Published in Soil Sci. Soc. Am. J. 68:719-724 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
DIVISION S-1—SOIL PHYSICS
Observations and Modeling of Profile Soil Water Storage above a Shallow Water Table
Mahmood Nachabe*,a,
Caroline Maseka and
Jayantha Obeysekerab
a Dep. of Civil and Environmental Engineering, University of South Florida, 4202 East Fowler Avenue, ENB 118, Tampa, FL 33620
b South Florida Water Management District, West Palm Beach, FL 33406
* Corresponding author (nachabe{at}eng.usf.edu).
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ABSTRACT
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The storage capacity of a soil profile (soil water storage capacity [SWSC]) is the depth of water required to raise a shallow water table to the land surface. The concept of SWSC is fundamental to many hydrological processes, including surface runoff by saturation excess, expansion, and contraction of wetlands, and estimation of the length of an overland flow plane. A model is introduced and tested to estimate SWSC using simultaneous observations of shallow water table fluctuations and soil moisture in a shallow, sandy soil (hyperthermic Aeric Alaquods). The water table at the selected site fluctuated between a shallow depth and the land surface during the summer, allowing frequent observation of surface inundation and profile storage. An equation of the form SWSC = AdB + Cd + D adequately described the variability of SWSC with d, depth to the water table. It is shown that parameters A, B, C, and D are easily derived from basic physical properties of the soil horizons, including porosity and water retention. The SWSC can be significantly limited by the capillary fringe above the water table, encapsulated air (the volume of air trapped under positive pressure beneath the water table), or the presence of a clay pan at shallow soil depths. The capillary fringe had some influence on SWSC in this sandy soil, but encapsulated air as high as 11.0% of the soil volume was observed at the site. Encapsulated air reduced the available soil storage and resulted in a rapid rise in water table. Ignoring encapsulated air significantly overestimated profile storage. Storage results including and excluding air encapsulation were compared as a function of water table depth.
Abbreviations: SWSC, soil water storage capacity
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INTRODUCTION
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IN HUMID ENVIRONMENTS, like Florida and the rest of the southeastern USA, the water table fluctuates between a shallow depth and land surface, creating a cycle of ground surface saturation recognized as the hydroperiod of an ecosystem (Ewel, 1990). Identifying the saturated zones of a landscape is needed to predict saturation excess runoff (VanderKwaak and Loague, 2001), to estimate the hydroperiod of wetlands (Arnold et al., 2001), and to determine pollutant sources from an overland flow plane (Yan and Kahawita, 2000). Recent evidence indicates that zones prone to frequent inundation and surface saturation by rising water tables contribute most of the rapid water and overland pollutant transport in the watershed. Fundamental to the identification of these variable saturation zones is the concept of SWSC, defined as the depth (volume per unit area) of water needed to raise a shallow water table to land surface. The SWSC capacity is the maximum infiltration depth that can be absorbed by the soil before the shallow water table rises to land surface initiating ponding or saturation excess overland flow.
Early observations of a quick and large response of shallow water tables were made by Meyboom (1967) and Duke (1972). Later, Gillham (1984) and Abdul and Gillham (1989) attributed this phenomenon to the high degree of saturation in the capillary fringe above the water table, resulting in a large water table rise for a small volume of water added. The ratio of added water depth to water table fluctuation is known as the specific yield of the water table aquifer (e.g., Duke, 1972). Duke (1972) introduced an equation to account for the capillary fringe influence on specific yield in a shallow water table environment. Recently, Nachabe (2002) modified the early work of Duke to account for the influence of large water table fluctuations on specific yield.
While the capillary fringe limits profile soil water storage above a shallow water table, Fayer and Hillel (1986) demonstrated that encapsulated air below the rising water table reduces further storage in the pore space. In a field study, Fayer and Hillel sprinkled water at a rate of 12.6 mm h–1 to bring the water table to land surface. For a fine sandy loam, they found that air encapsulation caused water table rises to be significantly higher than a soil without air encapsulation. The mechanism of air encapsulation is of significant importance to soil water storage, and was recognized in the early work of Peck (1969). Basically, when a shallow water table rises, some pores fill up before others, due to differences in velocities at the pore scale. This leads to air bubbles trapped below the water table, which are unable to escape to the atmosphere. Once encapsulated, air bubbles persist for days, even weeks, since the bubbles will dissipate from the matrix through the slow processes of dissolution or diffusion (Peck, 1969; Fayer and Hillel, 1986). Seymour (2000) surmised that large pores, particularly in sandy soils, increase the likelihood of discontinuous air bubbles being trapped in the soil matrix. This reduction in the available pore space led to the concept of water content at natural saturation because under natural recharge conditions, the soil is considered saturated although encapsulated air continues to fill a fraction of the pore space. The water content at natural saturation is the soil porosity minus encapsulated air. Wilson et al. (1982) approximated the volume of encapsulated air for one type of loamy sand as 15% of the porosity. Constantz et al. (1988) used CO2 injection during ponded infiltration tests to measure encapsulated air. They found that encapsulated air volumes account for 19% of the porosity in medium Olympic sand (fine, mixed, active, mesic Xeric Palehumults).
In this study, we monitor the water table and the soil moisture at eight depths in a shallow Floridian sand profile. The relatively high resolution of soil moisture with depth allowed simultaneous observations of encapsulated air and SWSC above a shallow water table. The objectives of this study were (i) to introduce an equation for SWSC as a function of depth to water table, (ii) to assess the influences of the capillary fringe and encapsulated air on SWSC, and (iii) to test and validate the concept of SWSC with field data. The main finding of the article is that the profile soil water storage can be expressed as a polynomial function of the depth to water table. The parameters of this function can be derived from the soil hydraulic and physical characteristics. Ignoring encapsulated air below the water table may result in significant overestimation of profile water storage.
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THEORY
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The soil water storage equation was derived as a function of water table depth, and it incorporates physical soil hydraulic properties. For a shallow water table environment, it is customary to assume a hydrostatic, equilibrium, water content profile since the thin unsaturated zone is in close hydraulic connection with the shallow water table. This assumption has been adopted before for estimating the specific yield of shallow water table aquifers (e.g., Duke, 1972; Nachabe, 2002), and for determining soil water storage in calculating saturation excess runoff (Troch et al., 1993). In this case, the capillary pressure head is equal to elevation z above the water table. The water content distribution in a homogenous soil profile is:
 | [1a] |
for z > hA, and
 | [1b] |
for z 
hA, where 
(z) is soil water content (m3 of water m–3 of soil) at elevation z above water table (z in m is zero at water table and positive upward), g is specific retention, s is saturated water content, hA is air entry pressure (in meters of water) and 
is the pore-size distribution index. The Brooks and Corey (Brooks and Corey, 1964) model of water retention is adopted in this study because representative values of its parameters have been documented in the literature, and can be easily estimated from soil texture data (e.g., Rawls et al., 1993). The maximum water depth that can be absorbed by the soil before the water table rises to the land surface is (see Fig. 1)
:
 | [2] |
where SWSC(d) is profile water storage (in meters), and d (in meters) is depth from the land surface to the water table. Replacing [1] in [2] and integrating yields
 | [3] |
for d > hA, and SWSC(d) = 0 for d < hA. The equation can be rearranged into a more convenient form such as
 | [4] |
which is expressed as a polynomial equation:
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where A, B, C, and D are sole functions of soil physical properties. The entire term in the left-most set of brackets in Eq. [4] is A, B is 1 – , C is the drainable porosity (s – g), and D is the term in the rightmost set of brackets. This equation accommodates the influence of the capillary fringe on SWSC. For a deep water table (large d), Eq. [5] approaches a straight line with slope equal to drainable porosity. To isolate the influence of the pore-size distribution on SWSC, it is convenient to write Eq. [4] in the dimensionless form
 | [6] |
where I*, a normalized storage equal to SWSC/[(s – g)hA], is expressed as a function of normalized depth, d*, equal to (d/hA).
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Fig. 1. Profile soil water storage above a shallow water table at depth d is represented by the hatched area.
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Equation [5] seems to capture the influence of the capillary fringe on SWSC, but this equation has not been tested before under field conditions with actual data. Also, this equation should be modified to account for encapsulated air when the water table rises to land surface. Theoretically, if encapsulated air is ignored, s should be equal to the total soil porosity. The role of encapsulated air in reducing SWSC can be accommodated by treating s in Eq. [2] as the water content at natural saturation, equal to porosity minus the encapsulated air volume. Currently, however, there is no systematic theory allowing estimation of encapsulated air below the water table. In this study, a field experiment was conducted to measure encapsulated air and to test the goodness of fit of Eq. [5] for profile water storage.
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MATERIALS AND METHODS
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The study area is in Lithia, near the planned Tampa Bay Regional Reservoir in the southeastern portion of Hillsborough County, Florida. Sandy marine sediments are the dominant parent materials for many soils in central and south Florida. The Myakka fine sand (sandy, siliceous, hyperthermic Aeric Alaquods) at this site is typical of poorly drained soil in Florida flatwoods. Carlisle et al. (1989) characterized the physical properties of Myakka fine sand, and Table 1 shows typical texture and hydraulic conductivity distributions with depth. The soil texture contains over 90% sand for all horizons, with slight variation in clay content with depth. The depth to water table at the site fluctuates between 0 and 2 m. Usually, the water table recesses to below land surface in the dry season (November through May), then gradually rises to inundate the land surface in the rainy season (June through September). Figure 2
shows the water table fluctuation at the site for a month in the wet season of 2002.
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Table 1. Soil texture, saturated hydraulic conductivity (Ks), and bulk density (Db) with depth for Myakka fine sand, a common Florida soil.
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To estimate profile soil water storage and measure encapsulated air, two EnviroSCAN soil moisture probes (Sentek, Adelaide, Australia) were inserted within 30.5 m of each other. Each probe had eight soil moisture sensors placed at depths of 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1, and 1.50 m below land surface. The sensors permitted continuous monitoring of soil moisture profiles at 5-min time intervals. The sensors use the principle of electrical capacitance (frequency-domain reflectometry) and are expected to provide volumetric water content ranging from oven dryness to saturation with a resolution of 0.1% (Buss, 1993). The default calibration equations provided by EnviroScan were used in this study. Indeed, these sensors were tested by a number of investigators in the past (e.g., Buss, 1993; Morgan et al., 1999), and more recently Fares and Alva (2000) found no significant difference in water content as measured by the probes and the gravimetric method for fine sand in central Florida. In addition to the moisture sensors, two screened water table wells recorded continuously the depth to water table every 5 min. The wells housed Instrumentation Northwest 0 to 3.45 Pa (0–5 psi) submersible pressure transducers (Instrumentation Northwest, Inc., Kirkland, WA), accurate to 34.5 Pa (0.005 psi). The wells had a total depth of 4.6 m. A typical well was made with 50.8-mm PVC pipe, with a slotted PVC screen extending below a bentonite clay seal. Silica sand was packed around the screen to allow only the passage of water.
Field Estimation of Encapsulated Air and Soil Water Storage
To illustrate how soil water storage and encapsulated air were analyzed from the data, Figure 3
shows the soil moisture profiles and the associated water table depths for a recharge (rainfall) event in which the water table raised from an initial depth of 1.37 m to a final equilibrium depth of 0.92 m below land surface. For these sandy soils, the final equilibrium water table depth is reached in about 1 d, when the water table becomes stable and ceases to exhibit any significant fluctuation with time. As expected, the soil water content is higher close to the water table (see Fig. 3) due to the capillary fringe effect, and all moisture sensors recorded an increase in water content above the newly risen equilibrium water table. The submerged sensor, 1 m below the land surface, is now under the new water table but never reached full porosity (see Fig. 3). Encapsulated air volume is calculated as the porosity minus the water content measured in the submerged sensor (e.g., Fayer and Hillel, 1986).
The profile soil water storage was estimated by numerically integrating Eq. [2] with depth using the trapezoidal rule of integration. Mathematically,
 | [7] |
where i is the recorded water content by the sensor at elevation i, si is the saturated water content (equal to full porosity, if encapsulated air is neglected, or porosity minus encapsulated air, if encapsulated air is accounted for), and 
zi is elevation distance between the moisture sensors i and i + 1. Calculations of SWSC are repeated for different values of d in Eq. [7]. Finally, Eq. [4] was fitted using regression to this SWSC(d) data to test the goodness of fit of this model to field observations.
In most practical applications, however, field observations from soil moisture probes will not be available to develop the SWSC(d) relationship. In this case, one has to use readily available soil water retention data (hC) for (z) in Eq. [7]. To test this approach, water retention data for two Floridian soils were selected: Immokalee fine sand (siliceous, hyperthermic Arenic Alaquod) and Smyrna sand (Sandy, siliceous hyperthermic Aeric Alaquod). Water retention characteristics were obtained from duplicate undisturbed soil cores placed in Tempe pressure cells (Soil Measurement Systems, Tucson, AZ), saturated and then extracted at different capillary pressures (Carlisle et al., 1989). Table 2 summarizes the soil water retention for these two soils. Once SWSC data from Eq. [7] were calculated, we fitted Eq. [4] to this data using a least squares regression technique.
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Table 2. Water retention data for Immokalee fine sand and Smyrna sand, and soil texture, saturated hydraulic conductivity, and bulk density.
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RESULTS AND DISCUSSION
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Effect of the Capillary Fringe on the Soil Water Storage Capacity Equation
The capillary fringe reduces the available water storage above a shallow water table, a behavior that can be captured by Eq. [4], which relates storage to depth to water table. Figure 4
shows a plot of the normalized storage I* versus d* for three values of . Theoretically, SWSC remains zero for water table depth less than the air entry pressure, then the SWSC asymptotically approaches a straight line as the water table gets deeper. Indeed, by taking the derivative of Eq. [4], the slope of the SWSC(d) relationship approaches the drainable porosity, (s – g), as d increases. For shallow water table environments, soils with a narrow pore-size distribution (large ) have more SWSC than soils with a wide pore-size distribution (small ). Also for all soil types, the influence of the capillary fringe seems limited to elevations of about 3hA above the water table (see Fig. 4). In hydrological applications, like the estimation of water balances for wetlands, one is usually interested in shallow water table environments; therefore the capillary fringe is likely to play a significant role in reducing profile storage in these environments.
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Fig. 4. Dimensionless soil water storage capacity (SWSC) equation where I* equals the normalized soil storage and d* equals the normalized water-table depth.
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Figure 5
shows the fit of Eq. [5] to the SWSC of Immokalee and Smyrna sands calculated through water retention data. Equation [5] provided a very good fit for storage with r2 = 0.99 for both soils. The regression constants for Eq. [5] for the Smyrna sand were A = 233, B = –0.015, C = 0.41, and D = –229 while the constants for the Immokalee fine sand were A = 147, B = –0.024, C = 0.45, and D = –144. The two soils had a pore-size distribution index slightly larger than one ( = 1 – B), reflective of fine sandy soils (e.g., Brooks and Corey, 1964). The drainable porosity for Immokalee fine sand (0.45) was larger than the drainable porosity for Smyrna sand (0.41), and that resulted in a steeper slope for SWSC(d) for deep water tables (large d values). If the influence of the capillary fringe is neglected, then one might erroneously consider that the volume of water to fill the soil storage would be depth to water table multiplied by the drainable porosity. For d = 0.50 m, one would then predict that the SWSC for Smyrna sand is 0.50 x 0.41 = 0.205 m, whereas the storage, taking into account the influence of the capillary fringe, is <0.07 m at this depth. Clearly, the influence of the capillary fringe on SWSC cannot be ignored. The goodness of fit of Eq. [4] is encouraging because soil water retention characteristics are documented in numerous references and are more readily available.
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Fig. 5. The soil water storage capacity (SWSC) equation applied to two Floridian soils. The SWSC was estimated through the numerical integration of Eq. [2] using water retention data. The solid lines show the fit of Eq. [5] to these data.
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Effect of Air Encapsulation on the Soil Water Storage Capacity Equation
Soil water retention data, however, are often determined in the laboratory under drainage conditions, and do not account for encapsulated air below a rising water table. Table 3 presents the average and the standard deviation of the observed air encapsulation at the eight moisture sensors on each probe. The averages were calculated from 1 to 4 measurements during different recharge events for each sensor depth. For the sake of comparison, the volumetric encapsulated air determined by Fayer and Hillel (1986) for a sandy loam soil was also included in this table. These latter values are somewhat smaller than those measured during our experiment, which might be attributed to soil texture differences and the high fraction of sand in Florida. Encapsulated air volumes at the site increased with depth up to a maximum of 11% at 0.40 m below the land surface, then decreased for greater depths. Similar behavior was observed for the data provided by Fayer and Hillel (1986). The relatively small value of encapsulated air at 0.20 m below land surface could be attributed to proximity from land surface, which facilitates the escape of air.
To assess the influence of encapsulated air on SWSC, porosity was adjusted using the encapsulated air volumes in Table 3. Figure 6
compares the SWSC(d) optimized fit using Eq. [5], with and without correction for encapsulated air. Encapsulated air reduced significantly the profile water storage capacity. For example, with the encapsulated air effect included, it takes only 0.07 m of water to raise the water table from a depth of 0.75 m to land surface (see Fig. 6). A SWSC equation that ignores encapsulated air would predict that 0.12 m of water would be needed to bring the water table to land surface, an over prediction of over 70%. These differences are large considering a water budget for a wetland or for estimating variable saturation areas.
Field Estimated Soil Water Storage
In this section, we compare profile storage calculated from the sensors on the moisture probes with the storage calculated from retention data. Figure 7
shows the fit with Eq. [5], while neglecting encapsulated air (full porosity is used in Eq. [7]). Although the fit is reasonable with an r2 of 0.88, the scatter around the curve can be attributed to at least two reasons. Equation [5] was developed assuming a homogenous soil profile and an equilibrium water content distribution. Both assumptions are not completely realistic in field conditions. The Myakka fine sand at this site had a fairly uniform soil texture profile with depth, which is typical of Florida's undeveloped soils. In well-developed soils, leaching of clay minerals over time may result in clear textural differences or clay pans at shallow depth, which may limit further the applicability of Eq. [5].
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Fig. 7. The solid line is Eq. [5] with parameters estimated by optimizing soil storage from retention data. Observed soil moisture probe storages (triangles) without correction for air are superimposed.
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Figure 8
shows the fit of the model to profile storage calculated from retention data after correcting for encapsulated air. Profile storage calculated from moisture sensors and corrected for air encapsulation is superimposed. The fit of Eq. [5] dropped to 0.75 when encapsulated air is considered. The increase in scatter around the fit can be attributed to the nonuniformity of encapsulated air with depth, which increases the variability of the water content at natural saturation (porosity minus encapsulated air). It is difficult to speculate on the physical mechanisms responsible for the large variability of encapsulated air with depth. During water table rise, microscopic variability in water velocity causes pores to fill before others, a phenomenon that isolates and traps air bubbles (e.g., Peck, 1969). Thus depending on the rate of recharge and water table rise, different volumes of air bubbles can be encapsulated. Other reasons that may influence variability with depth are soil textural differences in the profile, and proximity from land surface.
The regression parameters for Eq. [5] including and excluding the effects of encapsulated air, are presented in Table 4. The values of the Brooks–Corey parameters are obtained from the knowledge of their relationships to these regression parameters (see Eq. [4] and [5]), and are thus considered effective parameters for the profile. The pore-size distribution remained essentially the same whether encapsulated air was included or excluded from the regression fit. Inclusion of encapsulated air, however, increased the effective air entry pressure and reduced the effective drainable porosity. As expected, a higher air-entry pressure and a lower drainable porosity tend to reduce the profile soil water storage.
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Table 4. Brooks and Corey parameters derived from regression constants using Eq. [5] after optimization both without and with inclusion of air encapsulation.
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CONCLUSIONS
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The objective of this study was to introduce and test an equation to estimate the profile soil water storage above a shallow water table. Estimation of this storage is needed for prediction of variable saturation areas, which are prone to seasonal flooding by rising water tables. There is a growing awareness of the need to identify these critical areas to control pollutant transport by saturation excess overland flow.
Estimation of profile soil water storage is complicated by encapsulated air, the capillary fringe, and soil texture heterogeneity. Both the capillary fringe and encapsulated air act to reduce the profile soil water storage. Use of drainable porosity may substantially overestimate profile storage. While we have reproduced some representative values for encapsulated air in a sandy profile, encapsulated air varied substantially with depth. Future research should work on developing a coherent theory that allows better quantification of the physical mechanisms responsible for encapsulated air below rising water tables.
A simple equation was introduced to simulate profile water storage above the water table in a sandy profile. This equation assumes that (i) the soil profile is homogenous, and (ii) the water content distribution is at equilibrium. Although this equation seemed to fit reasonably well profile storage in this homogenous sand profile, it is unlikely that it remains valid in profiles where soil horizons exhibit sharp contrast in their texture (e.g., a clay pan at shallow depth). The profile storage equation is physically based, and the regression constants could be derived for a number of common soils using retention data. This should facilitate its use by practitioners. The equation was tested with field data and seemed to capture reasonably well the influence of capillary fringe on profile water storage. Correcting for encapsulated air, however, was necessary to simulate profile storage under natural recharge conditions.
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ACKNOWLEDGMENTS
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Funding for this work was provided by South Florida Water Management District (contract #C-13382) and the National Research Initiative Competitive Grant Program/USDA (CSREES award #2001-35102-10829). M. Nachabe is the PI on both awards.
Received for publication March 17, 2003.
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REFERENCES
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ABSTRACT
INTRODUCTION
