Modeling the impacts of soil hydraulic properties on temporal stability of soil moisture under a semi-arid climate

Journal of Hydrology 519 (2014) 1214–1224

Contents lists available at ScienceDirect

Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

Modeling the impacts of soil hydraulic properties on temporal stability of soil moisture under a semi-arid climate Tiejun Wang ⇑ School of Natural Resources, University of Nebraska-Lincoln, Hardin Hall, 3310 Holdrege Street, Lincoln, NE 68583, USA

a r t i c l e

i n f o

Article history: Received 7 May 2014 Received in revised form 29 July 2014 Accepted 27 August 2014 Available online 6 September 2014 This manuscript was handled by Corrado Corradini, Editor-in-Chief, with the assistance of Rao S. Govindaraju, Associate Editor Keywords: Soil moisture Temporal stability Soil hydraulic property Vadose zone model Semi-arid climate

s u m m a r y Despite the significant spatiotemporal variability of soil moisture, the phenomenon of temporal stability of soil moisture (TS SM) has been widely observed in field studies. However, the lack of understandings of the factors that control TS SM has led to some contradictory findings about TS SM. To resolve this issue, numerical models may offer an alternative way to complement field studies by quantifying different controls on TS SM. In this study, a 1-D vadose zone model was adopted to simulate daily soil moisture contents, which were used to compute the mean relative difference (MRD) and standard deviation of relative difference (SDRD) of soil moisture. Different from recent modeling studies, a soil dataset was employed with 200 samples of correlated soil hydraulic parameters for sandy soils. Compared to the results of previous modeling studies, more reasonable patterns of MRD and SDRD that resembled field observations were produced. By varying soil hydraulic parameter values, different patterns of MRD and SDRD could also be generated, implying variations in soil hydraulic properties could partly control the patterns of MRD and SDRD. More specifically, the residual soil moisture content (hr) was found to be the primary control on MRD, mainly due to the semi-arid climate that was simulated. By fixing hr, however, a highly nonlinear relationship emerged between MRD and the shape factor n in the van Genuchten model, which resulted in the positively skewed distributions of MRD widely observed for sandy soils in field experiments. Moreover, both the range and skewness of the distributions of MRD were affected by the range of n. In addition, with increasing n, a positive correlation between MRD and the shape factor l in the van Genuchten model was also found. The simulation results suggested that the control of soil hydraulic properties on MRD might weaken for areas under bare surface conditions or for regions with more humid climates due to elevated soil moisture contents. Therefore, the impacts of soil hydraulic properties on TS SM may vary under different climate regimes. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Soil moisture is a key state variable that is linked to a range of hydrological, ecological, climatic, and geological processes. At regional and global scales, soil moisture affects precipitation and land evapotranspiration (Eltahir, 1998; Koster et al., 2004; Jung et al., 2010). At catchment and field scales, soil moisture partly controls the partitioning of precipitation and net radiation, evapotranspiration, groundwater recharge, and subsurface solute transport (Robinson et al., 2008; Vereecken et al., 2008). Meanwhile, soil moisture has also been used for validating spatially distributed land surface and hydrological models (Houser et al., 1998; Nijssen et al., 2001; Vereecken et al., 2008).

⇑ Tel.: +1 402 472 0772. E-mail address: [email protected] http://dx.doi.org/10.1016/j.jhydrol.2014.08.052 0022-1694/Ó 2014 Elsevier B.V. All rights reserved.

As a result of complex interactions among different controlling factors and processes (e.g., soil, topography, vegetation, and climate), soil moisture exhibits significant spatial and temporal variability, which presents a great challenge for utilizing soil moisture data for different research and application purposes. To overcome this issue, there has been a rising interest in studying the temporal stability of soil moisture (TS SM). As first introduced by Vachaud et al. (1985), the phenomenon of TS SM has been widely observed in field experiments across various spatial (from tens of m2 to thousands of km2) and temporal (from days to years) scales (see the review by Vanderlinden et al. (2012)). By examining soil moisture data collected from three field plots, Vachaud et al. (1985) showed that soil moisture contents at certain locations were closer to and thus more representative of the areal average moisture condition, while other locations exhibited consistently either wetter or drier conditions compared to the areal average. Moreover, Vachaud et al. (1985) found a temporal persistence in

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

the spatial pattern of soil moisture. Since the seminal work of Vachaud et al. (1985), a large body of studies have been generated on the topic of TS SM for different research and application purposes, such as identifying representative locations, optimizing monitoring schemes, filling missing data, scaling soil moisture contents, improving the performance of hydrological models, and delineating water management zones (e.g., Grayson and Western, 1998; Cosh et al., 2004; Jacobs et al., 2004; Pachepsky et al., 2005; Starr, 2005; Guber et al., 2008; Brocca et al., 2010). Depending on local conditions, TS SM has been shown to be related to soil properties and depth, topography, vegetation, and moisture state (Vachaud et al., 1985; Grayson and Western, 1998; Gomez-Plaza et al., 2000; Mohanty and Skaggs, 2001; MartinezFernandez and Ceballos, 2003; Jacobs et al., 2004; Hu et al., 2010; Heathman et al., 2012; Zhang and Shao, 2013). However, previous field studies also led to some contradictory findings about the controlling factors on TS SM. For instance, Jacobs et al. (2004) found a positive correlation between TS SM and clay contents; whereas, Mohanty and Skaggs (2001) showed that TS SM was more pronounced in coarser soils. Moreover, there is still a debate as to whether TS SM is higher at dry conditions or wet ones (GomezPlaza et al., 2000; Martinez-Fernandez and Ceballos, 2003; Zhao et al., 2010; Jia et al., 2013; Zhang and Shao, 2013). With limited observational data, those contradictory results stem mainly from the lack of understandings of the factors and processes that control TS SM at different temporal and spatial scales (Vanderlinden et al., 2012). To further understand and more importantly quantify those controlling factors on TS SM, numerical models may offer an alternative way to complement field studies. Modeling approaches have been long used for studying spatial variability of soil moisture fields (Entekhabi and Rodriguez-Iturbe, 1994; Teuling and Troch, 2005; Ivanov et al., 2010). By comparison, modeling studies on TS SM are still very limited (Martinez et al., 2013, 2014). By employing a 1-D vadose zone model to simulate soil moisture dynamics, Martinez et al. (2013) attempted to quantify the impact of soil saturated hydraulic conductivity (KS) on TS SM along with the consideration of root water uptake, and found a negative linear relationship between the mean relative difference of soil moisture and lnKS. The same modeling approach was also used by Martinez et al. (2014) to further examine the impact of KS on TS SM under different climate regimes. For both studies, log-normal distributions of KS were generated to represent the spatial variability in soil hydraulic properties. However, as also noticed by Martinez et al. (2013), the simulated patterns of TS SM deviated from commonly observed patterns of TS SM in field studies. It was most likely due to the simplistic approach used to generate log-normally distributed KS for representing spatial variations in soil hydraulic properties. In reality, other soil hydraulic properties also vary in space, which may lead to spatial and temporal variability in soil moisture. Moreover, in a modeling study by Wang et al. (2009a), KS was shown to be less important in controlling groundwater recharge and actual evapotranspiration, compared to the shape factors in soil water retention and hydraulic conductivity functions, indicating a minor role of KS in affecting soil moisture dynamics and thus TS SM. Given the potential use of modeling approaches for resolving the existing contradictory findings about TS SM, there is still a need to use more realistic combinations of soil hydraulic parameters for examining the effects of soil hydraulic properties on TS SM. To this end, the soil dataset generated by Wang et al. (2009a) was used for the simulations of soil moisture dynamics. The soil dataset contained correlated soil hydraulic parameters for sandy soils. The main objectives of this study were to (1) examine whether more reasonable patterns of TS SM could be generated using the soil dataset of Wang et al. (2009a), (2) assess the impacts of different soil hydraulic parameters on TS SM, and (3) probe the possibility

1215

of using modeling approaches to explain some of the observed TS SM patterns for sandy soils in field experiments. 2. Methods and materials 2.1. Simulation of soil moisture dynamics A commonly used vadose zone model, Hydrus-1D (Simunek et al., 2005) was selected in this study for simulating soil moisture dynamics, as the accuracy of its numerical algorithm has been tested by analytical solutions (Zlotnik et al., 2007). The Hydrus1D model simulates soil moisture movement in vadose zone by solving 1-D Richards’ equation:

    @h @ @h  KðhÞ  SðhÞ KðhÞ ¼ @t @x @x

ð1Þ

where h [L3/L3] is volumetric soil moisture content, t [T] is time, x [L] is spatial coordinate, h [L] is water pressure head, S [1/T] is a sink term accounting for root water uptake, and K [L/T] is soil hydraulic conductivity. A standard atmospheric upper boundary condition was used in this study (Neuman et al., 1974), which depends on climatic conditions (i.e., precipitation – P and potential evaporation – Ep) and can switch from a prescribed flux to a prescribed head when limiting pressure heads are exceeded. When P exceeded soil infiltration capacity or soil became saturated, surface runoff occurred. A unit hydraulic gradient flow condition was imposed at the lower boundary (Small, 2005; Wang et al., 2009a). The length of simulated soil columns was 5 m with 501 nodes evenly distributed between the surface and bottom. Numerical experiments showed that further increasing the number of spatial nodes did not improve the model performance. Observational nodes were chosen at 25, 50, and 100 cm below the surface. Daily soil moisture contents were simulated for both vegetated and bare surface conditions. For the vegetated condition, potential evapotranspiration (ETp) was first partitioned into potential transpiration (Tp) and Ep based on Beer’s law (Ritchie, 1972):

Ep ðtÞ ¼ ET p ðtÞ  ekLAIðtÞ

ð2Þ

T p ðtÞ ¼ ET p ðtÞ  Ep ðtÞ

ð3Þ

where k is an extinction coefficient set to be 0.5 and LAI is leaf area index. The sink term S(h) for root water uptake was simulated according to the method of Feddes et al. (1978):

SðhÞ ¼ aðhÞ  Sp

ð4Þ

where a(h) [–] is a dimensionless function and varies between 0 and 1 depending on soil matric potentials, and Sp [1/T] is the potential root water uptake and assumed to be equal to Tp. The distribution of Sp over the root zone was based on root density distributions. The root parameters on pasture were used to determine the Feddes function (Wesseling, 1991). The research site chosen in this study was located at the University of Nebraska’s Barta Brothers Ranch (BBR) experimental site in the eastern Nebraska Sand Hills (42°140 N, 99°390 W; Fig. 1). The study area was covered by eolian sand deposits with a semi-arid continental climate (Wang et al., 2008). Daily hydrometeorological data that spanned over one year period were retrieved from a meteorological station at the BBR, which was operated by the High Plains Regional Climate Center (http://www.hprcc.unl.edu/). Measured LAI data at the BBR site during the same time period were first linearly interpolated into daily LAI data and then used to partition daily ETp. The obtained daily P, Ep, and Tp are plotted in Fig. 2. During the studied period, the total P, Ep, and Tp were 49.3, 131.3, and 44.4 cm, respectively. An exponential function

1216

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

Fig. 1. Location map of the study site at the Barta Brothers Ranch (BBR) experimental site.

Fig. 2. Daily meteorological data at the Barta Brothers Ranch site including precipitation (P), potential evaporation (Ep), and potential transpiration (Tp).

was fitted to describe the root density distribution based on field observations at the BBR site (Wang et al., 2009b). At the site, 60–70% of the total root mass occurred in the top 20 cm and 85–90% occurred in the top 50 cm. To minimize the effect of initial conditions, all the simulations were repeated at least 10 times until the soil moisture profiles were in equilibrium with climatic forcings (Small, 2005; Wang et al., 2009a). For each simulation, soil moisture contents were calculated at the end of each day, and the daily moisture contents from the last repetition of the simulations were retrieved at the depths of 25, 50, and 100 cm and used to compute TS SM. 2.2. Description of the dataset on soil hydraulic parameters The van Genuchten model (van Genuchten, 1980) was used to analytically describe the relations among h, h, and K in Eq. (1): m

hðhÞ ¼ hr þ ðhs  hr Þ=½ð1 þ jahjn Þ ; h < 0 or hðhÞ ¼ hs ;

hP0 h

 m i2 KðhÞ ¼ K S  Sle  1  1  Se1=m

conductivity, Se = (h  hr)/(hs  hr) is effective saturation degree, and a, n, and l are shape factors: a [1/L] is inversely related to air entry pressure, n [-] is a measure of pore size distribution with m = 1  1/n, and l [–] is a lumped parameter accounting for pore tortuosity and connectivity. It is well known that soil hydraulic properties affect soil moisture levels and thus TS SM. However, for modeling purposes, databases with complete sets of soil hydraulic parameters are very limited, particularly at field scales, as it is extremely time consuming and labor extensive to develop such databases. Thus, to promote the understandings of the impacts of soil hydraulic properties on TS SM, alternative methods for generating synthetic data are needed to mimic the spatial variability in soil hydraulic properties (Martinez et al., 2013, 2014). In Martinez et al. (2013, 2014), only log-normal distributions of KS were generated to represent the spatial variability in soil hydraulic properties, which led to some deviations of simulated TS SM patterns from field observations. In this study, the approach proposed by Wang et al. (2009a) was used to generate correlated soil hydraulic parameters for sandy soils to explore the impacts of those parameters on TS SM. The detailed description of the method for generating the dataset can be found in Wang et al. (2009a) and only a brief overview is given here. The soil dataset was derived from the UNSODA database (Nemes et al., 2001) by computing class average values of different hydraulic parameters (e.g., hs, hs, a, n, KS, and l) and a co-variance matrix for those parameters. A Monte-Carlo procedure proposed by Carsel and Parrish (1988) was then used to draw new samples with correlated soil hydraulic parameters from the co-variance matrix and class average values. A total of 200 generated samples were used in this study for simulations of daily soil moisture contents under different surface conditions. The statistical summary of the parameter values for the 200 samples is reported in Table 1.

ð5Þ 2.3. Statistical analysis of temporal stability of soil moisture

ð6Þ

where hr [L3/L3] is residual soil moisture content, hs [L3/L3] is saturated soil moisture content, KS [L/T] is saturated hydraulic

A number of techniques have been used to quantify TS SM (Vanderlinden et al., 2012). Among those techniques, the one proposed by Vachaud et al. (1985) has been mostly applied, which is based on the concept of relative difference (RD) of soil moisture:

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

1217

Table 1 Statistical summary of soil hydraulic parameters used for simulations of soil moisture dynamics (See Section 2.2 for the definitions of those soil hydraulic parameters).

Mean Standard deviation

RDij ¼

hr

hs

a

n

log KS

l

0.054 0.031

0.383 0.045

0.040 0.033

3.343 1.582

2.605 0.706

0.084 1.401

hij  hj hj

ð7Þ

hj where hij is the soil moisture content at location i and time j, and  is the areal average soil moisture content across the study area at time j. Given the total number of sampling locations N across the study area,  hj can be calculated as: N X hj ¼ 1 hij N i¼1

ð8Þ

By its definition, RDij represents the deviation of soil moisture content at location i from the areal average moisture content on day j. With a series of RDij over time, the mean relative difference (MRD) of soil moisture at location i is defined as:

MRDi ¼

m 1X RDij m j¼1

ð9Þ

where m is the total number of observations over the entire observation period at location i. The term MRD quantifies the wetness condition of soil moisture at a location relative to the field average over the observation period. Therefore, locations with MRD values close to zero can be used to represent the field average moisture conditions. The standard deviation of RD (SDRD) describes the temporal variability of RD and is used to measure TS SM:

" SDRDi ¼

m 1 X ðRDij  MRDi Þ2 m  1 j¼1

#0:5

Fig. 3. Ranked mean relative difference (MRD) with one standard deviation (vertical bars) under vegetated conditions at the depths of (a) 25 cm, (b) 50 cm, and (c) 100 cm. Red squares are the MRD for the sample with mean soil hydraulic parameter values (the same in the following figures). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

ð10Þ

Locations of high TS SM are defined as those with low values of SDRD. In this study, the technique based on MRD and SDRD was used as a diagnostic tool to investigate the impacts of soil hydraulic parameters on the pattern of TS SM, along with the considerations of different surface conditions. 3. Results and discussions 3.1. Temporal stability of soil moisture under vegetated conditions 3.1.1. Overall simulated pattern of MRD and SDRD The correlated soil hydraulic parameters for the 200 samples were used to represent the variations in soil hydraulic properties. Simulated daily moisture contents of the 200 samples were then used to calculate MRD and associated SDRD under different surface conditions. The ranked MRD and SDRD under vegetated conditions are plotted in Fig. 3 for the depths of 25, 50, and 100 cm. The statistical summary of those MRD and SDRD values is given in Table 2. By only varying soil hydraulic parameters in the soil water retention and hydraulic conductivity functions, Fig. 3 shows the resemblance of the simulated MRD patterns at all depths to commonly observed MRD patterns in field experiments (e.g., Vachaud et al., 1985; Grayson and Western, 1998; Gomez-Plaza et al., 2000; Martinez-Fernandez and Ceballos, 2003; Brocca et al., 2010; Hu et al., 2010; Zhang and Shao, 2013), indicating that the phenomenon of TS SM can be caused by variations in soil hydraulic properties. The MRD ranges varied between -0.856 and 1.978, 0.859 and

1.953, and 0.872 and 1.795 at the depths of 25, 50, and 100 cm, respectively. Those MRD ranges were larger than previously reported values for sandy soils (Martinez-Fernandez and Ceballos, 2003; Zhang and Shao, 2013). It was mainly due to the wide range of soil hydraulic parameter values used for the simulations. As suggested by Martinez-Fernandez and Ceballos (2003) and Brocca et al. (2010), the MRD ranges generally increase with the size of the study area and consequently with increasing spatial variability in soil textures. In addition, Hu et al. (2010) also observed similar MRD ranges in a 20 ha watershed to the ones presented in Fig. 3, owing to large spatial variability in soil textures. As illustrated in the next section, selection of samples with narrower ranges of soil hydraulic parameter values could significantly reduce the simulated MRD ranges. The criterion of MRD < ±5% (Hu et al., 2010) was used to identify representative samples with moisture conditions close to the average, which led to 14, 12, and 14 samples at the depths of 25, 50, and 100 cm, respectively. Although the number of representative samples was similar at different depths, only three samples had MRD < ±5% at all the depths, indicating that representative locations may vary with depth as observed by Martinez-Fernandez and Ceballos (2003) and Guber et al. (2008). As a highly nonlinear system, the change in representative samples with depth was probably the result of complex interactions of soil moisture with soil hydraulic properties and the processes of soil evaporation, root water uptake, and drainage, which deserves future investigations. The skewness of the distributions of MRD showed positive values (Table 2), meaning more samples with moisture conditions

1218

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

Table 2 Statistical summary of mean relative difference (MRD) and standard deviation of relative difference (SDRD) under different surface conditions. Surface condition

Depth (cm)

Range of MRD

Range of SDRD

Vegetated

25 50 100

0.856 0.859 0.872

1.978 1.953 1.795

0.018 0.018 0.016

Vegetated with fixed hr

25 50 100

0.232 0.259 0.327

2.533 2.498 2.269

Bare surface with fixed hr

25 50 100

0.358 0.378 0.395

2.388 2.390 2.361

drier than the average. This phenomenon has been widely observed for sandy soils in previous field studies (MartinezFernandez and Ceballos, 2003; Zhang and Shao, 2013) as well as in the modeling study of Martinez et al. (2013). The ranks of MRD for the sample with mean soil hydraulic parameter values (Table 1) are also highlighted in Fig. 3. As a result of the skewness effect, the sample with mean soil hydraulic parameter values exhibited drier-than-average conditions. It is consistent with the conclusion made by Wang et al. (2009a) that the use of average values of soil hydraulic parameters might be inappropriate for estimating areal average hydrological fluxes, due to the nonlinear nature of the system. The TS SM as indicated by SDRD values decreased with depth. The mean SDRD value was reduced from 0.129 at 25 cm to 0.118 at 50 cm and 0.080 at 100 cm. The pattern of decreasing SDRD with depth is in line with the results of previous field studies, which showed soil moisture was temporally more stable at deeper depths (e.g., Martinez-Fernandez and Ceballos, 2003; Guber et al., 2008; Jia et al., 2013). However, different from the simulation results of Martinez et al. (2013) for sandy soils, there was no correlation between MRD and SDRD in Fig. 3. In summary, by varying all the parameters in soil water retention and hydraulic conductivity models, it is possible to produce more reasonable patterns of MRD and SDRD that are similar to field observations, as demonstrated in Fig. 3. 3.1.2. Impacts of soil hydraulic properties on temporal stability of soil moisture One of the main applications of using modeling approaches for studying TS SM is to quantify the impacts of different controlling factors on TS SM. To this end, the relationships of MRD with different soil hydraulic parameters are shown in Fig. 4 for the depths of 25, 50, and 100 cm. In Martinez et al. (2013), only KS was varied according to log-normal distributions, which led to a negative linear relationship between MRD and ln KS; whereas, no correlation between MRD and lnKS was found in this study, suggesting that KS played a minor role in affecting soil moisture dynamics in sandy soils. Instead, MRD was largely controlled by the residual soil moisture content hr. With increasing hr, MRD also increased (Fig. 4). This apparent dependence of MRD on hr shown here can be attributed to the semi-arid climate that was simulated, in which the demand for evapotranspiration can greatly exceed precipitation such as at the BBR (Wang et al., 2009c). The high demand for evapotranspiration may result in very low soil moisture contents in sandy soils, especially in surface layers (soil moisture data at the BBR can be viewed from the High Plains Regional Climate Center at http:// www.hprcc.unl.edu/awdn/soilm/). Although hr was the primary control on MRD in this study, this conclusion may not hold in regions with more humid climates. This is also evident in the weaker dependence of MRD on hr at the depth of 100 cm, at which soil moisture contents became higher due to less demands from soil evaporation and root water uptake.

Mean SDRD

Skewness of MRD

0.333 0.337 0.199

0.129 0.118 0.080

1.121 1.143 1.110

0.042 0.034 0.029

0.338 0.301 0.211

0.112 0.104 0.071

3.801 3.538 2.846

0.026 0.030 0.027

0.319 0.310 0.304

0.067 0.067 0.064

2.754 2.646 2.530

It is therefore desirable to remove the effect of hr on MRD to have an overall understanding of the impacts of other soil hydraulic parameters on TS SM. For this purpose, a new set of simulations was performed under vegetated conditions. The same 200 samples were used in the new simulations except that hr was fixed to the average value (i.e., hr = 0.054; Table 1). Fig. 5 shows the relationships of newly derived MRD with different soil hydraulic parameters except for hr. Interestingly, by fixing hr, a highly nonlinear relationship emerged between MRD and the shape factor n. The shape factor n is a measure of pore size distributions. When n was approximately greater than 2, the MRD values remained largely below 0.1; whereas, when n varied between 1 and 2, the MRD values rapidly increased with decreasing n. Physically, higher n values generally correspond to coarser soils with larger pore sizes, leading to less water holding capacities and thus lower MRD values. Mathematically, at the same moisture level, the decrease in hydraulic conductivity with decreasing n grows stronger when n becomes smaller (Eq. (6)). This effect led to reduced drainage rates for samples with smaller n values, particularly when n was smaller than 2. As a result, soil moisture levels and consequently MRD values increased with decreasing n. Moreover, the nonlinear dependence of MRD on n was stronger within the root zone due to the processes of soil evaporation and root water uptake. With elevated soil moisture levels at the depth of 100 cm, the dependence of MRD on n weakened (Fig. 5). Similar to hr, it also indicates that for regions with more humid climates, the nonlinear control of n on MRD might weaken due to wetter soil moisture conditions. To show the patterns of MRD and SDRD derived from the simulations with fixed hr, the ranked MRD and SDRD are plotted in Fig. 6. The statistical summary of the MRD and SDRD values is also given in Table 2. Compared to the patterns of MRD and SDRD shown in Fig. 3, the ones with fixed hr differed mainly in two aspects. First, SDRD generally increased with MRD, indicating that soil moisture was more temporally stable at dry conditions. This phenomenon has been observed for sandy soils in the field study of Zhang and Shao (2013), who investigated TS SM in a desert area of northwestern China. Secondly, the distributions of MRD were more skewed at all the depths (Table 2). Interestingly, the patterns of MRD and SDRD shown in Fig. 6 exhibited great resemblances to the ones reported by Zhang and Shao (2013) (e.g., Fig. 6 in Zhang and Shao (2013)). Zhang and Shao (2013) speculated that the large ranges of MRD found in their study was most likely due to the relatively large size of their study site. In addition, Zhang and Shao (2013) found that locations with higher sand contents tended to have higher TS SM, which is essentially reflected in Fig. 6. As explained previously, coarser soils usually correspond to higher n values and lower MRD values (Fig. 5), and thus to higher TS SM as indicated by smaller SDRD values shown in Fig. 6. With the aid of the simulation results, the cause for the skewed distributions of MRD observed for sandy soils can be explained by the nonlinear effect of n on MRD. The highly nonlinear relationship

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

1219

Fig. 4. Relationships of mean relative difference (MRD) with soil hydraulic parameters under vegetated conditions (see Section 2.2 for the definitions of different soil hydraulic parameters).

between MRD and n resulted in a small number of finer-textured samples with very high moisture contents (Fig. 5), which significantly skewed the distributions of MRD. To further demonstrate

the control of n on the patterns of MRD and SDRD, simulated samples were grouped based on the range of n, which led to 45 samples for 1 < n < 2, 53 for 2 < n < 3, and 40 for 3 < n < 4. For each group,

1220

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

Fig. 5. Relationships of mean relative difference (MRD) with soil hydraulic parameters under vegetated conditions with fixed hr.

MRD and SDRD were computed, and the results from the depth of 25 cm are shown in Fig. 7 for an illustration purpose. Fig. 7 shows that both the range and skewness of the distributions of MRD were affected by the range of n. Due to that the nonlinear effect of n on

soil moisture levels decreased with increasing n, the skewness of the distributions of MRD was reduced significantly from 1.432 at 1 < n < 2 to 0.858 at 2 < n < 3 and 0.435 at 3 < n < 4. Furthermore, with narrower ranges of n, the ranges of MRD also decreased. The

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

1221

Fig. 6. Ranked mean relative difference (MRD) with one standard deviation (vertical bars) under vegetated conditions with fixed hr at the depths of (a) 25 cm, (b) 50 cm, and (c) 100 cm.

simulated ranges of MRD presented in Fig. 7b and c became similar to the ones commonly observed in field experiments (e.g., Grayson and Western, 1998; Gomez-Plaza et al., 2000; Martinez-Fernandez and Ceballos, 2003; Brocca et al., 2010). Fig. 7 thus supports the previously made conjecture that MRD ranges are partly determined by the spatial variability in soil textures. Intriguingly, it appeared that soil moisture was less temporally stable at the intermediate range of n between 2 and 3. Meanwhile, the samples with moisture conditions close to the average exhibited higher TS SM (Fig. 7b), which has been observed in a number of field studies (Vachaud et al., 1985; Jacobs et al., 2004; Brocca et al., 2010) as well as in the modeling study of Martinez et al. (2013). Clearly, by varying hr and n, different patterns of MRD and SDRD could be produced, which resembled observations of TS SM in different field studies. This suggests that the pattern of MRD and SDRD may partly reflect variations in soil hydraulic properties. Further examinations of the MRD based on grouped data revealed that depending on the range of n, MRD was also correlated with the shape factor l that is a lumped parameter accounting for pore tortuosity and connectivity. For the purpose of simplicity, only the relationships of MRD with n and l are shown in Fig. 8 for the depth of 25 cm. It can be seen from Fig. 8 that with increasing n, a positive correlation between MRD and l gradually emerged. Similar to the effect of n, l also affects soil moisture levels through controlling hydraulic conductivity (Eq. (6)), but at an opposite direction (i.e., hydraulic conductivity decreases with increasing l at the same moisture level). When n was smaller (e.g., 1 < n < 2), its impact on MRD outweighed the impact of l, and no correlation between MRD and l could be found. However, with the declining

Fig. 7. Ranked mean relative difference (MRD) with one standard deviation (vertical bars) under vegetated conditions with fixed hr for different ranges of n: (a) 1 < n < 2, (b) 2 < n < 3, and (c) 3 < n < 4.

effect of n on soil moisture levels when n became larger, the importance of l in controlling MRD gradually grew. The main application of TS SM is to identify monitoring sites with soil moisture conditions representative of field averages (Vachaud et al., 1985; Grayson and Western, 1998; Vanderlinden et al., 2012). Based on the above sensitivity analysis, it is reasonable to argue that information on spatial distributions of soil hydraulic properties in a field may offer some preliminary inferences to locate those representative locations, given that other factors play minor roles in controlling TS SM (e.g., topography). However, as mentioned previously, it is usually expensive and impractical to obtain spatial distributions of soil hydraulic parameters, even at plot scales. Indirect methods are thus preferred to first covert easily obtainable or readily available soil properties (e.g., bulk density, particle size distribution, and soil organic matter) to soil hydraulic parameters, such as pedotransfer functions (Schaap et al., 2001; Wösten et al., 2001). On the basis of obtaining spatial distributions of soil hydraulic parameters, hr can be used as a first order indicator for locating representative locations (e.g., locations with intermediate ranges of hr as evidenced in Fig. 4) in semiarid regions with soils of low holding capacities (e.g., sand). In addition, soil moisture at locations with larger n values (e.g., coarser soils) tends to be more temporally stable, although an offset value might be needed to acquire field averages (Heathman et al., 2009; Vanderlinden et al., 2012). It should be also stressed that the findings in this study

1222

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

Fig. 8. Relationships of mean relative difference (MRD) with the shape factors n and l at the depth of 25 cm under vegetated conditions with fixed hr for different ranges of n.

might not be applicable to other climatic regimes, which needs to be addressed in future studies.

3.2. Temporal stability of soil moisture under bare surface conditions Under bare surface conditions, simulations were also run for the 200 samples with fixed hr. The ranked MRD and SDRD from the simulations under bare surface conditions are plotted in Fig. 9 for the depths of 25, 50, and 100 cm, and the statistical summary is reported in Table 2. In general, Fig. 9 shows similar patterns of MRD to the ones under vegetated conditions as shown in Fig. 6; however, several differences in the patterns of MRD and SDRD can be observed. First, the skewness of the distributions of MRD was reduced under bare surface conditions (Table 2), suggesting that vegetation may strengthen the skewness of the distributions of MRD by creating lower soil moisture conditions. Secondly, soil moisture was more temporally stable under bare surface conditions. Without the presence of root water take, the dependence of SDRD on depth was also reduced. The modeling results corroborate the field observations that vegetation tended to increase temporal instability of soil moisture (Martinez-Fernandez and Ceballos, 2003; Guber et al., 2008; Jia et al., 2013). The impacts of different soil hydraulic parameters on MRD were also investigated under bare surface conditions. The results also showed the dominant control of n on MRD as illustrated in Fig. 10. Although MRD was still nonlinearly dependent on n under bare surface conditions, this nonlinear relationship deteriorated at the depths of 25 and 50 cm compared to the ones under vegetation conditions, mainly due to elevated soil moisture contents under bare surface conditions. As a result, the skewness of the distributions of MRD became smaller under bare surface conditions. Once again, the results suggest that the impacts of soil hydraulic properties on TS SM are partly determined by the wetness conditions of soil moisture and may vary under different climate regimes.

Fig. 9. Ranked mean relative difference (MRD) with one standard deviation (vertical bars) under bare surface conditions with fixed hr at the depths of (a) 25 cm, (b) 50 cm, and (c) 100 cm.

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

1223

Fig. 10. Dependence of mean relative difference (MRD) on the shape factor n under bare surface conditions with fixed hr at the depths of (a) 25 cm, (b) 50 cm, and (c) 100 cm.

Fig. 11. Comparison of mean relative difference (MRD) and standard deviation of relative difference (SDRD) between vegetated and bare surface conditions with fixed hr.

To further assess the impacts of root water uptake on TS SM, the MRD and SDRD under vegetated and bare surface conditions are compared in Fig. 11. The correlation of MRD under both surface conditions exhibited a very complex pattern. In general, there were a larger number of simulated samples with MRD > 0 under bare surface conditions, particularly at the depths of 25 and 50 cm. It was resulted from the less dependence of MRD on n. Thus, vegetation tended to produce more samples with moisture conditions drier than the average. In addition, when MRD was greater than 0.5, the correlation of MRD largely followed a 1:1 relationship. This is because that for those samples with higher MRD and thus smaller n values, water pressure heads in the root zone sometimes fell below the threshold for the root water uptake to occur; therefore, vegetation had a relatively smaller impact on soil moisture levels in those samples. Similarly, with less impacts of root water uptake at the depth of 100 cm, the relationship of MRD under both surface conditions converged to the 1:1 line. For the temporal stability in terms of SDRD, it is clear that soil moisture under bare surface conditions was more temporally stable and the differences in SDRD under both surface conditions decreased with depth.

4. Conclusions In this study, the impacts of soil hydraulic properties on the temporal stability of soil moisture (TS SM) were investigated using a 1-D vadose zone model and a soil dataset with correlated soil hydraulic parameters for sandy soils. Compared to the results of previous modeling studies, more reasonable patterns of mean relative difference (MRD) and standard deviation of relative difference (SDRD) that resembled field observations were produced by varying all the parameters in soil water retention and hydraulic conductivity models. More specifically, the residual soil moisture content (hr) was found to be the primary control on MRD, which was mainly due to the semi-arid climate that was simulated. By fixing hr, a highly nonlinear relationship was found between MRD and the shape factor n, which led to the skewed distributions of MRD widely observed for sandy soils. With increasing n, a positive correlation between MRD and the shape factor l was also found, due to the declining effect of n on soil moisture levels. By varying the range of n, different patterns of MRD and SDRD could also be generated, which resembled observed patterns of MRD and SDRD

1224

T. Wang / Journal of Hydrology 519 (2014) 1214–1224

in different field studies, implying that the pattern of MRD and SDRD may partly reflect the spatial variability in soil hydraulic properties. Finally, the simulation results showed that the control of soil hydraulic properties on MRD weakened at deeper soil depths and under bare surface conditions due to elevated soil moisture contents. It should be emphasized that the use of a 1-D vadose zone model for simulating soil moisture dynamics in this study unavoidably encounters certain limitations, as the model only simulates vertical soil moisture fluxes; however, the effects, such as lateral flow and topography (Grayson and Western, 1998; Jacobs et al., 2004; Heathman et al., 2012), on TS SM cannot be explicitly incorporated in this modeling approach. Therefore, future modeling studies (e.g., use of 2-D vadose zone models and land surface models) are needed to elucidate the role of soil hydraulic properties in controlling TS SM under different vegetation cover conditions and climate regimes as well as with the consideration of topographic effects. Acknowledgments The authors would like to thank the High Plain Regional Climate Center for providing the hydrometeorological data at the Barta Brothers Ranch site and two anonymous reviewers for their comments that led to improvements of this work. References Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2010. Spatial-temporal variability of soil moisture and its estimation across scales. Water Resour. Res. 46, W02516. http://dx.doi.org/10.1029/2009WR008016. Carsel, R.F., Parrish, R.S., 1988. Developing joint probability distributions of soil water retention characteristics. Water Resour. Res. 24 (5), 755–769. Cosh, M.H., Jackson, T.J., Bindlish, R., Prueger, J.H., 2004. Watershed scale temporal and spatial stability of soil moisture and its role in validating satellite estimates. Remote Sens. Environ. 92, 427–435. http://dx.doi.org/10.1016/ j.rse.2004.02.016. Starr, G., 2005. Assessing temporal stability and spatial variability of soil water patterns with implications for precision water management. Agric. Water Manag. 72, 223–243. http://dx.doi.org/10.1016/j.agwat.2004.09.020. Gomez-Plaza, A., Alvarez-Rogel, J., Albaladejo, J., Castillo, V.M., 2000. Spatial patterns and temporal stability of soil moisture across a range of scales in a semi-arid environment. Hydrol. Process. 14, 1261–1277. Grayson, R.B., Western, A.W., 1998. Towards areal estimation of soil water content from point measurements: time and space stability of mean response. J. Hydrol. 207, 68–82. Guber, A.K., Gish, T.J., Pachepsky, Y.A., van Genuchten, M.T., Daughtry, C.S.T., Nicholson, T.J., Cady, R.E., 2008. Temporal stability in soil water content patterns across agricultural fields. Catena 73, 125–133. Eltahir, E., 1998. A soil moisture-rainfall feedback mechanism – 1. Theory and observations. Water Resour. Res. 34, 765–776. Entekhabi, D., Rodriguez-Iturbe, I., 1994. Analytical framework for the characterization of the space-time variability of soil moisture. Adv. Water Resour. 17, 35–45. Feddes, R.A., Kowalik, P.J., Neuman, S.P., 1978. Simulation of Field Water Use and Crop Yield. John Wiley and Sons, New York, NY. Heathman, G.C., Larose, M., Cosh, M.H., Bindlish, R., 2009. Surface and profile soil moisture spatio-temporal analysis during an excessive rainfall period in the Southern Great Plains, USA. Catena 78, 159–169. http://dx.doi.org/10.1016/ j.catena.2009.04.002. Heathman, G.C., Cosh, M.H., Merwade, V., Han, E., Jackson, T.J., 2012. Multi-scale temporal stability analysis of surface and subsurface soil moisture within the Upper Cedar Creek Watershed, Indiana. CATENA 88, 91–103. Houser, P.R., Shuttleworth, W.J., Famiglietti, J.S., Gupta, H.V., Syed, K.H., Goodrich, D.C., 1998. Integration of soil moisture remote sensing and hydrologic modeling using data assimilation. Water Resour. Res. 34 (12), 3405–3420. Hu, W., Shao, M.A., Han, F.P., Reichardt, K., Tan, J., 2010. Watershed scale temporal stability of soil water content. Geoderma 158, 181–198. Ivanov, V.Y., Fatichi, S., Jenerette, G.D., Espeleta, J.F., Troch, P.A., Huxman, T.E., 2010. Hysteresis of soil moisture spatial heterogeneity and the ‘‘homogenizing’’ effect of vegetation. Water Resour. Res. 46, W09521. Jacobs, J.M., Mohanty, B.P., Hsu, E., Miller, D., 2004. SMEX02: Field scale variability, time stability and similarity of soil moisture. Remote Sens. Environ. 92, 436– 446. Jung, M., Reichstein, M., Ciais, P., et al., 2010. Recent decline in the global land evapotranspiration trend due to limited moisture supply. Nature 467, 951–954. Jia, X.X., Shao, M.A., Wei, X.R., Wang, Y.Q., 2013. Hillslope scale temporal stability of soil water storage in diverse soil layers. J. Hydrol. 498, 254–264.

Koster, R.D., Dirmeyer, P.A., Guo, Z.C., et al., 2004. Regions of strong coupling between soil moisture and precipitation. Science 305 (5687), 1138–1140. Martinez, G., Pachepsky, Y.A., Vereecken, H., Hardelauf, H., Herbst, M., Vanderlinden, K., 2013. Modeling local control effects on the temporal stability of soil water content. J. Hydrol. 481, 106–118. Martinez, G., Pachepsky, Y.A., Vereecken, H., 2014. Temporal stability of soil water content as affected by climate and soil hydraulic properties: a simulation study. Hydrol. Process. 28, 1899–1915. Martinez-Fernandez, J., Ceballos, A., 2003. Temporal stability of soil moisture in a large-field experiment in Spain. Soil Sci. Soc. Am. J. 67, 1647–1656. Mohanty, B.P., Skaggs, T.H., 2001. Spatio-temporal evolution and time-stable characteristics of soil moisture within remote sensing footprints with varying soil, slope, and vegetation. Adv. Water Resour. 24, 1051–1067. Nemes, A., Schaap, M.G., Leij, F.J., Wösten, J.H.M., 2001. Description of the unsaturated soil hydraulic database UNSODA version 2.0. J. Hydrol. 251, 151– 162. Neuman, S.P., Feddes, R.A., Bresler, E., 1974. Finite Element Simulation of Flow in Saturated-Unsaturated Soils Considering Water Uptake by Plants. Third Annual Report, Project No. A10-SWC-77, Hydraulic Engineering Lab, Technion, Haifa, Israel. Nijssen, B., Schnur, R., Lettenmaier, D.P., 2001. Global retrospective estimation of soil moisture using the VIC land surface model. J. Clim. 14, 1790–1808. Pachepsky, Ya., Guber, A., Jacques, D., 2005. Temporal persistence in vertical distributions of soil moisture contents. Soil Sci. Soc. Am. J. 69, 347–352. http:// dx.doi.org/10.2136/sssaj2005.0347. Ritchie, J.T., 1972. Model for predicting evaporation from a row crop with incomplete cover. Water Resour. Res. 8 (5), 1204–1213. Robinson, D.A., Campbell, C.S., Hopmans, J.W., Hornbuckle, B.K., Jones, S.B., Knight, R., Ogden, F., Selker, J., Wendroth, O., 2008. Soil moisture measurement for ecological and hydrological watershed-scale observatories: a review. Vadose Zone J. 7, 358–389. Schaap, M.G., Leij, F.J., van Genuchten, M.T., 2001. ROSETTA: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol. 251, 163–176. http://dx.doi.org/10.1016/S00221694(01)00466-8. Simunek, J., van Genuchten, M.Th., Sejna, M., 2005. The HYDRUS-1D Software Package for Simulating the One-dimensional Movement of Water, Heat, and Multiple Solutes in Variably-saturated Media, Version 3.0, HYDRUS Software Series 1, Department of Environmental Sciences, University of California Riverside, Riverside, CA, 270 pp. Small, E.E., 2005. Climatic controls on diffuse groundwater recharge in semiarid environments of the southwestern United States. Water Resour. Res. 41, W04012. http://dx.doi.org/10.1029/2004WR003193. Teuling, A.J., Troch, P.A., 2005. Improved understanding of soil moisture variability dynamics. Geophys. Res. Lett. 32, L05404. Vachaud, G., Silans, A.P.D.E., Balabanis, P., Vauclin, M., 1985. Temporal stability of spatially measured soil water probability density function. Soil Sci. Soc. Am. J. 49, 822–828. Vanderlinden, K., Vereecken, H., Hardelauf, H., Herbst, M., Martinez, G., Cosh, M., Pachepsky, Y., 2012. Temporal stability of soil water contents: a review of data and analyses. Vadose Zone J. van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898. Vereecken, H., Huisman, J.A., Bogena, H., Vanderborght, J., Vrugt, J.A., Hopmans, J.W., 2008. On the value of soil moisture measurements in vadose zone hydrology: a review. Water Resour. Res. 44, W00D06. Wang, T., Zlotnik, V.A., Wedin, D., Wally, K.D., 2008. Spatial trends in saturated hydraulic conductivity of vegetated dunes in the Nebraska sand hills: effects of depth and topography. J. Hydrol. 349, 88–97. Wang, T., Zlotnik, V.A., Šimunek, J., Schaap, M.G., 2009a. Using pedotransfer functions in vadose zone models for estimating groundwater recharge in semiarid regions. Water Resour. Res. 45, W04412. http://dx.doi.org/10.1029/ 2008WR006903. Wang, T., Wedin, D., Zlotnik, V.A., 2009b. Field evidence of a negative correlation between saturated hydraulic conductivity and soil carbon in a sandy soil. Water Resour. Res. 45, W07503. http://dx.doi.org/10.1029/2008WR006865. Wang, T., Istanbulluoglu, E., Lenters, J., Scott, D., 2009c. On the role of groundwater and soil texture in the regional water balance: an investigation of the Nebraska Sand Hills, USA. Water Resour. Res. 45, W10413. http://dx.doi.org/10.1029/ 2009WR007733. Wesseling, J.G., 1991. Meerjarige simulatie van grondwaterstroming voor verschillende bodemprofielen, grondwatertrappen en gewassen met het model SWATRE. Wageningen, DLO-Staring Centrum, Rapport 152, 63. Wösten, J.H.M., Pachepsky, Y.A., Rawls, W.J., 2001. Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics. J. Hydrol. 251, 123–150. http://dx.doi.org/10.1016/S00221694(01)00464-4. Zhang, P., Shao, M., 2013. Temporal stability of surface soil moisture in a desert area of north western China. J. Hydrol. 505, 91–101. Zhao, Y., Peth, S., Wang, X.Y., Lin, H., Horn, R., 2010. Controls of surface soil moisture spatial patterns and their temporal stability in a semi-arid steppe. Hydrol. Process. 24, 2507–2519. Zlotnik, V.A., Wang, T., Nieber, J.L., Simunek, J.A., 2007. Verification of numerical solutions of the Richards equation using a traveling wave solution. Adv. Water Resour. 30, 1973–1980.