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Dep. of Soil Science, North Dakota State Univ., P.O Box 5638, Fargo, ND 58105
* Corresponding author (lprunty{at}ndsuext.nodak.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: HOW, heat of wetting • ITT, infiltration transient temperature • S, specific surface area • SPL, Simulation Program for Land-Surface Heat and Transport software • TC, type T thermocouple
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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The liquid water potential energy and enthalpy changes lumped together constitute the HOW. Heat of wetting (heat of immersion) is defined experimentally as the heat evolved at constant temperature when material at a uniform initial water content, often oven dry, is completely immersed by liquid water. Measurements of HOW have been performed on many materials, including cotton and regenerated cellulosic fibers (Mizutani et al., 1999), xanthan powder (Andersen et al., 1995), wood products (Feng and Cheng, 1988; Guyer and Hossfeld, 1990; Avramidis and Dubois, 1992), and alfalfa tissue (Megee, 1935). The impact of various physical and chemical factors on HOW in soils has also been investigated. Examples include: the effect of several exchangeable soil cations (Baver, 1928), the effect of earthworms and wood lice (Samedov and Nadirov, 1990), the effect of irrigation (Utkaeva, 1998), and the effect of several organic polymers used to increase soil aggregate stability (Moen, 1983). Dimo and Utkayeva (1984) investigated the use of HOW as an indicator of soil physical properties related to fertility.
Experimental results have shown that soil HOW is largely governed by clay content and type, specific surface area (S), organic matter content, salinity level, cations, and water content. For example, Janert (1934) measured HOW as affected by the type of cation adsorbed to soil particles and found the order Ca > Mg > H > Na > K (highest HOW to lowest). Grim (1968) lists HOW values of 7.9, 49.4, and 16.7 J g–1 for kaolinite, montmorillonite, and illite clays, respectively. Moen (1983) measured HOW values of 24.3 and 19.8 J g–1 for Fargo silty clay and Glyndon silt loam soils, respectively, both of which contain smectitic clays. Heats of wetting of 29.5, 27.2, 15.4, 14.9, and 11.0 J g–1 were measured by Baver (1928) on Toledo silty clay (0–13 cm), Toledo silty clay (36–46 cm), Ellsworth silt loam (43–71 cm), Ellsworth silt loam (71–102 cm), and Clermont silt loam (0–20 cm) soils, respectively. Dimo and Utkayeva (1984) measured HOW values of 11.7, 7.2, and 17.4 to 27.7 J g–1 for A-horizon soils of loam, loamy sand, and clay loam textures, respectively, while also documenting effects on HOW of soil variables such as humus content, particle-size fraction, S, maximum hygroscopicity, and aggregate diameter.
The liquid–vapor phase transition is associated with heat of vaporization. It is independent of HOW because HOW requires no consideration of the vapor phase. Heat of vaporization can result in heat transfer and temperature gradients in materials and systems that do not exhibit HOW.
Only a few measurements of the heating effect that occurs at wetting fronts (ITT) have been reported in the past. These experiments were generally conducted by measuring temperatures at fixed points in unsaturated soil as a wetting front passed or an infiltration process proceeded. Such measurements were reported, for instance, in works by Anderson and Linville (1960), Anderson and Linville (1962), Anderson et al. (1963a)(1963b), and Fry (cited by Boersma et al. [1972][p. 97] as a 1968 M.S. thesis, which we have been unable to obtain). The four citations with Anderson as author constitute the prime example of previous work on this topic. However, the experimental results reported there were very limited in quantity and scope. Further, the data were not used and were not in fact suitable for testing coupled soil water and heat transport theories, the prime example of such a theory being that by de Vries (1958).
Several numerical models of simultaneous soil water and heat transport have been developed based on the de Vries (1958) theory since it was published. Although the complete de Vries (1958) theory includes HOW effects, some of the models developed from it have included this effect and some have not. One model which incorporates HOW according to the de Vries (1958) theory is that of Milly (1982). Benjamin et al. (1990) also incorporated a heat of wetting term into their model. Other noteworthy transport models, including those by Fayer (2000), Pruess (1987) and Pruess and Narasimhan (1985), Salzmann et al. (2000), and Jury (1973), did not. Model authors are clearly divided on the importance of including HOW in soil water transport models. The Milly model (Milly, 1982) appears to be the only model that is widely available, has been tested and applied in a variety of scenarios, and includes HOW effects somewhat in accordance to the de Vries (1958) theory.
Vaporization and condensation with their associated latent heat effects occur independently of HOW. While water vapor flow is an important heat transport mechanism in unsaturated soil and can result in measurable ITT, it can be shown that such ITT effects are expected to be of much smaller magnitude than those caused by HOW in fine-textured soils. It is of interest that all the models mentioned in the immediately previous paragraph include this smaller heat of vaporization (latent heat) effect. Also, Anderson and Linville (1960) attributed the temperature increases they measured as entirely due to adsorption from the vapor phase. On the contrary, we hypothesize that HOW is the dominant cause of temperature changes during infiltration independent of the phase of the water involved.
The first objective of this study was to experimentally determine ITT as influenced by soil type and initial water content. The experiment was designed to produce one-dimensional, vertical infiltration of water and also one-dimensional heat flow. The second objective was to critically compare results from a coupled soil water and heat transport model to the experimentally measured results. The model used was one previously published and verified, and included HOW effects. The de Vries (1958) theory of HOW has not previously been examined through this type of comparison. The final objective was to illustrate separation of heat of vaporization and HOW effects through use of the model.
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MATERIALS AND METHODS |
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Oven dry soil and a proportional amount of water necessary to produce the desired initial soil water content were thoroughly mixed. This soil was then packed into the column at the desired dry bulk density (Table 1) in uniform increments. The same soil was also packed at the same bulk density in a layer 0.4 cm thick over the top TC, followed by a Kimwipe and 0.1 cm more soil. The function of the layers over the top TC was to laterally disperse water applied to the soil surface. Thus, the water infiltration process was effectively one-dimensional. To minimize evaporation and convection heat transfer before and during the run, the open (fill) end of the column was covered with a layer of Parafilm (SPI Supplies, West Chester, PA), which was held in place with a rubber band.
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Soils used were Fargo silty clay (fine smectitic frigid Typic Epiaquert) and Glyndon loam (coarse-silty mixed superactive frigid Aeric Calciaquoll) at initial water contents ranging from 0.00 to 0.06 g g–1. All soil material passed a 1-mm sieve. Selected properties of the soils are given in Table 1.
Modeling
The model used to simulate ITT for the Fargo and Glyndon soils was the Simulation Program for Land-Surface Heat and Water Transport (SPLaSHWaTr) version 2.4 (available at ftp.gfdl.noaa.gov/pub/pcm/splash) hereafter called SPL. This model simulates water and heat movement in layered porous media based on a finite element, matric head formulation (Milly, 1982; Milly and Eagleson, 1980). The model follows the Philip and de Vries (1957) analysis of liquid water and water vapor transport and, as previously mentioned, includes HOW in somewhat the same manner as de Vries (1958).
The SPL model is a documented model, which was initially tested by its author against three examples (Milly, 1982) of previously solved problems. Example 1 was ponded and nonponded isothermal infiltration into Yolo light clay as reported by Haverkamp et al. (1977). The results from SPL for Example 1 converged to the established solution. Example 2 was a test of simulating isothermal infiltration and redistribution of water into initially very dry sand, considering hysteresis. The experimental data for this comparison was from Staple (1969). There was general but not better than modest agreement of the experimental and model results for this acknowledged difficult problem in modeling of soil water transient conditions. Example 3 was focused on testing the ability of SPL to replicate the dynamics of strong coupling of heat and water movement in a vapor-dominated system. In this example an initially dry and isothermal column is subjected to a sudden increase in vapor density at one end while the temperature there is forced to remain constant. Meanwhile, at the opposite end of the column the boundary condition is that of no heat or moisture flow. The analytical solution for this problem agreed closely with the SPL numerical results. The SPL model has also been tested in comparison with field data obtained from a Texas desert site and extending over a full year (Scanlon and Milly, 1994), with results reported as "remarkably consistent" between the experimental data and SPL simulation results. In addition, SPL has been used to assess the global impact of the thermal dependence of transport parameters on predictions of evaporation for different soils and climates (Milly and Eagleson, 1982; Milly, 1984). Inclusion of HOW effects makes SPL unique among well-known published models and is the primary reason for its use here.
Parameters used in the SPL model were based first on measured values for the soils used and secondarily on published values for soils of similar properties. Model parameters for various soils have been published by Scanlon and Milly (1994) and by Milly (1984). At the bulk densities used in our columns we measured Fargo hydraulic conductivity as 6.0 x 10–4 cm s–1 and Glyndon as 1.5 x 10–4 cm s–1. Differential HOW is calculated by SPL as proportional to the water film thickness on the soil particle surfaces (Milly and Eagleson, 1982), so S is an important property for the model. See the discussion section, however, for further clarification of the use of S in the model. We used an S value of 2 x 105 cm2 cm–3 for both soils. Our value was intermediate between a theoretical value based on 750 m2 g–1 for the smectitic clay fraction and the 1 x 105 cm2 cm–3 value provided with SPL in the silty clay sample data set. The theoretical calculation leads to an unrealistically high S of about 4 x 106 cm2 cm–3 for Fargo soil at a bulk density of 1 g cm–3. This high value (20 times the value we used) is because much of the surface area of smectitic materials included in the 750 m2 g–1 figure is internal and therefore is not effective in terms of HOW. The theory employed by SPL and our analysis of SPL output agrees on a linear relationship of S and the ITT temperature rise. The S value used was thus based partially on good agreement between the model results and experimental temperature data for the 0% initial water content soil experiments. Other parameters used with the model are listed in Table 2. Porosity and volume fractions of the solids were found from measured data.
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To address the final objective, the model was used to predict temperature changes due only to evaporation and condensation. To accomplish this, S was set to zero. This exercise was prompted by statements of Anderson and Linville (1960) implying that the only contributing factor to temperature change on passing of a wetting front was due to vaporization and condensation processes.
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RESULTS |
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Temperature changes predicted by the model (Fig. 6 and 7) were both larger and smaller than those observed. The pattern of temperature change, including the peaks, is very similar for the model and experiment. The most noticeable difference is that the experimental data show the temperature peaks at any given thermocouple depth occurring at later times. Elapsed time to the experimental peaks were generally up to 30% longer than time to the corresponding model peak. At 0.04 g g–1 water content for both the Fargo and Glyndon soils the simulated temperature drops more sharply and farther after the peaks than the experimental data. This is in contrast to the 0.00 g g–1 simulations, which show the temperatures trailing the peaks to be maintained at levels relatively close to the peaks and not greatly different than the experimental trailing temperatures.
Peak temperatures and trailing temperatures of experimental versus model results were tabulated and comparatively analyzed. Here trailing temperature means the temperature where the sharp drop from the peak breaks into the relatively flat plateau, which follows the peak. In Fig. 4 through 7 the break points defining the trailing temperatures are quite distinct. Data from TCs 1 through 5 only were used in this analysis because TC 6 was at the boundary of the soil, not in it.
For peak temperatures the experimental peak minus the initial temperature was taken as 1.00 and the corresponding model peak minus initial temperature was compared to it. The model/experimental peak temperature ratios for Fargo 0.00 g g–1, Fargo 0.04 g g–1, Glyndon 0.00 g g–1, and Glyndon 0.04 g g–1 averaged 1.18, 0.69, 1.05, and 0.82, respectively. Thus, peak temperatures indicated by the model were modestly above experimental results for 0.00 g g–1 runs and below for 0.04 g g–1 runs. Root mean square errors for the same comparisons were 0.21, 0.35, 0.08, and 0.24.
The trailing temperatures were first expressed as fractions of the corresponding peak temperatures. For instance, in Fig. 4 for TC 1 the temperature rise from 26.6 to 32.0 is the peak value and the trailing value is 31.0, which is 0.81 of the peak. In Fig. 6 the corresponding model peak is 33.0 and its training temperature is 31.6, which is 0.78 of the peak. The metric used for comparison is the ratio of these, that is, 0.78/0.81 = 0.96. The values of this measure of model versus experiment trailing temperature for Fargo 0.00 g g–1, Fargo 0.04 g g–1, Glyndon 0.00 g g–1, and Glyndon 0.04 g g–1 averaged 0.88, 0.47, 0.98, and 0.62. The preceding values indicate the model reproduced the relative temperature drop before trailing fairly closely for 0.00 g g–1 runs but the model trailing temperatures for 0.04 g g–1 runs were, relatively speaking, substantially lower. Root mean square errors for the same comparisons were 0.15, 0.54, 0.05, and 0.39.
Results of the evaporation/condensation (no HOW effect) model run (Fig. 8) show a temperature pattern very similar to that graphed by Anderson and Linville (1960) but much different in shape and smaller in magnitude than the corresponding data of Fig. 4 and 6. The model data indicated a temperature peak of 1.1°C above the initial temperature followed by a 0.3°C temperature depression compared with the original temperature. The time scale of our model results is expanded compared with that indicated by Anderson and Linville (1960) where for kaolinite the temperature peak width at 1.0 cm from the surface was about 2/3 of what we observed at 1.5 cm from the surface, a reasonable correspondence.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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Temperature change on wetting was directly, but not linearly, related to soil clay content. Clay content was 2.7 times higher in the Fargo than the Glyndon soil, but the maximum ITT in dry Fargo vs. dry Glyndon soil was only 1.5 times higher. The decreases in ITT between 0.00 and 0.02 g g–1 water contents were large for both soils, but the decreases in maximum ITT between 0.02 and 0.04 g g–1 were larger for the Fargo than the Glyndon soil. In fact, decreases in ITT in the Glyndon soil between 0.02 and 0.04 g g–1 water content were similar or smaller in magnitude than those from the Fargo soil between 0.04 and 0.06 g g–1 water content. This again demonstrates a nonlinear increase in free energy of water molecules as a function of soil water content. We did not determine ITT at 0.06 g g–1 water content for the Glyndon soil because of the small values for ITT obtained at 0.04 g g–1.
Maximum temperatures during the period of ITT observations tended to increase going downward (higher TC numbers). Conductive and/or vapor heat flow increased temperatures ahead of the apparent wetting front. Peak temperatures were interpreted as occurring at the wetting front as the heat of wetting reaction occurred. The temperature rise grew cumulatively larger as temperatures increased going down the column, generally speaking. This was not observed in the Fargo soil at 0.06 g g–1 water content because the higher initial water content increased the heat capacity ahead of the wetting front and minimized temperature change in lower layers.
Anderson and Linville (1960) conducted experiments similar to ours and presented a figure showing a 1°C temperature increase during infiltration of water into a kaolinitic clay followed rapidly by a 2°C decrease. They theorized that the observed temperature increase was due to latent heat of condensation (and absorption) of water vapor onto soil particles ahead of the wetting front while the wetting front itself was cooled by the evaporation of this water vapor. The cooled wetting front proceeding through the soil resulted in a rapid reduction in temperature as the front passed. Our observed temperature patterns (Fig. 3 and 4) were quite dissimilar to those of Anderson and Linville (1960) in that we did not observe a temperature decrease. In later work, however, Anderson and Linville (1962) found that the temperatures in these experiments did not drop below the initial values, but became stable at levels above the initial temperature. However, the graphical results presented by Anderson and Linville (1962)(Fig. 2) indicate a return to stable temperatures that were only a fraction of a one °C higher than the initial values. Our results, on the contrary, show nearly stable temperatures after the peaks, which are generally at greater than half the peak height and range up to more than 5°C greater than the initial temperatures.
Using physical properties of our soils and their components, we estimated the temperature increase expected when Fargo and Glyndon soils are saturated from the oven dry condition. We used bulk density values of 1.02 and 1.26 for Fargo and Glyndon soils, respectively, 1.37 g cm–3 for the particle density of humus (Baver et al., 1972), organic matter contents from Table 1, and Eq. [7] and [8] from Baver et al. (1972) to calculate heat capacity for Fargo and Glyndon soils. We then used HOW along with calculated heat capacity values from Table 1 and heat capacity of water to solve for the expected maximum temperature change from completely dry to saturation. Increases of 7.33 and 7.87°C were calculated to occur from the Fargo and Glyndon soils, respectively, on saturation, which are in the range of what we observed for our 0.00 g g–1 samples (Fig. 2 and 3). Glyndon shows a larger increase under the assumed conditions for the calculations, mostly because less water is required to reach saturation at Glyndon's higher bulk density. The experimental situation is different because at a given time in the experiment the same amount of water has been added to either soil.
To calculate an estimate of HOW based specifically on our measurements, we used average ITT for Segments 2 through 5 of the 0.00 g g–1 initial water content Fargo and Glyndon ITT columns, and bulk density and heat capacity values previously mentioned. We did not include ITTs from Segments 1 and 6 in the average to avoid end-of-column effects. The calculations were essentially the reverse of the temperature rise calculation above. That is, given the temperature rise to a stable level, the bulk densities, and water content changes, the heat of wetting can be extracted. These calculations resulted in HOW values of 31.9 and 17.6 J g–1 for Fargo and Glyndon soils, respectively. These values fall within the range of HOW values other researchers have measured for similar textured soils (see Introduction) and compare reasonably to the Moen (1983) HOW data of Table 1.
Model
The SPL model predicted the major features of the ITT experimental data. A temperature rise at each depth to a maximum followed by a sharp drop to a plateau above the initial temperature was seen in both experiment and model data. Peak temperatures agreed well for the 0.00 g g–1 model run compared with experimental data, as expected, because S was adjusted to achieve this agreement. At 0.04 g g–1, however, for both soils the model results did not agree with experiment as well, having, as noted earlier, smaller peaks and lower trailing temperatures. The manner of calculation of W, discussed later, could be a factor in these differences. The plateau temperatures increased with distance from the entry surface. As previously observed, the times of the model peak temperatures were in advance of the times for the corresponding experimental data.
The model parameters could have been adjusted by "inversing" to reproduce the experimental results more closely. In fact, we did find sets of parameters that resulted essentially in duplication of the amplitude and timing of the peaks of Fig. 4 and 5. When this was done values of some parameters were rather unrealistic. The saturated hydraulic conductivity parameter in particular was far different (lower) than we measured by the Klute (1965) constant head method. Using these optimum inversed parameters would give misleading credit to the model in spite of known shortcomings. Namely, the energy equation used in the model, from de Vries (1958), is valid in most respects but fails to fully conserve energy in a control volume (Prunty, 2004). It can be expected to yield good values of total energy release in a situation such as the ITT experiments in which free water is continuously added and water content is increasing everywhere. It does not account properly for the spatial distribution of the heat generated as the surface-introduced water redistributes to greater depths (Prunty, 2002). Thus, our interpretation of the model predictions is that the end result is first-order correct despite the presence of some fundamentally incorrect underlying theory.
The too early arrival of water predicted by SPL is consistent with unsaturated hydraulic conductivity values in the model being too great. Lower relative hydraulic conductivities in the dry range would restrict water redistribution, requiring greater water content near the surface and thus later arrival of the wetting front and temperature peaks. This same behavior of relative hydraulic conductivity has been observed previously (Prunty, 2003). Also, Milly and Eagleson (1980) reported that the computation of relative hydraulic conductivity used in SPL, that of Mualem (1976), resulted in a less-distinct wetting front than that produced by the optimum hydraulic conductivity function for Yolo light clay as reported by Haverkamp et al. (1977).
The HOW theory used in actual computation by SPL is not exactly that presented by de Vries (1958). In the early version of SPL, differential heat of wetting, W, was formulated (Milly and Eagleson, 1980) directly as indicated by de Vries (Eq. [12] of de Vries, 1958) using
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is soil water matric potential and T is temperature. The computation method used in SPL version 2.4 is somewhat different. It follows the ideas of Groenevelt and Kay (1974) as cited in Milly (1984), where W is given as
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l is liquid water density, 
is water film thickness on soil particle surfaces, and 
is the characteristic thickness associated with H. Specific surface is an important parameter for the model (Table 2) and enters into the calculations when is calculated by dividing the volumetric water content by S. Integration of Eq. [2] yields the theoretical HOW, which is found to be equal to the product of H and S appropriate for calculating . Our values of S multiplied by H match the Moen (1983) HOW values within about 20%. Note that S as used herein is that which produces HOW effects and is not necessarily the same as measured by chemical adsorption methods.
It is instructive to calculate an approximate upper limit for W and compare this value to the standard latent heat of vaporization, L. When water evaporates from pure liquid at 25°C, L = 2444 kJ kg–1. At oven dry condition, the matric potential of soil water is sometimes taken as = –980 kJ kg–1. Specifically, in SPL pF = 7 is assumed to be oven dry and at pF = 7, h = 107 cm = 105 m expressed as head of water, which corresponds to 9.8 m s–2 x 105 m = 980 kJ kg–1 negative water potential expressed as energy per unit mass. We will now use Eq. [1] to calculate W at the oven dry condition. To proceed to evaluate Eq. [1] we need the temperature dependence of . There has been much discussion and debate about this in the literature, but for present purposes we will adopt the approach used by Milly and Eagleson (1982), which says –
= 0.0068 K–1. Thus, W = –(1 + 0.0068T) so at oven dry and 25°C (298 K) we have W = 980.0(1 + 2.026) = 2966 kJ kg–1. Thus, at its maximum, W is about 20% greater than L.
Values of L and W of the same order of magnitude are at odds with the small stable temperature rise reported by Anderson and Linville (1962), as mentioned previously in the discussion of the experimental results. A rapid return to near the ambient temperature as reported by Anderson and Linville (1962) is, however, consistent with passing of the wetting front and a simultaneous large increase in thermal conductivity of the thin soil layer. As soon as the wetting front passed in the Anderson and Linville (1962) apparatus the elevated temperatures caused by both L and W could dissipate very rapidly into the surrounding ambient-temperature apparatus. Their apparatus, according to description and drawing, contained a soil sample only 3 mm in thickness and was not insulated and thus equilibrated fairly quickly with the ambient temperature. In our experiments, however, the top of the column was the only uninsulated path for heat loss. Mainly air was available at the top, however, to conduct heat, so the loss there should have been small, also.
Anderson and Linville (1960)(1962) seem to have been primarily interested in differentiation of vapor and liquid flow and subsequently argued (Anderson and Linville, 1962) that vapor flow dominates up to the time when the temperature peak occurs in ITT. The data still support that basic conclusion, but we suggest that greater detail on the relative amounts of vapor and liquid water transport at various points near the wetting front is still needed.
Anderson et al. (1963b) presented data on the dependence of maximum temperature change during ITT on the initial water content of the soil, somewhat similar to our data presented in Fig. 2 and 3. Anderson et al. (1963a) analyzed ITT data from the activation energy perspective.
The data produced (Fig. 8) by the model run with S equal to zero (implying evaporation/condensation heat effects only) closely mimicked results reported by Anderson and Linville (1960) for kaolinite, probably mainly because of the low HOW of kaolinite. This is another illustration of the general agreement of the SPL model results with experimental data. At the same time, the results of Fig. 8 versus those of Fig. 6a show strikingly the consequence of including HOW in the model. That is, while the model results shown in Fig. 6 (peak temperature rise of 8°C at the z = 4 level) are in reasonable agreement with the experimental results of Fig. 4 (peak rise of 7.5°C at TC2 at z = 4), removing HOW effects from the model, as in Fig. 8, produces results (peak rise of 1°C at z = 4) which are out-of-agreement with the experimental data by a factor of 7.5. Further, the drop below the initial temperature indicated in Fig. 8 was never found in either experimental or modeled results that included HOW effects.
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CONCLUSIONS |
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Also, the influence of ITT on the infiltration process has not been analyzed. A substantial temperature rise changes the viscosity of water and hence the hydraulic conductivity, for instance, and this should change infiltration calculations somewhat compared with an isothermal calculation. This topic needs further theoretical and experimental investigation.
A standard approach to modeling coupled heat and water flow, the Philip and de Vries (1957) and de Vries (1958) model, predicts the major characteristics of the experimental ITT temperature data, as illustrated by the results from the computer model SPL. There are, however, three identified shortcomings in the current model. First, the de Vries (1958) theory itself is incomplete. A more complete theory has been presented (Prunty, 2004) that eliminates some shortcomings. Second, calculation of differential HOW (W) according to the original de Vries (1958) equation (Eq. [1]) is based on the fundamental theory of Edlefsen and Anderson (1943) while Eq. [2] uses estimated values. A model using Eq. [1] should be written and a comparison made of model ITT results using Eq. [1] versus Eq. [2]. Third, the Mualem (1976) standard relative hydraulic conductivity function used by SPL may produce problems similar to those noted by Prunty (2003). Alternative relative K functions should be tested.
A reasonable and desirable goal for infiltration research would be to achieve a verified model, which fully accounts for ITT effects when infiltration takes place in very dry as well as moist soil. Additional experimental results suitable for testing such a model should be acquired. Another future desirable extension of this work would then be to calculate differences between water infiltration as calculated by the verified, updated model including full ITT effects as described above and a corresponding isothermal simulation. Achieving these would constitute an advance in basic soil physics and our understanding of simultaneous soil water and energy transport.
Received for publication June 30, 2004.
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