The analysis exploits the wide range and regular seasonal changes in soil moisture at sites near Boise ID, USA. In semiarid Mediterranean climates, seasonal patterns in soil moisture storage and streamflow follow seasonal changes in precipitation, temperature, and solar radiation (McNamara et al., 2005: Flerchinger et al., 2010; Seyfried et al., 2011). In this system, the water year begins with dry soil following the annual summer drought. As autumn rains arrive, the soil wets downward from the soil surface and soil profile water storage increases over a long wet period due to winter rains or snow melt. In spring, warming temperatures drive snowmelt and the annual hydrograph. Ultimately, precipitation decreases and plant water use depletes soil moisture as summer proceeds. In many years, this hydrologic setting imposes different soil surface boundary conditions in each season; intermittent surface wetting of the dry soil in fall, low flux snow melt in winter, high flux snow melt in spring and progressive soil drying over the summer (Figure 1).

Data were collected from five sites at two watersheds in southwest Idaho, Reynolds Creek Experimental Watershed (RCEW) and Critical Zone Observatory operated by the USDA Northwest Watershed Research Center and Dry Creek Experimental Watershed (DCEW) operated by Boise State University. Data for RCEW are available at http://www.ars.usda.gov/Research/docs.htm?docid=8281 and from Seyfried et al. (2001) and Chauvin et al. (2011). Data for DCEW are available at http://earth.boisestate.edu/drycreek/.

The Upper Sheep Creek watershed is located within the Reynolds Creek Experimental Watershed, in the Owyhee Mountains of southwestern Idaho. The site ranges in elevation from 1,840 to 2,036 mamsl and is underlain by basalt bedrock. Mean annual precipitation is 426 mm, about 60% of which is snow. The snow is redistributed by wind, resulting in snow accumulations of 3–4 m in drifts and <15 cm in scour zones. Deposition patterns are persistent and result in distinctive snow-soil-vegetation complexes (Flerchinger et al., 1998; Prasad et al., 2001; Chauvin et al., 2011). The low sagebrush complex (Low Sage) is found on shallow (<50 cm deep) soils on mostly west-facing slopes and ridges. Soil textures are loam in the upper 10–20 cm and clay loam and gravel in the subsoil below the argillic horizon. The mountain sagebrush complex (High Sage) is on deeper soils, about 1 m thick, and mostly on north-facing slopes. The aspen complex (Aspen) is on deep (>2 m) soils and are closely associated with snow drifts. Soils in the High Sage and Aspen complexes were formed in aeolian deposits and are highly uniform with depth, mostly categorized as silt loam. Upper Sheep Creek was burned by a prescribed fire in summer 2007. The Big Sage area burned completely, and was replaced with grasses and forbs by 2008. The Aspen was cut down and recovered, in a hydrologic sense, by 2009.

The Treeline and Lower Weather sites are located in the Dry Creek Experimental Watershed (DCEW) in the foothills of the Rocky Mountains of southwestern Idaho. The elevation of these sites is 1,620 mamsl at Treeline and 1,150 mamsl at Lower Weather. Both sites are underlain by weathered granite from the Idaho Batholith, although the Lower Weather site is below the shoreline of prehistoric Lake Idaho. Mean annual precipitation is 520 mm at Treeline and 300 mm at Lower Weather. Over the period of measurement, snow accounted for ~50% of precipitation at Treeline (Kormos et al., 2014) but Lower Weather receives mostly rain. Similar to Upper Sheep Creek, geologic processes including wind scour have formed deeper soils on north facing slopes at Treeline and snow accumulation up to 2 m currently enhances springtime soil water where the sensors for this study are located. The vegetation at the site is typical of a transition between lower elevation grass-lands and higher elevation forests; mountain big sagebrush and ceanothus shrubs, prunus subspecies, forbs, and grasses. The Lower Weather site is not subject to drifting due to the limited snowfall at the lower elevation. Soil texture at DCEW is sandy loam and ranges in depth up to 1.3 m (Gribb et al., 2009; Tesfa et al., 2009).

Soil water content data were collected from representative sites of each of the five soil/vegetation complexes. These sites represent various controls of soil texture, soil depth, vegetation, and annual precipitation (Flerchinger et al., 2010) on Θ (Figure 1). In each instance, a pit was hand-excavated to bedrock or saprolite and two parallel profiles of soil moisture instruments, separated by 2 m, were installed horizontally into the pit face. A summary of sensor depths, soil texture and mean annual precipitation or estimated annual soil water input is provided in Table 1. At Upper Sheep Creek, hourly data were collected with time domain reflectometers (TDR 100, Campbell Sci., Logan UT, USA), with 3-prong, 30 cm long rods. Data are reported on water year basis. At Dry Creek, hourly data were collected with frequency domain reflectometers (CS615, Campbell Sci., Logan UT, USA) calibrated with less frequent samples from co-located TDR waveguides (Chandler et al., 2004). Data were prepared for analysis by removing most electronic noise, out of range data or data from failed sensors (Nayak et al., 2008; Kormos et al., 2014) and are reported by calendar year. Data cleaning did not include removal of records during periods of frozen soil, which were most prominent within 15 cm of the soil surface and affected a limited number of sensors. Frequency distribution of Θ from single sensors was done by constructing histograms from the conditioned data. The frequency analysis of temporally coincident data from paired sensors was done by binning data in two dimensional frequency arrays with increments of 0.01 Θ for 0.0 < Θ < 0.65.

Limited laboratory and field analyses are used to relate the results of the developed methods to traditional capillary pressure-saturation techniques. Measurements from a 66 kPa field tensiometer co-located with the 60 cm TDR sensor at Aspen site represent the range from field-saturated conditions just after snowmelt on May 20, 2004 to the time of removal on August 8, 2004. Laboratory measurements of Ψ over the ranges of 1.4–430 kPa (HYPROP, UMS GMBH, Munich Germany), and Ψ and Θ (corrected for bulk density) 0.2–115 MPa (dewpoint psychometer, Decagon Devices, Pullman WA, USA) and Θ were made to construct characteristic curves for soil samples collected at depths of 0–3 and 41–43 cm. At Treeline, soil water potential was previously measured in a field experiment to determine FC by surface irrigation from dry initial conditions. The experiment was interrupted by rain during the drainage period and terminated when the tensiometer lost capillary connection to the soil at ~33 kPa. Soil water potential was monitored by automated tensiometers (Gribb et al., 2009).

Values of Θ measured during the natural cycle of wetting and drying provide the basic data used in this analysis. In all cases the soils are well drained, therefore there is no attractor at or near soil saturation. We define attractors as values of Θ that occur at high frequency and develop four analyses that are based on observations made in a climate with distinct annual wet and dry phases. Field Saturation is the maximum observed value of Θ. Since complete soil saturation is infrequent in well drained field soils, the maximum annual value of Θ_fs is likely to range between FC and Θ_s. Field Capacity is a moisture state that prevails under wet, low flux conditions. In well-drained conditions, saturated soils drain quickly to near FC, then more slowly. Where soil water potential (Ψ) is seasonally affected by plant water uptake, FC may vary slightly with diel changes in evapotranspiration. Conversely, dry soils wet to a Θ somewhat greater than FC before drainage begins. These two processes enhance the local data frequency near FC and result in a data attractor that we define as the “wet attractor.” Figure 2A shows a wet attractor near Θ of 0.20 throughout the winter months when drainage is minimal and transpiration is insignificant. We propose that this attractor is approximately equivalent to FC. Several other descriptive and mechanistic definitions of FC have been developed and are presented by Assouline and Or (2014), who suggest the stability of soil water retention is a function of disruption of liquid phase continuity. Plant Extraction Limit is the Θ at which existing vegetation does not extract soil water by transpiration. Conceptually similar to the PWP, PEL allows for variations among soil-plant combinations and acknowledges that the vegetation doesn't necessarily wilt when transpiration ceases (or becomes very slow). PEL is expected to be an attractor in environments with extended dry periods and perennial vegetation. Under these conditions, Θ declines during the dry season until PEL is reached, then remains unchanged until replenished with new rainfall or snowmelt except near the soil surface, which may be subject to direct evaporation and may proceed to values less than the PEL. These processes result in a “dry attractor” in the data. Plant Water Stress Initiation (Θ_ws) is not an attractor, but is a decrease in plant water use as governed by complex physiological traits that control stomatal aperture (Osakabe et al., 2014), and is an inflection in soil moisture records (Rodriguez-Iturbe et al., 1999; Smith et al., 2011) determined as d²Q/dt2 > 0.

Four methods of analysis to determine the parameters PEL, FC, and Θ_fs are presented. Throughout the remainder of the paper, these analyses will be referred to as time series, frequency, paired, and hysteresis, respectively.

Visual inspection of Θ records in time series is a simple approach to identify approximate values for each parameter for individual soil depths. Figure 2A shows this approach for one year of data from a 15 cm sensor at Treeline. At this site the minimal overlap between periods of slow drainage in winter and consistently low Θ in spring and summer. This allows subjective approximation of the wet and dry attractors, and clearly shows the maximum annual Θ, and an inflection in Θ(t) indicating a reduction in plant water use.

Frequency analysis of Θ distributions for single sensors show modal peaks in Θ at dry and wet soil moisture attractors for water year (Figure 2B) or period of record data. The maximum value of Θ is assumed to be equivalent to Θ_fs.

Paired sensors at similar depth, are often used to determine an average value of Θ, increase spatial representation of the measurement, or provide redundant data in case of instrument failure. These synchronous data can be plotted as x-y coordinates to determine high frequency attractors and extreme values. Figure 2C shows example data for a water year from paired sensors at 15 cm depth in soil pits separated by 2 m. Ideally, data pairs of Θ from paired sensors at similar depth will fall on a 1:1 line, bounded by the minimum and maximum Θ at the sensor depth. However, differences in the timing of wetting and drying result in divergence and spreading around a 1:1 line. In the example for one water year of data, Θ attractors emerge at dry Θ (≈0.05) and wet Θ (0.19–0.24) attractor values, respectively and the greatest measured values of Θ (0.30, 0.27) for Θ_fs on the respective axes of each sensor. Although, similar to the frequency analysis, the paired sensor analysis leverages twice as many sample locations per data point. The use of data pairs decreases the influence of erroneous or extreme values on the frequency of values near the data attractors on the central trend. Additionally, the resulting variance around the trend may provide the user greater guidance on the range of local variability in soil hydrologic properties than would a single sample location.

Hysteresis is often observed in the temporal behavior of Θ over seasonal wetting and drying periods for sensors at two depths in a vertical profile. The lag in both wetting and drying periods between the two depths enhances the relative frequency of wet and dry attractors, near the intersection of the wetting and drying limbs of the hysteresis loop. For example, Figure 2D shows hysteresis between Θ at 15 and 100 cm at Treeline. For the climate of this study, the water year begins near the end of the dry season, with Θ at near minimum values for both the surface and bottom of the soil profile. Accordingly, the Θ trace for a water year begins near the low Θ attractor. As autumn precipitation increases Θ at 15 cm depth, the Θ at 100 cm depth remains nearly constant until the wetting front arrives. For a water year at the example site, the horizontal wetting trace provides strong visual support for the interpretation of low Θ attractor from the small range in the ordinate. Along the right side of Figure 2D, wetting at the deep sensor is shown as the vertical trace up to the wet attractor, found at the intersection of the wetting and drying traces and identified by the black oval. As above, the maximum values on either axis represent Θ_fs. Finally, the drying limb terminates at the dry Θ attractor and provides visual support for identification of the dry Θ attractor for depth of the shallow sensor.

Figure 3 shows two visualizations of paired sensor analyses over the study period for Aspen (90 cm), Low Sage (10 cm), and Treeline (15 cm). Here, and below, we present data that demonstrate analyses over the broadest range in soil texture, soil depth, and vegetation class. For the Aspen the top panel shows semi-transparent data points with makers to represent the data attractors and the bottom panel shows color maps of log-transformed data frequency values. Many of the paired sensors at a depth, such as Aspen, 90 cm show a strong linear correlation between sensors (central trend) with occasional hysteresis traces outside of the central trend. Shallow paired sensors such as at Low Sage and Treeline (Figure 3) show much greater variability in Θ around the central trend. These features result from the temporally local hysteresis between sensors during input events, repeated over the annual period of changes in Θ.

Comparison of plots of raw data in the upper panel of Figure 3 with the log transformed frequency colormaps in the lower panel demonstrates the greater visual support of the transformed data for identification of attractor values. Whereas, the point values can be selected directly from the frequency value matrix, as was done to identify attractors for the upper panel, the colormaps simplify the interpretation of the frequency value matrix. In Figure 3 (lower panel) dry attractors for the period of record are clearly shown as dark red points in the colormaps, often near the minimum Θ, and are generally surrounded by a set of high frequency values which may include two or three modes. Similarly, the period of record wet attractor value is often diffuse, with weak frequency modes for the Aspen (silt loam) and Low Sage (clay loam) sites, but with a more distinct attractor for the Treeline (sandy) site. Variability between sensors extends to Θ_fs, which varies more by depth and year than the other paired analyses because it is an extreme value. The minimum and maximum of annual estimates (Table 2) bound the period of record estimates, and provide an approximation of the range in variability of the determined values. For the Treeline site, the range in annual estimates for individual sensors within the paired sensor configuration was zero to 0.02 Θ for both the attractors and Θ_fs, likely due to the high sand content at this site. At Low Sage and Aspen, the range increased progressively to 0.01–0.05 Θ and 0–0.11 Θ, respectively, primarily due to annual variability in Θ at depth. Spatial differences in Θ(t) resulted in variance from unity slope (1.00) for many sites and depths, but were similar within soil texture class: For the Aspen and High Sage sites the slope of the relation between paired sensors increased from a slope of 1.00–1.03 near the soil surface to as much as 1.33 at depth. At Low sage the slope of the relationship ranged from 1.10 to 1.19 from 10 to 40 cm depth, and 1.36 at 50 cm, in the C horizon, which is very stony. The Treeline and Lower Weather sites have low bulk density surface soil, with frequent macropores the slope of the trend at 5 cm depth (1.17–1.29) is much greater than for the deeper, stony soils (1.12).

Hysteresis plots of Θ for period of study data at Aspen, Low Sage, and Treeline show more complex wet and dry data attractors than are shown for an annual cycle in Figure 2D. Figure 4 presents visualizations of hysteresis between shallow and mid-profile depths, mid-profile and deep sensors, and log transformed colormaps of selected plots.

Despite differences in soil depth, texture, annual water input from rain and snow, and vegetation cover types, the hysteresis plots for most sites are similar in form, with a few important differences. All hysteresis plots with a near surface measurement (e.g., Figures 2D, 4A–C) show a marked inflection in the drying limb, whereas hysteresis plots for lower depths (e.g. Figures 4D,E) are more triangular, with the constant slope of the drying limb extending to near the dry attractor, indicating more uniform drying across depth. For some sites (e.g., Figure 4F) the hysteresis plot can vary annually between these forms, depending on the timing of precipitation. As a result, the range of the wet attractor over the depth of the soil profile is from 0.13 to 0.08 Θ at Aspen and less (0.02–0.07 Θ) at drier sites such as Low Sage and Treeline (Table 3). Similarly, the distribution of Θ frequency values within the hysteresis loop is quite different among Aspen, Low Sage and Treeline (Figures 4G–I). The differences in the distribution Θ frequency is directly related to differences in depth and timing of precipitation and snowmelt and soil drainage rates for the different soil textures.

Figure 5 compares the range of estimated values for Θ_fs(Figure 5A), and the wet (Figure 5B) and dry (Figure 5C) attractors for selected soil depths at the study sites. Data are presented as maxima and minima of all estimates for time series, frequency, paired, and hysteresis analyses. Representative estimated values for each parameter were determined by comparison of the average of annual estimated values to period of record estimated values. Θ_fs values are equated to the maximum Θ found by long term (decadal) frequency analysis (Figure 5A) and exceed average values from the paired and hysteresis analyses by 0.02–0.16 Θ. For the wet and dry attractors, value estimates from the paired and hysteresis analyses are often similar, despite differences in range, both of which are narrower than the value ranges for time series and frequency analyses (Figures 5B,C). The representative estimated value was determined as the most common value among period of record estimate, the average value of annual estimates of paired analyses, and the average value of six period of record hysteresis estimates. This approach generally resulted in a set of values which differed by <0.02 Θ. Context for the results in Figure 5 is provided by Θ estimates at 0 kPa, 33 kPa, and 1.5 MPa for the various soil textures by a commonly used pedotransfer function (Saxton and Rawls, 2006).

The inherent uncertainty in the determining representative attractor values is complicated by physical heterogeneity in soil properties and the somewhat subjective assignment of a single value from within a data attractor that may be weak, have multiple maxima (Figure 4G) or a wide value range (Figure 4H). Figure 6 provides a summary of data attractor results from Figure 5 with the addition of estimated point values of Θ_ws, determined as single values from time series analysis. The Θ_ws values ranged from 0.07 to 0.37 among sites, with the values from Treeline and Lower Weather ranging from 0.06 to 0.10, slightly less than or equal to the values determined by Smith et al. (2011) for sites in Dry Creek watershed. The Θ_ws values ranged from a seven to 38% of the difference between PEL and FC.

Table 4 compares estimated values of wet and dry attractors to data from soil water retention curves, field tensiometry and an intensive soil irrigation, and drainage experiment. We found that the example dry and wet attractors for Aspen and Treeline sites are equivalent to FC and PEL, respectively. Figure 7 shows the soil water retention curves for Aspen for samples from 1–3 cm (blue) and 41–43 cm (brown) and field tensiometer data at 60 cm (black). The wet attractor Θ values for both depths at Aspen (0.41, 0.41) nearly matched the Θ value (0.42, 0.42) at 10 kPa, commonly used as an approximation of FC. Similarly, the dry attractor Θ values (0.13, 0.13) for both depths at Aspen nearly matched the 1.5 MPa Θ values (0.12, 0.12). For Treeline at 60 cm the hysteresis method wet attractor Θ (0.21) compares well with the measured Θ (0.19) corresponding to a tensiometer value of 10 kPa. Although, not exhaustive, this evidence strongly supports the hypothesis that data attractors represent FC and PEL, and that other important soil hydrologic parameters can be determined from Θ records for sites with different soils, wetness and plant cover.

Additional inspection of Figure 7 and results from the frequency analysis of Θ are presented here to clarify the interpretation of Θ_s, and Θ_fs. For the Aspen the laboratory saturated (0 kPa) Θ ranges from Θ_s of 0.64 at 1–3 cm to 0.50 at 41–43 cm depth. The frequency method estimated value of Θ_fs at 10 cm depth (0.55) falls between these values and is substantially less than Θ_s for the soil surface measurement. This difference is likely due to either a decrease in soil porosity between 2 and 10 cm depth or a difference between Θ at Θ_s and Θ_fs. At greater depth the difference between the frequency method value for Θ_fs at 60 cm (0.51) and the value at for 0 kPa at 41–43 cm (0.50) is negligible, indicating Θ_fs is equivalent to Θ_s at these depths. For sandy soils at Treeline, constant irrigation achieved Θ_s at 60 cm (Θ = 0.39) and upon drainage, the air entry value (0.36) was similar to Θ_fs (0.34) as determined by the frequency method.

Saturation was uncommon in our data. All of the study sites are well-drained and did not show evidence of a water table. Therefore, it is not surprising that we found no attractor around saturation. However, near surface soil pipes and macropores may intermittently fill and appear as data outliers. This may explain why the maximum measured values of Θ can be quite different from the pedotransfer function estimates of saturation, especially near the soil surface. Results from our analyses for Aspen and Treeline sites show maximum Θ (Θ_fs) values of 0.55, 0.51, and 0.34 (Table 4) from controlled experiments and values of 0.64, 0.50, and 0.39 from field measurements. The difference in peak saturation for shallow soil at Aspen may arise from differences in porosity between the surface 3 cm and at 10 cm depth, or the greater capacity for occluded soil gas below the very dense mat of fine roots within above the mineral soil. We note that complete saturation of soils requires extensive irrigation, either in the field (Ellis and Lee, 1919; Hillel et al., 1972) or laboratory (Hazen, 1892; Watson, 1966) to ensure near complete removal of gas from the soil pores. Analysis of both laboratory and field measurements should be repeated for multiple depths in the soil profile.

At most sites, field saturation, Θ_fs, is a transient state achieved during infrequent periods of high flux and can range from FC to Θ_s in annual records (Figure 8). Assuming a consistent pore size distribution over time, it is logical to select the greatest recorded in situ value as Θ_fs either as a tail of the frequency analysis over the period of record. This selection requires judgment to determine if the extreme value is a valid measurement point or an artifact of measurement. This is likely an appropriate proxy value (Figure 5A) for most modeling purposes as long as the site remains freely draining. Θ_fs decreases with depth for all sites except Low Sage (which had a strong textural contrast), presumably in response to decreased porosity, decreased organic matter increased occluded volume by gravel or attenuation of flux by storage. These effects are lumped by the approach presented here. Due to the dependence of Θ on flux for well-drained sites, determination of Θ_fs is likely improved with longer data series and shorter time step data, especially for semi-arid or drier sites.

The most consistent representation of FC often corresponded with the intersection of the wetting and drying limbs of the hysteresis loops (Figure 2D) and near the low edge of the wet data attractor in the paired analysis, as shown for Aspen and Treeline (Figure 3). These constraints on selection of FC recognize that this attractor requires that soil wetting is followed by a period of several days with no evaporation. Therefore, FC is most evident after cool season precipitation events, which are dominant in the study environment. During snowmelt, radiation and temperature patterns drive diel fluctuations of melt water flux to the soil that can to lead to positive bias in estimation of FC.

We found very similar values for FC at all depths within Aspen, Treeline, and Lower Weather but variability in FC with depth at High Sage and Low Sage (Figure 6). Although, texture is a first-order control on FC, the values from our analyses were often quite different from the pedotransfer function predictions, and even the same texture: FC at High Sage ranges from 74 to 82% of FC at Aspen for the surface and deep sensors, respectively, which is remarkable, given the close proximity and nearly identical soils at these sites. The difference in attractor values between Aspen and High Sage is due to the different soil water input environments. Aspen site is located beneath a seasonal snow drift that is typically 3 m deep. This results in extended periods during which daily water inputs from snowmelt maintain soil water contents at values greater than FC. Winter snow cover at High Sage site is typically 50 cm. It therefore melts much earlier and is subject to periodic cool season rainfall events that allow for drainage to FC, thus shifting the attractor downward to a value more consistent with the concept of FC. The pedotransfer function predictions appear reasonable (with hindsight) for sites other than Aspen (Figure 6), but appear to correspond better to Θ_fs values presented for Low Sage and Treeline. These differences in representation of the mobile water fraction in soil are likely attributable to soil plant interactions such as litter cover and secondary soil structure and are important for careful parameterization for ecohydrological models.

PEL, like Θ_ws is an ecohydrologic parameter that represents an interaction among plant phenology, the surface energy balance, and soil water potential. For this study, the land surface cover is dominated by perennial vegetation with varying extent of litter and bare soil across sites, soil water input is primarily derived from spring snowmelt resulting in an extended dry growing season, and peak PET is in July (Seyfried et al., 2011). These conditions, in conjunction with the low mean annual precipitation outside of snow drifts all facilitate very dry soil states required for development of an attractor at PEL. The dry attractor values in this study were generally slightly less than those predicted by the pedotransfer function, and converse from Θ_fs, tended to increase with depth.

Our initial premise was that PEL at any depth is represented by a constant value of Θ for an extended period during the growing season, as shown for Treeline and Low Sage (Figure 8). For other sites, PEL may not be consistently represented across years for either the shallow or deep sensors for two reasons: First, Aspen is often energy limited and retains water at depth in most years, only achieving PEL in 2003, 2007, and 2012 (Figure 8). Similarly, other sites with insufficient energy to evaporate the mean annual precipitation are unlikely to reach PEL at depth. Second, Θ less than PEL commonly occurs in near surface soils. Records from Treeline and Lower Weather show Θ as low as 0.01 for sensors at 5 cm depth, but a PEL of 0.06 to 0.08 at depth (Figure 8). Evaporative drying near the soil surface can decrease Θ below PEL. In this case, when the evaporative potential at the leaf surface is balanced or exceeded by soil water tension, plant water use is negligible and vapor diffusion governs evaporation (Buckingham, 1907; Salvucci, 1997). This transition from viscous capillary (S1) to vapor diffusion (S2) control on evaporation (Brutsaert and Chen, 1995; Lehmann et al., 2008) is apparent in data, and complicates the interpretation of the dry attractor and PEL.

Thus, interpretation of the range of the dry attractor requires consideration, as with the wet attractor. Lower Weather receives the greatest energy and least precipitation among the study sites, and has coarse textured soils with a nearly bare surface, making it a good case study for dry soils. Initial estimates of the dry attractor Θ range from 0.04 at 15 cm to 0.08 at 100 cm (Figure 8). The much lower values of the dry attractor for 5 cm sensors at 0.00 < Θ < 0.02 (Figure 8) likely represents the limit of evaporation via vapor diffusion near the surface, for the available seasonal energy. We found a gradient 0.00 < Θ < 0.08 develops from 5 to 100 cm depth in response to the vapor diffusion gradient above PEL at 100 cm depth. These observations lead to the conclusion that near the soil surface, the shift from evapotranspiration to evaporation below PEL is difficult to distinguish using a data attractor.

Important features of soil drying below FC include the initiation of plant water stress, Θ_ws, the endpoint of plant water use, PEL, and the transition to evaporative drying by vapor diffusion. We found that the semi-arid climate of the study sites provided ideal conditions for soil drying through spring and summer, as shown by a nearly constant drying trend over approximately the middle half of the range in Θ for all sites (except Low Sage). Yet, a notable difference is evident between drying patterns for shallow and deep sensor locations: Soils at depths of 15 cm or less dried first and fastest at near steady state from below FC to near PEL (Figure 8). For soils below 15 cm the drying function Θ(t) was quasi-sinusoidal between FC and PEL, with a shift to faster drying when the shallow sensor reached Θ_ws. We attribute this initial increase in the rate of deep soil drying to consistent (energy-limited) plant water use from a smaller storage volume following surface drying below Θ_ws. For all sites, Θ_ws occurred annually for the shallow sensor depths, but was less consistent for the deep sensors. For example, Θ records from the deep sensors Aspen and High Sage regularly show linear declines until approximately Oct 1, when the water year ends with the onset of freezing nighttime air temperatures and abrupt termination of plant water use at these high elevation sites, e.g., WY 2008–2010 (Figure 8). Thus, as Θ_s may not be consistently achieved due to surface infiltration rates that seldom exceed soil profile drainage flux, Θ_ws may not be consistently achieved due to insufficient seasonal energy. Yet, the occasional dry years (e.g., WY 2006) at Aspen and High Sage are clearly water limited and are sufficient to estimate Θ_ws for the high elevation sites. Low Sage and the lower, elevation Treeline and Lower Weather sites are annually water limited and show consistent inflections indicating Θ_ws during July and August with values ranging from 0.20 for the deep clay soils at Low Sage to 0.07 for deep soils at Treeline (Figures 6, 8).

One approach to the uncertainty in evaluating contemporaneous soil moisture states is to visualize Θ(z) at a daily to weekly time step. Figure 9 shows Θ(z) for wetting and drying periods over one water year at Aspen and Treeline. Although, this approach is somewhat difficult to implement over multiple years, it provides insight on the gradation of soil hydrologic properties with depth and the different dynamics of wetting and drying across sites. This type of diagram is common in texts, but typically focuses attention on the dynamics of wetting and drying, rather than the predominant soil moisture states. For both sites, a vertical profile at FC emerges after the wetting front arrives at the base of the soil. Yet Θ(z) may not reach Θ_fs, as determined from the long term record for any depth in a given year. During soil drying, similar increasing gradients in Θ(z) emerge slightly below FC at both sites in response to plant water use, and indicate a rapid decline in drying associated with Θ_ws, near PEL. The much sharper inflection in Θ(z) near the soil surface at Treeline than Aspen reflects the difference in surface evaporation between sites. Finally, the much broader band of overlap among Θ(z) profiles at Treeline reflects the longer period and greater depth of plant water stress at that site.

Each approach to determining soil hydrologic properties has a different bias, but all are in general agreement. The applicability of measured data for this model parameterization depends on the nature of soil water dynamics under consideration. Selection of specific values for the wet and dry attractors by time series analysis is more subjective than by frequency analysis, as it depends on selection of a single value from a range of Θ near the extreme values. The two depth hysteresis method provides estimates that closely match the Θ at standard soil water potential values commonly used to define FC and PEL. The improvement over the other methods for determining these wet and dry attractors is related to the reduced overlap between valid data, and the invalid data and data errors which can skew the frequency distribution of the attractor. In particular, the juxtaposition of Θ for a sensor depth (a) with stable Θ to a sensor at a different depth (b) with either increasing or decreasing Θ develops a linear trace toward a point of inflection where the rate of change in sensor a increases and sensor b decreases. The relatively slow rate of change near the inflection enhances the frequency of (a,b) data at the attractor. Error values tend to fall at the margins of the hysteresis loop which reduces error distortion of the main attractors (e.g., Figure 4). Unlike the hysteresis analysis, the paired sensor approach can also be biased by any temporal lag in wetting front depth between the sensors.

Soil depth and cover effects are clearly represented in the presented analyses. We found the sites with very well drained soils (Treeline, Lower Weather) showed less uncertainty in Θ_fs and FC near the bottom of the soil profile (Figure 5), likely as a result of faster transit times and less retention. Similarly, the control of surface cover on evaporation is clearly represented in general across sites. PEL is not strictly a soil property, but also depends on vegetation where roots are active. The soil at High Sage has the same texture as Aspen, but the surface cover is dense shrub canopy 0.5–1.5 m over with 2–5 cm of litter and bare interspace and associated decreasing values of PEL at 60 cm (0.10) and 10 cm (0.08). This cover appears to effectively limit surface evaporation. Low Sage has a soil textural gradient from silt loam to clay loam and a bare soil surface and results in the strongest gradient in PEL (0.07–0.14) over the least depth of soil, 50 cm. Treeline and Lower Weather are both sandy sites with shrub cover and low bulk density surface, which supports extensive drying. Difference in PEL following vegetation removal by prescribed fire in 2007 are clear at the Aspen and High Sage sites.

There are two primary effects. First, electronic soil water sensors are based on relating measured permittivity to liquid water content, which is generally a robust relationship because the permittivity of liquid water (80) is so much greater than soil (5) or air (1). However, the permittivity of ice (3.1) is very similar to that of air, so frozen soil appears to have less water content and effectively approximates the liquid water content of the soil (Seyfried and Murdock, 1996). This effect is apparent when dramatic “drying” events during the winter appear as noise and stray from the FC attractor. Freezing effects are apparent in all four panels in Figure 2 and can be clearly seen by comparison of the soil moisture trends at 15 cm and 30 cm in Figure 9. Second, freezing effectively reduces the soil water potential. When the near-surface soil freezes, the normal downward hydraulic gradient is reversed and water moves upward toward the freezing front. This can cause either an increase or decrease in the measured soil water content, depending on the proximity of the sensor to the freezing front (Hillel, 1980). These are most pronounced near the soil surface, which commonly freezes in this environment. In this study the freezing front rarely exceeded 30 cm. There is evidence of occasional upward gradient effects apparent deeper in the soil profile. These artifacts can introduce erroneous data into the analysis. This is more problematic for the frequency and paired analyses, in which the surface sensors are likely to be similarly affected, but less important for the hysteresis analysis. We suggest that soil temperature records, which are commonly collected along with TDR or other soil moisture measurements, could be used to censor data during periods of soil frost prior to conducting the presented analyses.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.