determination of effective soil hydraulic properties - challenges and solution strategies ·...

Determination of Effective Soil Hydraulic Properties -Challenges and Solution Strategies

Wolfgang DurnerSascha IdenAndre PetersUlrike Jansen

initial hypothesis

• reliable characterization of the soil hydraulic behaviour is the base for further analyses of hillslope processes

� IntroRichards equation, hydraulic properties, retention and conductivity function

� Key questionsexistence, relevance, and accuracy

� Solution strategiesexperiments, models

� Conclusions

Der Begriffoutline

outline

– standard model to describe water movement in the unsaturated zone

Richards equation (Richards, 1931)

( ) ( ) sz

hhK

zt

hhC +

+∂∂

∂∂=

∂∂

1

– standard model to describe water movement in the unsaturated zone

– no agreement amongst hydrologists and soilphysicists with respect to ist suitability to describe processes on a larger scale (Beven: „Darcy is bullshit“)

intro�

air water solid fine pore macropore horizon profile catchment

Der Begriffrepresentative elementary volume

�intro

continuum approach

wat

er c

onte

nt, θ

Durner and Flühler, Encyclopaedia of Hydrological Sciences, 2005

soil hydraulic properties

Durner und Lipsius, Encyclopaedia of Hydrological Sciences, 2005

( )hK

intro�

( )θh




� Conclusions

Der Begriffoutline

outline

key questions in measuring hydraulic properties are

existence ?relevance ?accuracy ?

key questions�

Photo: Stamm, 1995

Effective Effective

Hydraulic Hydraulic

PropertiesProperties

are not are not

equivalentequivalent

toto

Mean Mean

PropertiesProperties

�

effective properties

• effective WRC:arithm. mean of local WRCs

• effective conductivity:arithm. mean of local conductivites

�existence?

loamabove sand

effective properties ?

• effective WRC:

it depends ...

• effective conductivity:harmonic mean

�existence?

isotropic random field of conductivities

yields

vertically orientedpreferential water

flow paths

(Roth, WRR, 1996)

effective properties ? �isotropic

random field of conductivities

yields

vertically orientedpreferential flow

paths

existence?

Der Begriff �relevance?

upscaling

Der Begriffcontinuous versus stepwise scale transitionupscaling �

relevance?

Der Begrifftest @ large lysimeter

Bous, 2004

mittel schluffiger

Sand

62 % Sand35 % Schluff3 % Ton

3 x 3 TDR-Sonden59, 34 und 8.5 cm

über unterem Rand

3 x 2 Tensiometer63.5, 38 und 16.5 cmüber unterem Rand

�accuracy?

Prediction of the hydraulic response of a lysimeter

Der Begrifftest casePrediction of the hydraulic response of a lysimeter

�accuracy?

directly measured saturated hydraulic conductivity [cm/d]

only of academic interest ?

Vereecken et al., Soil Science, 1997

inve

re e

stim

atio

n [c

m/d

]

�accuracy?




� Conclusions

Der Begriffoutline

outline

Strategy 1: Better Experiments!

1) Check existence:

Evaluation of dynamic flow observations byinverse modeling

better experiments �

tensiometer 1

tensiometer 2

pressure transducer lower boundary

soil column

porous plate

regulated pressure

bu

ret t

e

pressuretransducer

Typical MSO

Hopmans, Simunek, Romano and Durner, Methods of Soil Analysis, 2002

�better experiments

inflow/outflow experiment: modeling results �

2) Improve relevance:

Perform measurements in the moisture range of interest


restricted range (data from the UNSODA data base)

Diplomarbeit Michael Herbst, 2007

�

proposed functions of θ(h)


�

extraplation uncertainty: 14 different RETC models


�


�similarities of fits: 14 different RETC models

misfit: near saturation

Durner, Water Resources Research, 1994

�

Peters und Durner, Journal of Hydrology, in Review

�misfit: toward drynessData obtained by the evaporation method

better experiments

requirement: better sensors

Schematic of heat dissipation sensor CSI 229 [Campbell Scientific Inc., Logan, Utah].

�

2) Improve relevance:

Perform measurements in the moisture range of interest

Perform measurements on the scale of interest


2)

Perform measurements on the scale of interest

Der Begrifflysimeters are a useful intermediate scale

1010--44 mm33 1010--33 mm33 1010--22 mm33 101000 mm33

Stechzylinder

Hohe LaborsäuleLaborsäule

1010--11 mm33

Gestochenes Lysimeter

Durner et al., European Journal of Soil Science, 2008


Hydraulic properties on the lysimeter scale

still applicable?

−=⋅ )()()( hK

z

hhK

zt

hhC

∂∂

∂∂

∂∂

�

homogeneous lysimeter

Time [days]

�

Durner et al., European Journal of Soil Science, 2008

Strategy 2: Better Models!

better models ��

3) Improved accuracy...

– Integral fit of the retention function– Choice of a proper retention and conductivity model– Flexible parameterization

�solution strategies

�integral fit

solution: use accurate object function in the fitting

Peters and Durner, Water Resources Research, 2006

�solution

integral fit avoids smoothing artefact

Peters and Durner, Water Resources Research, 2006

�solutions

�

bimodal K-prediction

Priesack und Durner, VZJ, 2006

solutions�



solutions�

Der Begriffbiased conductivity prediction at small nvan Genuchten/Mualem: artefact near saturation

K(h) nach van Genuchten/Mualem

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02

0 1 2 3 4

pF-Wert

Rel

. Lei

tfähi

gkei

t Kr(

h) [-

]

Sand

Lehm

Schluff

Ton

Retentionskurven nach van Genuchten

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0 1 2 3 4

pF-Werte

vol.

Was

serg

ehal

t [-]

1.01

1.02

1.1

1.05

2.0

1.2

1.05

1.01

�

use in pedotransfer models ! �

Der Begriffexplicit consideration of the air entry point

Van Genuchten, WRR, 1980Vogel und Cislerova, TIPM, 1988Durner, WRR, 1994

�better models

validity of the Mualem model ?

gesättigt

kapillar

Filmfluss

Tuller und Or, WRR, 2001

�

Peters‘ conductivity model

vG unimodal Peters


�better models

Peters‘ conductivity model


�



solutions�

Retentionseigenschaften Cambisol FAL

10

20

30

40

50

60

70

1 10 100 1000 10000

Matrixpotential [cm WS]

Was

serg

ehal

t [%

]

20 cm Tiefe 40 cm Tiefe 60 cm Tiefe 80 cm Tiefe 20 cm 40 cm 60 cm 80 cm

field retention curves �

unimodal

(van Genuchten, WRR, 1980)

�

bimodal

(Durner, WRR 1994; Zurmühl und Durner, SSSAJ, 1998)

�

Free form

(Bitterlich et al., VZJ, 2004)

�

Bitterlich, Iden, Durner, Knabner, Vadose Zone Journal, 2004Iden und Durner, Water Resources Research, 2007Iden and Durner, European Journal of Soil Science, in press

free-form functions �

Inverse Simulation using Free-Form Functions and Glo bal OptimizationSynthetic Data Set – Free-Form Approach r = 2 �

Iden und Durner, Water Resources Research, 2007

�Inverse Simulation using Free-Form Functions and Glo bal OptimizationSynthetic Data Set – Free-Form Approach r = 3


�Inverse Simulation using Free-Form Functions and Glo bal OptimizationSynthetic Data Set – Free-Form Approach r = 9


Soil: Bayreuth Sandy Loam (Bt)

Experiment: MSO @ 14 cm high column

Data by Dr. Bernd Schultze

Application example: free-form SHyP �


�Inverse Simulation using Free-Form Functions and Glo bal OptimizationApplication – Bayreuth Sandy Loam n = 2


Resumèe: free-form functions

• avoid any systematic error in the parametrization of the retention and conductivity

• yield parameters with superior correlation structure

• allow to quantify the local uncertainties of estimated SHYP

• reflect exactly the information content of the measurment data

• can be used in tabular form by numerical simulation models

�




� Conclusions

Der Begriffoutline

outline

Only minimal progress is likely when methods which were useful before the availability of computers are being programmed for computer use.

S. J. Burgess. 1986. Trends and Directions in Hydrology, Water Resour. Res. 22(9):1S-5S

conclusions

• Better Experiments– larger measurement scales– intelligent experimental design– enhanced senors

• Better Models– more flexible constitutive relationsships– advanced evaluation methods

– improved sensors– larger measurement scales– suitable experimental design

– data analysis that avoids any systematic errors– more flexible constitutive relationsships– evaluation by robust inverse methods

conclusions

Thank you!

If interested, ask for reprints!

selected literature

• Durner, W., U. Jansen, and S.C. Iden (2008): Effective Hydraulic Properties of Layered Soils at the Lysimeter Scale Determined by Inverse Modelling, European Journal of Soil Science, 59, 114-124. doi: 10.1111/j.1365-2389.2007.00972.x

• Iden, S.C. and W. Durner (2008): Multiple batch extraction test to estimate contaminant release parameters using a Bayesian approach, Journal of Contaminant Hydrology 95(2008), 168-182, doi:10.1016/j.jconhyd.2007.09.004

• Durner, W., B. Scharnagl, S. Iden, L. Weihermüller, and H. Vereecken (2007): Übertragbarkeit hydraulischer Eigenschaften aus Laborversuchen auf ein Testlysimeter, Mitteilungen der Deutschen Bodenkundlichen Gesellschaft, Band 110, Heft 1, S. 87-88

• Iden, S.C., and W. Durner (2007): Free-Form estimation of the unsaturated soil hydraulic properties by inverse modelling using global optimization, Water Resour. Res. VOL. 43, W07451, doi:10.1029/2006WR005845.

• Peters, A., and W. Durner (2007): Optimierung eines einfachen Verdunstungsverfahrens zur Bestimmung bodenhydraulischer Eigenschaften, Mitteilungen der Deutschen Bodenkundlichen Gesellschaft, Band 110, Heft 1, S. 125-126

• Peters, A., and W. Durner (2006): Improved estimation of soil water retention characteristics from hydrostatic column experiments, Water Resour. Res.,42, W11401, doi:10.1029/2006WR004952.

• Priesack, E., and W. Durner (2006): Closed-form expression for the multi-modal unsaturated conductivity function, Vadose Zone Journal 5: 121-124

• Durner, W., and D. Or (2005): Chapter 73: Soil Water Potential Measurement, in: Anderson M.G. and J. J. McDonnell, Encyclopedia of Hydrological Sciences, Chapter 73, 1089-1102, John Wiley & Sons, Ltd.

• Durner, W., and H. Flühler (2005): Chapter 74: Soil Hydraulic Properties, in: Anderson M.G. and J. J. McDonnell, Encyclopedia of Hydrological Sciences, Chapter 74, 1103-1120, John Wiley & Sons, Ltd.

• Durner, W., and K. Lipsius (2005): Chapter 75: Determining Soil Hydraulic Properties, in: Anderson M.G. and J. J. McDonnell, Encyclopedia of Hydrological Sciences, Chapter 75, 1021-1144, John Wiley & Sons, Ltd.

• Peters, A., and W. Durner (2005): Verbesserte Methode zur Bestimmung der Retentionsfunktion aus statischen Säulenexperimenten, Mitteilungen der Deutschen Bodenkundlichen Gesellschaft. 107, 83-84

• Bitterlich, S., W. Durner, S.C. Iden, and P. Knabner (2004): Inverse Estimation of the Unsaturated Soil Hydraulic Properties from Column Outflow Experiments Using Free-Form Parameterizations, Vadose Zone Journal 3, 971-981.

• Hopmans, J.W., J. Šimunek, N. Romano, and W. Durner (2002): Simultaneous determination of water transmission and retention properties - Inverse methods. p 963-1008., In J.H. Dane and G.C. Topp (Eds.): Methods of Soil Analysis, Part 4: Physical Methods. 4thEdition. SSSA Book Series No. 5, American Society of Agronomy and Soil Science Society of America, 2002.

determination of effective soil hydraulic properties - challenges and solution strategies ·...

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