Soil Science Society of America Journal 65:1659-1666 (2001)
© 2001 Soil Science Society of America
DIVISION S-1 - SOIL PHYSICS
Soil Water Characteristic Determination from Concurrent Water Content Measurements in Reference Porous Media
Jon M. Wraith*,a and
Dani Orb
a Land Resources and Environmental Sciences Dep., Montana State Univ., P.O. Box 173120, Bozeman, MT 59717-3120
b Plants, Soils, and Biometeorology Dep., Utah State Univ., Logan, UT 84322-4820
* Corresponding author (jwraith{at}montana.edu)
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ABSTRACT
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We introduce and verify the use of calibrated reference soils or other porous media having known and reproducible water retention characteristics as a means to determine the unknown water retention properties of soils in situ. Pockets of the reference soil may be buried at experimental soil locations, with embedded time domain reflectometry (TDR) probes in both the target and adjacent reference media. Monitoring changes in water content by TDR allows inference of the soil water characteristic (SWC) properties of surrounding soil in hydraulic equilibrium via the known reference media SWC relationship. An expression relating the van Genuchten retention coefficients of any two paired porous media is used to estimate the unknown coefficients. Advantages include in situ measurements across the entire soil wetness range, an ability to closely match pore-size distributions (hence hydraulic continuity) with a wide range of porous media, and measurement efficiency based on using the same instrumentation for all measurements. Seven different soils were used in experiments conducted in a laboratory pressure plate apparatus, a greenhouse, and the field. Soil water characteristic relationships obtained using the reference soils approach were generally similar to those measured using pressure plate apparatus. Potential operational concerns include realizing consistent bulk densities for the buried reference soil pockets, and ensuring that water content (
) measurements are obtained near effective saturation in field applications. Practical utility of the proposed method may be enhanced by identification or manufacture of a range of reference porous media having reproducible SWCs, e.g., that are invariant under different packing conditions.
Abbreviations: h, pressure head • Ka, dielectric constant • SWC, soil water characteristic • TDR, time domain reflectometry • VG, van Genuchten model • , water content
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INTRODUCTION
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THE SWC FUNCTION , (h), describes the relationship between water content () and matric pressure head (h) under equilibrium conditions in variably wetted soils or other porous media (Or and Wraith, 1999a). The SWC is a primary soil hydraulic function and is required to predict water and chemical flow, to manage irrigation water, and to undertake many other soil and land management endeavors. The term water retention is conventionally used to identify the desorption, or drying, portion of the water characteristic function, and is more commonly measured than is the full relationship. Hysteretic response generally means that the wetting and drying curves are not identical, with the magnitude of differences depending on soil properties, wetness, and wetting history.
In situ measurements of (h) are highly desirable because of changes in pore-size distribution and pore continuity in collected samples which may substantially influence the measured SWC relationship, particularly near the wet end (h < 10 m) which is particularly important in many water flow processes. Common approaches to measuring (h) in intact field soils require paired and h sensors; however, most paired-sensor methods suffer from incompatibility in measurement range and in mismatched spatial and or temporal resolution of and h. For both field and laboratory measurement approaches, poor hydraulic coupling between porous ceramics, membranes, or porous matric sensors and soil can result in prohibitively long equilibration times (e.g., Gee et al., 1998; Or and Wraith, 1999b).
Time domain reflectometry provides a flexible means to measure at multiple locations, automatically, and without the requirement for soil-specific calibration in many cases. Precision of measurements is high in comparison with other methods. Lack of suitable h sensors has, therefore, remained the more limiting factor in obtaining improved paired-sensor (h) measurements. Or and Wraith (1999b) introduced a TDR-based porous matrix h sensor design, whereby porous ceramic and plastic disks having different known maximum pore sizes were stacked within a coaxial cage. The constant relationship between and h of the sensor's porous matrix was initially calibrated and subsequently used to infer the matric head of the surrounding soil, similar to porous heat dissipation or electrical resistance sensors. The of the sensor's porous matrix in hydraulic equilibrium with the surrounding soil was measured by TDR travel time analysis. Prototype sensors were constructed using disks having maximum pore diameters between 120 (corresponding to 0.25-m bubbling pressure using the capillary rise equation) and 
0.6 µm (50-m bubbling pressure). Or and Wraith (1999b) reported a tradeoff between the sensor's matric potential range and its sensitivity to changes in the surrounding soil. Additionally, they emphasized that a mismatch between the pore-size distributions of the sensor and the soil, mostly relevant to coarse-textured soils or media, can lead to hydraulic decoupling of these and other porous sensors.
Alternative TDR-based and h sensor designs were proposed by Baumgartner et al. (1994), Whalley et al. (1994), and Noborio et al. (1999). The first two designs relied on hollow TDR-probe conductors that functioned as tensiometers, thereby incurring the same functional constraints as conventional tensiometers, i.e., limited measurement range and a requirement for supply of water. Noborio et al. (1999) embedded a portion of single TDR probes in porous gypsum, with the remainder of the electrode rods surrounded by soil. The signal travel times through the two sequential media were separately analyzed to obtain their respective apparent dielectric constants (Ka). The Ka of the porous gypsum was calibrated against water content in pressure plate apparatus, similar to the approach of Or and Wraith (1999b). Both studies (Or and Wraith, 1999b; Noborio et al., 1999) identified a need for porous materials having a wide range of pore sizes as well as adequate equilibration times under conditions of rapid changes in soil wetness. These requirements are of course equally relevant to other sensors that equilibrate with soil wetness to infer hydraulic, thermodynamic, or thermal status.
This work extends concepts advanced by Or and Wraith (1999b) in using paired TDR sensors to obtain measurements of soil and h. To provide a flexible alternative to probes constructed using porous disks, we propose that previously characterized porous media having similar particle and/or pore-size distributions as those of soils or other media under investigation, may be used as the porous matrix for TDR-based h sensors. Use of reference porous media with TDR or other suitable measurements provides a number of desirable attributes often lacking in conventional sensors. These include ability to measure intact, undisturbed soils in the field, to measure across the entire soil wetness range, to measure and infer h with the same instrumentation, to match pore-size distributions of the sensor and target soils (i.e., maximize hydraulic continuity), and to automate continuous measurements for multiple field sensors. In sections below, we introduce and verify the concept of using calibrated reference soils or other porous media having known and reproducible water retention characteristics as a means to estimate the unknown (h) properties of soils in situ.
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MATERIALS AND METHODS
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Background and Theory
A commonly used parametric soil water retention model was proposed by van Genuchten (1980)(VG) as
 | [1] |
where 
and n are empirical fitting coefficients, h is matric head, and r and s are the residual and saturation water contents, respectively. The relationship between any two sets of VG water retention relationships is given by (Or and Wraith, 1999b)
 | [2] |
where mi = 
and subscripts 1 and 2 refer to the two media: two different soils, soil and porous sensor, etc. This provides an ability to use the known retention relationship for one porous medium, along with concurrent water content measurements for both media in hydraulic equilibrium, to infer the unknown water retention relationship (i.e., VG coefficients) for the second porous medium. One set of known retention coefficients is required to resolve the ratios 1/2 and n1/n2.
Hydraulic equilibrium for the target and reference soils is assumed. Although this is not always a good assumption for porous sensors as drying proceeds (Gee et al., 1998; Or and Wraith, 1999b), a distinct advantage of the calibrated reference soil approach is to facilitate selection of reference materials having pore-size distribution similar to that of the target soil, and hence obtaining similar hydraulic response times.
Laboratory Methods
Sieved and dried target and reference soils were packed in a pressure plate apparatus, with the target soils surrounding reference soils. About 1500 cm3 of each soil was used. Soils were wetted by gradual addition of water within the chamber until water and soil surface levels were equivalent. Volume water content was monitored for both soils subjected to multiple pressure steps in the range of 0 to 20 m, using two replicate TDR probes buried horizontally in each soil. Probes were three-rod type, 20 cm in length, with 2-cm rod spacing, and 0.32-cm diam. rods. Coaxial cables for TDR probes were extended through gas-tight openings machined in the pressure plate wall. WinTDR'99 software (available for download from the second author at http://psb.usu.edu/wintdr99/, verified 10 July 2001) was used for TDR control, waveform acquisition, and signal analysis. The Topp et al. (1980) empirical calibration relationship was used for all soils in this study (lab, greenhouse, field). Applicability of this relationship had been previously, and in many cases repeatedly verified for all soil materials used. Soils included a Brocko silt loam (Coarse-silty, mixed, superactive, frigid Aridic Calciustepts) and a Red-Yellow Oxisol (Latosolo Vermelho-Amarelo in Brazilian classification; Melamed et al., 1995). Compatible measurements for a Kidman loamy sand (coarse-loamy, mixed, superactive, mesic Calcic Haploxerolls) and a Millville silt loam (coarse-silty, carbonatic, mesic Typic Haploxerolls) collected within the same pressure plate apparatus as part of a previous study (Or and Wraith, 1999b), were also used. The resulting (h) measurements for each soil were fitted to Eq. [1] to derive best-fit retention coefficients. The measurements also provided an ability to independently predict (h) for either soil based on measured VG coefficients for the other soil (used as reference) plus paired measured for both probes, using Eq. [2]. Soil particle-size fractions are provided in Table 1.
Greenhouse Methods
Two rectangular plastic containers (33 by 50 by 20 cm deep) were filled with target soil, into which two reference soil pockets having known VG SWC coefficients were buried. All soils were sieved and dried before packing. Four three-rod TDR probes (20-cm length, 2-cm rod spacing, 0.32-cm rod diam.) were installed adjacent and horizontally, with the plane formed by the three rods parallel to soil surface. Probes were buried about 7 cm deep and 10 cm apart. Sensors buried in the target soil or reference soil pockets were interspersed within the containers. Reference soils extended about 2 cm beyond axial and radial limits of buried probes. Target soils included Flathead sandy loam (coarse-loamy, mixed Pachic Udic Haploboroll) and Amsterdam silt loam (Fine-silty, mixed, superactive, frigid Typic Haplustolls). Kidman loamy sand was used as reference (known [h]) soil with the Flathead, and Millville silt loam as reference medium with the Amsterdam soil. Soil water retention was previously measured for the two target soils using a pressure plate apparatus, in the h range of 0 to 150 m.
The soils were wetted to effective saturation by sequentially ponding water, with one side of the container initially raised above water level to facilitate exit of soil gas. Evaporative drying was enhanced by a small fan blowing across the soil surface. Several rewetting then drying cycles were imposed over a 2-mo period. A computer-controlled automated TDR system (Tektronix 1502C cable tester, Tetronix, Beaverton, OR; Campbell Scientific SDMX50 coaxial multiplexer, Campbell Scientific, Inc., Logan, UT; WinTDR'99 software available for download from the second author at http://psb.usu.edu/wintdr99/, verified 10 July 2001) measured and recorded soil water contents at 1-h intervals.
Field Methods
Time domain reflectometry probes were installed at a field location 13 km (8 miles) east of Helena, MT, as part of a separate study. Soils at the field site supported mixed native grasses, sagebrush (Artemisia L. spp.), and spotted knapweed (Centauria maculosa auct. non Lam.) vegetation. Paired adjacent TDR probes (30-cm length; other specifications as above) were buried about 7.5 cm apart at 5-cm depth in four plots, with access from the vertical face of small excavated pits. One probe of each pair was placed in a pocket of sieved reference soil, and the other inserted directly into the target soil. Amsterdam silt loam was used as reference soil for the local Rothiemay loam (fine-loamy, mixed, superactive, frigid Aridic Calciustolls) target soil.
Soil water contents were monitored at 6-h intervals over about 90 d, from late May to late August of 1999, with automated TDR (Tektronix 1502C, Tektronix, Beaverton, OR; Campbell Scientific 21X datalogger and SDMX50 coaxial multiplexer, Campbell Scientific, Inc., Logan, UT). The location experienced a gradual summer drydown through early August, except for a single convective storm that wetted the soils by about 0.05 volume water content at the 5-cm measurement depth during early June. Following this, two rainfall events during August increased measured by about 0.05 then 0.15 m3 m-3, respectively.
Calculation of Van Genuchten Soil Water Retention Coefficients
Concurrent paired measurements for reference and target soils were used along with known (fitted) VG coefficients of the reference soil to infer VG (h) of target soils using Eq. [2]. Nonlinear least-squares optimization (Wraith and Or, 1998) was used to fit all relationships, including fitting pressure plate (h) measurements to the VG function, and fitting known reference soil VG coefficients plus paired series for each soil to Eq. [2].
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RESULTS
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Because saturated or near-saturated conditions were not attained in some of our trials (e.g., field measurements), the target soil measurements did not include this critical wet range. Fitting an appropriate value for saturated water content (s) thus required fixing or constraining this parameter during the optimization process. Note that the known reference soil s does not provide sufficient information via Eq. [2] to infer the unknown target soil s. We therefore estimated s as calculated using bulk density for cases where the measured for target soils did not approach saturation.
Laboratory Measurements
Concurrent measurement for two soils in the same pressure plate apparatus during imposition of pressure steps provided a continuous desaturation time series (Fig. 1)
. The measurements of replicate probes in each soil were similar, confirming expected spatial similarity of water contents. Retention relationships for the Brocko and Oxisol soils derived using Eq. [2] were similar to those obtained using only the pressure equilibrium (h) steps from the same desaturation process (Fig. 1) as is conventionally done (except that measured for each pressure step were obtained using the embedded TDR probes rather than oven drying). Differences between the retention relationships measured using the two approaches were evident mainly in the h range from 0.8 to 5 m (Fig. 1c). Fitted VG (van Genuchten, 1980) soil water retention equation coefficients are provided in Table 2.
For the Millville-Kidman soils combination, measured during a previous study which included two consecutive desaturation sequences, paired for the two soils were available only at the pressure equilibrium steps. These were sufficient to obtain fitted VG retention relationships for both soils using the conventional and reference media approaches. Resultant (h) relationships were similar (Fig. 2)
, with some deviation between the two methods in the h range from 0.5 to 1 m for Kidman loamy sand, and h > 7 m for Millville silt loam. We fixed s during the optimization process for these two soils because measured for Millville was substantially greater than for Kidman and hence the Kidman reference soil did not cover sufficient range for the finer-textured Millville soil.
Greenhouse Measurements
The measured time series for Kidman soil illustrates more precipitous loss of water on drying than for the paired Flathead soil (Fig. 3a) , while patterns for the Amsterdam-Millville soils combination were more alike (Fig. 3b). Good agreement was observed for replicate TDR-probe measurements in all soils.
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Fig. 3. Measured time series for two replicate TDR probes in target and reference soils within the same containers (for each soil pair) in greenhouse trials. Every second data point plotted to improve clarity. For top panel (a) Kidman loamy sand reference soil pockets were buried within Flathead sandy loam, and for bottom panel (b) Millville silt loam reference soil pockets were buried within Amsterdam silt loam soil.
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Soil water retention for the Amsterdam silt loam soil measured using Millville silt loam reference soil in the greenhouse trial was comparable with two (h) relationships measured at different times by different investigators in pressure plate apparatus (Fig. 4)
. The reference-fitted (h) was intermediate between results of these two previous investigations, which used soil taken from the same storage container as used in the present study. One of the pressure plate retention curves was measured using gravimetric determination (converted to volumetric rather than mass water contents for consistency) while the other was obtained using two replicate embedded TDR probes. However, the different water content determination methods do not explain the substantial disparity between these curves, as we have repeatedly verified the TDR calibration relationship for this soil. The optimized r for the reference-fitted (h) was substantially lower than for the two pressure plate relationships (Table 2) even though the s were similar; this appeared to be functionally offset by fitted VG coefficients and n.
The Flathead retention relationship measured using the Kidman reference soil (Fig. 5a)
was more abrupt than was that measured in pressure plate apparatus (Fig. 5b). For the reference-fitted (h) relationship most water was lost between about 1 and 3 m, while that from the pressure plate exhibited a more gradual decrease in with increasing matric head. This may have been partially a result of using the coarser Kidman soil as reference, as the resultant Flathead (h) exhibits characteristics of a relatively more coarse porous medium.
Field Measurements
A portion of paired reference and target soil information was missed during the field measurements, as the automated-TDR system was transferred to another study location for part of the summer (Fig. 6a)
. However, when aggregated over the course of the season the measured were continuous throughout the wetness range encountered in the field (Fig. 6b). These measurements facilitated fitting of VG (h) coefficients for the target Rothiemay soil based on concurrent measured Amsterdam reference soil water contents and known Amsterdam soil VG coefficients (Fig. 6c). The reference-fitted (h) relationship for Rothiemay soil was very comparable with the one previously obtained using a pressure chamber (Fig. 6).
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DISCUSSION
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An initial equilibration period of one or a few wetting and drying cycles was required to obtain consistent reproducible measured relationships for the paired adjacent target and reference soils, in the pressure plate apparatus, greenhouse, and field trials. This was particularly true for the Flathead-Kidman combination, which did not appear to be a good hydraulic match. Most of the change in water content for the coarser Kidman soil occurred over a narrow range in changes for the Flathead soil (Fig. 5). This emphasizes the importance of matching reference and target soil retention properties, and is considered as equally relevant to design or application of other porous sensors where use of construction materials having hydraulic properties geared towards particular media under investigation may be more problematic.
Elucidating specific desired characteristics for paired reference and target soils a priori will likely require some additional theoretical and experimental investigation. For our studies, the Kidman loamy sand did not seem to provide a good match to the Flathead sandy loam or the Millville silt loam soils. Strongly nonlinear – relationships were measured for these two soils combinations (Fig. 2a, Fig. 5a), perhaps implicating this as a useful indicator criterion (we thank an anonymous reviewer for bringing this to our attention). We did not undertake a priori soils evaluations in selecting the paired target and reference soils used in this study. Rather, we selected for pairing those soils having reasonably similar textures from among those for which we had existing (h) measurements. In most cases, this approach provided fitted (h) comparable with those measured using pressure plate apparatus, supporting potential utility of the proposed new measurement approach.
Some design or operational considerations merit discussion. Constant physical properties (e.g., packing) of reference porous media is a primary requirement to ensure consistent soil water retention relationships as characterized by the fitted VG coefficients. This is reasonably ensured for rigid porous matrix sensors, but not for the method suggested in this paper which utilizes unconsolidated porous media for the calibrated sensor body. It appears that pretreatment by inducing one or a few cycles of wetting and drying greatly improves hydraulic contact and results in a more stable (and probably more reproducible) structure. Issues of packing are common to most standard methods for soil (h) determination (e.g., pressure plate) as evidenced by the differences depicted in Fig. 4b. This and other porous matric sensor designs rely on an inherent assumption of continuous hydraulic equilibrium between target and reference media, in contrast to pressure chamber methods where equilibrium is assumed only after waiting a sufficient time. Responsiveness of target and reference soils to changing wetness was similar for most paired soils, based on our measured time series. Hence, we believe an assumption of hydraulic equilibrium during routine use is tenable except in cases of large reference media volumes, substantial textural mismatch, or other situations where similar response times for changes in matric head are not expected. To ensure lack of sensitivity to surrounding target soil wetness, sensing volume could be explicitly constrained to the reference media by use of a screen enclosure (Wraith and Baker, 1991) or similar device to confine the TDR measurement.
Similar to our experiences, saturated or near-saturated conditions may not be expected in many field applications. Because the paired target and reference soil measurements would therefore not include this critical wet range under these conditions, the target soil s may need to be fixed near its porosity or similar meaningful magnitude during the optimization process, as was done for some cases in this study. Alternatively, we recommend that adjacent target and reference soil volumes be thoroughly wetted at least one time following emplacement. This serves the compatible purposes of settling the reference medium to more stable (reproducible) consistency, enhancing hydraulic contact between the two porous media, and ensuring concurrent measurements of near-saturated in both soil volumes. Wetting following emplacement is commonly done with tensiometers and with other porous matrix sensors to achieve similar objectives.
The (h) relationships measured in this study, using the reference porous media approach and from conventional pressure plate apparatus, were similar in most cases but never identical. Our abilities to provide quantitative inference regarding bounds on uncertainty associated with the several VG coefficients were constrained because of limited sample size. This translated into lack of a statistical measure for the degree of similarity among any two SWC relationships. Such inferences are further confounded by inevitable variations in the status of the soil samples themselves (e.g., packing, consolidation, phase entrapment) among the various tests, methods, and replicates. Repeatability of measured (h) has not been specifically studied to our knowledge, but we speculate that different individuals or laboratories, and different measurement apparatus or sensors, will render only moderate consistency of such measurements. For example, more than 20 different pressure plate measurements at 3.3- and 150-m matric pressure on the same soil by the same person over a 5-yr period in one university soils analysis laboratory with which we are familiar (and have confidence in procedures and protocols used) showed about 20% range in measured (J. Kotuby-Amacher, USU Soil Analytical Laboratory, personal communication, 2001). Such laboratory pressure plate apparatus measurements would likely be considered as a baseline approach, though these are recognized to be inaccurate indicators of field soil responses at the wet end because of soil disturbance during preparation. Loss of hydraulic contact between soils and porous plates or membranes may be an additional source of inaccuracy during routine use (Gee et al., 1998). Changes in fidelity of measured (h) resulting from disturbance of native soils during preparation for pressure plate measurements, and those resulting from lack of consistency in packing reference soil pockets are both expected in the range of h from 0 to 10 m. The at h > 10 m is primarily a result of wetted surface area rather than pore-size distribution (Or and Wraith, 1999a; Tuller et al., 1999; Or and Tuller, 1999). We therefore propose the reference porous media methodology as a viable alternative that is theoretically sound, applies in-situ, spans a wide range of or h, covers both wetting and drying, and is simple and economically viable. More definitive consensus concerning its practical utility will require extensive additional exploration.
A hysteretic influence on measured water contents during sequential wetting and drying is expected for many soils and other porous media. The approach demonstrated here for the greenhouse and field trials provided an averaged soil water characteristic that did not specifically discriminate the wetting and drying relationships. This may be a superior soil hydraulic relationship relative to the conventionally used desorption curve, for many applications including simulation modeling. In concept, reference porous media could be calibrated such that the drying and wetting branches (envelope) were known, and subsequently used to infer these same relationships for the target medium by concurrent measurements during drying from saturation and wetting from dry conditions, respectively.
Relative advantages of the reference porous medium approach include ease of use, low expense, and resultant flexibility particularly for many field applications. For example, the concept could be effectively used in a borehole to profile (h) of soils or formations. One probe could be inserted into the native material and another in a refilled section above, then sequentially recovered and moved deeper. Burial of reference soil pockets need not alter the in situ pore-size distribution of adjacent target soils. Measurements on intact soils, along with flexibility to optimize hydraulic continuity through compatible pore-size distributions, are probably the greatest potential advantages of the proposed method. Other sensors having desirable measurement attributes, such as dual probe heat pulse (Song et al., 1998; Bristow et al., 2001), could be used in place of TDR. The latter sensors would provide an ability to make the reference soil pockets substantially smaller in size, for example.
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SUMMARY AND CONCLUSIONS
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The concept of using calibrated reference porous media to infer unknown soil water characteristic relationships of target soils was introduced and verified using laboratory, greenhouse, and field measurements. The method may be used to obtain both wetting and drying relationships in contrast to many conventional techniques which generally provide only the desorption response. Use of calibrated reference media has several important advantages over alternative approaches. Among these are in situ characterization of intact soils, ability to measure over the entire soil wetness range, measurement economy in using only paired TDR (or alternative) sensors, and ability to maximize hydraulic continuity between the sensor and target soil through selection of reference media properties. Our measurements indicated that the ability to capture continuous paired over the entire wetness range using automated systems may provide more representative (h) than using pressure steps alone, as intervening information concerning sorption and desorption behavior is maintained. Potential limitations include realizing consistent bulk densities for the buried reference soil pockets, and obtaining measurements near (effective) saturation for some field applications. Initial wetting of target and reference soils following emplacement is recommended to address the latter issue, to maximize hydraulic contact, and to consolidate the reference soil medium thus resulting in a more consistent and repeatable pore-size distribution. Reproducibility of the proposed paired sensor method might also be enhanced by fabrication of well-characterized, cylindrical, soil or other porous media packets enclosed in water-permeable liners. Alternatively, use of porous materials having (h) that is relatively packing-invariant should be explored. Examples may include quartz powder, very fine sands, and zeolites.
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ACKNOWLEDGMENTS
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Partial funding for this study was provided by the Montana Agricultural Experiment Station, the Utah Agricultural Experiment Station, and the Israel-U.S. Binational Agricultural Research and Development Fund (BARD) through grant no. IS-2839-97. Approved as MAES contribution no. J-2000-93. Three careful anonymous reviews leading to an improved manuscript are appreciated.
Received for publication January 31, 2001.
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TOP
ABSTRACT
INTRODUCTION
