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WATER RESOURCES RESEARCH, VOL. 45, W10410, doi:10.1029/2009WR007944, 2009

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ArticleAn objective analysis of the dynamic nature of field capacity
Navin K. C. Twarakavi,1 Masaru Sakai,2 and Jirka Šimůnek2
Received 5 March 2009; revised 22 June 2009; accepted 9 July 2009; published 7 October 2009.

[1] Field capacity is one of the most commonly used, and yet poorly defined, soil

hydraulic properties. Traditionally, field capacity has been defined as the amount of soil
moisture after excess water has drained away and the rate of downward movement has
materially decreased. Unfortunately, this qualitative definition does not lend itself to an
unambiguous quantitative approach for estimation. Because of the vagueness in defining
what constitutes ‘‘drainage of excess water’’ from a soil, the estimation of field capacity
has often been based upon empirical guidelines. These empirical guidelines are either
time, pressure, or flux based. In this paper, we developed a numerical approach to estimate
field capacity using a flux-based definition. The resulting approach was implemented on
the soil parameter data set used by Schaap et al. (2001), and the estimated field capacity
was compared to traditional definitions of field capacity. The developed modelingapproach was implemented using the HYDRUS-1D software with the capability ofsimultaneously estimating field capacity for multiple soils with soil hydraulic parameterdata. The Richards equation was used in conjunction with the van Genuchten-Mualem
model to simulate variably saturated flow in a soil. Using the modeling approach toestimate field capacity also resulted in additional information such as (1) the pressure
head, at which field capacity is attained, and (2) the drainage time needed to reach field
capacity from saturated conditions under nonevaporative conditions. We analyzed theapplicability of the modeling-based approach to estimate field capacity on real-world soils
data. We also used the developed method to create contour diagrams showing the variationof field capacity with texture. It was found that using benchmark pressure heads toestimate field capacity from the retention curve leads to inaccurate results. Finally, asimple analytical equation was developed to predict field capacity from soil hydraulicparameter information. The analytical equation was found to be effective in its ability to
predict field capacities.
Citation: Twarakavi, N. K. C., M. Sakai, and J. Šimůnek (2009), An objective analysis of the dynamic nature of field capacity, Water
Resour. Res., 45, W10410, doi:10.1029/2009WR007944.

1. Introduction[2] Researchers studying various phenomena across thesoil-water-plant continuum have always been interested inmeasuring the amount of water a soil can hold. This measure has importance because of its usefulness in a range offields from hydrology to plant sciences. One of the earliest
similar measures, called ‘‘moisture equivalent,’’ was proposed by Briggs and McLane [1910, p. 141], who defined itas ‘‘the percentage of water which a soil can retain in
opposition to a centrifugal force 1000 times that of gravity’’for 30 min [Briggs and McLane, 1910; Briggs and Shantz,
1912]. Because of the lack of applicability of the moisture
equivalent for field soils and coarse-textured soils, Veihmeyerand Hendrickson [1931] introduced the concept of ‘‘field
capacity.’’ Veihmeyer and Hendrickson [1931] defined field
capacity as the amount of soil moisture or water content
1
Department of Agronomy and Soils, Auburn University, Auburn,
Alabama, USA.
2
Department of Environmental Sciences, University of California,
Riverside, California, USA.

Copyright 2009 by the American Geophysical Union.
0043-1397/09/2009WR007944$09.00

held in soil after excess water has drained away and the rate ofdownward movement has materially decreased. Although
this definition possesses qualitative clarity, ambiguity about
what constitutes a ‘‘lack of drainage’’ from a soil has led topractical problems in outlining a good approach to estimate
field capacity in the lab/field. Veihmeyer’s many works
approximate field capacity as the soil moisture attained after
a well-drainable soil profile is allowed to drain from complete
saturation while evaporation is inhibited. The underlying
assumption of this time-dependent definition of field capacity
is that drainage becomes negligible after the specified time.
Field capacity can be estimated by measuring the watercontent after wetting a soil profile, covering it (to prevent
evaporation), and monitoring the change in soil moisture in
the profile for a certain number of days (3 days for coarsetextured soils, six or even more days for medium andfine-textured soils) until the drainage ceases. Although atime-based definition of field capacity is used widely, thevalidity of this definition with respect to the concept of field
capacity needs to be properly investigated.
[3] In order to circumvent the aforementioned problem inthe time-based estimation of field capacity, several authors
have suggested using benchmark capillary pressures in soils
when field capacity is attained. While time-based approxi-

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mation is used to estimate field capacity in the field, pressurebased approximation has been used to estimate it in thelaboratory [Romano and Santini, 2002]. For example, acommonly used approximation of field capacity is the watercontent in a soil at a capillary pressure head of 330 cm(0.33 bar) for fine-textured soils [Richards and Weaver,1944] and 100 cm (0.10 bar) for coarse-textured soils[Romano and Santini, 2002]. However, a pressure-based
approximation of field capacity is inconsistent, because there
is no assurance that the drainage from the soil would become
negligible at these benchmark pressures [Hillel, 1998; Meyerand Gee, 1999]. There exists a fundamental problem in using
benchmark pressure-based approximations for field capacity,
due to the fact that the approach is static, while the soil
hydraulic property (field capacity) is highly dynamic [Hillel,
1980; Ahuja et al., 2008].
[4] Several researchers have attempted to develop techniques for estimating field capacity using dynamic
approaches [Campbell and Campbell, 1982; Campbell,
1985; Nachabe, 1998; Hillel, 1998; Zacharias and Bohne,
2008; Meyer and Gee, 1999]. Nachabe [1998] proposedthat the field capacity of a soil should correspond to thesoil water content when the drainage flux from the soil isequal to the daily evapotranspiration rate. Nachabe’s [1998]
definition of field capacity would make this term to be timedependent. Hillel [1998] recommended estimating field
capacity as the water content when the drainage flux fromthe soil reaches a value of 0.05 cm/d. Similarly as Hillel[1998], Meyer and Gee suggested field capacity as thewater content when the drainage flux from the soil reaches avalue between 0.001 cm/d and 0.1 cm/d, depending on thetype of field application. Dirksen and Matula [1994]
observed that the smallest amount of rainfall measured inmeteorological stations was 0.01 cm/d, which we believe
could also be used as a guideline for the negligible drainage
flux necessary during the determination of field capacity.
Using the negligible drainage flux approach, analyticalexpressions have been developed to estimate field capacity,such asqfc  qr¼
qs  qr

 b1
qfc
Ks

ð1Þ

where qfc is field capacity (L3/L3), qs is the saturated watercontent (L3/L3), qr is the residual water content (L3/L3), qfc
is the negligible drainage flux from the soil at field capacity(L/T), Ks is the saturated hydraulic conductivity (L/T), andb = (2 + 3l)/l, where l is the pore size distribution index of
the Brooks and Corey [1964] model. Meyer and Gee [1999]
showed that the analytical approach to estimate field capacity,with due consideration to its dynamic nature, performs better
than using benchmark pressure heads. While the analyticalexpression shown above used the Brooks and Corey parameters [Brooks and Corey, 1964], Schaap and Leij [2000],among others, have shown that the van Genuchten-Mualem
model [van Genuchten, 1980] is a better approximation of thehydraulic behavior of many soils. Using the concept of fluxbased dynamic field capacity, Zacharias and Bohne [2008]
presented a numerical approach for estimating field capacity.
The approach involved solving the Richards equation withthe van Genuchten-Mualem model for characterizing theretention and unsaturated conductivity properties of the soil.

W10410[5] Previous studies comparing flux-based definitions offield capacity have not been comprehensive, and have only
studied the applicability of such an approach for a few representative soils. Also, previous studies have not compared
the time-, pressure-, and flux-based definitions of field
capacity. In this study, we apply a flux-based dynamic
approach to estimate field capacities for a large real-world
soil data set. We compare the drainage fluxes of 0.001, 0.1(as suggested by Meyer and Gee [1999]), and 0.01 cm/d
[Dirksen and Matula, 1994] as possible candidates for
estimating field capacity dynamically. We use the van
Genuchten-Mualem model to represent the retention characteristics and the unsaturated hydraulic conductivity of asoil. We compare the results of our simulations with theapproaches described earlier for estimating field capacity.

2. Background and Theory[6] Variably saturated flow processes in soils are highly
nonlinear and dynamic phenomena. Most commonly usednumerical models for simulating variably saturated waterflow in the vadose zone employ the classical Richards equation [Richards, 1931]. For one-dimensional scenarios, theRichards equation is described mathematically as follows:


@qðhÞ
@
@h
¼
K ðhÞ  K ðhÞ  S
@t
@z
@z

ð2Þ

where q(h) is the volumetric water content at the pressure
head h (), t is time (T), z is the distance from reference
datum (L), and K(h) is the unsaturated hydraulic conductivity
as a function of h or q (L T1). We neglect root water uptake
in this research.
[7] A high nonlinearity in modeling variably saturated
water flow processes exists due to the dependence of thehydraulic conductivity, K(h), and the water content, q(h),on the capillary pressure head, h. Consequently, modelingvariably saturated water flow involves solving equation (2)along with a nonlinear model that characterizes the relationships between the water content, capillary pressure head,and unsaturated hydraulic conductivity. The Gardnerexponential model [Gardner, 1958], the Brooks and Coreymodel [Brooks and Corey, 1964], and the van GenuchtenMualem model [van Genuchten, 1980] are among the mostwidely used approaches for representing the dependence ofthe hydraulic conductivity and the water content on thecapillary pressure head during model simulations. Readers
are referred to Leij et al. [1997] for a detailed discussion of
the most commonly used soil hydraulic models. Of all theavailable soil hydraulic models, the van Genuchten-Mualem
model [van Genuchten, 1980] is perhaps the most widelyused model for characterizing the hydraulic conductivity
and water content dependence on the capillary pressure
head. The van Genuchten-Mualem model is described inequations (3a) – (3d):2 of 9qðhÞ ¼

8
<

qr þ

:

qs

qs  qrm½1 þ jahjn Se ðhÞ ¼

h<0

ð3aÞ

h0
qðhÞ  qr
qs  qrð3bÞ

TWARAKAVI ET AL.: DYNAMIC NATURE OF FIELD CAPACITY

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Table 1. Means and Standard Deviations of the Hydraulic Parameters for Soils From Different Textural Classes in the Combined Data
Seta
TextureNumberBDqr (cm3/cm3)

qs (cm3/cm3)

log10(a) (log10(1/cm))

log10(n)log10(KS) (log10(cm/d))

Sand
Loamy sand
Sandy loam
Sandy clay loam
Sandy clay
Clay
Silty clay
Silty clay loam
Clay loam
Loam
Silty loam
Silt

270
184
396
129
9
55
14
43
59
161
256
2

1.534 (0.127)
1.545 (0.193)
1.556 (0.176)
1.593 (0.18)
1.59 (0.088)
1.388 (0.229)
1.327 (0.16)
1.355 (0.118)
1.435 (0.227)
1.426 (0.204)
1.449 (0.121)
1.375 (0.007)

0.05 (0.025)
0.05 (0.044)
0.057 (0.062)
0.06 (0.072)
0.098 (0.101)
0.098 (0.118)
0.103 (0.124)
0.086 (0.091)
0.081 (0.093)
0.088 (0.083)
0.14 (0.121)
0.071 (0.001)

0.372 (0.058)
0.383 (0.073)
0.379 (0.068)
0.381 (0.063)
0.384 (0.038)
0.471 (0.077)
0.5 (0.087)
0.481 (0.078)
0.45 (0.083)
0.428 (0.076)
0.425 (0.047)
0.432 (0.068)

1.458 (0.247)
1.512 (0.469)
1.62 (0.492)
1.706 (0.633)
1.348 (0.593)
1.794 (0.705)
1.741 (0.729)
2.098 (0.541)
1.744 (0.648)
1.827 (0.512)
2.121 (0.458)
2.503 (0.048)

0.507 (0.186)
0.229 (0.132)
0.181 (0.126)
0.105 (0.092)
0.067 (0.047)
0.078 (0.061)
0.106 (0.068)
0.167 (0.148)
0.113 (0.089)
0.173 (0.12)
0.233 (0.151)
0.343 (0.106)

2.763 (0.63)
1.952 (0.671)
1.465 (0.696)
1.165 (0.809)
1.319 (0.333)
1.104 (0.772)
0.983 (0.573)
1.068 (0.662)
1.054 (0.89)
1.093 (0.83)
0.812 (0.921)
1.487 (0.081)

aNumber, number of samples in a particular textural class; BD, bulk density. Standard deviations are given in parentheses.

h

m i2
K ðhÞ ¼ Ks Sel 1  1  Se1=mm ¼ 1  1=n;

n>1

ð3cÞ

ð3dÞ

where q(h) is the volumetric water content at the pressure
head h (), qs and qr are the saturated and residual volumetricwater contents (), respectively; Se(h) is the degree ofsaturation at the pressure head h (), Ks is the saturated
hydraulic conductivity (L T1), a (L1) and n () are van
Genuchten’s shape parameters, and l is a tortuosity or poreconnectivity parameter estimated by Mualem [1976] to be
0.5.
[8] We base our research on the hypothesis that the Richards
equation used in conjunction with the van Genuchten-Mualem
model can satisfactorily describe variably saturated water flow
in soils. The modeling was performed using the HYDRUS-1D
simulation model, which numerically solves the Richards
equation, and has been used successfully in many applications [Šimůnek et al., 2008]. Here, we use the HYDRUS-1D
single-porosity uniform water flow formulation (with the van
Genuchten-Mualem soil hydraulic property model), andconsider only homogeneous soil profiles.

top of the profile. A free drainage boundary condition,
also called a unit gradient boundary condition, was usedat the bottom of the profile throughout the simulation.
This boundary condition allows only gravitational flow atthe bottom of the soil profile. Under these conditions,HYDRUS-1D was used to simulate changes in the watercontent of the profile until the flux at the bottom of the
profile reached a value of qfc. The water content at thebottom of the profile when the bottom flux reached qfc wasassumed to be equal to field capacity, qfc. The associatedtime needed to attain field capacity from saturation wasused to define the drainage time (tfc), and the pressure headcorresponding to field capacity was hfc. HYDRUS-1D,
which was adapted to run batch simulations in order tospeed up the computational time, is available from theauthors upon request.
3.2. Data Set[11] For estimating qfc, tfc,, and hfc using the Richards
equation and the van Genuchten-Mualem model, a real-world
database with soil hydraulic parameters (qr, qs, a, n, and Ks)

3. Materials and Methods
3.1. Modeling Field Capacity[9] In order to estimate field capacity using the modelingapproach, we defined it as follows: Field capacity is the soil
water content when the drainage flux from the initiallysaturated soil reaches a predefined negligibly small value(qfc). Here, we estimate field capacities for three different
drainage fluxes qfc: 0.001, 0.1 (as suggested by Meyer andGee [1999]), and 0.01 cm/d [Dirksen and Matula, 1994].
[10] The HYDRUS-1D software [Šimůnek et al., 2008]
was used to estimate field capacity qfc and the drainage time
tfc (time needed to reach qfc from saturated conditions). The
given estimates of the soil hydraulic parameters (a, n, Ks,
qs, and qr), qfc, hfc (the pressure head corresponding to field
capacity), and tfc were estimated using HYDRUS-1D. In themodel setup, one-dimensional profiles of different lengths(L = 1 cm, 10 cm, 100 cm) were considered in order toevaluate the dependence of estimated variables on the soil
profile depth. The profiles were initially assumed to besaturated. A no-flux boundary condition was used at the

Figure 1. Soil texture triangle showing the textural
distribution of the combined data set.

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Table 2. Means and Standard Deviation of qfc, tfc, and hfc Estimated Using HYDRUS-1D for Negligible Drainage Fluxes of 0.001, 0.01,
and 0.1 cm/d for Different Textural Classesa
qfc = 0.001 cm/d
Texturelog10(tfc)(log10(days))qfc(cm3/cm3)

qfc = 0.01 cm/dlog10(hfc)(log10(cm))

log10(tfc)(log10(days))qfc(cm3/cm3)

qfc = 0.1 cm/dlog10(hfc)(log10(cm))

log10(tfc)(log10(days))qfc(cm3/cm3)

log10(hfc)(log10(cm))

Sand
0.541 (0.331) 0.069 (0.033) 2.223 (0.339) 0.18 (0.279) 0.08 (0.041) 2.072 (0.283) 0.914 (0.233) 0.099 (0.054) 1.919 (0.234)
Loamy sand 1.044 (0.261) 0.138 (0.057) 2.61 (0.409) 0.202 (0.217) 0.168 (0.065) 2.318 (0.416) 0.675 (0.225) 0.21 (0.074) 2.006 (0.474)
Sandy loam 1.144 (0.205) 0.184 (0.052) 2.657 (0.438) 0.256 (0.17) 0.219 (0.057) 2.32 (0.463) 0.704 (0.233) 0.264 (0.062) 1.942 (0.534)
Sandy clay 1.114 (0.173) 0.257 (0.054) 2.655 (0.593) 0.12 (0.254)
0.29 (0.057) 2.221 (0.651) 1.042 (0.542) 0.325 (0.059) 1.597 (0.938)
loam
Sandy clay 0.966 (0.13) 0.309 (0.058) 2.342 (0.702) 0.035 (0.182) 0.332 (0.055) 1.888 (0.752) 1.173 (0.33) 0.355 (0.05) 1.342 (0.855)
Clay
1.101 (0.17) 0.372 (0.085) 2.698 (0.71) 0.069 (0.211) 0.403 (0.085) 2.226 (0.774) 1.229 (0.629) 0.433 (0.083) 1.55 (1.04)
Silty clay
1.241 (0.176) 0.348 (0.093) 2.638 (0.698) 0.258 (0.255) 0.392 (0.092) 2.214 (0.744) 0.925 (0.667) 0.44 (0.091) 1.647 (0.905)
Silty clay
1.246 (0.158) 0.284 (0.07) 2.991 (0.577) 0.317 (0.194) 0.328 (0.072) 2.621 (0.642) 0.752 (0.429) 0.381 (0.07) 2.164 (0.814)
loam
Clay loam 1.183 (0.186) 0.301 (0.064) 2.654 (0.573) 0.189 (0.266) 0.339 (0.066) 2.223 (0.639) 1.056 (0.695) 0.38 (0.065) 1.611 (0.904)
Loam
1.195 (0.165) 0.246 (0.072) 2.742 (0.436) 0.281 (0.166) 0.285 (0.075) 2.387 (0.477) 0.775 (0.396) 0.333 (0.074) 1.948 (0.624)
Silty loam 1.095 (0.245) 0.254 (0.094) 2.881 (0.494) 0.198 (0.256) 0.287 (0.089) 2.558 (0.541) 0.883 (0.541) 0.331 (0.079) 2.081 (0.854)
Silty
1.101 (0.007) 0.113 (0.01)
3.3 (0.24)
0.327 (0.038) 0.142 (0.01) 3.091 (0.185) 0.469 (0.085) 0.192 (0.006) 2.872 (0.127)aStandard deviations are given in parentheses; qfc is negligible drainage flux.

was needed. We developed such a data set by combining soil
data from two databases used by Schaap et al. [2001] andMinasny et al. [2004]. The database used by Schaap et al.
[2001] has the required information for 1306 soil samples.

Most of these samples were undisturbed and derived fromsoils in temperate to subtropical climates of North America
and Europe. The Minasny et al. [2004] data set consists of
310 undisturbed soil samples collected from three different

Figure 2. Plot showing the values of (a) field capacity (qfc), (b) the pressure head at field capacity (hfc),
and (c) drainage time (tfc) estimated using profile lengths (L) of 1 cm (x axis) and 10 and 100 cm (y axis)
for different negligible drainage fluxes (qfc) of 0.001 (red), 0.01 (green), and 0.1 (blue) cm/d.
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W10410negligible drainage fluxes (qfc = 0.001, 0.01, and 0.1 cm/d).
As expected, the computational time increased significantly
for smaller values of qfc and larger values of L. Figure 2
shows the values of qfc, tfc, and hfc estimated using different
combinations of L and qfc. It was observed that estimated qfc
and hfc were insensitive to the length of the profile, while
tfc was found to increase linearly with the profile length. A
linear relation between tfc and the soil profile depth L has
been observed in previous research [Meyer and Gee, 1999].
A profile length of 1cm resulted in quicker estimation of qfc,
tfc, and hfc, without compromising the accuracy of the estimates. Hence, for further analysis, we used a profile lengthof 1 cm.

Figure 3. Plot showing relationships between saturation at
field capacity (Sfc) and (a) the pressure head at field capacity(hfc) and (b) drainage time (tfc) estimated for the combined
data set using negligible drainage fluxes (qfc) of 0.001, 0.01,
and 0.1 cm/d.

field projects in California. The combined data set from
Schaap et al. [2001] and Minasny et al. [2004] was trimmed
further by removing soil samples that did not have otherancillary information (such as textural properties, bulk density, etc.) or possessing soil hydraulic parameters thatappeared to be clear outliers of the data set. The resulting
combined data set has 1578 soil samples. Table 1 lists thesummary statistics of the combined data set and Figure 1
shows the textural distribution of the data set. The data set iswell distributed throughout different soil textures, except forsilt soils. As is typical with most real-world databases, thetextural distribution is somewhat biased toward the sanddominated textures.

4. Results and Discussion
4.1. Model Sensitivity to Profile Length[12] For estimating the field capacity, it was necessary toestimate a technically ideal profile length, L, so that (1) qfc,
tf,c, and hfc were estimated accurately and (2) computationaltime was manageable for future applications. We estimatedthe qfc, tfc,, and hfc for the combined data set using threedifferent profile lengths (L = 1, 10, and 100 cm) and three

4.2. Flux-Based Estimation of Field Capacity[13] A profile length of 1 cm was used to estimate qfc, tfc,
and hfc. Table 2 shows means and standard deviations (inparenthesis) of qfc, tfc, and hfc estimated for the combined data
set considering negligible drainage fluxes (qfc) of 0.001, 0.01,
and 0.1 cm/d. It was observed that for qfc = 0.01 cm/d thepressure heads at field capacity, hfc, conform more to the
traditionally used benchmark pressure heads. However, values of hfc vary by several orders of magnitude across different
soil textures, making it difficult to assign a single universal
benchmark pressure head to estimate field capacity for all
soils. It is interesting to note that for the profile length of 1 cm,
the soil drainage time (tfc) is consistent with the traditionallyaccepted drainage time of 1 – 3 days for qfc = 0.01 cm/d. The
soil drainage times for other qfcs (0.001 cm/d, 0.01 cm/d) areorders of magnitude different from the traditionally accepteddrainage time. As expected, sand and clayey-textured soils
produce the smallest drainage times using our approach.
While sands drain very quickly to small water contents, clays
drain slowly, but persistently, because of their low hydraulicconductivity.
[14] For other profile lengths (L = 10 cm, 100 cm), Figure 2
shows that the estimated drainage times are in the same range
as the traditionally accepted drainage times for qfc = 0.1 cm/d.
However, as observed earlier, a qfc of 0.1 cm/d results in very
low estimates of hfc (Table 2). For a profile length of 1 cm,
one may conclude that qfc of 0.01 cm/d, suggested by Dirksen
and Matula [1994], seems to be a more appropriate value forthe negligible drainage flux, as compared to values suggested
by Meyer and Gee [1999].
[15] It is important to understand how the estimated qfc,
tfc, and hfc relate to each other in the combined data set. For
this purpose, we also estimated the saturation at field capacity(Sfc) for all soils:
Sfc ¼

qfc  qrqs  qrð4Þ[16] Figure 3 shows the relationships between Sfc, hfc, andtfc estimated for the combined data set using negligible
drainage fluxes (qfc) of 0.001, 0.01, and 0.1 cm/d. Note thatthe y axis has a logarithmic scale. A profile length of 1 cm
was used again. It is clear that a single value of a benchmark
pressure head (such as 330 cm) cannot represent the field
capacities derived using the flux-based approach, which more
realistically represents nonlinear nature of soil hydraulicproperties. As observed in Table 2, the drainage time (tfc) is

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W10410Figure 4. Plot showing (a) saturation at field capacity (Sfc), (b) the pressure head at field capacity (hfc),
and (c) drainage time (tfc) estimated using negligible drainage fluxes (qfc) of 0.01 cm/d on the x axis and0.001 and 0.1 cm/d on the y axis.

more consistent with traditionally accepted values forq fc = 0.01 cm/d.
[17] Figure 4 further explores relationships between Sfc,
tfc, and hfc estimated using negligible drainage fluxes (qfc) of
0.001, 0.01, and 0.1 cm/d. For field capacity, Figure 4a
indicates that qfc estimated using 0.01 cm/d seems to represent a good trade-off between those estimated using qfc of
0.001 and 0.1 cm/d. Figure 4b also clearly points out the
inaccuracies associated with using benchmark pressure
heads. One may note that the estimated hfc are scatteredacross a range spanning several orders of magnitudes. As
observed in Table 2, the drainage time (tfc) estimated using
qfc = 0.01 cm/d provides a good trade-off between thoseestimated using qfc of 0.001 cm/d and 0.1 cm/d.
4.3. Dependency of Field Capacity on Soil Texture[18] We would like to note that the concept of field
capacity was originally developed for well-drainable soils[Veihmeyer and Hendrickson, 1931]. However, the term has
since then been used for soils with a wide range of drainage
characteristics [Romano and Santini, 2002]. In view of thedifferent use of the term field capacity from its originalusage, it would be valuable to show using a contour
diagram how qfc, tfc, and hfc change with texture for qfc =0.01 cm/d. However, developing contour maps for qfc, tfc,
and hfc as a function of texture is difficult using the combined data set, because the real-world combined data set (1)has soil hydraulic parameters that do not vary smoothly
across textures, due to obvious sampling/estimation errors,and (2) is not sufficiently scattered enough across different
textures to develop a reliable contour diagram. For thispurpose, we used the ROSETTA pedotransfer functions toestimate the soil hydraulic parameters as a function of sand,silt, and clay. ROSETTA, as a mathematical paradigm, estimates soil hydraulic parameters that vary smoothly acrossdifferent textures.
[19] Five soil hydraulic parameters (qr, qs, a, n, and Ks)
throughout the entire soil textural triangle were estimatedusing the ROSETTA pedotransfer functions (PTFs), suchthat all soil textural possibilities (i.e., combinations of sand,silt, and clay percentages) were considered. The data set
was created by varying the sand, silt, and clay percentages
by 1%, leading to a set of 5151 data points. ROSETTA
predicted mean values and associated uncertainties for soil

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W10410Figure 5. Mean values of (a) qfc, (b) log10(hfc), and (c) log10(tfc) as a function of sand, silt, and clay
percentages obtained by flux-based simulations for soil hydraulic parameters estimated using ROSETTA
and for a negligible drainage flux of 0.01 cm/d.
hydraulic parameters for each of these 5151 soil data points.
In order to take into account the uncertainties associatedwith ROSETTA predictions, the mean and standard deviation (uncertainty) values of the five soil hydraulic parameters for all 5151 data points were used to develop 100 data
sets for soil hydraulic parameters using the Monte Carlosampling approach. HYDRUS-1D was then used in asimilar fashion as above for the real-world database to
estimate qfc, tfc, and hfc for all 100 data sets and for each of
the 5151 data points. Mean values of qfc, tfc, and hfc werethen calculated from the 100 data sets for all 5151 points,
and used as representative values to develop the contour
diagram. Figure 5a shows the mean estimate of qfc; Figure 5bshows the mean estimate of log10(hfc); and Figure 5c shows
the mean estimate of log10(tfc) as a function of sand, silt, andclay percentages obtained by the flux-based approach for soil
hydraulic parameters estimated using ROSETTA and for anegligible drainage flux of 0.01 cm/d. We have shown abovethat negligible drainage flux of 0.01 cm/d is a good approximation for estimating field capacity. The contour diagrams
show a sharp change in values of qfc, tfc, and hfc as the sandcontent increases.

4.4. Empirical Equation for Estimating Field Capacity[20] In the simulation above, qfc and qfc are estimated at
the bottom of the soil column. Alternatively, under unit
gradient conditions, when the flow occurs only in response
to gravity, one may also obtain field capacity by equating
the drainage rate to the unsaturated hydraulic conductivity(described in equation (3c)). The field capacity, qfc, can be
therefore estimated for any negligible drainage fluxes (qfc)
by solving the following equation:
qfc ¼ Ks

qfc  qrqs  qr

l "
1



qfc  qr1
qs  qr1=m !m #2
ð5Þ

Equation (5) is highly nonlinear and estimating the field
capacity using equation (5) requires a root-finding algorithm.
Often, one would prefer to have an empirical equation topredict field capacity directly from soil hydraulic parameters(e.g., using the van Genuchten-Mualem model), instead of
estimating it using a numerical simulation or solving ananalytical equation using a root-finding algorithm. On theother hand, the van Genuchten-Mualem model parameters

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TWARAKAVI ET AL.: DYNAMIC NATURE OF FIELD CAPACITY

W10410Ks for the combined data set using negligible drainage fluxes(qfc) of 0.001, 0.01, and, 0.1 cm/d. While Sfc and n show astrong power-based relationship, dependence between Sfc
and Ks appears to be weaker and inverse in nature. Whilefurther exploring different functional possibilities to relate
Sfc, n, and Ks, we found the following equation to be an
accurate empirical relationship for estimating field capacity:
Sfc ¼

qfc
qfc  qr
¼ n0:60 log10 ð Ks Þ
qs  qrð6Þ

Note that equation (6) is generic, and is dependent on thevalue of qfc. Assuming that a qfc of 0.01 cm/d is a reasonableapproximation for flux-based estimation of field capacity,
equation (6) can be further simplified as follows:
Sfc ¼

qfc  qr
¼ n0:60ð2þlog10 ðKs ÞÞ
qs  qr

ð7Þ

where Ks is the saturated hydraulic conductivity of the soilin cm/d.
[23] Figure 7 shows how well qfcs is predicted using
equation (7) compared with those estimated through simu-

Figure 6. Plot showing the relationship between fluxbased estimates of Sfc and (a) n and (b) Ks for the combined
data set using negligible drainage fluxes (qfc) of 0.001, 0.01,
and 0.1 cm/d.
can be estimated from textural and other easy-to-obtain
information using several available PTFs [e.g., Schaap et al.,
2001; Twarakavi et al., 2009].
[21] The use of equation (5) to estimate field capacity is
restricted to uniform soils. For such conditions, equation (5)is expected to yield similar results to those obtained by thenumerical approach described above. On the other hand, thenumerical approach can also be used for a variety of soil
formations and soil structures. Examples of cases where field
capacity can be estimated using the numerical approach andnot equation (5) include (1) layered soils, or (2) soils
exhibiting various preferential or nonequilibrium flow phenomena, which can be simulated using the dual-porosity or
dual-permeability features of HYDRUS [Šimůnek and van
Genuchten, 2008]. Understanding the field capacity of such
soils is a subject of our future research interest, and this paper
lays foundations for it.
[22] In order to develop an empirical equation to estimate
field capacity from van Genuchten-Mualem model parameters, various prospective relationships between the soil
hydraulic parameters (qr, qs, a, n, and Ks) and simulated
estimates of qfc for different negligible drainage fluxes (qfc)
were analyzed. As described in equation (5), it was found that
estimates of field capacity show a relationship with qr, qs, n,
and Ks. Figure 6 shows the relationship between Sfc and n and

Figure 7. Plot showing (a) relationships between qfc
estimated using simulations (x axis) and predicted using
equation (6) (y axis) and (b) differences between thepredicted and simulated qfc as a function of the simulated
value of qfc.

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lations. Equation (7) seems to predict field capacities quite
well for a variety of soil hydraulic parameter combinations.
Even though equation (7) is a simplification of equation (6)with a qfc of 0.01 cm/d, it seems to predict field capacities
even for other values of qfc reasonably well. The error in theprediction of field capacity is less than 0.04.

5. Summary and Conclusions[24] Field capacity is a soil property that is intrinsicallylinked with dynamic natural processes, and any attempt
to estimate it must take this into consideration. We havedeveloped a modeling-based approach to estimate field
capacity using the Richards equation and the van GenuchtenMualem model for describing soil hydraulic properties. For
the purposes of this study, field capacity was defined as thesoil water content when the drainage flux from the initiallysaturated soils reaches a predefined ‘‘negligibly small value(qfc).’’ We have estimated the field capacities for threedifferent values of qfc: 0.001, 0.1, and 0.01 cm/d. A negligible
drainage flux of 0.01 cm/d was found to result in good
estimates of field capacities across a range of soils. We also
compared the differences between time-, pressure-, and fluxbased approximations of field capacity. It was concluded thatusing benchmark pressure heads to estimate field capacityfrom retention curves is an inaccurate method. In comparison
to the pressure-based approximation of field capacity, thetime-based approach seems to be more robust. Finally, wedeveloped an empirical equation relating the soil hydraulicparameters to field capacity and tested it for its applicability.
[25] Since our work was based on the hypothesis that theRichards equation, in conjunction with the van GenuchtenMualem model, can satisfactorily describe variably saturated
water flow in homogeneous soils, our finding are valid only
for these conditions. The boundary conditions can have asignificant effect on our approach, and therefore need to beconsidered. We intend to use the numerical approach presented here in future research analyzing the field capacities
of nonuniform soils or soils exhibiting various preferential or
nonequilibrium flow phenomena.
[26] Acknowledgments. I would like to acknowledge Laurent
Bahaminyakamwe (Agronomy and Soils Department, Auburn University)
and Ajay Kalra (University of Nevada, Las Vegas) for assisting me with thedevelopment of research and the manuscript.

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M. Sakai and J. Šimůnek, Department of Environmental Sciences,
University of California, Riverside, CA 92521, USA.
N. K. C. Twarakavi, Department of Agronomy and Soils, Auburn
University, 258 Funchess Hall, Auburn, AL 36832, USA. (twarakavi@
auburn.edu)

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