Published online June 13, 2005

Analysis of Temperature Effects on Tension Infiltrometry of Low Permeability Materials
Paolo Castiglione, Peter J. Shouse,* Binayak P. Mohanty, and Martinus Th. van Genuchten
disk having an air entry pressure of approximately ⫺25 cm
of water, contact material, and a ring for holding thecontact material and leveling the supply disk (Fig. 1).
As water infiltrates across the soil surface, an equal volume of air enters the reservoir through Tubes B and C.
The procedure establishes a constant negative pressure
at the soil surface, which can be adjusted by manipulating Tube B in the Mariotte tower. The infiltration rateis measured (often by means of a pressure transducer)from water volume changes in the reservoir tower (Perroux and White, 1988; Ankeny et al., 1988).
An important feature of a well-designed infiltrometeris the presence of constant pressure at the soil surface
as the infiltration proceeds and the reservoir tower empties. Unfortunately, this feature can generally be attained only when all environmental conditions remain
constant. Because of extremely low infiltration rates
and associated long equilibration times, environmental
factors normally neglected during tests in soils may not
be negligible for tests on low permeability materials suchas unsaturated fractured rock (Castiglione et al., 2005).
Fluctuating ambient temperatures, in particular, can cause
dramatic variations in the applied pressure, thus affecting measurements of infiltration. This is due to the presence of air pockets inside the reservoir and Mariotte
towers (Fig. 1) that are not completely free to expand
or contract. This phenomenon is analogous to the widely
observed pressure changes in tensiometers responding
to diurnal temperature fluctuations (Richards et al.,1937; Butters and Cardon, 1998; Warrick et al., 1998).
Unlike with tensiometers, observations of temperature induced pressure fluctuations in the Mariotte towerof tension infiltrometers have not been made, mostly because measurements in soils typically last for only one
to several hours or less. Since high infiltration rates leadto short equilibration times, the entire test generally will
not last long enough to experience significant temperature variations. Our experience indicates that temperature effects become a major concern for low permeability systems, such as certain clay soils and landfill caps
or liners and unsaturated fractured rock formations.
Such low permeability media are different from mostsoils in that measurements may easily take from several
days (clays) to several months (rock formations) to reacha steady-state flow process. Accurate tension infiltrometer measurements in these situations require the useof an infiltrometer system that minimizes the effects oftemperature fluctuations on the Mariotte and reservoir
tower pressures.
Our objectives in this study were to analyze the effects
of temperature and pressure fluctuations in both a single
Mariotte tower and a complete tension infiltrometer system during static (no-flow) conditions. We provided a relatively simple model to predict pressure variations as afunction of temperature and then used the model to de-Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

ABSTRACT
Tension infiltrometers have become popular for in situ measurement of the near-saturated hydraulic conductivity as a function of thesoil water pressure head. Unfortunately, fluctuating ambient temperatures can cause dramatic pressure variations due to the presence ofconfined air inside the infiltrometer, thereby affecting the intended
pressure head to be applied to the soil surface and hence also the measured infiltration rate. This is especially true for low infiltration rates
and long equilibration times typical of low permeability materials,
including unsaturated fractured rock. We developed a model to analyze the effects of temperature changes on the static pressure of the confined air volume within tension infiltrometers. The model was tested
using several prototype infiltrometer designs in a computer-controlled
variable-temperature room. Experimental results confirmed the model
simulations. For example, predicted and measured changes in the pressure head in one experiment were 11.2 and 12.5 cm following a changeof 18.5ⴗC in the temperature. Using the model, we were able to optimize several infiltrometer designs that significantly reduced the undesired effects of temperature on tension infiltration results.

Tension infiltrometers (Perroux and White, 1988)
are now widely used to characterize field soil infiltration rates and infiltration parameters such as the sorptivity and the saturated or near-saturated hydraulic conductivity (e.g., Perroux and White, 1988; Clothier and White,1981). They are especially useful for soils that display preferential flow (Lin and McInnes, 1995; Jarvis and Messing, 1995; Mohanty et al., 1996, 1997; Bagarello et al.,2000). Others have used tension infiltrometry to characterize the size, continuity, and transport efficacy of soil
macropores (Watson and Luxmoore, 1986; Wilson andLuxmoore, 1988). By making specific assumptions about
the shape of the wetting front, it is possible to obtain thehydraulic conductivity corresponding to the applied tension (e.g., Wooding, 1968) or additional information about
the soil hydraulic functions from numerical or analyticalanalyses of cumulative infiltration data (Simunek et al.,
1998; Vandervaere et al., 2000; Schwartz and Evett, 2002).
The popularity of tension infiltrometers is in large partdue to the fact they are portable, easy to use, and relatively robust for field applications. Typically, a tension infiltrometer consists of a coupled Mariotte tower and reservoir tower connected to a permeable porous supply

P. Castiglione, Land Resources and Environmental Science Dep.,
Montana State Univ., 334 Leon Johnson Hall, Bozeman, MT 59717;
P.J. Shouse and M.Th. van Genuchten, USDA-ARS, George E. Brown,
Jr. Salinity Laboratory, 450 W. Big Springs Rd., Riverside, CA, 92507;
B. Mohanty, Dep. of Biological and Agricultural Engineering, 301
Scoates Hall, Texas A&M Univ., College Station, TX 77843-2117.
Received 17 Sept. 2004. *Corresponding author (pshouse@ussl.ars.
usda.gov).
Published in Vadose Zone Journal 4:481–487 (2005).
Original Research Paper
doi:10.2136/vzj2004.0134© Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

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VADOSE ZONE J., VOL. 4, AUGUST 2005

Fig. 1. Schematic of typical tension infiltrometer.

vise a measurement strategy that minimizes temperatureeffects. Since the model holds for no-flow conditions, thepredicted pressure changes should reflect a worst-casescenario of the effects of temperature on tension infiltrometer performance.

ANALYSIS OF TEMPERATURE EFFECTS
Mariotte Tower
Before discussing a complete tension infiltrometer system, let us first analyze the simple case of a single Mariotte tower. Consider for this purpose the Mariotte tower
depicted in Fig. 2a, and assume that Valve A is being
closed while air is bubbling from Tube B. The closureof Valve A will interrupt the air flux and “freeze” the initial pressure distribution (subscript “i”), as shown in
Fig. 2a. The question arises, how will this system respondto an increase in temperature? Since the air pocket in the
top of the tower cannot expand freely, its pressure willtend to increase. The increasing pressure will push water
into Tube B until a new equilibrium is achieved, as shownin Fig. 2b, with the position of the water meniscus determining the final pressure distribution (subscript “f”)
within the Mariotte tower. In particular, the pressurechange (⌬P) in the air pocket is given by⌬P ⫽ Pf ⫺ Pi ⫽ ⌬a ⫹ k[1]which indicates that ⌬P is the sum of the vertical air
pocket expansion (⌬a) and the vertical displacement of
the water meniscus (k) into Tube B. If s is the cross-sectional area of Tube B and S the difference between the
cross-sectional areas of the Mariotte tower and Tube B,then mass conservation requires that k and ⌬a are related throughk ⫽ ⌬aSs[2]

The pressure (P), volume (V), and temperature (T)Fig. 2. Schematic of conventional Mariotte tower under (a) flowing
conditions, (b) static conditions after increased ambient temperature and modified Mariotte tower under (c) flowing conditions and(d) static conditions after increased ambient temperature.

of the air pocket in the Mariotte tower are related by
the ideal gas law:PV ⫽ nRT[3]

where n is the mass of air in moles, and R the gas
constant (8.3145 J mol⫺1 K⫺1). Assuming that the air
mass does not change during an expansion of the air
pocket, we can write
PiVi (Pi ⫹ ⌬P)(Vi ⫹ ⌬V)⫽ nR ⫽ const⫽
Ti(Ti ⫹ ⌬T)

[4]

where subscript “i” indicates the initial state as before,and ⌬ refers to small changes in P, V, and T from theinitial state. Since Vi ⫽ Sai and ⌬V ⫽ S⌬a, Eq. [4] canbe rearranged to give冢Piai 1 ⫹冣⌬T⫽ (Pi ⫹ ⌬P)(ai ⫹ ⌬a)Ti[5]which on expansion simplifies toaiPi⌬T⫽ ⌬aPi ⫹ ai⌬P ⫹ ⌬a⌬P
Ti

Using Eq. [2] to eliminate k from Eq. [1] yields[6]www.vadosezonejournal.org⌬a ⫽ m⌬P

[7]

ε
s
⫽
S⫹s 1⫹ε

[8]

483

where

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

m⫽in which ε ⫽ s/S. Substituting Eq. [7] into Eq. [6] now
leads to the following second-order equation in ⌬P:m⌬P 2 ⫹ (mPi ⫹ ai )⌬P ⫺ aiPi

⌬T
⫽0
Ti

[9]

Only the positive root of Eq. [9] is physically meaningful.
Given the initial values Pi , ai , and Ti , and the geometriccharacteristic of the Mariotte tower (embedded in m),
Eq. [9] gives the change in pressure, ⌬P, corresponding
to an increase in temperature, ⌬T.
Before continuing, we first note that in a Mariotte
tower the pressure distribution is uniquely determinedby the position of the water meniscus in Tube B (thehigher the meniscus, the higher the pressure), consistent
with the hydrostatic condition given by Eq. [1]. The
minimum pressure for the system occurs for the equilibrium condition depicted in Fig. 2a, where the water
meniscus is at its lowest position. Assume now that thesystem, originally as shown in Fig. 2a, did undergo atemperature increase (⌬T1 ⬎ 0) and reached a new equilibrium as in Fig. 2b. If, starting from this new condition(Fig. 2b), a temperature reduction occurs (⌬T2 ⬍ 0),then the air pocket will shrink and its pressure will decrease, together with the position of the meniscus in
Tube B. Clearly, if |⌬T2| ⫽ |⌬T1|, the original conditions
shown in Fig. 2a will be reestablished. However, any
further temperature reductions beyond the minimumpressure condition (Fig. 2a) will no longer lead to further
changes in the pressure or volume of the air pocket, butrather will cause additional air to enter the system in theform of bubbles from Tube B. In actuality, the additionaltemperature drop will be compensated by an increasein the n term (i.e., of the air mass) of Eq. [2]. The additional mass of air (⌬n) that enters the system can becalculated from Eq. [3], with P and V constant:niTi ⫽ (ni ⫹ ⌬n)(Ti ⫹ ⌬T) ⫽ const[10]

In summary, when the Mariotte tower undergoes cyclic
temperature changes (e.g., diurnal temperature fluctuations) the pressure will vary according to the temperature, with the lowest temperature determining the maximum amount of air entering the system.

Tension Infiltrometer
The response of the tension infiltrometer to temperature variations is similar to that of a single Mariotte tower.
Variations in pressure within the system result from interactions between the volumes of confined air in the reservoir (subscript “R”) and Mariotte (subscript “M”) towers(Fig. 3). Let us assume that the pressure distribution in
the system initially is as shown in Fig. 3a, and that thewater flux through the disk (and therefore the air flow
through Tubes B and C) is interrupted. The system willthen respond in two different ways to increased temperature, as discussed below.

Fig. 3. (a) Schematic of typical Mariotte and reservoir system underflowing conditions (top), as well as for (b) static conditions withincreasing ambient temperature for reservoir pressures greaterthan the Mariotte pressure (Case A) and (c) less than the Mariottepressure (Case B).

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VADOSE ZONE J., VOL. 4, AUGUST 2005

Case A: ⌬PR ⬎ ⌬PM

Case B: ⌬PR ⬍ ⌬PM

If the pressure change in the reservoir air pocket (⌬PR)
is greater than that in the Mariotte air pocket (⌬PM),
water will be pushed from the reservoir into the interconnecting Tube C (Fig. 3b). Very much analogous to thedescription in the previous section, the pressure distribution at equilibrium is given by the set of equations:

If the pressure change in the Mariotte tower (⌬PM)
is greater than that in the reservoir tower (⌬PR), air will
be pushed (in the form of bubbles) from the Mariotte
air pocket into the reservoir so that, at equilibrium, thesystem is as shown in Fig. 3c. The final pressure distribution is given by the system of equations:⎧ ⌬PR ⫽ kR ⫹ ⌬aR ⫹ ⌬PM⎪⎪ ⌬PM ⫽ kM ⫹ ⌬aM⎪
sC
kR ⫽ εRKR⎪ ⌬aR ⫽SR⎪⎪
sB
kM ⫽ εMkM⎨ ⌬aM ⫽
SM⎪
⎪ PMiVMi (PMi ⫹ ⌬PM)(VMi ⫹ SM⌬aM ⫺ sBkR)⫽⎪
Ti ⫹ ⌬T⎪ Ti⎪ PRi aRi (PRi ⫹ ⌬PR)(aRi ⫹ ⌬aR)⫽⎪
Ti ⫹ ⌬T[11]⎩ Ti⎧ PMiVMi ⫽ mMRTi⎪⎪ PRi⌺RaRi ⫽ nRRTi⎪ (P ⫹ ⌬P )(V ⫹ S ⌬a ) ⫽ (n ⫺ ⌬n)R(T ⫹ ⌬T)
M
Mi
M
M
M
i
⎭ Mi
⎫ (PRi ⫹ ⌬PR)SRaRi ⫽ (nR ⫹ ⌬n)R(Ti ⫹ ⌬T)⎪⎪ ⌬PM ⫽ ⌬PR⎪[14]⎩ ⌬aM ⫽ mM⌬PM

where sB and sC represent the cross-sectional areas ofTubes B and C, respectively, SM is the difference between the cross-sectional area of the Mariotte tower andsB , and SR is the difference between the cross-sectional areaof the reservoir and sC . The meaning of the remaining symbols in Eq. [11] is evident from Fig. 3. The first two
equations of Eq. [11] express hydrostatic equilibrium inthe reservoir and Mariotte towers, respectively. The thirdand fourth equations account for conservation of mass,
while the last two equations represent the ideal gas law
as applied to the volumes of confined air in the two
towers. Notice that the initial volume of air subject toexpansion in the Mariotte (VMi) includes Tube C. Also
the third equation of Eq. [11] assumes that Tube C isperfectly vertical, while ignoring any contribution of theshort horizontal segment containing Valve A. Similarly,
as before leading to Eq. [9], the system of equations given
as Eq. [11] can be reduced to a system of two secondorder equations of the form (details omitted here):

冢

冣

⎧ SM
2
⎪ SR mM ⫹ mR ⌬P M ⫹⎪SMV⎪
mMPMi ⫹ Mi ⫺ mR(⌬PR ⫺ PMi )
⎪
SR
⌺R
⎭
⎫ ⌬PM ⫺ PMi mR⌬PR ⫹ VMi ⌬T ⫽ 0
SR T i⎪⎪ mR⌬P 2R ⫹ (mRPRi ⫹ aRi ⫺ mR⌬PM)⎪⎪ ⌬PR ⫺ PRi mR⌬PM ⫹ aRi ⌬T ⫽ 0
⎩
Ti

冤

冢

冢

冥

εM
εR
and mR ⫽1 ⫹ εM1 ⫹ εR(VMiPMi ⫹ SRaRiPRi )

⌬T
⫽0
Ti

[15]

To determine the exact temperature response of thetension infiltrometer (i.e., which of the above two scenarios will occur), it is convenient to assume that theprocess proceeds in two successive phases. Initially thesystem is as shown in Fig. 3a, but with the Mariotte tower
disconnected from the reservoir tower (Valve A closed).
Upon a temperature increase (⌬T ⬎ 0), the pressure inboth air pockets increases. Since there is no interaction
during this intermediate phase (subscript “int”), thechanges in pressure in the reservoir and Mariotte towers
are given by
⌬T
Ti

[16]

and
SMmM⌬P 2M,int ⫹ (VMi ⫹ mMSMPMi )⌬PM,int ⫺
[12]

where
mM ⫽

⌺MmM⌬P 2M ⫹ (SMmMPMi ⫹ VMi ⫹ SRaRi )⌬PM ⫺⌬PR,int ⫽ PRi冣冣

where ⌬n is the mass of air transferred from the Mariotte tower to the reservoir. The first four equations of
Eq. [14] express the ideal gas law applied to the volumesof confined air in the reservoir and Mariotte towers, respectively, for both the initial conditions (first and second equations) and the final conditions (third and fourth
equations). The fifth equation of Eq. [11] results fromthe hydrostatic pressure distribution, while the last equation again represents mass conservation analogous toEq. [7]. The above system of equations can be reduced
by repeated substitution to the following second-orderequation:[13]

As before, only the positive roots of Eq. [12] provide aphysically meaningful estimate of the pressure change⌬PM in response to a temperature change of ⌬T.

PMiVMi

⌬T
⫽0
Ti

[17]

respectively. Note that Eq. [17] is identical to Eq. [9],with the only difference being that the initial air volume
now includes Tube C. Next, on opening Valve A, water
will either move into Tube C (Fig. 3b) if ⌬PR,int ⬎ ⌬PM,int ,or air will bubble into the reservoir tower (Fig. 3c) if⌬PR,int ⬍ ⌬PM,int . The final pressure distribution of thisPhase 2 can be obtained by solving the system of equa-Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

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Fig. 4. Observed Mariotte pressure variations (P ) as affected by imposed ambient temperature fluctuations (T ) under no-flow conditions in controlled temperature room.

tions given by Eq. [12] (if ⌬PR,int ⬎ ⌬PM,int) or Eq. [15](if ⌬PR,int ⬍ ⌬PM,int). Note that the system of equations
given as Eq. [12] is nonlinear, and hence must be solved
iteratively. The system is most conveniently solved using
the intermediate pressure changes of Eq. [16] and [17]as initial values; the solution then usually converges within
two or three iterations.
The derivations above are for increasing temperatures.
The response to cooling is similar to that of a single Mariotte tower in that the pressure drops until the water menisci in tubes B and C are at their lowest positions, atwhich time additional air will enter the system (bubbles)
and no further reductions in the pressure take place.

VERIFICATION OF PROCEDURE
The above analytical model (Eq. [12]) for quantifying
the effects of temperature fluctuations on pressure distributions was tested during static (zero infiltration) conditions by placing the tension infiltrometer on an impermeable surface. The experiment was performed in
a computer-controlled variable-temperature room thatwas programmed for seven diurnal temperature cycles(Fig. 4) of about 20⬚C involving 12 h of heating (20–40⬚C), followed by 12 h of cooling (40–20⬚C). We useda Mariotte tower of the type shown in Fig. 1, made ofacrylic tubing 3.8 cm (1.5 inches) i.d. and 5.1 (2 inches)o.d. Rubber stoppers were sealed into the ends of the
Mariotte tower using high temperature RTV sealant(an automotive cooling system sealant), after which thetower was pressure tested to 20.7 kPa (3 psi). We subsequently instrumented the tower with a calibrated, temperature-compensated pressure transducer (with a temperature compensation range of 0 to 50⬚C) to measure
the pressure inside the air space in the top portion of the
Mariotte tower.
Room temperatures and Mariotte tower air space pressures were measured for 3 d using an automatic datalogger with a 30-s data acquisition interval. We started
the experiment when the room and Mariotte temperatures were approximately 33⬚C. The Mariotte tower wassealed such that we could observe air being released (bub-485bling) from the Mariotte tower when the room temperature decreased below 33⬚C on the initial cooling cycle
as predicted with the model for our setup. Calibrationof the transducers was carefully tested at several temperatures within the range of 20 to 40⬚C. Room temperatures
were measured using thermistor temperature sensors.
Our tests in the controlled temperature room confirmed the ability of the proposed model to predict thetemperature effects for different geometries of the tension infiltrometer. We describe here the response of asingle Mariotte tower to the imposed sinusoidal-like diurnal temperature variations (Fig. 4b). Figure 4a showsobserved pressures in the air pocket, along with theimposed temperatures. As expected, the pressure varied
in response to the changing temperature until bubbling
started after about 0.45 d when the temperature dropped
below Ti (i.e., when the meniscus reached its lowest position, and P ⫽ Pi ). Air entry ceased only after thetemperature started increasing again at 0.7 d. Since atthis time the minimum temperature was reached and the
maximum amount of air was stored in the Mariotte system, no more bubbling was observed for the remainderof the experiment. Notice that similar temperatures before and after bubbling (i.e., changes occurring in the massof air) corresponding to different air pressures (e.g., compare pressures and temperatures at 0.3 and 1.0 d in Fig.
4). Equation [9] may be used to calculate the maximum
change in pressure (⌬P) resulting from the imposed
maximum temperature change (⌬T ), in this case about
18.5⬚C (Fig. 4b). The model for our setup predicted avalue of 11.2 cm for ⌬P, which compared well with themeasured change of 12.5 cm (Fig. 4a). The calculation
was performed using the following parameter values forour experimental setup: Pi ⫽ ⫺18.0 cm, Ti ⫽ 20.0⬚C,⌬T ⫽ 18.5⬚C, ai ⫽ 5.0 cm, and ε ⫽ 0.33 (m ⫽ 0.25).

IMPLICATIONS FOR IMPROVEDTENSION INFILTROMETER DESIGN
Mariotte Tower
Equations [8] and [9] show that ⌬P depends on the
diameters of the Mariotte tower and the bubbling tube
(through parameter ε), and on the initial height of the
air pocket (ai ). In Fig. 5 we plotted calculated ⌬P values
as a function of ε for different values of ai. The predictedchanges in pressure correspond to a temperature increaseof 10⬚C, with Ti ⫽ 20⬚C and Pi ⫽ ⫺100 cm. For any ai ,⌬P decreases rapidly as the ratio ε increases, approachinga limiting value ⌬P∞ (depending on ai ) for large valueof ε. The shape of the curves in Fig. 5 reflects the factthat for large bubbling tubes (B; i.e., with large ε values)
the air pocket is relatively free to expand and therefore
to release part of the pressure buildup, whereas small
tubes restrict expansion of the air pocket. In the limit
when ε ⫽ 0 (no tube in the Mariotte) no expansion ispossible. The air pressure then builds up to a maximum(⌬P∞), which is independent of ai and can be obtained
from Eq. [4] with ⌬V ⫽ 0. Hence, to contain the pressurebuildup in the Mariotte tower in response to a tempera-

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486

VADOSE ZONE J., VOL. 4, AUGUST 2005

Fig. 5. Calculated pressure changes (⌬P ) as a function of εM for different values of the initial height (a ) of the air pocket.

ture increase, one simply needs to minimize ai and maximize the ratio ε.
A simple but very effective alternative design for largediameter bubbling tubes is illustrated in Fig. 2c. Air inthis case enters the Mariotte tower through an external
tube horizontally connected to the tower. Expansion of
the air pocket with increasing temperature now does
not affect the location of the water meniscus since k ⫽0, as shown in Fig. 2d, as long as water does not enterany vertical extension of the bubbling tube.

Tension InfiltrometerIn spite of the many parameters involved, the temperature model suggests several ways for improving the design of tension infiltrometers. A primary concern shouldbe the undesired overpressure ⌬PD at the disk; that is,⌬PD ⫽ ⌬PM ⫹ kR

[18]

since excessive fluctuations in the imposed pressure
head at the soil or rock surface may compromise theinfiltration experiment. Large disturbances in the reservoir air pocket are also to be avoided because they produce noise in the cumulative infiltration data.
Our analysis shows that the larger the initial heightsof the air pockets in the reservoir and the Mariotte towers(aRi and aMi in Fig. 3a), the more severe the pressurechanges within the infiltrometer system become. WhileaMi can usually be kept to a minimum when designing
the Mariotte tower, aRi is less easily controlled since thisparameter steadily increases during the infiltration process as the reservoir empties.
We also found that the response of the infiltrometersystem to temperature variations strongly depends on the
cross-sectional areas of the two towers, as well as on
the diameters of the bubbling tubes, Tubes B and C. In
general, the larger the ratio εM ⫽ sB /SM, the smaller thepressure variations. Figure 6 shows calculated pressurechanges at different points in the system (solid lines) as
a function of εM. For small εM values, the pressure increase in the Mariotte will eventually dominate the pressure increase in the reservoir, leading to bubbling as il-

Fig. 6. Calculated overpressure as a function of the Mariotte εM atdifferent locations within the infiltrometer system.

lustrated in Fig. 3c. We note that when air bubblingoccurs, the pressures at the disk and in the top parts ofboth the reservoir tower and the Mariotte tower are
predicted to become equal. As for a single Mariotte tube,
using external horizontal tubes is equivalent to imposing
infinitely large εM ratios, thus ensuring minimum pressure buildup.
The choice of an appropriate value for the ratio εR ⫽sC /SR is not as simple. The selection of a reservoir tower
is generally governed by the desired accuracy in theinfiltration rate measurements, which suggests using a
diameter that is as small as possible. An increase in the
diameter of Tube C connecting the Mariotte tower tothe reservoir tower will increase εR, but at the same time
will produce a larger VMi , which would have a negative
effect by increasing the effective air pocket volume of
the Mariotte tower. Our calculations indicate that theeffects of variable temperatures on infiltrometer pressure fluctuations can be minimized by adding a small
section of horizontal tubing to the base of the reservoir,connected to Tube C. In this way the section of the tube
can be kept small (thus minimizing VMi ), while reducing
the increase of the meniscus (kR ⫽ 0). The temperaturemodel indicates that this will reduce the pressure changes
considerably. In Fig. 6 the calculated ⌬P at the top of
the reservoir (top reserve H) and at the disk (Disk H)
are plotted against εM (open circles). Note that the overpressure at the disk is reduced from about 10 cm to ⬍2 cm
if Tube B is employed.
We also note that the temperature model in this study
assumed that the system is closed to mass exchange,
while the temperature varies (i.e., no air enters the Mariotte and no water leaves the reservoir tower). During
actual infiltration experiments water will flow throughthe disk into the soil, which will lead to decreasing waterlevels in the reservoir tower while an equivalent volume
of air will enter the system. This dynamic situation causes
an expansion of the air pocket, for which the overpressure resulting from ⌬T will be less severe than predictedwith the equations derived here. Hence, temperature ef-

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fects are a major concern only when the water level inthe reservoir tower decreases very slowly compared withthe rate at which temperature variations occur (e.g., because of rapidly changing temperature conditions and/or
very low infiltration rates). One or both of these conditions may occur during experiments with fractured
rocks, in which case proper tension infiltrometer design
becomes very important (e.g., Castiglione et al., 2005).

CONCLUSIONSOur main objective was to develop an analytical modelthat shows explicitly the effects of temperature on tension infiltrometer performance, and how to use the model
to design an improved infiltrometer that minimizes thetemperature effects. The effects can be significant undercertain environmental conditions, especially when theinfiltration rate is very low, such as for experiments withvery fine-textured soils or fractured rock formations.
We have shown that the proposed model based on theideal gas law can be used to predict the distribution ofpressures in a static infiltrometer system. While not as rigorous as a more comprehensive analysis for transientconditions involving infiltration, the static analysis nevertheless provides enough information to significantly improve the design of an infiltrometer that is far less temperature sensitive than most or all tension infiltrometerscurrently available commercially. Our ultimate goal wasto design an infiltrometer that can be used to characterize the flow regime of fractured rock and other low permeability media (e.g., landfill caps and clay liners) requiring long equilibration times. Although temperatureeffects may not be eliminated completely in many applications, our study indicates that tension infiltrometers
can be designed that are far less sensitive to temperature variations.
We also showed that response of the tension infiltrometer system depends greatly on its geometry througha large number of parameters. Some of these parameters
cannot be controlled, and/or must comply with other requirements of the device, whereas other parameters may
be optimized to minimize pressure variations throughout the system. We believe that the proposed temperature model represents a relatively simple, yet useful tool
to investigate the effects of the different parameters involved, thus potentially providing guidance for additional design improvements for tension infiltrometersin the future.

ACKNOWLEDGMENTS
This study was based on work supported in part by SAHRA(Sustainability of semi-Arid Hydrology and Riperian Areas)
under the STC Program of the National Science Foundation,
Agreement no. EAR-9876800.

REFERENCES
Ankeny, M.D., T.C. Kaspar, and R. Horton. 1988. Design for an
automated tension infiltrometer. Soil Sci. Soc. Am. J. 52:893–895.
Bagarello, V., M. Iovino, and G. Tusa. 2000. Factors affecting measurement of the near-saturated soil hydraulic conductivity. Soil Sci.
Soc. Am. J. 64:1203–1210.
Butters, G.L., and G.E. Cardon. 1998. Temperature effects on airpocket tensiometers. Soil Sci. 163:677–685.
Castiglione, P., P.J. Shouse, B. Mohanty, D. Hudson, and M.Th.
van Genuchten. 2005. Improved infiltrometers for measuring low
fluid flow rates in unsaturated fractured rock. Available at www.
vadosezonejournal.org. Vadose Zone J. 4 (this issue).
Clothier, B.E., and I. White. 1981. Measurement of sorptivity and soil
water diffusivity in the field. Soil Sci. Soc. Am. J. 45:241–245.
Jarvis, N.J., and I. Messing. 1995. Near-saturated hydraulic conductivity in soils of contrasting texture measured by tension Infiltrometers. Soil Sci. Soc. Am. J. 59:27–34.
Lin, H.S., and K.J. McInnes. 1995. Water flow in clay soil beneath atension infiltrometer. Soil Sci. 159:375–382.
Mohanty, B.P., R.S. Bowman, J.M.H. Hendrickx, and M.Th. van Genuchten. 1997. New piecewise-continuous hydraulic functions formodeling preferential flow in an intermittent flood-irrigated field.
Water Resour. Res. 33:2049–2063.
Mohanty, B.P., R. Horton, and M.D. Ankeny. 1996. Infiltration andmacroporosity under a row crop agricultural field in a glacial till
soil. Soil Sci. 161:205–213.
Perroux, K.M., and I. White. 1988. Designs for disc permeameters.
Soil Sci. Soc. Am. J. 52:1205–1214.
Richards, L.A., M.B. Russell, and O.R. Neal. 1937. Further developments on apparatus for field moisture studies. Soil Sci. Soc. Am.
Proc. 2:55–64.
Schwartz, R.C., and S.R. Evett. 2002. Estimating hydraulic propertiesof a fine-textured soil using a disc infiltrometer. Soil Sci. Soc.
Am. J. 66:1409–1423.
Simunek, J., D. Wang, P.J. Shouse, and M.Th. van Genuchten. 1998.
Analysis of field tension disk infiltrometer data by parameters
estimation. Int. Agrophys. 12:167–180.
Vandervaere, J.P., M. Vauclin, and D.E. Elrick. 2000. Transient flowfrom tension infiltrometers: II. Four methods to determine sorptivity and conductivity. Soil Sci. Soc. Am. J. 64:1272–1284.
Warrick, A.W., P.J. Wierenga, M.H. Young, and S.A. Musil. 1998.
Diurnal fluctuations of tensiometric readings due to surface temperature changes. Water Resour. Res. 34:2863–2869.
Watson, K.W., and R.J. Luxmoore. 1986. Estimating macroporosity
in a forested watershed by use of a tension infiltrometer. Soil Sci.
Soc. Am. J. 50:578–582.
Wilson, G.V., and R.J. Luxmoore. 1988. Infiltration, macroporosity,and mesoporosity distributions on two forested watersheds. Soil
Sci. Soc. Am. J. 52:329–335.
Wooding, R.A. 1968. Steady infiltration from large shallow circular
pond. Water Resour. Res. 4:1259–1273.