ORIGINAL ARTICLE

Spatial prediction of soil water content in karst areausing prime terrain variables as auxiliary cokriging variable

Qiyong Yang • Zhongcheng Jiang •

Zulu Ma • Hui Li

Received: 22 August 2013 / Accepted: 29 April 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract In karst areas, accurately measuring and man-

aging the spatial variability of soil water content (SWC) is

very critical in settling numerous issues such as karst rocky

desertification, ecosystem reconstruction, etc. In these

areas, SWC exhibits strong spatial dependence, and it is a

time and labor consuming procedure to measure its spatial

variability. Therefore, estimation of this kind of soil

property at an acceptable level of accuracy is of great

significance. This study was conducted to evaluate and

compare the spatial estimation of SWC by using ordinary

kriging (OK) and cokriging (COK) methods with prime

terrain variables, tending to predict SWC using limited

available sample data for a 2,363.7 km2 study area in

Mashan County, Guangxi Zhuang Autonomous Region,

Southwest China. The measured SWC ranged from 3.36 to

26.69 %, with a mean of 17.34 %. The correlation analysis

between SWC and prime terrain variables indicated that

SWC showed significantly positive correlation with ele-

vation (r is 0.46, P \ 0.01), and significantly negative

correlation with slope (r is -0.30, P \ 0.01); however,

SWC was not significantly correlated with aspect in the

study area. Therefore, elevation and slope were used as

auxiliary data together for SWC prediction using COK

method, and mean error (ME) and root mean square error

were adopted to validate the prediction of SWC by these

methods. Results indicated that COK with prime terrain

variables data was superior to OK with relative improve-

ment of 28.52 % in the case of limited available data, and

also revealed that such elevation and slope data have the

potential to improve the precision and reliability of SWC

prediction as useful auxiliary variables.

Keywords Soil water content � Geostatistics �Spatial pattern � Cokriging � Terrain variables

Introduction

Soil water content (SWC) is an important part of surface

water resources, which is the basic link between the

hydrologic cycle and energy budget (Martinez-Fernandez

and Ceballos 2003; Delworth and Manabe 1988; Maso-

omeh et al. 2009). It impacts the soil erosion, soil aeration,

vegetation growth and distribution, soil microbial activi-

ties, concentration of toxic substances, transportation of

soil nutrients to roots, and weather prediction at a local to

regional scale (Koster et al. 2004), which is spatial in the

karst mountain areas. Therefore, it is important to under-

stand the spatial variability of SWC, which is a result of the

comprehensive effects of topography, soil type, land use

(vegetation), weather (rain) and other factors (Qiu et al.

2007; Gomez-plaza et al. 2001; Hawley et al. 1983). Zhang

et al. (2011a) selected a field plot (100 m 9 50 m) to

characterize the variability and patterns of upper 15 cm

SWC by using ordinary kriging in a karst depression area

of Huanjiang County, Guangxi Zhuang Autonomous

Region of Southwest China. In order to characterize the

variation and patterns of SWC at depth of 0–16 cm and to

investigate their influencing factors in a karst depression

area of Southwest China, Zhang et al. (2011b) studied the

structure and spatial distribution of SWC using ordinary

Q. Yang (&) � Z. Jiang � Z. Ma � H. Li

Key Laboratory of Karst Ecosystem and Treatment of Rocky

Desertification, Institute of Karst Geology, Chinese Academy

of Geological Sciences, Guilin 541004, China

e-mail: yangqiyong0739@163.com

Q. Yang

School of Geographical Sciences, Southwest University,

Chongqing 400715, China

123

Environ Earth Sci

DOI 10.1007/s12665-014-3329-z

kriging. However, in karst areas, there are positive and

negative landforms, namely peak cluster and depression,

which make landforms in karst areas complex and

changeful. There are so few roadways in karst areas that

even walking there is very difficult. Thus it is time-con-

suming and strenuous to obtain enough soil samples to

describe the spatial variability of SWC. In order to mini-

mize the outside work of investigation and save the funds,

it is significant to predict SWC with auxiliary variables.

Geostatistics is a powerful interpolation tool that can

reduce the uncertainty of estimation and prediction so as to

reduce investigation costs (Ferguson et al. 1998). With

COK method, auxiliary covariates, which are usually more

intensively sampled, can be used to assist in prediction.

There are many studies having demonstrated the superi-

ority of COK to OK (Yates and Warrick 1987; Yanl et al.

2007; Wu et al. 2009), but few considered two or more

variables during the processing COK method. Satellite

could get remotely sensed images, which may help pro-

mote the prediction of SWC (Ammarin et al. 2006).

However, there are always many mountain shadows in the

remotely sensed images of karst mountain areas, which

may bring high ratio of errors in the regression modeling

(Yang et al. 2012). Therefore, it is not easy to obtain a

satisfactory SWC prediction using a remote sensing based

model when there are many mountain shadows in the

satellite images.

Terrain variables, including prime terrain indices and

second terrain indices, have been widely used in mapping

soil properties as auxiliary variables (Luca et al. 2007;

Sumfleth and Duttmann 2008; Bell et al. 2000; Mueller and

Pierce 2003). They can enhance the map quality and reduce

the cost of sampling in three aspects (Tao et al. 2010): (1)

Terrain variables are derived from a digital elevation model

(DEM), and hence can be acquired easily at a low cost; (2)

Terrain variables are exhaustive and spatially continuous,

and can provide relevant information at unsampled loca-

tions; (3) There is a significant correlation between terrain

variables and soil properties, which is probably the most

important aspect. Studies have also revealed that SWC can

be modeled quantitatively by terrain indices (Beven and

Kirkby 1979; Western et al. 1999).

A better understanding of variability of SWC is impor-

tant for improving sustainable land use management and

providing a valuable base, on which subsequent and future

measurements can be evaluated. In this study, elevation

and slope, two of the prime terrain variables, derived from

a DEM, were selected as auxiliary data to predict the

spatial distribution of SWC in Mashan County. The

objectives of this study were to describe the spatial vari-

ability and obtain spatial distribution of SWC in Mashan

County in karst mountain area. As this county is a repre-

sentative of ecological reconstruction areas since 2008, this

study could provide valuable insights for other similar

areas in the same region of Southwest China.

Materials and methods

Study area

Mashan County is located in the middle part of Guangxi

Zhuang Autonomous Region, Southwest China. It is a

mountainous county, and can be divided into two parts, the

eastern big mountains and western hills. It is bounded by

east longitude between 107�410 and 108�290 and north

latitude between 23�240 and 24�020, covering a total area of

2,363.7 km2 with 11 townships (Fig. 1). It has a subtropi-

cal monsoon humid climate with a mean annual tempera-

ture of 21.3 �C and abundant but seasonally uneven

rainfall. Annual mean precipitation is 1,667.1 mm but over

80 % of this falls during the rainy season (April–October).

The topography is characterized by typical karst peak

cluster depression landscape (a combination of clustered

peaks with a common base) with the altitude ranging from

105 to 1,350 m (Fig. 1). Carbonate rocks cover an area of

Fig. 1 DEM (a) and location (b) of the study area, and distribution of lithology (b) in study area

Environ Earth Sci

123

1,830.3 km2 or about 77.4 % of the total area. This county

is short of surface water resources, cultivated land and

firewood, and is one of the poorest counties in Southwest

China.

Soil sampling and SWC analysis

Soil samples were taken at 182 locations (Fig. 2) from

topsoil, almost distributed in all villages throughout the

county in July 2012, using an irregular sampling scheme,

considering all geomorphic surfaces including summit,

shoulder, backslope, footslope, toeslope and depression

during sampling. Geo-positions (latitude and longitude) of

sampling site were determined using a global positioning

system receiver (Juno ST).

SWC was measured gravimetrically. The SWC is

expressed as a dimensionless ratio of mass of water to total

mass of soil which contains this water. This ratio is

reported as a decimal fraction or percentage after multi-

plied by 100 (Yu et al. 1993), which was computed as:

SWC ¼ 100 %�WW �WD

WW

ð1Þ

where SWC is SWC in %, WW, weight of wet soil samples

(g), WD, weight of dry soil samples (g).

Spatial data

Digital elevation model (DEM) is the most commonly

used data source in digital terrain analysis, which calcu-

lates varieties of terrain parameters. In this paper, the

ASTER GDEM (30 m), with coordinate system of

WGS_1984_UTM_Zone_48 N, was used to derive the

prime terrain parameters, such as elevation, slope and

aspect, and the satellite was launched by NASA and

Ministry of Economy, Trade and Industry in 2009. These

data were downloaded from Computer Network Infor-

mation Center, Chinese Academy of Sciences (http://

datamirror.csdb.cn/).

Geostatistics analysis

Geostatistical methods can be used in unbiased prediction

with minimum variance for the soil properties of interest

(Stein and Corsten 1991). Kriging and cokriging are two

typical geostatistical prediction methods. To determine the

degree of spatial correlation of the SWC under study,

experimental semivariograms and cross-semivariogram

were calculated from the sampled data and terrain variable

data. The estimator for the semivariogram and cross-

semivariogram is expressed as (Boyer et al. 1991; Cahn

et al. 1994):

cijðhÞ ¼1

2nðhÞXnðhÞ

i¼1

ziðxÞ � ziðxk þ hÞ½ � zjðxÞ � zjðxk þ hÞ� �� �

ð2Þ

where cij is the semivariance (when i = j) with respect to

random variable zi, h is the separation distance, n(h) is the

number of pairs of zi (xk) and zj (xk) is in a given lagged

distance interval of (h ? dh). Where cij is the cross-semi-

variogram (when i = j), which is a function of h (Yates

and Warrick 1987).

In this study, the semivariograms for SWC, elevation

and slope were fit for using a spherical model (Eq. 3), a

Gaussian model (Eq. 4) and an exponential model (Eq. 5),

respectively. All the cross-semivariograms were suitable

for using a Gaussian model (Eq. 4):

cðhÞ ¼C0 þ C1 for h� a

C0 þ C1

3h

2a� 1

2

h

a

� �3" #

for h\a

8><

>:ð3Þ

cðhÞ ¼ C0 þ C1 1� exp � h2

a2

� �� ð4Þ

cðhÞ ¼ C0 þ C1 1� exp � h

a

� �� ð5Þ

where C0 is the nugget variance, C1 is the sill, a is the

range, and h is the lagged distance. Further detailed pre-

sentations about COK method are given in Odeh et al.

(1995), Boyer et al. (1991) and Cahn et al. (1994).

Software version 7.0 of GS ? Geostatistics for the

Environmental Sciences (Gamma Design Sot ware, Plain-

well, MI) was used to perform the geostatistical compu-

tations and model validations for SWC. The semivariogram

for the other auxiliary variables and the cross-Fig. 2 General location and distribution of 145 training data sites and

37 test data sites

Environ Earth Sci

123

semivariograms with auxiliary variables were performed

on GIS (software version 9.2 of ArcGIS) by applying the

best-fit mathematical functions of the semivariogram. The

spatial distributions of SWC were predicted on GIS. And

validation was carried out simultaneously after the pre-

diction finished on GIS.

Validation

The soil sample data were randomly divided into two

groups, that is, training (interpolation) data, which were

used for the computation of spatial models, and test (val-

idation) data, which were used for validating the spatial

models, the latter representing about 20 % of the whole

sample data (Fig. 2), using the Creat Subset operation

within the Geostatistical Wizard of ArcGIS 9.2.

The accuracy of estimates was assessed by mean error

(ME), root mean squared error (RMSE) and the coefficient

of determination (R2) between the predicted values and the

measured values. The ME and RMSE are defined as:

ME ¼ 1�Pn

i¼1 ðPi � OiÞ2Pni¼1 ðOi �� �OÞ2

ð6Þ

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xn

i¼1

ðPi � OiÞ2s

ð7Þ

where Pi is the predicted value, Oi is the measured value, �Ois the average of measured values and n is the number of

data pairs. Ideally, for a perfect estimate, ME = 1 and

RMSE is minimized.

Results and discussion

Descriptive data of SWC, elevation and slope

Table 1 shows the correlation between SWC and the pri-

mary terrain attributes of elevation, slope and aspect. Sig-

nificant positive correlation was observed between SWC

and elevation, and significant negative correlation between

SWC and slope. But the value of correlation coefficient

between SWC and aspect was only 0.09. So the elevation

and slope were chosen as the auxiliary variables during the

geostatistics. Table 2 describes the SWC corresponding to

different elevation ranges and different slope degrees. As

can be seen, the SWC increases with the elevation

increasing, while it decreases with the slope increasing in

the study area.

Figure 3 summarizes the statistical characteristics of the

sample data for SWC, elevation and slope. The measured

SWC ranged between 3.62 and 26.69 %. The highest SWC

(26.69 %) was measured in Longlao, a village of Lidang

Town in the eastern part of the study area. And the lowest

one (3.62 %) was founded in Chaonan, a village of Zhoulu

Town, western of the study area. The elevation of the

samples ranged between 115.04 and 513.01 m. The highest

elevation was measured in Mingle village of Lidang Town

in the eastern part of Mashan County. The degrees of slope

for the samples ranged between 0.32 and 47.62�. The

highest degree of slope was measured in Baishan Town in

the middle part of Mashan County. Skewness for SWC,

elevation and slope were -0.23, 0.68 and 0.49 respec-

tively, and all of them were normally distributed tested by

Kolmogorov–Smirnov method. However, for elevation, the

logarithmic transformation was performed to find that the

skewness decreased from 0.68 to 0.11. And for slope, the

skewness decreased from 0.49 to -0.14 when square root

algorithm extraction from slope. Therefore, all the fol-

lowing analyses for elevation and slope were based on the

transformation.

Spatial dependences of SWC

The application of geostatistical techniques requires that

the measured data should exhibit a spatial structure. The

degree of spatial dependence of a measured variable can be

quantified with the nugget (C0) to sill (C0 ? C) ratio (abbr.

NSR). According to Cambardella et al. (1994), NSR from 0

to 25 % indicates a strongly structured (S) spatial depen-

dence, which are usually caused by intrinsic factors (e.g.

factors of soil formation); NSR [75 % is indicative of a

weakly structured (W) spatial correlation coupled with a

high degree of unexplained variability, which are normally

affected by extrinsic factors, such as soil management and

tillage practices; NSR ranging from 25 to 75 % points to a

moderately structured (M) variability and it is usually

Table 1 Correlation coefficient between SWC and primary terrain

attributes

Variables Correlation coefficient

Aspect 0.09

Elevation 0.46**

Slope -0.30**

** Correlation is significant at the 0.01 level (2-tailed); n = 182

Table 2 SWC (degree) distribution of different elevation classes and

slope degrees in Mashan County

Elevation (m) Mean of SWC (%) Slope (�) Mean of SWC (%)

\200 16.46 \5 18.53

200–300 15.04 5–15 16.88

300–400 18.89 15–25 16.37

[400 21.68 [25 16.45

Environ Earth Sci

123

caused by both intrinsic factors and extrinsic factors. To

directly compare the semivariogram parameters and the

calculated NSR, a spherical variogram model, a gaussian

variogram model and an exponential model were used for

SWC, elevation and slope, respectively; and a Gaussian

crossvariogram model for all the COK method with aux-

iliary elevation and slope. Table 3 summarizes the vario-

gram parameters and the NSR values for SWC, elevation

and slope.

The SWC revealed a moderately structured variation

with NSR of 38.22 % and both elevation and slope revealed

strong structured variation. And all crossvariogram models

exhibited strong structured variation when using elevation

and slope as auxiliary data. Autocorrelation lengths (range)

of about 25,790–75,188 m were found in these variables,

which amounted to dozens of times of the sampling density.

Comparison of spatial predictions by two methods

From maps of predicted SWC developed by both kriging

and cokriging with elevation and slope data (Fig. 4), it was

found that the SWC had strong spatial variability in the

study area. In general, the distribution of SWC displayed a

patchy and banded structure in the two maps, which

Fig. 3 Statistical characteristics for SWC, elevation, ln (elevation), slope, and sqrt (slope)

Table 3 Variograms model for SWC, elevation and slope, and crossvariogram model with auxiliary data

Sample properties Model Nugget variance (C0) Total sill (C0 ? C) Range (m) a RSS R2 NSR (%) Class of spatial

dependence

SWC Sa 8.61 22.530 38,460 33.8 0.892 38.22 Md

Ln (elevation) Gb 4.30E-04 4.18E-04 25,790 3.33E-07 0.883 9.60 Se

Sqrt (slope) Ec 0.001 0.729 27,418 0.495 0.692 0.14 Se

COK1 Gb 0.01 0.128 27,349 0.013 0.718 7.81 Se

COK2 Gb 0.001 3.012 75,188 1.68 0.877 0.03 Se

COK3 Gb 0.0216 0.101 37,689 0.001488 0.888 21.34 Se

COK1 crossvariogram model for SWC and Ln (elevation), COK2 crossvariogram model for SWC and slope, COK3 crossvariogram model for

SWCa S spherical, b G Gaussian, c E exponential, d M moderate, e S strong

Environ Earth Sci

123

decreased from northeast to southwest. The SWC was

higher in the east and northeast of the study area and lower

in the southwest (Fig. 4). However, differences between

the two maps were discernible. The map developed from

ordinary kriging was smoother than that developed from

cokriging. (1) The predicted SWC map by kriging was less

spatially detailed (more uniform) than that by cokriging in

certain local areas such as the central part in the study area,

as shown in the SWC prediction map (Fig. 4). (2) There

were two more grades distributed (the lowest grade and the

highest grade, e.g., grade of 3.78–10.08 % and grade of

24.49–26.35 %) in the predicted SWC map by cokriging

than that by kriging (Fig. 4). (3) There were more high and

low value centres distributed for SWC in the predicted

SWC map by cokriging, which were similar to the distri-

bution of karst peak-cluster depression.

Table 4 summarized statistics of kriging and cokriging

interpolation results, and revealed that the prediction values

by COK method were closer to the value of sampling data

than those by OK method. The minimum and maximum

values of SWC prediction by kriging were 10.08 and

24.49 %, respectively; and the minimum and maximum

values of SWC prediction by cokriging with elevation and

slope data were 3.78 and 26.35 %, respectively. Whereas,

the minimum and maximum values of SWC derived from

182 soil samples were 3.36 and 26.69 %, respectively. The

mean and CV values of SWC prediction by the two methods

were 16.77 and 16.58 % for kriging, 16.88 and 21.98 % for

cokriging, respectively; and the mean and CV values of

SWC from 182 soil samples were 17.34 and 26.38 %,

respectively. After interpreting the descriptive statistics, it

was found that the variances of the predicted SWC by both

kriging and cokriging were less than that of the 182 soil

samples, and the variance of the predicted SWC by kriging

was less than that by cokriging. So, the smoothing effect of

kriging was more obvious than that of cokriging.

Prediction of SWC and prediction performance

Semivariogram model of training samples was utilized to

estimate validation sites. The ME and RMSE for different

spatial prediction methods with different combination of

auxiliary variables were calculated via Eqs. (6, 7). In order

to quantify the improvement on prediction precision of one

method relative to the other method, a relative improve-

ment (RI) in RMSE, which was used to measure the

improvement on the prediction accuracy of COK over OK,

was defined as (Sumfleth and Duttmann 2008):

RI ¼ RMSEOK � RMSECOK

RMSEOK

� 100 % ð8Þ

where RMSECOK and RMSEOK were the RMSE value of

COK method and OK method, respectively. OK method for

this paper was the reference method.

Coefficient of determination (R2), ME and RMSE for the

37 validation sites were summarised in Table 5. Bigger R2

Fig. 4 Predicted SWC (%) by a kriging and b cokriging

Table 4 Descriptive statistics

of SWC derived from 182

samples, kriging and cokriging

estimates (n = 59,075)

Sample properties Mean Standard

deviation

Minimum Maximum Coefficient of

variation (%)

Measured data (%) 17.34 4.57 3.36 26.69 26.38

Kriging estimates (%) 16.77 2.88 10.08 24.49 16.58

Cokriging estimates (%) 16.88 3.71 3.78 26.35 21.98

Table 5 Results of validation

for OK and COK methods with

elevation and slope

OK COK

R2 0.469 0.612

ME 0.436 0.658

RMSE 3.472 2.481

RI (%) – 28.52

Environ Earth Sci

123

was obtained for COK method (Fig. 5). The ME for OK

method was 0.436, which was smaller than that of COK,

while the RMSE for OK was bigger than that with com-

bination of auxiliary variables elevation and slope. The

results indicated that the introduction of terrain variables,

such as elevation and slope, can improve the prediction

accuracy for a given prediction method. Compared with

OK, the application of COK resulted in relative improve-

ment (RI) of 28.52 %. Yates and Warrick (1987) found that

cokriging gave better predictions than kriging when sample

correlations exceeded 0.5 and when the auxiliary variable

was oversampled. There were more studies have demon-

strated that cokriging was only minimally superior to

ordinary kriging when auxiliary variables were not highly

correlated to primary variables (Shouse et al. 1990; Mar-

tinez-Cob 1996; Triantafilis et al. 2001). In this study, the

correlations between SWC, elevation and slope were not

exceeded 0.5. However, the prediction precise even got

promote, when both elevation and slope as the auxiliary

variables together. This study suggests that use of more

than one auxiliary variable is important to obtain successful

results from cokriging when the covariates are not highly

correlated.

Conclusions

It is critical to select appropriate auxiliary variables for

the prediction of SWC in karst areas. In this study, though

the correlations between SWC, elevation and slope were

significant, the values of correlation coefficient were not

exceeded 0.5. This study aimed to improve prediction

accuracy of SWC using cokriging with elevation and

slope as auxiliary variables. The prediction of SWC by

cokriging with these terrain variables data was an

improvement over that by kriging as measured by

descriptive statistics, ME, RMSE and R2. This study

demonstrates that both elevation and slope as the auxiliary

variables together can improve the prediction of SWC. It

suggests that use of more than one auxiliary variable is

effective to obtain successful results from cokriging when

the covariates are not highly correlated. In addition, there

are many other variables that may contribute to the further

improvement of the results, when they are highly corre-

lated with SWC.

Acknowledgments This research was supported by the Guangxi

Natural Science Foundation (No. 2012GXNSFAA053186), the

Remote Sensing Survey and Ground Monitoring on Karst Rocky

Desertification in Southwest China (No. 1212011220958), the Min-

istry of Water resources of China (No. 2005SBKK05), the Ministry of

Science and Technology of China (No. 2010BAE00739), and the

Institute of Karst Geology, CAGS (No. 2012015). We acknowledge

all the reviewers and editors of the journal for their valuable com-

ments, suggestions, and revisions on this paper. We would also like to

thank Ms. Lily Zeng for polishing the English language of the paper,

which greatly improved the original manuscript.

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