and 6a). During calibration period, the EFs had the worst accuracy with the lowest mean r value of 0.991 and largest mean RMSE value of 0.011 m3 m−3. Both of Theta and Theta+TSA had the relatively better accuracies than other approaches (mean r values of 0.997 and mean RMSE value of 0.004 m3 m−3). The TSA had the secondary

Fig. 6. Boxplots of the RMSE of the estimated and measured (a) surface mean soil water contents, and (b) subsurface mean soil water contents during calibration and validation periods, with the number of representative sites ranging from 6 to 20 identified by TSA, EFs, EFs + TSA, Theta, Theta + TSA. As the statistical characteristics of r were generally similar among different approaches, only the statistical features of RMSE of different approaches were displayed. The Box-Whisker plots show the minimum, maximum, mean, lower quartile and upper quartile values. 369

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of representative sites. The EFs had the secondary accuracy (mean r value of 0.978 and mean RMSE value of 0.008 m3 m−3), and the TSA had the worst accuracy with the largest mean RMSE value of 0.011 m3 m−3.

Table 2 The accuracies in estimating surface and subsurface mean soil water contents using six representative sites identified by TSA, EFs, EFs + TSA, Theta and Theta + TSA, and the spatial standard deviation of soil water content based on these six representative sites (SD of θt ). The θt is the temporal mean soil water content.

3.4. Accuracies in estimating subsurface mean soil water contents At least six representative sites were also needed in estimating subsurface mean soil water when adopting the same representative sites identified for surface mean soil water content estimation (Fig. 5). Below the threshold, substantial increasing of r and decreasing of RMSE were observed with the increasing number of representative sites. Above the threshold, relative stable accuracies were achieved. For all five approaches, the r were generally above 0.950 and the RMSE were generally below 0.020 m3 m−3 during calibration period, while the r were generally above 0.800 and the RMSE were generally below 0.020 m3 m−3 during validation period. Therefore, the boxplots of RMSE were also figured to better reveal the different performances of these approaches with the number of representative sites ranging from 6 to 20 (Fig. 6). The performances of these five approaches during calibration period were also different from that during validation period when the number of representative sites was no less than six (Figs. 5 and 6b). During calibration period, the TSA had the best performance with distinct low RMSE (mean value of 0.006 m3 m−3). The EF had second best performance with the lower mean RMSE value (0.010 m3 m−3), and both of the r and RMSE values were stable with the increasing number of the representative sites. The EFs + TSA had the worst performance with the mean RMSE value of 0.015 m3 m−3, and the Theta and Theta + TSA had moderate performances (mean RMSE values about 0.013 m3 m−3). However, during validation period, both of TSA and Theta+TSA had the worst performance with the relative large RMSE (mean RMSE values of 0.015 m3 m−3 and 0.016 m3 m−3, respectively). The EFs had the best and most stable performance with mean RMSE value of 0.009 m3 m−3. The EFs + TSA and Theta had the similar mean RMSE value of 0.011 m3 m−3, while the EFs + TSA had relative low mean value of r (0.920).

Method

Depth

Period

r

RMSE (m3 m−3)

6 sites

SD of θt (m3 m−3)

TSA

Surface

Calibration Validation Calibration Validation

0.987 0.966 0.972 0.945

0.008 0.011 0.006 0.019

0.010 0.014 0.051 0.045

Calibration Validation Calibration Validation

0.986 0.955 0.978 0.899

0.011 0.009 0.016 0.016

Calibration Validation Calibration Validation

0.994 0.976 0.969 0.810

0.006 0.006 0.021 0.014

Calibration Validation Calibration Validation Calibration Validation Calibration Validation

0.993 0.985 0.970 0.921 0.993 0.985 0.970 0.921

0.006 0.007 0.011 0.009 0.006 0.007 0.011 0.009

14, 22, 34, 35, 65, 69 28, 31, 37, 51, 59, 75 12, 18, 19, 48, 52, 71 9, 30, 35, 62, 71, 76 9, 30, 35, 62, 71, 76

Subsurface

EFs

Surface Subsurface

EFs + TSA

Surface Subsurface

Theta

Surface Subsurface

Theta + TSA

Surface Subsurface

0.048 0.061 0.054 0.074 0.049 0.063 0.049 0.072 0.082 0.092 0.079 0.103 0.082 0.092 0.079 0.103

this hillslope regardless of the approaches. Therefore, six can be determined as the optimal number of representative sites on this study hillslope (Table 2). The optimal number of representative sites was also identified in previous studies. For example, in the study by Brocca et al. (2012), using random combination method, two measurement sites were sufficient to estimate the mean soil water contents with RMSE < 0.02 m3 m−3. Zhao et al. (2013) also concluded that generally 13 randomly distributed sites in the study domain were required to ensure the correlation coefficient ≥ 0.99 and RMSE ≤ 0.02 m3 m−3. She et al. (2015) indicated 2–5 of the time-stable locations were sufficient to determine the areal-mean soil water content on a 6.9 km2 watershed. The optimal six representative sites were varied as identified by different approaches, except for the Theta and Theta + TSA (Table 2). Generally, the six representative sites identified by Theta and Theta + TSA had better performances in estimating both the surface and subsurface mean soil water contents, with relative higher r values (> 0.920) and lower RMSE values (< 0.011 m3 m−3). Besides, the spatial variations of these six representative sites were also diverse for different approaches (Table 2). The standard deviations of the soil water contents at the six representative sites were smaller than the standard deviations of the hillslope soil water contents for TSA, and close to for EFs and EFs + TSA, larger than for Theta and Theta + TSA.

4. Discussion 4.1. The optimal number of representative sites Larger errors (lower r and larger RMSE) were observed when only one site was selected in estimating the mean soil water contents, regardless of the approaches used (Figs. 4 and 5). Although acceptable accuracies were achieved when only one site was identified for some approaches, obvious improvements were still observed with the increasing number of representative sites. This is consistent with the studies by Zhao et al. (2013), Van Arkel and Kaleita (2014) and Ran et al. (2017), which all concluded an obvious lower accuracy in estimating spatial mean soil water contents when only a single site was selected. Discrepant accuracies in estimating the spatial mean soil water content by TSA derived from previous studies (e.g., Vivoni et al. 2008; Zhao et al. 2010; Penna et al. 2013) also demonstrated that large uncertainty existed when only one representative site was selected. In addition, large representative errors in estimating the mean soil water contents have also been reported when only one sampling site were selected using other sampling methods (e.g., statistical method, random combination method) (e.g., Brocca et al. 2012; Gao et al. 2013). For all five approaches, a threshold of six for the number of representative sites was distinguished for estimating the mean soil water contents on the study hillslope (Figs. 4 and 5). Below the threshold, the accuracies in estimating the spatial mean soil water contents were sensitive to the number of representative sites; above the threshold, the accuracies kept almost stable. This indicated that six representative sites were sufficient to estimate the spatial mean soil water contents on

4.2. Comparison of different approaches Compared with other approaches, the TSA performed better during calibration period, but worse during validation period (Figs. 4, 5 and 6). According to Martínez-Fernández and Ceballos (2005), the observations that covered 1 year (a complete seasonal cycle) of measurements were sufficient to determine the representative sites. Thus, in this study, the first 25 dates (covering > 1.5 year) used as calibration period were sufficient to identify the representative sites. Even so, the decline of accuracy during validation period was inevitable, which concluded a lowest prediction efficiency (the ratio of the prediction accuracies during calibration period and validation period). This may be attributed 370

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Fig. 7. Boxplots of the RMSE of the estimated and measured (a) surface mean soil water contents, and (b) subsurface mean soil water contents during dry and wet periods of the validation period, with the number of representative sites ranging from 6 to 20 identified by TSA, EFs, EFs + TSA, Theta, Theta + TSA. The BoxWhisker plots show the minimum, maximum, mean, lower quartile and upper quartile values.

the soil properties and terrain attributes with the observed soil water contents can improve the prediction accuracy, which consistent with the study by Liao et al. (2017). However, Liao et al. (2017) did not investigate the feasibilities of both EF and EFs + TSA in identifying representative sites to estimating subsurface mean soil water contents. The EFs had the highest prediction efficiency in estimating subsurface mean soil water contents. This meant that the k-means clusters with environmental factors as inputs could better reflect the spatial heterogeneity of subsurface soil water contents. This may be attributed to that comparing to the soil water content, the soil/terrain information existed higher spatial dependence, especially in vertical direction. Therefore, the EFs is supposed to be a promising approach in identifying the representative sites for simultaneously estimating the surface and subsurface mean soil water contents. We perceived that when the spatial variation of soil water content was greatly influenced by the soil properties and terrain attributes, the EFs was more feasible in identifying multiple representative sites. In addition, the EFs required only a one-time collection of soil properties and terrain attributes, and these soil/terrain information can be retrieved by remote sensing approach (Mulder et al. 2011). Thus, it is more convenient to find the representative sites by EFs than by traditional TSA (Van Arkel and Kaleita 2014; Liao et al. 2017).

to: (i) the selected representative sites by TSA were these closest to the mean soil water contents, thus the spatial heterogeneity of soil water contents could not be well expressed (Table 2) (Zhao et al. 2013); (ii) simple averaging the soil water contents at these representative sites is unreasonable, since the representative sites had individual weights on the mean soil water contents (Van Arkel and Kaleita 2014). The TSA performed much better than other approaches in estimating subsurface mean soil water contents during the calibration period (Fig. 5). This is because of the high r between the surface and subsurface soil water contents (Fig. 2c). For example, the r value was 0.63 (p < 0.05) between the ITS of surface and subsurface soil water contents. Using the same soil water content dataset as TSA, the Theta and Theta + TSA had advantages in identifying representative sites for estimating surface mean soil water contents during both calibration and validation periods (Fig. 4). This implied that stratifying the study hillslope by k-means clustering and estimating mean soil water contents by weighted averaging the soil water contents on the representative sites can improve the prediction efficiency. Van Arkel and Kaleita (2014) and Liao et al. (2017) also concluded that the k-means clustering algorithm with observed soil water contents as inputs had better performances than TSA during validation period. Besides, the Theta+TSA exhibited a more stable performance than Theta (Fig. 6). This indicated that the combination of k-means clustering and TSA can be more effective than TSA. In previous, few studies investigated the feasibility of Theta or Theta + TSA in estimating subsurface mean soil water contents with surface soil water contents as inputs. In our study, due to the differences of spatial distributions of soil water contents at surface and subsurface, both Theta and Theta + TSA performed poor in estimating subsurface mean soil water contents. What's more, worse performance of Theta + TSA was observed than Theta, due to that the representative sites identified by Theta + TSA relied much more on the spatial characteristics of surface soil water contents. This demonstrated trade-off states between the accuracies in estimating surface and subsurface mean soil water contents existed for the above approaches. The EFs and EFs + TSA had better performances in estimating both surface and subsurface mean soil water contents during validation period (Figs. 4, 5 and 6). Practically, the accuracies of these two approaches, especially the EFs, were independent of the temporal variations of observed soil water contents (Van Arkel and Kaleita 2014). However, as the observed soil water contents were more temporal fluctuated during calibration period than during validation period (Fig. 2), relative worse prediction accuracies of EFs were observed during the calibration period (Fig. 6). Compared with the EFs, the EFs + TSA had better performance in estimating surface mean soil water contents during validation period. This indicated that combining

4.3. The validation errors affected by soil wetness conditions Various performances of the validation errors in estimating both surface and subsurface mean soil water contents can be observed between the dry and wet periods by these five approaches (Fig. 7). The TSA, EFs and EFs + TSA were slightly better during dry period than wet period in estimating both surface and subsurface mean soil water contents. This can be attributed to that the spatial variance of soil water contents increased with the soil wetness condition on this study hillslope. Thus the soil water contents had higher spatial homogeneity during the dry period. However, both the Theta and Theta + TSA had better performances in estimating surface mean soil water contents during the wet period than dry period. This indicated that spatial partitioning the observed soil water contents to identify the representative sites may have advantage in estimating surface mean soil water contents during wet period. Because during wet period, the soil water contents usually had better spatial organization and structure and thus less randomly distributed (Grayson et al. 1997; Western et al. 1999). 5. Conclusions Five approaches by integrating the TSA and k-means clustering 371

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(TSA, EFs, EFs + TSA, Theta, Theta + TSA) were evaluated in this study in identifying multiple representative sites to estimate both surface and subsurface mean soil water contents. Results showed the optimal number of representative sites was six on this study hillslope. When multiple representative sites were selected (i.e. > 6), the TSA had lower prediction accuracies comparing with other approaches, especially during the validation period. The Theta and Theta + TSA had advantages in identifying representative sites for estimating surface mean soil water contents. However, to estimate the hillslope surface and subsurface soil water contents simultaneously, the EFs and EFs + TSA had superiority over the other approaches, especially the EFs. What's more, relative to the EFs + TSA, the EFs was more promising since only one-time collection of soil properties and terrain attributes were required. However, the validation accuracies of these approaches may be varied by the soil wetness conditions. These findings of this study may have great significance in the validation procedure of remotely sensed soil water contents, especially in identifying representative sites for validating the subsurface soil water contents. Nevertheless, as these results were derived from a small study area (0.6 ha), deep investigations were still needed on large study regions to further confirm the above conclusions.

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