WATER
RESOURCES
RESEARCH,
VOL. 33, NO. 12, PAGES 2655-2664, DECEMBER
1997
Frequency distribution of water and solute transport properties
derived from pan sampler data
Jan Boll, • John S. Selker,2 Gil Shalit,3 and Tammo S. Steenhuis4
Abstract. Modeling of water and solutemovementrequiresknowledgeof the nature of
the spatialdistributionof transportparameters.Only a few of the field experiments
reportedin the literature containedenoughmeasurementsto discriminatestatistically
betweenlognormaland normal distributions.To obtain statisticallysignificantdata sets,six
field experimentsat four different siteswere performed. Different degreesof macropore
and matrix flow occurredat each site. In each experimenta solutepulsewas added
followedby artificialor natural rainfall. Sixteenthousandspatialdistributedfluxesand
soluteconcentrations
were collectedwith wick and gravitysamplers.Spatial distributions
of solutevelocity,dispersioncoefficient,water flux, and soluteconcentrationwere
determinedover different timescalesrangingfrom 1 hour to the duration of the
experiment.A chi-squaretest was usedto discriminatebetweenthe type of frequency
distributions.The spatiallydistributedwater and solutetransportparameterswhen
averagedover the experimentalperiod were found to fit the lognormaldistributionwhen
macroporeflow dominates.Otherwise,when only matrix flow occursa normal distribution
fitted the data better. Under no-till cultivation,hourly concentrationand water flux are
lognormallydistributed,while tillage makesthe tracer concentrationto be normally
distributed.Spatialfrequencydistributionsof daily soluteconcentrationchangein time:
Concentrationswere normally distributedwhen the bulk of the solutebroke throughwith
the highestconcentrationsand lognormallydistributedin the beginningand end of the
experiment.Daily water flux wasfound to be lognormallydistributedthroughoutthe
experiment,but the distributionvaried betweenwater applications:Shortlyafter water
application,when wick and gravitypan samplerscollectedwater predominantlyfrom
macroporesand normallydistributedat later timeswhen mostlymatrix poreswere
sampledwith wick pan samplers.
1.
Introduction
The quality of groundwaterand surfacewaters is increasinglybeingcompromisedthroughrechargewater that still contains significantconcentrationsof surface-appliedchemicals
suchas fertilizersand pesticides[Clothieret al., 1996].Spatial
distributionof the invadingsoluteis an importantfactor in the
amount of solutesthat reach the groundwater[Juryet al.,
1982]. Realistic modelingin field soilsrequire, therefore, the
spatial and temporal variation of the parametersdescribing
water andsolutetransport[BiggarandNielsen,1976;Jury,1982,
1985;Simmons,1982;Spositoet al., 1986].
Numerousstudieshave focusedon the spatialvariabilityof
water and solutetransport.The mostnotablestudieswere by
Biggarand Nielsen [1976]. A review of other early works is
givenby Jury [1985]. Moisture contentwas found to be normally distributed[Rogowski,1972; Nielsenet al., 1973; Bababola, 1978; Russoand Bresler,1981], while infiltration rate,
•Department
of Biological
andAgricultural
Engineering,
University
of Idaho, Moscow.
2Department
of Bioresource
Engineering,
OregonStateUniversity,
Corvallis.
3Department
of Agricultural
Engineering,
Technion,Haifa, Israel.
4Department
of Agriculturaland BiologicalEngineering,
Cornell
University,Ithaca, New York.
Copyright1997by the American GeophysicalUnion.
Paper number 97WR02588.
0043-1397/97/97WR-02588509.00
solute velocity, saturated hydraulic conductivity,and dispersion coefficient were usually lognormally distributed [Rogowski, 1972; Nielsen et al., 1973; Biggar and Nielsen, 1976;
Warrick et al., 1977; Van De Pol et al., 1977; Bababola, 1978;
Russoand Bresler,1981;Sissonand Wierenga,1981;Wilsonand
Luxmoore,1988].
There are several shortcomingsin the above mentioned
studies,makingtheir resultstentativeat best.The samplesizes
were usuallytoo small.About 20-30 observationsare required
to distinguishbetween normal and lognormal distributions
[Raoet al., 1979].Only Nielsenet al. [1973],Biggarand Nielsen
[1976], Warricket al. [1977], Nassehzadeh-Tabrizi
and Skaggs
[1983], and Hagerman [1990] had data sets that were large
enough.Another drawbackwasthat visualinspectionwasused
for establishingnormality or lognormality. More rigorous
methodsare the chi-squaretest [Russoand Bresler,1981] and
the Kolmogorov-Smirnov
test [Rao et al., 1979].In this regard
it is of interestthat in the sufficientlylarge data setsof Nassehzadeh-Tabriziand Skaggs[1983] and Hagerman [1990] the
hypothesisof either normality or lognormalityusingthe Kolmogorov-Smirnovtest could not alwaysbe accepted.
We carried out six experimentsat four different locationsin
whichwe observedthe spatialdistributionof water and solutes
flow with grid pan samplerswith the goal to summarizethe
spatial distribution of these parameters.The grid pan samplers, consistingof 25 individuallysampledcells of 6.1 by 6.1
cm, are superiorover porouscup samplersin samplingwater
and solute fluxes in the unsaturatedsoil [Boll, 1995]. The
2655
2656
BOLL ET AL.: FREQUENCY
DISTRIBUTION
OF TRANSPORT
PARAMETERS
Willsboro, New York
Ithaca, New York
Georgetown, Delaware
Figure 1. Location of experimentalsites.
spatialdistributionof fluxes,velocitiesand dispersioncoeffi- loam) andcoarsematerial,typicalof Pleistocenefluvialdeposcientsare examined.The effect of macroporesand averaging its, occurbelow0.8 m depth.For the upper 0.3 m the average
over different
2.
Materials
hydraulic
conductivity
is4 m d-•, andfor the30-60 cmdepth
it is 2.5 m d- • [IrelandandMatthews,
1974].
timescales is discussed as well.
and Methods
2.3.
Six experiments
were carriedout at four sites(Figure 1). In
each experimenta pulse of nonadsorbedtracer (chlorideor
bromide)wasappliedandwasfollowedby irrigationor natural
rainfall.Sampleswere collectedregularlywith wick andgravity
pan samplers,installedat a depth of 0.6-0.7 m in 0.9-m-long
tunnels excavatedin the side of a trench (Figure 2). Each
samplerconsistedof 25 cells, each 6 by 6 cm, which were
sampledseparately.Cellsof wick samplershavewicksthat are
45 cm long. The solutionswere collectedin bottlesthat were
changedperiodically.The trenchwasleft opento facilitatethe
sampling.In all, 25 breakthroughcurveswere obtainedfor
eachpan sampler.Additional detailsfor the individualexperimentsare outlinedin Table 1 and are givenafter the four sites
are described.
The four experimentalsiteswere the Universityof Delaware
ResearchCenter in Georgetown("Delaware"); Cornell University'sThompsonVegetable Farm near Freeville, New York
("Freeville"); Cornell University's Experimental Research
Farm in Willsboro,New York ("Willsboro");andCornellUniversity'sorchardin Ithaca,New York ("Orchard").Described
below are land usesand the soilsfor each of the four experimental
2.1.
sites.
The soil at the Freeville
The Hudson silty clay loam consistsof a pale brown finegrainedsoilwith a subangularblockystructureand hexagonal
shapedpeds of 0.2-0.3 m in diameter. Surface connected
crackswere present,someaswide as 10-20 mm. For the upper
25cmthehydraulic
conductivity
ranges
from40to 120cmd-•,
and for depthsfrom 0.25-1.10 m the conductivityis between1
and40cmd- • [Neeley,
1965].Duringthesummer
wemeasured
much higher conductivitiesbecause of the flow of water
throughthe macropores[Metwin et al., 1994].
2.4.
site is a well-drained
Genesee
silt
Willsboro
The upper0.4 m of the RhinebeckVariant clay(illitic, mesic
Aeric Ochraqualfs)is grayishbrownwith a moderatemedium
granular structurepenetrated by many roots. Lower in the
profile,the structurebecameangularblockywith rockspresent
and fewer roots. In the 0-0.3 m soil layer, the averagecon-
ductivity
is60cm[Bro,1984].It decreases
to lessthen1 cmd- •
for the layer between 30 and 60 cm. At deeper depthsthe
conductivity
increases
againto approximately
60 cm d-• [Olsonet al., 1982].Water movementin the layerfrom 30 to 60 cm
is throughmacroporesonly [Steenhuis
et al., 1990].
2.5.
Freeville
Orchard
Experimental Procedures
Two experimentswere performed at the Freeville site, E1
and E2; two at Delaware, E3 and E4; one in the orchard, E5;
loam (fine-loamy,mixed, nonacid,mesic Typic Udifluvent),
and one at Willsboro,E6. Of theseexperiments,one wascarcharacterizedby 0.6 m of dark brown loamy soil containing
30,000-50,000 worm and root channelsper square meter in
diametersrangingfrom 0.5 to 3 mm, overlyinga dark brown
silt loam to very fine sandyloam. A substratumof layersof
gravel and sandexistsat approximately1.8 m. The saturated
hydraulic
conductivity
is between35 and120cmd-• [Neeley,
1965].
2.2.
Access• ......
Delaware
,.
The upper 0.6-0.8 m of the Evesborosandyloam (mesic,
coatedTypicQuartzipsamment)
is a ratherstructureless,
single
grain,yellowish-brownloamysandwith remnantsof rootsfrom
an old tree stand.Layersof fine sand(or occasionally
grayish
-
.
::::•: lm:i•
Pan sampler
Figure 2. Samplingsetup.
BOLL ET AL.: FREQUENCY
DISTRIBUTION
OF TRANSPORT
Orchard
Delaware
PARAMETERS
2657
Table 1. Summaryof Field Experiments
Freeville
1
Freeville
2
1
Delaware
2
Willsboro
Soil type
silt loam
silt loam
siltyclayloam
sandyloam
sandyloam
sandyclayloam
Type of tracer
Type of pulse application
bromide
solution
bromide
solution
bromide
solution
chloride
solution
bromide
solution
chloride nitrate
flakes
Pulseconcentration
7.8X 10-3
kg L-1
14.5X 10-3
kg L-1
7.8X 10-3
kg L-1
2.2X 10-3
kg L-1
i X 10-2
kg L-1
4000kg C1ha-1,
23 kg N ha-1
Pulse length, cm
4
4
3.5
4
2
NA
Type of water application
Durationof rainfall
sprinkler
2-3 h d-•
sprinkler
13.5hours
sprinkler
2-3 h d-1
sprinkler
6 hours:10 min on,
naturalrainfall
variable
sprinkler
2 events:7,
Rainfall rate, cm h-1
Length of study,days
Total appliedwater, cm
Depth to sampler,cm
Samplertype(number)
1.5
21
84
60
wick(2),
gravity(2)
1.5
1
20
60
wick(2),
gravity(2)
1.5
21, 12
49, 35
60
wick(2),
gravity(2)
1.5
21
63
60-70
wick(2)
variable
131
40
60-70
wick(2)
0.9
2
15
60
wick(4)
35 min off
ried out with natural rainfall, four had daily intermittent rainfall, and one had continuous rainfall.
2.5.1. ' Experiment 1 (El). Two wick and two gravitypan
samplerswere installedin a grasscoveredplot in Freeville.
Twenty millimetersof artificial rainfall were applied twice a
day(10 A.M. and4 P.M.) startingon July25, 1990.The rainfall
4.75 hours
2.5.5. Experiment5 (E5). In the orchard,two plotswere
used,offsetby 20 m: a mowed-grass-covered
plot and a mosscoveredplot. Each plot had one wick and one gravity pan
samplerinstalled.On July 18, 1991, water was applied to the
grass
plotat a rateof 10-15mmh-• for 3-4 hours.A pulseof
6 g L bromidewas addedto the first irrigation.Irrigationwas
ratewas10-15 mm h-•. On August2, aftera constant
pan continueddaily until August 12 exceptfor 6 days.The moss
sampleroutflowpatternhadbeenachieved,
a 7.8 g L -• bro- plot wasirrigateddaily (exceptthree times)from July29 until
mide solutionwas applied for 1 day, followed by 22 days of
artificialrainfall asbefore.Water sampleswere collecteddaily
August
12.Thefirstirrigation
contained
6.8g L-• bromide.
to determine
ume and bromide
outflow
volume
and bromide
concentration.
Drainageoutflowwas alsomeasuredbetweenthree irrigation
eventsas follows:starting15 daysafter bromide application,
sampleswere taken 4 and 16 hoursafter the 4 P.M. irrigation
and, on the following day, 0 and 3 hours after the 10 A.M.
irrigationand 0 and 2 hoursafter the 4 P.M. irrigation.
2.5.2. Experiment 2 (E2). This experimentwas also carried out in Freeville and usedthe samefour samplersasin El.
The grasscoveredplot wasirrigatedthree timeswith 20 mm of
water on June 24, 1991. The next day, a pulse of 20 mm of
Water sampleswere collecteddaily to determine outflowvol2.5.6.
concentration.
Experiment 6 (E6).
For the Willsboro site two wick
pan samplerswere installedin a no-till plot (NT) and two in a
conventionally
tilled plot (CT). Twenty-three
kg N ha-• on
May 5, 1993,and4000kg C1ha-• on August17, 1993,were
surface-applied
followed
bytwo9 mmh- • irrigationeventson
August18 and 19, 1993,lasting7 hourson the first day and 4.75
hoursthe secondday.Sampleswere collectedseventimes:0, 2,
15, and 18 hoursafter the end of the first irrigation and 0, 2,
and 18 hoursafter the end of the secondirrigation.For each
watercontaining
14.5g L -• bromidewasapplied.Thebromide sample,outflowvolume and NO 3 and C1concentrationswere
pulsewas followed immediatelyby a continuouswater appli- determined.
cationof 11.5hoursat a rateof 15-20mmh-•. Watersamples
were collectedfrom all four samplers1.5, 4, 5.5, 7.5, 9.5, 11.5, 2.6. Data Analysis
and 13.5hoursafter the startof pulseapplicationand analyzed
The first stepin the data analysiswasto reducethe approxfor outflow volume and bromide concentration.
imately 6000 data pointsof concentrationand flow to proper2.5.3. Experiment 3 (E3). At the Delaware site four wick ties related to the transportof water and solutesfor each cell.
pan samplerswere installed:one in a plot which was under Then we averagedthe transportparametersoverdifferenttime
ridge tillage (RT), two under reducedtillage (chiselplow and periodsand determinedthe spatialfrequencydistributionsfor
disk) and an applicationof poultrymanure(PM1 and PM2), the data. Finally,we performedstatisticalanalysisand checked
and one under reducedtillage with a winter covercrop of rye if the spatialdistributionwas lognormalor normal.
andwhite clover(WC). The plotswere irrigatedtwicewith 40
mm of water and on July 16, 1992, a 40 mm of a solutionwith 2.7. Transport Properties
2.2g L -• chloridesolution
wasappliedto eachplot,followed The transportrelated parameterswere averagedover three
by 21 daysof artificialrain. The rain was appliedfrom 6 A.M. timescales:hour, day, and the experimentalperiod defined as
until noonin cyclesof 10 min on and35 min off. The total amount the time from the pulse applicationtill the water application
ofrainontheplotswas40mmd-•. Watersamples
werecollected was stopped.At this time, the soluteconcentrationwas small.
daily to determineoutflowvolume and chlorideconcentration. For eachcell, the parametersaveragedover the experimental
2.5.4. Experiment4 (E4). The locationand the samplers period consistedof solutevelocity(rs), dispersioncoefficient
were identical
to those in E3. E4 was carried out from October
1992to March1993.A 10g L- • bromidesolution
in 20 mmof
artificial rainfall was followed by approximately400 mm of
naturalrainfall during131 days.Sampleswere collectedweekly
to biweekly, dependingon the occurrenceof rain events,to
determine
outflow volume
and bromide
concentration.
(D), andthe averageflux,(qavg);VsandD werefoundby
fitting cumulativeoutflow and bromide or chlorideconcentration to the convective-dispersiveequation with flux type
boundaryconditionsusingCXTFIT [Parkerand van Genuchten, 1984].An estimateof Vsand D for the orchardand Willsboro experimentscould not be obtainedbecausethe convec-
2658
BOLL ET AL.: FREQUENCY
DISTRIBUTION
OF TRANSPORT
PARAMETERS
0.5
d
Vs= T
ß
(2)
0.4-
whered is the depthof the sampler.The averageflux per cell,
qavg,
wascalculated
by dividingthe cumulative
drainage
vol-
0.3-
ume from each cell by the duration of the experiment.
Daily averagedparametersinclude the flux (qd) and the
concentration
(Cd) andwere computedfor three experiments:
El, E3, and E5. The other experimentswere of too short a
durationto obtain sufficientdata points.For E3, qd and Cd of
only days3 through 12 were analyzedbecauseconcentrations
wereverylow from days13 through21;qd and Cd of both plots
in E5 were analyzedseparatelybecausethe experimenton the
grassplot started 10 daysbefore the experimenton the moss
ß
0.2-
o.oß
ß ßßß ßßßßß
o.o-
10
15
20
plot. The flux (qh) and concentration
(Ch), whichwere averaged over periods of severalhours,were determinedfor experimentsE1 and E6. In theseexperiments,detailedsampling
25
Time(days)
occurredbetweenirrigation events.
0.10
b
2.8.
0.08
-
Data from the 25 cell wick samplerswere noninteracting,
providingsamplesrepresentative
of the nativesoilfluxthrough
eachregion.The cellswere physicallyseparatedandanylateral
flowthroughthe soilwasunlikelybecausethe abilityto take up
water in the wick is largecomparedto the soilwater fluxes.For
example,the saturatedhydraulicconductivityof the wick is 800
cm/h [Knutsonand Selker,1994];for a sandyloam it is 4.4 cm
0.06
•)
0.04 -
._
E
ß
0.02
ß
-
ßß
0.00
h-•, for a sandyclayloamit is 1.3cmh-•, for a siltloamit is
0.45cmh-•, andfor a siltyclayloamit is0.07cmh-• [Carsel
ßß ß
-
10
i
t
15
20
25
Time (days)
Figure 3. Example breakthroughcurvesfor a cell: (a) orchardsite (cell 22 in gravitysamplerin E5) and (b) Freeville
site (cell 11 in wick samplerin El).
tive-dispersive
equationcouldnot describesoluteflow through
macroporesat thesesites.Figure 3a is a typicalbreakthrough
curveat the orchardand Willsborosites.Thesetypesof curves
can be representedby a model in which the soluteis distributed in a surfacelayer to the macropores[Steenhuiset al.,
1994].Figure3b is an exampleof a breakthroughcurvefor the
Freeville and Delaware sites.Fitting the datawith CXTFIT for
the Freeville and Delaware sitesrequiresthe assumptionthat
a variablewater applicationrate canbe replacedby the cumulative drainage.Wierenga[1977] showedthat this assumption
was valid. CXTFIT cannot estimate pore volumes directly.
Therefore the followingprocedurewas used:A pore volume
was estimatedand used as input for the CXTFIT, which returned a retardationfactor. To obtain the actualpore volume
(P v), the estimatedpore volumewasmultipliedby the calculated retardationfactor. The travel time (T) to the sampler
was found
as
r =
Pv
qavgA
Frequency Distributions
and Parrish,1988].Although the mathematicalanalysisof the
flow pattern abovethe wick is very complicated,it is obvious
from the analysisof Rimmetet al. [1995]that for homogeneous
soilswhen the ratio of flux to the conductivityof the wick is
large,the disturbancein flowis small.The gravitypan samplers
form capillaryfringe above the sampler and, as we will see
later, the assumptionof noninteractingis not valid anymore.
Only for the siltyclayloam the flux-conductivity
ratio couldbe
closeto 1. In this case the soil is not homogeneousand the
water movementtakesplacethroughthe more permeablesoils
betweenthe densepeds.The densepedspreventany sideways
flow. For this reason,gravitypan and wick samplersgive the
sameresult for these silty clay soils.
Normal and lognormal distributionswere consideredbecausethey are usedmostfrequentlyfor describingthe spatial
variabilityof soil and water transportproperties[Rao et al.,
1979].Goodness-of-fittestswere appliedto the grid pan sam-
plerdatato characterize
the spatialvariabilityof Vs,D, qavg,
qd, qh, Cd, andCh. A )(2analysis
wasusedto testtwonull
hypotheses,
Ho: (1) The observations
were drawnfrom a populationwith a normaldistribution,N(/•, o-), and (2) the observations
were drawnfrom a lognormaldistribution,In N(/•,
o-).TheX2analysis
isa comparison
between
theactualnumber
of observationsand the expectednumber of observationsaccording to the hypothesizeddistribution, as measured in a
selected set of intervals [Snedecorand Cochran, 1967]. A
smaller
)(2valuemeansthatthedatamoreclosely
approach
the
selecteddistribution.The numberof degreesof freedomis the
number of classintervalsreducedby 3. Note that a fit of the
(•)
actual data to the normal
distribution
does not exclude the fit
of the natural logarithm of the actual data to the normal
whereqavgis the average
waterfluxoverthe durationof the distribution, and vice versa.
The maximumpossiblesamplesize(n) was 100 (four samexperimentandA is the area of the cell. Finally,the average
solutevelocitywas calculatedas
plerswith 25 cellseach). When pan samplertypesor tillage
BOLL
ET AL.: FREQUENCY
DISTRIBUTION
OF TRANSPORT
PARAMETERS
2659
Table 2. Selection
of Data Setsfor X2 Analyses
Experiment
Total Data Set
Subset1
Subset2
Subset3
Delaware 1
Delaware 2
Freeville 1
Freeville 2
Orchard
4 wick
4 wick
2 wick, 2 gravity
2 wick, 2 gravity
2 wick, 2 gravity
4 wick
1 wick in RT*
1 wick in RT*
2 gravity
2 gravity
1 wick, 1 gravityin
mossplot
2 wick in CT plot
1 wick in WC
1 wick in WC
.-.
.-.
...
Willsboro
2 wick in PM1, PM2
2 wick in PM1, PM2
2 wick
2 wick
1 wick, 1 gravityin
grassplot
2 wick in NT plot
...
Subsetswere basedon tillage treatment or samplertype. Wick, wick pan sampler;gravity,gravitypan
sampler;PM, poultrymanure;RT, ridge tillage;WC, winter cover;NT, no-till; CT, conventionaltillage.
*Insufficientdata for analyses,samplesize <25.
treatmentswere different,the data were analyzedwith both
the maximumpossiblesampleSizeand the appropriatesubset(s)(Table 2). More specifically,
in E1 and E2, in Freeville,
datafrom all four samplersand, separately,data from wick and
gravitypan samplerswere analyzed.In E3 and E4, in Delaware, data from all four plots (poultry manure (PM1 and
PM2), ridge tillage (RT), and winter covercrops(WC)) and
from one subset(PM1 and PM2) were tested.Data from the
RT and WC plotscouldnot be analyzedasa subsetbecauseof
low samplesize(n < 20-30). In E5, in the orchard,datafrom
all four samplerswere analyzed and subsetswere based on
managementpractice,one wick pan and one gravitypan sampler for eachplot. In E6, at Willsboro,subsetswere createdby
tillage treatment: two wick pan samplersin the NT plot and
two in the CT plot (Table 2).
Throughoutthe sections3 and 4 the followingconventionis
average
watercontent.
TheX2values
fortheVs,D, qavg,
and
samplesize are shownin Table 3. In general,the data fit the
lognormaldistributionin more casesthan the normal distribution. Specifically,in experimentsE1 and E2, at Freevilleon the
silt loamsoil,vs,D, andqavgfit the lognormaldistribution
(lowestX2) underintermittentrainfall(El) and the normal
distributionundercontinuousrainfall (E2), althoughnot in all
casessignificantat the 5% level. A trend similar but lessdistinct canbe seenfor experimentsE3 andE4 for the sandyloam
soilin Delaware.Experiment
E3, whichhadthelowX2 values
for the lognormaldistribution,took place during the summer
with high amountsof (intermittentartificial) rainfall. In contrast, experiment E4, for which the parameterswere more
normallydistributedthan for E3, occurredduringthe winter,
when there wasless(and more uniform) rechargeunder natural rainfall conditions.Table 3 also showsthat for experiused:If the X2 analyses
showedthat the maximumpossible mentswhere the irrigationwater was applied daily (experisamplesizehad the sametypeof distributionasthe subset(s), mentsEl, E3, and E5), qavgwas lognormally
distributed;
the overallresultsare presented.Otherwise,if the distributions however,note that the differencebetweennormalityand logwere different, the subsetsare displayed.
normalitywas lessfor lighter-texturedsoilsthan for the more
clayeysoils.
3.
3.2. Xz TestsAppliedto ParametersMeasuredDaily
Results
In experimentsEl, E3, and E5 samplebottleswere collected
TheX2of thespatialfrequency
distribution
aregivenfor the
parametersetsthat are averagedover either the experimental daily.Changesin the frequencydistributionof the dailywater
period, day, or (several)hours.First, the "experimentalaver- flux, qa, and daily bromide concentration,Ca, are illustrated
for experimentswith wick pan sampler1 of experimentE1 in
aged" spatialfrequencydistributionsare presented.
Figure 4. The qa and Ca in the 25 cellsof wick pan samplers
3.1. Xz TestsAppliedto ParametersAveragedOverthe
are shownfor days4, 10, and 19. On day4, Ca varied strongly
Experimental Period
within the sampler.Note that in Figure 1 the cell in the middle
Solutevelocity(vs), dispersion
coefficient(D), andaverage of the samplerwith high concentrationis likely causedby a
waterflux(qavg)areproperties
describing
the average
water pore directlyconnectedto the surface.On day 10, when the
and solutetransportin each cell over the whole experimental peak concentrations
in the sampleroccurred,the spatialvariperiod. Note that the solutevelocitywas derivedfrom the ation of Ca had decreasedconsiderably.The middle cell with
concentrationdata and not by dividingthe averageflux by an the high concentrationon day4 hason day 10 a concentration
Table3. Results
of X2 Testof Goodness-of-Fit
of theNormalDistribution,
Applied
to v•, In v•,D, InD, qavg,
andIn qavg
Experiment
Delaware 1, wick (n = 50)*
Delaware 2, wick (n = 43)
Freeville 1, wick (n = 50)
Freeville 1, gravity(n = 47)
Freeville 2, wick and gravity(n = 72)
Orchard,wick and gravity(n = 100)
Willsboro,wick (n = 100)
Vs
In Vs
D
In D
13.17(7)
25.0?(7)
16.1(7)
109 (6)
18.4(5)
............
............
9.5?(7)
18.07(7)
8.6?(7)
14.3 (6)
37.8(5)
48.7 (7)
16.5(7)
64.1 (7)
320 (6)
11.97(6)
10.17(7)
12.47(7)
25.3 (7)
11.97(6)
44.5 (6)
Observedfrequenciesin each classintervalwere made the same;degreesof freedom are givenin parentheses.
*n, samplesize.
?Null hypothesisis acceptedat the 0.05 level [Snedecor
and Cochran,1967].
qavg
14.2(7)
9.5?(7)
22.0 (7)
34.8 (7)
9.7?(7)
77.3 (7)
45.9 (9)
In qavg
9.17 (7)
13.97(7)
11.57(7)
3.5? (7)
20.3 (7)
4.2?(7)
13.07(9)
2660
BOLL ET AL.: FREQUENCY DISTRIBUTION
OF TRANSPORT PARAMETERS
Day 4
800
400
200
::::::::::::::::::::::::::::::::::::
...
Frontof sampler
Frontof sampler
Day10
Day10
===============================================================
:::::
.-'[•5:::•:J:i
-'"•{:::•:
' •:::i •: :::::::::::::::•:::::
':::::
:::•::::: ===============================================
• ::::i:il•g5'::::•
.::::
-
Frontofsampler
Frontofsampler
Day19
Day19
• 600
,.. 800
•
•:.-!:½
.'"
•200..i,<i•-•!:!:
.'...........
!•,'•:::::::::::::::::::::::::
Frontofsampler
Frontof sampler
Figure4. Dailywaterflux(qa) andbromideconcentration
(Ca) for 25 cellsin wickpansampler1 for days
4, 10, and 19 in experiment1 (El).
that is relativelylower than the remainingcells: Solute-free
rainwaterwasnowcarriedthroughthe samesurfaceconnected
macropore.Towardsthe endof the experiment(day 19), bromide concentrationswere low and the spatial variation was
samplers.The gravitypan samplers(Figure 6) showeda different distributionthan the wick pan samplers.The wick pan
samplerscollectedall of the water and more than 80% of the
bromidemass.Thegravitypansamplers
hadrecoveries
of less
less.The spatialdistribution
of dailywaterflux,qd, did vary than 50% for water and bromide,indicatinghorizontalmovemuchlessthan the solutespatialdistributionof the concentra- ment (and bypassflow) in the capillaryfringeabovethe samtions. For example,the front most left cell alwayshad the plers.As will be more clearlater, gravitypan samplerscannot
be usedin sandysoilsfor collecting
samples.
For experiment
highestflux.
in thesubsoil
(Figure8), qa always
fit
ßFigures
5-8 showthe)(2valuesforq•tandCa asa function E5 withthemacrop0res
distribution,
whileforCdthe)(2testindicated
a
of timefor El, E3 (subset
PM1 andPM2), andE5. The )(2 thelognormal
valuesbelowthe horizontalline are significantat the 5% level. fit to both the normal and lognormaldistribution.The latter
sizes
forCa,because
some
of th•
The trendsobservedin Figure4 are confirmedby the analysis maybedueto lowSample
withthelowconductivity
pedsdidnotcollect
in Figure 5. While the daily flux, qa, fitted the lognormal cellsin contact
distributionbestthroughoutthe experimentalperiodfor all enoughsamplefor chemicalanalysis.
three experiments,the spatialdistributionof the daily solute
concentrations,
Ca, changedin time andbetweenexperiments. 3.3. X2 TestsAppliedto ParametersMeasuredHourly
For the three experimentsEl, E2, and E6 sampleswere
For experiments
E1 and E3, whichusedthe wick samplerson
the light texturedsoil,the solutedistributionclearlyfitted the collectedat intervalsOflessthan a dayfor at leastpart of the
normaldistribution
whenthe peakconcentrations
occurred, experiment.The distributionsfor E6 and E1 are the most
whichwasaroundday 11 in the E1 (Figure6) and day4 in the interestingand the resultsare shownbelow.
PM plotsin E3 (Figure7) [Boll,1995].Beforeandafterthe
For experiment
E6 in Willsboro
withconventional
tilled
peakConcentration,
the Ca'sof E1 andE3 fittedthelognormal (CT) andtheno-till(NT) plots,Table4 liststhe)(2goodness•
distribution
better than the normal distribution
for the wick
of-fitof thenormalandlognormal
distribution
of hourlywater
BOLL ET AL.: FREQUENCY
DISTRIBUTION
OF TRANSPORT
PARAMETERS
2661
lOO
lOO
O >100
90
O
ß
Br
Flux
8o
(a)
90
o
80
0.05 level
70
o
0
0.05 level
50
o
30
o o o
40
o
ß
O
20
lO
OoO
o
ß
o
30
o
20
ßo
ß ß ß •ee ©
ø¸oß
ß
lO
o¸
i
Flux
60
50
4o
cI
ß
70
oooo
60
(a)
¸
o
I
lOO
i
i
lOO
o
In
Br
ß
In Flux
90
80
--
(b)
0.05 level
90
¸
In CI
80
ß
In Flux
70
70
60
60
50
50
40
40
30
30
20
20
0.05 level
O,•,•ch
ß
v
jj
lO
- _
•O•e©
o
Oe•
lO
o
i
(b)
-
ß
i
0
5
O¸
ßeoi
i
o o
i
5
ß
ß
10
i
i
15
20
Time (days)
Time (days)
Figure5. Resultsof )(2 testsfor goodness-of-fit
of the (a)
Figure7. Resultsof )(2testsfor goodness-of-fit
of the (a)
normaland(b) lognormaldistributions
to dailywaterflux (qd)
normaland (b) lognormaldistributionsto dailywater flux (q•)
and dailybromideconcentration
(Cd) versustime for wick and to daily chlorideconcentration(C•) versustime for wick
samplersin experiment3 (E3).
samplersin experiment1 (El).
flUX,qh, and hourlyconcentration,Ch, of chlorideand nitrate. showedextensivepreferentialflow,especiallyin the layerfrom
Chloride was applied the day before the water application, 30 to 60 cm. In a soilwith macroporeflow, qh fits the lognorNO 3wasapplied3 monthsearlier.Previousexperimentsat the mal distribution better than the normal distribution. As exsame site [Shalitand Steenhuis,1996; Steenhuiset al., 1990] pected, lognormalityof qh in the NT plot was much more
lOO
lOO
O>100
90
80
70
-I
0 Br
level
ß0.05
Flux
ßo
--
_
60
50
.
o
40
ß ß0
30
_
lO
ß
•o •
ß
ß
0
mossplot:[]
80
ß
ß
70
o
Br ß
--
Flux
0.05 level
ß
60
ß
50
0
ß
ß
ß
40
O
o
_•
o
o
o
o
ß
20
o
lO
o
o
lOO
lOO
0 InBr
90
80
grass
plot:
O Br ß Flux(a)
90
30
ß
20
(a)
ß
--
(b)
o cDC•]
00
i
[]o []0 •0 o
i
70
70
60
60
50
50
40
40
30
30
20
20
lO
lO
o
o
i
0.05 level
ß
o•--o
ßo
o
© •o
-,
_
0
Time (days)
o00
i
80
level
Figure6. Resultsof )(2testsfor goodness-of-fit
of the (a)
ß
grass
plot:
0
Brß InInFlux
Flux
(b)
mossplot:
[] In
InBrß
90
In Flux
0.05
[]
o
5
10
15
20
Time (days)
Figure 8.
Resultsof X2 testsfor goodness-of-fit
of the (a)
normal and (b) lognormaldistributionsappliedto dailywater
normaland (b) lognormaldistributions
to dailywater flux (q•)
and daily bromide concentration(C•) versustime for gravity flux (q d) and dailybromideconcentration(C•) plottedversus
time for wick and gravitysamplersin experiment5 (E5).
samplersin experiment1 (El).
2662
BOLL ET AL.: FREQUENCY
DISTRIBUTION
OF TRANSPORT
PARAMETERS
Table 4. Resultsof X2 Test of Goodness-of-Fit
of the NormalDistributionfor qh, In qh, andCh, andIn Ch (C1andNO3)
in Willsboro, Experiment E6
No Tillage
ConventionalTillage
SamplingTime
After Irrigation
0 hours after 1st
2 hours after 1st
15 hours after 1st
18 hours after 1st
0 hours after 2nd
2 hours after 2nd
18 hours after 2nd
n
qh
In qh
n
C1
50
50
50
49
49
50
50
42.2
29.5
21.1
41.1
28.6
27.7
22
2.92*
1.52'
1.52'
10.8
1.71'
1.43'
1.24'
49
49
47
48
47
50
50
30.8
28.6
26.1
27.5
29.7
8.8*
4.3*
All data combined? 347 214.6 11.2'
340 152.8
In C1 n
NO3 In NO3 n
qh
In qh n
8.0*
3.4*
4.7*
3.9*
13.3
4.0*
3.8*
6.3*
16.9
21.1
9.2*
11.7
26.2
27.8
2.8*
9.1'
12.3
3.1'
6.8*
8.5*
11.6
12.8
11.5
27.6
38.7
51.9
29.3
11.6
22.8
12.2
12.4
14.7
5.4*
7.7*
8.5*
12.4' 327 103.2
24.5
49
50
49
30
49
50
50
38
43
47
39
50
48
50
315 113.4 28.3
38
43
43
39
49
48
50
C1
6.2*
5.7*
2.1'
3.9*
10.8
7.7*
2.6*
In C1 n
23
9.9
15.4
13.2
3.1'
11.8
8.0*
310 10.1' 59.1
38
43
47
29
49
48
50
NO3 In NO3
6.0*
4.0*
7.1'
2.6*
4.8*
3.6*
1.2'
5.3*
1.8'
3.5*
1.2'
5.4*
4.8*
2.6*
305 23.2
6.8*
Expectedfrequenciesin eachclassintervalwere madeequal;degreesof freedom- 4; n, samplesize.
?Degreesof freedom = 9.
*Null hypothesis
is acceptedat the 0.05 level [Snedecor
and Cochran,1967].
significant
(asindicated
bythelowerX2values)thanin theCT wasacceptedat the 0.05 level are marked.For the gravitypan
plot. Nitrate that wasdistributedthroughoutthe profileat the sampler,qh clearlyfit the lognormaldistribution,while qh of
•fit thelognormal
distribution
in the
time of the experiment3 monthsafter applicationalsoshowed thewickpansamplers
samplesthat representthe irrigationevent itself. In the cona lognormal distribution.
For chloride the concentrationCh fit the lognormaldistri- sequentsamplingrepresentingthe drainagephasethe spatial
butionin the no-till (NT) plot andfit the normaldistributionin frequencydistributionfor the flux becomesmore normally
the conventional
tilled (CT) plot. Similarly,for NO3, the Ch fit distributedfor the wick samplersbut not for the gravity pan
more closelythe lognormaldistributionin the NT plot. In the samplers.It is likely that macroporesare significantcontribuCT plot, however,Ch fit the normalandlognormaldistribution tors during the irrigation event (hence a lognormaldistribuequallywellwhendataof eachsamplingintervalwereanalyzed tion). During this drainagephasethe matrix flow dominates
separately.
ForthelattertheX2testwasnotverystrong
(Table and one would expecta more normal distribution.The gravity
4). Previousexperiments
on thesetypesof soils[Steenhuis
et
pan samplersdo not showthistrend becauseof their inability
al., 1994]haveshownthat the plow layer actsas a distribution
zone that equalizesthe concentrations
and funnelswater and
solutesinto the macropores.This type of processcan be describedby a linear reservoirthat is mathematicallyequivalent
to a well-mixedreservoir.The no-till plot doesnot have sucha
well developeddistributionzone. Intensivemixingin the distribution layer leads to a normal distributionas will be dis-
to collect matrix flow.
cussed later.
The two gravityandwick samplersfor the experimentEl, at
Freeville, are usedto highlightthe differencesin gravityand
4.
Discussion
Unlike earlier research in which usually only parameters
that averagedthe properties over the experimentalperiod
were analyzed,this studyshowsthat the spatialdistribution
patternsare complexandvaryin time andbetweensoiltypes.
Despitethis,somegeneralizations
canbe made:When macropore flow dominates,the spatial frequencydistributionfor
distribution
(qavg
forE5 andE6 in
wickpansamplers.
Table5 shows
theresults
of the)(2testof waterfluxfitsthelognormal
Table 3). Under matrixflow conditionsand uniformpercolation rates,waterfluxbecomesmorenormallydistributed(E2
and E4 in Table 3). Intermittent applicationslead to lognormally distributedfluxes.
The daily soluteconcentrationpatternsfollow more or less
the sametrendsas the averagewater fluxeswith the exception
Table 5. Resultsof X2 Test of Goodness-of-Fit
of the
that whenthe bulk of the solutesbreaksthrough(i.e., whenthe
Normal Distribution,Applied to Hourly Drainage Flux,
highestconcentrations
occur),the spatialdistributionbecomes
qh, and In qh of Wick and GravityPan Samplersin the
normal. The concentrationfindings are in accordancewith
Freeville 1 Experiment15 Days After Start of Application
findingsof Germann[1988, 1991] and Germanand DiPietro
Gravity Pan Sampler
Wick Pan Sampler
[1996],who statedthat for any type of diffusivetransporta
minimum mixing length, L, is needed to apply theoretical
Time After
qh,
In qh,
qh,
In qh,
equation.If L is far
Irrigation
n mLh- • mLh- • n mLh- • mLh- • equationssuchasthe convective-dispersive
smallerthan the depth of the sampler,one expectsa normal
4 hours after 1st
50
23.6
8.6'
50
96.0
16.8
distributionof the flux densityof the transportmedium. We
16 hours after 1st 50
17.6
53.8
2
......
can expecta small L in a homogeneoussoil with a stable
0 hours after 2nd 50
47.6
11.8'
25
35.4
6.6*
wettingfront.Field soilsare seldomhomogeneous
[Fluryet al.,
3 hours after 2nd 50
18.8
2.2*
25
31.4
5.0*
1994],and L can vary over a wide range.In situationswhere
0 hours after 3rd
50
143
16.6
42
58.9
6.6*
2 hours after 3rd
49
13.2'
6.1'
35
17.8
7.0*
there are many relatively small macropores, such as in
Freeville,one can expectunder steadystaterainfall a normal
Expectedfrequenciesin each classintervalwere made equal; despatial distributionfor most parameterswhen all pores are
greesof freedom = 4; n, samplesize.
*Null hypothesis
is acceptedat the 0.05level[Snedecor
and Cochran, contributing.This was the casefor E2. The L becomeslarge
for profileswith soilsthat havea smallconductivityand pores
19671.
goodness-of-fit
of the normal and lognormaldistributionfor
hourlywaterflux (qh) for wickandgravitypan samplersin El,
startingat 15 daysafter the tracer application.TestswhereHo
BOLL ET AL.: FREQUENCY
DISTRIBUTION
goingdirectlyfrom the surfaceto the sampler.The no-till plot
at Willsboro and the moss-coveredplot in the orchard are
examples.At these sitesthe densematrix prevent any intermixing and we found that a lognormaldistributionfitted the
daily concentrationdata best. The other treatments at the
sametwo sites,grassand conventionaltillage,were characterizedby a distributionlayerat the surfacewherethe solutesand
water are funneled in the macropore.Becausethe soluteparticles travel along different length streamlinesto the macropores in the subsoil,this is equivalentto intensivemixing
[Gelhatand Wilson,1974] and a smallL.
Another aspect that affects L is the water application
method. For short high water pulses, such as those for
Freeville, in experimentEl, and for Delaware, in experiment
E3, the depthsoverwhichcompletemixingtake placeis longer
than for steadystate conditions.An explanationwhy can be
derivedfrom the early works of Laweset al. [1882], who reported that profiles drain from the top down through the
macropores.Thus drainagegivesa few poresthe opportunity
to drain the water and solutesfrom the surfaceto the sampler.
This concentrationis higher initially shortlyafter application
than the matrix flow. Figure 4 showsthisvery well for the cell
in the middle. Under steady state recharge conditions in
Freeville (E2) there is no drainagephaseand natural rainfall
conditionsduringthe winter in Delaware (E4) the amountof
dailyrainfallis smalland consequently
drainageeffectsare less.
OF TRANSPORT
PARAMETERS
2663
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1984.
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Gelhar, L. W., and J. L. Wilson, Ground water quality modeling,
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Zone, edited by P. J. Wierenga and D. Bachelet, pp. 111-119, Int.
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1990.
Ireland, W., Jr., and E. D. Matthews, Soil Surveyof SussexCounty,
Delaware, U.S. GovernmentPrinting Office, Washington,DC, 1974.
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5.
Conclusions
differentwater applicationrates after soluteapplication.The Knutson,J. H., and J. S. Selker, Unsaturatedhydraulicconductivities
resultsof this studysuggestthat thesewater and solutetransof fiberglasswicksin designingcapillarywick pore-water samplers,
Soil Sci. Sac. Am. J., 58, 721-729, 1994.
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Compositionof the Rain and DrainageWaterCollectedat Rothamplacein all pore spaces(i.e., the mixinglengthwassufficiently stead,Williams Clowesand Sons,Ltd., London, 167 pp., Originally
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311-350;XVIII (1882), 1-71, 1882.
appropriatefor describingthe distributionof water and solute
Merwin, I. A., W. C. Stiles,and H. M. van Es, Orchard ground cover
transportproperties.
Under no-till, water flux and the concentration of chloride
applieda day prior to irrigationwere lognormallydistributed,
while the presenceof a tillage layer causedchlorideconcentration to be normally distributedand water flux lesssignificantlylognormal.Under transientconditions,frequencydistributions of daily tracer concentrationwere not constantover
time. Shortly after tracer application,when solute transport
through macroporesoccurred,tracer concentrationwas lognormally distributed. When the bulk of the solutes broke
through,tracer concentrationbecamenormallydistributed.In
contrast,water flux remained lognormally distributed at all
times.Finally,when pan samplerscollectedwater mainlyfrom
macropores,water flux was lognormallydistributed.On the
other hand, when matrix poreswere sampled,the water flux
best fit the normal
distribution.
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PARAMETERS
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(e-mail:tssl@cornell.edu)