Measurement and inference of profile soil-water dynamics at different hillslope positions in a semiarid agricultural watershed



[1] Dynamics of profile soil water vary with terrain, soil, and plant characteristics. The objectives addressed here are to quantify dynamic soil water content over a range of slope positions, infer soil profile water fluxes, and identify locations most likely influenced by multidimensional flow. The instrumented 56 ha watershed lies mostly within a dryland (rainfed) wheat field in semiarid eastern Colorado. Dielectric capacitance sensors were used to infer hourly soil water content for approximately 8 years (minus missing data) at 18 hillslope positions and four or more depths. Based on previous research and a new algorithm, sensor measurements (resonant frequency) were rescaled to estimate soil permittivity, then corrected for temperature effects on bulk electrical conductivity before inferring soil water content. Using a mass-conservation method, we analyzed multitemporal changes in soil water content at each sensor to infer the dynamics of water flux at different depths and landscape positions. At summit positions vertical processes appear to control profile soil water dynamics. At downslope positions infrequent overland flow and unsaturated subsurface lateral flow appear to influence soil water dynamics. Crop water use accounts for much of the variability in soil water between transects that are either cropped or fallow in alternating years, while soil hydraulic properties and near-surface hydrology affect soil water variability across landscape positions within each management zone. The observed spatiotemporal patterns exhibit the joint effects of short-term hydrology and long-term soil development. Quantitative methods of analyzing soil water patterns in space and time improve our understanding of dominant soil hydrological processes and provide alternative measures of model performance.

1. Introduction

[2] Land-surface and subsurface water fluxes are central to various agroecological systems and processes, including water uptake by plants and chemical transport processes. Dryland (rainfed) agricultural systems depend on the storage of soil water in the root zone to sustain a crop during dry periods. Space-time storage and flow of water can be highly variable due to spatial variability in terrain and soil properties, as well as weather patterns.

[3] There has been broad interest in the dynamics of volumetric soil water content (θ, m3 m−3) among the fields of agriculture, soil science, ecology and hydrology. Automated data recording of the responses of electronic sensors allow for frequent (near-continuous) temporal measurements at multiple spatial locations, making it possible to explore detailedθ in space and time. Soil water flow and variability in θ have been the emphasis of several studies [e.g., Daly and Porporato, 2005; Kim and Kim, 2007; Lin et al., 2006; Schmidt et al., 2007; Zhu and Lin, 2011]. A few studies in water-limited environments [Gómez-Plaza et al., 2000; Hoover and Wolman, 2005; Ivanov et al., 2008; Newman et al., 2006; Zhu and Shao, 2008] are most relevant to the present work in terms of climate. In terms of methods, previous studies explored spatial patterns of θ using visual inspection of synoptic spatial images [Tromp-van Meerveld and McDonnell, 2006; Kim and Kim, 2007; Liu and Zhang, 2007; Zhu and Shao, 2008], time series graphs of θ at different locations and depths [Ensign et al., 2006] statistical distributions [Lin et al., 2006; Zhu and Lin, 2011], and geostatistical methods [Brocca et al., 2007; Zhu and Shao, 2008]. Guber et al. [2008] and Brocca et al. [2010]explored space-time patterns using temporal rank stability based on the method of Vachaud [Pachepsky et al., 2005; Vachaud et al., 1985]. We propose a new method of analyzing temporal dynamics of θ based on first principles of soil water flow. Other than a field experiment on four small (∼4 ha each) instrumented watersheds in Beltsville, Maryland [De Lannoy et al., 2006; Guber et al., 2008], the soil water monitoring system presented here is unique in terms of its intensity of space-timeθ data.

[4] Fang et al. [2010] calibrated RZWQM2 [Ma et al., 1998, 2009], a one-dimensional numerical model based on the Green-Ampt infiltration and Richards' equation for vertical redistribution. Despite rigorous parameter estimation methods, the model tended to produce more “flashy” responses inθthan measured responses. One explanation may be the use of relatively homogeneous, coarse-resolution soil horizons needed to reduce the parameter set, even though numerical computations were performed on much finer spatial resolutions (1 cm vertical numerical mesh). The present high-temporal resolution data set is essential for identifying and addressing these types of issues in process models.

[5] Simulated soil water in semiarid agricultural fields are often assumed to be dominantly vertical, such that a one-dimensional model suffices. At hillslope length scales and over seasonal time periods, however, soil layering may occur parallel to the land surface and induce lateral flow even in thick, well-drained soil profiles [McCord and Stephens, 1987; Sinai and Dirksen, 2006]. Such unsaturated subsurface lateral flow can cause the soil water distribution to be related to terrain, as observed in the field [Sinai et al., 1981; Zaslavsky and Sinai, 1981] and simulated for hypothetical hillslopes [Green, 1994]. The present study was not designed to measure lateral fluxes directly, but soil profile dynamics may have a bearing upon the inference of multidimensional soil water flow.

[6] The main aims of this study were to develop methods that quantify dynamic soil water content over a range of hillslope positions, to infer vertical soil profile water fluxes at discrete depths, and to identify locations most likely influenced by multidimensional flow in an undulating semiarid landscape. The soil water flux divergence is related to the temporal rate of change in storage, by which soil water processes are inferred at different hillslope/landscape positions. Data processing to derive water content required a new method of temperature correction described in section 2.2.

2. Materials and Methods

[7] The space-time dynamics of soil water content (θ) were measured at four depths along two transects (16 probes) plus 5 to 10 depths at two additional probes (“E1” and “E2” in the northwest corner) within an undulating agricultural field. In-situ frequency domain dielectric sensors [e.g.,Paltineanu and Starr, 1997; Schwank et al., 2006] were used to determine θ values, and surface topographic attributes were computed from gridded elevations (for more details see Erskine et al. [2006] and Green et al. [2009a]).

2.1. Site Description

[8] The field site in eastern Colorado (40.61°N, 104.84°W) is on a producer-owned and operated farm. The elevation ranges from approximately 1559 to 1588 m, with land-surface slopes ranging from 0 to more than 13% (m m−1 × 100%). The average annual precipitation and potential evaporation depths are approximately 350 and 1200 mm, respectively. These values yield an aridity index (AI) of 0.29, where the global range for a semiarid classification is 0.2 < AI < 0.5 [UNEP, 1992]. The undulating terrain at the site is composed of aeolian silt and sand deposits over sedimentary rock and fluvial deposits (see Green et al. [2009a, 2009b] for more details). The relatively massive soils have only minor clay accumulations in the B horizon and transition zones (see Table 1 for some examples). No saturated groundwater or perched water has been detected within the root zone.

Table 1. Surveyed Soil Horizons and Associated Particle Size Fractions (Percentages) and Texture Classes for Selected Probe Locationsa
SiteHorizonDepthb (cm)Sand (%)Silt (%)Clay (%)Texture Classc
  • a

    Each horizon is based on the average of two replicated soil profile samples for horizon depth and texture. (Dunn et al., personal communication, 2009).

  • b

    Depth to the bottom of each soil horizon.

  • c

    L is loam; SCL is sandy clay loam; CL is clay loam.


[9] The 56 ha watershed (Figure 1) lies mostly within a farm field of winter wheat, where a wheat–fallow rotation is practiced across 120 m wide strips indicated in Figure 1a with some exceptions. Soils have been mapped (Figure 1a) and subsequently sampled in greater detail for soil horizon depths and texture. G. Dunn, D. Palic, and M. Christensen (personal communication, 2010) recently delineated soil horizons and transition layers (e.g., Bt from 25 to 53 cm) and analyzed samples for soil texture (Table 1 shows example data for five of the soil profiles discussed below). Soil texture classes range from loam (L) to clay loam (CL). In order to avoid interference with tillage operations, none of the sensors were placed in the A horizon, although some (e.g., 0.3 and 0.6 m sensors at site A1) lie within the Btk (transitional) horizon.

Figure 1.

Field site maps showing (a) plan view of instrument locations with elevation (color map), soil units (patterns), and a watershed boundary (green line) delineated for the runoff flume on the eastern edge and (b) three-dimensional perspective view of the field and catchment area (outlined in red) withloge (specific catchment area) overlaid on topography to show potential surface flow paths using the D method (modified from Green et al. [2009b]).

[10] Locations of the soil water probes were selected to sample a broad range of hillslope positions, soil units, and topographic attributes (Figure 1). The two main transects, which were constrained by crop management and wiring distances from buried sensor probes to edge-of-field data loggers, traverse some of the steepest gradients in soil and topographic attributes. The fractal geometry of measured steady infiltration rates has been analyzed [Green et al., 2009a] at the present study site. One highlight of previous research on this watershed was the degradation of (multi)fractal behavior at scales greater than about 300 m. Green et al. [2009a] concluded that hillslope processes acting over a range of up to 200–400 m may account for the observed fractal behavior. In the present context it is not possible to explore spatial variability of soils within each hillslope position, and soil properties are likely to vary in three dimensions.

2.2. Measurement and Processing of Data for Soil-Water Content

[11] Capacitance sensors (Sentek EnviroSMART® and EnviroSCAN®—brand names are used for readers to find more detailed specifications about these instruments. USDA-ARS and the authors do not have any vested interest in any of the cited commercial products) were used to deriveθfrom frequency-based dielectric measurements [Kelleners et al., 2004; Schwank and Green, 2007; Schwank et al., 2006]. Soil profiles were augered carefully by hand while advancing plastic access tubes to ensure contact between the soil and access tube. Probes were sealed in the access tubes and buried with the tops at 0.25 m below the ground surface. Each probe along the main two transects (probes A1–D4) contains four ring capacitors centered at depths of 0.3, 0.6, 0.9, and either 1.2 or 1.5 m. Probe E1 includes sensors at all five depths, and E2 initially had sensors at 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.2, 1.5, and 1.7 m (some changes over time occurred at 0.7 and 0.8 m). Wires running from the probes to data loggers at the edge of the field were buried to allow various management operations (including shallow soil tillage) above every probe. In this way, probe installation and monitoring did not affect surface conditions after the initial reconsolidation of soils. Cable lengths should not affect measurements, because digital signals are converted from analog resonant-frequency measurements on the probe circuitry within each access tube. The vertical measurement interval of each sensor is approximately 0.08 m, and the signal support volume comprises a soil annulus of less than 0.10 m. Previous studies [Evett et al., 2006; Paltineanu and Starr, 1997; Schwank et al., 2006] have provided more information on the measurement volume of these sensors.

[12] The vendor (Sentek Technologies, Inc.) provided a default, universal calibration equation to relate θ to the normalized or scaled resonance frequency (SRF) of the sensor. For each sensor, the absolute frequency or “raw count” (R) must be measured in air and water (Ra and Rw, respectively) at approx. 25°C; this is usually done in a laboratory before field deployment. Values of θ using the default calibration with SRF were then logged in the field. EnviroSCAN systems store both Rand the site-specific or defaultθ (θR), while EnviroSMART systems typically store only θR. Either way, field values of SRF can be computed as

display math

where [a, b, c]default = [0.1957, 0.404, 0.02852], and the factor of 100 is used to convert θ to a percent volumetric water content. In our case, all raw values of θR were based on the default calibration parameters. Initial data screening and quality control were based on the default values.

[13] At a measurement frequency of approximately 130 MHz, however, the apparent values of permittivity (ε*) and associated estimate of θ (θ*) are affected by the soil temperature [e.g., Baumhardt et al., 2000; Evett et al., 2006; Fares et al., 2007]. The dominant temperature dependence relates to the imaginary part of ε*, and bulk electrical conductivity σ is the main factor at the measured frequency [Schwank and Green, 2007]. Temperature sensitivity of bound water may also be a factor [Schwartz et al., 2009a, 2009b], but only σ-related effects are considered here. The procedure for site-specific temperature correction is diagrammed inFigure 2. Sensor raw counts and SRF are shown in the upper left, but the entry values are θRusing the default parameters for all sensors. Limited gravimetric sampling did not allow for probe/sensor-specific calibration. Although that may be desirable for water balance, it is not essential for assessing soil water dynamics as described below, because absolute errors are eliminated in the temporal differences used to infer water flux at each sensor. Intersensor variability due to electronics is negligible [Schwank et al., 2006] after normalizing or scaling each sensor raw count (R) to air and water (Ra and Rw, respectively).

Figure 2.

Procedure for correcting raw soil water content (θR) for soil temperature (T) effects on the apparent permittivity (ε*). Relevant equations and references are indicated for each computed value. Under the “Dielectric Sensor” column, Sentek “Raw” counts are denoted R with subscripts a and w for air and water, respectively. Scaled resonance frequency (SRF) is computed in the field from R, and θR is logged based on the default calibration parameters in equation [1] (inversed). ΔθR is the change in θR from one hour to the next (a filter to remove artificial spikes), and % denotes a trigger value in percent volumetric water content for missing values (“NA”). Apparent permittivity ε* is computed from [2], then corrected for bulk electrical conductivity (σ) using a site-specific relationship [3] forσ (θ at 15°C), and σ is further corrected for temperature [4]. The permittivity correction δe using σ(θ,T) is based on simulated results [Schwank and Green, 2007]. Tm denotes measured temperature at a depth (z) of 0.3 or 0.6 m. Missing T data and deeper values are estimated (Te) using a calibrated time-depth temperature variation function [5]. The temperature corrected real permittivityε′(T) is used to estimate hourly θ from Topp et al. [1980], which is finally averaged up to daily values. Daily values of θ are considered missing (“NA”) if more than 18 h of hourly θ are missing.

[14] Hourly values of θR were screened for random errors by computing backward differences ΔθR to detect random jumps. If ΔθR > 0.8% (0.008 m3 m−3) (determined empirically), hourly values of θR were assigned missing values (“NA”). Figure 2 does not show that missing values were replaced with the average of nonmissing hourly values within each day, only if fewer than 18 out of 24 values were missing.

[15] Next, an adjusted calibration of equation (1) was used to estimate SRF*, where [a, b, c]adjusted = [0.2025, 0.365, 0.0280] for all sensors. These “adjusted” parameters were calibrated manually to approximate SRF* values generated from the polynomial Topp equation [Topp et al., 1980] by Schwank et al. [2006, Figure 16]. This new universal calibration corrects for biases in θ particularly at high values of SRF. The resulting values of SRF* were used to estimate ε* based on the laboratory experimental results of Schwank et al. [2006, equation (29)]:

display math

where εa = 1 and εa ≈ 80 are the real permittivity values of air and water at 20°C, respectively, and the empirical fitting parameters are [β, χ] = [1.15008, 6.66056]. As diagrammed in Figure 2, these estimated hourly values of ε* were converted to θ* using the Topp equation. The purpose of computing θ* here was solely to estimate σas a site-specific function ofθ and temperature. McCutcheon et al. [2006]measured in-situσ using a VerisTM instrument and related σ to gravimetric samples of θ collected at 100 profiles across the same field studied here. Thus, their relationship [McCutcheon et al., 2006, equation (1)] serves as a field-specific function for estimatingσ from θ at the average soil temperature during their study (approximately 15°C),

display math

Values of σ were further corrected for soil temperature using the method of Sheets and Hendrickx [1995] after Seyfried and Grant [2007] as follows:

display math

where T is either the measured soil temperature Tm(z,t) or the reference temperature (To = 15°C in this case). The resulting family of functions σ (θ, T) is shown in Figure 3a.

Figure 3.

(a) Bulk electrical conductivity as a function of soil water content and temperature (T in °C). (b) Soil temperature (T in °C) as a function of time (day of year) and depth (m) generated after Hillel [1982] using equation (3). This pattern repeats across all years.

[16] Soil temperature was measured hourly at a horizontal distance of 30 cm from each capacitance probe at depths of 30 and 60 cm using a buried thermocouple sensor and logger (Onset Computer Corporation's WaterTemp ProTM). Deeper soil temperatures were not measured, except at two locations near probes C2 and D1 for part of 2010. These data (not shown) were used to check the amplitude of seasonal (intra-annual) variations in soil temperature down to 90 cm using the method ofHillel [1982]given below. General consistency in the intra-annual variability of soilT at 30 and 60 cm across all locations indicates that a universal fit is reasonable. Excursions from the seasonal pattern are dampened with depth, which justifies the universal relationship at 90 cm and below.

[17] The general equation for soil temperature variation as a function of depth and time by Hillel [1982] is

display math

where the soil temperature Ta was set based on the mean measured temperature of 10.85°C, and d = 2.0 m assuming a thermal diffusivity of 4 × 10−7 m2 s−1. The other parameters were calibrated to match the observed pattern of T(z, t) across all years at z = 30 and 60 cm, and for about 6 months at 90 cm. The resulting parameter values in equation (5) were A = 16°C and to= 43 d. The intra-annual patterns ofT(z, t) are illustrated in Figure 3b for z= 0, 30, 60, 90, 120, and 150 cm. Although the high-frequency variations inT(not shown) dampen rapidly with depth, the lower-frequency seasonal patterns propagate to 1.5 m, such that the seasonal temperature estimation and corrections charted inFigure 2 are necessary for all depths.

[18] Once the σ(ε*, T) values were computed, corrections to the permittivity were computed based on Schwank and Green [2007, equation (31)]:

display math

where values of δε(ε*, σ) were interpolated based on a thin-plate spline fitted through tabular values computed by Schwank and Green (unpublished data). The tabular values were sufficiently dense to minimize any interpolation errors, and this approach avoided resimulating the electrical fields for each new combination of measuredε* and σ (θ, T). The resulting temperature-corrected permittivities (ε′(T) in Figure 2) were fed into Topp's equation to compute hourly θ, then summed to daily values of θ. This procedure produced time series of daily θ at each sensor for the subsequent analysis of temporal dynamics. Again, more than 18 h of missing data in any given day led to exclusion of that day from the analysis (i.e., missing daily values). Missing values were extensive at some sensors due to cut wires, occasional power loss, or moisture intrusion causing corrosion on sensors. After losing a large period of data in 2005, sensors were replaced with new or cleaned sensors, and downhole electronics were protected with polyurethane, which is now standard practice for new sensors.

2.3. Temporal Data Analyses

[19] The temporal dynamics of θwere evaluated at each slope position and depth by computing changes in storage and the rates of change over different temporal scales (lag-1 daily to semiannual). Within-day (hourly) measurements could also be used for analyses at higher temporal frequencies than explored here. However, the dominant changes in water content typically occur over longer time scales (>1 week). Multitemporal changes in the soil water dynamics with depth revealed differences between landscape positions, allowing inference of the potential for lateral subsurface flow.

[20] Imploring conservation of mass, the rate of change in θ within a given volume equals the water flux divergence minus a distributed sink term (ω, root water uptake):

display math

where θ (m3 m−3) represents water in the measurement support volume V, the tensor q represents water flux per unit area (m3 d−1 m−2 or m d−1) or Darcy flux tensor across a three-dimensional surfaceS encompassing V, t is time (d), ω(t) is the time-variable sink strength (m3 d−1 m−3) for root water uptake (time variable), ∇• is the divergence operator, and ∮ denotes integration over a surface. Spatial integration yields a volume of water per unit time. Integration of equation (7) over the time period Δt gives the change in θ equal to the cumulative change in volume of water over Δt,

display math

[21] Letting V = 1, or a unit volume, the measured change in θ equals the flux divergence integrated over the surface of V during an arbitrary time period Δt, less the root water uptake:

display math

[22] It is worth noting here in the context of this special section of Water Resources Research, that Professor Burges regularly advocated “first principles” as the keys to scientific and engineering advancements. He also endorsed the work of Dooge [1986], who stated that conservation of mass is the fundamental law of hydrology.

[23] In this study, changes in θ at each probe location and sensor depth are analyzed. At this point, it is instructive to consider some limiting or dominant conditions that may be invoked in these mass balance issues:

[24] 1. Let the sink term ω(root water uptake) go to zero, which occurs under fallow conditions (mid-July to September–October of the following year, depending upon harvest and planting dates for winter wheat), and when transpiration is negligible (most of November–February even when wheat is planted). In this case, changes inθ equal the flux divergence integrated over the sensor volume and time period.

[25] 2. Assume the flux divergence goes to zero under uniform gravity drainage across the measurement interval of a given sensor. In this case, root water uptake over the vertical interval can be computed directly from the measured change in θ over Δt. This simple case is actually problematic, because uniform gravity drainage is the exception in this landscape due to infrequent wetting events. However, such conditions may occur for brief periods (e.g., order of one week) after the passing of a vertical wetting front, and for longer periods of drying.

[26] 3. Most certainly, when the measured change in θ (left side of equation (9)) is zero, the integrated flux divergence equals the root water uptake over the sensor interval. Of course this assumes perfect measurement of Δθ. Instrumental precision of a given sensor is excellent (0.0034 m3 m−3 based on laboratory experiments by Schwank et al. [2006]), providing that the procedure in Figure 2 corrects for temporal changes in permittivity due to temperature.

[27] At each sensor depth we computed Δθ on the left hand side of equation (9) for time periods Δt = 1, 2, 3, … , 182 days. Next, we computed an average rate of change (Δθt) for each Δt. Finally, time periods for wetting and drying cycles that displayed the strongest dynamics were identified.

3. Concepts and General Hypotheses

[28] The following ideas are presented as a framework for interpreting the results presented in section 4. If horizontal soil water flux gradients are small relative to vertical flux gradients, total flux divergence is dominated by vertical processes. Sharp wetting fronts, for example, cause large flux divergence as the wetting fronts cross the upper surface of V. These high divergence fronts are typically followed by smaller flux divergences of the opposite sign as the wetting fronts move below the lower surface. The same change in θ could result from a more diffused wetting front after the front passes completely through the measured depth interval (approximately 0.08 m for these sensors). However, the soil water dynamics will differ within the period of integration. Thus one might think of the maximum positive value of Δθtas the passing of a wetting front across a certain depth, and this information between adjacent sensors can be used to compute average vertical velocities of wetting fronts at each probe. Over the time period of a wetting event, this assumes that flow is dominantly vertical. Conversely, we do not assume that lateral subsurface flow is negligible over longer periods. Indeed, lateral subsurface flow in such semiarid landscapes is theoretically significant over long time periods and at quasi-steady state due to state-dependent anisotropy in soil hydraulic conductivity [Green and Freyberg, 1995].

[29] We hypothesize that unsaturated subsurface lateral flow affects profile water dynamics primarily as follows: (1) accumulation of subsurface flow causes the soil profile to be wetter at downslope and convergent topographic positions; and (2) focused lateral flow wets deeper soils directly, in addition to wetting from above. Horizontal gradients in both q and θ (equation (7)) are typically small compared with vertical gradients, but gravity combined with sloping soil layers (anisotropy in unsaturated hydraulic conductivity) may suffice to drive significant lateral flow profiles [McCord and Stephens, 1987; Sinai and Dirksen, 2006]. Hypothesis 1 implies more dynamic responses of wetter soils to the same surface flux due to decreased storage capacity and increased hydraulic conductivity. Spatially differential development of soil along a catena or hillslope may complicate the hypothesis testing. That is, side-slope positions tend to have relatively coarse soil textures, and lower hillslope positions tend to have finer soils that retain more water at the same capillary pressure. The potential for differential infiltration of overland flow (runon accumulation) may affect profile soil water responses in similar ways to accumulation of subsurface lateral flow. Rigorous testing of these hypotheses is beyond the scope of the present study, primarily because definitive sourcing of water (subsurface versus surface flow paths) would require a chemical or isotopic tracer. The present analysis of soil water dynamics is useful to identify the potential for multidimensional flow concentration but not sufficient for discriminating between surface and subsurface water sources, unless deep subsurface lateral flow (hypothesis 2 above) is dominant.

4. Results and Discussion

4.1. Space-Time Soil Water Content

[30] Field measurements of soil water content were initiated during a relatively dry period throughout the vertical soil profile (e.g., Figure 4c). High precipitation in March–April 2003 (Figure 4a) wet only the shallower horizons, whereas April 2005 precipitation during a fallow period at probe E2 wet the full soil profile (measured to 1.7 m) due to higher antecedent moisture in near-surface soils. Spatially, Probe E1 is located in a strongly convergent topographic position (Figure 1), whereas E2 has very little potential upslope contributing area (despite its proximity to a topographic drainage line). The solid lines in Figures 4b and 4care the same for equivalent depths, showing that the patterns of wetting and drying are quite different at these two slope positions. Drying was observed during the crop period (out of phase between E1 and E2) at all depths, but drainage and soil evaporation also occur under fallow conditions. The low-frequency intra-annual (seasonal) temporal pattern is most evident at E1 (Figure 4b). While the wetting front is much sharper at E2, drainage is more rapid at E1. Nevertheless, soils tend to stay wetter at E1's topographically convergent position than at E2 (divergent surface). Agronomically wetting of the full root zone of wheat in 2005 led to high grain yields in 2006 (i.e., wheat plants harvested the stored water). Grain yields in 2005 were also above average at E2 (and other crop strips in the same phase).

Figure 4.

Time series of (a) daily precipitation and summed precipitation within each year (“Yearly Cumulative”), (b) volumetric soil water content for probe E1 (5 sensors) and (c) for probe E2 (10 sensors). Cropped and fallow periods are indicated for the winter wheat-fallow rotation. SeeFigure 1 for probe locations and strips of alternating crop rotation (out of phase).

[31] Soil water data versus time are compared across all probes in the two main transects (A–D) at four sensor depths for the year 2003 (Figure 5) when continuous daily values were available for all sensors starting on 20 February 2003. At this time scale the spring wetting front noted at the E probes (Figure 4) is seen clearly. Again, soil water responses vary by landscape position. Higher-frequency temporal fluctuations and deep wetting are particularly notable at probes A3 and B3 near the main drainage line inFigure 1, which carries concentrated surface runoff on rare occasions (based on field observations).

Figure 5.

Calendar year 2003 time series of daily precipitation and summed precipitation (top plot), and volumetric soil water content for all sensors (4 per probe) on probes A–D (as labeled). Months of the year are indicated (JFM … OND). Cropped and fallow periods coincide with E1 for A and C probes, and with E2 for B and D probes (see Figure 4). See Figure 1 for probe locations and strips of alternating crop rotation (out of phase).

[32] Looking across columns in Figure 5, we see similarities in temporal patterns between A and C, and between B and D, that are controlled by plant water uptake. The A and C probes are in the same transect (Figure 1a) and have the same cropping pattern as shown for probe E1 (Figure 4b), while probes B and D, like E2 (Figure 4c), were under fallow conditions until October 2003. The lack of root water uptake under fallow (A and C probes) constitutes one limiting condition, as defined in section 2, such that the sink term in equation (9)is negligible, and flux divergence can be inferred from temporal changes in water content. There are also differences going downslope within the same transect. For example going downslope (south to north) from D1 to D4, we see dramatic differences in the soil recharge to 1.5 m, but in an apparently nonlinear fashion. At the summit (D1), the sharp wetting front reaches 0.9 m almost a month after reaching 0.3 m, but there is only a low-amplitude seasonal rise at 1.5 m. At D2, the full profile wets up, but going downslope to D3, it behaves more like D1. Why? Surface topographic attributes (Table 2) provide some insight. Although D3 is on a side-slope approximately 6 m below D2 in elevation, the specific contributing area (a) at D2 is significantly higher (see Table 2 and Figure 1b). This may also explain why the initial water content at 1.5 m at D2 is higher than at any other location. Interestingly, the estimated curvature is slightly negative at D2, so the surface soils will not tend to accumulate ponded water, and the shallower sensors at D2 are not particularly wet in January. Also, the differences in specific contributing area between D1 (ln a = 2.81) and D2 (ln a = 6.39) are great despite only 1.36 m elevation difference. Another feature worth noting in Figure 5 is the persistence of relatively high water contents in the A and C probes in the absence of plant transpiration. Despite low rainfall in July and early August (little surface infiltration), water contents at 0.3 m are maintained, indicating low values of drainage flux.

Table 2. Surface Topographic Attributes at Probe Locations Computed Using Survey-Grade Elevation Data at 5 m Horizontal Spacing [afterErskine et al., 2006]
ProbeElevation (m)Slope (m m−1100%)Aspect (Degrees From N)Curvaturea(m−1 × 100)ln abTWIc
  • a

    Convex up is negative.

  • b

    ais the upslope potential catchment area per unit contour (or grid cell) length, usually called the “specific contributing area” (m) computed using the D-infinity method [Tarboton, 1997].

  • c

    TWI is the topographic wetness index computed from ln(a) and slope.


4.2. Soil-Water Dynamics Based on Temporal Analyses

[33] While much can be learned from the type of descriptive assessment of soil water contents discussed in section 4.1, more quantitative analyses of temporal responses using equation (9) and its finite temporal derivative give further insights into soil water dynamics. Figures 4 and 5were given to help the reader understand some of the space-time features of soil water content using a portion of the data set. Insection 4.2 we move from the state variable θ to its multitemporal changes and rates of change related to water fluxes.

[34] Figure 6 shows some dynamics of θ at probe A1, for example, first for θ (Figure 6b), then for the change in θ (equation (8)) (Figure 6c), and finally for the average rate of change Δθt at each time over all values of Δt (Figures 6d and 6e). It is difficult to visualize the changes and their rates in two dimensions, or even efficiently in three dimensions, so we plotted only the maximum, median, and minimum values for each t at one sensor (0.3 m depth at A1 in Figures 5c and 5d). Based on conservation of mass (equations (7)(9)), maximum and minimum values of Δθ indicate positive and negative extremes in flux divergence, respectively, at each sensor depth.

Figure 6.

Time series of (a) daily precipitation with cumulative amounts within each year and (b) daily soil water content θ for probe A1 (see Figure 1) at four sensor depths. For illustration at one sensor, maximum, median, and minimum (c) changes and (d) rates of change in θ at 0.3 m depth computed for all forward time lags of Δt = 1, 2, 3, … , 182 d. (e) The maximum rates of change over all Δt and four sensor depths at probe A1, where maxima for 0.3 m that exceed 4 m3 m−3 d−1 are shown in Figure 6d. Gaps exist due to missing data. Due to the forward difference method, values are plotted only through early in 2010.

[35] The maximum change in soil water content Δθt) at each sensor depth reveals the intra-annual or seasonal variation inθ. If Δθ < 0, the given soil layer is drying by drainage and/or root water uptake (scenarios 1 and 2 in section 2.3). The wetting and drying events at 0.3 m are clearly seen in Figure 6c. Figures 6c–6e show Δθ or Δθt versus time (horizontal axis) over multiple forward time increments Δt. Thus there are ranges of these values at each time, which we represent simply by the minimum, median, and maximum values. These provide quantitative assessments of the change (maximum or minimum) or rate of change at each time (using forward differences of Δt). For example, infiltration and vertical redistribution in the early months of 2003 are reflected in positive maximum and median values of Δθ for all Δt values, and minima near zero, followed by drainage reflected in negative minimum and median values, with maxima near zero. Other parts of the time series are less straightforward to interpret, but strong wetting and drainage events are evident.

[36] Figure 6e shows the full record of maximum rates of change at A1 over all four depths. The range of values in Figure 6e is limited to 4 m3 m−3 d−1 for graphical purposes to see the dynamics at the deeper sensors, but the full range for 0.3 m can be seen in Figure 6d. For most infiltration events at A1, the inferred magnitude of water flux dampens rapidly with depth, as might be expected in a semiarid environment with well-drained soils.

4.3. Space-Time Patterns

[37] Based on the time series presented in Figure 6, the timings of max/min flux divergence with depth were computed. Each time lag is a response time in the vertical direction. At probe A1 in 2003, time differences between the maximum rate of change in θ were 21 d from 0.0 to 0.6 m and 28 d from 0.6 to 0.9 m. The response at 1.2 m was small and highly dampened in 2003. The wetting front moved to 1.2 m more rapidly in 2005. Those familiar with soil profile wetting under more humid conditions may be surprised by the relatively slow advancement of the wetting front at most slope positions, where “field capacity” may not be obtained in even two weeks to a depth of 60 cm. In this landscape, a common assumption of reaching field capacity 2 days after a heavy rain or ponded infiltration may not be valid.

[38] Spatially, soil water dynamics vary with landscape/hillslope position. For example, let us compare the two strongest wetting events in more detail at probes A1 and B3. At the B3 toe-slope position, which is in the same soil unit as A1, the wetting front rapidly penetrated all sensor depths. In March 2003, before there was any response at the 0.3 m sensor at A1 (Figure 5), the water content was rising at the 0.9 m sensor at B3. Furthermore, the peak value of θ at 0.9 m in probe A1 occurred much later in June 2003 (Figure 5), while both A3 and B3 responded to smaller infiltration events at 0.3, 0.6, and 0.9 m, and the wetting front reached 1.5 m at B3. Similar examples could be given in 2005 (not shown). Given the similarity in soil horizons in terms of texture (Table 1), the pronounced differences in soil water dynamics appear to be controlled more by slope position and the associated short-term hydrology than by long-term soil development. To our surprise, clay contents are greater at A1 than at B3, and higher still at D2 (clay loam over the entire depth). In any case the water holding capacity is similar among slope positions.

[39] It is not possible to show the details plotted in Figure 6 for all sensors, so the maximum rates of change are summarized in Figure 7 using box and whisker plots, primarily displaying extreme values above the upper whisker. Individual sensors are plotted for each probe (A1–D4) for a year (2003) with the least missing data across these 64 sensors. It has been noted above that there are significant gaps in some periods at some probes due to equipment failures ranging from individual sensors to full probes to a data logger controlling eight probes. Given our emphasis on methods for analyzing dense temporal data, missing data analysis and possible estimation of missing data are left for future work.

Figure 7.

Box and whisker plots of the maxima rate of change in soil water content (Δθt) for each sensor (four depths) in probes A1 to D4 (see Figure 1). Each boxplot represents the temporal distribution for year 2003, when nearly complete records were available for all probes and sensors. Small circles denote values above the whiskers marking 1.5 times the interquartile range above the 75th percentile (main boxes are not visible in most cases). Red dashed lines indicate a value (4 m3 m−3 d−1) of strong responses in flux divergence down to 0.9 m, a secondary value (0.4 m3 m−3 d−1) set to 10% of the primary value, and green ovals highlight the greatest depths where these values were exceeded.

[40] In Figure 7 “extreme values” of the rate of change (Δθt) at each sensor are plotted with small black circles above the box and whisker plots, which are otherwise difficult to see (i.e., values below the 75th percentile are not generally visible). A value of 4 m3 m−3 d−1 is delineated with dashed red lines in the upper three depths to illustrate some differences between soil water dynamics at different probe locations. At the deepest sensor (1.2 or 1.5 m), the maximum rate never reached 4 m3 m−3 d−1, so a second value of 0.4 m3 m−3 d−1 was selected, and only four sensors at these depths showed distinct responses (circled in green ovals). Green ovals or circles indicate the deepest sensor at each probe where the inferred flux exceeded these values, which were exceeded at one or more of the deepest two sensors for 8 out of the 16 probes shown. Thus, in this specific case, these values identify 50% exceedence spatially.

[41] Probes at upslope locations to the north (A1 and B1) did not exceed the delineated threshold response at any depth. By contrast, probes C1 and D1 at summit positions to the south responded to 1.2 and 0.9 m, respectively. As noted above, D2 responded deeper than probes D3 and D4 further downslope. A4 and B4 are positioned near the bottom of a long (∼400 m) northeast-facing hillslope, but there is very little deep response (at 0.9 m or more) in these probes, indicating a lack of soil water supply from upslope.Table 2 shows that both A4 and D4 have negative curvature (convex up), indicating the potential to shed surface water. Probes A3 and B3 responded strongly at 1.2 and 1.5 m, respectively, and these locations have the highest specific contributing areas (ln a > 11 for both probes, as well as the highest values of TWI in Table 2). The topographic curvature at A3 is also much higher (concave up) than any other probe, because it is located near the bottom of an eroded ephemeral channel. Tillage operations smooth the terrain, such that full gully formation is not allowed.

[42] Finally, quantile-quantile (q-q) plots of all six combinations of four sensors per probe are shown for the A and B probes side-by-side inFigure 8. Again, Figure 8shows more details than can be discussed here, but it illustrates some key differences between probes at different landscape positions. Probes A1 and B1 display behaviors that may be expected for vertical infiltration into relatively dry soils. Inferred vertical fluxes are similar (near the 1:1 line) between the two shallow sensors (0.3 and 0.6 m), and at A1 there is a small tendency for the maximum fluxes to be greater at the shallower sensor. This effect is much more pronounced going to 0.9 and 1.2 m. The q-q plots of maximum rates at 1.2 m versus 0.9 m show very diminished fluxes at these depths for most sensors. The major exception is A3, where q-q comparisons for all depth combinations fall near the 1:1 lines. This implies that wetting fronts do not dampen with depth at A3, such that infiltration events are transmitted over the whole profile (to 1.2 m). Since this position is cropped in the same manner as all others in that management zone (strip), there must be a lateral supply of water to the soil profile that differs dramatically from other slope positions, including B3. Tracer experiments would be needed to distinguish the source of water between overland and subsurface lateral flow accumulation.

Figure 8.

Quantile-quantile plots of the maximum rates of change in soil water content (Δθt, m3 m−3 d−1) for six combinations of four depths at eight example probes A1–A4 and B1–B4 (see Figure 5). Sensor depths are labeled on the plot axes. Red 1:1 lines are shown for reference. The axes ranges are consistent in all six subplots for each probe, but differ between probes based on the maximum rate of Δθt encountered over all depths.

5. Summary and Conclusions

[43] In this field study we analyzed data for soil water content (estimated from capacitance sensors, and corrected for soil temperature) and temporal rates of change throughout the soil profiles at different slope positions. We related the temporal dynamics of water content to water flux. Our analytical methods were based on the “first principle” of conservation of mass in the measured volume for each sensor. The relative accuracy of differential temporal measurements at a single sensor was employed, because spatial differences are less accurate due to soil spatial variability.

[44] At many of the hillslope positions profile soil water dynamics may be explained by vertical flow processes with additional water supplied by surface runon (in addition to rainfall infiltration at each location). However, runoff is rarely observed at the 56 ha catchment outlet, so a spatially differential source of surface infiltration would be highly irregular in time. Would such infrequent runoff/on events be adequate to account for the pronounced differences in subsurface dynamics? We also identified some interesting combinations of surface terrain attributes, particularly those at probe D2, which may help explain some of the soil water dynamics without having a local surface depression (no accumulation of surface water is expected).

[45] Improved understanding of causation should benefit from integrating high-resolution temporal soil water and temperature data (as presented here) with new applications of robust process models. Flux divergence at multiple depths can be simulated in such models for comparison with dynamics inferred here from water content measurements. The flux divergence approach presented here is recommended as an alternative quantity for model calibration/testing in addition to more traditional comparisons with the state variableθin space and time. Future work may also use process-based numerical models to help understand and explain complex feedbacks and process interactions better.


[46] This paper is dedicated to Steve Burges with gratitude for his many contributions to the education and career of the first author. We also commemorate one of Steve's heroes, Jim Dooge, who inspired fundamental thinking in hydrology. We are thankful for the cooperation of David Drake which made it possible to conduct this on-farm research over the last 8 years. Mike Murphy, USDA-ARS Hydrologic Technician, provided valuable technical support for installation and maintenance of the capacitance probes. Comments and insights from the reviewers and editor, and helpfulness of the editorial staff in completing the revisions are sincerely appreciated.