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Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture
Journal of Hydrology xxx (2014) xxx–xxx
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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture Gonzalo Martínez García a,b,⇑, Yakov A. Pachepsky b,1, Harry Vereecken c,2 a
Dept. of Agronomy, University of Cordoba, Ctra. Madrid, km 396, 14071 Córdoba, Spain USDA-ARS – Environmental Microbial and Food Safety Lab, 10300 Baltimore Avenue, BARC-East Bldg. 173, Beltsville, MD 20705, USA c Agrosphere (IBG-3), Institute of Bio- and Geosciences, Forschungszentrum Jülich GmbH, IBG-3, 52428 Jülich, Germany b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Soil moisture Variability Soil hydraulic properties Climate
s u m m a r y Knowledge of spatial mean soil moisture and its variability over time is needed in many environmental applications. We analyzed dependencies of soil moisture variability on average soil moisture contents in soils with and without root water uptake using ensembles of non-stationary water flow simulations by varying soil hydraulic properties under different climatic conditions. We focused on the dry end of the soil moisture range and found that the magnitude of soil moisture variability was controlled by the interplay of soil hydraulic properties and climate. The average moisture at which the maximum variability occurred depended on soil hydraulic properties and vegetation. A positive linear relationship was observed between mean soil moisture and its standard deviation and was controlled by the parameter defining the shape of soil water retention curves and the spatial variability of saturated hydraulic conductivity. The influence of other controls, such as variable weather patterns, topography or lateral flow processes needs to be studied further to see if such relationship persists and could be used for the inference of soil hydraulic properties from the spatiotemporal variation in soil moisture. Published by Elsevier B.V.
1. Introduction Understanding topsoil water content variability is critical for improving the performance of hydrologic and atmospheric models and for up- and down-scaling remotely sensed soil moisture (Vereecken et al., 2008). Surface soil moisture variability has been shown to be related with spatially-averaged soil moisture content and that has been demonstrated at different scales (Choi et al., 2007; Famiglietti et al., 2008, 1999; Martinez-Fernández and Ceballos, 2003; Mittelbach and Seneviratne, 2012; Rosenbaum et al., 2012; Teuling and Troch, 2005; Vereecken et al., 2007). Soil water content spatial variability was shown to be affected by several local and non-local factors (Grayson et al., 1997). Such controls are: vegetation (Teuling and Troch, 2005), climate (Teuling et al., 2007a), soil hydraulic properties (Vereecken et al., 2007), topography (Grayson et al., 1997) and antecedent soil mois-
⇑ Corresponding author at: USDA-ARS – Environmental Microbial and Food Safety Lab, 10300 Baltimore Avenue, BARC-East Bldg. 173, Beltsville, MD 20705, USA. Tel.: +1 301 504 5841. E-mail addresses: [email protected], [email protected] (G. Martínez García). 1 Tel.: +1 301 504 7468. 2 Tel.: +49 2461 61 4570.
ture (Ivanov et al., 2010). Contradictory reports have been published on the shape of the relationship between the spatial mean soil moisture (hhi) and its variability (rh). Works can be found that report an increasing variability with decreasing mean moisture (Famiglietti et al., 1999), decreasing variability with decreasing mean moisture (Martinez-Fernández and Ceballos, 2003) and an increase up to a certain value of hhi followed by a decrease (Brocca et al., 2010, 2012; Rosenbaum et al., 2012). The range of soil moisture measured in each case (dry or wet states or the full range of soil moisture) can be one of reasons for such differences. The body of literature that addressed this topic for more than a decade (from Famiglietti et al., 1998 to Rosenbaum et al., 2012) generally shows that the graph of this relationship is typically convex (Choi et al., 2007; Rosenbaum et al., 2012; Teuling and Troch, 2005). Regression models for the ‘rh–hhi’ (referred as rh from here after) relationship have been proposed, including an exponential model (Famiglietti et al., 2008), a third-order polynomial (Rosenbaum et al., 2012) and a linear equation for the dry-end (Teuling et al., 2007b). Soil properties, and more specifically soil hydraulic propertiesrelated parameters, often had the largest influence on the variability of soil moisture (Choi et al., 2007). The dependence of the standard deviation of soil moisture rh on average soil moisture as affected by soil hydraulic properties was previously studied by
http://dx.doi.org/10.1016/j.jhydrol.2014.01.069 0022-1694/Published by Elsevier B.V.
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Vereecken et al. (2007) using an analytical solution of a stochastic steady state flow model. They used the Brooks-Corey moisture retention characteristic parameters, the saturated hydraulic conductivity and joint-Gaussian spatial distribution of hydraulic parameters with exponential covariance functions and negligible correlation between the hydraulic parameters. They found that the mean water content at which the standard deviation became maximal depended on the shape parameters of the moisture retention characteristic. More specifically, on the parameter describing the pore-size distribution of soils. This work was based on results of the work of Zhang et al. (1998), which stemmed from strong assumptions of stationary flow, gravity-dominated flow, and spatial autocorrelation of parameters. These assumptions are hardly appicable to dry conditions, and using modeling of non-stationary flow with evaporation dominating most of the time may provide more realistic information about soil moisture variability in time and space. In dry conditions, there exists a decoupling of the rate of drying and the vertical profiles of soil moisture in the topsoil (Capehart and Carlson, 1997). This type of conditions are predominant in arid and semiarid conditions. The objective of this work was to examine the effects of soil texture and climate in the rh for a non-stationary flow model framework. We provide also an explanation to the differences observed in the literature regarding the positive or negative relationship between rh and hhi. Finally, we show that the linearization of the dry part of the relationship rh may be useful to evaluate and estimate soil hydraulic properties and more specifically the spatial variability of Ks and the parameter ‘‘n’’ that measures the pore-size distribution in the van-Genuchten model.
2. Methods 2.1. Simulations setup We used the HYDRUS code (Šimu˚nek and van Genuchten, 2008) to simulate water flow by solving the Richard equation numerically. Time-dependent atmospheric boundary conditions were imposed at the soil surface and a constant head boundary condition was imposed at the bottom of a 3-m depth profile. The Initial condition was obtained from a spin up model run of 1 year. Simulations were performed in a 1-D soil profile with homogeneous properties. The profile was deep enough to make the soil moisture of the top 1 m layer insensitive to the bottom boundary condition. We used different climatic conditions to run our simulations. For that, we generated the corresponding time series of daily rainfall, maximum and minimum temperatures, and solar radiation with the CLIGEN weather generator (Nicks et al., 1995). The daily potential evapotranspiration was calculated following a modified version of the Hargreaves equation (Williams et al., 2008). Selected climates were: humid subtropical (Cfa), humid continental (Dfa), cold semiarid (BSk) and hot semiarid (BWh). Humid subtropical weather (Cfa) is characterized by mild temperatures, with a minimum temperature during the coldest month between 3 and 18 °C, warm summer and rainfall occurring during most of the year. Humid continental (Dfa) weather alike the Cfa has rainfalls during the whole year, the main difference between the two is in temperatures with an average temperature during the coldest month below -3 °C. Dry (semiarid and arid) climates are represented by the BSk (steppe) and BWh (dessert) climates and are characterized by higher potential evapotranspiration than precipitation. The main difference between them comes from the magnitude of dryness and the temperatures. Representative locations for those climates were College station (TX), 30.58°N, 93.35°W, 94 msl for the Cfa, Indianapolis (IN), 39.73°N, 86.27°W, 240 msl for the Dfa, Moscow (ID), 46.73°N, 117.00°W, 801 msl for the BSk, and
Tucson (AZ, 32.25°N, 110.83°W, 771 msl) for the BWh. The monthly parameters defining their weather (means, standard deviations, skewness, etc.) were obtained from the CLIGEN database. Fig. 1 shows the generated time series of rainfall and evapotransporation. Sets of parameters corresponding to seven soil textural classes were used in the analysis (Table 1) and the van Genuchten– Mualem model was chosen for the soil hydraulic properties. For a particular soil and climate we ran an ensemble of models defined with variable saturated hydraulic conductivity (Ks), following the commonly encountered lognormal distribution (Jury, 1985). The value of the spatial variability of ln Ks (rlnKs) used in the simulations was 0.8 as it lies inside the range observed for most of the soils (Cosby et al., 1984). Values of rlnKs between 0.2 and 1 were also used to illustrate the effect of increasing rlnKs on the rh for a soil with the hydraulic properties of the loamy soils and the cold semiarid weather. We simulated spatial variability through an array of point and one-dimensional profiles by fixing soil moisture characteristic parameters and varying Ks. We used a double porosity model to account for the effects of macropores on preferential flow (Jiang et al., 2010) for the silty clay loam soil following the model proposed by Durner (1994). This model divides the porous medium into two or more overlapping regions in which a van Genuchten–Mualem type of model (Eq. (1)) of the soil hydraulic properties is used.
hðhÞ ¼ hr þ
hs hr n 11=n
½1 þ ðajhjÞ
ð1Þ
where hs and hr are the saturation and residual soil moisture respectively [L3 L3], h is suction pressure [L], a is related to the inverse of the air entry suction [L1] and n is a measure of the pore-size distribution (dimensionless). We assumed that macropores account for 5% of the entire pore space that a for the macropores is 100 times larger than for the micropores and n is also larger for the macropores than for the micropores following a similar approach as in Šimu˚nek and van Genuchten (2008) for fine-textural soils. We performed simulations of the loamy soil with vegetation also, besides the bare soil cases, to evaluate the effect of evapotranspiration on rh. For that, we simulated root water uptake from a well-established grass (100% soil surface coverage) with a root system extending homogenously to a depth of 0.5 m, under the humid continental weather and with the loamy soil. The imposed rainfall, evaporation or evapotranspiration was kept homogenous throughout all the simulations. 2.2. Data analysis One-year data of simulated soil moistures for the 0–5 cm depth were used for the analysis as this is widely used depth in many of the remote sensing works for validation of soil moisture products, e.g. Famiglietti et al. (1998) or Teuling et al. (2007a). A spin-up period of one year was chosen to avoid the effect of the initial conditions on the simulated soil moisture data. For each day of simulation we computed the average (average across all different Ks runs) soil moisture for the 0–5 cm depth of the ensemble of simulations and its standard deviation to obtain the rh relationship. We evaluated the effect of increasing the simulation period from one year to two on rh and did not observed any relevant difference. To illustrate the effect of a different rlnKs and to compare effects of soil hydraulic properties and climate we limited our analysis of the rh to its dry part. Tuller and Or (2001) suggested that the dependence of Ks on matric potential changes from capillary flow to film flow. Although film flow might become important in the dry range, we speculate that it would not affect the general tendency in that part and it might not affect the scaling of Ks
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Fig. 1. Rainfall and evaporation data for a two-year time series at four different locations across the US that have a different Köppen climate classification: (A) humid subtropical (Cfa) from College station (TX), (B) humid continental (Dfa) from Indianapolis (IN), (C) cold semi-arid (Bsk) from Moscow (ID), and (D) hot semiarid (BWh) from Tucson (AZ). First year of simulations was used to spin-up the model.
Table 1 Soil hydraulic properties used in simulations. Values obtained from the Rawls database (Schaap and Leij, 1998).
Loamy sand Sandy loam Sandy clay loam Loam Silt loam Clay loam Silty clay loam
Label
hs (cm3 cm3)
hr (cm3 cm3)
a (cm1)
n
m
ln Ks (cm day1)
LS SL SCL L SiL CL SiCL
0.41 0.41 0.39 0.43 0.45 0.41 0.43
0.06 0.06 0.10 0.08 0.07 0.10 0.09
0.125 0.060 0.059 0.032 0.019 0.019 0.010
2.271 1.892 1.480 1.560 1.414 1.320 1.230
0.560 0.471 0.324 0.359 0.293 0.242 0.187
5.73 5.01 3.18 2.78 3.70 2.56 2.46
assumed in this study. The cutoff hhi that defined the dry part of rh was obtained by trimming the data with hhi larger than the peak hhi (e.g. average of the hhi corresponding to the 99 percentile of the rh). A linear regression was applied to the resulting data in order to get the slope of the dry part of rh, as it was done in Teuling et al. (2007b). Linear models instead of non-linear or higher order models simplify the interpretation of results and reduce the number of parameters that define the relationship. 3. Results and discussion The typical convex shape of rh shown in some of the field data of Brocca et al. (2012); Rosenbaum et al. (2012) could be observed by running a non-stationary flow model with an ensemble of variable Ks in most of the soils studied (Fig. 2). A clear peak could not
be seen with the LS and SL textures as previously reported for the steady-state flow case (Vereecken et al., 2007) The textures with a high percentage of sand show a linear increase of rh with increasing hhi where no peak could be determined. This situation was observed by Martinez-Fernández and Ceballos (2003) and is a consequence of an arid environment. Ivanov et al. (2010) suggested that vertical soil moisture redistribution and evapotranspiration control the dry side whereas precipitation, vegetation, infiltration, and soil moisture are the major controls in the wet side. The range of measured hhi in other works explains the fact that in some works the rh relationship is positive while in others it is negative. Under dry environments (hhi smaller than peak hhi, e.g. in Martinez-Fernández and Ceballos, 2003) it is harder to find the wet end in which the rh decreases with increasing hhi and the rh is assumed to be positive. In contrast, for wet environments (hhi larger
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Fig. 2. The rh relationship for soils with different hydraulic properties and a spatial variability determined by a standard deviation ln Ks of 0.8 under a humid continental climate. The linear regression fitted (dashed line) to the dry-part (pre-peak) of the rh relationship is superposed.
than peak hhi, e.g. Famiglietti et al., 1999) it is difficult to observe the rh decrease with decreasing hhi and the rh is assumed to be negative. The effect of vegetation is illustrated for a loamy soil with cold semiarid climate. Root water uptake modified the characteristics of the rh relationship (Fig. 2g and h for the cases of bare and vegetated loamy soil respectively). Slopes were significantly different
(p-value <0.001) for the cases with and without root water uptake. The slope of the root water uptake case halved that of the bare soil. The maximum rh was smaller in the bare than in the vegetated cases with a similar corresponding the hhi at the rh peak. A hysteretic behavior can be observed better in the simulations done with vegetation in accordance with the observations done by Rosenbaum et al. (2012); Ivanov et al. (2010) who previously had
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Table 2 Average soil water content and standard deviation at the peak of the rh and slope of the rh dry-part of the modeled soils with the humid continental climate.
Loamy sand Sandy loam Sandy clay loam Loam Loam under vegetation Silt loam Clay loam Silty clay loam
Peak hhi
Peak rh
Slope LM
R2
0.24 0.30 0.33 0.36 0.34 0.38 0.37 0.34
0.033 0.034 0.023 0.030 0.033 0.029 0.020 0.023
0.18 0.15 0.09 0.11 0.04 0.09 0.06 0.07
0.97 0.99 0.86 0.89 0.44 0.65 0.61 0.81
The peak was not reached. Therefore the maximum rh and its corresponding hhi were used.
observed the effect of evaporation in this kind of behavior. Fig. 2h shows, inside ellipses, data from winter, summer and fall. Extracting the data from these three groups and fitting a linear model yielded significantly different slopes at the p = 0.001 level. The observed dispersion, especially near the driest end, in some of the plots of Fig. 2 (e.g. silt loam, silty clay loam and loam both with and without root water uptake) can be caused by the intensity of the evaporation flux. Texture was responsible for the differences between peak rh and the corresponding hhi values (Table 2) with values ranging between 0.022 and 0.034. There was a substantial difference between the average moisture content at the rh peak calculated with the stationary approximation and Brooks-Corey parameters in Vereecken et al. (2007) and the non-stationary approximation with the van Genuchten parameters in our case (Table 2). We observed larger values of hhi at the rh peak than in the similar cases of Vereecken et al. (2007). One explanation for this difference is that the model of Brooks-Corey used by Vereecken et al. (2007) determines the location of the rh peak by setting the air entry value. Values of hhi at the rh peak for a silty clay loam obtained in our simulations and in Vereecken et al. (2007) (0.34 and 0.20 m3 m3, respectively) are smaller than in Rosenbaum et al. (2012), 0.39 m3 m3, though our non-stationary simulations provided results closer to the field study of Rosenbaum et al. (2012). This difference with observed values in the field can be explained by the effects of vegetation, as has been shown in the comparison of the root water uptake vs bare loamy soil described before, and the difference between the generalized moisture retention parameters used in the simulations and the actual values in the experimental site. Slopes in linear regressions hhi vs rh depended on textures and were significantly different among them (p < 0.001, Table 2). Larger
Fig. 4. Digitized LAGO dataset from Brocca et al. (2012). Selected points to fit the dry-part are included inside a rectangle.
slopes were found for the coarser soils. The slope for the SL was lower in this work than in the field experiment of Martinez-Fernández and Ceballos (2003) with soils of similar texture. That probably reflected the role of the weather pattern (e.g. variable rainfall depth and evapotranspiration), vegetation and topography as generators of a larger variability of soil moisture in large-scale field studies. A strong relationship between the slope of the linearized prepeak soil moisture variability and the ‘‘n’’ parameter of the van Genuchten moisture retention equation was observed (Fig. 3A). The relationship found between the soil moisture variability and a water retention curve parameter could be useful to assess large-scale water retention properties from soil moisture monitoring data. While that could only be done for weak perturbations of the standard deviation in Vereecken et al. (2007), the approach of this work is more robust and does not have not such limitation. To illustrate the potential of this approach, we fitted a linear regression to the points with soil moisture smaller than 25% in the LAGO dataset (Fig. 4) from Brocca et al. (2012) and considered the point hhi = 0.24, rh = 0.036 as an outlier. This dataset covers an area of
Fig. 3. Textural effect on the slope of the dry part of the rh relationship: (A) effect of the ‘‘n’’ parameter in the van Genuchten’s model for the soil moisture characteristic curve; (B) effect of ln Ks. Labels reflect the textural class (Table 1).
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Table 3 Average soil water content and standard deviation at the peak of the rh and slope of the rh dry-part of a loamy soil subject to four different climates. Climate
Peak hhi
Peak rh
Slope
R2
Humid subtropical Humid continental Cold semiarid Dry semiarid
0.349 0.36 0.363 0.296
0.030 0.030 0.023 0.026
0.09 0.11 0.11 0.11
0.75 0.89 0.85 0.63
The peak was not reached. Therefore the maximum rh and its corresponding hhi were used.
178 km2 in which we can assume an homogenous distribution of rainfall. For the LAGO case we obtained a slope of 0.15. Therefore, assuming that the standard deviation of ln Ks is 0.8 and applying the regression shown in Fig. 3A we obtained an ‘‘n’’ value of 2.0. This value correponds to n-values for soils having the LS texture. These soils represent the dominant textural class in the LAGO area. Deriving hydraulic parameters for the van Genuchten–Mualem model from the rh using the presented approach opens perspectives for generating directly effective hydraulic properties at different scales from soil moisture content measurements that can be used in hydrological models. This may present an alternative or complement to pedotransfer functions based on site-specific knowledge. However, it needs to be tested for systems affected by topography, soil layering, and different kinds of vegetation among other controls. Different climates caused significantly different slopes at the 99% confidence level (Table 3). Average moisture at the peak rh was practically insensitive to the differences in climate with a coefficient of variation between the cold semiarid and the humid weathers of 2%. The effect of climate on the relationship between mean soil moisture and its variability was reported previously by Teuling et al. (2007a) and was highly influenced by differences in the vegetation development. Rosenbaum et al. (2012) did not observe seasonal differences in rh in the intermediate h range within groundwater-distant upslope areas. The small, though statistically significant, difference that we observe may explain why they did not observe the seasonality. Maximum variability of soil moisture (ranging from 0.023 to 0.030) and the slope of the dry part of rh (0.09–0.11) depended on the climate. Nevertheless these ranges are smaller than those reported above for different textures (Table 2) and shows larger effect of texture on rh than that of climate. As previously observed with field data by Choi et al. (2007), soil hydraulic properties-related parameters had the largest influence in the variability of soil moisture followed by climate
and topography. This has been proven even for the simplified case of this study were local controls are only considered. However, the effect of the variability in the weather patterns at different scales on the variability of soil moisture still needs to be evaluated. Its relative influenced compared to that of soil properties is a subject of further study and might be approached using radar data. We observed an increase in the slope of the rh dependence on hhi proportional to rlnKs for the same soil texture, and to the mean ln Ks for different textures (Figs. 5B and 3B respectively). This result is in disagreement with the observations of Famiglietti et al. (1998); Vereecken et al. (2007) who found that variability in soil moisture is controlled strongly by porosity and hydraulic conductivity under wet conditions but not under drier conditions. Knowledge of the spatial variability of saturated hydraulic conductivity (Ks) is required for hydrological modeling (Braud et al., 1995). Several attemps have been made to characterize it. Geostatistical methods were used by Regalado and Muñoz-Carpena (2004). Indirect methods such as through temporal stability analisys of soil moisture as was done by Martinez et al. (2013) or by characterizing porosity as in Ahuja et al. (1989) were used also to characterize the spatial variability of Ks. Differences in rlnKs had a minimum effect on the peak hhi. The average hhi at the peak for the five levels of Ks variability was 0.362 with a coefficient of variation of only 0.5%. An increase in the rlnKs implied a proportional increase in the peak of rh (Fig. 5B). Rosenbaum et al. (2012) observed that the differences between rh at 5 and 20 cm depth were more pronounced at intermediate moisture levels and especially for the peak of rh. They attributed those differences to the strong effect of redistribution by vertical flow, lateral flow, and evapotranspiration in that range and also agreed with the commonly described effect of texture. Those differences could be also a reason of the strong dependence shown here of the peak of rh on rlnKs as a smaller variability and smaller values of ln Ks could be expected in the subsurface. Some local (soil moisture characteristic parameters and porosity) and non-local controls (e.g. topography and soil layering) of soil moisture at the spatial scales that correspond to the variability in Ks proposed in this study are very likely to be variable. Correlations among soil hydraulic properties have been reported in the literature, e.g. Carsel and Parrish (1988), and have been useful to understand the effect of local controls on soil moisture variability and temporal stability. However, for exploratory purposes we preferred to simplify the approach and focus only on the variability of Ks. Our results indicate that it may be interesting to look for a relationship between the slope of the rh and rlnKs combined with
Fig. 5. Effect of the ln Ks spatial variability characterized by the standard deviation rlnKs on: (A) the peak soil moisture spatial variability (peak rh) and (B) the slope of the dry part of the soil variability and average moisture relationship (rh).
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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the relation observed by Martinez et al. (2013) between the latter and the temporal stability of soil moisture. Some useful upscaling relationships may emerge. Also, topography might be included in the hydraulic parameter scaling algorithm as suggested by Jana and Mohanty (2012) and see whether a better agreement with field experiments could be obtained. 4. Conclusion We reproduced the shape of rh presented in several field studies by running ensemble simulations of a non-stationary flow model and variable soil hydraulic parameters and climate conditions. For bare soil conditions we were able to show the effect of rlnKs on the slope of the rh relationship in its dry end and on the maximum value of rh. In vegetated soils, root water uptake is a factor that affects the rh relationship giving flatter shapes than the bare soil case and increased the maximum rh. Soil hydraulic properties rather than climate controlled the value of soil water content at which the maximum variability was observed. As a result of that we observed an increase in the slope of the rh dependence on hhi proportional to rlnKs for the same soil texture, and to the mean ln Ks for different textures. The relationship between the n parameter of the soil moisture characteristic curve and the slope of the dry part of rh found in this study may be of relevance for deriving soil hydraulic properties using soil moisture networks and remotely sensed data as the data can be interpreted directly. However, this approach should be handled with care as the homogenous weather pattern was chosen for all the soil columns. Evaluating the strength of such relationships in natural systems would be beneficial to validate the utility of soil moisture network data to estimate the pore size distribution parameter in the van Genuchten model and the spatial variability of saturated hydraulic conductivity. Acknowledgements This study was partially supported by US Department of Agriculture and US Nuclear Regulatory Commission Interagency Agreement IAA-NRC-05-005 on ‘‘Model Abstraction Techniques to Simulate Transport in Soils’’. The first author wishes to thank the Spanish Ministry of Education for the mobility Grant EX20090433. The authors would like to thank the valuable and useful contribution of two anonymous referees. References Ahuja, L.R., Cassel, D.K., Bruce, R.R., Barnes, B.B., 1989. Evaluation of spatial distribution of hydraulic conductivity using effective porosity data. Soil Sci. 148, 404–411. Braud, I., Dantas-Antonino, A.C., Vauclin, M., 1995. A stochastic approach to studying the influence of the spatial variability of soil hydraulic properties on surface fluxes, temperature and humidity. J. Hydrol. 165, 283–310. Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2010. Spatial-temporal variability of soil moisture and its estimation across scales. Water Resources Research 46, W02516. http://dx.doi.org/10.1029/2009WR008016. Brocca, L., Tullo, T., Melone, F., Moramarco, T., Morbidelli, R., 2012. Catchment scale soil moisture spatial–temporal variability. J. Hydrol. 422–423, 63–75. Capehart, W.J., Carlson, T.N., 1997. Decoupling of surface and near-surface soil water content: a remote sensing perspective. Water Resour. Res. 33, 1383– 1395. Carsel, R.F., Parrish, R.S., 1988. Developing joint probability distributions of soil water retention characteristics. Water Resour. Res. 24, 755–769.
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Spatial variability of soil physical parameters in solute migration: a critical literature review. EPRI-EA-4. second ed. Dep. of Soil and Environ. Sci. University of California, Riverside, California. 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-Fernández, J., Ceballos, A., 2003. Temporal stability of soil moisture in a large-field experiment in Spain. Soil Sci. Soc. Am. J. 67, 1647–1656. Mittelbach, H., Seneviratne, S.I., 2012. A new perspective on the spatio-temporal variability of soil moisture: temporal dynamics versus time-invariant contributions. Hydrol. Earth Syst. Sci. 16, 2169–2179. Nicks, A.D., Lane, L.J., Gander, G.A., 1995. CLIGEN weather generator. In: Flanagan, D.C., Nearing, M.A. (Eds.), USDA–Water Erosion Prediction Project: Hillslope Profile and Watershed Model Documentation. USDA–ARS National Soil Erosion Research Laboratory, West Lafayet, pp. 2.1–2.22. Regalado, C.M., Muñoz-Carpena, R., 2004. Estimating the saturated hydraulic conductivity in a spatially variable soil with different permeameters: a stochastic Kozeny-Carman relation. Soil Tillage Res. 77, 189–202. Rosenbaum, U., Bogena, H.R., Herbst, M., Huisman, J.A., Peterson, T.J., Weuthen, A., Western, A.W., Vereecken, H., 2012. Seasonal and event dynamics of spatial soil moisture patterns at the small catchment scale. Water Resour. Res. 48, W10544. Schaap, M.G., Leij, F.J., 1998. Database-related accuracy and uncertainty of pedotransfer functions. Soil Sci. 163, 765–779. Šimu˚nek, J., van Genuchten, M.T., 2008. Modeling nonequilibrium flow and transport processes using HYDRUS. Vadose Zone J. 7, 782–797. Teuling, A.J., Troch, P.A., 2005. Improved understanding of soil moisture variability dynamics. Geophys. Res. Lett. 32, L05404. Teuling, A.J., Hupet, F., Uijlenhoet, R., Troch, P.A., 2007a. 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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture Gonzalo Martínez García a,b,⇑, Yakov A. Pachepsky b,1, Harry Vereecken c,2 a
Dept. of Agronomy, University of Cordoba, Ctra. Madrid, km 396, 14071 Córdoba, Spain USDA-ARS – Environmental Microbial and Food Safety Lab, 10300 Baltimore Avenue, BARC-East Bldg. 173, Beltsville, MD 20705, USA c Agrosphere (IBG-3), Institute of Bio- and Geosciences, Forschungszentrum Jülich GmbH, IBG-3, 52428 Jülich, Germany b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Soil moisture Variability Soil hydraulic properties Climate
s u m m a r y Knowledge of spatial mean soil moisture and its variability over time is needed in many environmental applications. We analyzed dependencies of soil moisture variability on average soil moisture contents in soils with and without root water uptake using ensembles of non-stationary water flow simulations by varying soil hydraulic properties under different climatic conditions. We focused on the dry end of the soil moisture range and found that the magnitude of soil moisture variability was controlled by the interplay of soil hydraulic properties and climate. The average moisture at which the maximum variability occurred depended on soil hydraulic properties and vegetation. A positive linear relationship was observed between mean soil moisture and its standard deviation and was controlled by the parameter defining the shape of soil water retention curves and the spatial variability of saturated hydraulic conductivity. The influence of other controls, such as variable weather patterns, topography or lateral flow processes needs to be studied further to see if such relationship persists and could be used for the inference of soil hydraulic properties from the spatiotemporal variation in soil moisture. Published by Elsevier B.V.
1. Introduction Understanding topsoil water content variability is critical for improving the performance of hydrologic and atmospheric models and for up- and down-scaling remotely sensed soil moisture (Vereecken et al., 2008). Surface soil moisture variability has been shown to be related with spatially-averaged soil moisture content and that has been demonstrated at different scales (Choi et al., 2007; Famiglietti et al., 2008, 1999; Martinez-Fernández and Ceballos, 2003; Mittelbach and Seneviratne, 2012; Rosenbaum et al., 2012; Teuling and Troch, 2005; Vereecken et al., 2007). Soil water content spatial variability was shown to be affected by several local and non-local factors (Grayson et al., 1997). Such controls are: vegetation (Teuling and Troch, 2005), climate (Teuling et al., 2007a), soil hydraulic properties (Vereecken et al., 2007), topography (Grayson et al., 1997) and antecedent soil mois-
⇑ Corresponding author at: USDA-ARS – Environmental Microbial and Food Safety Lab, 10300 Baltimore Avenue, BARC-East Bldg. 173, Beltsville, MD 20705, USA. Tel.: +1 301 504 5841. E-mail addresses: [email protected], [email protected] (G. Martínez García). 1 Tel.: +1 301 504 7468. 2 Tel.: +49 2461 61 4570.
ture (Ivanov et al., 2010). Contradictory reports have been published on the shape of the relationship between the spatial mean soil moisture (hhi) and its variability (rh). Works can be found that report an increasing variability with decreasing mean moisture (Famiglietti et al., 1999), decreasing variability with decreasing mean moisture (Martinez-Fernández and Ceballos, 2003) and an increase up to a certain value of hhi followed by a decrease (Brocca et al., 2010, 2012; Rosenbaum et al., 2012). The range of soil moisture measured in each case (dry or wet states or the full range of soil moisture) can be one of reasons for such differences. The body of literature that addressed this topic for more than a decade (from Famiglietti et al., 1998 to Rosenbaum et al., 2012) generally shows that the graph of this relationship is typically convex (Choi et al., 2007; Rosenbaum et al., 2012; Teuling and Troch, 2005). Regression models for the ‘rh–hhi’ (referred as rh from here after) relationship have been proposed, including an exponential model (Famiglietti et al., 2008), a third-order polynomial (Rosenbaum et al., 2012) and a linear equation for the dry-end (Teuling et al., 2007b). Soil properties, and more specifically soil hydraulic propertiesrelated parameters, often had the largest influence on the variability of soil moisture (Choi et al., 2007). The dependence of the standard deviation of soil moisture rh on average soil moisture as affected by soil hydraulic properties was previously studied by
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Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Vereecken et al. (2007) using an analytical solution of a stochastic steady state flow model. They used the Brooks-Corey moisture retention characteristic parameters, the saturated hydraulic conductivity and joint-Gaussian spatial distribution of hydraulic parameters with exponential covariance functions and negligible correlation between the hydraulic parameters. They found that the mean water content at which the standard deviation became maximal depended on the shape parameters of the moisture retention characteristic. More specifically, on the parameter describing the pore-size distribution of soils. This work was based on results of the work of Zhang et al. (1998), which stemmed from strong assumptions of stationary flow, gravity-dominated flow, and spatial autocorrelation of parameters. These assumptions are hardly appicable to dry conditions, and using modeling of non-stationary flow with evaporation dominating most of the time may provide more realistic information about soil moisture variability in time and space. In dry conditions, there exists a decoupling of the rate of drying and the vertical profiles of soil moisture in the topsoil (Capehart and Carlson, 1997). This type of conditions are predominant in arid and semiarid conditions. The objective of this work was to examine the effects of soil texture and climate in the rh for a non-stationary flow model framework. We provide also an explanation to the differences observed in the literature regarding the positive or negative relationship between rh and hhi. Finally, we show that the linearization of the dry part of the relationship rh may be useful to evaluate and estimate soil hydraulic properties and more specifically the spatial variability of Ks and the parameter ‘‘n’’ that measures the pore-size distribution in the van-Genuchten model.
2. Methods 2.1. Simulations setup We used the HYDRUS code (Šimu˚nek and van Genuchten, 2008) to simulate water flow by solving the Richard equation numerically. Time-dependent atmospheric boundary conditions were imposed at the soil surface and a constant head boundary condition was imposed at the bottom of a 3-m depth profile. The Initial condition was obtained from a spin up model run of 1 year. Simulations were performed in a 1-D soil profile with homogeneous properties. The profile was deep enough to make the soil moisture of the top 1 m layer insensitive to the bottom boundary condition. We used different climatic conditions to run our simulations. For that, we generated the corresponding time series of daily rainfall, maximum and minimum temperatures, and solar radiation with the CLIGEN weather generator (Nicks et al., 1995). The daily potential evapotranspiration was calculated following a modified version of the Hargreaves equation (Williams et al., 2008). Selected climates were: humid subtropical (Cfa), humid continental (Dfa), cold semiarid (BSk) and hot semiarid (BWh). Humid subtropical weather (Cfa) is characterized by mild temperatures, with a minimum temperature during the coldest month between 3 and 18 °C, warm summer and rainfall occurring during most of the year. Humid continental (Dfa) weather alike the Cfa has rainfalls during the whole year, the main difference between the two is in temperatures with an average temperature during the coldest month below -3 °C. Dry (semiarid and arid) climates are represented by the BSk (steppe) and BWh (dessert) climates and are characterized by higher potential evapotranspiration than precipitation. The main difference between them comes from the magnitude of dryness and the temperatures. Representative locations for those climates were College station (TX), 30.58°N, 93.35°W, 94 msl for the Cfa, Indianapolis (IN), 39.73°N, 86.27°W, 240 msl for the Dfa, Moscow (ID), 46.73°N, 117.00°W, 801 msl for the BSk, and
Tucson (AZ, 32.25°N, 110.83°W, 771 msl) for the BWh. The monthly parameters defining their weather (means, standard deviations, skewness, etc.) were obtained from the CLIGEN database. Fig. 1 shows the generated time series of rainfall and evapotransporation. Sets of parameters corresponding to seven soil textural classes were used in the analysis (Table 1) and the van Genuchten– Mualem model was chosen for the soil hydraulic properties. For a particular soil and climate we ran an ensemble of models defined with variable saturated hydraulic conductivity (Ks), following the commonly encountered lognormal distribution (Jury, 1985). The value of the spatial variability of ln Ks (rlnKs) used in the simulations was 0.8 as it lies inside the range observed for most of the soils (Cosby et al., 1984). Values of rlnKs between 0.2 and 1 were also used to illustrate the effect of increasing rlnKs on the rh for a soil with the hydraulic properties of the loamy soils and the cold semiarid weather. We simulated spatial variability through an array of point and one-dimensional profiles by fixing soil moisture characteristic parameters and varying Ks. We used a double porosity model to account for the effects of macropores on preferential flow (Jiang et al., 2010) for the silty clay loam soil following the model proposed by Durner (1994). This model divides the porous medium into two or more overlapping regions in which a van Genuchten–Mualem type of model (Eq. (1)) of the soil hydraulic properties is used.
hðhÞ ¼ hr þ
hs hr n 11=n
½1 þ ðajhjÞ
ð1Þ
where hs and hr are the saturation and residual soil moisture respectively [L3 L3], h is suction pressure [L], a is related to the inverse of the air entry suction [L1] and n is a measure of the pore-size distribution (dimensionless). We assumed that macropores account for 5% of the entire pore space that a for the macropores is 100 times larger than for the micropores and n is also larger for the macropores than for the micropores following a similar approach as in Šimu˚nek and van Genuchten (2008) for fine-textural soils. We performed simulations of the loamy soil with vegetation also, besides the bare soil cases, to evaluate the effect of evapotranspiration on rh. For that, we simulated root water uptake from a well-established grass (100% soil surface coverage) with a root system extending homogenously to a depth of 0.5 m, under the humid continental weather and with the loamy soil. The imposed rainfall, evaporation or evapotranspiration was kept homogenous throughout all the simulations. 2.2. Data analysis One-year data of simulated soil moistures for the 0–5 cm depth were used for the analysis as this is widely used depth in many of the remote sensing works for validation of soil moisture products, e.g. Famiglietti et al. (1998) or Teuling et al. (2007a). A spin-up period of one year was chosen to avoid the effect of the initial conditions on the simulated soil moisture data. For each day of simulation we computed the average (average across all different Ks runs) soil moisture for the 0–5 cm depth of the ensemble of simulations and its standard deviation to obtain the rh relationship. We evaluated the effect of increasing the simulation period from one year to two on rh and did not observed any relevant difference. To illustrate the effect of a different rlnKs and to compare effects of soil hydraulic properties and climate we limited our analysis of the rh to its dry part. Tuller and Or (2001) suggested that the dependence of Ks on matric potential changes from capillary flow to film flow. Although film flow might become important in the dry range, we speculate that it would not affect the general tendency in that part and it might not affect the scaling of Ks
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Fig. 1. Rainfall and evaporation data for a two-year time series at four different locations across the US that have a different Köppen climate classification: (A) humid subtropical (Cfa) from College station (TX), (B) humid continental (Dfa) from Indianapolis (IN), (C) cold semi-arid (Bsk) from Moscow (ID), and (D) hot semiarid (BWh) from Tucson (AZ). First year of simulations was used to spin-up the model.
Table 1 Soil hydraulic properties used in simulations. Values obtained from the Rawls database (Schaap and Leij, 1998).
Loamy sand Sandy loam Sandy clay loam Loam Silt loam Clay loam Silty clay loam
Label
hs (cm3 cm3)
hr (cm3 cm3)
a (cm1)
n
m
ln Ks (cm day1)
LS SL SCL L SiL CL SiCL
0.41 0.41 0.39 0.43 0.45 0.41 0.43
0.06 0.06 0.10 0.08 0.07 0.10 0.09
0.125 0.060 0.059 0.032 0.019 0.019 0.010
2.271 1.892 1.480 1.560 1.414 1.320 1.230
0.560 0.471 0.324 0.359 0.293 0.242 0.187
5.73 5.01 3.18 2.78 3.70 2.56 2.46
assumed in this study. The cutoff hhi that defined the dry part of rh was obtained by trimming the data with hhi larger than the peak hhi (e.g. average of the hhi corresponding to the 99 percentile of the rh). A linear regression was applied to the resulting data in order to get the slope of the dry part of rh, as it was done in Teuling et al. (2007b). Linear models instead of non-linear or higher order models simplify the interpretation of results and reduce the number of parameters that define the relationship. 3. Results and discussion The typical convex shape of rh shown in some of the field data of Brocca et al. (2012); Rosenbaum et al. (2012) could be observed by running a non-stationary flow model with an ensemble of variable Ks in most of the soils studied (Fig. 2). A clear peak could not
be seen with the LS and SL textures as previously reported for the steady-state flow case (Vereecken et al., 2007) The textures with a high percentage of sand show a linear increase of rh with increasing hhi where no peak could be determined. This situation was observed by Martinez-Fernández and Ceballos (2003) and is a consequence of an arid environment. Ivanov et al. (2010) suggested that vertical soil moisture redistribution and evapotranspiration control the dry side whereas precipitation, vegetation, infiltration, and soil moisture are the major controls in the wet side. The range of measured hhi in other works explains the fact that in some works the rh relationship is positive while in others it is negative. Under dry environments (hhi smaller than peak hhi, e.g. in Martinez-Fernández and Ceballos, 2003) it is harder to find the wet end in which the rh decreases with increasing hhi and the rh is assumed to be positive. In contrast, for wet environments (hhi larger
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Fig. 2. The rh relationship for soils with different hydraulic properties and a spatial variability determined by a standard deviation ln Ks of 0.8 under a humid continental climate. The linear regression fitted (dashed line) to the dry-part (pre-peak) of the rh relationship is superposed.
than peak hhi, e.g. Famiglietti et al., 1999) it is difficult to observe the rh decrease with decreasing hhi and the rh is assumed to be negative. The effect of vegetation is illustrated for a loamy soil with cold semiarid climate. Root water uptake modified the characteristics of the rh relationship (Fig. 2g and h for the cases of bare and vegetated loamy soil respectively). Slopes were significantly different
(p-value <0.001) for the cases with and without root water uptake. The slope of the root water uptake case halved that of the bare soil. The maximum rh was smaller in the bare than in the vegetated cases with a similar corresponding the hhi at the rh peak. A hysteretic behavior can be observed better in the simulations done with vegetation in accordance with the observations done by Rosenbaum et al. (2012); Ivanov et al. (2010) who previously had
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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Table 2 Average soil water content and standard deviation at the peak of the rh and slope of the rh dry-part of the modeled soils with the humid continental climate.
Loamy sand Sandy loam Sandy clay loam Loam Loam under vegetation Silt loam Clay loam Silty clay loam
Peak hhi
Peak rh
Slope LM
R2
0.24 0.30 0.33 0.36 0.34 0.38 0.37 0.34
0.033 0.034 0.023 0.030 0.033 0.029 0.020 0.023
0.18 0.15 0.09 0.11 0.04 0.09 0.06 0.07
0.97 0.99 0.86 0.89 0.44 0.65 0.61 0.81
The peak was not reached. Therefore the maximum rh and its corresponding hhi were used.
observed the effect of evaporation in this kind of behavior. Fig. 2h shows, inside ellipses, data from winter, summer and fall. Extracting the data from these three groups and fitting a linear model yielded significantly different slopes at the p = 0.001 level. The observed dispersion, especially near the driest end, in some of the plots of Fig. 2 (e.g. silt loam, silty clay loam and loam both with and without root water uptake) can be caused by the intensity of the evaporation flux. Texture was responsible for the differences between peak rh and the corresponding hhi values (Table 2) with values ranging between 0.022 and 0.034. There was a substantial difference between the average moisture content at the rh peak calculated with the stationary approximation and Brooks-Corey parameters in Vereecken et al. (2007) and the non-stationary approximation with the van Genuchten parameters in our case (Table 2). We observed larger values of hhi at the rh peak than in the similar cases of Vereecken et al. (2007). One explanation for this difference is that the model of Brooks-Corey used by Vereecken et al. (2007) determines the location of the rh peak by setting the air entry value. Values of hhi at the rh peak for a silty clay loam obtained in our simulations and in Vereecken et al. (2007) (0.34 and 0.20 m3 m3, respectively) are smaller than in Rosenbaum et al. (2012), 0.39 m3 m3, though our non-stationary simulations provided results closer to the field study of Rosenbaum et al. (2012). This difference with observed values in the field can be explained by the effects of vegetation, as has been shown in the comparison of the root water uptake vs bare loamy soil described before, and the difference between the generalized moisture retention parameters used in the simulations and the actual values in the experimental site. Slopes in linear regressions hhi vs rh depended on textures and were significantly different among them (p < 0.001, Table 2). Larger
Fig. 4. Digitized LAGO dataset from Brocca et al. (2012). Selected points to fit the dry-part are included inside a rectangle.
slopes were found for the coarser soils. The slope for the SL was lower in this work than in the field experiment of Martinez-Fernández and Ceballos (2003) with soils of similar texture. That probably reflected the role of the weather pattern (e.g. variable rainfall depth and evapotranspiration), vegetation and topography as generators of a larger variability of soil moisture in large-scale field studies. A strong relationship between the slope of the linearized prepeak soil moisture variability and the ‘‘n’’ parameter of the van Genuchten moisture retention equation was observed (Fig. 3A). The relationship found between the soil moisture variability and a water retention curve parameter could be useful to assess large-scale water retention properties from soil moisture monitoring data. While that could only be done for weak perturbations of the standard deviation in Vereecken et al. (2007), the approach of this work is more robust and does not have not such limitation. To illustrate the potential of this approach, we fitted a linear regression to the points with soil moisture smaller than 25% in the LAGO dataset (Fig. 4) from Brocca et al. (2012) and considered the point hhi = 0.24, rh = 0.036 as an outlier. This dataset covers an area of
Fig. 3. Textural effect on the slope of the dry part of the rh relationship: (A) effect of the ‘‘n’’ parameter in the van Genuchten’s model for the soil moisture characteristic curve; (B) effect of ln Ks. Labels reflect the textural class (Table 1).
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Table 3 Average soil water content and standard deviation at the peak of the rh and slope of the rh dry-part of a loamy soil subject to four different climates. Climate
Peak hhi
Peak rh
Slope
R2
Humid subtropical Humid continental Cold semiarid Dry semiarid
0.349 0.36 0.363 0.296
0.030 0.030 0.023 0.026
0.09 0.11 0.11 0.11
0.75 0.89 0.85 0.63
The peak was not reached. Therefore the maximum rh and its corresponding hhi were used.
178 km2 in which we can assume an homogenous distribution of rainfall. For the LAGO case we obtained a slope of 0.15. Therefore, assuming that the standard deviation of ln Ks is 0.8 and applying the regression shown in Fig. 3A we obtained an ‘‘n’’ value of 2.0. This value correponds to n-values for soils having the LS texture. These soils represent the dominant textural class in the LAGO area. Deriving hydraulic parameters for the van Genuchten–Mualem model from the rh using the presented approach opens perspectives for generating directly effective hydraulic properties at different scales from soil moisture content measurements that can be used in hydrological models. This may present an alternative or complement to pedotransfer functions based on site-specific knowledge. However, it needs to be tested for systems affected by topography, soil layering, and different kinds of vegetation among other controls. Different climates caused significantly different slopes at the 99% confidence level (Table 3). Average moisture at the peak rh was practically insensitive to the differences in climate with a coefficient of variation between the cold semiarid and the humid weathers of 2%. The effect of climate on the relationship between mean soil moisture and its variability was reported previously by Teuling et al. (2007a) and was highly influenced by differences in the vegetation development. Rosenbaum et al. (2012) did not observe seasonal differences in rh in the intermediate h range within groundwater-distant upslope areas. The small, though statistically significant, difference that we observe may explain why they did not observe the seasonality. Maximum variability of soil moisture (ranging from 0.023 to 0.030) and the slope of the dry part of rh (0.09–0.11) depended on the climate. Nevertheless these ranges are smaller than those reported above for different textures (Table 2) and shows larger effect of texture on rh than that of climate. As previously observed with field data by Choi et al. (2007), soil hydraulic properties-related parameters had the largest influence in the variability of soil moisture followed by climate
and topography. This has been proven even for the simplified case of this study were local controls are only considered. However, the effect of the variability in the weather patterns at different scales on the variability of soil moisture still needs to be evaluated. Its relative influenced compared to that of soil properties is a subject of further study and might be approached using radar data. We observed an increase in the slope of the rh dependence on hhi proportional to rlnKs for the same soil texture, and to the mean ln Ks for different textures (Figs. 5B and 3B respectively). This result is in disagreement with the observations of Famiglietti et al. (1998); Vereecken et al. (2007) who found that variability in soil moisture is controlled strongly by porosity and hydraulic conductivity under wet conditions but not under drier conditions. Knowledge of the spatial variability of saturated hydraulic conductivity (Ks) is required for hydrological modeling (Braud et al., 1995). Several attemps have been made to characterize it. Geostatistical methods were used by Regalado and Muñoz-Carpena (2004). Indirect methods such as through temporal stability analisys of soil moisture as was done by Martinez et al. (2013) or by characterizing porosity as in Ahuja et al. (1989) were used also to characterize the spatial variability of Ks. Differences in rlnKs had a minimum effect on the peak hhi. The average hhi at the peak for the five levels of Ks variability was 0.362 with a coefficient of variation of only 0.5%. An increase in the rlnKs implied a proportional increase in the peak of rh (Fig. 5B). Rosenbaum et al. (2012) observed that the differences between rh at 5 and 20 cm depth were more pronounced at intermediate moisture levels and especially for the peak of rh. They attributed those differences to the strong effect of redistribution by vertical flow, lateral flow, and evapotranspiration in that range and also agreed with the commonly described effect of texture. Those differences could be also a reason of the strong dependence shown here of the peak of rh on rlnKs as a smaller variability and smaller values of ln Ks could be expected in the subsurface. Some local (soil moisture characteristic parameters and porosity) and non-local controls (e.g. topography and soil layering) of soil moisture at the spatial scales that correspond to the variability in Ks proposed in this study are very likely to be variable. Correlations among soil hydraulic properties have been reported in the literature, e.g. Carsel and Parrish (1988), and have been useful to understand the effect of local controls on soil moisture variability and temporal stability. However, for exploratory purposes we preferred to simplify the approach and focus only on the variability of Ks. Our results indicate that it may be interesting to look for a relationship between the slope of the rh and rlnKs combined with
Fig. 5. Effect of the ln Ks spatial variability characterized by the standard deviation rlnKs on: (A) the peak soil moisture spatial variability (peak rh) and (B) the slope of the dry part of the soil variability and average moisture relationship (rh).
Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069
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the relation observed by Martinez et al. (2013) between the latter and the temporal stability of soil moisture. Some useful upscaling relationships may emerge. Also, topography might be included in the hydraulic parameter scaling algorithm as suggested by Jana and Mohanty (2012) and see whether a better agreement with field experiments could be obtained. 4. Conclusion We reproduced the shape of rh presented in several field studies by running ensemble simulations of a non-stationary flow model and variable soil hydraulic parameters and climate conditions. For bare soil conditions we were able to show the effect of rlnKs on the slope of the rh relationship in its dry end and on the maximum value of rh. In vegetated soils, root water uptake is a factor that affects the rh relationship giving flatter shapes than the bare soil case and increased the maximum rh. Soil hydraulic properties rather than climate controlled the value of soil water content at which the maximum variability was observed. As a result of that we observed an increase in the slope of the rh dependence on hhi proportional to rlnKs for the same soil texture, and to the mean ln Ks for different textures. The relationship between the n parameter of the soil moisture characteristic curve and the slope of the dry part of rh found in this study may be of relevance for deriving soil hydraulic properties using soil moisture networks and remotely sensed data as the data can be interpreted directly. However, this approach should be handled with care as the homogenous weather pattern was chosen for all the soil columns. Evaluating the strength of such relationships in natural systems would be beneficial to validate the utility of soil moisture network data to estimate the pore size distribution parameter in the van Genuchten model and the spatial variability of saturated hydraulic conductivity. Acknowledgements This study was partially supported by US Department of Agriculture and US Nuclear Regulatory Commission Interagency Agreement IAA-NRC-05-005 on ‘‘Model Abstraction Techniques to Simulate Transport in Soils’’. The first author wishes to thank the Spanish Ministry of Education for the mobility Grant EX20090433. The authors would like to thank the valuable and useful contribution of two anonymous referees. References Ahuja, L.R., Cassel, D.K., Bruce, R.R., Barnes, B.B., 1989. Evaluation of spatial distribution of hydraulic conductivity using effective porosity data. Soil Sci. 148, 404–411. Braud, I., Dantas-Antonino, A.C., Vauclin, M., 1995. A stochastic approach to studying the influence of the spatial variability of soil hydraulic properties on surface fluxes, temperature and humidity. J. Hydrol. 165, 283–310. Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2010. Spatial-temporal variability of soil moisture and its estimation across scales. Water Resources Research 46, W02516. http://dx.doi.org/10.1029/2009WR008016. Brocca, L., Tullo, T., Melone, F., Moramarco, T., Morbidelli, R., 2012. Catchment scale soil moisture spatial–temporal variability. J. Hydrol. 422–423, 63–75. Capehart, W.J., Carlson, T.N., 1997. Decoupling of surface and near-surface soil water content: a remote sensing perspective. Water Resour. Res. 33, 1383– 1395. Carsel, R.F., Parrish, R.S., 1988. Developing joint probability distributions of soil water retention characteristics. Water Resour. Res. 24, 755–769.
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Please cite this article in press as: Martínez García, G., et al. Effect of soil hydraulic properties on the relationship between the spatial mean and variability of soil moisture. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.069