Temporal stability of soil water storage in diverse soil layers

Catena 95 (2012) 24–32

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Temporal stability of soil water storage in diverse soil layers Lei Gao a, c, Mingan Shao b,⁎ a State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling 712100, Shaanxi, China b Key Laboratory of Ecosystem Network Observation and Modeling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China c Graduate University of Chinese Academy of Sciences, Beijing 100049, China

a r t i c l e

i n f o

Article history: Received 27 July 2011 Received in revised form 5 February 2012 Accepted 20 February 2012 Keywords: Soil moisture Temporal stability Spatio-temporal variability Hillslope scale Depth dependency

a b s t r a c t Knowledge of soil water storage (SWS) within soil profiles is crucial when selecting appropriate practices for the restoration of vegetation. To study the temporal stability of SWS and identify representative locations in diverse soil layers, an analysis of temporal stability was performed using Spearman rank correlation coefficients and relative differences. From July 2008 to October 2010, the SWS of three soil layers (0–1, 1–2, and 2–3 m) were measured using a neutron probe at 91 locations on a hillslope on the Loess Plateau, China. A total of 20 SWS datasets were collected over the period of measurement. The results showed that the variability of SWS decreased over time and increased over space with the increase in soil depth. High Spearman rank correlation coefficients (p b 0.01) indicated a strong temporal stability of spatial patterns for all soil layers. Temporal stability increased with increasing soil depth. Furthermore, the closer two soil layers were within a given profile and the deeper any two adjacent soil layers were, the more similar were the temporal patterns. A significant negative correlation (p b 0.01) existed between the status of soil moisture and temporal stability, and the dependency increased with soil depth. With increasing soil depth, more locations were able to estimate the mean SWS of the area. None, however, represented the mean values for all three soil layers separately. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Soil water storage (SWS) is an important state variable in hydrologic and biologic processes (Choi and Jacobs, 2007). It has important effects on runoff, erosion, and transport of solute (Georgakakos, 1996). SWS, especially in upper soil layer, plays a key role in controlling water and energy fluxes in soils (Vereecken et al., 2007), influencing the partitioning of rainfall into infiltration and runoff and the partitioning of net radiation into sensible and latent heat (Pachepsky et al., 2003). Additionally, SWS plays an important role in the production of vegetation, especially in semi-arid environments, which is a limiting factor for the restoration of vegetation on the Loess Plateau, China (Hu et al., 2009). Soil moisture, however, is highly variable in space, due mainly to soil variability, and in time, due to climate. In the past several decades, many studies have endeavoured to understand the spatio-temporal dynamics of soil moisture (Brocca et al., 2009; De Lannoy et al., 2006; Green and Erskine, 2011; Henninger et al., 1976; Hills and Reynolds, 1969; Mohanty and Skaggs, 2001; Moore et al., 1988; Nyberg, 1996; Thierfelder et al., 2003). The large variability of soils requires the

⁎ Corresponding author. Tel.: + 86 29 87018861; fax: + 86 29 87012334. E-mail address: [email protected] (M. Shao). 0341-8162/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.catena.2012.02.020

collection of many samples from an area to extract sufficient information of soil moisture, which is costly in time and money. Vachaud et al. (1985) were among the first to show that spatial patterns of soil moisture changed little with time despite large variation over time and space in the field. This phenomenon has been called temporal stability. The concept of temporal stability was thereafter extensively used to judge whether the spatial pattern for soil moisture in an area was persistent. For example, Comegna and Basile (1994) found no indication of temporal stability when the spatial patterns of soil moisture were investigated, and Kamgar et al. (1993) reported that the time-stable patterns of soil moisture could be observed only to a depth of 2.85 m. The temporal stability for soil moisture, however, is widely recognised by most authors (Brocca et al., 2009; Coppola et al., 2011; Cosh et al., 2004, 2008; da Sivaro et al., 2001; Martínez-Fernández and Ceballos, 2003). Identifying time-stable locations to estimate the status of mean soil moisture for an area of interest has been one of the most important applications of the concept of temporal stability. Monitoring representative locations can determine the mean soil moisture of large areas at a small cost. This strategy is advantageous because it can significantly reduce the required number of samples while maintaining a high accuracy of prediction. Schneider et al. (2008) further pointed out that the selected locations were appropriate to estimate mean soil moisture of the study area for multiple years. More studies thus focused on identifying representative locations

L. Gao, M. Shao / Catena 95 (2012) 24–32

(De Lannoy et al., 2007; Fernandez and Ceballos, 2003; Grayson and Western, 1998). In addition, temporal stability of soil moisture was shown to be linked to many other factors, such as soil depth (Cassel et al., 2000), soil-water conditions (Martínez-Fernández and Ceballos, 2003), scale of interest (Gómez-Plaza et al., 2000), and soil texture (Mohanty and Skaggs, 2001). Biswas and Si (2011) further examined the controlling factors of SWS at different scales of measurement using wavelet coherence. Many studies only examine a single soil layer (usually the upper 20 cm) (Cosh et al., 2008; Famiglietti et al., 1998; Gómez-Plaza et al., 2000; Goovaerts and Chiang, 1993; Hu et al., 2009; Schneider et al., 2008; Van Wesenbeeck and Kachanoski, 1988), and some only observe the soil profile within 0–1 m layer (Comegna and Basile, 1994; Guber et al., 2008; Hu et al., 2010a; Hupet and Vanclooster, 2002; Kachanoski and de Jong, 1988; Martínez-Fernández and Ceballos, 2003; Starks et al., 2006). Few, however, investigate the profile beyond 1 m (Hu et al., 2010b; Kamgar et al., 1993; Tallon and Si, 2004). More research on the temporal stability of SWS in different soil layers is therefore needed to determine whether the temporal stability of SWS is dependent on depth.

25

For a deeper insight into these questions, the SWS of three layers (0–1, 1–2, and 2–3 m) were observed at 91 locations on 20 occasions from July 2008 to October 2010. The specific objectives of this study were: (i) to study the temporal stability of spatial patterns for SWS at three soil layers and analyse how those patterns vary with increasing soil depth; (ii) to observe the relationships between the status of soil moisture and temporal stability and test whether they further show a depth dependency; and (iii) to identify representative locations of each soil layer for future prediction of the mean SWS of this area.

2. Materials and methods 2.1. Description of field site The study area is located on a hillslope (~14°) in the Liudaogou watershed (110°21′–110°23′ E, 38°46′–38°51′ N) of Shenmu County, Shaanxi Province, China (Fig. 1). This area is characterised by a large number of deep gullies and undulating loessial slopes. The climate is

b

a

c

61

32

91

1

60

31

Fig. 1. The distribution of 91 neutron access tubes across the hillslope (c) located in the Liudaogou watershed (b) on the Loess Plateau of China (a). Intervals between adjacent transects and the spaces between adjacent locations are both approximately 10 m.

26

L. Gao, M. Shao / Catena 95 (2012) 24–32

moderate-temperate and has an average annual air temperature of 8.4 °C. Frost damage may frequently occur in the spring. The climate is semi-arid with an average annual precipitation of 437.4 mm. The heaviest rainfall usually occurs between July and September and amounts to about 50% of the annual total. The average annual potential evapotranspiration is 785.0 mm. A serious deficit of soil water is thus present. The mean aridity index is 1.8, and an annual average of 135 days are frost-free (Zheng et al., 2006). The study area is situated in the centre of the water-wind erosion crisscross region, which sustains serious soil erosion. The dominant soil types of this small watershed are sand, loamy sand, sandy loam, and silty loam (taxonomy of the U.S. Department of Agriculture). The dominant of the selected slope is grassland, which includes mainly bunge needlegrass (Stipa bungeana Trin.) with some alfalfa (Medicago sativa L.) and Artemisia scoparia Waldst. et Kit. A low planting density of apricot trees (Prunus armeniaca) with undergrowth and farmland for millet production are also distributed on the hillslope. Basic descriptions of the soil properties for this hillslope are shown in Table 1.

whether the location ranks persisted over the study period. With this approach, Rij is the rank of the variable SWSj(i) observed at location i on day j, and Rij′ is the rank of the same variable at the same location, but on day j′. The Spearman rank correlation coefficient is calculated as:

2.2. Sampling and measurement

where

Down the length of the hillslope (~350 m), 91 aluminium neutronprobe access tubes, 3 m in length, were installed along three transects (Fig. 1). The intervals between adjacent transects and the spaces between adjacent locations are both approximately 10 m. Between July 2008 and October 2010, twenty datasets of SWS (0–1, 1–2, and 2–3 m) were collected at these 91 locations using a neutron probe. Slowneutron counting measurements were taken at intervals of 0.1 m to a depth of 1 m, and at 0.2 m intervals at depths below 1 m. Volumetric soil water contents, θ(%), at each depth were calculated from slowneutron counting rates, CR, using the following calibration curve:

SWSj ¼


2 θ ¼ 0:6483  CR−0:0102 R ¼ 0:9;

pb0:001



ð1Þ

The calibration curve was obtained from nearly the same area and considered valid for all depths by Hu et al. (2009). The SWS (mm) of location i at timej, SWSj(i), was calculated from θ(i, j, k) (%, v/v) data (k refers to different soil depths, mm). The SWS of the 0–1, 1–2, and 2–3 m layers was calculated by the following trapezoidal rules, respectively: SWSjð0−1mÞ ðiÞ ¼ 100  ½θði; j; 100Þ þ θði; j; 200Þ⋯ þ θði; j; 1000Þ

ð2Þ

SWSjð1−2mÞ ðiÞ ¼ 200  ½θði; j; 1200Þ þ θði; j; 1400Þ⋯ þ θði; j; 2000Þ

ð3Þ

SWSjð2−3mÞ ðiÞ ¼ 200  ½θði; j; 2200Þ þ θði; j; 2400Þ⋯ þ θði; j; 3000Þ

ð4Þ

2.3. Method of data analysis Following Vachaud et al. (1985), two techniques were employed in the present work to evaluate temporal stability. The nonparametric Spearman's rank correlation test was used to determine

2 N
P Rij −Rij′  r s ¼ 1− i¼1  2 N N −1 6

ð5Þ

where N is the number of observing locations. The closer the value is to 1, the more stable the analysed process. In the second technique, relative-difference analysis was employed based on the difference (Δij) between an individual measurement of SWSij at location i and time j and the daily average soil water storage SWSj at the same time from all locations: Δij ¼ SWSij −SWSj

N 1X SWSij N i¼1

ð6Þ

ð7Þ

From Eqs. (6) and (7), relative differences (δij) are then calculated from: δij ¼ Δij =SWSj

ð8Þ

A temporal mean relative difference (MRD) δ i and its standard deviation (SDRD) σ(δi) are defined as: δi ¼

M 1X δ M j¼1 ij

ð9Þ

and vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M
2 u 1 X δij −δi σ ðδi Þ ¼ t M−1 j¼1

ð10Þ

where M is the number of sampling days. Relative-difference analysis is mainly used to identify the locations that systematically either represent the average SWS of the study area or under- or overestimate it while at the same time yielding a measure of variability (Mohanty and Skaggs, 2001; Vachaud et al., 1985). Eqs. (9) and (10) are used to rank and plot the locations (from the lowest mean relative difference to the highest) and assess temporal stability at each location. Values of δ i near zero at locations indicate that their SWS are close to the mean value of the study area, whereas other locations with δ i higher or lower than zero are over- or underestimating, respectively, the mean of the area. Locations with low values of σ(δi) are considered to be temporally stable. 3. Results and discussion 3.1. Spatio-temporal analysis of SWS in diverse soil layers

Table 1 Basic description of the hillslope based on the soil samples collected from 91 locations of the study area.

Mean SD CV

Clay/%

Silt/%

Sand/%

KS/mm min− 1

BD/g cm− 3

SOC/‰

18.8 3.7 19.7

48.8 4.7 9.6

32.4 6.8 21.0

0.5 0.3 49.7

1.3 0.1 7.5

2.1 0.5 26.2

KS, soil saturated hydraulic conductivity; BD, soil bulk density; SOC, soil organic carbon; SD, standard deviation; CV, coefficient of variation.

The time series in the mean SWS over space in diverse soil layers (Fig. 2a) with corresponding statistical parameters (Table 2) showed that the temporal changes were mainly observed for the shallow soil layer (0–1 m). During the study period, the spatial mean SWS of this layer ranged from 74.5 to 178.4 mm, with a time-averaged value of 126.9 mm. For deeper soil layers, the mean SWS of this hillslope underwent relatively small temporal changes. The time-averaged mean SWS values were 132.0 and 134.0 mm, ranging from 97.8 to

L. Gao, M. Shao / Catena 95 (2012) 24–32

Mean SWS / mm

200 160 120 80

0-1 m 1-2 m 2-3 m

40 0

a

60

SDS / mm

50 40 30 0-1 m

20

1-2 m

10 0

2-3 m

b

40 35

CVS / %

30 25 20 15

0-1 m

10

1-2 m

5 0

2-3 m

c 07-20- 09-20- 04-05- 06-25- 08-28- 10-29- 05-12- 07-11- 08-17- 09-2408 08 09 09 09 09 10 10 10 10

Date / Month-Day-Year Fig. 2. Time series of (a) the mean soil water storage (SWS) over space, (b) its associated standard deviation (SDS), and (c) coefficient of variation (CVS) for various soil layers.

165.4 mm and 100.7 to 160.6 mm for the 1–2 and 2–3 m soil layers, respectively. Although the mean SWS over time increased from 126.9 to 134.0 mm with increasing soil depth, no significant Table 2 Temporal statistics for spatial mean soil water storage (SWS) its corresponding standard deviations (SDS), and coefficients of variation (CVS) in various soil layers over the period of measurement between July 2008 and October 2010. Spatial variablesa Mean SWS

SDS

CVS

Temporal statisticsb Mean (mm) Max. (mm) Min. (mm) SDT (mm) CVT (%) Mean (mm) Max. (mm) Min. (mm) SDT (mm) CVT (%) Mean (%) Max. (%) Min. (%) SDT (%) CVT (%)

0–1 m

1–2 m

2–3 m

126.9 ac 178.4 74.5 26.3 20.7 29.6 a 37.7 21.6 4.8 16.3 23.8 a 29.9 18.6 3.9 16.6

132.0 a 165.4 97.8 18.2 13.8 43.7 b 53.3 33.4 5.3 12.5 32.4 b 34.3 29.7 1.2 3.8

134.0 a 160.6 100.7 16.8 12.6 46.9 c 56.7 35.8 5.3 11.3 35.5 c 37.0 33.7 0.8 2.4

a SDS of SWS is the standard deviation of the spatial SWS; CVS of SWS is the coefficient of variation of the spatial SWS. b Statistics in the second column are derived from the time series of statistics in the first column. Therefore, SDT refers to the standard deviation of the time series of the mean spatial SWS, SDS of the spatial SWS, or CVS of the spatial SWS; CVT refers to the coefficient of variation of the time series of the mean spatial SWS, SDS of the spatial SWS, or CVS of the spatial SWS. c Means followed by the same letter are not significantly different at p b 0.05.

27

differences were found among the three soil layers based on a paired-sample t-test. This result agreed with the finding of Hu et al. (2010a) who observed no significant differences for soil water content among soil depths of 0.4, 0.6 and 0.8 m within the same watershed. However, these observations are not universal, because Hu et al. (2010b) found that the SWS of deeper soil layers were significantly lower than that of the 0–1 m layer on another hillslope, separated by a deep gully from the slope in the present study. The SWS is a variable affected by the combined factors of rainfall, infiltration, upward water movement, and water uptake by plant roots. The different results may be caused by differences in land-use cover: the first two studies involved more complex land use than the last study. Standard deviation and coefficient of variation over time (SDT and CVT) of SWS for the various soil layers indicated that temporal changes for the mean SWS decreased with increasing soil depth, with SDT values of 26.3, 18.2, and 16.8 mm and CVT values of 20.7%, 13.8%, and 12.6% for the 0–1, 1–2, and 2–3 m layers, respectively (Table 2). Several environmental factors (e.g. evaporation and rainfall) may cause greater variability in the shallow soil layer than in the lower layers. Consistent results were also observed by (Choi and Jacobs, 2007), but within a shallow soil layer (0–0.25 m). The temporal changes in standard deviations and coefficients of variation of SWS over space (SDS and CVS) (Fig. 2b and c) showed that SWS of deeper soil layers had greater spatial variability, which was significant (p b 0.05) by a paired-sample t-test (Table 2). The time-averaged SDS values of SWS for the soil layers with increasing depth were 29.6, 43.7, and 46.9 mm, and the time-averaged CVS values were 23.8%, 32.4%, and 35.5%, respectively. Spatial variability of SDS and CVS, similar to the mean SWS, changed more over time for the shallow soil layer (0–1 m) than for the deeper layers. The values of CVT for the SDS and CVS of SWS were 16.3% and 16.6% for the 0–1 m soil layer and 11.3% and 2.4% for the 2–3 m soil layer, respectively. This indicated that the spatial variability of the mean SWS tended to be temporally more stable for deeper soil layers. Although both variables decreased with increasing soil depth, the decrease in CVS was much quicker than in SDS, from 16.6% to 2.4% and 16.3% to 11.3% when soil depth increased from 0–1 to 2–3 m, respectively (Table 2). Additionally, this decrease was mainly observed in the upper soil layer. The values of CVT for the SDS and CVS of the 1–2 m soil layer were 12.5% and 3.8%, which were more similar to those of the 2–3 m soil layer than of the 0–1 m layer. This difference was probably caused by the increase of the mean SWS with soil depth. These results are consistent with previous observations (Cassel et al., 2000; Guber et al., 2008; Hu et al., 2010b; Lin, 2006). Figure 3 shows the mean SWS and the variance associated with each observing date for the three soil layers, indicating a clear positive correlation between the two variables (p b 0.01). This result indicated that SWS was more heterogeneously distributed in this area under wetter than under drier conditions. The result was consistent with previous findings (Famiglietti et al., 1998; Hu et al., 2009; Martínez-Fernández and Ceballos, 2003). Hupet and Vanclooster (2002), however, found a negative relationship between spatial mean soil moisture and its standard deviation. Different statuses of soil moisture may be one important reason. Penna et al. (2009) reported that variability in soil moisture was greatest at conditions of soil moisture of 23–29%. When soil moisture was below this range, mean values and standard deviations were positively correlated. In contrast, when soil moisture was above 23–29%, the standard deviation of soil moisture decreased with an increase in soil moisture. When soil moisture is low (e.g. b20%), the soil is unsaturated. Under the control of matric potential, soil water is hard to move. Variability thus increases with availability of soil water. When the soil water content exceeds 30%, though, soils gradually become saturated, and soil water easily moves from regions of higher soil water potential to regions of lower potential, which decreases the spatial variability of soil moisture.

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L. Gao, M. Shao / Catena 95 (2012) 24–32

Variance / mm2

1600

a

1200

y = 6.16x + 114.97 R2 = 0.33

800

400

0 40

90

190

140

3000

b

Variance / mm2

2500

y = 24.32x - 1360.3 R2 = 0.91

2000 1500 1000 500 0 80 3500

120

140

160

180

140

160

180

c y = 28.86x - 1641.1 R2 = 0.97

2800

Variance / mm2

100

2100

1400

700

0 80

100

120

Mean soil water storage / mm Fig. 3. Variance of soil water storage (SWS) (mm2) versus mean SWS (mm) using the full data set for the soil layers of (a) 0–1 m, (b) 1–2 m, and (c) 2–3 m.

We further found that this positive correlation increased with soil depth. The linear determination coefficients between mean SWS and the variance based on the full dataset were 0.33, 0.91, and 0.97 for the soil layers of 0–1, 1–2, and 2–3 m, respectively (Fig. 3). Increasing correlations may be related to surface evaporation, water uptake by plant roots, and soil properties. Deeper layers typically have somewhat less variability than shallower layers. The higher dependency indicated that conditions of soil moisture became a more dominant factor in determining the spatial heterogeneity of SWS with increasing soil depth. Collecting more samples in the period with high soil moisture content is thus a reasonable measure for improving the precision of prediction. The effect is more notable for deeper soil layers.

Spearman correlation coefficients, decreased largely for the 0–1 m soil layer with increasing time lags. For example, the coefficients for the dataset of July 20, 2008 decreased from 0.95 to 0.73, with the time lags increasing from three months to twenty-seven months (Table 3), while the time lags had less influence on the temporal patterns of SWS in deeper soil layers. For example, with an increase in the same time lags (from three months to twenty-seven months), the coefficients only decreased from 0.98 to 0.92 and from 0.99 to 0.96 for the 1–2 and 2–3 m soil layers, respectively. The results of a one-way analysis of variance (one-way ANOVA) showed significant differences between the 0–1 and 1–2 m (p = 0.036) and between the 0–1 and 2–3 m (p = 0.013) layers, while no significant differences were found between the 1–2 and 2–3 m (p = 0.607) layers. The effect of time lags on the temporal stability of spatial patterns was thus a function of soil depth. These results have consequences for identifying the period of validity of the temporal stability. Accordingly, the soil layers should be considered separately, with longer periods of stability for deeper soil layers than for shallower layers. Many studies focus on the relationship between temporal patterns of soil moisture and soil depth. In the present work, the mean rank correlation coefficients increased significantly with increasing soil depth (Table 4). The mean values were 0.86, 0.96, and 0.98, ranging from 0.58 to 0.98, 0.92 to 0.99, and 0.96 to 0.99, for the 0–1, 1–2, and 2–3 m soil layers, respectively. This result is consistent with the findings of Cassel et al. (2000) and Guber et al. (2008) for cropland and Lin (2006) for forested watersheds. Although Hu et al. (2009) found that the most pronounced stability was at a soil depth of 0.2 m, they also found a significant increase of stability at depths of 0.4, 0.6, and 0.8 m. Two main reasons could explain the increasing temporal stability with soil depth. Firstly, the impact of water uptake by the vegetation's roots and pedogenetically derived variations at deeper layers conserved a relatively stable pattern through time (Kamgar et al., 1993). Secondly, the dynamics of soil structure and the ability to retain water, which is much more pronounced in shallow soil layers (Korsunskaya et al., 1995), can contribute to increased temporal stability with soil depth. In addition, the scattered distribution of land use in the study area introduced more variability of SWS for the root-zone soil layer (~ 0.6 m), and hence decreased the temporal stability of the shallow soil layer. Furthermore, the closer two soil layers were within a given profile and the deeper any two adjacent soil layers were, the larger was the Spearman rank correlation coefficient. For example, the mean Spearman rank correlation coefficients over the whole period of measurement were 0.86, 0.64, and 0.42 for the mean SWS of 0–1 vs. 0–1, 0–1 vs. 1–2, and 0–1 vs. 2–3 m layers, respectively (Table 4). From Table 4 we also found that the deeper any two adjacent soil layers were, the greater was the Spearman rank correlation coefficient. For example, although the intervals were both 1 m, the mean coefficients increased from 0.64 to 0.80 when 0–1 vs. 1–2 and 1–2 vs. 2–3 m layers were observed. A one-way ANOVA showed that all the differences of the coefficients were significant (p b 0.01). The results were in agreement with the findings of Hu et al. (2010b), who investigated the SWS along a transect on a hillslope located in the same watershed.

3.2. Temporal patterns of SWS for the three soil layers 3.3. Temporal stability analysis of SWS in the three soil layers Owing to the large amount of space that it would occupy, the matrix of rank correlation coefficients corresponding to all 91 observing locations made on the 20 dates of measurement for three soil layers has not been included here. In that matrix, all the coefficients are significant at the 0.01 probability level, indicating a strong temporal stability in all the three layers. The temporal stability, however, shows a timeassociated drift, especially in the shallow soil layer. The correlation appears to degrade with increasing time lags as evidenced by the smaller coefficients. Only the coefficients of eight chosen 8 dates (April, July, and October of each year) for the three soil layers are shown (Table 3). Based on this table, the similarity of temporal patterns, denoted by the

The rank ordered MRD in SWS and associated SDRD for various soil layers (Fig. 4) showed that these two variables behaved differently in diverse soil layers (Table 5). The ranges between the minimum and maximum values for the MRD in the 0–1, 1–2, and 2–3 m layers were 93.2%, 159.8%, and 172.3%, changing from −44.9% to 48.3%, −61.8% to 98.0%, and −64.4% to 108.0% for soil layers of 0–1, 1–2, and 2–3 m, respectively. The increasing ranges of MRD were due to the stronger spatial heterogeneity of SWS with increasing soil depth, which is shown in Fig. 2b and c. The absolute values of the minimum values, in the present study, were lower than the maximum values for MRD in all three soil

L. Gao, M. Shao / Catena 95 (2012) 24–32

29

Table 3 Matrix of Spearman's rank correlation coefficients from comparisons of soil water storage (SWS) measurements made at 91 field locations on eight measurement dates in different soil layers.

A1 A2 A3 A4 A5 A6 A7 A8 B1 B2 B3 B4 B5 B6 B7 B8 C1 C2 C3 C4 C5 C6 C7 C8

A1

A2

A3

A4

A5

A6

A7

A8

B1

B2

B3

B4

B5

B6

B7

B8

C1

C2

C3

C4

C5

C6

C7

C8

1.00 0.95 0.91 0.91 0.90 0.83 0.91 0.73 0.74 0.74 0.73 0.75 0.67 0.67 0.70 0.67 0.53 0.56 0.54 0.57 0.56 0.54 0.54 0.54

1.00 0.98 0.94 0.96 0.91 0.93 0.76 0.69 0.70 0.70 0.72 0.64 0.65 0.67 0.64 0.48 0.49 0.47 0.50 0.49 0.47 0.48 0.48

1.00 0.92 0.96 0.94 0.91 0.73 0.67 0.66 0.67 0.69 0.61 0.62 0.64 0.59 0.44 0.44 0.44 0.45 0.45 0.44 0.43 0.43

1.00 0.91 0.85 0.92 0.74 0.71 0.72 0.72 0.76 0.70 0.66 0.71 0.66 0.49 0.49 0.47 0.51 0.52 0.48 0.49 0.49

1.00 0.94 0.94 0.80 0.67 0.66 0.67 0.69 0.62 0.64 0.66 0.63 0.44 0.46 0.43 0.45 0.46 0.44 0.43 0.46

1.00 0.87 0.76 0.64 0.63 0.65 0.67 0.60 0.64 0.63 0.59 0.42 0.42 0.41 0.43 0.43 0.43 0.41 0.42

1.00 0.80 0.68 0.69 0.69 0.71 0.65 0.65 0.70 0.67 0.49 0.51 0.47 0.51 0.51 0.48 0.49 0.51

1.00 0.62 0.65 0.63 0.65 0.64 0.61 0.67 0.70 0.40 0.42 0.40 0.42 0.45 0.41 0.44 0.49

1.00 0.98 0.97 0.97 0.95 0.96 0.95 0.92 0.80 0.81 0.81 0.82 0.83 0.81 0.82 0.81

1.00 0.97 0.97 0.97 0.95 0.96 0.94 0.79 0.81 0.80 0.81 0.83 0.80 0.82 0.82

1.00 0.98 0.97 0.98 0.97 0.94 0.80 0.80 0.81 0.81 0.82 0.80 0.82 0.82

1.00 0.97 0.97 0.98 0.94 0.76 0.78 0.77 0.79 0.80 0.78 0.80 0.80

1.00 0.97 0.98 0.96 0.79 0.80 0.80 0.81 0.84 0.81 0.84 0.84

1.00 0.97 0.94 0.80 0.80 0.81 0.81 0.82 0.81 0.82 0.83

1.00 0.96 0.79 0.80 0.80 0.81 0.82 0.80 0.83 0.84

1.00 0.78 0.80 0.79 0.80 0.83 0.79 0.82 0.84

1.00 0.99 0.99 0.98 0.97 0.98 0.98 0.96

1.00 0.99 0.99 0.98 0.98 0.98 0.96

1.00 0.99 0.97 0.99 0.99 0.97

1.00 0.97 0.99 0.99 0.97

1.00 0.98 0.98 0.97

1.00 0.98 0.97

1.00 0.97

1.00

All comparisons were significant at the 0.001 probability level. The capital letters A, B, and C refer to the soil layers of 0–1 m, 1–2 m, and 2–3 m, respectively. The numbers of 1 to 8 refer to the measurement dates July 20 and October 20 in 2008; April 05, July 26, and October 29 in 2009; and April 09, July 11, and October 20 in 2010, respectively.

Table 4 Summary statistics of Spearman rank correlation coefficients between different layers based on all measurements made between July 2008 and October 2010. 0–1 vs. 0–1 1–2 vs. 1–2 2–3 vs. 2–3 0–1 vs. 1–2 1–2 vs. 2–3 0–1vs. 2–3 Mean Min. Max. SD CV

0.86 a§ 0.58 0.98 0.100 11.7

0.96 b 0.92 0.99 0.015 1.56

0.98 c 0.96 0.99 0.008 0.80

0.64 d 0.47 0.76 0.067 10.5

§ All means are significantly different at p b 0.01.

0.80 e 0.76 0.85 0.017 2.1

0.42 f 0.25 0.52 0.068 16.2

patterns of SWC at different times, while SDRD is used to characterise the degree of temporal invariability for a certain location. Hence, in this study, the changes of spatial patterns at different times and increasing soil depths were consistent with the temporal stability of the locations. Hu et al. (2010a), however, found the opposite. The temporal stabilities of their locations at 0.2 m were weaker than

Mean relative difference / %

layers, which are comparable to the results reported by Cosh et al. (2008) and Hu et al. (2010b) but are in contrast to the findings of Schneider et al. (2008). Furthermore, Starks et al. (2006) suggested that the relative size of the two variables varied with depth. Soil texture and structure had important effects on soil moisture beyond MRD values (Zhao et al., 2010). In the study area, most of the locations have sandy soils with low SWS. Additionally, the soils of loessial deposits exhibited a unique vertical homogeneity in soil textural properties, which may account for the same relative sizes of the two variables among the three soil layers. The associated SDRD also differed among soil layers. The mean values of SDRD decreased with increasing soil depth (Table 5), being 8.9%, 5.2%, and 3.9% for the 0–1, 1–2, and 2–3 m layers, respectively (p b 0.001). Similar results were also reported by Hu et al. (2010b) on a hillslope in the same watershed. The SDRD is widely used to describe the temporal stability of soil moisture. The decreasing SDRD with soil depth meant the SWS tended to be more stable at deeper soil layers. The soil moisture at deeper soil layers is expected to be more time-stable due to the reduced dependence on the climatic, biological, and hydrological factors that determine the dynamics of soil moisture. The decreasing SDRD is a direct result of the decreasing temporal variability with soil depth shown in Fig. 2. In this study, the results of temporal stability as indicated by SDRD agree with those based on the Spearman's rank correlation coefficient. The indices of Spearman's correlation coefficient and SDRD are two different concepts of temporal stability; Spearman's rank correlation coefficient is used to describe the similarity of spatial

140 120 100 80 60 40 20 0 -20 -40 -60 -80 140 120 100 80 60 40 20 0 -20 -40 -60 -80 140 120 100 80 60 40 20 0 -20 -40 -60 -80

a 2358 75 5928 448421 7 12 91 67 56 47 90 17 81 49 417766 13 24 79 22 39 86 76 18 62 83 10 42 29 64 7116 2746 55 48 11 78 26 89 31 5 20 36 1 60 15 80 30 54458573 87 19 6 63 368 35 52 51 38 8857 50 8 14 5337 74 82 70 69 34 722532 43 6540 9 61 2 4 33

b

58

59 29 84 91 60 28 50 85 78 31 11 9 76 6 432720 8123 55 56 48 18 517712 8786 90 80 83 69 2457 70 52 19 82 44 75392142153054 10 38 88 79 37 40 17 53 6749 5 36 7 13 462 26 22 41 47 73 6645 71 32 338 72 68 61 16 89 1 14 74 34 25 64626563 4 353

c

28 58 38

823081 53 319143 50 29 59 47 77 8380 90 5152208727 66 56 6 84 54 60 1489 5740 69 10 55 72 121819 7644 78 48 49 15 63 45 24 86238826 5 2175 98579 17 42 16 37 70 74 2 39 25 22 11 61 8 3373 71 46 62 3 4 4136 7 13 65 64 1 34 68 35 6732

0

5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Rank Fig. 4. Rank ordered mean relative differences of soil water storage (SWS) at each location for the soil layers of (a) 0–1 m, (b) 1–2 m, and (c) 2–3 m. Vertical bars represent ± one standard deviation of relative difference.

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L. Gao, M. Shao / Catena 95 (2012) 24–32 25

Table 5 Statistical summary of the mean relative difference (MRD) and its standard deviation (SDRD) for soil water storage (SWS) in various soil layers.

SDRD/%

Parameters

0–1 m

1–2 m

2–3 m

Min. Max. Range SD NMean Min. Max. Range SD CV N+

− 44.9 48.3 93.2 22.2 19 8.9 a§ 3.3 20.8 17.6 3.3 37.2 6

− 61.8 98.0 159.8 32.0 11 5.2 b 2.0 10.8 8.9 2.1 40.2 46

− 64.4 108.0 172.3 34.8 10 3.9 c 1.3 9.8 8.4 1.6 41.8 72

N — number of locations with mean relative difference ranging from − 5% to + 5%; N + Number of sites with standard deviation of relative difference b 5%; and §All means are significantly different at p b 0.001.

those at 0.6 and 0.8 m, but the spatial pattern of soil water content distribution at the same depth was strongest when the temporal stability of the upper 0.8 m soil layer was investigated based on the two indices. This difference may largely be due to the different depths of sampling. At the depth of 0.2 m, the temporal variability of soil moisture was larger than in deeper soil layer, which leads to a weaker temporal stability of the locations. However, the larger variability of soil moisture over time in producing a better spatial pattern may occasionally be advantageous. The degree of temporal stability in drier versus wetter locations is under debate. Some authors found greater stability for drier locations (Cosh et al., 2008; Jacobs et al., 2004; Martínez-Fernández and Ceballos, 2003), while Schneider et al. (2008) and Guber et al. (2008) did not find a dependency of temporal stability on the status of average soil water at particular locations. We found a significant positive correlation (p b 0.01, Pearson test) between the mean SWS and associated SDRD in the present study was observed (Fig. 5). This positive correlation indicated that the sampling locations representing the dry conditions of our study area were always more stable than the wetter locations. This correlation, however, does not mean the locations with low mean soil moisture were time stable, but were only more probable to be temporally stable, because the correlations were low, especially in the 0–1 m soil layer, with a linear determination coefficient of 0.097. These identified time-stable locations may thus have low MRD values far from zero, but they can be well used to estimate the mean SWS of the watershed if a constant offset is introduced, as suggested by Grayson and Western (1998). We further found that the dependency of temporal stability on the status of soil moisture increased with soil depth, with linear determination coefficients of 0.097, 0.21, and 0.35 for soil layers of 0–1, 1–2, and 2–3 m, respectively (Fig. 5). This result, however, is inconsistent with the findings of Martínez-Fernández and Ceballos (2003), who found no clear relationship between the dependency and the soil depth shown within a 0–1 m soil profile. These differences can be explained by two aspects. Firstly, our study was conducted at the scale of hillslope while the latter study was conducted in an area of 1285 km2. Larger areas are likely to have more variations derived from climate, landuse cover, and topography (Western and Blöschl, 1999). Secondly, the loess in our study exhibited unique vertical homogeneity in soil textural properties, while the soil texture in the latter study area was more variable, e.g. soil clay content increased in the upper 50-cm soil layer, with a coefficient of variation of 30.4% (Ceballos et al., 2002). Following the proposal of Vachaud et al. (1985), the average SWS monitoring locations, i.e. the locations with MRD values close to zero and with the minimum associated SDRD, were identified by the method of relative difference. Although Grayson and Western (1998) later suggested one alternative and Hu et al. (2010b) more

y = 0.037x + 4.17 2 R = 0.097

15 10 5

Standard deviation of relative difference / %

MRD/%

a 20

0 50

100

150

200

12

b 9

y = 0.023x + 2.19 2 R = 0.21

6

3

0 0 12

50

c

100

150

200

250

300

150

200

250

300

y = 0.02x + 1.12 2

R = 0.35

9

6

3

0 0

50

100

Soil water storage / mm Fig. 5. The linear relation between the standard deviation of relative difference and the soil water storage for three soil layers: (a) 0–1 m, (b) 1–2 m, and (c) 2–3 m.

recently developed a new criterion — the mean absolute bias error, most studies still focus on relative difference (Brocca et al., 2009; Cosh et al., 2004, 2008; Martínez-Fernández and Ceballos, 2005), due to the time-stable locations identified by which method could directly represent the mean value of a study area. Relative difference method was also used in the present study. If the allowable bias from the mean for MRD is 5%, i.e. the MRD values range from −5% to +5%, then the number of locations meets the required decrease with soil depth. The number of locations with absolute values of MRD lower than 5% was 19, 11, and 10 for 0–1, 1–2, and 2–3 m soil layers, respectively (Table 5). The decreasing values with soil depth were due to the stronger spatial variability in SWS for deeper soil layers (Fig. 2b and c). An MRD value close to zero is only a necessary but not a sufficient condition for identifying temporally stable locations to estimate the mean SWS of a study area. Another condition that must be fulfilled in the locations is a low standard deviation across the entire period of measurement. Starks et al. (2006) identified locations as timestable those with SDRD values lower than 5%. Based on this principle, the number of time-stable locations in the present study increased with increasing soil depth (Table 5), which agreed with the findings of Hu et al. (2010b). Only six locations in a total of 91 spatial observations were time stable for the 0–1 m soil layer. The number of locations increased to 46 for the 1–2 m soil layer, which accounted for more than half of the total number of spatial observations. For the 2–3 m soil layer, most of the locations were temporally stable; up to 76 locations produced an SDRD lower than 5%. The decreasing

L. Gao, M. Shao / Catena 95 (2012) 24–32

variability of mean SWS with soil depth over time (Fig. 2a) was the main reason for the increasing number of locations with soil depth. Locations can directly represent the mean SWS of the study area only if they meet both of these requirements. Based on this principle, the number of locations in this study that could be used to directly predict the mean SWS of the area increased with increasing soil depth; 3, 5, and 8 representative locations for the soil layers of 0–1, 1–2, and 2–3 m, respectively. As mentioned above, the temporal variability of SWS decreased and its variability in space increased with an increase in soil depth. The large variability of soil moisture may increase the uncertainty. Decreasing temporal variability induced more locations with smaller SDRD values, and increasing spatial variability meant that MRD was distributed in a more extensive range, resulting in fewer locations with MRD values close to zero. More locations were able to represent the mean SWS of the hillslope with an increase in soil depth, suggesting that changes in the temporal variability of soil moisture had a more important effect than changes in spatial variability on identifying representative locations. In addition to those reported in other studies (Gao et al., 2011; Guber et al., 2008; Tallon and Si, 2004), representative locations have been indentified in this study for the three soil layers (Fig. 4). The identified representative locations are sites 48, 57, and 83 for 0–1 m layer; 17, 19, 51, 67, and 77 for the 1–2 m layer; and 14, 18, 19, 23, 26, 57, 86, and 89 for the 2–3 m layer. Obviously, no single location could represent the mean SWS for all three soil layers. Only location 19 was able to estimate the mean SWS for both the 1–2 and 2–3 m soil layers. Two main reasons may explain the differences in the locations at different soil depths. Firstly, vertical variability of soil properties, especially the soil texture, can have an important effect on the temporal patterns of soil moisture (Zhao et al., 2010). Although the soils in the study area have weak vertical variability in properties of soil texture, due to the activity of soil organisms, soil erosion, and the lengthy periods of growth of the vegetation, variability along soil profiles is introduced, especially in the shallow soil layer. Secondly, the temporal stability of SWS depends on the combined effects of soil, vegetation, and topographic properties. However, these factors, such as plant roots, had diverse effects on soil moisture at different soil depths.

4. Conclusions Based on the datasets of the SWS (0–1, 1–2, and 2–3 m layers) of 91 locations on 20 observing dates, the following conclusions were drawn: (1) With increasing soil depth, the temporal variability for SWS decreased, but spatial variability increased. The shallow layer (0–1 m) had the strongest variability over time but the weakest variability over space, which was opposite to the deepest soil layer (2–3 m). Accordingly, sampling density should be increased over time for shallower layers, and more samples should be collected over space for deeper soil layers. (2) The SWS during this study was more heterogeneously distributed in this watershed under wetter than under drier conditions. The dependency increased with increasing soil depth. (3) The temporal stability was stronger with an increase in soil depth, based on either the Spearman correlation coefficient or the SDRD index. Furthermore, the closer two soil layers were within a given profile and the deeper any two adjacent soil layers were, the more similar was the temporal pattern. (4) The sampling locations that were representative of the dry conditions in the study area were always more stable, and the wetter locations were less stable (p b 0.01). The correlation between the status of soil water and temporal stability increased with increasing soil depth.

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(5) More locations estimated the mean SWS of the study area accurately in deeper soil layers than in shallower layers. None of the locations, however, were able to represent the mean SWS for all three layers. Temporal variability played a more important role than variability in space in determining the number of representative locations.

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