If your life's work can be accomplished in your lifetime, you're not thinking big enough. Wes Jacks

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You're not going to master the rest of your life in one day. Just relax. Master the day. Than just keep

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Be like the sun for grace and mercy. Be like the night to cover others' faults. Be like running water

[i]Delonix regia[i]

No amount of guilt can solve the past, and no amount of anxiety can change the future. Anonymous

"l_%i-rff4i"i

If you feel beautiful, then you are. Even if you don't, you still are. Terri Guillemets

event i event i

Goodbyes are only for those who love with their eyes. Because for those who love with heart and soul

I

How wonderful it is that nobody need wait a single moment before starting to improve the world. Anne

SAXTON

ET AL.: ESTIMATING

Estimating ,

Generalized

GENERALIZED

Soil-water

SOIL-WATER

CHARACTERISTICS

Characteristics

from ,

1031

Texture1

J

K.

(i: ,

E.

SAXTON,

W.

J.

RAWLS,

J.

S.

ABSTRACT

~ ,,

Soil-water

,

soil-water

potential content

all

and hydraulic

are needed

ROMBERGER,

conductivity

for many

plant

relationships

with

and soil-water

studies.

AND

inclusive

R.

textures.

I.

PAPENDICK2

Similarly,

equations

were

developed

for

un-

saturated hydraulic conductivities for all inclusive textures. While the developed equations only represent a statistical estimate and only

the

textural

influence,

they

provide

quite

useful

estimates

i;'

for

,},i 1

Measurement

of these

relationships

is costly,

difficult,

and

often

many

usual

soil-water

cases.

The

equations

provide

excellent

" ,

comI

impractical.

For

many

purposes,

general

estimates

based

on more

putational

efficiency

for model

applications

and the textures

can be

!

~;

\

,it,

readily

available

cent studies ture

and

between

information

such

have developed

selected

soil

selected

soil

as soil texture

statistical

potentials

correlations

using

textures

and

jective ematical of equations this study for was continuous to extend

are sufficient.

a large

hydraulic

between data

base,

conductivity.

Re-

soil texand

also

The

ob-

used

as calibration

characteristic compared

data with

parameters

where

are available.

several

field

Predicted

independent

or laboratory values

measurements

soil

"

water

I:'i

Ij Ii" i

were successfully of soil-water

po-

I

f

tential.

these estimates resultsover by broad providingranges math-of

.1ddltlonal

[ndex

~ords:

soll-,,:ater

potential,

hydraulIc

conduc-

! i!

soil from

texture,

water

t.he recent

potentials

for

multivariate

a wide analyses

I Contribution the College Washingto~

potentials, s.tatistical

from

and

hydraulic

analy~es

range

of soil

to provide Agric.

were textures,

continuous

conductivities. used then

these

potential

Res. Serv ., USDA,

of Agric. and Home State Univ., Pullman,

Economics, WA 99164.

Results

to calculate were

estimates

in cooperation

tlVlty, Saxton,

fit

by

Estimating

for

Sci. Soc. Am.

Received

10

June

K.E.,

W.J.

moisture Rawls,

generalized

equations. J.S. Romberger,

soil-water

~d.R.I.

charactenstlcs

Papendick. from

texture.

198~. SoIl

J. 50: 1031-1036.

with

Agric. Res. Center, Scientific Paper no. D

6911.

unsaturated

water

ELATIONSHIPS

OF

SOIL-WATER

POTENTIAL

and

hy-

1985.

," "

I

I

~

J

~

j

, "

j

[I' i .

"

(

I "'

"

I

"

",,",

'

,

f

;, !~~ ";il:, !;1 ,1 ~jii,i:;

SOIL

1032

SCI. SOC. AM.

Table 1. Summary of coefficients for linear regression Eq. [4) by Rawls et al. (1982).

10 20 33 60 100 200 400 700 1000 1500

0.4118 0.3121 0.2576 0.2065 0.0349 0.0281 0.0238 0.0216 0.0205 0.0260

-0.0030 -0.0024 -0.0020 -0.0016 0.0014 0.0011 0.0008 0.0006 0.0005

0.0023 0.0032 0.0036 0.0040 0.0055 0.0054 0.0052 0.0050 0.0049 0.0050

0.0317 0.0314 0.0299 0.0275 0.0251 0.0220 0.0190 0.0167 0.0154 0.0158

0.81 0.86 0.87 0.87 0.87 0.86 0.84 0.81 0.81 0.80

50, 1986

bution from particle size distribution, bulk density, and particle density. Then the pore radii are converted to equivalent soil-water tensions using the equation of capillarity at the corresponding volumetric water content. Gupta and Larson (1979) used multiple linear regression equations of the form ep = a (% sand) + b (% silt) + c (% clay) + d (% organic matter) + e (bulk density, Mg/m3) [3]

water stress. These investigations commonly require soil-water potential and hydraulic conductivity for the computations of soil-water storage or soil-water flow. Soil-water potential and hydraulic conductivity vary widely and nonlinearly with water content for different soil textures. Moreover, these relationships are relatively difficult and expensive to measure or are not feasible for short-term or remote investigations. Experience has shown that soil texture predominately determines the water-holding characteristics of most agricultural soils. Textural information is often either available or can be estimated by simple methods (Bouyoucos, 1951) and could readily serve as the principal input variable to a mathematical method for estimatihg soil-water characteristic relationships. For many numerical models, measured data at selected values are often used in tabular form with interpolation. Equational representation of these rela-

tionships over the necessary ranges of soil-water content and soil texture would greatly reduce input data requirements, computer storage space, and execution time of matheIJlatical models. It would be highly beneficial to have a computationally efficient method to estimate soil-water characteristics with reasonable accuracy from readily available inputs. The objective of this study was to develop such a procedure from results of previous statistical analyses of a large data base. SO IL- W A TER POTENTIAL The relationship between soil-water potential and water content has been describedin several ways. Brooks and Corey ( 1964) fitted the equation '¥ = '¥ ,,[(e -e,)/(es -e,)]B [ 1] to the soil-water potential curves where 'I1 is soil-water potential (kPa), 'I1" is soil-water potential at air entry (kPa), e is soil-water content (m3/m3), es is saturation soil-water content (m3/m3),e, is residual soil-water content (m3/m3),which is an empirical value to straighten curved data on a log-log scale, and B is a fitted value. Equation [ 1] can be simplified to the form \}! = A eB

J., VOL.

[2]

by setting er = O and A = \J!" e;B. This equational fonn has been supported by several recent studies (Campbell, 1974; Clapp and Homberger, 1978; Gardner et al., 1970a,b; Rogowski, 1971; Williams et al., 1983; McCuen et al., 1981). Arya and Paris (1981) presented a model to predict the soil-water tension curve from particle size distribution and bulk density data. Their model calculates a pore size distri-

to predict the soil-water content (8p! m3/m3) for 12 given soil-water potentials where a, b, c, d, and e are regression coefficients. Intermediate values could be linearly interpolated between the calculated points. Rawls et al. (1982) also reported a multiple linear regression analysis of soil-water content at 12 soil-water potentials with soil attributes using a very extensive data set (2541 soil horizons with a wide range of each correlated variable). They used three linear regression equations of which the simplest is ep = a + b (% sand) + c (% silt) + d (% clay) +e (% organic matter) + J(bulk

density, Mg/m3) [4]

where a, b, c, d, e, and f are regression coefficients and textures defined by the USDA system. The other two regression equations included: (i) the addition of 1500 kPa water retention to those variables ofEq. [4], and (ii) the addition of both 33 and 1500 kPa' water retention as correlated variables. Equations and coefficients containing the 33 and 1500 kPa moisture values were not further considered here since these data are often not readily available or obtainable. Only one or two of the three coefficients b, c, and d were simultaneously considered because of their dependency. Using step-wise regression, Rawls et al. (1982) correlated only the most statistically significant variables in Eq. [4]. These coefficients are summarized in Table 1 for selected measured potentials from 10 to 1500 kPa. Some coefficients are zero showing insignificant effects; for example, at potentials of 10 kPa and greater, bulk density did not effect water content, which is consistent with other literature (Borg, 1982). The equations have a small sensitivity to organic matter, as can be seenfrom the coefficients of Table I. A 1%increase in organic matter caused a 3.2 and 1.5%by volume increase in moisture content at 10 and 1500 kPa, respectively. Organic matter has a very small range (0-3%) for most agricultural soils. Soil texture, defined by the USDA system where sand = 2.0 to 0.05 mm, silt = 0.05 to 0.002 mm, and clay <0.002 mm, is the dominant factor in the soil-water potential-content relationship. Oay content is the most important texture factor as seen by the coefficients in Table I. Cosby et al. ( 1984) also clearly demonstrated that soil texture could be related to hydraulic characteristics when they applied regression and discriminant analysis to these and other data. The results ofEq. [4] with the coefficients of Table 1 represent a valuable summary of an extensive data set. For ready application to soil-water computations, however, these water content values at selected potentials must be interpolated over the whole of the useful moisture range in a nonlinear fashion. To be computationally efficient and accurate, equations are needed; thus we conducted the subsequent analysis. To select the equational forms, it is known that potential curves cannot be representedfrom saturation to wilting point by a straight line on log-log axesor any other first- or secondorder equation becauseof the double inflection in the curve. However, at potentials greater than about 10 kPa, a log-log equation provides a reasonable estimate. A linear relationship is a good approximation from 10 kPa to air entry potential. At air entry potential and less, the soil is essentially

~

SAXTON

ET AL.: ESTIMATING

GENERALIZED

SOIL-WATER

100~

CHARACTERISTICS

Table 2. Summary of derived soil-water characteristic equations. ~-Applied tension range, kPa > 1500 to 10

, ,

*

Sa

c

100.0 B = e + f (%C)" + 9 (%S)"- + 9 (%S)"(%C) 'l' = 10.0 -(9 -9,o)(10.0 -'l'e)I(9. -9,0) 9,0 = exp[(2.302 -In A)IB] 'l'e = 100.0 [m + n (9.)] 9. = h + j (%S) + k log,o (%C) 9 = 9. K = 2.778 x 10-. {exp[p + q (%S) + [r +

L

10 to'l'e

"0 c ca (/)

.."

L

,,

+

! c

,

L

!

" 'i 81

L

'l'e to 0.0 >1500 to 0.0

c

, I

"

Equation 'l' = A eB A = exp[a + b (%C) + c (%S)" + d (%S)"(%C)]

s. L !

I ' I. !

,

t (%S) + u (%C) + v (%C)"](119)]}

:\ I ,,

81 C L ,

Coefficients

:81 C',

10

20

30

40

I. Applicable

textural

70 80

50

Clay, Fig.

1033

region

100

%

{clear)

for the derived

equations.

at saturation moisture content and the water content changes very little; thus a constant water content value is reasonable. Therefore, the complete water potential-water content curve can be represented by three equations for the ranges of (i) saturation to air entry, constant; (ii) air entry to 10 kPa, linear; and (iii) 10 to 1500 kPa and greater, curvilinear by Eq. (2]. For the range > 10 kPa, we used Rawls' regression equations with an average organic matter content of 0.66% to generatemoisture content values e (m3/m3) for a systematic variation of textures for the 10 potentials \1!(kPa) shown in Table I. The soil texture triangle was divided into grids of 10% sand and 10% clay content increments. The 55 grid midpoints were used to generate the moisture contents for the 10 potential values from 10 to 1500 kPa. Of the 55 sets of values this produced, values were omitted for textures with >60% clay content, <5% sand, and <5% clay, because they exceededthe range of all but a few of the original data used in the stati~tical analyses by Rawls et al. ( 1982). The remaining 44 sets of values were correlated with Eq. (2] as the model. The 44 A and B coefficients were separately correlated with sand and clay (USDA classification) content using stepwise multiple nonlinear regression techniques. The resulting v

1500r

ro a. ~ ~ :;:; c 0) o a... 0) ro

.

= = = = = =

Iv

9 h j k m n

= = = = = =

-3.484 0.332 -7.251 0.1276 -0.108 0.341

x 10-. X 10-.

p q r t u v

= = = = = =

I'

12.012 -7.55 x 10-1 -3.8950 3.671 x 10-1 -0.1103 8.7546 x 10-.

Definitions

saturation,

9,0 = water content at 10 kPa, m./ma K = water conductivity, m/s (%S) = percent sand (e.g., 40.0) (%C) = percent clay (e.g., 30.0)

maIm"

equation for A (n = 44, R2 = 0.99) was A = exp [ -4.396 (% sand)2 -4.285

-0.0715

(% clay) -4.880

B = -3.140

X 10-4

,

X 10-5 (% sand)2

(% clay)] 100.0 and that representing B (n = 44, R2 = 0.99) was -0.00222

I~ , ,"I, i

[5]

(% clay)2 -3.484

:

': , It

X 10-5 (% sand)2 (% clay) .[6] The value of 100.0 was"included in Eq. [5] to convert from the original data units of bars to kilopascals. Thus, the potential-moisture content relationship of Eq. [2] for all potentials > 10 kPa can be estimated by soil texture with a Curve

200

-4.396 -0.0715 -4.880 x 10-. -4.285 x 10-. -3.140 -2.22 x 10-.

'l' = water potential, kPa 'l'e = water potential at air entry, kPa 9 = water content, m./ma 9. = water content at

a b c d e f

O c o 6 V O

% Sand

Texture

% Clay

loamy

sand

80

10

sandy

loam

65

15

45

15

loam silt clay clay

loam loam

20

15

35

35

25

45

900 . A

~

600

~"~'{ vi' ,1 ;

$:

.0 (/)

a b c d e f

0 300

0 0 0

Fig. 2. Comparison

10

20 30 40 50 60 Moisture Content, % Volume of results from the derived equations with those from correlations by Rawls et al. (1982).

II J

1034

SOIL SCI. SOC. AM. ]., VOL. 50, 1986 ii

1500

~

9

e!

Curve

Texture

-'

% Sand 20 8 10 35 20 40 60 65 82 92

1200

"' 0. ~ ""tU .-I C 0) O 0.

900

% Clay 60 45 35 35 15 18 28 10 6 5

I 600

300j

0

10

20

30

Moisture Fig. 3. Predicted potential

40

Content,

basis of the same 2500 samples correlated by Rawls et al. (1982). For potentials <10 kPa, we first correlated saturation moisture content and air entry tension to soil texture. Using the saturation moisture contents reported by numerous literature sources and summarized by Strait et al. (1979) for 10 soil texture classes,we obtained the following regression equation: E>s= 0.332 -7.251 X 10-4 (% sand)

texture (0-1500

kPa range).

saturation moisture content using reported air entry potential values for 10 texture classes reported by Rawls et al. (1982) resulting in 'I!" = 100.0 [ -0.108 + 0.341 (0..)] [8] where'!1" is air entry potential (kPa) (n = 10, R2 = 0.94). Having estimated es from soil texture data, '!I" from 8" and '!I at 10 kPa from Eq. [2], the 10 kPa to '!I" linear segment and '!I " to 0.0 kPa constant segment can be defined to complete the low tension portion of the potential-moisture relationship. Thus the complete characteristic curve may be estimated from soil texture data.

[7]

where es is moisture content at saturation (m3/m3), (n = 10, R2 = 0.99). Air entry tension was then correlated to

The combined equation set ([2], [5], [6], [7], and [8]) was tested over the range of the texture triangle to determine any

c

fQe

50 r-

60

% Volume

curves for soil class centroid

+ 0.1276 loglo (% clay)

50

Curve

Texture

% Sand

% Clay 60 45 35

401

35 15 18 28

~ Do ~ "tU :;: c: <1> 0 Do

10

30

6 5

201

10

0

10

20

30

Moisture

Content,

Fig. 4. Predicted potential

40

50

60

% Volume

curves for soil class centroid texture (0-50 kPa range).

~

SAXTON

ET AL.: ESTIMATING

0

1500r-

GENERALIZED

SOIL-WATER

1200

~ c:

900

Q) O 0.. ... Q) (0

1035

v Curve

(0 ~

CHARACfERISTICS

a b c d e

600

Texture

loamy sand sandy loam silt loam silty clay loam sandy clay loam

O o o A V

% Sand

% Clay

85 66 16 14 66

4 15 21 30 31

[J

J fli J,tt, ,':

:s:

0 (/)

300

~

0

f" i:{

6

0 0

10

20

30

40

50

et !'[ ~

60

,I

I ,

II,

Moisture Content. % Volume of predicted equations with independent measured data.

Fig. s. Comparison

The three curves, b, c, and d, in Fig. 2 show the sensitivity to change in sand content; while the three curves, d, e, and f, largely show the greater sensitivity to clay content. Figures 3 and 4 show predicted high and low ranges of potential curves for the centroid textures of soil classesusing the derived equation set as summarized in Table 2. Shifts of texture away from the centroid values but remaining within the texture classesof Fig. I show that significant potential changes can result even for soils with the same general textural classification. Independent sources of measured potential-soil-water content data with associated texture data (Arya et al., 1982;.. Williams et al., 1983; D. Miller, 1984, personal communication) were also used to verify Eq. [2], [5], and [6]. The comparisons shown in Fig. 5 illustrate that a generally good estimate was obtained using the derived equations. Some water potential measurement error, especially for the sandy clay loam soil, may well be present. The worth of the derived equation set is to approximate

areas of unreasonable result. At some low and high clay contents, the equations produced low potential moisture contents that exceededthe saturation moisture content. Figure I shows the region within the texture triangle for which the equations appear quite valid and is approximately defined as 5% ~ % sand ~ 30% with 8 ~ % clay ~ 58%, and 30% ~ % sand ~ 95% with 5% ~ % clay ~ 60% . Figure 2 shows some example comparisons of results from the equation set with those of Eq. [4], which was used to derive the equations. The degree of agreement is generally good over the wide range of soil textures. These examples show that a statistical comparison with the original data used to derive Eq. [4] would have produced a slightly reduced level of correlation than reported by Rawls et al. ( 1982), but the lack of uniform methods and textural definitions in these data made such an analysesof limited value. 102

~ 1,.c 1 E u >. .> :;: u ~ -0 c o U 'Q) "'

10. c

100

/ 1(

~,~.

~ ""

10-

Iii

10-2

I

, ", .

Rawls et al (1982) Curve Equation

10-3

10

Texture

~~~..

% Sand

%

Clay

"" 5 6

$:

10

.0 (/)

15

10-..

35 45

10-

0

10

50 60 20 30 40 Moisture Content, % Volume Fig. 6. Comparison of unsaturated hydraulic conductivity results from Eq. (10] with original curves from Rawls et al. (1982). (Multiply cm/ h by 2.778 X 10-6 to obtain m/s.)

1

1036

SOIL SCI. SOC. AM. J., VOL. 50, 1986

the full moisture range of the potential characteristic with minimal input data. While the derived relationships depend only on texture, other factors such as bulk density, structure, organic matter, clay type, and hysteresis may all have a secondary impact (Williams et al., 1983). Thus it is expected that the results from the derived equation set will only be an estimate, albeit a quite reasonable one, based on the large underlying data set. Should some field or laboratory data be available, it would be quite reasonable to moderately shift inputted textures (principally clay content due to its strong sensitivity) to cause appropriate matching. HYDRAULIC

CONDUCTMTY

Early models to predict soil-water conductivity were either empirical or theoretical relationships with soil particle size or porosity. These models were usually based on conductivity at saturation and not readily applied to unsaturated conditions. Later models related unsaturated conductivity to moisture content or potential such as Campbell (1974), who used a form of

K = a0b

[9]

where K is unsaturated conductivity (JD S-I), e is JDoisture content (JD3/JD3), b is a function of B in Eq. [2], and a is a function of saturation moisture content. These models usually require calibration using measured data, although Bloemen ( 1980) developed reasonable relationships using soil texture and pore size distribution index. Rawls et al. ( 1982) reported hydraulic conductivity curves for 10 texture classes that were averages of numerous reported curves. These hydraulic conductivity data did not correlate well with an equation of the form of Eq. [9]. Multiple nonlinear regression techniques were applied to these 10 curves using moisture content, percent sand, and percent clay as the independent variables. We derived the following equation for hydraulic conductivity using 230 selected data points ~niformly spaced on the 10 curves (n = 230, R2 = 0.95). K = 2.778 X 10-6 {exp [12.012 -0.0755 (% sand) + [ -3.8950

+ 0.03671 (% sand) -0.1103

+ 8.7546 X 10-4 (% clay)2] (I/0)]}

(% clay) .[10]

Equation [10] was found to provide quite reasonable values over at least the same textural range as those for water potential. Figure 6 shows hydraulic conductivity curves calculated using Eq. [10] for the centroid class textures and the curves (in the original units) from which the data were obtained (Rawls et al., 1982). For the extreme condition of near saturation or very dry and very high clay contents, the calculated values do not match reported values as well as desired; however, it is a good fit for a single equation over a large range of commonly encountered textures. Some adjustments may be appropriate for near saturation values for high clay content soils. Just as for potentials, other soil attributes than texture could well causesome deviations from the estimates by Eq. [ 10]. CONCLUSIONS This study examined previous methods for estimating the relationships of soil-water content to potential and hydraulic conductivity. Using the results of previous broad-based correlations, equations were derived to estimate continuous relationshps of soilwater moisture content to potentials and hydraulic conductivity from soil textures. The potential re1a-

tionship is continuous and nonlinear from 10 to 1500 kPa, linear from 10 kPa to air entry potential, and a constant water content below air entry potential. The hydraulic conductivity relationship is continuous and nonlinear from saturation moisture content to near air dry. A complete summary of the derived equations and coefficients is provided in Table 2. The equations are valid for a wide range of textures. They are computationally efficient to allow easy use with a digital computer and they provide reasonably accurate estimates of the unsaturated potentials and hydraulic conductivities with a minimum of readily available data. Comparisons with independent measured soil-water characteristic curves verified these results. Textural ranges within generally defined texture classescan cause significant changesof potentials and hydraulic conductivities. The estimated curves should be adjusted for effects of organic matter, clay type, density, structure, etc., to represent measured values or hysteresis by slight adjustments of the texture (clay primarily) when these secondary effects can be defined. REFERENCES Arya, L.M., and J.F. Paris. 1,981.A physioempirical model to predict the soil moisture characteristic ftom particle-size distribution and bulk density data. Soil Sci. Soc. Am. J. 45: 1023-1030. Arya, L.M., J.C. Richter, and S.A. Davidson. 1982. A comparison of soil moisture characteristics predicted by the Arya-Paris model with laboratory-measured data. Report no. SM-t2-04247; JSC17820. National Aeronotics and Space Administration, Lyndon B. Johnson Space Center, Houston, TX. Borg, H. 1982. Estimating soil hydraulic properties ftom textural data. Ph.D. thesis. Washington State Univ., Pullman (Diss. Abstr. 83-03292). Bouyoucos. G.J. 1951. A recalibration of the hydrometer method for making mechanical analysis of soil. Agron. J. 43:434-438. Bloemen, G. W. 1980. Calculation of hydraulic conductivities of soils ftom texture and organic matter content. Z. Pflanzenernaehr. Bodenkd. 143:581-605. Brooks, R.H., and A. T. Corey. 1964. Hydraulic properties of porous media. Hydrology Paper no.3. Colorado State University, Fort Collins. Campbell, G.S. 1974.A simple method for determining unsaturated conductivity ftom moisture retention data. Soil Sci. 117:311-314. Clapp, R.B., and G.M. Hornberger. 1978. Empirical equations for some soil hydraulic properties. Water Resour. Res. 14:601-604. Cosby, B.J., G.M. Hornberger, R.B. Clapp, and T.R. Ginn. 1984. A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils. Water Resour. Res. 20:682-690. Gardner, W.R., D. Hillel, and Y. Benyamini. 1970a. Post irrigation movement of soil water: I. Redistribution. Water Resour. Res. 6:851-861. Gardner, W.R., D. Hillel, and Y. Benyamini. 1970b. Post irrigation movement of soil water: II. Simultaneous redistribution and evaporation. Water Resour. Res. 6(4):1148-1153.

Gupta, S.C., and W.E. Larson. 1(979.Estimating soil water retention characteristics ftom particle size distribution, organic matter content, and bulk density. Water Resour. Res. 15:1633-1635. McCuen, R.H., W.J. Rawls, and D.L. Brakensiek. 1981. Statistical analyses of the Brooks-Corey and the Green-Ampt parameters across soil textures. Water Resour. Res. 17:1005-1013. Rogowski, A.S. 1971. Watershed physics: Model of the soil moisture characteristic. Water Resour. Res. 7:1575-1582. Rawls, W.J., D.L. Brakensiek, and K.E. Saxton. 1982. Estimation of soil water properties. Trans. ASAE 25:1316-1320. Strait, S., K.E. Saxton, and R.I. Papendick. 1979. Pressure and hydraulic conductivity curves for various soil textures. Internal Re~ort. USDA-ARS, Washington State University, Pullman.

Williams, J., R.E. Prebble, W.T. Williams, and C.T. Hignett. 1983. The influence of texture, structure, and clay minerology on the soil moisture c~aracteristic. Aust. J. Soil Res. 21:15-32.

ET AL.: ESTIMATING

Estimating ,

Generalized

GENERALIZED

Soil-water

SOIL-WATER

CHARACTERISTICS

Characteristics

from ,

1031

Texture1

J

K.

(i: ,

E.

SAXTON,

W.

J.

RAWLS,

J.

S.

ABSTRACT

~ ,,

Soil-water

,

soil-water

potential content

all

and hydraulic

are needed

ROMBERGER,

conductivity

for many

plant

relationships

with

and soil-water

studies.

AND

inclusive

R.

textures.

I.

PAPENDICK2

Similarly,

equations

were

developed

for

un-

saturated hydraulic conductivities for all inclusive textures. While the developed equations only represent a statistical estimate and only

the

textural

influence,

they

provide

quite

useful

estimates

i;'

for

,},i 1

Measurement

of these

relationships

is costly,

difficult,

and

often

many

usual

soil-water

cases.

The

equations

provide

excellent

" ,

comI

impractical.

For

many

purposes,

general

estimates

based

on more

putational

efficiency

for model

applications

and the textures

can be

!

~;

\

,it,

readily

available

cent studies ture

and

between

information

such

have developed

selected

soil

selected

soil

as soil texture

statistical

potentials

correlations

using

textures

and

jective ematical of equations this study for was continuous to extend

are sufficient.

a large

hydraulic

between data

base,

conductivity.

Re-

soil texand

also

The

ob-

used

as calibration

characteristic compared

data with

parameters

where

are available.

several

field

Predicted

independent

or laboratory values

measurements

soil

"

water

I:'i

Ij Ii" i

were successfully of soil-water

po-

I

f

tential.

these estimates resultsover by broad providingranges math-of

.1ddltlonal

[ndex

~ords:

soll-,,:ater

potential,

hydraulIc

conduc-

! i!

soil from

texture,

water

t.he recent

potentials

for

multivariate

a wide analyses

I Contribution the College Washingto~

potentials, s.tatistical

from

and

hydraulic

analy~es

range

of soil

to provide Agric.

were textures,

continuous

conductivities. used then

these

potential

Res. Serv ., USDA,

of Agric. and Home State Univ., Pullman,

Economics, WA 99164.

Results

to calculate were

estimates

in cooperation

tlVlty, Saxton,

fit

by

Estimating

for

Sci. Soc. Am.

Received

10

June

K.E.,

W.J.

moisture Rawls,

generalized

equations. J.S. Romberger,

soil-water

~d.R.I.

charactenstlcs

Papendick. from

texture.

198~. SoIl

J. 50: 1031-1036.

with

Agric. Res. Center, Scientific Paper no. D

6911.

unsaturated

water

ELATIONSHIPS

OF

SOIL-WATER

POTENTIAL

and

hy-

1985.

," "

I

I

~

J

~

j

, "

j

[I' i .

"

(

I "'

"

I

"

",,",

'

,

f

;, !~~ ";il:, !;1 ,1 ~jii,i:;

SOIL

1032

SCI. SOC. AM.

Table 1. Summary of coefficients for linear regression Eq. [4) by Rawls et al. (1982).

10 20 33 60 100 200 400 700 1000 1500

0.4118 0.3121 0.2576 0.2065 0.0349 0.0281 0.0238 0.0216 0.0205 0.0260

-0.0030 -0.0024 -0.0020 -0.0016 0.0014 0.0011 0.0008 0.0006 0.0005

0.0023 0.0032 0.0036 0.0040 0.0055 0.0054 0.0052 0.0050 0.0049 0.0050

0.0317 0.0314 0.0299 0.0275 0.0251 0.0220 0.0190 0.0167 0.0154 0.0158

0.81 0.86 0.87 0.87 0.87 0.86 0.84 0.81 0.81 0.80

50, 1986

bution from particle size distribution, bulk density, and particle density. Then the pore radii are converted to equivalent soil-water tensions using the equation of capillarity at the corresponding volumetric water content. Gupta and Larson (1979) used multiple linear regression equations of the form ep = a (% sand) + b (% silt) + c (% clay) + d (% organic matter) + e (bulk density, Mg/m3) [3]

water stress. These investigations commonly require soil-water potential and hydraulic conductivity for the computations of soil-water storage or soil-water flow. Soil-water potential and hydraulic conductivity vary widely and nonlinearly with water content for different soil textures. Moreover, these relationships are relatively difficult and expensive to measure or are not feasible for short-term or remote investigations. Experience has shown that soil texture predominately determines the water-holding characteristics of most agricultural soils. Textural information is often either available or can be estimated by simple methods (Bouyoucos, 1951) and could readily serve as the principal input variable to a mathematical method for estimatihg soil-water characteristic relationships. For many numerical models, measured data at selected values are often used in tabular form with interpolation. Equational representation of these rela-

tionships over the necessary ranges of soil-water content and soil texture would greatly reduce input data requirements, computer storage space, and execution time of matheIJlatical models. It would be highly beneficial to have a computationally efficient method to estimate soil-water characteristics with reasonable accuracy from readily available inputs. The objective of this study was to develop such a procedure from results of previous statistical analyses of a large data base. SO IL- W A TER POTENTIAL The relationship between soil-water potential and water content has been describedin several ways. Brooks and Corey ( 1964) fitted the equation '¥ = '¥ ,,[(e -e,)/(es -e,)]B [ 1] to the soil-water potential curves where 'I1 is soil-water potential (kPa), 'I1" is soil-water potential at air entry (kPa), e is soil-water content (m3/m3), es is saturation soil-water content (m3/m3),e, is residual soil-water content (m3/m3),which is an empirical value to straighten curved data on a log-log scale, and B is a fitted value. Equation [ 1] can be simplified to the form \}! = A eB

J., VOL.

[2]

by setting er = O and A = \J!" e;B. This equational fonn has been supported by several recent studies (Campbell, 1974; Clapp and Homberger, 1978; Gardner et al., 1970a,b; Rogowski, 1971; Williams et al., 1983; McCuen et al., 1981). Arya and Paris (1981) presented a model to predict the soil-water tension curve from particle size distribution and bulk density data. Their model calculates a pore size distri-

to predict the soil-water content (8p! m3/m3) for 12 given soil-water potentials where a, b, c, d, and e are regression coefficients. Intermediate values could be linearly interpolated between the calculated points. Rawls et al. (1982) also reported a multiple linear regression analysis of soil-water content at 12 soil-water potentials with soil attributes using a very extensive data set (2541 soil horizons with a wide range of each correlated variable). They used three linear regression equations of which the simplest is ep = a + b (% sand) + c (% silt) + d (% clay) +e (% organic matter) + J(bulk

density, Mg/m3) [4]

where a, b, c, d, e, and f are regression coefficients and textures defined by the USDA system. The other two regression equations included: (i) the addition of 1500 kPa water retention to those variables ofEq. [4], and (ii) the addition of both 33 and 1500 kPa' water retention as correlated variables. Equations and coefficients containing the 33 and 1500 kPa moisture values were not further considered here since these data are often not readily available or obtainable. Only one or two of the three coefficients b, c, and d were simultaneously considered because of their dependency. Using step-wise regression, Rawls et al. (1982) correlated only the most statistically significant variables in Eq. [4]. These coefficients are summarized in Table 1 for selected measured potentials from 10 to 1500 kPa. Some coefficients are zero showing insignificant effects; for example, at potentials of 10 kPa and greater, bulk density did not effect water content, which is consistent with other literature (Borg, 1982). The equations have a small sensitivity to organic matter, as can be seenfrom the coefficients of Table I. A 1%increase in organic matter caused a 3.2 and 1.5%by volume increase in moisture content at 10 and 1500 kPa, respectively. Organic matter has a very small range (0-3%) for most agricultural soils. Soil texture, defined by the USDA system where sand = 2.0 to 0.05 mm, silt = 0.05 to 0.002 mm, and clay <0.002 mm, is the dominant factor in the soil-water potential-content relationship. Oay content is the most important texture factor as seen by the coefficients in Table I. Cosby et al. ( 1984) also clearly demonstrated that soil texture could be related to hydraulic characteristics when they applied regression and discriminant analysis to these and other data. The results ofEq. [4] with the coefficients of Table 1 represent a valuable summary of an extensive data set. For ready application to soil-water computations, however, these water content values at selected potentials must be interpolated over the whole of the useful moisture range in a nonlinear fashion. To be computationally efficient and accurate, equations are needed; thus we conducted the subsequent analysis. To select the equational forms, it is known that potential curves cannot be representedfrom saturation to wilting point by a straight line on log-log axesor any other first- or secondorder equation becauseof the double inflection in the curve. However, at potentials greater than about 10 kPa, a log-log equation provides a reasonable estimate. A linear relationship is a good approximation from 10 kPa to air entry potential. At air entry potential and less, the soil is essentially

~

SAXTON

ET AL.: ESTIMATING

GENERALIZED

SOIL-WATER

100~

CHARACTERISTICS

Table 2. Summary of derived soil-water characteristic equations. ~-Applied tension range, kPa > 1500 to 10

, ,

*

Sa

c

100.0 B = e + f (%C)" + 9 (%S)"- + 9 (%S)"(%C) 'l' = 10.0 -(9 -9,o)(10.0 -'l'e)I(9. -9,0) 9,0 = exp[(2.302 -In A)IB] 'l'e = 100.0 [m + n (9.)] 9. = h + j (%S) + k log,o (%C) 9 = 9. K = 2.778 x 10-. {exp[p + q (%S) + [r +

L

10 to'l'e

"0 c ca (/)

.."

L

,,

+

! c

,

L

!

" 'i 81

L

'l'e to 0.0 >1500 to 0.0

c

, I

"

Equation 'l' = A eB A = exp[a + b (%C) + c (%S)" + d (%S)"(%C)]

s. L !

I ' I. !

,

t (%S) + u (%C) + v (%C)"](119)]}

:\ I ,,

81 C L ,

Coefficients

:81 C',

10

20

30

40

I. Applicable

textural

70 80

50

Clay, Fig.

1033

region

100

%

{clear)

for the derived

equations.

at saturation moisture content and the water content changes very little; thus a constant water content value is reasonable. Therefore, the complete water potential-water content curve can be represented by three equations for the ranges of (i) saturation to air entry, constant; (ii) air entry to 10 kPa, linear; and (iii) 10 to 1500 kPa and greater, curvilinear by Eq. (2]. For the range > 10 kPa, we used Rawls' regression equations with an average organic matter content of 0.66% to generatemoisture content values e (m3/m3) for a systematic variation of textures for the 10 potentials \1!(kPa) shown in Table I. The soil texture triangle was divided into grids of 10% sand and 10% clay content increments. The 55 grid midpoints were used to generate the moisture contents for the 10 potential values from 10 to 1500 kPa. Of the 55 sets of values this produced, values were omitted for textures with >60% clay content, <5% sand, and <5% clay, because they exceededthe range of all but a few of the original data used in the stati~tical analyses by Rawls et al. ( 1982). The remaining 44 sets of values were correlated with Eq. (2] as the model. The 44 A and B coefficients were separately correlated with sand and clay (USDA classification) content using stepwise multiple nonlinear regression techniques. The resulting v

1500r

ro a. ~ ~ :;:; c 0) o a... 0) ro

.

= = = = = =

Iv

9 h j k m n

= = = = = =

-3.484 0.332 -7.251 0.1276 -0.108 0.341

x 10-. X 10-.

p q r t u v

= = = = = =

I'

12.012 -7.55 x 10-1 -3.8950 3.671 x 10-1 -0.1103 8.7546 x 10-.

Definitions

saturation,

9,0 = water content at 10 kPa, m./ma K = water conductivity, m/s (%S) = percent sand (e.g., 40.0) (%C) = percent clay (e.g., 30.0)

maIm"

equation for A (n = 44, R2 = 0.99) was A = exp [ -4.396 (% sand)2 -4.285

-0.0715

(% clay) -4.880

B = -3.140

X 10-4

,

X 10-5 (% sand)2

(% clay)] 100.0 and that representing B (n = 44, R2 = 0.99) was -0.00222

I~ , ,"I, i

[5]

(% clay)2 -3.484

:

': , It

X 10-5 (% sand)2 (% clay) .[6] The value of 100.0 was"included in Eq. [5] to convert from the original data units of bars to kilopascals. Thus, the potential-moisture content relationship of Eq. [2] for all potentials > 10 kPa can be estimated by soil texture with a Curve

200

-4.396 -0.0715 -4.880 x 10-. -4.285 x 10-. -3.140 -2.22 x 10-.

'l' = water potential, kPa 'l'e = water potential at air entry, kPa 9 = water content, m./ma 9. = water content at

a b c d e f

O c o 6 V O

% Sand

Texture

% Clay

loamy

sand

80

10

sandy

loam

65

15

45

15

loam silt clay clay

loam loam

20

15

35

35

25

45

900 . A

~

600

~"~'{ vi' ,1 ;

$:

.0 (/)

a b c d e f

0 300

0 0 0

Fig. 2. Comparison

10

20 30 40 50 60 Moisture Content, % Volume of results from the derived equations with those from correlations by Rawls et al. (1982).

II J

1034

SOIL SCI. SOC. AM. ]., VOL. 50, 1986 ii

1500

~

9

e!

Curve

Texture

-'

% Sand 20 8 10 35 20 40 60 65 82 92

1200

"' 0. ~ ""tU .-I C 0) O 0.

900

% Clay 60 45 35 35 15 18 28 10 6 5

I 600

300j

0

10

20

30

Moisture Fig. 3. Predicted potential

40

Content,

basis of the same 2500 samples correlated by Rawls et al. (1982). For potentials <10 kPa, we first correlated saturation moisture content and air entry tension to soil texture. Using the saturation moisture contents reported by numerous literature sources and summarized by Strait et al. (1979) for 10 soil texture classes,we obtained the following regression equation: E>s= 0.332 -7.251 X 10-4 (% sand)

texture (0-1500

kPa range).

saturation moisture content using reported air entry potential values for 10 texture classes reported by Rawls et al. (1982) resulting in 'I!" = 100.0 [ -0.108 + 0.341 (0..)] [8] where'!1" is air entry potential (kPa) (n = 10, R2 = 0.94). Having estimated es from soil texture data, '!I" from 8" and '!I at 10 kPa from Eq. [2], the 10 kPa to '!I" linear segment and '!I " to 0.0 kPa constant segment can be defined to complete the low tension portion of the potential-moisture relationship. Thus the complete characteristic curve may be estimated from soil texture data.

[7]

where es is moisture content at saturation (m3/m3), (n = 10, R2 = 0.99). Air entry tension was then correlated to

The combined equation set ([2], [5], [6], [7], and [8]) was tested over the range of the texture triangle to determine any

c

fQe

50 r-

60

% Volume

curves for soil class centroid

+ 0.1276 loglo (% clay)

50

Curve

Texture

% Sand

% Clay 60 45 35

401

35 15 18 28

~ Do ~ "tU :;: c: <1> 0 Do

10

30

6 5

201

10

0

10

20

30

Moisture

Content,

Fig. 4. Predicted potential

40

50

60

% Volume

curves for soil class centroid texture (0-50 kPa range).

~

SAXTON

ET AL.: ESTIMATING

0

1500r-

GENERALIZED

SOIL-WATER

1200

~ c:

900

Q) O 0.. ... Q) (0

1035

v Curve

(0 ~

CHARACfERISTICS

a b c d e

600

Texture

loamy sand sandy loam silt loam silty clay loam sandy clay loam

O o o A V

% Sand

% Clay

85 66 16 14 66

4 15 21 30 31

[J

J fli J,tt, ,':

:s:

0 (/)

300

~

0

f" i:{

6

0 0

10

20

30

40

50

et !'[ ~

60

,I

I ,

II,

Moisture Content. % Volume of predicted equations with independent measured data.

Fig. s. Comparison

The three curves, b, c, and d, in Fig. 2 show the sensitivity to change in sand content; while the three curves, d, e, and f, largely show the greater sensitivity to clay content. Figures 3 and 4 show predicted high and low ranges of potential curves for the centroid textures of soil classesusing the derived equation set as summarized in Table 2. Shifts of texture away from the centroid values but remaining within the texture classesof Fig. I show that significant potential changes can result even for soils with the same general textural classification. Independent sources of measured potential-soil-water content data with associated texture data (Arya et al., 1982;.. Williams et al., 1983; D. Miller, 1984, personal communication) were also used to verify Eq. [2], [5], and [6]. The comparisons shown in Fig. 5 illustrate that a generally good estimate was obtained using the derived equations. Some water potential measurement error, especially for the sandy clay loam soil, may well be present. The worth of the derived equation set is to approximate

areas of unreasonable result. At some low and high clay contents, the equations produced low potential moisture contents that exceededthe saturation moisture content. Figure I shows the region within the texture triangle for which the equations appear quite valid and is approximately defined as 5% ~ % sand ~ 30% with 8 ~ % clay ~ 58%, and 30% ~ % sand ~ 95% with 5% ~ % clay ~ 60% . Figure 2 shows some example comparisons of results from the equation set with those of Eq. [4], which was used to derive the equations. The degree of agreement is generally good over the wide range of soil textures. These examples show that a statistical comparison with the original data used to derive Eq. [4] would have produced a slightly reduced level of correlation than reported by Rawls et al. ( 1982), but the lack of uniform methods and textural definitions in these data made such an analysesof limited value. 102

~ 1,.c 1 E u >. .> :;: u ~ -0 c o U 'Q) "'

10. c

100

/ 1(

~,~.

~ ""

10-

Iii

10-2

I

, ", .

Rawls et al (1982) Curve Equation

10-3

10

Texture

~~~..

% Sand

%

Clay

"" 5 6

$:

10

.0 (/)

15

10-..

35 45

10-

0

10

50 60 20 30 40 Moisture Content, % Volume Fig. 6. Comparison of unsaturated hydraulic conductivity results from Eq. (10] with original curves from Rawls et al. (1982). (Multiply cm/ h by 2.778 X 10-6 to obtain m/s.)

1

1036

SOIL SCI. SOC. AM. J., VOL. 50, 1986

the full moisture range of the potential characteristic with minimal input data. While the derived relationships depend only on texture, other factors such as bulk density, structure, organic matter, clay type, and hysteresis may all have a secondary impact (Williams et al., 1983). Thus it is expected that the results from the derived equation set will only be an estimate, albeit a quite reasonable one, based on the large underlying data set. Should some field or laboratory data be available, it would be quite reasonable to moderately shift inputted textures (principally clay content due to its strong sensitivity) to cause appropriate matching. HYDRAULIC

CONDUCTMTY

Early models to predict soil-water conductivity were either empirical or theoretical relationships with soil particle size or porosity. These models were usually based on conductivity at saturation and not readily applied to unsaturated conditions. Later models related unsaturated conductivity to moisture content or potential such as Campbell (1974), who used a form of

K = a0b

[9]

where K is unsaturated conductivity (JD S-I), e is JDoisture content (JD3/JD3), b is a function of B in Eq. [2], and a is a function of saturation moisture content. These models usually require calibration using measured data, although Bloemen ( 1980) developed reasonable relationships using soil texture and pore size distribution index. Rawls et al. ( 1982) reported hydraulic conductivity curves for 10 texture classes that were averages of numerous reported curves. These hydraulic conductivity data did not correlate well with an equation of the form of Eq. [9]. Multiple nonlinear regression techniques were applied to these 10 curves using moisture content, percent sand, and percent clay as the independent variables. We derived the following equation for hydraulic conductivity using 230 selected data points ~niformly spaced on the 10 curves (n = 230, R2 = 0.95). K = 2.778 X 10-6 {exp [12.012 -0.0755 (% sand) + [ -3.8950

+ 0.03671 (% sand) -0.1103

+ 8.7546 X 10-4 (% clay)2] (I/0)]}

(% clay) .[10]

Equation [10] was found to provide quite reasonable values over at least the same textural range as those for water potential. Figure 6 shows hydraulic conductivity curves calculated using Eq. [10] for the centroid class textures and the curves (in the original units) from which the data were obtained (Rawls et al., 1982). For the extreme condition of near saturation or very dry and very high clay contents, the calculated values do not match reported values as well as desired; however, it is a good fit for a single equation over a large range of commonly encountered textures. Some adjustments may be appropriate for near saturation values for high clay content soils. Just as for potentials, other soil attributes than texture could well causesome deviations from the estimates by Eq. [ 10]. CONCLUSIONS This study examined previous methods for estimating the relationships of soil-water content to potential and hydraulic conductivity. Using the results of previous broad-based correlations, equations were derived to estimate continuous relationshps of soilwater moisture content to potentials and hydraulic conductivity from soil textures. The potential re1a-

tionship is continuous and nonlinear from 10 to 1500 kPa, linear from 10 kPa to air entry potential, and a constant water content below air entry potential. The hydraulic conductivity relationship is continuous and nonlinear from saturation moisture content to near air dry. A complete summary of the derived equations and coefficients is provided in Table 2. The equations are valid for a wide range of textures. They are computationally efficient to allow easy use with a digital computer and they provide reasonably accurate estimates of the unsaturated potentials and hydraulic conductivities with a minimum of readily available data. Comparisons with independent measured soil-water characteristic curves verified these results. Textural ranges within generally defined texture classescan cause significant changesof potentials and hydraulic conductivities. The estimated curves should be adjusted for effects of organic matter, clay type, density, structure, etc., to represent measured values or hysteresis by slight adjustments of the texture (clay primarily) when these secondary effects can be defined. REFERENCES Arya, L.M., and J.F. Paris. 1,981.A physioempirical model to predict the soil moisture characteristic ftom particle-size distribution and bulk density data. Soil Sci. Soc. Am. J. 45: 1023-1030. Arya, L.M., J.C. Richter, and S.A. Davidson. 1982. A comparison of soil moisture characteristics predicted by the Arya-Paris model with laboratory-measured data. Report no. SM-t2-04247; JSC17820. National Aeronotics and Space Administration, Lyndon B. Johnson Space Center, Houston, TX. Borg, H. 1982. Estimating soil hydraulic properties ftom textural data. Ph.D. thesis. Washington State Univ., Pullman (Diss. Abstr. 83-03292). Bouyoucos. G.J. 1951. A recalibration of the hydrometer method for making mechanical analysis of soil. Agron. J. 43:434-438. Bloemen, G. W. 1980. Calculation of hydraulic conductivities of soils ftom texture and organic matter content. Z. Pflanzenernaehr. Bodenkd. 143:581-605. Brooks, R.H., and A. T. Corey. 1964. Hydraulic properties of porous media. Hydrology Paper no.3. Colorado State University, Fort Collins. Campbell, G.S. 1974.A simple method for determining unsaturated conductivity ftom moisture retention data. Soil Sci. 117:311-314. Clapp, R.B., and G.M. Hornberger. 1978. Empirical equations for some soil hydraulic properties. Water Resour. Res. 14:601-604. Cosby, B.J., G.M. Hornberger, R.B. Clapp, and T.R. Ginn. 1984. A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils. Water Resour. Res. 20:682-690. Gardner, W.R., D. Hillel, and Y. Benyamini. 1970a. Post irrigation movement of soil water: I. Redistribution. Water Resour. Res. 6:851-861. Gardner, W.R., D. Hillel, and Y. Benyamini. 1970b. Post irrigation movement of soil water: II. Simultaneous redistribution and evaporation. Water Resour. Res. 6(4):1148-1153.

Gupta, S.C., and W.E. Larson. 1(979.Estimating soil water retention characteristics ftom particle size distribution, organic matter content, and bulk density. Water Resour. Res. 15:1633-1635. McCuen, R.H., W.J. Rawls, and D.L. Brakensiek. 1981. Statistical analyses of the Brooks-Corey and the Green-Ampt parameters across soil textures. Water Resour. Res. 17:1005-1013. Rogowski, A.S. 1971. Watershed physics: Model of the soil moisture characteristic. Water Resour. Res. 7:1575-1582. Rawls, W.J., D.L. Brakensiek, and K.E. Saxton. 1982. Estimation of soil water properties. Trans. ASAE 25:1316-1320. Strait, S., K.E. Saxton, and R.I. Papendick. 1979. Pressure and hydraulic conductivity curves for various soil textures. Internal Re~ort. USDA-ARS, Washington State University, Pullman.

Williams, J., R.E. Prebble, W.T. Williams, and C.T. Hignett. 1983. The influence of texture, structure, and clay minerology on the soil moisture c~aracteristic. Aust. J. Soil Res. 21:15-32.

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