watershed scale temporal stability of soil water...

Geoderma 158 (2010) 181–198

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Geoderma

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Watershed scale temporal stability of soil water content

Wei Hu a, Mingan Shao b,⁎, Fengpeng Han b, Klaus Reichardt c, Jing Tan d

a Key Laboratory of Water Cycle and Related Surface Processes, Institute of Geographic Sciences and Natural resources Research, Chinese Academy of Sciences, Beijing 100101, Chinab State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A & F University,Chinese Academy of Sciences and Ministry of Water Resource, Yangling 712100, Shaanxi, Chinac Laboratory of Soil Physics, Center for Nuclear Energy in Agriculture, University of São Paulo, CEP 13418-900, CP 96, Piracicaba, SP, Brazild State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural resources Research, Chinese Academy of Sciences,Beijing 100101, China

⁎ Corresponding author. Tel.: +86 029 87012405; faxE-mail addresses: [email protected] (W. Hu), ma

0016-7061/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.geoderma.2010.04.030

a b s t r a c t
a r t i c l e i n f o
Article history:Received 5 June 2009Received in revised form 15 March 2010Accepted 29 April 2010Available online 1 June 2010

Keywords:Temporal stabilitySoil water contentGeostatistical analysisSpatial variability

The recognition of temporally stable locations with respect to soil water content is of importance for soilwater management decisions, especially in sloping land of watersheds. Neutron probe soil water content(0 to 0.8 m), evaluated at 20 dates during a year in the Loess Plateau of China, in a 20 ha watersheddominated by Ust-Sandiic Entisols and Aeolian sandy soils, were used to define their temporal stabilitythrough two indices: the standard deviation of relative difference (SDRD) and the mean absolute bias error(MABE). Specific concerns were (a) the relationship of temporal stability with soil depth, (b) the effects ofsoil texture and land use on temporal stability, and (c) the spatial pattern of the temporal stability. Resultsshowed that temporal stability of soil water content at 0.2 m was significantly weaker than those at the soildepths of 0.6 and 0.8 m. Soil texture can significantly (Pb0.05) affect the stability of soil water content exceptfor the existence of an insignificant difference between sandy loam and silt loam textures, while temporalstability of areas covered by bunge needlegrass land was not significantly different from those covered bykorshinsk peashrub. Geostatistical analysis showed that the temporal stability was spatially variable in anorganized way as inferred by the degree of spatial dependence index. With increasing soil depth, the range ofboth temporal stability indices showed an increasing trend, being 65.8–120.5 m for SDRD and 148.8–214.1 mfor MABE, respectively. This study provides a valuable support for soil water content measurements for soilwater management and hydrological applications on sloping land areas.

: +86 029 [email protected] (M. Shao).

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© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Soil water content is a key variable controlling water andenergy fluxes in soils (Vereecken et al., 2007). It acts as one crucialfactor for vegetation production, mainly in semi-arid environ-ments. It varies not only in space but also in time, however, a largebody of data has proven to follow the so called concept of temporalstability (Grayson and Western, 1998; Comegna and Basile, 1994;Cassel et al., 2000; Mohanty and Skaggs, 2001; Thierfelder et al.,2003; Martínez-Fernández and Ceballos, 2003, 2005; De Lannoyet al., 2006; Teuling et al., 2006; Lin, 2006; Brocca et al., 2009,2010), which was described as the time invariant associationbetween a spatial location and classical statistical parameters byVachaud et al. (1985).

Temporal stability of soil water content has been mostly observedduring the soil moisture sampling campaigns aimed at the validation

of remotely sensed mean soil moisture estimation (Jacobs et al., 2004;Cosh et al., 2006; Starks et al., 2006; Cosh et al., 2008; Vivoni et al.,2008). Therefore, most efforts on temporal stability analysis of soilwater content have focused the surface soil layer and very few reportsrefer to the whole soil profile, exception made for the very latestcontributions of Martínez-Fernández and Ceballos (2005), Pachepskyet al. (2005), Starks et al. (2006), De Lannoy et al. (2006), and Guberet al. (2008). Temporal stability has been widely recognized overdifferent areas worldwide, e.g. Ontario-Canada (da Silva et al., 2001),Spain (Martínez-Fernández and Ceballos, 2003), USA-Oklahoma(Cosh et al., 2004), Italy (Brocca et al., 2009). With exception to therecent work by Hu et al. (2009), this concept has not yet been widelyapplied to measurements taken on the Loess Plateau in China, wherethe water content of the different soil depths is the most crucial factorfor vegetation restoration. In fact, the study of temporal stability ofsoil water contents for different soil depths on the sloping land of thisand other similar watersheds can be very important for theirmonitoring, mainly related to soil water management during theprocess of vegetation restoration.

With the aim of identifying locations of temporal stability of soilwater content, many studies have been conducted to look for the

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182 W. Hu et al. / Geoderma 158 (2010) 181–198

contributing factors of this temporal stability. Grayson and Western(1998) and Vivoni et al. (2008) believed that the best locations torepresent the mean soil water content of a catchment should be thelocations which capture the average characteristics of that catchment,e.g., near to mid slopes or mid aspects (Grayson and Western, 1998)or mid elevation (Vivoni et al., 2008). Gómez-Plaza et al. (2000)observed that at the transect scale, when the factors affecting soilwater content were limited to topographical position or localtopography, spatial patterns presented time stability, which was inagreement with the findings of Thierfelder et al. (2003) and Broccaet al.(2009). On the other hand, Tallon and Si (2003) found poorrelationships between temporal stability locations and soil andtopographic properties. Jacobs et al. (2004) observed that samplinglocations with moderate to moderately high clay content tended tohave a more pronounced time stability, whereas Mohanty and Skaggs(2001) believed that sandy loam soils were more time stable than siltloams. Therefore, no consistent conclusions have been drawn oncontributing factors to temporal stability. With the main aim ofexploring the effects of calibration procedures on the temporalstability of neutron probe soil water storage, Hu et al. (2009) foundthat soil particle size and organic matter content were the mainfactors influencing temporal stability, but their conclusions are madebased on soil water storage data from only 12 sampling locations.Thus, besides the inherent differences of contributing factors totemporal stability, the subjective choice of factors and the low numberof samples may also explain the differences of contributing factors.

The spatial pattern of soil water content has been well recognized(Western et al., 1998a, 1998b; Bárdossy and Lehmann, 1998;Wendroth et al., 1999; Walker et al., 2001; Wang et al., 2001;Western et al., 2004; Brocca et al., 2007; Hu et al., 2008), and severalfields were proven to have soil water contents spatially variable in anorganized way. In addition, the spatial patterns of temporal stabilityindicators were also discussed by some researchers (Petrone et al.,2004; Zhou et al., 2007; Brocca et al., 2009; Williams et al., 2009). Todate, however, no report referred to the geostatistical analysis of thespatial pattern of temporal stability indicators. Sufficient samplingnumbers required for the geostatistical techniques may be one of thelimits for the analysis of their spatial patterns. In fact, spatial patternanalysis of temporal stability by geostatistical techniques can be veryimportant for the identification of stable locations for mean soilmoisture estimation in a watershed. If the temporal stability has asound spatial structure, then the locations close to the observed stablelocations should also tend to be stable. In this way, stable locationswould not only be limited to a given sampling location, but thestability could be extended to a broader area, which would greatlyfacilitate the identification of stable locations.

The standard deviation of relative difference (SDRD) was widelyused to identify the temporally stable sampling locations (Graysonand Western, 1998; Gómez-Plaza et al., 2000; Cosh et al., 2006; Coshet al., 2008; Brocca et al., 2009). In these situations, a temporal stablelocation is characterized by a low value of SDRD. Other indices thatjudge the temporal stability can also be found. Jacobs et al. (2004)introduced the root mean square error (RMSE) of the relativedifferences, which is computed from the mean relative differenceand associated variance to identify the best representative locations.According to Jacobs et al. (2004), the location with the mostpronounced time stability is identified as the one with the lowestRMSE. Guber et al. (2008) employed a new temporal stability index Tik,which was computed as the width of the 90% empirical toleranceinterval of empirical probability distribution functions of relative soilwater content. In this case, lower values of Tik correspond to morepronounced temporal stability. Furthermore, Guber et al. (2008) usedthe root-mean-squared differences, Dik, to select the locations thatappeared to be the best for estimating the average water contents atdifferent depths. With these indices, a temporal stable location can beidentified for the mean soil water content estimation for a scale of

interest. However, they cannot be directly related to the estimationerror with the exception of Dik developed by Guber et al. (2008). Fromthe point of view of the mean soil moisture estimation whenconsidering the constant relative differences of stable locations assuggested by Grayson and Western (1998), Hu (2009) and Hu et al.(2010) developed an index of mean absolute bias error (MABE) toidentify the temporal stable locations. The lower MABE refers to astronger stability. In this sense, theMABEwas not only an index for theidentification of stable locations, but also a direct reflection of the errorof the mean soil water content estimation for a given period of time.

This study explored the temporal stability of soil water content forvarious layers (0–0.8 m)measured over one year in a small watershedon the Loess Plateau in China. Two indices, SDRD and MABE werecompared to judge the temporal stability. Specific concerns were:1) the relationship of temporal stability with soil depth; 2) the effectsof soil texture and land use on temporal stability; and 3) the spatialpattern of temporal stability.

2. Materials and methods

2.1. Watershed description

A small watershed called LaoYeManQu (LYMQ, about 20 ha) wasselected inside the larger Liudaogou watershed (110°21′ to 110°23′ Eand 38°46′ to 38°51′ N), Shenmu County, Shaanxi Province, China(Fig. 1). This area is particular for its special environmental conditions,where severe soil and wind erosions concur. The Liudaogouwatershed is characterized by a large number of deep gullies andundulating loess slopes. Climatic conditions are characterized by amean annual temperature of 8.4 °C, and a mean annual precipitationof 437 mm (Tang et al., 1993). The elevations of the LYMQ watershedrange from 1056 to 1130 m. Eight kinds of land uses on the slopeswere recognized according to the dominant vegetation, its coverage,and soil type (Fig. 1(c)). Aeolian sandy soils (sand or loamy sand) andUst-Sandiic Entisol soils (sandy loam or silt loam) dominate the area(Fig. 2). Both soil profiles are characterized by an A horizon (organic,10–30 cm in depth) and a C horizon (parent material), but the Ust-Sandiic Entisol soils have different content of illuvial CaCO3 in theC layer. The basic soil properties for 0–0.1 m soil layer, topographicalproperties, and land surface and vegetation are summarized in Table 1by land use type.

2.2. Sampling locations and measurements

2.1.1. Neutron probe measurement and calibrationAluminum neutron probe access tubes were installed at 124

locations of the LYMQ watershed (Fig. 1(c)), whose distribution overdifferent land uses is summarized in Table 1. From June 11, 2007 toJuly 23, 2008, slow neutron counting rates (CR) were obtained for 20dates at soil depths of 0.1, 0.2, 0.4, 0.6, and 0.8 m. Among the 124locations, 12 sampling locations were selected to establish calibrationcurves (Fig. 1(c)). The criteria for this selection is that the mean andthe range of neutron counting data of these 12 tubes approximate tothose of 124 tubes based on the first seven neutron countingobservations. Furthermore, the geographical locations of the 12tubes should cover the entire watershed to ensure the various soiland vegetation types of this area. Gravimetric soil water contents(u, g/g) of the 12 calibration locations were determined for each of thecorresponding depths at four dates, about 0.5 m away from eachneutron tube. These measurements covered different soil waterconditions, ranging from very dry before the rainy season in April,2008 to very wet just after the rainy season at October, 2008. At eachlocation, a 1 m deep pit was excavated to take undisturbed soilsamples for soil bulk density (BD, g/cm3) determinations andtransform u into corresponding volumetric soil water contents(θ, %). Calibration work was conducted for each layer k with its

Fig. 1. Location of the study area (LYMQ watershed) and sampling sites (marked is the sampling number) on different land uses.

183W. Hu et al. / Geoderma 158 (2010) 181–198

corresponding data sets of CRk versus θk. Therefore, the calibrationequation for each layer k was written as:

θk = akCRk + bk ð1Þ

where ak and bk are the fitting parameters. The coefficients ofdetermination (R2) ranged from 0.869 to 0.939 at the significancelevel of Pb0.01, assumed to be sufficient to produce reasonable θkvalues from CRk readings.

2.1.2. Measurement of other main characteristicsAt each location, disturbed soil samples of the 0–0.1 m soil layer

were also taken during aluminum tube installation, which werepassed through a 1 mm sieve before laboratory analysis. Soil particlesizes were evaluated using the MasterSizer2000 apparatus manufac-tured by Malvern. The proportion of clay (b0.002 mm), silt (0.002–0.05 mm), and sand (N0.05 mm) content was calculated. Soil organicmatter content (OM, %) was determined by the dichromate oxidationmethod (Nelson and Sommers, 1975). One fourth of the 1 mm soil

samples were passed through a 0.25 mm sieve for the measurementof total nitrogen (TN, %) and total phosphorus (TP, %). TNwas valuatedby the semi-micro Kjeldahl method using a KJELTEC SYSTEM1026Distilling Unit, and TP was measured colorimetrically after wetdigestion with H2SO4+HClO4. Undisturbed soil samples of 0.05 mheight (0.025 to 0.075 m soil depth) and 0.002 m2 cross section wereused to measure BD by the gravimetrical method.

On September, 2008, crust coverage (%), stone coverage (%),and grass coverage (%) were visually estimated over areas of1×1 m2 centered in the neutron probe access tube. The relativeerrors of the visual estimates were within 10% compared to theresults obtained by digital photographing and treating technique(Zhu and Shao, 2008). Above ground grass was oven dried toobtain dry yield (kg/m2) of each location. After the elimination ofthe vegetation the surface roughness was measured by the rollerchain method (Saleh, 1993), averaging 10 measurements for eachlocation. Over areas of 5×5 m2, shrub and wood coverage (%) werealso visually estimated, and the corresponding dry yield (kg/25 m2)was determined by combined sampling and visual estimation.

Fig. 2. Maps of (a) soil type and soil texture (S—sand; LS—loamy sand; SaL—sandy loam; SiL—silt loam) and (b) ordinary kriged clay content (%).


Elevation was measured every 1 to 3 three meters for the wholewatershed with a differential, kinematic GPS to construct a digitalelevation model (DEM) with resolution of 1 m×1 m, and severalterrain-based attributes: elevation, Tan (slope)(tanb), Cos (aspect),profile curvature, planform curvature, relief degree of land surface,upstream flow length, downstream flow length, specific contributionarea(a), coarse degree(1/Cos(b)), and wetness index (ln(a/tanb))were derived by using the software ArcMap 9.2 (Table 1).

2.3. Statistical methods

2.3.1. Standard deviation of relative difference (SDRD) and meanabsolute bias error (MABE)

Two indices were employed to analyze the temporal stability ofsoil water content for each depth k. They are both based on theparametric test of the relative differences. Specifically, the relativedifference of soil water content, δikj, for each sampling location i atdepth k for measurement time j is defined as:

δikj =Δikj

θkjð2Þ

where θ―

kj is themean θ at depth k for all the 124 sampling locations attime j, and Δikj is the difference of the soil water content at location iand mean for depth k, expressed as:

Δikj = θikj−θkj: ð3Þ

For each depth k at location i, the mean relative difference (MRD),δik , and the standard deviation of relative difference (SDRD), σ(δik),considering all dates j, are given by:

δik =1M

∑M

j=1δikj ð4Þ

σ δikð Þ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M−1∑M

j=1δikj−δik

� �2s

ð5Þ

where M is the total sampling days.Therefore, the first index to characterize temporal stability is SDRD.

Obviously, a “stable” location in time is characterized by a low value of

SDRD (Brocca et al., 2009). In this sense, the lower the value of SDRD is,the more stable a certain location i would be.

The second index to characterize temporal stability is the meanabsolute bias error (MABE), introduced by Hu (2009). FollowingEqs. (2) and (3), the mean θ at depth k at time j, θkj, can be expressedas:

θkj =θikj

1 + δikj: ð6Þ

According to Grayson and Western (1998), when assuming aconstant offset δik , which is the time averaged value of δikj for a certainperiod, the estimated value of mean θ at any time j for depth k, θkj, canbe calculated as:

θ′kj =θikj

1 + δik: ð7Þ

Therefore, the bias error (BE) of mean θ,ωikj, at time j at depth k forlocation i can simply be written as:

ωikj =θ′kj−θkj

θkjð8Þ

Introducing Eqs. (6) and (7) into Eq. (8), ωikj can be expressed as:

ωikj =δikj−δik1 + δik

: ð9Þ

Taking the absolute value of bias error (ABE), the MABE,Pjωikj, and

the associated standard deviation with time, σ(|ωik|), can be definedas:

Pjωikj =∑M

j=1jωikjj

Mð10Þ

σ jωikjð Þ =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑M

j=1jωikjj−

Pjωikj� �2

M−1

vuuut: ð11Þ

Table 1Main characteristics and sampling numbers for different land uses.

Land use Bungeneedlegrass

Sparse korshinskpeashrub

Dense korshinskpeashrub

Farmland

Almond Sand korshinskpeashrub

Sand mixedshrub

Poplar Total oraverage

Sampling number 42 21 9 8 8 8 18 10 124

Soil properties (0–0.1 m) Soil texture SaL, SiL SaL, SiL SaL, SiL SaL, SiL SaL, SiL S, LS S S SaL, SiL, LS, SClay (%) 5.29a/0.23b 6.02/0.71 2.88/0.65 5.48/0.69 5.35/0.86 1.89/0.69 0.23/0.14 0.27/0.09 3.90/0.26Silt (%) 48.55/1.26 48.20/2.62 33.29/4.76 45.25/3.37 48.11/3.29 22.19/6.30 4.87/0.93 7.88/1.12 35.82/1.80Sand (%) 46.16/1.46 45.79/3.21 63.84/5.36 49.26/4.02 46.54/3.94 75.93/6.98 94.90/1.07 91.85/1.21 60.28/2.05Bulk density (g/cm3) 1.40/0.01 1.39/0.01 1.39/0.03 1.32/0.03 1.33/0.01 1.50/0.04 1.54/0.01 1.52/0.01 1.42/0.01Organic matter content (%) 0.72/0.05 0.46/0.04 0.54/0.14 0.84/0.09 0.70/0.04 0.43/0.09 0.17/0.02 0.36/0.07 0.54/0.03Total nitrogen (%) 0.44/0.02 0.42/0.03 1.11/0.75 0.49/0.04 0.41/0.03 0.35/0.04 0.26/0.02 0.35/0.04 0.45/0.06Total phosphorus (%) 0.44/0.02 0.39/0.02 0.39/0.04 0.35/0.02 0.37/0.02 0.28/0.03 0.20/0.02 0.26/0.03 0.36/0.01

Topographical properties Elevation (m) 1096.2/2.1 1109.0/2.5 1097.3/3.5 1111.3/2.9 1107.5/4.0 1096.8/1.5 1088.9/2.4 1068.2/4.4 1096.9/1.4Cos(Aspect) −0.30/0.06 −0.33/0.11 0.68/0.02 0.57/0.12 0.75/0.09 0.75/0.10 0.36/0.12 0.20/0.15 0.09/0.05Tan(Slope) (tanb) 0.26/0.02 0.24/0.02 0.20/0.02 0.20/0.03 0.28/0.06 0.28/0.06 0.30/0.03 0.41/0.07 0.27/0.01Profile curvature (°) 77.46/2.53 81.68/1.82 80.57/4.76 82.72/2.11 78.62/5.08 82.84/1.04 85.48/0.81 81.38/3.11 80.64/1.08Planform curvature (°) 57.95/2.96 64.48/3.29 57.14/6.43 62.36/6.10 65.96/2.84 71.24/3.12 64.97/4.37 75.39/2.89 63.08/1.53Relief degree of land surface 0.69/0.04 0.70/0.05 0.55/0.06 0.53/0.07 0.81/0.17 0.76/0.14 0.90/0.09 1.13/0.18 0.75/0.03Upstream flow length (m) 10.0/3.0 4.9/1.6 4.0/2.4 3.3/1.7 19.3/10.7 2.8/0.9 13.5/8.3 19.0/11.1 9.6/2.0Downstream flow length (m) 364.0/25.8 547.2/25.8 608.5/29.3 510.3/59.6 578.5/21.3 414.6/29.5 350.8/19.0 312.6/32.2 433.2/14.5Specific contribution area (a) 35.3/13.3 10.3/4.1 7.6/3.9 5.4/2.7 145.6/119.3 4.6/1.4 86.6/71.8 92.1/58.1 44.3/14.5Coarse degree (1/Cos(b)) 1.04/0.004 1.03/0.006 1.02/0.004 1.02/0.006 1.05/0.017 1.05/0.017 1.05/0.010 1.10/0.030 1.04/0.004Wetness index ln(a/tanb) 3.08/0.29 2.82/0.32 2.72/0.47 2.71/0.42 4.13/1.02 2.56/0.39 2.88/0.50 3.16/0.70 3.00/0.16

Land surface andvegetation properties

Surface roughness 0.011/0.001 0.011/0.001 0.008/0.001 0.015/0.003 0.018/0.002 0.013/0.003 0.016/0.002 0.016/0.002 0.013/0.001Crust coverage (%) 34.86/1.48 39.90/4.55 33.00/4.74 33.38/9.13 20.00/8.50 42.63/3.96 33.94/3.83 29.50/6.46 34.46/1.52Stone coverage (%) 0.12/0.05 0.31/0.16 1.33/1.33 0.13/0.13 0.38/0.18 0.25/0.25 0.08/0.08 0.00/0.00 0.25/0.10Grass coverage (%) 31.95/2.54 19.81/2.51 25.223.88 23.75/8.24 17.38/3.94 26.88/10.35 2.11/0.92 3.50/1.31 20.98/1.64Grass dry yield (kg/m2) 0.132/0.008 0.088/0.011 0.106/0.014 0.079/0.021 0.089/0.013 0.010/0.035 0.008/0.005 0.013/0.007 0.087/0.006Shrub and wood coverage (%) 1.31/0.96 10.76/3.74 26.11/8.60 0.63/0.63 6.25/1.62 29.13/8.02 29.94/4.66 14.20/6.69 11.98/1.69Shrub and wood dry yield (kg/25 m2) 0.172/0.116 1.363/0.279 4.803/1.374 0.625/0.625 3.056/1.221 3.177/0.807 2.672/0.522 1.262/0.336 1.570/0.210Total vegetation yield (kg/25 m2) 3.480/0.221 3.567/0.415 7.451/1.286 2.601/0.687 5.278/1.181 5.673/1.245 2.882/0.512 1.580/0.403 3.744/0.230

S—sand; LS—loamy sand; SaL—sandy loam; SiL–silt loam.a Mean value.b Standard error.

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Table 2Results of the principal component analysis of various properties.

Statistic PC #1 PC #2 PC #3 PC #4 PC #5 PC #6 PC #7 PC #8

Eigenvalue 6.532 2.989 2.764 2.560 2.052 1.309 1.070 1.016% of variance 25.122 11.495 10.631 9.845 7.890 5.036 4.116 3.907Cumulative % 25.122 36.618 47.249 57.094 64.984 70.020 74.136 78.043

Factor loading/eigenvectorVariables

Soil properties (0–0.1 m) Clay (%) 0.824 0.065 −0.095 −0.120 0.246 −0.069 −0.122 0.212Silt (%) 0.917 0.168 −0.029 −0.075 0.165 −0.091 −0.077 0.177Sand (%) −0.914 −0.156 0.038 0.082 −0.177 0.089 0.084 −0.184Bulk density (g/cm3) −0.741 −0.224 −0.133 0.016 −0.282 0.116 −0.061 −0.067Organic matter content (%) 0.590 0.344 0.182 0.286 −0.195 −0.015 0.064 −0.065Total nitrogen (%) 0.111 0.031 0.577 0.275 0.032 −0.178 −0.392 0.053Total phosphorus (%) 0.640 0.313 0.009 0.012 −0.069 0.017 −0.296 0.134

Topographical properties Elevation (m) 0.535 −0.216 0.076 −0.269 0.565 0.114 0.078 −0.122Cos(Aspect) −0.413 0.000 0.305 0.129 0.170 0.033 0.385 −0.052Tan(Slope) (tanb) −0.426 0.790 0.160 −0.328 0.058 −0.021 0.031 0.057Profile curvature (°) −0.076 −0.070 0.180 0.030 0.034 0.766 −0.228 0.084Planform curvature (°) −0.210 0.073 −0.010 −0.351 0.173 0.647 −0.176 0.075Relief degree of land surface −0.489 0.753 0.137 −0.286 0.106 −0.003 −0.015 0.051Upstream flow length (m) −0.205 0.438 −0.425 0.680 0.286 0.075 −0.058 −0.028Downstream flow length (m) 0.305 −0.271 0.177 −0.165 0.682 0.088 0.034 −0.137Specific contribution area (a) −0.202 0.417 −0.379 0.624 0.294 0.137 −0.090 −0.062Coarse degree (1/Cos(b)) −0.437 0.777 0.145 −0.306 0.064 −0.035 0.045 0.039Wetness index ln(a/tanb) −0.007 0.086 −0.462 0.719 0.282 0.004 0.018 −0.029

Land surface and vegetation properties Surface roughness −0.419 0.252 −0.011 −0.197 0.356 −0.227 0.103 0.160Crust coverage (%) −0.007 −0.121 −0.181 0.154 −0.294 0.118 0.242 0.802Stone coverage (%) 0.041 −0.120 0.001 0.016 0.435 0.110 0.546 0.139Grass coverage (%) 0.649 0.312 0.214 0.186 −0.376 0.231 0.290 −0.124Grass dry yield (kg/m2) 0.730 0.296 0.207 0.125 −0.299 0.214 0.257 −0.171Shrub and wood coverage (%) −0.542 −0.262 0.441 0.303 0.158 −0.035 −0.091 0.267Shrub and wood dry yield (kg/25 m2) −0.334 −0.110 0.768 0.346 0.202 −0.090 −0.083 0.098Total vegetation yield (kg/25 m2) 0.167 0.091 0.834 0.396 −0.009 0.056 0.091 −0.021

PC—principal component.Underlined factor loadings are considered highly weighted when within 10% of variation of the absolute values of the highest factor loading in each PC.

Fig. 3. Evolution of mean air temperature, rainfall, and mean soil water content over time for various soil depths.


Fig. 4. Experimental (symbols) and theoretical (lines) semivariances of the meanrelative difference of soil water content for various soil depths. Semivariance was fittedby the spherical variogram model.


Therefore, MABE at location i directly describes the time averagedbias error of using location i to produce mean θ when persistentlyassuming the offset δik . The lower value of MABE at location i, the lessbias error is found, hence we have a more marked stability in thesense of mean θ estimation. σ(|ωik|) indicates the extent of thedeviation of |ωikj| from

Pjωikj, a low σ(|ωik|) means persistently eitherlow or high estimation error.

2.3.2. Geostatistical analysisSemivariograms were used to evaluate the spatial dependence of

soil water content (expressed as itsMRD) and the calculated values ofthe stability indices SDRD andMABE for each depth k as well as variousenvironmental properties all expressed as z, taking into considerationtheir position x within the watershed. Based on the regionalizedvariable theory and intrinsic hypotheses (Nielsen and Wendroth,2003), a semivariogram can be expressed as:

γ hð Þ = 12N hð Þ∑ z xð Þ−z x + hð Þ½ �2 ð12Þ

where γ(h) is the semivariance, h is lag distance,N(h) is the number ofsampling couples of the variable z in the interval h, z(x) and z(x+h)are values of z at positions x and x+h (Feng et al., 2004). The obtainedempirical semivariograms were fitted to theoretical semivariogrammodels to produce geostatistical parameters, including nuggetvariance (C0), structured variance (C1), sill variance (C0+C1), andrange R.

The degree of spatial dependence (GD), which is the ratio betweenthe nugget variance and the sill variance,C0/(C0+C1), was used tocharacterize the spatial dependency of soil water content and itstemporal stability for each depth k as well as various environmentalproperties. GDb0.25 indicates a strong spatial dependency, GDN0.75 aweak spatial dependency, otherwise the spatial dependency ismoderate. All the geostatistical analyses were conducted with the

Table 3Results of multiple stepwise regression analysis for the minimum data set (MDS) of proper

Soil depth (m) Variables Coefficients S.E.

0.1 Constant −250.894 158.611Sand −1.380 0.088Tan(Slope) −154.838 54.774Crust coverage 0.319 0.116Stone coverage 3.790 1.693Coarse degree 348.748 165.819Adjusted R2 0.710S.E. of the estimate 21.581

0.2 Constant 99.215 9.850Sand −1.677 0.113Crust coverage 0.350 0.150Tan(Slope) −42.200 20.017Stone coverage 4.331 2.182Adjusted R2 0.680S.E. of the estimate 27.841

0.4 Constant −40.784 8.580Silt 1.465 0.135Tan(Slope) −43.771 20.928Adjusted R2 0.525S.E. of the estimate 29.414

0.6 Constant −65.860 7.851Silt 1.500 0.135Crust coverage 0.352 0.161Adjusted R2 0.505S.E. of the estimate 30.164

0.8 Constant −60.429 7.540Silt 1.371 0.144Wetness index 3.777 1.586Adjusted R2 0.435S.E. of the estimate 32.097

S.E.—standard error.

Gstat software (Pebesma and Wesseling, 1998). To fit the empiricalsemivariograms, theoretical models were employed including Spher-ical, Gaussian, and the Pure nugget model. The detailed formulas canbe found in Nielsen and Wendroth (2003).

Based on the analysis of semivariance, the spatial distribution ofsoil water content and the temporal stability for all soil depths wereevaluated by ordinary kriging. The detailedmethods can also be foundin Nielsen and Wendroth (2003) and Goovaerts (1999).

ties obtained by principal component analysis versus mean relative difference (MRD).

t-value Significance level Explained variability (%)

−1.582 0.116−15.659 0.000 65.5−2.827 0.006 2.3

2.745 0.007 1.52.238 0.027 0.92.103 0.038 0.8

10.072 0.000−14.817 0.000 64.7

2.336 0.021 1.6−2.108 0.037 1.0

1.985 0.049 0.8

−4.753 0.00010.826 0.000 51.2−2.092 0.039 1.3

−8.389 0.00011.078 0.000 49.02.187 0.031 1.5

−8.015 0.0009.514 0.000 41.42.382 0.019 2.2

Fig. 5. Mean relative difference (%) of soil

Table 4Geostatistical summary of the mean relative difference (MRD) for various soil depths(spherical variogram model).

Soildepth(m)

Nuggetvariance(%2)

Structuredvariance(%2)

Range(m)

Sillvariance(%2)

GD MSE(%2)

R2

0.1 359.3 1610.3 178.1 1969.6 0.18 8489.4 0.983⁎⁎

0.2 385.4 2649.5 186.0 3034.9 0.13 29,002.9 0.981⁎⁎

0.4 272.9 1946.1 152.7 2219.0 0.12 19,434.1 0.973⁎⁎

0.6 386.9 1899.6 154.8 2286.5 0.17 17,603.9 0.973⁎⁎

0.8 491.2 1758.4 151.1 2249.6 0.22 13,237.9 0.977⁎⁎

MSE—mean square error; GD—the degree of spatial dependence.⁎⁎ Significant at Pb0.01.


2.3.3. Traditional statistical analysisPrincipal component analysis (PCA) was performed on all the

properties to obtain a minimum data set (MDS) of properties (Mandalet al., 2008). Note that only principal components (PCs) witheigenvalues N1.0 and only variables with highly weighted factorloading, (i.e., those with absolute values for factor loading within 10%of the highest value), were retained for the MDS. The multiplestepwise regressions were run using the final MDS properties asindependent variables and MRD of soil water content, SDRD, andMABE as dependent variables to explore the influencing factors of soilwater contents and their temporal stability (Wang et al., 2009).

water content for various soil depths.


Pearson correlation analysis was used to analyze the relationships ofMRD of soil water content and temporal stability indices (SDRD andMABE). The confidence intervals (C.I.) for determining whether aPearson correlation coefficient is significantly different from zero ornot can be calculated by (Nielsen and Wendroth, 2003):

C:I: = Fpffiffiffin

p ð13Þ

where p is the cumulative probability for a standardized normaldistribution (e.g. ±1.96 for 95% probability), and n is the number ofobservations. In this study, Pearson correlation coefficients greaterthan 0.5 indicate a strong correlation, less than 0.3 a weak correlation,otherwise a medium correlation. The relative error was used topresent the deviation of two data or data sets. Paired samples T testwas employed to compare the soil water content and temporalstability between different soil depths. One way analysis of varianceand independent samples T test were used to test the significance ofdifferences in temporal stability among various soil textures(sand,sandy loam, and silt loam) and different land uses (bunge needlegrassand korshinsk peashrub (sparse korshinsk peashrub and densekorshinsk peashrub combined)), making use of Statistical Programfor Social Sciences (SPSS) 11.0.

3. Results and discussion

3.1. Temporal stability of soil water contents for different soil depths

3.1.1. Soil water content dynamicsFrom June 11 to August 22 in 2007, a large fluctuation of soil water

contents expressed as themean volumetric soil water contents amongall the locations was recognized for the soil depths of 0.1 m and 0.2 m(Fig. 3) as influenced by precipitation measured by a weather stationabout 50 m away from the northwest of the watershed, while for thedeeper soil depths, the averaged soil water content showed only aslight decrease under the combined effects of precipitation and soilwater uptake by roots. From August 22 to October 25 in 2007, soilwater content for all the soil depths persistently increased because ofthe precipitation and possibly decreasing evapotranspiration due tothe decrease of the air temperature for this period (Fig. 3). Later, soilwater content for all soil depths decreased until June 21 in 2008because of the low precipitation and higher evapotranspirationcaused by the increase of the air temperature. The remarkableincrease of soil water content for June 21 was obviously linked to thelarge rainfall of 49.8 mm on June 15. After that, soil water content

Table 5Geostatistical analysis of the minimum data set (MDS) of properties obtained by principal c

Modela Nugget variance Structured

Silt (%) G 63.0 567.4Sand (%) G 84.6 717.5Tan(Slope) (tanb) G 0.001 0.018Profile curvature (°) S 35.5 86.9Relief degree of land surface G 0.002 0.134Upstream flow length (m) N – –

Downstream flow length (m) G 297.5 30,412.5Coarse degree (1/Cos(b)) S 0.00 2.16E−03Wetness index ln(a/tanb) N – –

Crust coverage (%) S 72.0 202.1Stone coverage (%) S 0.1 0.7Shrub and wood dry yield (kg/25 m2) G 2.4 5.2Total vegetation yield (kg/25 m2) S 0.10 0.50

S—spherical model, G—Gaussian model, N—nugget effect model; fitted parameters are notMSE—mean square error; GD—the degree of spatial dependence.

a For the total vegetation yield, log-transformed data are analyzed; all the other variable⁎⁎ Significant at Pb0.01.⁎ Significant at Pb0.05.

below 0.4 m decreased again and for the shallow 0–0.2 m layer, thesoil water content presented oscillations caused by rainfall events.Obviously, the soil moisture at the 0–0.2 m layer was much moresensitive to precipitation than the deeper soil layers.

Time averagedmean θ showed an increasing trendwith soil depth,with θ values of 7.9%, 8.3%, 10.9%, 11.3%, and 11.2%, respectively, in thesame way as previous observations in the Loess Plateau (Qiu et al.,2001). However, results of paired samples T test showed that nosignificant differences were observed among the three deeper soildepths (0.4, 0.6, and 0.8 m).

3.1.2. Influencing factors of soil water contentPCA resulted in eight PCs which had eigenvalues N1.0 and

accounted for 78.0% of the variance in the data (Table 2). In PC1, siltand sand contents were the greatest contributors to the principalcomponent as given by the factor loading and there were 13 out of 26variables, which consisted of the MDS properties, which had highlyweighted factor loading for all the eight PCs. Therefore, multiplestepwise regression analyses on the MDS properties and MRD wereconducted (Table 3) to find influencing factors. Since the soil particlecomponent of the surface 0–0.1 m layer can affect the process of soilwater infiltrating to deeper layers, it is expected that the distributionof soil water content of deeper soil layers may be influenced by thesoil particle of the 0–0.1 m layer. Therefore, multiple regressionanalyses between MRD of all the soil depths versus silt and sandcontents of the 0–0.1 m were carried out. As Table 3 shows, sandcontent can explain up to 65.5% and 64.7% of the variation of MRD forsoil depths of 0.1 m and 0.2 m, respectively, and silt content canexplain 51.2%, 49.0%, and 41.4% of the variation of MRD for soil depthsof 0.4 m, 0.6 m, and 0.8 m. Other properties such as Tan(Slope), coarsedegree, wetness index, crust coverage, and stone coverage can alsocontribute but with an obviously lower proportion to the variation ofMRD. It can be concluded, therefore, that soil particle size distributionwas the main factor influencing soil water content distribution. Inaddition, the proportion of variation of MRD explained by silt or sandcontent decreasedwith soil depth (Table 3), whichmeans that surfacelayer soil characteristics were not representative for the deeper layersand the soil water contents for the deeper depthswere less affected bythe soil particle content of the surface layer.

3.1.3. Spatial pattern of soil water contentQ–Q plots of MRD showed that for all soil depths data were

normally distributed (not shown), and therefore, no data transfor-mation was made before geostatistical analysis. The semivariograms

omponent analysis.

variance Sill variance Range (m) GD MSE R2

630.4 218.7 0.10 1259.1 0.966⁎⁎

802.1 218.8 0.11 2030.9 0.966⁎⁎

0.018 40.1 0.03 1.4E−06 0.908⁎⁎

122.4 49.3 0.29 314.1 0.379⁎

0.136 38.0 0.02 8.3E−05 0.910⁎⁎

– – – – –

30,709.9 295.2 0.01 438,692.3 0.994⁎⁎

0.00 49.8 0.00 5.8E−08 0.817⁎⁎

– – – – –

274.1 69.2 0.26 569.6 0.854⁎⁎

0.7 64.8 0.09 0.1 0.266⁎

7.7 247.9 0.32 0.62 0.854⁎⁎

0.60 122.9 0.17 9.09E−4 0. 966⁎⁎

included for nugget effect model in this table.

s are analyzed by the no transformed data.


indicated that the soil moisture field was stationary since all exhibitclear plateau (sill) at a certain lag distance (Fig. 4). The sphericalvariogram model could be well fitted to the experimental semivar-iance of MRD with the significance level of Pb0.01 (Table 4). Thegeostatistical parameters varied with soil depth. Nugget varianceincreased with soil depth except for 0.4 m. The structured variancewas the lowest for soil depth of 0.1 m, and it decreased with soil depthfrom 0.2 to 0.8 m. The sill variance showed that the smallestvariability of soil water content was observed for the 0.1 m depth,

Fig. 6. Rank ordered mean relative differences (MRD) of soil water content for various soil deover time. Sampling sites with different soil water conditions are presented orderly accord

the largest for 0.2 m, and very similar variability for the soil depths of0.4, 0.6, and 0.8 m (with relative error being less than 3.0% for the sillvariance of the three layers). At the Da nangouwatershed on the LoessPlateau, however, Wang et al. (2001) found that the sill increasedwith soil depth for a 0–0.75 m soil profile. Part of the reason for thedifference may be attributed to the different variables involved. Forthis study, MRD rather than θ was used to describe the soil moisturecondition. The phenomenon that θ increased with soil depth may beone of the contributors to the increased sill variance with soil depth

pths. Vertical bars correspond to ±standard deviations of the relative difference (SDRD)ing to the MRD.

Table 6Pearson correlation coefficients between standard deviation of relative difference(SDRD), mean absolute bias error (MABE), and mean relative difference (MRD).

0.1 m 0.2 m 0.4 m 0.6 m 0.8 m

SDRD–MABE 0.515⁎⁎ 0.044 0.381⁎⁎ 0.402⁎⁎ 0.485⁎⁎

SDRD–MRD 0.412⁎⁎ 0.695⁎⁎ 0.577⁎⁎ 0.617⁎⁎ 0.451⁎⁎

MABE–MRD −0.457⁎⁎ −0.606⁎⁎ −0.461⁎⁎ −0.420⁎⁎ −0.504⁎⁎

⁎⁎ Significant at Pb0.01.

Fig. 7. Relationships of mean absolute bias error (MABE) and standard deviations of the relavarious soil depths.


for the data of Wang et al. (2001). The values of GD for all the soildepths were less than 0.25, implying that the soil moisture of all soildepths in this watershed showed strong spatial dependency. Thecorrelation length reflected by the range was larger for the 0.1 and0.2 m depths than those below 0.4 m, being 178.1 m, 186.0 m,152.7 m, 154.8 m, and 151.1 m, respectively. These values fall intothe range (20–300 m) of most small catchments as Western et al.(2004) concluded. The distribution of MRD for all the soil depths wassimilar (Fig. 5), which indicated a similar spatial structure of soil

tive difference (SDRD) versus mean relative differences (MRD) of soil water content for

Fig. 8. Location averaged standard deviation of relative difference (SDRD) and meanabsolute bias error (MABE) for various soil depths. Vertical bars correspond toassociated standard error. Bars with the same lowercase and capital do not showsignificant difference at Pb0.05.


moisture for different soil layers in this watershed. This can be verifiedby the significant Pearson correlation coefficients (ranging from 0.718to 0.963) among the MRD values for different soil layers. Obviously, arelative dry area can be found in the middle left side of the watershedwhere sand or loamy sand soils are located. Likewise, the relative wetareas can also be identified where sandy loam or silt loam soils arelocated (Figs. 2 and 5).

In this study, geostatistical analyses were also made to comparethe spatial pattern of soil water content and the MDS of properties.Except for some topographical properties such as upstream flowlength and wetness index, all other properties were spatiallycorrelated (Table 5). Among them, except for profile curvature,crust coverage, and shrub and wood dry yield which showedmoderate spatial dependency (GD of 0.25–0.75), all the otherproperties presented a strong spatial dependency, as soil watercontent did. Western et al. (2004) discussed the identification of thedominating factors for soil moisture by comparing the correlationlengths of environmental factors with those of soil moisture. In thisstudy, the ranges of many properties can be comparable to the rangesof MRD (Table 5), suggesting the possible influences of theseproperties. As for the main influencing factors of soil water content,the ranges of silt content and sand content were 218.7 and 218.8 m,being comparable to the ranges of MRD (151.1–186.0 m) whenconsidering the length of the watershed (about 600 m).

3.1.4. Standard deviation of relative difference (SDRD) and meanabsolute bias error (MABE)

The rank orderedMRD and its associated SDRD, as well as locationswithMRD of±5% and the driest andwettest 10 locations are shown inFig. 6. From 0.1 to 0.8 m, the ranges of MRD were 178.3% (−59.1%–119.2%), 206.9% (−74.2%–132.7%), 183.1% (−71.3%–111.8%), 178.9%(−66.4%–112.5%), 172.9%(−66.7%–106.2%), respectively. Except forthe soil depth of 0.2 m, which showed the greatest range of MRD, theranges of MRD were almost the same for all other soil depths. Thelargest range ofMRD for 0.2 m echoed the largest spatial variability asreflected by the largest sill variance. The range of MRD was greaterthan those of other comparable areas such as the Tarrawarrawatershed (Grayson and Western, 1998), LW13 and LW21 footprintfrom the SGP97 Hydrology Experiment (Mohanty and Skaggs, 2001),and Boise Idaho (Grant et al., 2004). The main reason for the greaterrange of MRD may be the wider range of soil texture which coveredfrom silt loam to sand for this area. Obviously, as many others found(Martínez-Fernández and Ceballos, 2003; Starks et al., 2006), the rankof MRD varied with soil depth. However, the MRD of locations 57 and91 were within ±5% except for the depth of 0.8 m where their MRDwere within ±10%. Therefore, locations 57 and 91 can directlyrepresent the mean soil water conditions for all soil depths. Likewise,locations 29 and 79 can be representative of dry conditions, andlocations 58 and 115 of wet conditions. Note that locations 57 and 58are arranged closely in space but characterized by very differentMRD.This may be related to the combined effects of various factors, amongwhich the different soil texture, sandy loam for location 57 and siltloam for location 58, may be the main reason.

SDRD was widely used to describe the temporal stability of soilwater content. For this study, SDRD varied greatly in space for varioussoil depths (Fig. 6). From 0.1 to 0.8 m, the ranges of SDRD were 4.8%–59.2%, 5.0%–40.7%, 4.1%–37.3%, 4.5%–32.1%, and 5.1%–33.3%, respec-tively. Pearson correlation coefficients (ranging from 0.412 to 0.695)showed that the SDRD was positively correlated to MRD for all soildepths (Pb0.01) (Table 6). This implies in the fact that the value ofSDRD tended to be lower for the drier locations (Fig. 7), which is inagreement with the findings of Martínez-Fernández and Ceballos(2003) who attributed this to the inability of the soils to retain wateras a result of the predominance of the sandy fraction. Therefore, in thissense, soil water content may be temporally more stable for drierareas.

MABE also varied greatly with sampling locations. From 0.1 to0.8 m, the ranges of MABE were 4.4%–35.2%, 3.5%–33.0%, 4.3%–30.3%,3.0%–30.3%, and 4.0%–30.8%, respectively. The MABE was generallylower in the wetter areas (Fig. 7). Pearson correlation coefficients(−0.420 to−0.606) showed that theMABEwas negatively correlatedwith MRD for all soil depths (Pb0.01) (Table 6).Therefore, if MABE isused, soil moisture may be recognized as much more temporallystable for wetter areas where sandy loam or silt loam soils are located.Based on the different relationships between SDRD–MRD and MABE–MRD, negative relationship of SDRD and MABE may be expected.However, Pearson correlation analyses (Table 6) showed that SDRDwas positively correlated with MABE at the significance level ofPb0.01 with exception to the soil layer of 0.2 m. The paradox resultsimply that these two indices behave the same characteristics in termsof describing temporal stability at some situations. However, whenweaim to choose the “representative site” to directly give an estimationof the average soil water content for a given area, the minimum ofSDRD should be considered (Brocca et al., 2009). Note that althoughthe SDRD for the drier areas was generally lower, the drier areas didnot necessarily produce the best mean soil moisture according toEq. (7). This relates the sensitivity of MABE to the bias of relativedifference. According to Eq. (9), under the same bias of relativedifference (jδikj−δik j), the absolute value of the bias error ABE, henceMABE, would be greater for lower δik (corresponding to drier areas).Take a jδikj−δik j of 5% for example, 50% of δik yields only 3.3% of ABE,while −50% of δik yields up to 10.0% of ABE. This implies in the factthat it is dangerous to identify locations for mean soil water contentbased on the parameter of SDRD when using Eq. (7) according toGrayson and Western (1998) and in this situation, MABE should be abetter alternative since it directly shows the estimation error. Notethat with the aim of identifying a “representative” location to obtainthe mean soil water content for a given area using either SDRD orMABE, a previous soil moisture campaign should be carried out. If a“representative” field is not previously identified, thenmore locationsshould be selected for reliable mean soil water content estimation assuggested by Brocca et al. (2010).

Location averaged SDRD and MABE for various soil depths arepresented in Fig. 8 to explore the relationship of temporal stabilitywith soil depth. The exact ranks of the SDRD for different soil depthswere 0.2, 0.1, 0.4, 0.8, 0.6 m, with mean SDRDs of 14.2%, 14.0%,13.5%, 12.5%, 12.5%, respectively. Paired samples T test showed thatsignificant (Pb0.05) differences could only be found between 0.2–0.8 m and 0.2–0.6 m. As for MABE, its rank according to soil depthdiffered to some extent from SDRD, which were 0.2, 0.4, 0.8, 0.1,

Table 7Comparison of average standard deviation of relative difference (SDRD) and mean absolute bias error (MABE) among different soil textures (sand, sandy loam, and silt loam) anddifferent land uses (bunge needlegrass and korshinsk peashrub).

Samplingnumber

SDRD MABE

0.1 m 0.2 m 0.4 m 0.6 m 0.8 m 0.1 m 0.2 m 0.4 m 0.6 m 0.8 m

Soil texture Sand 38 11.31a 10.66a 12.90a 10.74a 12.38a 14.17a 19.96a 17.08a 14.67a 16.60aSandy loam 43 15.07b 13.97b 12.70a 12.16ab 12.25a 10.25b 11.09b 10.08b 9.69b 9.85bSilt loam 43 15.43b 17.63b 14.88a 14.31b 12.86a 8.88b 9.86b 8.94b 8.48b 7.87c

Land use Bunge needlegrass 42 14.11A 13.67A 11.74A 11.98A 11.53A 9.36A 9.90A 8.68A 8.27A 8.19AKorshinsk peashrub 30 15.34A 17.69B 14.39A 13.63A 13.17A 9.20A 10.92A 9.82A 9.71A 9.86A

The lowercase and the capital after the number indicate the significance. Numbers with the same lowercase or capital are not significant at Pb0.05.


0.6 m, with mean MABE values of 13.4%, 11.8%, 11.2%, 11.0%, 10.8%,respectively. Paired samples T test showed that significant (Pb0.05)differences could be found between 0.2 and 0.1 m, between 0.2 and0.4 m, between 0.2 and 0.6 m, between 0.2 and 0.8 m, between 0.4and 0.1 m, and between 0.4 and 0.6 m. The common characteristicswere that temporal stability of soil water content in 0.2 m wassignificantly weaker than that in 0.6 and 0.8 m (Pb0.05). Thisdisagreed with the results obtained for the same watershed whenSpearman's rank correlation coefficients were used (Hu et al.,2009). According to Hu et al. (2009), the temporal stability of soilwater content at 0.2 m was greater than those at deeper soil layers.This is due largely to the different concept of these two indices.Spearman's rank correlation coefficient is used to describe thesimilarity of the spatial pattern of soil water content distribution forthe whole area at different times, while SDRD and MABE are used tocharacterize the degree of temporal invariability for a certainlocation.

3.2. Effects of soil texture and land use on temporal stability

The sequence of SDRD for the different soil textures was in generalsandbsandy loambsilt loam for all soil depths (Table 7). For the soildepths of 0.1and 0.2 m, a significant difference in SDRD could only be

Table 8Results of multiple stepwise regression analysis for the minimum data set (MDS) of propdifference (SDRD) and mean absolute bias error (MABE).

Soildepth(m)

SDRD

Variables Coefficients S.E. t-value Significancelevel

Explainedvariability (%)

0.1 Constant 18.992 1.914 9.922 0.000Sand −0.082 0.030 −2.764 0.007 5.1Adjusted R2 0.051S.E. of the estimate 7.513

0.2 Constant 22.044 1.526 14.446 0.000Sand −0.130 0.024 −5.476 0.000 19.1Adjusted R2 0.191S.E. of the estimate 5.989

0.4 a

0.6 Constant 16.050 1.378 11.650 0.000Sand −0.059 0.021 −2.776 0.006 5.2

Adjusted R2 0.052S.E. of the estimate 5.407

0.8 Constant 11.815 1.529 7.725 0.000WI 0.830 0.249 3.328 0.001 6.5SWY 0.001 0.000 2.892 0.005 4.4DFL −0.006 0.003 −2.191 0.030 2.7

Adjusted R2 0.136S.E. of the estimate 5.043

DFL—downstream flow length; S.E.—standard error; SWY—shrub and wood dry yield; TVY—a—No sound multiple stepwise regression model was found.

found between the sand and sandy loam, and between sand and siltloam. For the soil depth of 0.6 m, a significant difference in SDRD wasonly found between sand and silt loam. Two reasons may contributeto the soil texture associated temporal stability: (1) SDRD wascorrelated to the soil particle size composition of the 0–0.1 m layer,although the sand content can only explain 5.1%, 19.1%, and 5.2% ofthe variation of SDRD (Table 8); (2) there was a significant differencein particle size composition among soil textures (Table 9). As for thesandy loam and silt loam textures, although significant differencesin soil particle size existed, no significant differences in SDRD wereidentified. The possible reason was that the differences in the soilparticle componentwere not large enough, although being significantlyat Pb0.05, to produce significant differences in SDRD. As for 0.4 and0.8 m, soil texture did not significantly affect the SDRD. Part of thereasons was that the SDRD of these layers was not affected by the soilparticle composition of the 0–0.1 m layer (Table 8). Likewise, soiltexture of the 0–0.1 m layer could have affected theMABE of various soildepths. The value of MABE generally ranked in the sequence ofsandNsandy loamNsilt loam. Except for sandy loam and silt loam forthe soil depths of 0.1, 0.2, 0.4, and 0.6 m, the difference between eachpair of soil textures was significant at Pb0.05. This was also related tothe fact thatMABEwasmainly correlated to the soil particle component,i.e., about 29.7% to 47.2% of variation ofMABEwas caused by silt content

erties obtained by principal component analysis versus standard deviation of relative

MABE

Variables Coefficients S.E. t-value Significancelevel

Explainedvariability (%)

Constant 15.048 0.641 23.483 0.000Silt −0.114 0.016 −7.278 0.000 29.7Adjusted R2 0.297S.E. of the estimate 3.480Constant 21.494 0.883 24.352 0.000Silt −0.226 0.022 −10.526 0.000 47.2Adjusted R2 0.472S.E. of the estimate 4.793Constant 18.452 0.793 23.274 0.000Silt −0.185 0.019 −9.566 0.000 42.4Adjusted R2 0.424S.E. of the estimate 4.305Constant 16.335 1.068 15.297 0.000Silt −0.135 0.017 −7.890 0.000 35.8TVY 0.000 0.000 2.373 0.019 1.9DFL −0.004 0.002 −1.991 0.049 1.5Adjusted R2 0.392S.E. of the estimate 3.657Constant 18.175 1.202 15.123 0.000Silt −0.164 0.020 −8.157 0.000 46.5SWY 0.001 0.000 3.548 0.001 3.2DFL −0.005 0.002 −2.228 0.028 2.0UFL 0.034 0.017 2.029 0.045 1.2Adjusted R2 0.530S.E. of the estimate 4.027

total vegetation yield; UFL—upstream flow length; WI—wetness index.

Table 9Comparison of the minimum data set (MDS) of properties obtained by principalcomponent analysis among different soil textures (sand, sandy loam, and silt loam) anddifferent land uses (bunge needlegrass and korshinsk peashrub).

Soil texture Land use

Sand Sandyloam

Silt loam Bungeneedlegrass

Korshinskpeashrub

Sampling number 38 43 43 42 30

Silt (%) 7.94a 41.75b 54.53c 49.49A 47.50ASand (%) 91.65a 54.23b 38.62c 45.10A 46.87ATan(Slope) (tanb) 0.32a 0.25ab 0.24b 0.26A 0.23AProfile curvature 82.46a 79.62a 80.06a 78.06A 81.86ARelief degree of landsurface

0.91a 0.69b 0.67b 0.70A 0.65A

Upstream flowlength (m)

14.14a 5.93a 9.36a 8.80A 4.33A

Downstream flowlength (m)

376.38a 436.37ab 480.37b 368.64A 555.18B

Coarse degree(1/Cos(b))

1.06a 1.04ab 1.03b 1.04A 1.03A

Wetness indexln(a/tanb)

3.08a 2.81a 3.12a 2.98A 2.77A

Crust coverage (%) 34.97a 34.30a 34.16a 34.49A 37.50AStone coverage (%) 0.36a 0.12a 0.29a 0.12A 0.25AShrub and wood dryyield (kg/25 m2)

2.394a 1.658ab 0.753b 0.108A 2.349B

Total vegetation yield(kg/25 m2)

2.997a 4.850b 3.298a 3.497A 4.679A

The lowercase and the capital after the number indicate the significance. Numbers withthe same lowercase or capital are not significant at Pb0.05.

Fig. 9. Experimental (symbols) and theoretical (lines) semivariance of (a) standarddeviation of relative difference (SDRD) and (b) mean absolute bias error (MABE) forvarious soil depths. Semivariances were fitted by the spherical variogram model.

Table 10Geostatistical summary of the standard deviation of relative difference (SDRD) andmean absolute bias error (MABE) (spherical variogram model).

Soildepth(m)

Nuggetvariance(%2)

Structuredvariance(%2)

Sillvariance(%2)

Range(m)

GD MSE(%2)

R2

SDRD 0.1 35.4 31.3 66.7 65.8 0.53 63.3 0.408⁎

0.2 23.0 23.9 46.9 116.3 0.49 29.8 0.740⁎⁎

0.4 24.8 14.3 39.1 108.6 0.63 5.5 0.740⁎⁎

0.6 18.7 14.7 33.4 112.4 0.56 7.1 0.687⁎⁎

0.8 14.5 18.3 32.9 120.5 0.44 8.2 0.806⁎⁎⁎⁎


(Table 8). Therefore, soil texture can significantly affect the temporalstability of soil moisture except for the soil depth of 0.4 and 0.8 mwhenSDRDwas used. In exception to a few cases such asMABE for 0.8 m andSDRD for 0.6 m, significant differenceswere observed between sand andsandy loam, and sand and silt loam textures. When SDRD is used, thesandy soil had themost pronounced stability, whilewhenMABE is used,the sandy soil was the weakest in terms of temporal stability (Table 7).This can be explained by the negative correlation of SDRD with sandcontent and negative correlation of MABE with silt content (Table 8).

In order to analyze the effects of land use on temporal stability,only land use on sandy loam and silt loam textures was considered.Furthermore, because of the limited area and limited sampling onfarm land and almond, only the temporal stability of bungeneedlegrass and korshinsk peashrub (sparse korshinsk peashruband dense korshinsk peashrub) was compared. As it can be seen,although the values of SDRD andMABEwere in general greater for thekorshinsk peashrub than for bunge needlegrass, no significantdifferences were found except for the SDRD of the 0.2 m depth(Table 7). Therefore, it can be said that land use did not affect thetemporal stability of soil water contents in this watershed, whichagrees well with the conclusion obtained from the data sets of 0–1 msoil water storage in the same watershed when only 12 samplingswere used (Hu et al., 2009). Part of the reason was that there were nosignificant differences in many SDRD and MABE correlated properties,especially for the soil particle component between bunge needlegrassand korshinsk peashrub (Table 9). Note that the relative magnitude ofSDRD andMABEwas the same between the two land uses but differentamong soil textures, this may support the paradox fact that SDRD andMABE were positively correlated but had different relationships withMRD of soil water content (Table 6).

MABE 0.1 12.0 8.0 20.0 148.8 0.60 4.6 0.6160.2 7.5 51.7 59.2 208.1 0.13 8.3 0.968⁎⁎

0.4 9.0 32.5 41.5 209.6 0.22 4.3 0.958⁎⁎

0.6 4.2 23.3 27.5 190.5 0.15 1.0 0.980⁎⁎

0.8 2.1 47.8 49.9 214.1 0.04 5.0 0.976⁎⁎

MSE—mean square error; GD—the degree of spatial dependence.⁎⁎ Significant at Pb0.01.⁎ Significant at Pb0.05.

3.3. Spatial pattern of temporal stability

The semivariances both for SDRD and MABE approximated aplateau at a certain distance (Fig. 9). This implies that also thetemporal stability of soil water contents was spatially correlated.


Therefore, if a location is temporally stable, the locations nearbytend also to be stable. The experimental semivariance data of SDRDand MABE and the geostatistical parameters are summarized inTable 10. As for SDRD, the nugget variance, structured variance, andsill variance generally decreased with soil depth, which indicatesthat the variability of the stability expressed by SDRD decreasedwith soil depth. As for MABE, the nugget variance generallydecreased with soil depth, but no obvious trend of structuredvariance and sill variance with soil depth was found, which was thegreatest for the 0.2 m, and the smallest for the 0.1 m layers. Therange of MABE (148.8 m–214.1 m) was greater than that of SDRD

Fig. 10. Standard deviation of relative difference (SDR

(65.8 m–120.5 m), implying that MABE can be spatially correlatedin a broader domain than SDRD. Meanwhile, the ranges of MABEwere closer to the ranges of the soil particle component than thoseof SDRD. This may explain why MABE was more correlated with soilparticle size than SDRD did (Table 8). With increasing soil depth,the range of the indices showed in general increasing trends, whichindicated that the temporal stability was more organized fordeeper soil. The GD value of SDRD showed no obvious trend withsoil depth, ranging from 0.44 (0.8 m) to 0.63 (0.4 m), which refersto a moderate spatial dependency for all soil depths. The GD valueof MABE generally decreased with soil depth, ranging from 0.04

D%) of soil water content for various soil depths.

Fig. 11. Mean absolute bias error (MABE%) of soil water content for various soil depths.


(0.8 m) to 0.60 (0.1 m). Except for the soil depth of 0.1 m whichshowed moderate spatial dependency, the spatial dependency ofMABE for the other soil depths was strong, and the spatialdependency increased with soil depth.

Based on the spatial pattern analysis, the spatial distributionof SDRD and MABE was estimated using ordinary kriging (Figs. 10and 11). The spatial patterns of SDRD and MABE were similar inrelation to the different soil depths, which can be verified by themoderate or strong correlation (with Pearson correlation coeffi-cients of 0.351–0.794) for both indices among different soil depths(Pb0.01). Obviously, the drier areas correspond to the smaller

SDRD value but greater MABE value by comparing Fig. 5 andFigs. 10 and 11. Therefore, from Figs. 10 and 11, we may identifyareas of temporal stability of soil water content. With the map ofSDRD, the locations with zero MRD and the minimum SDRD couldbe identified for the direct estimation of mean soil water content;with the map of MABE, the locations of temporal stability could beidentified to estimate the mean soil water content indirectly withEq. (7) as Grayson and Western (1998) suggested. These stableareas do not limit to the existing observation locations, but can alsobe extended to other places with no access tubes. However, sincethe kriging interpolation tends to smooth the spatial variability, the


accuracy of the temporal stability map might be improved by othertechniques such as the stochastic simulation. This would be veryimportant for the estimation of the mean soil water content at thewatershed scale.

4. Conclusions

(1) Temporal stability reflected by the standard deviation ofrelative differences (SDRD) was generally more pronouncedfor the dry areas, however when characterized by the meanabsolute bias error (MABE) tended to be more pronounced forthe wet areas. Therefore, from the point of view of mean soilwater content estimation, considering the constant offset of atemporally stable location as suggested by Grayson andWestern (1998), it is considered advisable to choose thelocation with the minimum value of MABE.

(2) Comparison of SDRD and MABE estimations among differentsoil depths showed that the temporal stability of 0.2 m wassignificantly weaker than those at 0.6 and 0.8 m.

(3) Geostatistical analysis on the mean relative difference of soilmoisture showed that the greatest spatial variability of soilwater content was found at soil depth of 0.2 m, and thesmallest for 0.1 m. The degree of spatial dependence indicatedthat soil water contents of various soil depths presented astrong spatial dependency. The correlation length of soil watercontents was larger for the surface 0–0.2 m layer.

(4) Temporal stability of soil water contents was mainly controlledby soil particle size distribution. Soil texture affected thetemporal stability, however, no significant difference wasfound between sandy loam and silt loam textures. Temporalstabilities of soil water content were not significantly differentbetween bunge needlegrass and korshinsk peashrub probablydue to the low variability of the soil particle size distributionbetween these two land uses.

(5) Temporal stability of soil water content was spatially correlat-ed. The spatial dependence of SDRD was moderate, while thatof MABE was strong except for the soil depth of 0.1 m. Thevalues of the range for MABE were greater than those of SDRD,implying that MABE can be spatially correlated in a broaderdomain than SDRD. From the ordinary kriging map of MABE,stable locations might be identified to indirectly produce themean soil water content of the watershed for various soildepths using the equation suggested by Grayson and Western(1998).

Acknowledgements

The study was financially supported by the National Key BasicResearch Project (2007CB106803), the “Innovative Team” program ofthe Ministry of Education (IRT0749), the “Innovative Team” programof the Chinese Academy of Sciences, the Knowledge InnovationProject (KZCX2-XB2-13 & KSCX2-YW-N-003) of Chinese Academy ofSciences, and the Open Fund of State Key Laboratory of Soil Erosionand Dryland Farming on the Loess Plateau (10501-269). We thank thetwo anonymous reviewers for their constructive comments thatgreatly improved the earlier version of this manuscript.

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