1.1 curso de hydrus 1d
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Table of Contents
Lecture 1: Vadose zone flow and transport modeling: An overview. 3
Lecture 2: The HYDRUS-1D software for simulating one-dimensional variably-
saturated water flow and solute transport. 33Computer Session 1: HYDRUS-1D: Infiltration of water into a one-dimensional soil
profile. 37
Lecture 3: On the characterization and measurement of the hydraulic properties ofunsaturated porous media. 43
Lecture 4: Application of the finite element method to variably-saturated water flow and
solute transport. 59
Computer Session 2: HYDRUS-1D: Water flow and solute transport in a layered soil
profile. 65
Lecture 5: Inverse modeling. 77Computer Session 3: HYDRUS-1D: One- or multi-step outflow experiment. 89
Lecture 6a: Application of the finite element method to 2D variably-saturated water flow
and solute transport. 95
Lecture 6b: HYDRUS (2D/3D) software for simulating two- and three-dimensional
variably-saturated water flow and solute transport. 99
Computer Session 4: HYDRUS (2D/3D): Subsurface line source. 109
Computer Session 5: HYDRUS (2D/3D): Furrow infiltration with a solute pulse. 119
Computer Session 6: HYDRUS (2D/3D): Flow and transport in a transect to a stream.125
Computer Session 7: HYDRUS (2D/3D): Three-Dimensional Water Flow and Solute
Transport. 135
Lecture 7: Preferential and Nonequilibrium Flow and Transport. 143Computer Session 8: HYDRUS-1D: Nonequilibrium Flow and Transport. 155
Lecture 8: Coupled movement of water, vapor, and energy. 161Computer Session 9: HYDRUS-1D: Coupled movement of water, vapor, and energy.167
Lecture 9: Multicomponent biogeochemical transport modeling using the HYDRUS
computer software packages;Introduction to the HP1 code, which was obtained
by coupling HYDRUS-1D with the PHREEQC biogechemical code. 173Computer Session 10: Application of HP1 to a simple solute transport problem
involving cation exchange. 187
Lecture 10: Other applications and future plans in HYDRUS development. 195
References 207
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Contents-1
VadoseZoneFlowandTransportModeling:AnOverview
IntroductiontoHY
DRUS-1D,itsFunctionsandWindows
ComputerSession1:Infiltrationinto1DSoilProfile
UnsaturatedSoilH
ydraulicProperties,RETCandRosett
a
NumericalSolution
sfor1DVariably-SaturatedFlowand
SoluteTransport
ComputerSession2:TransientWaterFlowandSolute
TransportinaLayeredSoilProfile
ParameterEstimationandInverseModeling
ComputerSession3:InversemodelingOne-orMulti-step-
OutflowMethod
Contents-2
2D/3DNumericsforVariably-SaturatedFlowan
dTransport
IntroductiontoHYDRUS(2D/3D),itsStructure
and
Windows
Computer
Session4:InfiltrationfromSubsurfaceSource
Computer
Session5:FurrowIrrigationwithaSolutePulse
Computer
Session6a:WaterFlowtoaStream
Computer
Session6b:SolutePlumeMigratingtoaStream
Computer
Session7:3DWaterFlowandSolute
Transport
OtherTop
ics,OpenSession
Contents-3
PreferentialandN
onequilibriumFlowandTransport
ComputerSession
8:NonequilibriumFlowandTransport
CoupledMovementofWater,VaporandEnergy
ComputerSession
9:CoupledWater,VaporandEnergy
Transport
BiogeochemicalTransport-IntroductiontoHP1(couple
d
HYDRUS-1Dand
PHREEQC)andUNSATCHEM
ComputerSession
10:ApplicationofHP1toCation
Exchange
OtherApplication
s,FuturePlans
OpenSession
VadoseZoneFlowandTransport
Modeling
AnOverview
Jirk
aimnek1andRienvanGenuch
ten2
1DepartmentofEnvironmentalSciences
UniversityofCalifornia,Riverside,CA
2DepartmentofMechanicalEngineerin
g,
FederalUniversityofRiodeJaneiro,Br
azil
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Agricultural
Applications
Precipitation
Irrigation
Runoff
Evaporation
Transpiration
RootWaterUptake
CapillaryRise
DeepDrainage
Fertigation
Pesticides
Fumigants
Colloids
Pathogens
Industria
landEnvironmentalApp
lications
Control
Planes
SourceZone
Observationwells
IndustrialP
ollution
MunicipalP
ollution
LandfillCovers
WasteRepo
sitories
Radioactive
Waste
DisposalSit
es
Remediation
BrineRelea
ses
Contaminant
Plumes
Seepageof
Wastewater
from
LandTreatment
Systems
Environmental
Applications H
illel(2003
)
EcologicalApps
CarbonStorageand
Fluxes
HeatExchangeand
Fluxes
NutrientTransport
SoilRespiration
Microbiological
Processes
EffectsofClimate
Change
RiparianSystems
Stream-Aquifer
Interactions
GoverningEquations
Variably-S
aturatedWaterFlow(Richards
Equation)
h
Kh
Kh
S
t
z
z
()
()
=
HeatMov
ement
SoluteTr
ansport(Convection-DispersionEquation)
p
w
w
C
T
T
qT
C
CST
t
z
z
z
()
()
=
s
c
cD
qc
t
t
z
z
(
)
(
)
=
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HYDRUSGraphical
Interface
HYDRUSGraphical
Interface
Input,Output,Meshgen
HYDRUSM
odularStructure
HYDRUS
HYDRUSMainModule
MainModule
WaterFlow
SoluteTransport
HeatTransport
InverseOptimization
EquationSolvers
SoilHydraulicProperties
PedotransferFunctions
RootUptake
HYDRU
SSoftwarePackages
WaterFlow
:
WaterFlow
:
Richardse
quationforvariably-saturatedwaterflow
Variousmodelsofsoilhydraulicproperties
Hysteresis
Sinktermtoaccountforwateruptakebyplantroots
HeatTransport:
HeatTransport:
Conductionandconvectionwithflowingwater
SoluteTran
sport:
SoluteTran
sport:
Convective
-dispersivetransportintheliquidphase,diffu
sioninthe
gaseousph
ase
Nonlinearnonequilibriumreactionsbetweenthesolidan
dliquidphases
Linearequ
ilibriumreactionsbetweentheliquidandgaseousphases
Zero-orderproduction
First-orderdegradationreactions
Physicalnonequilibriumsolutetransport
HYDRUS-R
eferences
imnek,J.,M.ejna,H.
Saito,M.Sakai,andM.Th.vanGenuchten,T
he
HYDRUS
HYDRUS--1D1DSoftwarePackageforSimulatingtheOne
One--Dimensional
Dimensional
MovementofWater,Heat,andMultipleSolutesinVariably-SaturatedMedia,
Version4.0,HYDRUSSoftwareSeries1,DepartmentofEnvironmental
Sciences,UniversityofCa
liforniaRiverside,Riverside,CA,pp.315,200
8.
imnek,J.,M.Th.vanG
enuchten,andM.ejna,TheHYDRUS
HYDRUSSoftw
are
PackageforSimulatingTwo
Two--andThree
andThree--Dimensional
DimensionalMovementofWater,
Heat,andMultipleSolute
sinVariably-SaturatedMedia,TechnicalManual
TechnicalManual,
Version1.0,PCProgress,
Prague,CzechRepublic,pp.241,2007.
imnek,J.,M.ejna,andM.Th.vanGenuchten,TheHYDRUSSoftw
are
PackageforSimulatingTwo
Two--andThree
andThree--Dimensional
DimensionalMovementofWater,
Heat,andMultipleSolute
sinVariably-SaturatedMedia,UserManual
UserManual,
Version1.0,PCProgress,
Prague,CzechRepublic,pp.161,2007.
http://www.pc-pro
gress.com/en/Default.aspx
HYDRU
S-HistoryofDevelopm
ent
Israel:Neuman[1972]-UNSAT
U.ofArizona:D
avisandNeuman[1983]
Princeton
U.:
vanGenu
chten[1978]
Agr.Univ.inWageningen:
Feddesetal.[1978]
Vogel[1987]-SWMII
MIT:Celia
etal.[1990]
US
SL-SWMS-2D
im
neketal.[1992]
USSL-HYDRUS-2D(1.0)
imneketal.[1996]
USSL-CHAIN-2D
imnekandvan
Genuchten[1994]
IGWMC-HYD
RUS
HYD
RUS--2D2D(2.0)
imneketal.[1999]
UCR,PC-ProgressHYDR
US(2D/3D)
HYDR
US(2D/3D)
imneketal.[2007]
USSL-SWMS-3D
imneketal.[1995]
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CapillaryRise
Whenasmallcylindric
alglasscapillarytubeisinsertedinawater
reservoiropentoatmosphere,waterwillriseupwardinthetube.
Lap
lace
Lap
lace
Equa
tion:
Equa
tion:
2
cos
H
gR
=
surfacetension
contactangle
bulkdensityof
water
ggravitationalacceleration
Rcapillaryradiu
s
Hcapillaryrise
Retention
Curve
Soil-waterch
aracteristiccurve
-characterizestheenergystatusofthesoilwater
RetentionCu
rve
Soil-watercharacteristiccurve
Characterizestheenergy
statusofthesoilwater
0100
200
300
400
500
0
0
.1
0.2
0.3
0.4
0.5
WaterContent[-]
|Pressurehead|[cm]
Loam
Sand
Clay
WaterF
lowinSoils
Groundwaterflow(DarcysLaw)
(
)
s
s
P
z
dH
q
K
K
L
dz
+
=
=
Unsaturatedwaterflow(Darcy-Buckingh
amLaw)
(
)
()
()
h
z
dH
q
Kh
Kh
L
dz
+
=
=
H-sumofthematric(h)andgravitational(z)head
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WaterFlow-
RichardsEquation
Thegoverningflowequationforone-dimensionalisothermal
Darcianflowinavaria
bly-saturatedisotropicrigidporous
medium:
-volumetricwatercontent[L3L-3]
h
-pressurehead[L]
K
-unsaturatedhydraulicconductivity[LT-1]
z
-vertical
coordinatepositiveupward[L]
t
-time[T]
S
-rootwateruptake[T-1]
()
()
()
()
h
h
=
Kh
+Kh
Sh
t
z
z
()
()
h
q
=
Sh
t
z
WaterF
low-RichardsEquation
()
()
()
A
A
ij
iz
i
j
h
h
=
Kh
K
+K
Sh
t
x
x
Thegovernin
gflowequationfortwo-dimensionalis
othermal
Darcianflow
inavariably-saturatedisotropicrigid
porous
medium:
-volumetricwatercontent[L3L-3]
h
-pressurehead[L]
K
-unsaturatedhydraulicconductivity[LT-1]
KijA-componentsofaanisotropytensor[-]
xi
-spatialcoordinates[L]
z
-verticalcoordinatepositiveupward[L]
t
-time[T]
S
-rootwateruptake[T-1]
RetentionCu
rve,
(h)
Soil-watercharacteristiccurve
Characterizestheenergy
statusofthesoilwater
0100
200
300
400
500
0
0
.1
0.2
0.3
0.4
0.5
WaterContent[-]
|Pressurehead|[cm]
Loam
Sand
Clay
Hydrau
licConductivity,K()
-characteriz
esresistanceofporousmediatowater
flow
-10-8-6-4-2024
0
0.1
0.2
0.3
0.4
0.5
WaterContent[-]
log(HydraulicConductivity)[cm/d]
Loam
Sand
Clay
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HydraulicConductivity,K()
Unsa
tura
tedhy
drau
liccon
duc
tiv
ity
decreasesasvo
lume
tricwa
terconten
t
decreases:
Cross-sec
tiona
lareaof
wa
ter
flow
decreases
Tortuos
ity
increases
Drag
forces
increase
Thus,
theunsa
tura
tedhyd
rau
liccon
duc
tiv
ity
isanon
linear
func
tionof
an
dh
.
Hydrau
licConductivity,K(h)
-characteriz
esresistanceofporousmediatowater
flow
-10-8-6-4-2024
0
1
2
3
4
5
log(|PressureHead|[cm])
log(HydraulicConductivity[cm/d])
Loam
Sand
Clay
RetentionCurve
BrooksandCorey[1964]:
vanGenuchten[1980]:
Kosugi[1996]:
s-saturatedwatercontent[-]
r-residualwaterconten
t[-]
n,h0,-empiricalpar
ameters[L-1],[-],[L],[-]
Se-effectivewatercontent[-]
11/
1
(1
)
e
n
n
S
h
=
+
-
-1/
|
|1
-1/
n
e
h
h
S
h
q=?
Tiledrains
Tiledrains
Bounda
ryConditions(System-Dependent)
Imperm
eablelayer
Soilsurface
Tiledrain
Groun
dwatertable
1DsoilprofileE
P
Drain
age
TheHYDRU
SSoftwarePackages
Variably-SaturatedFlow(RichardsEq.)
RootWaterUptake(waterandsalinitystress)
RootWaterUptake(waterandsalinitystress)
SolutesTransp
ort(decaychains,ADE)
-NonlinearS
orption
-ChemicalN
onequilibrium
-PhysicalNo
nequilibrium
HeatTranspor
t
PedotransferF
unctions(hydraulicproperties)
ParameterEstimation
InteractiveGraphics-BasedInterface
HYDRUS(2D/3D)andAdditionalModules
RootW
aterUptake
Feddesetal.[
1978]
01
Tp
=1mmd
-1
PressureHead,h
[L]
h1
h2
h3high
h3low
h4
Tp
=5mmd
-1
StressResponseFunction,[-]
01
Tp
=1mmd
-1
PressureHead,h
[L]
h1
h2
h3high
h3low
h4
Tp
=5mmd
-1
StressResponseFunction,[-]
(
)
()
(
)
()
(
)
(
)()
p
p
p
p
S
z,t=bzT
Sz,t=
hS
z,t
h
bzT
=
b
normalizedwateruptakedistribution[L-1]
Sp
potentialrootwateruptake[T-1]
S
actualrootwateruptake[T-1]
Tp
potentialtranspiration[LT-1]
stressresponsefunction[-]
x
z
R
S
Ta
Lt
b(x,z
)
x
z
R
S
Ta
Lt
b(x,z
)
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StressResponseFunctions
Waterandsolutestr
ess:
1
2
50
50
50
1
(,)
1 1
1
(,
)
1
1
p
p
p
hh
h
hh
hh
h
h h
h
=
+
+
=
+
+
stressresponsefunction[-]
h
pressurehead[L
]
hf
osmotichead[L]
h50
pressureheadat
whichwaterextractionrateisreducedby50%
[L]
h50
dittoforosmotic
head[L]
p1,p2
experimentalcon
stants[-](=3)
Transp
irationRates
(,)
(,)
(,)()
R
R
R
p
p
L
a
p
L
L
T
S
hzdz
T
Shzdz
T
ahzbzdz
=
=
=
b
normalizedwateruptakedistribution[L-1]
stressresponsefunction[-]
Sppotentialrootwateruptake[T-1]
S
actualrootwateruptake[T-1]
Tp
potentialtranspiration[LT-1]
Ta
actualtranspiration[LT-1]
SpatialRootD
istributionFunction
(
)
*
*
,
1
1
z
r
m
m
m
m
p
p
z
z
x
x
Z
X
z
x
bxz
Z
X
e
+
=
(
)
*
*
*
,,
1
1
1
y
x
z
m
m
m
p
p
p
x
x
y
y
z
z
X
Y
Z
m
m
m
x
y
z
bxyz
e
X
Y
Z
+
+
=
(Vrugtetal.,2001)
RootG
rowth
0
0
0
()
()
()
(
)
R
m
rt
m
L
t
Lft
L
ft
L
L
Le
=
=
+
LR
rootingdepth[L]
L0
initialrootingdepth[L]
Lm
maxim
umrootingdepth[L]
f
rootgr
owthcoefficient(Verhulst-Pearllogist
icfunction)
r
growth
rate[T-1]
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TheHYDRU
SSoftwarePackages
Variably-Satur
atedFlow(RichardsEq.)
RootWaterUptake(waterandsalinitystress)
SolutesTransport(decaychains,ADE)
SolutesTransp
ort(decaychains,ADE)
--NonlinearS
orption
NonlinearS
orption
--ChemicalN
onequilibrium
ChemicalN
onequilibrium
--PhysicalNo
nequilibrium
PhysicalNo
nequilibrium
HeatTransport
PedotransferF
unctions(hydraulicproperties)
ParameterEst
imation
InteractiveGraphics-BasedInterface
HYDRUS(2D/3D)andAdditionalModules
SoluteT
ransport-Convection-Dispersio
nEquation
One-dimensionalchemicaltransportduringtransientwater
flowinavariablysaturatedrigidporousmedium
c
-solutionconcentration[ML-3]
s
-adsorbedconcentration[MM-1]
-watercontent[L3L-3]
-soilbulkdensity[ML-3]
D
-dispersioncoefficient[L2T-1]
q
-volumetricflux[LT-1]
-rateconstantrepresentingreactions[ML-3T-1]
()
(
)
c
s
cD
qc
t
t
z
z
=
GeneralStructureoftheSystemofSolutes
HYDRU
SSoluteTransport
Radion
uclides:238Pu->234U->230Th->226Ra
Nitroge
n:(NH2)2CO->NH4+->NO2-->NO3-
Pesticid
es:aldicarb(oxime)->sulfone(sulfoneoxime)->sulfoxide(sulfoxide
oxime)
Chlorin
atedHydrocarbons:PCE->TCE->c-DCE->VC
->ethylene
Pharmaceuticals,hormones:Estrogen(17bEstradiol->Estrone->Estriol),
Testosterone
Explosives:TNT(->4HADNT->4ADNT->TAT),RDXH
MX
Transportofsingleions
Transportofmultipleions(sequentialfirst-orde
rdecay)
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GoverningSo
luteTransportEquatio
ns
(
)
(
)
c
s
cD
qc
t
t
z
z
=
'
'
'
'
,
,
,
,
,
,
1
1
'
'
1
1
1
1
,
,
,
,
(
)
(
)
(
)
(2,)
w
g
k
k
k
k
k
k
k
k
wk
wk
k
sk
sk
k
gk
gk
k
w,k
k
s,k
k
g,k
k
wk
sk
gk
rk
s
c
s
ag
c
g
qc
+
+
=
D
+
aD
-
-
t
t
t
z
z
z
z
z
-
+
c-
+
s-
+
ag+
c
+
s
-
ag
+
+
+
a
Sc
k
n
w,s,g
subscriptscorrespondingwiththeliquid,solidand
gaseousphases,respectively
c,s,g
concentratio
ninliquid,solid,andgaseousphase,
respectively
GoverningSoluteTransportEq
uations
qi
volumetricflux[LT-1]
soilbulkdensity[ML-3]
a
aircontent[L3L-3]
S
sinkterminthewaterflowequation[T-1]
cr
concentrationofthesinkterm[ML-3]
Dw,D
g
dispersioncoefficientsfortheliquidandgaseousph
ase[L2T-1],
respectively
k
subscriptrepresentingthekthchainnumber
w,s,
g
first-orderrateconstantsforsolutesintheliquid,solid,and
gaseousphases[T-1],respectively
w,s,
g
zero-orderrateconstantsfortheliquid[ML-3T-1],solid[T-1],and
gaseousphases[ML-3T-1],respectively
w',
s',
g'first-orderrateconstantsforsolutesintheliquid,so
lidand
gaseousphases[T-1],respectively;theserateconstantsprovide
connectionsbetweentheindividualchainspecies.
ns
numberofsolutesinvolvedinthechainreaction
SoluteTrans
port-BoundaryConditions
First
First--type
type(orDirichlettype)boundaryconditions
Third
Third--type
type(Cauchytype)boundaryconditions
Second
Second--type
type(N
eumanntype)boundaryconditions
0
for(
)
ij
i
N
jc
D
n=
x,z
x
0
for(
)
ij
i
ii
ii
C
jc
-D
n
+qnc=qnc
x,z
x
0
(
)
(
)
for(
)
D
cx,z,t=
cx,z,t
x,z
SoluteTransportDispersionCo
efficient
Bear
Bear[1972]:
[1972]:
7/3 2 s
=
d
D=
|q|+D
Dd
-ionicormoleculardiffusio
ncoefficient
infreewater[L2T-1]
-tortuosityfactor[-]
-longitudinaldispersivity[L]
-watercontent[L3L-3]
q
-Darcysflux[LT-1]
MillingtonandQuirk[1961]:
s
-saturatedwatercontent[-]
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SoluteTrans
port-DispersionCoefficien
t
Bear
Bear[1972]:
[1972]:
(
)ji
ij
T
ij
L
T
d
ij
qq
D=D|
q|
+D-D
+
D
|q|
Dd
-ionicormoleculardiffusioncoefficientinfreewater[L2T-1]
-tortuosityfactor
[-]
ij
-Kroneckerdelta
function(ij=1ifi=j,and
ij=0otherwise)
DL,DT-longitudinal
andtransversedispersivities[L]
2
2
2
2
(
)
x
z
xx
L
T
d
z
x
zz
L
T
d
x
z
xz
L
T
q
q
D
=D
+D
+
D
|q|
|q|
q
q
D
=D
+D
+
D
|q|
|q| q
q
D
=D-D
|q|
Disper
sivityasaFunctionofScale
Gelharetal.(1985)
TheHYDRUSSoftwarePackages
Variably-SaturatedFlow(RichardsEq.)
RootWaterUptake(waterandsalinitystress)
SolutesTransport(decaychains,ADE)
-NonlinearSorption
-ChemicalN
onequilibrium
-PhysicalNonequilibrium
HeatTransport
PedotransferFunctions(hydraulicproperties)
ParameterEstimation
InteractiveGr
aphics-BasedInterface
HYDRUS(2D/3D)andAdditionalModules
Convec
tion-DispersionEquation
Linea
rAdsorption
1
d
d
K
s
Kc
R
=
=
+
ij
i
i
j
Rc
c
D
qc
t
x
x
=
+
Kd
-distributioncoefficient[L3M-1]
R
-retardationfactor[-]
s
-solidphaseconcentration[MM-1]
c
-liquidphaseconcentration[ML-3]
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Convection-DispersionEquation
TransientTr
ansport(2D)
Steady-State
Transport(1D)
ij
i
i
j
Rc
c
D
qc
t
x
x
=
+
22
22
R
R
c
c
c
R
D
v
t
z
z
c
c
c
D
v
t
z
z
=
=
DR
-retarded
dispersioncoefficient[L2T-1]
vR-retarded
velocity[LT-1]
Nonline
arEquilibriumAdsorp
tion
Equation
Model
Reference
s=kc+k
1
2
Linear
LapidusandAmundson[195
2]
Lindstrometal.[1967]
2
1
k
s=
kc
Freundlich
Freundlich[1909]
12
1kc
s=
+
k
c
Langmuir
Langmuir[1918]
3
3
12
1
k
k
kc
s=
+
k
c
Freundlich-Langmuir
Sips[1950]
1
3
2
4
1
1
kc
k
c
s=
+
+kc
+kc
DoubleLangmuir
ShapiroandFried[1959]
2
3
1
k
/k
c
s=
kc
ExtendedFreundlich
Sibbesen[1981]
1
2
3
1
kc
s=
+kc+k
c
Gunary
Gunary[191970]
2
1
3
k
s=k
-k
c
Fitter-Sutton
FitterandSutton[1975]
4
3
1
2
{1[1
]}k
k
s=k
-
+k
c
Barry
Barry[1992]
2
1
ln(
)
RT
s=
kc
k
Temkin
BacheandWilliams[1971]
1
2
exp(2
)
s=kc
-ks
Lindstrometal.[1971]
vanGenuchtenetal.[1974]
s s
c
c
k
c
c
k
c
c
T
T
T
=
+
[
(
)exp{
(
)}]
1
2
2
modifiedKielland
LaiandJurinak[1971]
NonlinearEquilibriumAdsorption
HYDRUSassumesnonequilibriuminteractionsbetween
the
solution(c)andad
sorbed(s)concentrations,andequilibrium
interactionbetwee
nthesolution(c)andgaseous(g)
concentrationsofthesoluteinthesoilsystem.
Liquid-Solid:
ageneralizednonlinear
nonlinear
(Freundlich-Langmuir)empiricalequation
ks,,empirica
lconstants
1skc
s=
+c
TheHY
DRUSSoftwarePackages
Variab
ly-SaturatedFlow(RichardsEq.)
RootW
aterUptake(waterandsalinity
stress)
SolutesTransport(decaychains,ADE)
-Non
linearSorption
-Che
micalNonequilibrium
-Phy
sicalNonequilibrium
HeatT
ransport
PedotransferFunctions(hydraulicprop
erties)
ParameterEstimation
InteractiveGraphics-BasedInterface
HYDR
US(2D/3D)andAdditionalModules
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Non-EquilibriumAdsorptionEquations
Equation
Model
Reference
1
2
(
)
s=
kc+
k
-s
t
Linear
LapidusandAmundson[1952]
Oddsonetal.[1970]
2
1
(
)
k
s=
k
-s
c
t
Fr
eundlich
HornsbyandDavidson[1973]
vanGenuchtenetal.[1974]
12
1
s
kc
=
-s
t
+kc
La
ngmuir
Hendricks[1972]
3
3
12
1
k
k
s
kc
=
-s
t
+kc
Fr
eundlich-
La
ngmuir
imunekandvanGenuchten[1994]
1
(
)sinh
T
T
T
i
s
s
s
=
s
-s
k
t
s
s
FavaandEyring[42]
2
1
2
exp(
){
exp(2
)
}
s=
ks
kc
-ks
-s
t
Lindstrometal.[1971]
1
2
k
k
s=
c
s
t
LeenheerandAhlrichs[1971]
Enfieldetal.[1976]
NonequilibriumTwo-SiteAdsorptionModel
se
Ty
pe-1siteswithinstantaneoussorption
sk
Ty
pe-2siteswithkineticsorption
f
fra
ctionofexchangesitesassumedtobeat
equilibrium
e
k
s=s+s
(1
)
(1
)
1
k
s
k
ks
s
s
kc
=
-
-
-
+
-f
f
s
s
t
+
c
es
s
=f
t
t
Two-SiteChemicalNonequilibriumTranspo
rt
,
[(1
)
]
k
k
k
d
sk
s=
-fKc-s-
s
t
(
)
(
)
[(1
)
]
d
k
d
d
l
s,e
c
+fK
c=
D
-qc-
t
z
z
-fK
c-s-
c-fK
c
Linearsorption:
Mo
bile
Co
llo
ids,
Cc
Stra
ine
dCo
llo
ids,
Sc
str
Attac
he
dC
ollo
ids,
Sc
att
Air-Wa
ter
Interface
Co
llo
ids,
c
kac
kdc
kstrk
aca
kdca
aca
s
str
s
Air
Wa
ter
So
lid
Colloid,Virus,andBacteriaTransport
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Colloid,Virus,andBacteriaTransport
2
1
2
2
s
s
c
c
c
D
v
t
t
t
x
x
+
+
=
1
1
a
t
d
s
k
c
ks
t
=
max m
ax
max
1
t
s
s
s
s
s
=
=
kstr
-straining[T-1]
ka
-deposition(attachment)coefficient[T-1]
kd
-entrainment(detachment)coefficient[T-1]
-reductionofattachmentcoefficientduetoblockageofsorptionsites
2
str
str
s
k
c
t
=
0
c
str
c
d
x
x
d
+
=
Attachment/Detach
ment
Attachment/Detach
ment
Straining
Straining
TheHY
DRUSSoftwarePacka
ges
Variably-SaturatedFlow(RichardsEq.)
RootW
aterUptake(waterandsalinitystress)
Solutes
Transport(decaychains,ADE)
-NonlinearSorption
-ChemicalNonequilibrium
-PhysicalNonequilibrium
HeatTransport
PedotransferFunctions(hydraulicproperties)
ParameterEstimation
Interac
tiveGraphics-BasedInterface
HYDRUS(2D/3D)andAdditionalModu
les
Two-RegionPhy
sicalNonequilibriumTransp
ort
(
)
,
,
(
)(
)
m
m
d
m
m
m
m
m
im
m
wm
d
ms
m
c
+fk
c=
D
-qc
-
c-c
-
+fk
c
t
z
z
,
,
[
(1
)
]
(
)[
(
)
]
im
im
d
m
im
im
wim
d
simim
c
+
-f
k
=
c-c
-
+1-f
k
c
t
Two-RegionPhysicalNonequilibriumTransport
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Interaction
AmongPhases
Liquid-Gas:
alinear
linearrelation(HenrysLa
w)
kg
emp
iricalconstantequalto(KHRTA)-1
KH
Hen
ry'sLawconstant
R
universalgasconstant
TA
absolutetemperature
g
g=kc
Volatilization
(
)
(
)
(
)
w
a
w
a
ij
ij
i
i
i
j
j
s
c
ag
c
g
+
+
=
D
+aD
-qc-qg+
t
t
t
x
x
x
g
g
kc
=
Steady-State(anewretardationfactorandeffectiv
ediffusion
coefficient):
2
2
1
w
a
g
i
i
g
w
a
d
ij
ij
g
i
j
i
E
E
ij
i
i
j
i
a
k
q
qk
K
c
a
c
c
+
=
D
D
k
-
t
xx
x
c
c
c
R
=D
-q
t
xx
x
+
+
+
TemperatureDependenceofTransportand
ReactionCoefficients
ar,aT
coefficientvaluesatareferenceabsolutetemperatu
re,
TrA,andabsolutetemperature,T
A,respectively
E
activationen
ergyofthereactionorprocess
(
)
exp
A
A r
T
r
A
A r
ET
-T
a=a
RTT
Mostofthediffusion
(Dw,Dg),distribution(ks,
kg),andreaction
rate(w,s,g,w
',s',
g',w,s,and
g)coefficientsare
stronglytemperature
dependent.HYDRUSassumesthatth
is
dependencycanbeexpressedbyanArrheniusequation
[StummandMorgan
,1981].
TheHYDRUSSoftwarePackages
Variably-SaturatedFlow(RichardsEq.)
RootW
aterUptake(waterandsalinitys
tress)
Solutes
Transport(decaychains,ADE)
-NonlinearSorption
-ChemicalNonequilibrium
-Phys
icalNonequilibrium
HeatTr
ansport
Pedotra
nsferFunctions(hydraulicproperties)
Parame
terEstimation
InteractiveGraphics-BasedInterface
HYDRU
S(2D/3D)andAdditionalModu
les
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GoverningH
eatTransportEquation
Sophocleous[197
9]:
ij()
apparentther
malconductivityofthesoil
C(),C
w
volumetriche
atcapacitiesoftheporousmediumandthe
liquidphase,respectively
deVries[1963]:
volumetricfraction
n,o,g,wsubscriptsrep
resentingsolidphase,organicmatter,gaseous
phase,andliq
uidphase,respectively.
()
n
n
o
o
w
g
C
=C
+C
+C
+Ca
()
()
ij
w
i
i
j
i
T
T
T
C
=
-Cq
t
x
x
x
Therma
lConductivity
0(
)thermalconductivityoftheporousmedium(solid
plu
swater)intheabsenceofflow
L,T
longitudinalandtransversethermaldispe
rsivities,
respectively
ChungandHorton[1987]
b1,b2,b3
empiricalparameters
0
()
(
)
(
)
i
j
ij
T
w
ij
L
T
w
ij
qq
=
C|q|
+
-
C
+
|q|
0.5
0
1
2
3
()
w
w
=b+b
+b
TheHYDRUS
SoftwarePackages
Variably-SaturatedFlow(RichardsEq.)
RootWaterUp
take(waterandsalinitystress)
SolutesTransport(decaychains,ADE)
-NonlinearSorption
-ChemicalNonequilibrium
-PhysicalNonequilibrium
HeatTransport
PedotransferFunctions(hydraulicproperties)
ParameterEstimation
InteractiveGra
phics-BasedInterface
HYDRUS(2D/3D)andAdditionalModules
PTFsbyCarselandParrish(1
988)
Averagevalues
ofselectedsoilwaterretentionparametersfor12major
soiltexturalgroups
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Pedotransfer
Functions:Rosetta
Schaapetal.(2001)
Model
InputData
TXT
TexturalClass
SSC
Sand,Silt,Clay%
SSCBD
Same+BulkDensity
SSCBD+
33
SSCBD+
at33kPa
SSCBD+
33+
1500
Same+
at1500kPa
Pedotra
nsferFunctions:Rosetta
TexturalCla
ssAverages:Rosetta
Texturalclass
r
s
n
Ks
[L3L-3]
[L3L-3]
[cm-1]
[-]
[cmd-1]
Sand
0.053
0.375
0.035
3.18
643.
LoamySand
0.049
0.390
0.035
1.75
105.
SandyLoam
0.039
0.387
0.027
1.45
38.2
Loam
0.061
0.399
0.011
1.47
12.0
Silt
0.050
0.489
0.007
1.68
43.7
SiltyLoam
0.065
0.439
0.005
1.66
18.3
SandyClayLoam
0.063
0.384
0.021
1.33
13.2
ClayLoam
0.079
0.442
0.016
1.41
8.18
SiltyClayLoam
0.090
0.482
0.008
1.52
11.1
SandyClay
0.117
0.385
0.033
1.21
11.4
SiltyClay
0.111
0.481
0.016
1.32
9.61
Clay
0.098
0.459
0.015
1.25
14.8
SoilhydraulicparametersfortheanalyticalfunctionsofvanGenuchten(1980)forthe
twelvetexturalclassesofthe
USDAtexturaltriangleobtainedwiththeRosettaligh
t
program(Schaapetal.,2001
).
TheHY
DRUSSoftwarePacka
ges
Variably-SaturatedFlow(RichardsEq.)
RootW
aterUptake(waterstress)
Solutes
Transport(decaychains,ADE)
-NonlinearSorption
-ChemicalNonequilibrium
-PhysicalNonequilibrium
HeatTransport
PedotransferFunctions(hydraulicproperties)
ParameterEstimation
Interac
tiveGraphics-BasedInterface
HYDRUS(2D/3D)andAdditionalModu
les
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ParameterEstimationwithHYDRUS
ParameterEst
imation:
ParameterEst
imation:
-Soilhydraulicparameters
-Solute
transportandreactionparameters
-Heatt
ransportparameters
Sequence:
Sequence:-Independently
-Simultaneously
-Sequentially
Method:
Method: -Marquardt-Levenbergoptimization
Objective
FunctionforInversePro
blems
2
*
,
1
1
2
*
1
1
2
*
1
(,,
)
[
(,)-
(,,)]
[
()-
(,)]
[
-
]
q
qj
q
pj
b
m
n
j
ij
j
i
j
i
j
i
m
nj
ij
j
i
j
i
j
i
n
j
j
j
j
bqp
v
w
gxt
gxtb
v
w
p
p
b
b
b
v
=
=
=
=
=
=
1stterm:
1stterm:
de
viationsbetweenmeasuredandcalculatedspa
ce-time
va
riables
2ndterm:
2ndterm:
differencesbetweenindependentlymeasured,pj*,andpredicted,
pj,soilhydraulicproperties
3rdterm:
3rdterm:
pe
naltyfunctionfordeviationsbetweenpriorkn
owledgeofthe
soilhydraulicparameters,bj*,andtheirfinalestimates,bj.
Formulation
oftheInverseProblem
Theproblemcanbesimplifiedinto
theWeightedLeast
theWeightedLeast--SquaresProblem
SquaresProblem
wi-weightofapar
ticularmeasuredpoint
2
*
1
()
n
i
i
i
i
w
q
q
=
=
TheHY
DRUSSoftwarePacka
ges
Variably-SaturatedFlow(RichardsEq.)
RootW
aterUptake(waterstress)
Solutes
Transport(decaychains,ADE)
-NonlinearSorption
-ChemicalNonequilibrium
-PhysicalNonequilibrium
HeatTransport
PedotransferFunctions(hydraulicproperties)
ParameterEstimation
Interac
tiveGraphics-BasedInterface
HYDRUS(2D/3D)andAdditionalModu
les
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Cut-offWall
FiniteElementMesh
Cut-offWall
SolutePlume
PlumeMovementin
a
TransectwithStream
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-
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TheHYDRU
SSoftwarePackages
Variably-SaturatedFlow(RichardsEq.)
RootWaterU
ptake(waterstress)
SolutesTransport(decaychains,ADE)
-NonlinearSorption
-ChemicalN
onequilibrium
-PhysicalNonequilibrium
HeatTransport
PedotransferFunctions(hydraulicproperties)
ParameterEstimation
InteractiveGr
aphics-BasedInterface
HYDRUS(2D
/3D)andAdditionalModules
HYDRU
S(2D/3D)NewFeatu
res
Waterflowinadual-porositysystemallowingforpreferentialflow
infractures
ormacroporeswhilestoringwaterinthematrix.
Rootwateruptakewithcompensation.
Spatialroot
distributionfunctionsofVrugtetal.(2002
).
SoilhydraulicpropertymodelsofKosugi(1995)andD
urner(1994).
Transportofviruses,colloids,and/orbacteriausingan
attachment/detachmentmodel,straining,filtrationtheory,and
blockingfun
ctions.
Aconstructedwetlandmodule(onlyin2D).
ThehysteresismodelofLenhardetal.(1991)toelimin
atepumping
bykeepingt
rackofhistoricalreversalpoints.
Newprintm
anagementoptions.
Dynamic,sy
stem-dependentboundaryconditions.
Flowingpar
ticlesintwo-dimensionalapplications.
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HYDRUS(2D
/3D)NewFeatures
CompletelynewGUI
basedonHi-End3Dgraphicslibraries.
MDIarchitecturem
ultipleprojectsandmultipleviews.
Neworganizationofg
eometricobjects.
Navigatorwindowwithanobjectexplorer.
Manynewfunctionsimprovingtheuser-friendliness,suchasdrag-
and-dropandcontextsensitivepop-upmenus.
Improvedinteractive
toolsforgraphicalinput.
SavingCross-SectionsandMesh-Linesforchartswithinagiven
project.
DisplayOptionsall
colors,linestyles,fontsandotherparameters
ofgraphicalobjectscanbecustomized.
Extendedprintoptions.
Extendedinformation
intheProjectManager(includingproject
preview).
Manyadditionalimprovements.
Geochem
icalModeling
HYDRUS
HYDRUS--1D1D(imneketal.,1998)
-variablysatura
tedwaterflow
-heattransport
-rootwateruptake
-solutetranspor
t
UNSATCHE
M
UNSATCHE
M(imneketal.,1996)
-carbondioxide
transport
-majorionchem
istry
-cationexcha
nge
-precipitation-dissolution(instantaneousandkinetic)
-complexatio
n
HYDRUS-1D
+UNSATCHEM
HYDRU
S-1D+UNSATCHEM
H4SiO4,
H3SiO4-,H2SiO42
-
3
Silicaspecies
6
PCO2,
H2CO3
*,
CO3
2-,HCO
3-,H+,
OH-,
H2O
7
CO2-H2O
species
5
Ca,
Mg,
Na,
K
4
Sorbeds
pecies
(exchangeable)
4
CaCO3,
CaSO4
2H2O,
Mg
CO3
3H2O,
Mg5(CO3)4(OH)2
4H2O,
Mg2Si3O7.5
(OH)
3H2O,CaMg(CO3)2
6
Precipita
ted
species
3
CaCO3o,
CaHCO3+,
CaSO4o,
MgCO3o,
MgHCO3+,
MgSO4o,
NaCO
3-,NaHCO3o,
NaSO4-,KSO4-
10
Complex
ed
species
2
Ca2+,
Mg2+,
Na+,
K+,
SO4
2-,Cl-,
NO3-
7
Aqueous
components
1Kineticreactio
ns:calciteprecipitation/dissolution,dolomitedissolution
Activitycoefficients:extendedDebye-Hckelequations,Pitzerexpressions
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LysimeterStu
dy
Gonalvesetal.(2006)
HYDRUS
HYDRUS
--1D1D[[imimnekneketal.,1998]:
etal.,1998]:
VariablySaturatedWaterFlow
SoluteTransport
Heattransport
Rootwateruptake
PHREEQ
C
PHREEQ
C[ParkhurstandAppelo,1999]:
[ParkhurstandAppelo,1999]:
Availablechemicalreactions:
Aqueouscom
plexation
Redoxreactions
Ionexchange(Gains-Thomas)
Surfacecom
plexationdiffusedouble-layermodelandnon-
electrostatic
surfacecomplexationmodel
Precipitation/dissolution
Chemicalkinetics
Biologicalre
actions
HP1-CoupledHYDRUS-1DandPHREEQC
HYDRUS-1D
GUIforHP1
HP1examples
Transportofheavymetals(Zn2+,Pb2+,andCd
2+)
subjecttomultiplecationexchange
Transportwithmineraldissolutionofamorph
ousSiO2
andgibbsite(Al(OH)3)
Heavym
etaltransportinamediumwithapH
-
dependentcationexchangecomplex
Infiltrationofahyperalkalinesolutioninacla
ysample
(thisexampleconsiderskineticprecipitation-d
issolution
ofkaolinite,illite,quartz,calcite,dolomite,gypsum,
hydrota
lcite,andsepiolite)
Long-te
rmtransientflowandtransportofmajor
cations(Na+,K
+,Ca2+,andMg2+)andheavym
etals
(Cd2+,Z
n2+,andPb2+)inasoilprofile.
Kinetic
biodegradationofNTA(biomass,coba
lt)
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Mathematica
lVerification
Question:Whena
llnonlinear,coupled,and/ortransient
processesareintro
ducedintothemodel,howdoweknow
thatthecomputer
codegivesaccuratenumericalresults?
ApproximateTests:
Massbalanceerrors
Self-consistency
(differentgridsandtimesteps)
Comparisonwithothercodes
Mathem
aticalVerification
Doestheco
mputercode(model)provideanaccurate
solutionofthegovernmentPDEsfordifferen
tinitialand
boundaryc
onditionswithintherangeofpossiblemodel
parametervalues?
Verificationofpartsofthecode:
Comparewithanalyticalsolutions(steady-stateflow)
Comparewithlinearizedsolutions(simplifiedconstitutiverelationships)
Steady-state
solutions
Homogeneou
smedia
Simplifiedin
itialandboundaryconditions
ModelValidation
Doesthemodel(i.e.,theequationsembeddedinthe
code)correctly
representtheactualprocesses?
Amodelisasimplified
representationoftherealsystemorproc
ess
Approximationsarise
becauseof
Incorporationofa
limitednumberofprocesses
Limitedunderstandingoftheactualprocess
Inabilitytotranslateobservedprocessesintousablemathematics
(howtoquantifythings?)
Inconsistencyofsm
all-scaleheterogeneitieswithnumericalg
rid
(effectiveparameters)
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TheHYDRUS
-1DSoftwareforSimulating
One-Dimen
sionalVariably-Saturated
WaterFlowandSoluteTransport
Jirkaim
nek,RienvanGenuchten,
andMiroslavejna
DepartmentofEnv
ironmentalSciences,UniversityofCalifornia
Riverside,CA
FederalUniversityofRiodeJaneiro,RiodeJaneiro,Brazil
PC-Prog
ress,Ltd.,Prague,CzechRepublic
HYDR
US-1D-Functions
D
ataandProjectManagement
D
ataPre-Processing
-Inputparameter
-Transportdomaindesign
-Finiteelementgridgenerator
-Initialandboundarycondition
s
C
omputations
D
ataPost-Processing
-Graphicaloutput
-ASCIIoutput
HYDRUS-1D
-ModelStructure
HYDRUS1D
HYDRUS1D
-majormodule
POSITION
POSITION
-projectmanager
PROFILE
PROFILE
-flowdomaindesign
-finiteelementgenerator
-initialconditionsanddomain
properties
HYDRUS
HYDRUS
-waterflowandsolutetransport
calculations
HYDRU
S-1D-FortranApplic
ation
Water,Solute,andHeatMovement
Water,Solute,andHeatMovement:
-one-dim
ensionalporousmedia
RichardsE
quation
RichardsE
quation-saturated-unsaturatedwaterflow
-porousmedia:
-unsaturated
-partiallysaturated
-fullysaturated
-sinkterm-wateruptakebyplantroots
-waterstress
-salinitystress
SoilHydra
ulicProperties
SoilHydra
ulicProperties
-vanGen
uchten[1980]
-Brooksa
ndCorey[1964]
-modifiedvanGenuchtentypefunctions[VogelandCislerov
a,1989]
-dual-porositymodelofDurner[1994]
Hysteresis
Hysteresis
-Scottetal.[1983],
KoolandParker[1988]
RootGrow
th
RootGrow
th-logisticgrowthfunction
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HYDRUS-1D
-FortranApplication
SoluteTransport
SoluteTransport-convection-dispersionequation
-liquid,solid,andgaseousphase
-nonlinearadso
rption[Freundlich-Langmuirequations]
-nonequilibirum
[two-sitesorptionmodel,mobile-immobilewater]
-HenrysLaw
-convectionand
dispersioninliquidphase,diffusioningaseousphase
-zero-orderpro
ductioninallthreephases
-first-orderdeg
radationinallthreephases
-chainreactions
HeatTransport
HeatTransport-co
nvection-dispersionequation
-heatconductio
n
-convection
NonuniformSoils
Scaling
ScalingProcedurefo
rHeterogeneousSoils
HYDRUS-1D-FortranApplication
ThreeStabilizingOptions
StabilizingOptionstoavoidoscillationinthen
umerical
solutionof
thesolutetransportequation:
-upstreamweighting
-artificialdispersion
-performanceindex
WaterFlowBoundaryConditions:
WaterFlowBoundaryConditions:
-prescribedheadandflux
-atmosph
ericconditions
-seepageface
-freedrainage
-deepdrainage
-horizont
aldrains
Flowand
Transport:
Flowand
Transport:
-verticaldirection
-horizontaldirection
-generallyinclineddirection
HYDRUS-1D
MajorModule
HYDRU
S-1D-MajorModule
Mainprog
ramunit
Mainprog
ramunitofthesystem
Controlse
xecutionoftheprogram
Determines
whichotheroptionalmodulesarenecessaryforap
articular
application
PrePre--processingunit
processingunit
-specificationofallparametersneededtosuccessfullyru
nHYDRUS
-smallcatalogofsoilhydraulicproperties
-Rose
ttapedotransferfunctionsbasedonNeuralNetworks
Post
Post--processingunit
proce
ssingunit
-simp
lex-ygraphsforgraphicalpresentationofsoilhydraulicproperties
andotheroutputresults
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HYDRUS-1D
-MajorModule
Pre-processing
Post-processing
HYDRU
S-1D-Preprocessing
WaterFlo
wModels
SoluteTransp
ortModels
HYDRUS-1D
Post-processing
ProfileInformation
ObservationNodes
POSITION-ProjectManager
Manages
dataof
existingp
rojects
Locates
Opens
Copies
Deletes
Renames
--desiredprojectsor
selectedinpu
tand/or
outputdata
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PROFILE-Dom
ainDesign,Mesh
Generator,DomainProperties
Discretization
Discretization
ofthesoilprofileintofiniteelements
InitialConditions
InitialConditionsforpressureheads,water
contents,temp
eratures,andconcentrations
RootUptakeD
istribution
RootUptakeD
istribution
MaterialLaye
rs
MaterialLaye
rs-parameterswhichdescribethe
propertiesoft
heflowdomain
-material
distribution
-scalingfactors
ObservationN
odes
ObservationN
odes
PROFILE
-DomainDesign,MeshGenerator,
DomainPr
operties
HYDRUS-1D
-3000
-2500
-2000
-1500
-1000
-5000
0.0
0.1
0.2
0.3
0.4
0.5
WaterContents[-]
-40
-200
20
40
60
50
100
150
200
250
300
Time[days]
potTop
potRoot
actTop
actRoot
actBot
CumulativeFluxes
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
50
100
1
50
200
250
300
T
ime[days]
AllFluxes
-300
-200
-1000
100
200
50
100
150
200
250
300
Time[days]
ObservationNodes
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Computer Session 1
Computer Session 1
The purpose of Computer Sessions 1, 2, and 3 is to give users hands-on experience
with the HYDRUS-1D software package (version 3.0). Three examples are given
to familiarize users with the major parts and modules of HYDRUS-1D (e.g., the
project manager, Profile and Graphics modules), and with the main concepts and
procedures of pre- and post-processing (e.g., domain design, finite element
discretization, initial and boundary conditions specification, and graphical display
of results).
The following three examples are considered in Computer Sessions 1, 2, and 3,
respectively:
I. Direct Problem: Infiltration into a one-dimensional soil profile (ComputerSession 1)
A. Water flow
B. Solute transport
C. Possible additional modifications
II. Direct Problem: Water flow and solute transport in a multilayered soil profile
(Computer Session 2)
III. Inverse Problem: One-step outflow method (Computer Session 3)
The first example represents the direct problem of infiltration into a 1-meter deep
loamy soil profile. The one-dimensional profile is discretized using 101 nodes.
Infiltration is run for one day. Ponded infiltration is initiated with a 1-cm constant
pressure head at the soil surface, while free drainage is used at the bottom of the
soil profile. The example is divided into three parts: (A) first, only water flow is
considered, after which (B) solute transport is added. Several other modifications
are suggested in part (C). These include (1) a longer simulation time, (2)
accounting for solute retardation, (3) using a two-layered soil profile, and (4)
implementing an alternative spatial discretization. Users in this example becomefamiliar with most dialog windows of the main module, and get an introduction
into using the external graphical Profile module with which one specifies initial
conditions, selects observation nodes, and so on.
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Computer Session 1
A. Infiltration of Water into a One-Dimensional SoilProfile
Project ManagerButton "New"
Name: Infiltr1
Description: Infiltration of water into soil profile
Button "OK"
Main ProcessesHeading: Infiltration of water into soil profile
Button "Next"
Geometry InformationButton "Next"
Time InformationFinal Time: 1
Initial Time Step: 0.0001
Minimum Time Step: 0.000001
Button "Next"
Print InformationNumber of Print Times: 12
Button "Select Print Times"
Button "Next"
Water Flow - Iteration CriteriaButton "Next"
Water Flow - Soil Hydraulic ModelButton "Next"
Water Flow - Soil Hydraulic ParametersCatalog of Soil Hydraulic Properties: Loam
Button "Next"
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Computer Session 1
Water Flow - Boundary ConditionsUpper Boundary Condition: Constant Pressure Head
Lower Boundary Condition: Free Drainage
Button "Next"
Soil Profile - Graphical EditorMenu: Conditions->Initial Conditions->Pressure Head
or Toolbar: red arrow
Button "Edit condition", select withMouse the first node and specify 1
cm pressure head.
Menu: Conditions->Observation Points
Button "Insert", Insert nodes at 20, 40, 60, 80, and 100 cm
Menu: File->Save Data
Menu: File->Exit
Soil Profile - SummaryButton "Next"
Execute HYDRUS
OUTPUT:Observation Points
Profile InformationWater Flow - Boundary Fluxes and Heads
Soil Hydraulic Properties
Run Time Information
Mass Balance Information
-100
-80
-60
-40
-20
0
20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time [days]
N1
N2
N3
N4
N5
Observation Nodes: Pressure Heads
-100
-80
-60
-40
-20
0
-100 -80 -60 -40 -20 0 20
h [cm]
Profi le Info rmatio n: Pressure Head
Close Project
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Computer Session 1
B. Infiltration of Water and Solute into
a One-Dimensional Soil Profile
Project ManagerClick on Infiltr1Button "Copy"
New Name: Infiltr2
Description: Infiltration of Water and Solute into Soil Profile
Button "OK", "Open"
Main ProcessesCheck "Solute Transport"
Button "OK"
Solute Transport - General InformationButton "Next"
Solute Transport - Transport ParametersDisp. = 1 cm
Button "Next"
Solute Transport - Reaction ParametersButton "Next"
Solute Transport - Boundary ConditionsUpper Boundary Condition: 1
Lower Boundary Condition: Zero Gradient
Button "Next"
Execute HYDRUS
OUTPUT:Observation Points
Profile Information
Solute Transport - Boundary Actual and Cumulative Fluxes
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Computer Session 1
C. Possible Modifications
1. Longer simulation time:
Project ManagerClick on Infiltr2
Button "Copy"
New Name: Infiltr3
Button "OK", "Open"
Time Information:Final Time: 2.5 d
Print Information
Button "Select Print Times"Button "Default"
Button "Next"
2. Retardation:Solute Transport - Reaction ParametersKd = 0.5
3. Two Soil Horizons:Geometry Information
Number of Soil Materials: 2
Water Flow - Soil Hydraulic Parameters1. line - Silt
Solute Transport - Reaction ParametersKd= 0
Soil Profile - Graphical EditorButton "Edit condition", select withMouse the lower 50 cm and specify
Material 2.
Menu: File->Save Data
Menu: File->Exit
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Computer Session 1
4. Different Spatial Discretization:
Soil Profile - Graphical EditorMenu: Conditions->Profile Discretization
or Toolbar: ladderButton "Insert Fixed", at 50 cm
Button "Density", at 50 cm 0.5, at the soil surface 0.3
Menu: Conditions->Initial Conditions->Pressure Head
or Toolbar: red arrow
Button "Edit condition", select withMouse the first node and specify 1
cm pressure head.
Menu: Conditions->Observation Points
Button "Insert", Insert nodes at 20, 40, 60, 80, and 100 cm
Menu: File->Save DataMenu: File->Exit
-100
-80
-60
-40
-20
0
-100 -80 -60 -40 -20 0 20
h [cm]
Prof i l e Infor mation : Pressure Head
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.0 0.5 1.0 1.5 2.0 2.5
Time [days]
N1
N2
N3
N4
N5
Observation Nodes: Water Content
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OntheCharac
terizationandMeasurement
oftheH
ydraulicPropertiesof
Unsatu
ratedPorousMedia
RienvanG
enuchten1andJirkaimnek
2
1Departm
entofMechanicalEngineering
FederalUniversityofRiodeJaneiro,Brazil
2Departm
entofEnvironmentalSciences
UniversityofCalifornia,Riverside,CA
RichardsE
quationforVariably-Satura
tedFlow
()
()
()
h
h
=
K
+K
t
z
z
SoilW
aterRetentionCurve,(h)
Hydr
aulicConductivityFunction,K(h)orK
()
-
volumetricwatercontent[L3L-3]
h-
pressurehead[L]
K-
unsaturatedhydraulicconductivity[LT-1]
z-
verticalcoordinatepositiveupward[L]
t-
time[T]
S-
rootwateruptake[T-1]
SoilWaterR
etentionCurve,
(h)
HydraulicConductivityFuncti
on,K()
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SoilWaterH
ysteresis
Outlin
e
DirectMeasurementsofHydraulicProperties
StatisticalPore-SizeDistributionModels
Pedot
ransferFunctions
TheR
osettaPTFcode
TheU
NSODADatabase
StructuredMedia
Ongoing/FutureResearch
Unsaturated
HydraulicConductivity
Steady
Steady--StateMethods
StateMethods
UsingDarcysla
w:q=-K(h)(dh/dz-1)
Long-ColumnM
ethod
CentrifugeMeth
ods
DirectTransientMethods
DirectTransientMethods
HorizontalInfiltration(BruceandKlute,1956)
SorptivityMethods(Dirksen,1975)
One-Step/Multi-StepOutflowMethod(Passioura,1975)
Hot-AirMethod
(Aryaetal.,1975)
EvaporationMe
thod(Boelsetal.,1978)
ParameterOptimizationMethods
ParameterOptimizationMethods
(Kooletal.,1985;imnekandvanGenuchten,1996)
LaboratoryMetho
ds
Tempe
PressureCell
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PeteShouses
TempeCellSetupatUSSalinityLaboratory
UnsaturatedHydraulicCondu
ctivity
DirectMethods
DirectMethods
InstantaneousProfileMethods(Watson,1966)
Unit-GradientMethods(Sissonetal.,1980)
Plane
-of-Zero-FluxMethod
Sorpt
ivityMethods(ClothierandWhite,1981)
ConstantHeadPermeameters(Reynoldsetal.,1983)
Tensi
onInfiltrometers(WhiteandPerroux,1988)
Param
eterOptimizationMethods
Param
eterOptimizationMethods
Russo
etal.(1991)
Abba
spouretal.(1996)
imneketal.(1998,2000)
...
FieldMeth
ods
Schematicof
TensionInfiltrometer
Thesupply
pressurehead
hwet=h2-h1
=
=
22/
(
)e
s
e
K
S
=K
S
+
+
Se
-effectivewaterconten
t
r,
s
-residualandsaturatedwatercontents
,n,m(=1-1/n),land
-emp
iricalparameters
Ks
-saturatedhydraulicconductivity
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LognormalDistributionModel(Kosugi,1996):
(
)
0
ln
/
()
1
()
2
2
r
e
s
r
hh
h
S
h
erfc
=
=
(
)
2
0
ln
/
1
()
2
2
l
s
e
hh
Kh
KS
erfc
=
+
Se
-effectivewatercontent
r,
s
-residualan
dsaturatedwatercontents
h0,,andl-empiricalp
arameters
Ks
-saturatedh
ydraulicconductivity
SoilHydraulicPropertyModels
10-2
10-1
100
101
102
103
10
So
ilWa
ter
Pressure
Hea
d(-mm
)
10-7
10-6
10-5
10-4
10-3
10-2
10-
HydraulicConductivity(mm/sec)
Observed
BimodalHydraulicConductivity
Durner(1994):
Se
-effectivewatercontent
r,s
-residualand
saturatedwatercontents,respectively
k
-numberofoverlappingsubregions
wi
-weightingfactorsforthesub-curves
i,ni,mi(=1-1/ni),andl-empiricalparametersofthesub-curves.
1
()
1
()
(1
)i
i
k
r
e
i
m
n
i
s
r
i
h-
S
h=
=
w
-
+
h
=
2
1/
1
2
1
11-(1-
)
()
i
i
i
i
k
m
me
i
i
k
i
l
s
e
i
k
i
i
i
i
w
S
K
=
wS
K
w
=
=
=
Thehydrauliccharacteristics
contain4+2kunknownparameters:
r,
s,i,ni,
l,andK
s.
Ofthese,
r,
s,andK
shavea
clearphysicalmeaning,whereasi,niandlareessentially
empiricalparametersdetermi
ningtheshapeoftheretentionandhydraulicconductivity
functions[vanGenuchten,19
80].
SoilHydraulicPropertyModels
00
.10
.20
.30
.40
.50
.6-1
0
1
2
3
4
5
Log
(|PressureHead[cm]|)
WaterContent[-]
Total
Matrix
Fracture
-10-8-6-4-20
-1
0
1
2
3
4
5
Log(|Pressu
reHead[cm]|)
Log(Conductivity[cm/days])
Total
Matrix
Fracture
Exampleofcom
positeretention(left)andhydraulicconductivity(right)
functions(r=0.00,
s=0.50,1=0.01cm-1,n1=1.50,l=0.5,Ks=1cmd-1,w1=0.975,
w2=0.025,
2=1.00cm-1,n2=5.00).
Durner(19
94):
SoilHyd
raulicPropertyModels
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PedotransferFunctions
Predictthehydraulicpropertiesfrom
moreeasily
measureddata:
SoilTexture(classorparticle-sizedistribution)
BulkDensity
Porosity
OrganicMatterContent
SoilStructure
ClayMineralogy
ChemicalProper
ties(EC,pH,SAR,)
TwoApproaches:
TwoApproaches:
-Predictspecificr
etentionvalues
-Predictsoilhydr
aulicparameters
PTFsbyCarselandParrish(1
988)
PTFsbyCarselandParrish(1988)
PTFsbyCarselandParrish(1
988)
Averagevalues
ofselectedsoilwaterretentionparametersfor12major
soiltexturalgroups
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HierarchicalNeural-NetworkBootstrapApproach
Hierarchy:tryto
matchvariouslevelsofdataavailability
Neuralnetworks:toprovidethemostaccurate
predictions
Bootstrap:gener
ateconfidenceintervalsofthe
predictions
Predictionof:wa
terretention,Ks,andtheunsaturated
hydraulicconductivity
Rosetta(Schaapetal.,2001)
Rosetta(Schaapetal.,2001)
Pedotra
nsferFunctions:Rosetta
Schaapetal.(2001)
Model
InputData
TXT
TexturalClass
SSC
Sand,Silt,Clay
%
SSCB
D
Same+BulkDensity
SSCB
D+
33
SSCBD+
at3
3kPa
SSCB
D+
33+
1500
Same+
at1500kPa
Predicted
parameters+
uncertainties
Hierarchica
lModels
Inputdata
Pedotransfer
Functions:Rosetta
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Pedotransfer
Functions:Rosetta
0
100
0
20
80
20
40
60
40
60
40
60
80
20
80
100
0
100
Clay
[%]
Silt[%]
San
d[%]
LL
0
100
0
20
80
20
40
60
40
60
40
60
80
20
80
100
0
100
Clay
[%]
Silt[%]
San
d[%
]
SlS
sL
L
siL
Si
sc
L
cL
sicL
siC
sC
C
RosettasCalibrationData
R
etention
(N=2134)
UnsaturatedCo
nductivity
(N=235
)
Waterretention
SaturatedConductivity
R2
RMSEw
R2
RMSEs
Model
Input
r
s
Log
Logn
cm3/cm3 LogKs
(-)
H1
TexturalClass
0.06
6
0.1
43
0.2
03
0.4
52
0.0
72
0.4
27
0.7
39
H2
SSC
0.08
6
0.1
78
0.2
38
0.4
73
0.0
70
0.4
61
0.7
17
H3
SSCBD
0.09
4
0.5
81
0.2
65
0.4
95
0.0
60
0.5
35
0.6
66
H4
SSCBD
33
0.12
1
0.6
05
0.4
17
0.5
99
0.0
41
0.6
40
0.5
86
H5
SSCBD
33
1500
0.38
7
0.6
00
0.5
77
0.7
60
0.0
39
0.6
47
0.5
81
Directfittodata
-
-
-
-
0.0
12
-
-
RosettasP
erformance
SSC:
Sand,silt,
claypercentages
BD:
Bulkdensity
33,1500
Watercon
tentat33and1500kPa
RosettasClass-AveragePTFs
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Pore-ConnectivityParameterL
(
)
2
1/
1
1
m
L
m
s
e
e
K
KS
S
=
UNSODA2UnsaturatedSoilHydraulicDatabase
http://www.ussl.ars.usda.gov/models.htm
MS-ACCESS
FlexibleQu
eries
Graphicssu
pport
Downloadable
DripIrrigation(Skaggsetal.,2004)
DripIrrigation(Skaggsetal.,2004)
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HYDRUS
-0.93
1.3
1.4
0.023
0.33
0.021
l
Ks(cmhr-1)
n
s
r
Hydraulicproperties
Hydraulicproperties
estimatedusingRo
setta
estimatedusingRo
setta
pedotransferfunction
pedotransferfunction
(sand,silt,andclay
,bulk
(sand,silt,andclay
,bulk
density,1/3and15
bar
density,1/3and15
bar
watercontent)
watercontent)
0
10
20
30
40
50
60
DISTANCE(cm)
0
10
20
30
40
50
60
DISTANCE(cm)
-70
-60
-50
-40
-30
-20
-100
DEPTH(cm)
Observed
Predicted
0.1
0.1
2
0.1
4
0.1
6
0.1
8
0.2
0.2
2
0.2
4
0.2
60.2
8
0.3
Vo
lume
tricWa
ter
Con
ten
t
Trial1:5hourirrigation,20L/mappliedwater
Time=5.5h
r
0.1
0.1
2
0.1
4
0.1
6
0.1
8
0.2
0.2
2
0.2
4
0.2
60.2
8
0.3
Vo
lume
tricWa
ter
Con
ten
t
0
10
20
30
40
50
60
DISTANC
E(cm)
-70
-60
-50
-40
-30
-20
-100
DEPTH(cm)
0
10
20
30
40
50
60
DISTANCE(cm)
Observed
Predicted
Trial1:5hourirrigation,20L/mappliedwater
Time=28hr
0.1
0.1
2
0.1
4
0.1
6
0.1
8
0.2
0.2
2
0.2
4
0.2
60.2
8
0.3
Vo
lume
tricWa
ter
Con
ten
t
0
10
20
30
40
5
0
60
DISTANCE(cm)
0
1
0
20
30
40
50
60
DISTANCE(cm)
-70
-60
-50
-40
-30
-20
-100
DEPTH(m)
Observed
Predicted
Trial2:10
hourirrigation,40L/mappliedwater
Time=10.7
5hr
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0.1
0.1
2
0.1
4
0.1
6
0.1
8
0.2
0.2
2
0.2
4
0.2
60.2
8
0.3
V
olume
tricWa
ter
Con
ten
t
0
10
20
30
40
50
60
DISTANCE(cm)
0
10
20
30
40
50
60
DISTANCE
(cm)
-70
-60
-50
-40
-30
-20
-100
DEPTH(cm)
Predicted
Obse
rved
Trial2:10hourirrigation,40L/mappliedwater
Time=31hr
0.1
0.1
2
0.1
4
0.1
6
0.1
8
0.2
0.2
2
0.2
4
0.2
60.2
8
0.3
Vo
lume
tricWa
ter
Con
ten
t
0
10
20
30
40
50
60
DISTANCE(cm)
0
10
20
30
40
50
60
DISTANCE(cm)
-70
-60
-50
-40
-30
-20
-100
DEPTH(m)
Observed
Predicted
Trial3:15
hourirrigation,60L/mappliedwater
Time=16h
r
0.1
0.1
2
0.1
4
0.1
6
0.1
8
0.2
0.2
2
0.2
4
0.2
60.2
8
0.3
Vo
lume
tricWa
ter
Con
ten
t
0
10
20
30
40
50
60
DISTANCE(cm)
0
10
20
30
40
50
60
DISTANC
E(cm)
-70
-60
-50
-40
-30
-20
-100
DEPTH(cm)
Predicted
Observed
Trial3:15hourirrigation,60L/mappliedwater
Time=39hr
0
-10
-20
-30
-40
-50
DEPTH
(cm)
00.10.20.3
WATERCONTENT
DISTANCE=
0
0
-10
-20
-30
-40
-50
DEPTH
(cm)
00.10.20.3
WATERCONTENT
DISTANCE=
10
0
10
20
30
40
DISTANCE(cm)
00
.10
.20
.3
DEPTH=-1
0
0
10
20
30
40
DISTANCE(cm)
00
.10
.20
.3
DEPTH=-2
0
Trial1:5h
ourirrigation,20L/mappliedwater
Time=5.5hr
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0
-10
-20
-30
-40
-50
DEP
TH
(cm)
00
.10
.20
.3
WATERCONTENT
DISTANCE
=0
0
-10
-20
-30
-40
-50
DEP
TH
(cm)
00
.10
.20
.3
WATERCONTENT
DISTANCE
=10
0
10
20
30
40
DISTANCE(cm)
00
.10
.20
.3
DEPTH=-1
0
0
10
20
30
40
DISTANCE(cm)
00
.10
.20
.3
DEPTH=-2
0
Trial1:5hourirrig
ation,20L/mappliedwater
Time=28hr
Genericversussite-specificPTFs
Effectsofsoilstructure
Effectsofchemistryandclaymineralogy
-NRCSsoilcharacterizationdatabase
Lab
oratoryversusfielddata
Continuedatamining(UNSODA)
Future
PlansRosetta
HydraulicPr
operties-Challenges
Hysteresis
Dryendeffects;residualsaturation,r
Dynamiceffec
ts;non-equilibriumflow
Airentrapment(sversusporosity)
Swellingsoils;
effectsofchemistry
Descriptionnearsaturation
Secondordercontinuityin(h)(n
1.0)
Structuredmedia;preferentialflow
ScaleIssues(u
pscaling;effectiveproperties)
RequiredAccuracy(fluxvsprofilecontrolledinf.)
...
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ApplicationofFiniteElementMethodto
1DVariably-SaturatedWaterFlow
andS
oluteTransport
Jirkaimnek
1andRienvanGenuchten2
1DepartmentofEnvironmentalSciences
Universityo
fCalifornia,Riverside,CA
2DepartmentofMechanicalEngineering
FederalUnive
rsityofRiodeJaneiro,Brazil
ApplicationofFiniteElementMethod
to1DVariably-SaturatedFlow
RichardsEquation:
cos
h
q
=
K
+
-S
-S
t
x
x
x
=
Finalfinite
differencescheme:
1,
1
1
1
1/2
1/2
-
-
j
k
j
j
j
j
i
i
i
i
i
q
q
=
S
t
x
+
+
+
+
+
12/1
1
11
12/
1
12/1
++
+
++
+ +
+ +
=
=
j i
i
j i
j i
j i
j i
K
xh
h
K
q
K
xh
K
q
xi+1
xi
xi-1
ti
ti+1
x
xi
xi-1
j ih1
j ih
1j ih
+
1j ih+
11j ih+
11j ih+
+
t
ApplicationofFiniteElementMethod
to1DVariably-SaturatedFlow
RichardsEquation:
cos
h
q
=
K
+
-S
-S
t
x
x
x
=
Finalfinitedifferencescheme:
1,
1
1,
1
1,
1,
+1,
+1
1,
1
1,
1
1
-1
1/2
-1/2
1,
1,
1/2
-1/2
1
-
1
-
-
-
+
-
j
k
j
k
j
k
jk
j
k
j
j
k
j
k
i
i
i
i
i
i
i
i
j
k
j
k
ji
i
i
i
i
h
h
h
h
K
K
=
S
K
K
t
x
x
x
x
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
where:
+1
1
1
1
1
1
1
1
1
1
1
1
1
1
1/2
1/2
-
=
=
2
2
j
j
i
i
i
i
i
i
i
i
j
,k
j
,k
j
,k
j
,k
i
i
i
i-
j+
,k
j
,k
i+
i-
t=
t
t
x-
x
x=
x
x
-x
x
x-x
2
+
+
K
K
K
K
=
=
K
K
+
+
+
+
+
+
+
+
ApplicationofFiniteElementMethodto
1DV
ariably-SaturatedFlow
MatrixForm:
Thesymmetrical
tridiagonalmatrix[Pw
]
hastheform:
+1,
+1
+1,k
[
{
={
}
}
]
j
k
j
w
w
P
h
F
d
e
e
d
e
e
d
e
.
.
.
.
.
.
e
d
e
e
d
e
e
d
=
P
N
N
N
N
N
N
N
N
w
1
1
1
2
2
2
3
3
3
2
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
]
[
ApplicationofFiniteElementMethodto1D
Variably-SaturatedFlow
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Themass
Themass--conservativemethod
conservativemeth
odproposedbyCeliaetal.[1990],inwhich
j+1,k+1isexpandedinatrun
catedTaylorserieswithrespecttohabou
t
theexpansionpointhj+1,k,is
usedinthetimedifferencescheme:
+1,
+1
+1,
+1
+1,
+1,
+1,
+1
+1,
+1,
+1,
1
1
1
+1,
-
-
- -
-
+
t
j
k
j
j
k
j
k
j
k
j
j
k
j
k
j
k
j
i
i
i
i
i
i
i
i
i
i
j
k
j
j+
,k
j+
,k
i
i
j
k
i
i
i
=
=
=
t
t
t
t
h
h
C
t
+
+
+
=
ApplicationofFiniteElementMethod
to1DVariably-SaturatedFlow
Thediagonal
entriesdiandabove-diagonalentrieseiofthematrix[Pw
],
andtheentrie
sfiofvector{Fw
},aregivenby:
1
11
1
1
11
k,1+
2
+
2
+
+
+
+
+
i
,k
ji-
,k
ji
i
,k
ji
,k
ji+
ji
i
xK
+
K
xK
+
K
Ctx
=d
i
,k
ji+
,k
ji
i
xK
K-
=e
2
+
11
1
+
+
x
S
K
K+
tx
h
Ctx
=f
ji
,k
ji
,k
ji+
j i
k
j i
,k
ji
k
ji
i
-
2-
)
-
(
-
11
11
,1+
1
,1+
+
+
ApplicationofFiniteElementMethod
to1DVariably-SaturatedFlow
ImplementationoftheUpperFluxBoundaryCondition:
ImplementationoftheUpperFluxBoundaryCondition:
q
=-
-S
t
x
ThemassbalanceequationinsteadofDarcy'slaw
isdiscretized.
Discretizationgives:
Expandingthetimederivativeonthelefthand[Celiaetal.,1990],an
d
usingthediscretizedformo
fDarcy'slawforqN-1/2leadsto:
S
x
q
q(
-=
t
jN
N
,k
j N-
j N
j N
k
j N
-)
-
2
-
1
12/1
1+
1+,
1+
+
1
11
1
,1+
1
2
+
+
N
,k
jN-
,k
+jN
k
jN
N
N
x
K
+
K
Ct
2
x=
d
q
-
S
x
K
K
-)
tx
h
C
t
2x
=f
+j N
jN
N
,k
jN-
k
jN
j i
k
j N
,k
jN
k
jN
N
N
1
1
11
,
1+
,1+
1
,1+
1
2
-
2+
-
(
2
-
+
+
qNistheprescribedsoilsurfaceboundaryflux
ApplicationofFiniteElementMethod
to1DVariably-SaturatedFlow
ComputationofNodalFluxes:
Computatio
nofNodalFluxes:
S
+
t
x
-
+
x
h-
h
K-=
q
x
+
x
x
+
xh
-
h
K-
x
+
xh
-
h
K-
=
q
+
xh
-
h
K-
=
q
jN
jN
+jN
N
N
+j-N
+jN
+j-N
+j N
i
i
i
-i
+j -i
+ji
+j -i
-i
i
+ji
+j+i
+j+i
+j i
i
+j
+j
+j+
+j
-
2
1
1
1
11
1
1
11
1
12/1
1
1
1
11
1
12/1
1
1
11
12/1
1
1
1
12
12/11
1
1
ApplicationofFiniteElementMethod
to1DVariably-SaturatedFlow
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IterativeProcess:
IterativeProcess:Picard
Picardlinearization
linearization
j-timestep
k-iteration
1)Firsttimestep:hj+1,1=hinit,j=1,k=1
2)Derivationofthesystemoflinearizedalgebraicequations
usinghj+1,k,q
j+1,k,K
j+1,k,C
j+1,k
3)Gaussianelimination-hj+1,k+1,q
j+1,k+1
4)ToleranceCriteria:
abs(hj+1,k+1-hj+1,k)Grid - Height: 0.05
Menu: Condition->Profile Discretization
Button"Number": 50
Button"Insert Fixed" at 3.95 cm
Button"Density": deselect "Use upper", upper density =0.1 at 3.95 cm
Menu: Condition->Initial Condition->Pressure Head
Button"Edit condition"
Select entire profile: Top value=-2, Bottom value=2.52
Deselect "Use top value for both"
Lowest node = -1000 cm
Menu: Condition->Material Distribution
Button"Edit condition"
Select the ceramic plate and specify "Material Index"=2
Ditto for "subregions"Observation Points?
Soil Profile - Summary
Execute HYDRUS
OUTPUT:Water Flow - Boundary Fluxes and Heads
Cumulative Bottom FluxSoil Hydraulic Properties
Inverse Solution Information
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.001 0.01 0.1 1 10 100
Time [hours]
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Computer Session 3
Exercises:
Multistep Outflow Experiments (SGP97 project):
Height of the soil sample:5.9 cm
Thickness of the ceramic: 0.5 cm
Conductivity of the ceramic, boundary conditions, and output data
depend on the sample (see the Excel file).
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0 500000 1e+006 1.5e+006
Time [sec]
Cum. Bottom Flux
-600
-500
-400
-300
-200
-100
0
0 500000 1e+006 1.5e+006
Time [sec]
Bottom Pressure Head
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Application
ofFiniteElementMethod
to2DVariably-SaturatedWaterFlow
and
SoluteTransport
Jirka
imn
ek1andRienvanGenuchten
2
1Departm
entofEnvironmentalSciences
Universit
yofCalifornia,Riverside,CA
2DepartmentofMechanicalEngineering
FederalUniversityofRiodeJaneiro,Brazil
DiscretizationUsingFiniteEle
ments
Examplesofthe
unstructuredtriangularfiniteelementgridsforreg
ular(left)and
irregular(right)
two-dimensionaltransportdomains.
ApplicationofFiniteElementMethodto
2DVariably-SaturatedFlow
TheTheGalerkin
Galerkinmethod:
method:
ApplyingGreen'sfirstidentityandreplacinghbyh0
A
A
ij
iz
n
i
jh
-
K
K
+K
+S
d
=
t
x
x
(
)
'
e
e
e
A
n
n
ij
e
j
i
A
A
ij
iz
i
n
j
e
A
n
iz
n
e
i
h
+KK
d
=
t
x
x
h
K
K
+
K
n
d
+
x
-KK
-S
d
x
e
representsthedomainoccupiedbyelemente
e
isaboundarysegmentofelemente
Inmatrixfor
m:
}
{
}
{
}
{
}
]{
[
}{
]
[
D-
B-
Q
=h
A
+
dt
d F
[
(
)
]
4
e
n
m
A
l
nm
l
ij
e
i
j
A
A
A
xx
m
n
xz