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Soil Water Hysteresis at Low Potential
Pedosphere 17(4): 436–444, 2007 ISSN 1002-0160/CN 32-1315/P c 2007 Soil Science Society of China Published by Elsevier Limited and Science Press
Soil Water Hysteresis at Low Potential L. PRUNTY and J. BELL Department of Soil Science, North Dakota State University, Fargo, ND 58105 (USA). E-mail: [email protected] (Received December 19, 2006; revised May 17, 2007)
ABSTRACT Knowledge of the soil water characteristic curve is fundamental for understanding unsaturated soils. The objective of this work was to find scanning hysteresis loops of two fine textured soils at water potentials below wilting point. This was done by equilibration over NaCl solutions with water potentials of −6.6 to −18.8 MPa at 25 ◦ C. When cycled repeatedly through a series of potentials in the range noted previously both soils exhibited a hysteresis effect. The experimental differences in water content between the drying and wetting soils at the same water potential were much too large to be accounted for by failure to allow sufficient time to attain equilibrium as predicted by the exponential decay model. The wetting versus drying differences were relatively small, however, at only 4 mg g−1 or less in absolute terms and about 3% of the mean of wetting and drying, in relative terms. Hysteresis should be a consideration when modeling biological and physical soil processes at water contents below the wilting point, where small differences in water content result in large potential energy changes. Key Words:
adsorption, dry soil, equilibration, matric potential, soil water characteristic
Citation: Prunty, L. and Bell, J. 2007. Soil water hysteresis at low potential. Pedosphere. 17(4): 436–444.
INTRODUCTION The dependence of soil water content on matric potential, represented graphically as the soil-water characteristic curve (SWCC), has long been recognized as hysteretic. Scanning hysteresis near saturation or at matric potentials near zero can be pronounced and has been studied rather extensively. Relatively little mention is found in the literature about hysteresis in the SWCC at matric potentials lower than a few tenths of a megapascal below zero. Jackson (1964), an exception, does present adsorption-desorption plots for two soils spanning nearly the complete relative humidity range, 0 to 100 percent. Puri et al. (1925) did early work that included some observations of hysteresis. Gillham et al. (1976) showed experimentally determined hysteresis of the SWCC for a dune sand. The separation of the wetting and drying curves becomes maximum (Figs. 3 and 4 of Gillham et al., 1976) at about −25 to −27 cm pressure head, where it is about 0.15 cm3 cm−3 . At the lowest head shown, −60 cm, the curves are separated by only about 0.01 cm3 cm−3 . Li et al. (2005) recently reported field-measured SWCCs, in addition to laboratory-determined ones. They found that the field SWCCs showed negligible hysteresis. Wood fibers also exhibit different adsorption and desorption curves (Peralta, 1995). At low water contents, below −10 MPa, Tuller and Or (2005) considered adsorption to be the dominant determiner of the SWCC and expressed no reason to consider hysteresis a factor when using the SWCC to estimate specific surface area of natural soils. Globus and Neusypina (2004) also studied measurement of the SWCC in relation to specific surface. Hysteresis would be important in this application, if present at −10 MPa, because it could cause differences in measured water contents and thus uncertainty in estimation of surface area. Whitmore and Heinen (1999) related SWCC hysteresis to how microbial activity is represented in computer models, agreeing with Tuller and Or (2005) on the importance of the SWCC with respect to biological activity in drier soils. Hysteresis of the SWCC has been a subject of numerous and varied studies. Hysteresis has been found important as a feature of mathematical models of infiltration and drainage (Si and Kachanoski,
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2000) and solute transport (Mitchell and Mayer, 1998). Solute and water transport are both influenced by hysteresis in variably saturated soils (Jaynes, 1992; Gillham et al., 1979; Kaluarachchi and Parker, 1987). Hysteresis has been estimated from cone permeameter measurements (Simunek et al., 1999). The hysteresis effect in soil water has been attributed to more than one mechanism. Jury and Horton (2004) described three mechanisms: bottlenecks between pores; pores with multiple water surface radii at the same water content; and contact angle. Haines (1930) provided one of the earliest descriptions of the bottleneck mechanism. The purpose of this paper is to present scanning hysteresis loop characteristics of two fine textured soils. Attention in this preliminary study is confined to soil water conditions drier than the permanent wilting point, −1.5 MPa. A model analysis of the dynamics of transition between equilibrium water content levels is presented for the purpose of distinguishing hysteresis and potential non-equilibrium differences. In addition, the results of cycling multiple times over a specific range of soil water potentials are presented. Hysteresis data presented here represent “scanning” loops rather than the main hysteresis loop, as those terms were used by Poulovassilis and El-Ghamry (1978). MATERIALS AND METHODS Experimental Bulk samples of Fargo silty clay (fine smectitic frigid Typic Epiaquert) and Glyndon loam (coarsesilty mixed superactive frigid Aeric Calciaquoll) soils were air dried, crushed and sieved to < 1 mm, then uniformly divided with sub-samples being stored in air-tight plastic containers containing approximately 350 mL soil. The two soils differed in texture and organic matter content (Table I). When needed, individual subsamples were oven dried at 105 ◦ C and stored in a desiccator. Oven drying may produce some permanent alteration of water adsorption characteristics, but “produces no great alteration of the fundamental structure of the soil (Puri et al., 1925).” TABLE I Soil composition Soil
Particle-size distribution Sand (> 0.050 mm)
Organic matter Silt (0.002–0.050 mm)
Clay (< 0.002 mm)
mg g−1 (%) Fargo Glyndon
36 (3.6) 521 (52.1)
439 (43.9) 287 (28.7)
525 (52.5) 192 (19.2)
60 (6.0) 50 (5.0)
The experimental method was to equilibrate soil samples with the moist air over salt solutions in closed containers. Solutions of NaCl were prepared in a range of concentrations (expressed in mol kg−1 ) to produce water potentials from −6.6 to −18.8 MPa (Table II). Water potentials were calculated according to Lang (1967) or found from a tabulation (Brown and Van Haveren, 1971) originating from the same (1967) calculation method. Small and large sample-amounts were used in independent experiments. Small samples were about 3.5 g and large samples were about 30.0 g. Small and large sample methods are described separately below. In small sample experiments, soil weighing about 3.50 g (dry) was placed in each of twenty 40-mm inside diameter by 50-mm high weighing bottles. Ten bottles contained Fargo soil and ten contained Glyndon soil. The range of dry soil weights was from 3.41 to 3.63 g. Initial weights of all bottles empty and with the dry soil were obtained to 0.0001 g resolution on an electronic analytical balance. Temperature was maintained at a constant 25 ◦ C by keeping all samples and solutions continuously in a constant temperature room, with 25 ◦ C maintained within 1 ◦ C. The salt solutions were held in one liter capacity glass jars with sealing metal lids (home canning jars). A 100 mL beaker with several
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TABLE II Sodium chloride solution concentration and water potentials (ψ) used for equilibration at 25 ◦ C NaCl solution concentration mol 1.4 1.5 1.8 2.0 2.5 3.5
kg−1
ψ MPa −6.62 −7.13 −8.70 −9.79 −12.62 −18.85
metal washers was placed in each jar. The salt solution in each jar surrounded the beaker to a depth of about half the height of the beaker (40 mm). Each soil-containing weighing bottle, without lid, was placed on top of the washers inside a beaker for vapor equilibration, through air, with the salt solution. Prior to beginning the 25 ◦ C work, the samples were exposed over 2.0 mol kg−1 NaCl solutions at various temperatures. This resulted in initiation of the 25 ◦ C equilibration experiments at water contents not far from the 25 ◦ C with 2.0 mol kg−1 NaCl equilibrium values. Determination of the weighing bottle sample weights to 0.1 mg resolution was conducted regularly, usually once each day or every other day, as follows. The canning jar retaining band was unscrewed and set aside. Then the weighing bottle lid was grasped with tongs and positioned near the jar mouth for quick placement. The jar lid was removed smoothly to create as little air turbulence as possible, and the weighing bottle lid was immediately lowered into place to seal the bottle. Then the bottle and lid were removed from the jar using the same tongs and the jar lid replaced. The weighing bottle was then taken to the analytical balance and weighed without delay. The reverse process was used to return the weighing bottle to the sealed jar. The solution strength was changed regularly, most commonly after 7 to 11 days as determined by the data indicating that equilibrium had been reached because successive weighings were negligibly different. Thus, the usual equilibration time was from 170 to 270 hours. The Glyndon samples were exposed to solutions of NaCl concentrations in the order 2.0, 1.8, 1.5, 2.0, 2.5, 3.5, 2.5, 2.0, 1.8, 1.5, 1.8, 2.0, 2.5, 3.5, 2.5, 2.0, 1.8, 1.5, 2.5, 3.5 mol kg−1 . Note that the 1.8 mol kg−1 concentration was skipped on the first pass (between 1.5 and 2.0 mol kg−1 ). The Fargo samples were exposed to the same NaCl concentrations, but the series was 2.0, 2.5, 3.5, 2.5, 2.0, 1.8, 1.5, 1.8, 2.0, 2.5, 3.5, 2.5, 2.0, 1.5, 2.5 mol kg−1 . Large sample (30 g) experiments were conducted in a room without special temperature control, but where observations confirmed that it was generally about 23 ◦ C. Five Glyndon samples and four Fargo samples were used. These larger samples were placed in aluminum soil-moisture cans (6.4 cm diameter × 4.6 cm high) suspended over solutions in the same type of canning jars used for the smaller samples. Two perpendicular wires were connected to each moisture can through small holes drilled near the top of the can to provide a suspension mechanism. A hook attached to individual can’s suspension wires allowed weighing without removing the can from its jar. Sample weights were determined on an electronic balance with 10 mg resolution. When not being weighed each jar was sealed by a septum on the shank of the suspending hook. Equilibration times were typically 240 to 360 h, again determined by when successive weighings indicated no further change was taking place. The 30 g samples were exposed to NaCl concentrations in the order 2.0, 1.8, 1.4, 2.0, 2.5, 3.5, 2.5, 2.0, 1.5, 2.0, 2.5, 3.5, 2.5, 2.0, 1.5 mol kg−1 . After the conclusion of the experimental work, the salt solutions were analyzed for any change in strength. Approximately 30 mL samples were taken from two jars each with solutions of nominal strengths of 1.5, 1.8, 2.0, 2.0, 2.5, and 3.5 mol kg−1 . The samples were placed in weighing bottles and dried in an oven. The initial sample weights, dry weights, and weighing bottle tare weights were used to find the final molalities of the solutions. All solutions were found to analyze within, usually well within, one part in 100 of the intended value. For example, four 2.0-mol kg−1 nominal solutions analyzed in
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the range 2.006 to 2.019 mol kg−1 . Modeling The exponential decay model applies to many physical systems such as radioactive decay, capacitor discharge through a fixed resistance, and frictional damping of harmonic mechanical motion. Here we hypothesize that it also governs the dynamics of soil-water vapor equilibration experiments. In typical systems, represented by the preceeding examples, a change in an energy level dictates a new equilibrium level in a material quantity. As applied here the energy level is the water potential determined by the salt solution concentration and temperature while the material quantity is the mass of water adsorbed on the soil. The exponential decay model says that the departure of the material quantity from its previous equilibrium value (at the initial energy level) is halved with each passage of the half-life time period, so long as the subsequent new energy level remains constant. The physical vapor equilibration system used in these experiments approximately satisfies two criteria necessary for its analog, the capacitor charging through a resistor, to be accurate. First, vapor transport by Fick’s law through the air is analogous to conduction of electricity through the resistor. Second, the amount of water transported through the air and deposited on the soil during an equilibration is large compared to the change in total water vapor content of the air during the equilibration. The second is analogous to the resistor having small stray capacitance in the electrical system. Based on 500 cm3 air volume in an equilibration jar, 0.96 relative humidity (RH) at −6 MPa, 0.86 RH at -20 MPa, and saturated water vapor density of 23 g m−3 at 25 ◦ C (List, 1951) we calculate a maximum vapor change in air for the system as (5 × 10−4 m3 ) × (0.96 − 0.86) × (23 g m−3 ) = 1.2 mg. The minimum change in adsorbed water, occurring with the the 3.5 g Glyndon samples, is calculated based on our experimentally determined water content change of about 8 mg g−1 from −6 to −20 MPa as 28 mg. So, the vapor transported to the soil, 28 mg, is quite large compared to the change in vapor stored in the air, less than 1.2 mg. The first criteria, transport by an ohm’s law analog, is supported in that the range of RH involved, 0.86 to 0.96, is small and therefore the use of a constant vapor diffusion coefficient in Fick’s law should introduce correspondingly small error. We will next calculate the magnitude of the failure to achieve equilibrium that is expected from the exponential decay model when no hysteresis is present. Later, the actual difference in experimental wetting and drying values will be compared to this (hypothetical) no-hysteresis calculated value. The exponential decay model of the vapor equilibrium experiments of interest here is presented as our hypothesis because it is reasonable and simple. Consider a system with three material equilibrium values, y, of 1, 0, and −1. The system is sequentially placed in states to approach values 1, 0, −1, 0, 1 and so forth for a very large number of cycles of equal temporal duration. Within each cycle are four equilibration periods of duration d. If the difference between the equilibrium value and the actual value the start of an equilibration period is b, then the difference at the end of the equilibration period is a fraction f of this value, bf. If n is the number of half lives in a period, the value of f is (1/2)n . After a large number of cycles (Fig. 1a) a uniform, periodic cycling pattern is established. In this uniform pattern, the value approached after a change in equilibrium value from 1 to 0 is designated as ‘a’ and the value approached for the change from −1 to 0 by symmetry must be ‘−a’. Under these conditions the departure from equilibrium at the beginning of each period is b = (1 + a), so we have at time = 1 (quarter cycle of Fig. 1a) y(1) = −a + (1 + a)(1 − f )
(1)
where y(1) is the material level at 1 on the horizontal axis of Fig. 1. Since a = y(1)f it follows that the value of a can be found by using Eq. (1) to write a = [−a + (1 + a)(1 − f )]f
(2)
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and solving this for a. The solution of Eq. (2) for a is a = f (1 − f )/(1 + f 2 ) = [(1/f ) − 1]/[(1/f 2 ) + 1]
(3)
For small f , a nearly equals f . For example, for 3, 6, and 10 half lives and using Eq. (3) the corresponding values of (f, a) are (1/8, 7/65), (1/64, 63/4096), and (1/1024, 1023/1048577), or expressed in decimal, (0.125, 0.1077), (0.015675, 0.01538), and (0.0009765675, 0.0009756).
Fig. 1 Uniform cycling (a) with exponential decay through equilibrium states having relative material levels of −1, 0, and 1 and (b) through non-symmetric states (e − d not equal to d − c) for the values shown.
Now consider a more general situation. Again, we are considering the levels attained by the system after a sufficient number of cycles between three identical energy states such that the material levels approach repeating, uniform values (Fig. 1b). We identify the low and high ultimate equilibrium levels as c and e. These are the values that would be approached if the equilibration were allowed to progress indefinitely. Actual levels attained during the cyclic equilibration process are f , d− , d+ , and g. The intermediate long-term equilibrium value is d (Fig. 1b). Call the departures from equilibrium ∆dg = g−d and ∆fd = d − f . The departures from d are δde = d+ − d and δcd = d − d− . The character of the exponential decay system specifies δde = f ∆dg and δcd = f − ∆fd so, using ∆ = ∆dg + ∆fd and δ = δde + δcd leads to δ = f∆
(4)
See Fig. 1b for a specific numerical example. Estimates of ∆ can be obtained from experimental data, as can expected values of f , based on half-life estimates arising from the time-dependent approach to apparent equilibrium values. Then, Eq. (4) allows calculation of the expected non-hysteretic difference δ for comparison to experimentally determined actual differences. Only a few equilibration steps are needed before values closely approach the repeating levels. For instance, consider a system with f = 1/16 and initially at +2, but with equilibrium values of +1, 0, and −1. For an initial equilibration at 0, then at −1, 0, +1, 0, etc. the resulting material levels are respectively 2 × (1/16) = 0.125, 0.125 − (1 + 0.125)(15/16) = −0.9297, −0.9297(1/16) = −0.05811, −0.5811 + (1 + 0.5811)(15/16) = 0.9339, 0.9339(1/16) = 0.058367, etc. From Eq. (3) the value of a for long-term cycling is (16 − 1)/(256 + 1) = 0.058366. This is closely approached (in magnitude) at the third step above (−0.5811) and at the fifth step (calculations not shown) is within one part in 50 000. RESULTS Experimental Glyndon soil demonstrated distinct scanning curve hysteresis when cycled through water potentials ranging from −18.85 MPa (3.5 mol kg−1 ) to −6.62 (1.4 mol kg−1 ) (Fig. 2a and b). The large samples (Fig. 2b) had slightly higher average water content than the small samples (Fig. 2a) but the separation
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of the wetting and drying points was nearly the same for each.
Fig. 2 Mean water contents of (a) 9 samples versus water potential for 3.5 g Glyndon samples, (b) 5 samples versus water potential for 30 g Glyndon soil samples, (c) 10 samples versus water potential for 3.5 g Fargo soil samples, and (d) 4 samples versus water potential for 30 g Fargo soil samples. The numbers identify the sequence of vapor equilibration over NaCl solutions.
Fargo soil samples also had distinct hysteresis when cycled through similar water potentials (Fig. 2c and d). The maximum wetting-drying difference for Fargo samples was about 4 mg g−1 , about twice as large as for Glyndon samples. For Fargo samples, also, the large samples had higher water contents at the same potentials by about 4 mg g−1 , on the average. Variability of the results was evaluated using a linear additive model, similar to Hicks (1973), to find the implied random error for each measurement as eij = Yij − Yi. − Y.j + Y..
(5)
where Yij is the observed water content of sample i at equilibration step j and the dots indicate averaging over the index of the corresponding position. The mean square (s2 ) of e was calculated by analysis of variance (SAS ANOVA, SAS Institute, 1999). The least significant difference was calculated by Steel and Torrie (1960) equation 7.9 as LSD(0.01 ) = t0.01 sd = 2.797(2s2 /r)1/2
(6)
where r is the number of observations per mean, t0.01 is the t statistic value at 0.01 significance level, and s2 is error variance. The values found for LSD are shown on Fig. 2. Compared to the difference between wetting and drying equilibrium values at internal points of the loops, the LSD values were small. Individual soil samples exhibited a range of moisture contents when subjected to the same vapor equilibration conditions. The range of water contents due to sample was about 1.2 mg g−1 for the small Glyndon samples and also about 1.2 mg g−1 for the large Glyndon samples. The range of water contents due to sample was about 1.6 mg g−1 for the small Fargo samples and about 1.4 mg g−1 for the large. Clearly, avoiding the experimental error contributed by individual differences in soil samples by equilibrating each sample at a series of water potentials contributed to obtaining the small LSD values. This is in contrast to the approach of Peralta (1995) for wood samples, where individual samples were equilibrated at only one relative humidity each, assuming negligible sample-to-sample variability.
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The small LSD values mean that for each equilibrium condition the samples tracked each other closely. However, Fig. 2b–d also showed that the average of the samples traced slightly different paths on successive loops. For instance, Fig. 2c path 3, 4, 5, 6 and path 9, 10, 11, 12 are not as close as one would expect based on the errors eij of Eq. (5). The source of this experimental “drift” error is unknown. Model Data was obtained on the time-dependence of the absorption process for each soil by obtaining additional data during some of the equilibration steps for the 3.5 g samples. Five samples of each soil were weighed at frequent intervals after change of the equilibrating solution. The resulting average absorbed water changes (Fig. 3) were used to evaluate the half life implied for each soil. Both soils indicate (Fig. 3 and other data not shown) a half life of 11–13 h, since about half of the ultimate change is achieved in 11–13 h and three quarters in 22–26 h. For Glyndon soil the minimum equilibration time (3.5 g samples) actually provided in the experimental work was about 120 h. This would indicate about 10 half lives and therefore an f value (1/210 ) of less than 0.001. For Glyndon samples ∆ is about 8 mg g−1 (see Fig. 2a), so using δ = f ∆ (Eq. 4) with the value of f computed just above gives the theoretical value δ = 0.008 mg g−1 , less than 10% of the LSD0.01 shown on Fig. 2a and b. Computed similarly for Fargo samples, using ∆ = 16 mg g−1 (see Fig. 2c), δ = 0.016 mg g−1 , again less than 10% of the LSD0.01 of Figs. 2c and d.
Fig. 3 Change in mass due to water absorption or desorption versus time equilibrated over a new solution strength for (a) Glyndon samples of Fig. 2a upon change from 2.5 to 2.0 mol kg−1 NaCl and (b) Fargo samples of Fig. 2c after change from 2.5 to 3.5 mol kg−1 NaCl.
DISCUSSION The scanning loop hysteresis displayed by the small and large Glyndon samples was clear (Fig. 2a and b), with the average maximum difference between wetting and drying water contents being about 3% of their average. This is a small relative difference between wetting and drying water contents compared to that found for coarse-textured soils near saturation, as illustrated by data of Gillham et al. (1976). Also, Janes (1984) shows a typical hysteresis loop starting at saturation in which the loop width at some points is greater than the average of the wetting and drying legs. Fargo samples had higher water contents than Glyndon samples, but similar hysteresis behavior (Fig. 2c and d). For Fargo samples the actual difference between wetting and drying moisture contents was larger, 2.5 to 3.5 mg g−1 , compared to about 1.5 mg g−1 difference for Glyndon samples. On a relative basis the Fargo sample difference was nearly the same, about 3%. In all cases the solution strengths for samples were not changed until consecutive weighings a day or more apart indicated little, if any, change in absorbed water. Also, values of d calculated by Eq. (4) using the exponential decay model were found to be less than 0.1 of the experimental LSD0.01 . Thus, the separation of data points associated with desorbing and adsorbing equilibrium at identical solution
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strengths must reasonably be ascribed to hysteresis. Generally, the water content difference between most recent adsorbing and desorbing points far exceeded the LSD0.01 values (Fig. 2). This is strong evidence of hysteresis in the SWCC for these soils at water potential less than −5 MPa. Hysteresis is defined by quasistable states. That is, over very long time periods or perturbing influences the apparently stable state can change. Also, the exponential decay model may not strictly apply at all times, even though the behavior shown in Fig. 3 indicates that it is reasonably well-followed up to 75 h or more. Beyond that, the remaining departure from equilibrium quickly becomes smaller than typical experimental errors (see results section). A considerable range of equilibration times was used, i.e., 120 to 380 h for the small Glyndon samples, without evidence that the longer times resulted in further measurable approach to an ultimate value. This last observation is additional justification for viewing the data as representing true hysteresis rather than failure to allow sufficient time for equilibration. It is the criteria used in previous studies, specifically as described in Puri et al. (1925). Fig. 2b through 2d provide experimental evidence that long-term drift in water content exists in these experiments, since successive points of a subsequent cycle bear only a slowly changing relationship to those of the previous cycle. Another possible explanation for changing water content from one cycle to the next is that successive scanning loops are being followed toward an ultimate stable loop. CONCLUSIONS The existence and magnitude of scanning hysteresis loops in the SWCC at soil moisture contents in the range below −5 MPa, well below the permanent wilting point, has herein been well supported by experimental evidence for two fine-textured soils. The exponential decay model of non-hysteretic cycling cannot account for the observed loops. The relative magnitude of hysteresis is much smaller in terms of the ratio of wetting to drying water content than it is with matric heads nearer zero. Here it was found that the difference in adsorbing and desorbing water contents was only about 3% of their average for the portion of the SWCC below −5 MPa for the finer soils examined in this work. In contrast, sands near saturation typically have hysteresis loops with main drying water content three times as great as the wetting water content. However, when precise evaluation of soil moisture dynamics is required and soil water matric head is below about −5 MPa provision should be made to account for the hysteretic effects. Accurate SWCCs at the dry end are considered important for modeling biological processes. Ultimately, details of scanning loops predicted by the independent domain and other hysteresis models will need to be tested against experimental data. The techniques used in this study appear to be of sufficient accuracy and precision to serve such a purpose. REFERENCES Brown, R. W. and Van Haveren, B. P. (eds.). 1971. Psychrometry in Water Relations Research. Proceedings of the Symposium on Thermocouple Psychrometers, Utah State University, USA. Gillham, R. W., Klute, A. and Heerman, D. F. 1976. Hydraulic properties of a porous medium: Measurement and emperical representation. Soil Sci. Soc. Am. J. 40(2): 203–207. Gillham, R. W., Klute, A. and Heerman, D. F. 1979. Measurement and numerical simulation of hysteretic flow in a heterogeneous porous medium. Soil Sci. Soc. Am. J. 43(6): 1 061–1 067. Globus, A. M. and Neusypina, T. A. 2004. Determination of the water hysteresis and specific surface of soils by electronic microhygrometry and psychrometry. Eurasian Soil Science. 39(3): 270–277. Haines, W. B. 1930. Studies in the physical properties of soil. J. Agric. Sci. 20(1): 97–116. Hicks, C. R. 1973. Fundamental Concepts in the Design of Experiments. 2nd Edition. Holt, Rinehart, and Winston, New York. 349pp. Jackson, R. D. 1964. Water vapor diffusion in relatively dry soil. III. Steady-state experiments. Soil Sci. Soc. Am. Proc. 28(4): 467–470. Janes, D. B. 1984. Comparison of soil-water hysteresis models. J. Hydrology. 75: 287–299. Jaynes, D. B. 1992. Estimating hysteresis in the soil water retention function. In van Genuchten, M. T. (ed.) Proceedings of the International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils. Univ. of Calif., Riverside. pp. 219–232.
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Jury, W. A. and Horton, R. 2004. Soil Physics. John Wiley & Sons, Inc., Hoboken, NJ. 370pp. Kaluarachchi, J. J. and Parker, J. C. 1987. Effects of hysteresis with air entrapment on water flow in the unsaturated zone. Warer Resour. Res. 23(10): 1 967–1 976. Lang, A. R. G. 1967. Osmotic coefficients and water potentials of sodium chloride solutions from 0 to 40 ◦ C. Aust. J. Chem. 20: 2 017–2 023. Li, A. G., Tham, L. G., Yue, Z. Q., Lee, C. F. and Law, K. T. 2005. Comparison of field and laboratory soil-water characteristic curves. J. Geotech. Geoenviron. Eng. 131(9): 1 176–1 180. List, R. J. S. (ed.). 1951. Smithsonian Meteorological Tables. 6th Revised Edition. Smithsonian Institution Press, Washington, DC. 527pp. Mitchell, R. J. and Mayer, A. S. 1998. The significance of hysteresis in modeling solute transport in unsaturated porous media. Soil Sci. Soc. Am. J. 62(6): 1 506–1 512. Peralta, P. N. 1995. Sorption of moisture by wood within a limited range of relative humidities. Wood and Fiber Sci. 27(1): 13–21. Poulovassilis, A. and El-Ghamry, W. M. 1978. The dependent domain theory applied to scanning curves of any order in hysteretic soil water relationships. Soil Sci. 126(1): 1–8. Puri, A. N., Crowther, E. M. and Keen, B. A. 1925. The relation between the vapor pressure and water content of soils. J. Agric. Sci. 15(2): 68–88. SAS Institute, Inc. 1999. SAS/IML User’s Guide. Version 8. SAS Institute, Inc, Cary, NC. Si, B. C. and Kachanoski, R. G. 2000. Unified solution for infiltration and drainage with hysteresis: Theory and field test. Soil Sci. Soc. Am. J. 64(1): 30–36. Simunek, J., Kodesova, R., Gribb, M. M. and van Genuchten, M. T. 1999. Estimating hysteresis in the soil water retention function from cone permeameter experiments. Water Resour. Res. 35(5): 1 329–1 345. Steel, R. G. D. and Torrie, J. H. 1960. Principles and Procedures of Statistics. McGraw-Hill, New York. 481pp. Tuller, M. and Or, D. 2005. Water films and scaling of soil characteristic curves at low water contents. Water Resour. Res. 41. W09403, doi: 10.1029/2005 WR004142. Whitmore, A. P. and Heinen, M. 1999. The effect of hysteresis on microbial activity in computer simulation models. Soil Sci. Soc. Am. J. 63(5): 1 101–1 105.
Soil Water Hysteresis at Low Potential L. PRUNTY and J. BELL Department of Soil Science, North Dakota State University, Fargo, ND 58105 (USA). E-mail: [email protected] (Received December 19, 2006; revised May 17, 2007)
ABSTRACT Knowledge of the soil water characteristic curve is fundamental for understanding unsaturated soils. The objective of this work was to find scanning hysteresis loops of two fine textured soils at water potentials below wilting point. This was done by equilibration over NaCl solutions with water potentials of −6.6 to −18.8 MPa at 25 ◦ C. When cycled repeatedly through a series of potentials in the range noted previously both soils exhibited a hysteresis effect. The experimental differences in water content between the drying and wetting soils at the same water potential were much too large to be accounted for by failure to allow sufficient time to attain equilibrium as predicted by the exponential decay model. The wetting versus drying differences were relatively small, however, at only 4 mg g−1 or less in absolute terms and about 3% of the mean of wetting and drying, in relative terms. Hysteresis should be a consideration when modeling biological and physical soil processes at water contents below the wilting point, where small differences in water content result in large potential energy changes. Key Words:
adsorption, dry soil, equilibration, matric potential, soil water characteristic
Citation: Prunty, L. and Bell, J. 2007. Soil water hysteresis at low potential. Pedosphere. 17(4): 436–444.
INTRODUCTION The dependence of soil water content on matric potential, represented graphically as the soil-water characteristic curve (SWCC), has long been recognized as hysteretic. Scanning hysteresis near saturation or at matric potentials near zero can be pronounced and has been studied rather extensively. Relatively little mention is found in the literature about hysteresis in the SWCC at matric potentials lower than a few tenths of a megapascal below zero. Jackson (1964), an exception, does present adsorption-desorption plots for two soils spanning nearly the complete relative humidity range, 0 to 100 percent. Puri et al. (1925) did early work that included some observations of hysteresis. Gillham et al. (1976) showed experimentally determined hysteresis of the SWCC for a dune sand. The separation of the wetting and drying curves becomes maximum (Figs. 3 and 4 of Gillham et al., 1976) at about −25 to −27 cm pressure head, where it is about 0.15 cm3 cm−3 . At the lowest head shown, −60 cm, the curves are separated by only about 0.01 cm3 cm−3 . Li et al. (2005) recently reported field-measured SWCCs, in addition to laboratory-determined ones. They found that the field SWCCs showed negligible hysteresis. Wood fibers also exhibit different adsorption and desorption curves (Peralta, 1995). At low water contents, below −10 MPa, Tuller and Or (2005) considered adsorption to be the dominant determiner of the SWCC and expressed no reason to consider hysteresis a factor when using the SWCC to estimate specific surface area of natural soils. Globus and Neusypina (2004) also studied measurement of the SWCC in relation to specific surface. Hysteresis would be important in this application, if present at −10 MPa, because it could cause differences in measured water contents and thus uncertainty in estimation of surface area. Whitmore and Heinen (1999) related SWCC hysteresis to how microbial activity is represented in computer models, agreeing with Tuller and Or (2005) on the importance of the SWCC with respect to biological activity in drier soils. Hysteresis of the SWCC has been a subject of numerous and varied studies. Hysteresis has been found important as a feature of mathematical models of infiltration and drainage (Si and Kachanoski,
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2000) and solute transport (Mitchell and Mayer, 1998). Solute and water transport are both influenced by hysteresis in variably saturated soils (Jaynes, 1992; Gillham et al., 1979; Kaluarachchi and Parker, 1987). Hysteresis has been estimated from cone permeameter measurements (Simunek et al., 1999). The hysteresis effect in soil water has been attributed to more than one mechanism. Jury and Horton (2004) described three mechanisms: bottlenecks between pores; pores with multiple water surface radii at the same water content; and contact angle. Haines (1930) provided one of the earliest descriptions of the bottleneck mechanism. The purpose of this paper is to present scanning hysteresis loop characteristics of two fine textured soils. Attention in this preliminary study is confined to soil water conditions drier than the permanent wilting point, −1.5 MPa. A model analysis of the dynamics of transition between equilibrium water content levels is presented for the purpose of distinguishing hysteresis and potential non-equilibrium differences. In addition, the results of cycling multiple times over a specific range of soil water potentials are presented. Hysteresis data presented here represent “scanning” loops rather than the main hysteresis loop, as those terms were used by Poulovassilis and El-Ghamry (1978). MATERIALS AND METHODS Experimental Bulk samples of Fargo silty clay (fine smectitic frigid Typic Epiaquert) and Glyndon loam (coarsesilty mixed superactive frigid Aeric Calciaquoll) soils were air dried, crushed and sieved to < 1 mm, then uniformly divided with sub-samples being stored in air-tight plastic containers containing approximately 350 mL soil. The two soils differed in texture and organic matter content (Table I). When needed, individual subsamples were oven dried at 105 ◦ C and stored in a desiccator. Oven drying may produce some permanent alteration of water adsorption characteristics, but “produces no great alteration of the fundamental structure of the soil (Puri et al., 1925).” TABLE I Soil composition Soil
Particle-size distribution Sand (> 0.050 mm)
Organic matter Silt (0.002–0.050 mm)
Clay (< 0.002 mm)
mg g−1 (%) Fargo Glyndon
36 (3.6) 521 (52.1)
439 (43.9) 287 (28.7)
525 (52.5) 192 (19.2)
60 (6.0) 50 (5.0)
The experimental method was to equilibrate soil samples with the moist air over salt solutions in closed containers. Solutions of NaCl were prepared in a range of concentrations (expressed in mol kg−1 ) to produce water potentials from −6.6 to −18.8 MPa (Table II). Water potentials were calculated according to Lang (1967) or found from a tabulation (Brown and Van Haveren, 1971) originating from the same (1967) calculation method. Small and large sample-amounts were used in independent experiments. Small samples were about 3.5 g and large samples were about 30.0 g. Small and large sample methods are described separately below. In small sample experiments, soil weighing about 3.50 g (dry) was placed in each of twenty 40-mm inside diameter by 50-mm high weighing bottles. Ten bottles contained Fargo soil and ten contained Glyndon soil. The range of dry soil weights was from 3.41 to 3.63 g. Initial weights of all bottles empty and with the dry soil were obtained to 0.0001 g resolution on an electronic analytical balance. Temperature was maintained at a constant 25 ◦ C by keeping all samples and solutions continuously in a constant temperature room, with 25 ◦ C maintained within 1 ◦ C. The salt solutions were held in one liter capacity glass jars with sealing metal lids (home canning jars). A 100 mL beaker with several
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TABLE II Sodium chloride solution concentration and water potentials (ψ) used for equilibration at 25 ◦ C NaCl solution concentration mol 1.4 1.5 1.8 2.0 2.5 3.5
kg−1
ψ MPa −6.62 −7.13 −8.70 −9.79 −12.62 −18.85
metal washers was placed in each jar. The salt solution in each jar surrounded the beaker to a depth of about half the height of the beaker (40 mm). Each soil-containing weighing bottle, without lid, was placed on top of the washers inside a beaker for vapor equilibration, through air, with the salt solution. Prior to beginning the 25 ◦ C work, the samples were exposed over 2.0 mol kg−1 NaCl solutions at various temperatures. This resulted in initiation of the 25 ◦ C equilibration experiments at water contents not far from the 25 ◦ C with 2.0 mol kg−1 NaCl equilibrium values. Determination of the weighing bottle sample weights to 0.1 mg resolution was conducted regularly, usually once each day or every other day, as follows. The canning jar retaining band was unscrewed and set aside. Then the weighing bottle lid was grasped with tongs and positioned near the jar mouth for quick placement. The jar lid was removed smoothly to create as little air turbulence as possible, and the weighing bottle lid was immediately lowered into place to seal the bottle. Then the bottle and lid were removed from the jar using the same tongs and the jar lid replaced. The weighing bottle was then taken to the analytical balance and weighed without delay. The reverse process was used to return the weighing bottle to the sealed jar. The solution strength was changed regularly, most commonly after 7 to 11 days as determined by the data indicating that equilibrium had been reached because successive weighings were negligibly different. Thus, the usual equilibration time was from 170 to 270 hours. The Glyndon samples were exposed to solutions of NaCl concentrations in the order 2.0, 1.8, 1.5, 2.0, 2.5, 3.5, 2.5, 2.0, 1.8, 1.5, 1.8, 2.0, 2.5, 3.5, 2.5, 2.0, 1.8, 1.5, 2.5, 3.5 mol kg−1 . Note that the 1.8 mol kg−1 concentration was skipped on the first pass (between 1.5 and 2.0 mol kg−1 ). The Fargo samples were exposed to the same NaCl concentrations, but the series was 2.0, 2.5, 3.5, 2.5, 2.0, 1.8, 1.5, 1.8, 2.0, 2.5, 3.5, 2.5, 2.0, 1.5, 2.5 mol kg−1 . Large sample (30 g) experiments were conducted in a room without special temperature control, but where observations confirmed that it was generally about 23 ◦ C. Five Glyndon samples and four Fargo samples were used. These larger samples were placed in aluminum soil-moisture cans (6.4 cm diameter × 4.6 cm high) suspended over solutions in the same type of canning jars used for the smaller samples. Two perpendicular wires were connected to each moisture can through small holes drilled near the top of the can to provide a suspension mechanism. A hook attached to individual can’s suspension wires allowed weighing without removing the can from its jar. Sample weights were determined on an electronic balance with 10 mg resolution. When not being weighed each jar was sealed by a septum on the shank of the suspending hook. Equilibration times were typically 240 to 360 h, again determined by when successive weighings indicated no further change was taking place. The 30 g samples were exposed to NaCl concentrations in the order 2.0, 1.8, 1.4, 2.0, 2.5, 3.5, 2.5, 2.0, 1.5, 2.0, 2.5, 3.5, 2.5, 2.0, 1.5 mol kg−1 . After the conclusion of the experimental work, the salt solutions were analyzed for any change in strength. Approximately 30 mL samples were taken from two jars each with solutions of nominal strengths of 1.5, 1.8, 2.0, 2.0, 2.5, and 3.5 mol kg−1 . The samples were placed in weighing bottles and dried in an oven. The initial sample weights, dry weights, and weighing bottle tare weights were used to find the final molalities of the solutions. All solutions were found to analyze within, usually well within, one part in 100 of the intended value. For example, four 2.0-mol kg−1 nominal solutions analyzed in
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the range 2.006 to 2.019 mol kg−1 . Modeling The exponential decay model applies to many physical systems such as radioactive decay, capacitor discharge through a fixed resistance, and frictional damping of harmonic mechanical motion. Here we hypothesize that it also governs the dynamics of soil-water vapor equilibration experiments. In typical systems, represented by the preceeding examples, a change in an energy level dictates a new equilibrium level in a material quantity. As applied here the energy level is the water potential determined by the salt solution concentration and temperature while the material quantity is the mass of water adsorbed on the soil. The exponential decay model says that the departure of the material quantity from its previous equilibrium value (at the initial energy level) is halved with each passage of the half-life time period, so long as the subsequent new energy level remains constant. The physical vapor equilibration system used in these experiments approximately satisfies two criteria necessary for its analog, the capacitor charging through a resistor, to be accurate. First, vapor transport by Fick’s law through the air is analogous to conduction of electricity through the resistor. Second, the amount of water transported through the air and deposited on the soil during an equilibration is large compared to the change in total water vapor content of the air during the equilibration. The second is analogous to the resistor having small stray capacitance in the electrical system. Based on 500 cm3 air volume in an equilibration jar, 0.96 relative humidity (RH) at −6 MPa, 0.86 RH at -20 MPa, and saturated water vapor density of 23 g m−3 at 25 ◦ C (List, 1951) we calculate a maximum vapor change in air for the system as (5 × 10−4 m3 ) × (0.96 − 0.86) × (23 g m−3 ) = 1.2 mg. The minimum change in adsorbed water, occurring with the the 3.5 g Glyndon samples, is calculated based on our experimentally determined water content change of about 8 mg g−1 from −6 to −20 MPa as 28 mg. So, the vapor transported to the soil, 28 mg, is quite large compared to the change in vapor stored in the air, less than 1.2 mg. The first criteria, transport by an ohm’s law analog, is supported in that the range of RH involved, 0.86 to 0.96, is small and therefore the use of a constant vapor diffusion coefficient in Fick’s law should introduce correspondingly small error. We will next calculate the magnitude of the failure to achieve equilibrium that is expected from the exponential decay model when no hysteresis is present. Later, the actual difference in experimental wetting and drying values will be compared to this (hypothetical) no-hysteresis calculated value. The exponential decay model of the vapor equilibrium experiments of interest here is presented as our hypothesis because it is reasonable and simple. Consider a system with three material equilibrium values, y, of 1, 0, and −1. The system is sequentially placed in states to approach values 1, 0, −1, 0, 1 and so forth for a very large number of cycles of equal temporal duration. Within each cycle are four equilibration periods of duration d. If the difference between the equilibrium value and the actual value the start of an equilibration period is b, then the difference at the end of the equilibration period is a fraction f of this value, bf. If n is the number of half lives in a period, the value of f is (1/2)n . After a large number of cycles (Fig. 1a) a uniform, periodic cycling pattern is established. In this uniform pattern, the value approached after a change in equilibrium value from 1 to 0 is designated as ‘a’ and the value approached for the change from −1 to 0 by symmetry must be ‘−a’. Under these conditions the departure from equilibrium at the beginning of each period is b = (1 + a), so we have at time = 1 (quarter cycle of Fig. 1a) y(1) = −a + (1 + a)(1 − f )
(1)
where y(1) is the material level at 1 on the horizontal axis of Fig. 1. Since a = y(1)f it follows that the value of a can be found by using Eq. (1) to write a = [−a + (1 + a)(1 − f )]f
(2)
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and solving this for a. The solution of Eq. (2) for a is a = f (1 − f )/(1 + f 2 ) = [(1/f ) − 1]/[(1/f 2 ) + 1]
(3)
For small f , a nearly equals f . For example, for 3, 6, and 10 half lives and using Eq. (3) the corresponding values of (f, a) are (1/8, 7/65), (1/64, 63/4096), and (1/1024, 1023/1048577), or expressed in decimal, (0.125, 0.1077), (0.015675, 0.01538), and (0.0009765675, 0.0009756).
Fig. 1 Uniform cycling (a) with exponential decay through equilibrium states having relative material levels of −1, 0, and 1 and (b) through non-symmetric states (e − d not equal to d − c) for the values shown.
Now consider a more general situation. Again, we are considering the levels attained by the system after a sufficient number of cycles between three identical energy states such that the material levels approach repeating, uniform values (Fig. 1b). We identify the low and high ultimate equilibrium levels as c and e. These are the values that would be approached if the equilibration were allowed to progress indefinitely. Actual levels attained during the cyclic equilibration process are f , d− , d+ , and g. The intermediate long-term equilibrium value is d (Fig. 1b). Call the departures from equilibrium ∆dg = g−d and ∆fd = d − f . The departures from d are δde = d+ − d and δcd = d − d− . The character of the exponential decay system specifies δde = f ∆dg and δcd = f − ∆fd so, using ∆ = ∆dg + ∆fd and δ = δde + δcd leads to δ = f∆
(4)
See Fig. 1b for a specific numerical example. Estimates of ∆ can be obtained from experimental data, as can expected values of f , based on half-life estimates arising from the time-dependent approach to apparent equilibrium values. Then, Eq. (4) allows calculation of the expected non-hysteretic difference δ for comparison to experimentally determined actual differences. Only a few equilibration steps are needed before values closely approach the repeating levels. For instance, consider a system with f = 1/16 and initially at +2, but with equilibrium values of +1, 0, and −1. For an initial equilibration at 0, then at −1, 0, +1, 0, etc. the resulting material levels are respectively 2 × (1/16) = 0.125, 0.125 − (1 + 0.125)(15/16) = −0.9297, −0.9297(1/16) = −0.05811, −0.5811 + (1 + 0.5811)(15/16) = 0.9339, 0.9339(1/16) = 0.058367, etc. From Eq. (3) the value of a for long-term cycling is (16 − 1)/(256 + 1) = 0.058366. This is closely approached (in magnitude) at the third step above (−0.5811) and at the fifth step (calculations not shown) is within one part in 50 000. RESULTS Experimental Glyndon soil demonstrated distinct scanning curve hysteresis when cycled through water potentials ranging from −18.85 MPa (3.5 mol kg−1 ) to −6.62 (1.4 mol kg−1 ) (Fig. 2a and b). The large samples (Fig. 2b) had slightly higher average water content than the small samples (Fig. 2a) but the separation
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of the wetting and drying points was nearly the same for each.
Fig. 2 Mean water contents of (a) 9 samples versus water potential for 3.5 g Glyndon samples, (b) 5 samples versus water potential for 30 g Glyndon soil samples, (c) 10 samples versus water potential for 3.5 g Fargo soil samples, and (d) 4 samples versus water potential for 30 g Fargo soil samples. The numbers identify the sequence of vapor equilibration over NaCl solutions.
Fargo soil samples also had distinct hysteresis when cycled through similar water potentials (Fig. 2c and d). The maximum wetting-drying difference for Fargo samples was about 4 mg g−1 , about twice as large as for Glyndon samples. For Fargo samples, also, the large samples had higher water contents at the same potentials by about 4 mg g−1 , on the average. Variability of the results was evaluated using a linear additive model, similar to Hicks (1973), to find the implied random error for each measurement as eij = Yij − Yi. − Y.j + Y..
(5)
where Yij is the observed water content of sample i at equilibration step j and the dots indicate averaging over the index of the corresponding position. The mean square (s2 ) of e was calculated by analysis of variance (SAS ANOVA, SAS Institute, 1999). The least significant difference was calculated by Steel and Torrie (1960) equation 7.9 as LSD(0.01 ) = t0.01 sd = 2.797(2s2 /r)1/2
(6)
where r is the number of observations per mean, t0.01 is the t statistic value at 0.01 significance level, and s2 is error variance. The values found for LSD are shown on Fig. 2. Compared to the difference between wetting and drying equilibrium values at internal points of the loops, the LSD values were small. Individual soil samples exhibited a range of moisture contents when subjected to the same vapor equilibration conditions. The range of water contents due to sample was about 1.2 mg g−1 for the small Glyndon samples and also about 1.2 mg g−1 for the large Glyndon samples. The range of water contents due to sample was about 1.6 mg g−1 for the small Fargo samples and about 1.4 mg g−1 for the large. Clearly, avoiding the experimental error contributed by individual differences in soil samples by equilibrating each sample at a series of water potentials contributed to obtaining the small LSD values. This is in contrast to the approach of Peralta (1995) for wood samples, where individual samples were equilibrated at only one relative humidity each, assuming negligible sample-to-sample variability.
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The small LSD values mean that for each equilibrium condition the samples tracked each other closely. However, Fig. 2b–d also showed that the average of the samples traced slightly different paths on successive loops. For instance, Fig. 2c path 3, 4, 5, 6 and path 9, 10, 11, 12 are not as close as one would expect based on the errors eij of Eq. (5). The source of this experimental “drift” error is unknown. Model Data was obtained on the time-dependence of the absorption process for each soil by obtaining additional data during some of the equilibration steps for the 3.5 g samples. Five samples of each soil were weighed at frequent intervals after change of the equilibrating solution. The resulting average absorbed water changes (Fig. 3) were used to evaluate the half life implied for each soil. Both soils indicate (Fig. 3 and other data not shown) a half life of 11–13 h, since about half of the ultimate change is achieved in 11–13 h and three quarters in 22–26 h. For Glyndon soil the minimum equilibration time (3.5 g samples) actually provided in the experimental work was about 120 h. This would indicate about 10 half lives and therefore an f value (1/210 ) of less than 0.001. For Glyndon samples ∆ is about 8 mg g−1 (see Fig. 2a), so using δ = f ∆ (Eq. 4) with the value of f computed just above gives the theoretical value δ = 0.008 mg g−1 , less than 10% of the LSD0.01 shown on Fig. 2a and b. Computed similarly for Fargo samples, using ∆ = 16 mg g−1 (see Fig. 2c), δ = 0.016 mg g−1 , again less than 10% of the LSD0.01 of Figs. 2c and d.
Fig. 3 Change in mass due to water absorption or desorption versus time equilibrated over a new solution strength for (a) Glyndon samples of Fig. 2a upon change from 2.5 to 2.0 mol kg−1 NaCl and (b) Fargo samples of Fig. 2c after change from 2.5 to 3.5 mol kg−1 NaCl.
DISCUSSION The scanning loop hysteresis displayed by the small and large Glyndon samples was clear (Fig. 2a and b), with the average maximum difference between wetting and drying water contents being about 3% of their average. This is a small relative difference between wetting and drying water contents compared to that found for coarse-textured soils near saturation, as illustrated by data of Gillham et al. (1976). Also, Janes (1984) shows a typical hysteresis loop starting at saturation in which the loop width at some points is greater than the average of the wetting and drying legs. Fargo samples had higher water contents than Glyndon samples, but similar hysteresis behavior (Fig. 2c and d). For Fargo samples the actual difference between wetting and drying moisture contents was larger, 2.5 to 3.5 mg g−1 , compared to about 1.5 mg g−1 difference for Glyndon samples. On a relative basis the Fargo sample difference was nearly the same, about 3%. In all cases the solution strengths for samples were not changed until consecutive weighings a day or more apart indicated little, if any, change in absorbed water. Also, values of d calculated by Eq. (4) using the exponential decay model were found to be less than 0.1 of the experimental LSD0.01 . Thus, the separation of data points associated with desorbing and adsorbing equilibrium at identical solution
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strengths must reasonably be ascribed to hysteresis. Generally, the water content difference between most recent adsorbing and desorbing points far exceeded the LSD0.01 values (Fig. 2). This is strong evidence of hysteresis in the SWCC for these soils at water potential less than −5 MPa. Hysteresis is defined by quasistable states. That is, over very long time periods or perturbing influences the apparently stable state can change. Also, the exponential decay model may not strictly apply at all times, even though the behavior shown in Fig. 3 indicates that it is reasonably well-followed up to 75 h or more. Beyond that, the remaining departure from equilibrium quickly becomes smaller than typical experimental errors (see results section). A considerable range of equilibration times was used, i.e., 120 to 380 h for the small Glyndon samples, without evidence that the longer times resulted in further measurable approach to an ultimate value. This last observation is additional justification for viewing the data as representing true hysteresis rather than failure to allow sufficient time for equilibration. It is the criteria used in previous studies, specifically as described in Puri et al. (1925). Fig. 2b through 2d provide experimental evidence that long-term drift in water content exists in these experiments, since successive points of a subsequent cycle bear only a slowly changing relationship to those of the previous cycle. Another possible explanation for changing water content from one cycle to the next is that successive scanning loops are being followed toward an ultimate stable loop. CONCLUSIONS The existence and magnitude of scanning hysteresis loops in the SWCC at soil moisture contents in the range below −5 MPa, well below the permanent wilting point, has herein been well supported by experimental evidence for two fine-textured soils. The exponential decay model of non-hysteretic cycling cannot account for the observed loops. The relative magnitude of hysteresis is much smaller in terms of the ratio of wetting to drying water content than it is with matric heads nearer zero. Here it was found that the difference in adsorbing and desorbing water contents was only about 3% of their average for the portion of the SWCC below −5 MPa for the finer soils examined in this work. In contrast, sands near saturation typically have hysteresis loops with main drying water content three times as great as the wetting water content. However, when precise evaluation of soil moisture dynamics is required and soil water matric head is below about −5 MPa provision should be made to account for the hysteretic effects. Accurate SWCCs at the dry end are considered important for modeling biological processes. Ultimately, details of scanning loops predicted by the independent domain and other hysteresis models will need to be tested against experimental data. The techniques used in this study appear to be of sufficient accuracy and precision to serve such a purpose. REFERENCES Brown, R. W. and Van Haveren, B. P. (eds.). 1971. Psychrometry in Water Relations Research. Proceedings of the Symposium on Thermocouple Psychrometers, Utah State University, USA. Gillham, R. W., Klute, A. and Heerman, D. F. 1976. Hydraulic properties of a porous medium: Measurement and emperical representation. Soil Sci. Soc. Am. J. 40(2): 203–207. Gillham, R. W., Klute, A. and Heerman, D. F. 1979. Measurement and numerical simulation of hysteretic flow in a heterogeneous porous medium. Soil Sci. Soc. Am. J. 43(6): 1 061–1 067. Globus, A. M. and Neusypina, T. A. 2004. Determination of the water hysteresis and specific surface of soils by electronic microhygrometry and psychrometry. Eurasian Soil Science. 39(3): 270–277. Haines, W. B. 1930. Studies in the physical properties of soil. J. Agric. Sci. 20(1): 97–116. Hicks, C. R. 1973. Fundamental Concepts in the Design of Experiments. 2nd Edition. Holt, Rinehart, and Winston, New York. 349pp. Jackson, R. D. 1964. Water vapor diffusion in relatively dry soil. III. Steady-state experiments. Soil Sci. Soc. Am. Proc. 28(4): 467–470. Janes, D. B. 1984. Comparison of soil-water hysteresis models. J. Hydrology. 75: 287–299. Jaynes, D. B. 1992. Estimating hysteresis in the soil water retention function. In van Genuchten, M. T. (ed.) Proceedings of the International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils. Univ. of Calif., Riverside. pp. 219–232.
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Jury, W. A. and Horton, R. 2004. Soil Physics. John Wiley & Sons, Inc., Hoboken, NJ. 370pp. Kaluarachchi, J. J. and Parker, J. C. 1987. Effects of hysteresis with air entrapment on water flow in the unsaturated zone. Warer Resour. Res. 23(10): 1 967–1 976. Lang, A. R. G. 1967. Osmotic coefficients and water potentials of sodium chloride solutions from 0 to 40 ◦ C. Aust. J. Chem. 20: 2 017–2 023. Li, A. G., Tham, L. G., Yue, Z. Q., Lee, C. F. and Law, K. T. 2005. Comparison of field and laboratory soil-water characteristic curves. J. Geotech. Geoenviron. Eng. 131(9): 1 176–1 180. List, R. J. S. (ed.). 1951. Smithsonian Meteorological Tables. 6th Revised Edition. Smithsonian Institution Press, Washington, DC. 527pp. Mitchell, R. J. and Mayer, A. S. 1998. The significance of hysteresis in modeling solute transport in unsaturated porous media. Soil Sci. Soc. Am. J. 62(6): 1 506–1 512. Peralta, P. N. 1995. Sorption of moisture by wood within a limited range of relative humidities. Wood and Fiber Sci. 27(1): 13–21. Poulovassilis, A. and El-Ghamry, W. M. 1978. The dependent domain theory applied to scanning curves of any order in hysteretic soil water relationships. Soil Sci. 126(1): 1–8. Puri, A. N., Crowther, E. M. and Keen, B. A. 1925. The relation between the vapor pressure and water content of soils. J. Agric. Sci. 15(2): 68–88. SAS Institute, Inc. 1999. SAS/IML User’s Guide. Version 8. SAS Institute, Inc, Cary, NC. Si, B. C. and Kachanoski, R. G. 2000. Unified solution for infiltration and drainage with hysteresis: Theory and field test. Soil Sci. Soc. Am. J. 64(1): 30–36. Simunek, J., Kodesova, R., Gribb, M. M. and van Genuchten, M. T. 1999. Estimating hysteresis in the soil water retention function from cone permeameter experiments. Water Resour. Res. 35(5): 1 329–1 345. Steel, R. G. D. and Torrie, J. H. 1960. Principles and Procedures of Statistics. McGraw-Hill, New York. 481pp. Tuller, M. and Or, D. 2005. Water films and scaling of soil characteristic curves at low water contents. Water Resour. Res. 41. W09403, doi: 10.1029/2005 WR004142. Whitmore, A. P. and Heinen, M. 1999. The effect of hysteresis on microbial activity in computer simulation models. Soil Sci. Soc. Am. J. 63(5): 1 101–1 105.