influence of hysteresis on moisture flow in an undisturbed soil monolith1

5
Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith 1 F. BEESE AND R. R. VAN DER PLOEG Z ABSTRACT still 'not clear how the hysteresis phenomenon of the soil ~. . . . . .. . . . ., .... . , moisture characteristic should be handled in soil water The moisture dynamics of an undisturbed soil monolith were stud- . . TT . ... , ,, , ,. ied during a lysimeter experiment. Daily measurements were made of models. Usually hysteresis is Ignored, although Rubin the soil suction at 10 depths. Also daily measured were the precipita- (1967) and Giesel et al. (1973) among others have shown tion, the seepage, and the evaporation from the monolith during a 3- that with enough experimental data on hysteresis properly year period. For selected periods, a drying (desorption) curve and a functioning soil moisture models can be developed without wetting (sorption) curve of the soil moisture characteristic were deter- a full insight into the hysteresis phenomenon. Poulovassilis mined from field data. Also the capillary conductivity was determined (1962) proposed an explanation and a mathematical descrip- with use of daily monolith observations. With use of these hydraulic tion of hysteresis, but Topp (1969) and Vachaud and Thony functions, the unsaturated soil moisture flow equation was solved (1971) questioned the adequateness of the independent do- numerically for one-dimensional vertical flow. In order to determine main ± Q{ Pou i ovassilis . Recently Royer and Vachaud the effect of hysteresis on the suction distribution m the monolith, ? and WatSQn ^ ^ 9? ^^ ^ h ^ ^ calculations were performed either with the desorption curve or with . , , , - . . , . ,-.u the sorption curve without scanningbetween these curves. Neither of to ° ™portant to be neglected in models that deal with unsat- the two curves leads to complete agreement between observed and urated moisture flow under field conditions. Although Pou- calculated soil suction values; the desorption curve usually gives too lovassilis (1973) and Mualem and Dagan (1975) have modi- high values, the sorption curve too low values. fied the independent domain theory of hysteresis, it still has to be shown, especially for conditions in the field, if this Additional Index Words: unsaturated moisture flow, lysimeter, nu- modified theory is adequate. merical methods, simulation, hydraulic functions. In the present work, no attempt is made to model the ———————————————— moisture distribution in the soil with use of scanning be- tween sorption and desorption parts of the soil moisture A LTHOUGH IT has been shown that the unsaturated soil chara cteristic. Instead either an apparent boundary sorption /•\ moisture flow equation can be used successfully to curve or a desorption curve of the moisture characteristic describe moisture dynamics in ideal porous media under controlled laboratory conditions, its usefullness under field ————— conditions is Still questioned. In addition to the difficulties 'Contribution from the Inst. of Soil Science and Forest Nutrition, Georg- , . • • , ^ t_ j ,- -,i- ^ /•! August Univ., 2 Bueseenweg, 34 Goettingen, West Germany. Received in determining the appropriate hydraulic soil functions (soil 10 fj ov )975 Appr0 ve d 26 March 1976. moisture characteristic and the capillary conductivity), it is 2 Research Soil Scientists.

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Page 1: Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith1

Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith1

F. BEESE AND R. R. VAN DER PLOEGZ

ABSTRACT still 'not clear how the hysteresis phenomenon of the soil~. . . . . „ .. . . . ., .... . , moisture characteristic should be handled in soil waterThe moisture dynamics of an undisturbed soil monolith were stud- . . TT „ . ... , ,, , „ ,.

ied during a lysimeter experiment. Daily measurements were made of models. Usually hysteresis is Ignored, although Rubinthe soil suction at 10 depths. Also daily measured were the precipita- (1967) and Giesel et al. (1973) among others have showntion, the seepage, and the evaporation from the monolith during a 3- that with enough experimental data on hysteresis properlyyear period. For selected periods, a drying (desorption) curve and a functioning soil moisture models can be developed withoutwetting (sorption) curve of the soil moisture characteristic were deter- a full insight into the hysteresis phenomenon. Poulovassilismined from field data. Also the capillary conductivity was determined (1962) proposed an explanation and a mathematical descrip-with use of daily monolith observations. With use of these hydraulic tion of hysteresis, but Topp (1969) and Vachaud and Thonyfunctions, the unsaturated soil moisture flow equation was solved (1971) questioned the adequateness of the independent do-numerically for one-dimensional vertical flow. In order to determine main ± Q{ Pouiovassilis. Recently Royer and Vachaudthe effect of hysteresis on the suction distribution m the monolith, ? and WatSQn ^ 9? ^^ h ^ ^calculations were performed either with the desorption curve or with . , , , - . . , . , - . uthe sorption curve without scanning between these curves. Neither of to° ™portant to be neglected in models that deal with unsat-the two curves leads to complete agreement between observed and urated moisture flow under field conditions. Although Pou-calculated soil suction values; the desorption curve usually gives too lovassilis (1973) and Mualem and Dagan (1975) have modi-high values, the sorption curve too low values. fied the independent domain theory of hysteresis, it still has

to be shown, especially for conditions in the field, if thisAdditional Index Words: unsaturated moisture flow, lysimeter, nu- modified theory is adequate.

merical methods, simulation, hydraulic functions. In the present work, no attempt is made to model the———————————————— moisture distribution in the soil with use of scanning be-

tween sorption and desorption parts of the soil moistureA LTHOUGH IT has been shown that the unsaturated soil characteristic. Instead either an apparent boundary sorption

/•\ moisture flow equation can be used successfully to curve or a desorption curve of the moisture characteristicdescribe moisture dynamics in ideal porous media undercontrolled laboratory conditions, its usefullness under field —————conditions is Still questioned. In addition to the difficulties 'Contribution from the Inst. of Soil Science and Forest Nutrition, Georg-

, . • • , • ^ t_ j ,- - , i - ^ / • ! August Univ., 2 Bueseenweg, 34 Goettingen, West Germany. Receivedin determining the appropriate hydraulic soil functions (soil 10fjov )975 Appr0ved 26 March 1976.moisture characteristic and the capillary conductivity), it is 2Research Soil Scientists.

Page 2: Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith1

BEESE & VAN DER PLOEG: INFLUENCE OF HYSTERESIS ON MOISTURE FLOW 481

SOIL SUCTION (cm of wa te r )200 300 AOO 500 600 700

A U G U S T

40-

80-

' 120

160

200Fig. 1—Soil suction profiles between 5 Aug. and 29 Aug. 1973 in a

loess monolith during a drying (desorption) period.

was used to describe infiltration and redistribution of thesoil water. The purpose of the study was to determine theerror one makes if no scanning is done between sorption anddesorption curves. The agreement or disagreement betweencalculated and measured soil suction values in the monolithis used as error criterium. Since no independent soil mois-ture determinations were made, a check between the theo-retical and experimental moisture content in the soil profileis not possible.

MATERIALS AND METHODSA grey brown podzolic soil (Hapludic Eutroboralf) was used in

the experiment. A cylindrical monolith, 2 m in length and 40 cm indiameter, was isolated from the surrounding soil, and covered onthe sides with a tight polyester-glass fiber coating. The monolithwas placed on a ceramic plate, so that suction could be applied atthe bottom. The monolith was then transported to the lysimeterstation of the Institut fuer Bodenkunde, Georg-August University,Goettingen, and placed on an electromechanical balance, in such away that the surface of the monolith was at the same level as thesurrounding soil. In this way the monolith was left exposed to theprevailing weather conditions. Details on the preparation of themonolith and on the electromechanical balance may be found inHomeyer et al. (1973 a, 1973 b).

In the monolith duplicate tensiometers were horizontally in-stalled at the 10-, 20-, 40-, 60-, 80-, 100-, 120-, 140-, 160-, and180-cm depths. The surface of the monolith was kept bare. Thetensiometers were read once a day. Also the precipitation, the totalevaporation and the seepage at the bottom of the monolith were de-termined on a daily basis. Measurements were taken over a periodof 3 years.

The hydraulic functions of the monolith soil were determined intwo different ways. In the laboratory with undisturbed soil samplesthat were taken immediately adjacent to the location from wherethe monolith was isolated, a soil moisture characteristic (pF-curve), and a conductivity curve were determined for differentdepths according to standard procedures (pressure-plate methodand double-membrane method, respectively). In the field, on themonolith, these same functions were determined with in situmethods. The pF-curves were determined according to an ex-tended version of the method as proposed by Wind (1966), and thecapillary conductivity was determined according to Richards, etal. (1956).

For the field-determination of the hydraulic functions, two rela-tively short periods out of the three-year observation period werechosen: the period 5 Aug.-20 Oct. 1973, and the period 20Mar.-24 Apr. 1974. In the first period, the month of August waswarm and dry; from 5 Aug. through 29 Aug. no rain occurred, andthe average potential evaporation over this period (measured witha Piche evaporimeter) was 4.48 mm/day. The actual evaporation

SOIL SUCTION (cm of water )100 200 300 490 590 600 TOO

40-

80-

160'

200

Fig. 2—Soil suction profiles between 29 Aug. and 20 Oct. 1973 in theloess monolith during rewetting (sorption).

of the monolith over this period was 2.07 mm/day (determinedover the balance). During this period the measured soil suctionvalues were the highest of those taken during the 3-year observa-tion period. It was assumed that the relation between the soil suc-tion and the conductivity is free of hysteresis.

The soil suction profile as a function of time for the period inAugust 1973 is shown in Fig. 1. It may be observed that duringthis period there was a water divide in the profile at the 120-cmdepth. The location of the divide coincides with a physical discon-tinuity in the profile. Above the divide water moved upward,below the divide it flowed downward. The total amount of seep-age, measured with the suction plate, was 1.65 mm.

Figure 2 shows the suction profiles as the soil became rewettedduring the period 29 Aug.-20 Oct. 1973. Only a few soil suctionprofiles are shown. The amount of seepage measured over thisperiod was 5.49 mm, the total precipitation was 148.3 mm and theaverage actual evaporation was 0.98 mm/day.

In 1974, from 20 Mar. through 24 Apr., another dry period oc-curred. Precipitation (6 mm on 29 Mar.) occurred only once. Thepotential evaporation during this period was in average 3.01mm/day, the actual average evaporation was 1.35 mm/day.

With use of the data collected over these two periods, correctedpF-curves were constructed according to an extension of the itera-tive curve fitting scheme proposed by Wind (1966). The curve fit-ting is done in such a way that the sum of the sectional moisturechanges in the monolith per day, calculated by means of the dailytensiometer readings and auxiliary pF-curves, agrees with the ac-tually measured total daily moisture change. It is necessary that theabsolute amount of moisture in the soil column is known at one in-stant. In our experiment the absolute amount of water in the col-umn was never known, and the balance registered only relativechanges. In order to work with Wind's method it was for conve-nience assumed that during the highest degree of dryness in thecolumn hysteresis could be neglected. With use of the laboratorydetermined pF-curve, and field-determined soil suctions it wasthen possible to calculate the absolute amount of moisture in thecolumn of 29 Aug. The laboratory pF-curve is the first auxiliarypF-curve, and the iteration is continued until acceptable agreementbetween the calculated and the measured water content is reached.For the soil under study the procedure was stopped after the fourthiteration. In Fig. 3 a comparison is made between cumulativecalculated evaporation and measured evaporation for the 1973 andthe 1974 periods mentioned before. The numbers along the curvesdenote the total amount of evaporation at the end of the observa-tion periods. One can see that the calculated evaporation is almostidentical with the measured one. The potential evaporation asmeasured with a Piche evaporimeter is also shown in Fig. 3.

After the agreement between calculated and measured evapora-tion was attained, it was assumed that the pF-curves were correct.These corrected pF-curves for the various depths of the monolithwere then used in accordance with a method as proposed by Rich-ards et al. (1956) for determination of the capillary conductivity.

Page 3: Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith1

482 SOIL sci. soc: AM. ;., VOL. 40, 1976

100

rroQ.<

UJ! 50 i

/107.43 /105.42

——— LYSIMETER VALUES /——— VAILUES FROM CORRECTED /

PF-OJRVES / '- EVAPORIMER /

DEPTH : 50-70 cm

TOi 20fl!ME (days )

30

Fig. 3—Comparison between: cumulative evaporation as determinedby weighing of the monolith, and by calculation from the moisturecharacteristics with use of tensiometer values.

TOO-DEPTH : 10-30cm

. LABORATORY•DESORPTION CURVE

(1973); SORPTION.DESORPTION CURVE

IN 1974 BEFORE6mm OF RAIN

DESORPTIONCURVE IN 19*

AFTER 6mmOF RAIN

.01

s:u

.001

28 32 36 40VOL. MOISTURE CONTENT

___.LABORATORYo———> LYSIMETER

100 1000SOIL SUCTION (cm of water)

Fig. 4—Laboratory and field determined hydraulic functions of the10- to 30-cm soil layer: (left) the soil moisture characteristic, and(right) the capillary conductivity.

The hydraulic functions were then used to solve the unsaturatedsoil moisture flow equation numerically according to a methoddescribed by van der Ploeg (1974). The equation was solved twice;once with a corrected desorption pF-curve, and once with a cor-rected sorption pF-curve. As a boundary condition at the soil sur-face, daily measured precipitation and evaporation values wereused. At the lower end of the flow region (= 120 cm depth at thewater divide) a no-flux condition was applied. A measured soilsuction profile was used as the initial condition.

RESULTS AND DISCUSSIONFigure 4 shows the soil moisture characteristic and capil-

lary conductivity data of the monolith soil between the 10-and 30-cm depth. Shown in the figure are the laboratory-determined desorption curve, which was determined aftercomplete saturation of a soil sample, and some field-determined curves. The field determined (corrected) curveswere constructed from data collected between 5 Aug. and29 Aug. 1973 (a desorption curve), and from data collectedbetween 20 Mar. and 24 Apr. 1974. This last period also

o*300oe.'200

o-

5?,100

aT3

.01

>•a:<

34' 38 42 w

VOL. MOISTURECONTENT (cm3/cm 3)

c.001

10 100 1000SOIL SUCTION (cm of water)

Fig. 5—Laboratory and field determined hydraulic functions of the50- to 70-cm soil layer: (left) the soil moisture characteristic, and(right) the capillary conductivity.

caused a continuous drying of the monolith soil. However,on 29 March a rain storm caused 6 mm of precipitation. Thesorption curve was determined from data collected between29 Aug. and 20 Oct. 1973 when the soil was (although withinterruptions) rewetted. It was assumed that on 29 August1973 the soil did not exhibit hysteresis. As mentionedbefore, the highest soil suction values during the three yearsof observations were measured on 29 Aug. 1973. As can beseen from the figure, the largest difference in moisture con-tent at the same suction occurs at about 300 cm of suction.

Also shown in Fig. 4 is the capillary conductivity of the10- to 30-cm layer as a function of the soil suction. It can beseen that the laboratory-determined curve lies well belowthe field determined function.

In Fig. 5 the same functions as in Fig. 4 are shown for thedepth of 50-70 cm. The observed hysteresis effects at thisdepth are far less evident than in the shallower depth of theprevious figure. Here also the capillary conductivity as de-termined in the laboratory and in the field shows differentresults. A reason for the deviation between conductivityvalues obtained in different ways may be the hard-to-evaluate soil-membrane resistance to moisture flow of thelaboratory method. The same effect may be thought respon-sible for deviations in the moisture characteristic.

In the model calculations, six sets of field-determinedhydraulic functions of the kind shown in Fig. 4 and 5 wereused for the depths 10-30 cm, 30-50, 50-70, 70-90,90-110, and 110-120 cm. As was also found by Ehlersand van der Ploeg (1976), the laboratory determined func-tions provided unsatisfactory results. For the 3-year periodof study it was assumed that the corrected sorption anddesorption curves could be considered as boundary curves.It is likely however, that under more extreme meteo-rological conditions different curves would have beenfound. This is especially true for the sorption curves, sincethe suction range under study (700 cm of water was themaximum observed) only forms a small part of the possiblerange.

In Fig. 6, 7, and 8 some modeling results will be shown.Soil moisture behavior was simulated for a period of 76days (5 Aug. - 20 Oct. 1973) in order to see if the hydraulic

Page 4: Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith1

BEESE & VAN DER PLOEG: INFLUENCE OF HYSTERESIS ON MOISTURE FLOW 483

EVAPORATION RATE ( m m / d a y ) 5 . EVAPORATION RATE ( m m / d a y )

^^—————^ .-nrV^-^-^W-^-. 0 ^—————--- --nn-^..^————.J-JUn^^,° RAIN INTENSITY n n . ,n RAIN INTENSITY n* (^/dcy) p , _ _ ll _nrJ]JJ]/1 ' JnMlday) ^ _ f]^ _p j

S600 ^ —— MEASURED VALUES T^' —— f™™™^- /\ - CALCULATED - —— CALCULATED°500 J I————-J "" (DESORPTION CURVE) i400' (DESORPTION CURVE° / I /-^A ---CALCULATED * ^XSITI k ~"~~ CALCULATED

g400 / ^ "" I (SORPTION CURVE) £,300' ^X^^*"^\ (SORPTION CURVE )

z300 / k/^ §200 y^ \\O / '• \ ^ <*^ ''S-- * V-v

§2°° M ,, 3100 D E P T H : 60cm X^t\"> DEPTH : 20cm W'/ s, o ~\A,- 10° V / V=> 0 .R \A ' ' " ° ^ ^ ^ ^ ^ ^° ^0 ____,____,____,____,_____,____,____,____,__ T I M E (days)

0 10 20 30 «0 50 60 70 80 Fjg 7_calculated and measured soil suction values for the period 5T I M E ( d a y s ) Aug _20 Oct 1973 for a soU depth of 60 cm.

Fig. 6—Calculated and measured soil suction values for the period 5Aug.-20 Oct. 1973 for a soil depth of 20 cm.

. , . j . j c EVAPORATION RATE ( m m / d a y )functions, determined in the way as just described, can 5-,indeed be used for modeling purposes. In the figures the ^-%i—^_^^ ^^r-iILn.^^.-^calculated soil suction values for a particular depth are com- °" —RAIN iNTENSifY"'^^^1^"'^"'^" ————T^——pared with the measured values of the 76-day period. 10" ( m m / d a y ) n f i n d n f l r m

,-,. ^ , . . ' r i / i r * i ^ i - T n i-a__________IL^ ^____II p-JU^jn ^IIHI J IH I___Figure 6 shows this comparison for the 20-cm depth. In u ~ ——————— ——— — — ——the upper part of Fig. 6, and also in Fig. 7, and 8, the daily ^oo- ~ cSl^EoTDE^ORPTiON CURVE)precipitation and evaporation rates are also shown. Q- - _ • (SORPTION C U R V E !

In Fig. 7 the same comparison as in Fig. 6 is made for the £ * 20°" ^^_--sss ss:s^SS5'E! rr!:*5 --N60-cm depth. Finally, in Fig. 8 results for the 100-cm depth ^ o ^^^^'^^^^^^ ^~~" ^]are depicted st™"' D E P T H : 100 cm VU

From Fig. 6-8 can be seen that the calculated soil suction "> - Q _^___ *values are in reasonable agreement with measured values. o 10 20 30 AO 50 60 70 80For this particular soil, and under the prevailing field condi- TIME (days)tions, not much difference in calculated soil suction values Fig. 8—Calculated and measured soil suction values for the period 5is obtained if either the boundary-drying curve or the boun- Aug.-20 Oct. 1973 for a soil depth of 100 cm.dary-wetting curve of the soil moisture characteristic isused. Often, the measured suction values lie in between val- cury bm which lacks h justificati apparentlyues calculated with the boundary curves, t is likely that a ided useful ^ ^ t

Jho method7as use^

better agreement between measured and calculated soil sue- R and Vachaud Qr ^atson ^tion values would have been obtained, if a scanning proce- • ,, , t , . • ,j . •, • .,, , ,, , , - i • , • might be expected to yield more accurate soil suction-soildure between t h e boundary curves during t h e simulation ; , . . A » U J » r»u L J ^ O.,, , ... J,.,r. , „,. /,r,-,Cx water relations. Another advantage of the methods of Royerwould have been applied as did Dane and Wierenga( 1975), . w , ,j,-im«\ ^ r\\r* t i / imc\ • .u . IuT j nr > ^imc\ T c- ^ - u u . .u and Vachaud (1975) and or Watson et al. (1975) is that theor Lees and Watson (1975). In Fig 6 it can be seen, that the ±eOKtic&ll derived moisture distribution through the pro-measured soil suction values fall below both calculated ones file can b/checked experimentally.at the start or a precipitation period. A reason for this mightbe that the boundary wetting curves used, are only apparent ACKNOWI FDPMFNTones. The real boundary wetting curves may lie more to theleft Of the ones shown in Fig. 4 and 5. But since the weather I,The authors want to express their thanks to Prof. Dr. Brunk Meyer,

... 6. . Director of the Institut fuer Bodenkunde in Goettmgen, for his valuable ad-condltions over the Observation penod of 3 years were not vice during the course of the experiment. The Institut fuer Medizinischeextreme enough, the actual boundary-wetting curves for the Datenverarbeitung in Goettingen is acknowledged for letting us use itsvarious depths were not observed. Another reason might be IBM 370/148 comPuter-that part of the infiltrating rain water flows through theupper part of the soil profile as noncapillary water, a featurealso discussed by Ehlers and van der Ploeg (1976).

To save space, only results for three different depths inthe monolith are shown. It appears, also from figures thatare not shown, that the unsaturated moisture flow equationmay be used under field conditions, if the needed hydraulicfunction are determinated in the proper way. The empiricalapproach which was followed for determining the pF-

Page 5: Influence of Hysteresis on Moisture Flow in an Undisturbed Soil Monolith1

484 SOIL sci. soc. AM. j., VOL. 40, 1976