Field
quantification
of
wetting–drying
cycles
to
predict
temporal
changes
of
soil
pore
size
distribution
G.
Bodner
*
,
P.
Scholl,
H.-P.
Kaul
DepartmentofCropSciences,DivisionofAgronomy,UniversityofNaturalResourcesandLifeSciences,BOKUVienna,GregorMendelStraße33,A-1190Vienna,Austria
1. Introduction
Hydraulic properties of the soil depend on texture and structure.Inthesaturatedandnear-saturatedrangesoilstructure essentiallycontrolsthetwofundamentalrelationsforwaterflow, i.e.theretentionandhydraulicconductivityfunctions(Cresswell etal.,1992).Soilstructuralporosityisahighlydynamicproperty that respondstovarious external factorsof environmental and human nature. Therefore knowledge of spatial and temporal variabilityofsoilhydraulicpropertiesisfundamentaltoaccurately
describeprocesseslikewaterinfiltrationandstorage(vanEsetal.,
1999).
In a tillage experiment, Schwen et al. (2011) showed that seasonalvariabilityofhydraulicpropertieswashigherthantillage induced variability. Bodner et al. (2008) studied the effect of different cover crop canopy and residue coverageon hydraulic propertiesandfoundsignificantoverwinterdecreaseinhydraulic conductivityandflowweightedporeradiusforalltreatments.The effect was more pronounced in bare soil. Also, irrigation can introduce strong temporal changes of hydraulic properties dependingonsoiltype andirrigationmethod(Angulo-Jaramillo
etal.,1997;Zengetal.,2013).
The role of environmental influences on soil structure formation wasreviewedbyHorn andSmucker(2005).Inarid, semi-aridandsubhumidregionswetting–drying(WD)cyclesare essentialforsoilaggregation(DalalandBridge,1996).Intensity, number and duration of swelling and shrinkage cycles were identifiedaskeyprocessesofaggregateformationandstrength. Capillaritywasthedrivingfactorofsoilaggregationupondrying, whilerewettingincreasedstructuralinstability(Pengetal.,2007;
Ladoetal.,2004).
ARTICLE INFO
Articlehistory:
Received15February2013 Receivedinrevisedform25April2013 Accepted7May2013
Keywords:
Wetting–dryingcycles Soilporesizedistribution Spectralanalysis Temporalvariability Tensioninfiltrometer
ABSTRACT
Wetting–drying(WD)cyclessubstantiallyinfluencestructurerelatedsoilpropertiesandprocesses. MoststudiesonWDeffectsarebasedoncontrolledcyclesunderlaboratoryconditions.Ourobjective wasthequantificationofWDcyclesfromfieldwatercontentmeasurementsandtheanalysisoftheir relationtothetemporaldriftinthesoilporesizedistribution.Parameters oftheKosugihydraulic propertymodel(rm,Kosugi,sKosugi)werederivedbyinverse optimization fromtensioninfiltrometer
measurements.SpectralanalysiswasusedtocalculateWDcycleintensity,numberanddurationfrom watercontenttimeseries.WDcycleintensitywasthebestpredictor(r2=0.53–0.57)forthetemporal
driftinmedianporeradius(rm,Kosugi)andporeradiusstandarddeviation(sKosugi).Atlowersoilmoisture
conditionstheeffectofcycleintensitywasreduced.AbivariateregressionmodelwasderivedwithWD intensityandameteorological indicatorfordryingperiods(ET0,climaticwaterbalancedeficit) as
predictorvariables. This model showed that WDenhanced macroporosity (higherrm,Kosugi) while
decreasingporeheterogeneity(lowersKosugi).AdryingperiodwithhighcumulativevaluesofET0ora
strongclimaticwaterbalancedeficitonthecontraryreducedrm,KosugiwhileslightlyincreasingsKosugi
duetohigherfrequencyatsmallporeradiusclasses.Thetwoparameterregressionmodelwasappliedto predictthetimecourseofsoilporesizedistributionparameters.Theobservedsystemdynamicswas capturedsubstantiallybetterbythecalculatedvaluescomparedtoastaticrepresentationwithaveraged hydraulic parameters. The study showed that spectral analysis is an adequate approach for the quantificationoffieldWDpatternandthatWDintensityisakeyfactorforthetemporaldynamicsofthe soilporesizedistribution.
ß2013TheAuthors.PublishedbyElsevierB.V.
Abbreviations:WD,wetting–drying;PSD,poresizedistribution;f,totalporosity; us, water content atsaturation; ur, residual watercontent;hm,Kosugi, median pressurehead;rm,Kosugi,medianporeradius;sKosugi,poreradiusstandarddeviation.
*Correspondingauthor.Tel.:+431476543331;fax:+431476543342. E-mailaddress:[email protected](G.Bodner).
ContentslistsavailableatSciVerseScienceDirect
Soil
&
Tillage
Research
j o urn a l hom e pa g e :ww w . e l se v i e r. c om / l oca t e / st i l l
0167-1987ß2013TheAuthors.PublishedbyElsevierB.V.
http://dx.doi.org/10.1016/j.still.2013.05.006
Open access under CC BY-NC-ND license.
SoilporositywasfoundtoincreaseaftertheapplicationofWD cycles(Piresetal.,2005).Piresetal.(2009)observedanevolution frommassivestructurestostructureswithagreatnumberoflarge and connected pores after WD cycles. Also the pore size distribution(PSD) is modified in response to internal capillary stresses.Sartorietal.(1985)andPagliaietal.(1987)discussedthe overallinfluenceofWDcyclesontotalporosity,poreshapeand poresizedistribution.Theirresultsdemonstrateanincreaseinthe volume of pores in the range of 30
m
m to 1mm and strong modificationsinshapeandsizedistribution.Anincreaseincoarseporesduringdryingwasdescribedasa consequenceofcrackandmicrocrackformation(BruandandProst,
1987;Hornetal.,2002;SeguelandHorn,2006).Piresetal.(2005)
alsofoundanincreaseinthenumberofmicroporesandmesopores with subsequent WD cycles. Sarmah et al. (1996) however observeda decreasein water infiltration rateafter WD cycles. Thiswasprobablyduetotheslakingandcollapseofaggregates.
Also Phogat and Aylmore (1989) found a decrease in
macro-porosity after cycles of soil wetting and subsequent drying. Macroporesaregenerallymoresensitivetosoildeformationthan microporesbecauseoflowerporerigidity(Kutı´leketal.,2006). However,Braudeauetal.(2004)suggestedthatshrinkagecapacity ofmacropores can alsobe less thanthat of micropores due to smallercapillarystressesinlargepores.
Pengetal.(2007)conductedadetailedlaboratorystudyonpore
changesundervaryingWDcycleintensityand number.Intense WDcyclesenhancedthevolumeoflargeporesmarkedlyinmost soils they analyzed. Their data also suggested higher pore heterogeneity with increasing cycle number. However, if soils weresubjectedtointenseWD cycles,thefrequency dependent effectfaded.Severalauthorsshowedthattheimpactofthefirst WD cycle on soil structure is greatest and decreases with subsequentcycles(Basmaetal.,1996;Tripathyetal.,2002;Leij etal.,2002).Theeffecthoweveralsodependsontheinitialstateof soil(pre-shrinkagestress;BaumgartlandHorn,1999).
MostquantitativeknowledgeonWDeffectsonsoilproperties hasbeenobtainedfromlaboratoryexperimentwithsoilsamples subjecttocontrolledcycles.Butalsoinfieldexperimentsseveral authorsreferredtoWDasmajorinfluenceonhydraulicproperty andsoilstructurechanges (e.g.Mapaet al.,1986;Pagliaietal.,
2004;Mubaraketal.,2009).Amaingapinourcurrentknowledge
istounderstand how irregularcyclestypicallyoccurring under fieldconditionsmodifyhydraulicproperties.Aquantificationof the natural WD pattern in field experiments would be highly necessaryinordertobetterunderstandtheirroleasadriverfor hydraulicpropertyand soilstructuredynamicsina naturalsoil environment.Thiscouldhelptobridgeprocessbased understand-ingfromlaboratoryworkandqualitativefieldobservations.
Theobjectiveofourstudythereforewastodevelopamethodto quantifytheWDpatternfromfieldsoilwatercontenttimeseries usingspectralanalysis. Wethen analyzedtherelationbetween WDandtemporalchangesofKosugi’sretentioncurveparameters thatcapturetheshapeoftheporesizedistribution.Finallyouraim was to test a regression model to predict the time course of Kosugi’sporeparametersfromenvironmentalvariables.
2. Materialsandmethods 2.1. Fieldexperiment
A field experiment was conducted over three years (2009– 2012) to study factors underlying temporal changes in soil hydraulic properties. The experiment is described in detail by
Bodneretal.(2013).Inshort,itwaslocatedonanarablefieldnear
Raasdorf,LowerAustria(488140N,168350E,156masl).Themain experimental factor was three differentpost-harvest soil cover
treatments.Forthepresentevaluation,weaverageddatafromall plots(n=9)asourfocuswasonthemeantemporaldynamicsat thesite. Climaticallythelocationischaracterizedbysub-humid conditions (pannonic) with an average annual precipitation of 525mm,ameanannualtemperatureof9.88C,andameanrelative humidityof75%.Weatherdatawererecordedbyanautomated weatherstation(AdconTelemetryGmbH,Austria)directlyonthe field.Fig.1showsrainfall,temperatureandreference evapotrans-piration(ET0)forthethreeexperimentalyears.
Thesoilis classifiedas ChernozemintheWRB(IUSS,2007). BasicsoilpropertiesaregiveninTable1.
Soilwatercontentwasmonitoredcontinuouslyineachplotby capacitance sensors (CProbe, Adcon Telemetry GmbH, Austria) installedviaaccesstubes.Sensorswerepreviouslynormalizedand comparedtogravimetricreferencesamples.Fig.2showsthesoil waterdynamicsintheuppersoillayer(5cmsoildepth)whichwas usedfortheanalysisofWDcycles.
2.2. Determinationofsoilporesizedistributionparameters Soil pore size distribution parameters were determined by inverse analysis of tension infiltrometer data. Infiltration mea-surementswereconductedtwelvetimesbetweenSeptember2009 andJuly2012.Allmeasurementswereperformedusingatension infiltrometer (Soil Measurement Systems Inc., Tucson, AZ) and takenat thesoil surfacewhere moststructural dynamicswere expected.DetailsofmeasurementaregiveninBodneretal.(2013). The inverseanalysisof infiltrationmeasurementsrequires a numericalsolutionoftheRichardsequationforDarcianflowina radial symmetric 2D domain. We followed the procedure presented by Sˇimu˚nek et al. (1998). Soil water retention was described by the model of Kosugi (1996) which is based on a lognormalporesizedistribution.SoilwaterretentionSe(h)isgiven by
SeðhÞ¼0:5Erfc logðh=ðhffiffiffi m;KosugiÞÞ 2
p
s
Kosugi !(1) whereSeistheeffectivesaturationcorrespondingtoð
u
u
rÞ=ðu
su
rÞ withu
(cm3cm3) being volumetric water content,u
r(cm3cm3)residualwatercontentand
u
s(cm3cm3)saturation
watercontent.Erfcisthecomplementaryerrorfunction,hm,Kosugi
(cm)themedianpressureheadofthesoilwaterretentioncurve whereSe(hm,Kosugi)=0.5,and
s
Kosugithestandarddeviationofthelog-transformedpressurehead.Themedianporeradius(rm,Kosugi)
canbecalculatedfromhm,KosugiusingtheYoung–Laplaceequation.
Parameter estimation is done by minimizing the objective functionasdefinedbySˇimu˚nekandvanGenuchten(1996)using theprogramHYDRUS2D/3D(Sˇimu˚neketal.,2006)whichappliesa Levenberg–Marquardtnonlinear minimization algorithm. Initial parameter estimates were derived from the texture based
Fig. 1. Monthly averaged precipitation, air temperature and reference evapotranspiration(ET0)attheexperimentalsite.
pedotransfer function Rosetta (Schaap et al., 2001) (input parameters:soiltextureandbulkdensity).Toreducetheamount ofunknownvariables,
u
rwasfixedto0.067cm3cm3,aspredictedbyRosetta.
u
svalues weresetequal totalporosity fromsamplecylindermeasurements, and Ks was used fromdirect Wooding
analysisofinfiltrationdata(Sˇimu˚neketal.,1998;Bodneretal., 2013).Theremainingparameters
s
Kosugi,andhm,Kosugiwerethenestimatedinversely.
2.3. Quantificationofwetting–dryingcycles
WDcycleswerequantifiedbyspectralanalysisofsurfacenear soil water content time series (5cm soil depth) using theSAS procedurePROCSPECTRA(SAS/STAT,2009).Spectralanalysisisa statisticalmethodthatcandiscerncyclicpatternsinasoilproperty
(Nielsen and Wendroth, 2003; Si, 2008). We quantified the
intensity of WD cycles by spectral density and calculated the numberofcyclesfromspectralwavelength(cycleduration)via Ncycles¼
pi
D
ti;iþi(2)
whereNcyclesisthenumberofwetting–dryingcycles,pi(days)is
thewavelengthofaspectralpeakand
D
ti,i+1(days)isthelengthofthe analyzed time series. Fig. 3 exemplifies our approach to quantificationofWDcycles.
Beforeapplyingspectralanalysisdataaredetrendedbylinear regression of water content vs. time (Worrall and Burt, 1998,
Fig.3a). For eachperiod it istested ifthe detectedspectraare differentfromrandomscattering(whitenoise)byaFisher’sKappa andBartlett’sKolmogorov–Smirnovstatisticswhichareavailable intheSASspectralprocedure.
Spectralanalysisthenproducesestimatesofspectraldensities byafiniteFouriertransformwhichdecomposesthedataseriesinto a sum of sine and cosine waves of different amplitudes and wavelengths(Eq.(3)): xt¼ a0 2 þ Xm k¼1
½akcosð
v
ktÞþbksinðv
ktÞ (3)Herextisthevalueofatimeseriesattimet,misthenumberof
frequencies intheFourier decomposition(m¼n=2ifnis even, m¼n1=2ifnisodd,wherenisthenumberofobservationsin thetimeseries),a0isthemeanterm(2x),akandbkarethecosine
andsinecoefficientsrespectivelyand
v
karetheFourierfrequen-cies (
v
k¼2p
k=n). The periodogram of amplitude at each frequencykisgivenby Jk¼ n 2ða 2 kþb2kÞ (4)Fig. 3b gives an example of a periodogram with spectral densitiesfor thedetrendedseries.Thewhitenoise spectrumas wellasthe95%confidencelimitforpeakssignificantlydiffering fromwhite noiseare calculatedfollowing Torrence and Compo
(1998).Theperiodogramcanbeinterpretedascontributionofthe
kthharmonic
v
ktothetotalsumofsquaresinthedecompositionof theprocess.Thusa highspectral densityquantifiesa strong cyclicdeviationfromthemeanofthetimeseries.Fig.3cshowsthe wavefunctionofthedominantspectrumfortheexampleseries,i.e. thesumofcosineandsinecomponentsweightedbyakandbkat
frequency 0.161 over time. When summing up all significant spectraaccordingtoEq.(4)thereconstructedtimeseriesshownin
Fig. 3d is obtained. To reduce volatility of the periodogram, generally spectraare smoothed usinge.g. a moving average to obtainthefinalspectraldensityestimates(SAS/STAT,2009).We appliedathirdordermovingaverage forsmoothingthe period-ograms.
2.4. Statisticalanalysesandmodeling
Statisticalanalysesofthedatacomprised(i)analysisofvariance ofsoilporesizedistributionparameters,(ii)regressionanalysisof therelationbetweenporeparametersandWDpattern,and(iii) evaluation of a regression based predictivemodel for thetime courseofsoilporesizedistributionparameters.
2.4.1. Analysisofvariance
Soilhydraulicparameters(
s
Kosugiandrm,Kosugi)weresubmittedto an analysis of variance to determine periods of significant temporaldrift.WeusedtheMIXEDprocedureinSAStoproperly considerrepeated measurementsover time. PROCMIXED com-putesWald-typeF-statisticsusinggeneralizedleastsquares(GLSE) basedonrestrictedmaximumlikelihoodestimatesofthevariance components(Littelletal.,1998).Incaseofsignificantdifferencesin theWald-F-statisticforp<0.05,treatmentmeanswerecompared usinga two-sidedt test.Toaccountfortheserialcorrelationof non-randomized repeated measures on thesame experimental unit,i.e.measurementdate,anadequatecorrelationmodelwasfit tothedatabasedontheAkaikeInformationCriterion(Piephoetal.,
2004).
2.4.2. Regressionmodel
Regression analysis was used to determine the relation betweentemporaldriftinsoilporesizedistributionparameters andWDcharacteristics.Theobjectivewastoobtainapredictive model for hydraulic parameter change over time driven by independent environmental variables. TheSAS procedure PROC REGwiththeRSQUAREselectionmethodwasusedtofindsubsets Table1
Soilpropertiesoftheexperimentalfield. Horizon Depth(cm) Sand(kgkg1
) Silt(kgkg1
) Clay(kgkg1
) TextureUSDA Corg(kgkg1) Fieldcapacity(cm3cm3) Wiltingpoint(cm3cm3)
A 0–40 0.19 0.57 0.24 SiL 0.025 0.32 0.15
AC 40–55 0.23 0.54 0.23 SiL 0.015 0.27 0.10
C >55 0.22 0.62 0.16 SiL 0.008 0.25 0.07
Fig.2.Soilwatercontentinthesurfacenearsoillayer(5cmsoildepth).Grayarea showsthestandarddeviation(n=9),verticaldottedlinesindicatemeasurement datesandnumbersdefineperiodsbetweeninfiltrationmeasurements.Arrows showperiodsoffrozensoil.Gapsareduetosensorremovalduringharvestand seedingoperations.
of independent variables that best predicted the hydraulic parameters.We restrictedtounivariate andbivariatemodelsin ordertoavoidover-parameterizationandensuremodel interpret-ability.
BesideWDindicators(cycleintensity,numberandduration), someotherenvironmentalvariableswereincluded.Alongertime interval is likely to show higher temporal change. Thus the influence of the length of time separating two measurements (
D
ti,i+1)wastested.Theinitialvalueatticanalsoinfluencethesubsequentdriftascertainhydraulicpropertyconfigurations(e.g. astatewithmoremacropores)mightbelessstableandtherefore undergohigher change. Therelation between initial value and subsequentdriftwasthereforeanalyzed.Alsohighersoilmoisture couldincreasestructuralinstabilityresultinginhighertemporal drift. This was tested by the influence of initial and average moisture. Beside a cyclic WD pattern, also a general trend of wettingor dryingcaninfluences hydraulic properties.Moisture trend,calculatedastheslopeofalinearregressionthroughwater contentvs.timebetween,andmeteorologicalindicatorsofwetting vs.dryingperiods(cumulativevaluesofET0,rainfallandclimatic
waterbalancedeficit)wereincluded.Theclimaticwaterbalance deficitwascalculatedasthecumulativesumofrainfallminusET0
overtime.
2.4.3. Modelapplicationandevaluation
The regressionmodel obtained fromtheaboveanalysis was then used to predict the temporal dynamics of pore size distribution parameters at a weekly time step. An initial soil watercontentseriesofthreeweekswasusedtoensureasufficient lengthofthetimeseriesforspectralanalysis.Thereaftertheseries wasincreasedstepwisewiththesubsequentsevendaysofwater contentmeasurements.Amainquestionwasatwhichvaluethe thresholdsfordrivingvariablesshouldbesetthatdeterminewhen hydraulicparametersareupdated.Wecalibratedthesethresholds based on the values which separated periods of statistically significantvs.non-significantdriftinmeasuredporeparameters.
Comparing measured and predicted parameters using varying thresholdsrevealedthatmeanvaluesattheperiodsofsignificant change in measured hydraulic parameters were the most appropriatetresholds.Wheneverthesethresholdswereachieved, soilhydraulicparameterswereupdatedbytheregressionmodel. Afterwardsanalysisrestarted withthesubsequentthree weeks dataasinitialtimeseries.
Thefunctional formofthetemporal driftbetween two data points cannot beanswered fromourdata. We applieda cubic hermite spline interpolation between data points using the MATLAB pchip-function to obtain a continuous time course of poreparameters.
Themodelwasevaluatedwithdifferentgoodnessoffitindices. Rootmeansquarederror(RMSE)isadimensionalsquaredstatistic fordifferencebetweenmeasuredandmodeledvalues.Modeling efficiency(EF)andtheindexofagreement(d)arebothextensions ofthecommonr2statisticsofregressionlines.EFcangeteither positiveornegativevalues,1beingtheupperlimit,whilenegative infinityis thetheoreticallower bound.EF values lower than 0 resultfroma worsefit thantheaverage of measurements.The valuesoftheindexofagreementliebetween0and1,with1being theupperlimit. Finally theslope andr2 between modeledand
measuredvaluesisindicated.Allindiceswerecalculatedusingthe IRENEsoftware(Filaetal.,2003).
3. Resultsanddiscussion
3.1. Temporalvariabilityofsoilporesizedistributionparameters
Table2givesasummaryoftheparametersofKosugi’sretention
modelobtainedbyinverseparameteroptimizationfromtension infiltrometermeasurements.Wefocusontheparameters describ-ing theshape of thepore sizedistribution (rm,Kosugi,
s
Kosugi). AcompanionpaperofBodneretal.(2013)alsodemonstratedthat
u
sshowedonlyminortemporalchangesatsite. Thereforewejust consideredtheshapeparametersofKosugi’sretentionmodel. Fig.3.Spectralanalysisofwatercontenttimeseries.(a)Detrendingoftheinitialseries,(b)spectraldensityperiodogramoftheserieswithwhitenoisespectrumand95% confidencelimits,(c)wavefunctionofthedominantspectrum,and(d)reconstructedtimeseriesfromallsignificantspectra.
Sˇimu˚nek et al. (1998) demonstrated that in the dry range retentioncurvesfrominverseestimationdeviatedfromlaboratory measurementswithapressureplateextractor.Theyshowedthat the inversely estimated curves could better reproduce a field measuredinfiltrationprocessinaforwardsimulation.Therefore weconsidertheinverseestimatesfromfielddataappropriateto describehydraulicproperties,particularlyforthestructuralrange whichwearestudyinghere.
Hayashi et al. (2006) demonstrated that Kosugi’s pore
parametersareproperindicatorsforstructuralporosity.Ahigh rm,Kosugifora givensoiltextureclassrevealstheimportanceof
macroporosity.Anarrowporesizedistribution(low
s
Kosugi)witha high frequency of the dominant pore radius class is characteristic for less structured soils. Sˇimu˚nek (2006) gives Kosugi parameters fora range of texture classes. The average values we obtained by parameter optimization (hm,Kosugi
126.5cm,
s
Kosugi 1.98) were between those of sandy loams(hm,Kosugi27.4cm,
s
Kosugi1.26)andsiltyloams(hm,Kosugi325.9cm,s
Kosugi2.30)indicated by Sˇimu˚nek(2006). Wenoticethattheaveragehm,Kosugi(126.5cm) hastobecalculateddirectlyfrom
the optimization results as for mathematical reasons ð1=nÞPð1=xÞ6¼1=ð1=nPxÞ
ð Þitcannotberecalculated fromthe
averagerm,KosugigiveninTable2.Thecoefficientofvariationwas
higherforrm,Kosugicomparedto
s
Kosugi.Thetemporalfactorwasthe dominant contribution to the overall variance and was significantforbothhydraulicparameters.Inaverage
s
Kosugialsodiffered among soil cover treatments. However there was no interactionofthetreatmentmaineffectwithtime.Thereforethe useofmeanvaluesateachmeasurementpointprovidedagood representation of the soil specific parameter range and the temporaldynamicsatthesite(Fig.4).
FromFig.4atendencyofoverwinterincreaseofrm,Kosugiand
aconcomitantdecreasein
s
Kosugicanbeobserved.Over-winterfreezing–thawing has been described to induce aggregate breakdown(Oztas andFayetorbay,2003)whichwouldexplain structure homogenization as expressed by the reduction of
s
Kosugi. Unger (1991) described soil loosening over winterleadingtohigheraggregatemeanweightdiameterandreduced bulk density. These processes could result in higher macro-porosityasobservedinourmeasurements.Duringthesummer monthadecreasingtrendinrm,Kosugiandanincreasein
s
Kosugicould beobserved. This mightbe related tocapillary induced soilshrinkage reducingthemedianradius ofporeswhilepore heterogeneity increased by formation of microfissures (Leij etal.,2002).Duringtherestoftheseason,periodsofincreaseas well as decrease in hydraulic parameters were found with a particularly pronounced change between spring and early summer2010.
3.2. Wetting–dryingdynamics
Laboratoryexperimentsdemonstratedthedominantinfluence ofWDcyclesonhydraulicproperties(e.g.Pengetal.,2007).Also field studies with simulated rainfall and subsequent drying
(Mubarak et al., 2009) reported strong effects of WD. Under
naturalconditionsthecyclicpatternismorecomplexandirregular comparedtoinducedWD.Thisischallengingwhenstudyingthe impact on field soil properties.We appliedspectral analysis of watercontenttimeseriestoquantifycycleintensity,numberand duration fromspectral densityand wavelength.Fig.5givesthe spectraldensityperiodogramsshowingthecyclicpatternduring eachperiodbetweenhydraulicpropertymeasurements.
Allperiodshadcycleswithspectrasignificantlydifferentfrom whitenoise.Fig.5clearlyshowsthatthevalueofspectraldensity expressedthestrengthoftemporalfluctuationsofwatercontent (cf. period 1 vs. period 9). Periods with both low and high frequency water content fluctuations resulted in bimodal to multimodalspectralperiodograms(cf.periods7and8),although the secondary spectral peaks were frequently below the 95% confidencelimit(cf.period7).
Periodonetofiveaswellasperiod11hadadominantspectral peakatthelowestFourierfrequency,indicatingthattherewasone dominant WDcycle. Periodone had the lowestcycle intensity which is obviousregarding thelow water contentfluctuations. Periodthreetofiveand period11 onthecontraryhadallhigh spectralpeaksindicatinganintenseWDcycle.
Periodsixtotenshoweddominantspectraathigherfrequency, representingcyclesof shorter durationwith repeatedWD over time.Forexampleperiodeighthadamarkedbimodalperiodogram correspondingtotwo(firstpeak)andseven(secondpeak)cyclesof similarintensitythatoccurredduringthisperiod.
ThestrongestcycleintensitieswerefoundbetweenApriland June 2010and between November2011and April 2012.These periods were characterized by frequent rainfall events which Table2
Resultsofanalysisofvarianceforsoilhydraulicparameters.
rm,Kosugi(mm) sKosugi Statisticssummary Mean 0.077 1.98 SD 0.078 0.58 CV% 100.8 29.1 Levelofsignificance Coverage(C) NS * Time(T) *** *** Replicate(R) NS NS CT NS NS RT NS NS NSisnonsignificant. * Significantatp<0.05. *** Significantatp<0.001.
Fig.4.TemporalvariabilityoftheparametersfromKosugi’s(1996)waterretention model. Statistical comparison indicates if changes between two consecutive measurementdatesaresignificantatp<0.05(ns
nonsignificant,*significantat p<0.05,**significantatp<0.01,***significantatp<0.001).
partially explained the intensity of the WD pattern (r2=0.51,
p=0.01).DuringOctober2010toJune2011therewereperiods withahighnumberofcycles(highfrequencyfluctuations).This season was substantially drier than the long-term average (176.6mmvs.360.5mm).Howevertherewasnometeorological variableotherthanthenumberofrainevents,whichhadonly anintermediater2,toreliablypredictthecyclicbehaviorofsoil
WD.Spectralanalysisthusprovidesauniquedrivingparameter for the analysis of soil processes and properties under field conditions.
3.3. Wetting–dryinginducedchangeinsoilporesizedistribution In a recent study of Bodner et al. (2013) on the same experiment,theydemonstratedthatwithin-seasonvariabilityof theporesizedistributionwasstronglyrelatedtoWD,while over-season dynamics were mainly influenced by soil mechanical disturbanceandcroprotation.
Following quantification of the WD pattern, we therefore analyzeditspredictivepowerfortemporalchangesinKosugi’sPSD parameters.BesideWD,alsotheinfluenceof(i)initialvaluesofthe respective hydraulic variable, (ii) different length of periods between two measurements, and (iii) other moisture related parameters (moisture trend, average moisture, initialmoisture, cumulativerain,ET0,climaticwaterbalancedeficit)wastested.
Table3showstheresultsofregressionanalysis.Forthebivariate
case,onlythebestmodelforeachparameterisreported. WDwasthebestsinglepredictorvariableforthetemporaldrift in both hydraulic parameters. Changes in rm,Kosugi were also
significantly influenced by the climatic water balance deficit. AlthoughtherewasnodirecteffectofaveragesoilmoistureonWD cycle intensity(r2=0.04), it can still modify its impacton soil
properties (Watts et al., 1996). We therefore introduced the averagesoilmoistureasaweightingfactor.Theconsistentincrease inr2confirmedtheassumptionthatWDeffectsonporeparameters
arestronglymediatedbytheprevailingmoistureconditions,with Fig.5.SpectraldensityperiodogramsofWDcyclesfortheperiodsbetweenhydraulicpropertymeasurements.Theunderlyingdetrendedwatercontentseriesisshowninthe rightcornerofeachperiodogram.
decreasingimpactunderlowmoistureconditions.Wealsotested otherweightingfactorsforWDintensitysuchascyclenumberand cycleduration.Theunderlyingassumptionwasthatmorefrequent or longer cycles had a stronger impact. However this did not improvethepredictivepowerofcycleintensityalone.Itconfirms thedominantinfluenceofcycleintensityonporesizedistribution parameters,whilecyclenumberand durationbeingof subordi-natedimportance(Pengetal.,2007).
Asexpectedbivariateregressionmodelsachievedahigherr2
(cf. Table 3). The intercept in the bivariate models was
non-significant, while both predictor variables were significant. Therefore weused zero-interceptmodels.Beside the higherr2, the bivariate models also allow a better interpretation of the distinct variables driving increase vs. decrease in hydraulic parameters.Fig.6 showstheregressionmodelswithhighestr2
forthetemporaldriftintheKosugiparameters.
The change in PSD predicted by the regression models is resumedinFig.7.IntenseWDcyclesincreasedthemedianpore radius (+8.0% per unit cycle intensity), while the pore radius
standarddeviationdecreased(3.5%perunitcycleintensity).A prolongeddryperiod(indicatedbyahighET0andahighclimatic
waterbalancedeficitrespectively)ledtoareductionofthemedian pore radius(3.0% per10mm decreasein thewater balance deficit), whileslightlyincreasingporeradiusstandarddeviation (+1% per 10mm increase in cumulative ET0) with a higher
frequencyoffinepores.
AlsoPengetal.(2007)reportedageneralincreaseinporosity
(between2.6and16.5%dependingonclaycontent)withWDcycle intensityandhighestchangesinthemacroporefraction.Onthe otherhandLeijetal.(2002)showedthatdryingreducedstructural porosity due to aggregate coalescence. They also reported an increaseinfineporefrequency.Ourmodelsuggeststhatthecyclic patternofWDdrivestheformationofstructural(macro)porosity, whilecapillarydrivenaggregatecoalescenceisthepredominant processduringageneraldryingphaseincreasingtheamountof smallerporeclassesattheexpenseofmacropores.
We want to point out that theeffect of WD is expectedto strongly interact with other drivers of changes in structural porositysuchastillage.Aloosesoilaftertillagewillshowdifferent responsetorepeatedWDcomparedtoamorestableno-tillsoil (e.g.Pagliaietal.,2004).Alsodifferentsoiltextureswillrespond differentlytoWDasshownbyPengetal.(2007).
3.4. Predictionofporesizedistributionparameters
Theregressionmodelswereusedtopredictthetimecourseof Kosugi’sporeparameters.WDwascalculatedfromwatercontent data by spectral analysis with a weekly time step. ET0 and
cumulative water balance were obtained from meteorological data.Thethresholdvalueforthemoistureweightedcycleintensity wasset tosixfor both
Ds
Kosugi andD
rm,Kosugi.Periods ofnon-significantchangeinKosugiparametershadanaverageweighted cycle intensity of 3.8, while those periods showing significant changes had an intensityof 6.3. Thussix seemed a reasonable intensitythresholdtoupdatethehydraulicparametersbasedon theregressionmodel.ThresholdsforcumulativeET0weresetat
100mm (
Ds
Kosugi) and for climatic water balance deficit at50mm (
D
rm,Kosugi). Fig. 8 shows the predicted temporaldynamicsofthehydraulicparameterscomparedtotherangeof measureddata.
Generally thehydraulicpropertydynamicswerereproduced satisfactorilybythemodelwithaslighttendencytounderestimate themeasuredvalues.Amajordeviationbetweenthemodeledtime course and observed values occurred during autumn 2011 (measurement point in November 2011) where the model did notcapturethedecreaseinrm,Kosugiandtheincreasein
s
Kosugi.Theautumnseason2011wasparticularlydry(47.8mmvs.107.8mm long-term average rainfall). It is likely that the ET0-based
meteorologicalvariablesinourmodeldidnotsufficientlyreflect soilsurfacedryingandconcomitanthydraulicparameterdriftin thisperiod.
The deviationbetween themeasurement pointin December 2009andthemodeledtimecourseismainlyrelatedtotheproblem ofinterpolation.Themodelpredicatedthefirstupdateinhydraulic parametersforthe3rdFebruary2010withWDcyclehigherthan the set threshold. When linking the initial values with the calculateddatapointsatthisdatebyacubic splinehowever,it wasnotpossibletocapture theprolonged periodofunchanged poreparametersinthebeginning.Asmentionedabove,ourmodel isnotabletopredicttheexactfunctionalbehaviorbetweentwo datapoints.
Table4givesthegoodnessoffitindicesbetweenmeasuredand
calculatedhydraulicparameters.
Inhydrologicalmodelinggenerallystatichydraulicparameters areused.Theindiceshowevershowedclearlythatthecalculated Table3
Regressionmodelstopredictchangesinsoilhydraulicpropertyparameters.(Bold valuesindicatemodelswithallpredictorvariablesbeingsignificant.).
rm,Kosugi sKosugi Initialvalue 0.20 0.10 Periodlength 0.03 0.04 Cycleintensity 0.43 0.50 Cyclenumber <0.01 <0.01 Cycleduration 0.04 <0.01
Cycleintensityweighted 0.53 0.57
Averagemoisture 0.33 0.22
Initialmoisture 0.01 0.08
Sumrain >0.01 0.04
SumET0 0.18 0.18
Rain-ET0 0.43 0.10
Intensityweighted+rain-ET0 0.81 0.50
Intensityweighted+sumET0 0.74 0.78
Fig.6.Bivariateregressionmodelsbetweenenvironmentaldrivingforcesandthe temporaldriftintheparametersofKosugi’shydraulicpropertymodel.
hydraulicparametersareabetterrepresentationoftheobserved dynamicbehaviorthanusingaveragevalues.Amodelingefficiency (EF)greater0 indicates that theagreement between thesingle measuredandestimatedvaluesisbetterthanusingtheaverageof measurement.Thevaluesof0.58and0.60forEFthereforeconfirm thesubstantialimprovementin capturingthesystemdynamics when using dynamic parameters predicted by our model. This confirmstheconclusionofSchwenetal.(2011)thatthereliability ofwater transportsimulation couldbeimprovedwhen usinga dynamicinsteadofastatichydraulicpropertydescription. 4. Conclusions
Thisstudypresentsa quantificationofWD cyclesfromfield water content time series using spectral analysis. The method allowsextractingthebasiccharacteristicsofWD(cycleintensity, numberandduration)fromthecomplexandirregularpatternthat is typicallyobservedunder fieldconditions. WDcycleintensity was strongly related to thetemporal drift in the median pore radius and pore radius standard deviation of Kosugi’s water retentionmodel.ThisconfirmslaboratoryfindingsthatWDcycle intensityisadominantdrivingfactorofstructuralporositywhich isalsovalidunderfieldconditions.Theeffectofcycleintensitywas mediatedbysoilmoisture,withdrysoilreducingitsimpactonthe hydraulic parameters. Using a bivariate regression model we showed that WD intensity increased macroporosity while de-creasing pore heterogeneity. During a general drying phase, expressedinourmodelbyahighcumulativeET0orhighclimatic
waterbalancedeficit,themedianporeradiuswasreducedwhile poreheterogeneityincreasedduetohigherfrequencyofsmallpore radiusclasses.Thisprobablyreflectstheeffectofcapillarydriven aggregatecoalescence.Wedemonstratedthattemporalchangesin pore size distribution could be predicted from environmental variables. The modeled values captured the observed system dynamics substantiallybetterthan a static representationwith averaged parameters.Time seriesof water content or pressure head are frequently measured in hydrological field studies. Spectral analysis provides a method tomake additional use of suchmeasurementsbyextractingquantitativeinformationonthe Fig.7.DynamicsoftheporesizedistributiondrivenbywettinganddryingindicatorsaspredictedbytheregressionmodelsinFig.6.
Fig.8.Timecourseofsoilhydraulicparameters,predictedbytheregressionmodels showninFig.7,comparedtotherangeofmeasuredvalues(meansSD).
Table4
Goodnessoffitindicesformeasuredandpredictedhydraulicpropertyparameters.
rm,Kosugi sKosugi RMSE 0.035 0.29 EF 0.58 0.60 d 0.89 0.88 r2 (slope) 0.84(0.89) 0.86(0.96)
WDpattern.OurstudyconfirmedthatWDisanimportantdriverof within-seasonvariabilityofstructurerelatedsoilpropertiesand processes. Therefore the application of spectral analysis can enhance our understanding of pore and aggregate temporal dynamicsunder fieldconditions and provideanimportantlink tolaboratoryinvestigations.Furtherinvestigationscouldusethis methodforquantitativelyassessingtheinteractionsofWDwith otherrelevantfactorsdrivingtemporalchangesinthesoilporesize distributionsuchastillage,irrigationandcroprotation.
Acknowledgement
The present study was funded by the Austrian Science Foundation (FWF) by grant number P 21836-B16. The authors aregratefulforthefinancialsupportprovidedtotheirwork. References
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