Field measurements of topsoil moisture p

Untitled Field measurements of topsoil moisture profiles by vertical TDR probes Roberto Greco *, Andrea Guida Dipartimento di Ingegneria Civile, CIRIAM – Centro Interdipartimentale di Ricerca in Ingeg[.]

Field measurements of topsoil moisture profiles

by vertical TDR probes

Dipartimento di Ingegneria Civile, CIRIAM – Centro Interdipartimentale di Ricerca in Ingegneria Ambientale,

Seconda Universita` di Napoli, Via Roma 29, 81031 Aversa (CE), Italy

Received 27 July 2006; received in revised form 27 July 2007; accepted 10 October 2007

KEYWORDS

Time domain

reflectometry;

Moisture profiles;

Inverse problems;

Infiltration;

Evaporation;

Field monitoring

Summary A recently developed inverse method for the estimation of water content pro-files from single time domain reflectometry (TDR) waveforms in laboratory has been adapted and applied to field measurements of topsoil moisture profiles in a pyroclastic sandy loam Three metallic probes of the lengths of 30 cm, 45 cm and 60 cm were verti-cally installed in an experimental field for the measurement of vertical water content pro-files One 15 cm long probe was inserted vertically into soil surface and five 10.5 cm long probes were buried horizontally at various depths for the measurement of local values of mean water content by means of the classical TDR approach The experimental campaign lasted 28 days, during which daily rainfall heights and daily maximum and minimum tem-peratures were measured at the experimental field TDR waveforms acquisition was car-ried out twice a day The agreement between local volumetric water content measurements and vertical profiles was in general satisfactory, although some of the ver-tical profiles failed in detecting a layer with systemaver-tically smaller water content values indicated by the horizontal probe buried at the depth of 30 cm below soil surface Such small water content values could be probably ascribed to the presence of a large amount

of pumice stones in the soil around that depth, affecting the water content measured by TDR probes and thus increasing estimated moisture spatial variability

ª2007 Elsevier B.V All rights reserved

Introduction

Time domain reflectometry (TDR) has been widely used in

the last decades for monitoring topsoil water content

In-deed, TDR provides easy and cheap water content

estima-tions with relatively small disturbance to the investigated soil TDR measurement of soil water content, based on the strong correlation observed between relative dielectric permittivity of wet soil and its volumetric water content h (Campbell, 1990), consists of measuring travel time Tp of

an electromagnetic pulse along a metallic waveguide of known length Lpinserted into the soil The volume averaged value of soil relative dielectric permittivity er, affecting the

0022-1694/$ - see front matter ª 2007 Elsevier B.V All rights reserved.

doi:10.1016/j.jhydrol.2007.10.013

* Corresponding author.

E-mail address: Roberto.Greco@unina2.it (R Greco).

a v a i l a b l e a t w w w s c i e n c e d i r e c t c o m

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j h y d r o l

velocity of propagation of electromagnetic waves along the

metallic waveguide, is given by (Topp et al., 1980)

er¼ c0Tp

2Lp

In Eq.(1)c0is the propagation velocity of electromagnetic

waves in the vacuum space

Several expressions of the relationship between erand h

have been proposed, empirically stated (Topp et al., 1980)

as well as based on semi-analytical approach to dielectric

mixing models (Roth et al., 1990; Whalley, 1993;

Heimova-ara et al., 1994)

So far, TDR field applications suffered the limitation due

to the capability of the technique of estimating only the

mean water content in the volume investigated by the

probe Whereas the knowledge of non-homogeneous

verti-cal water content profiles was needed, it was necessary to

install either several vertical probes of different length or

several horizontal probes placed in the soil at different

depths, in both cases strongly increasing soil disturbance

as well as the complexity of the measurements For the sake

of brevity, from now on the TDR measurements techniques

providing the volume averaged water content will be

re-ferred to as ‘classical’ TDR approach

Several studies have been recently dedicated to the

devel-opment of inversion methods aimed to extract more

informa-tion from TDR waveforms, in some cases concerning soil

dielectric properties (Heimovaara, 2001; Weerts et al.,

2001; Lin, 2003), in others dealing with estimating

non-homo-geneous moisture profiles along the probe axis A common

feature of all these methods is that the electromagnetic

tran-sient through the wet soil along the metallic probe is

mathe-matically modeled, assuming that the unknown soil

properties correspond to the best agreement between

simu-lated and measured waveforms In some cases the soil is

mod-eled as a series of small layers with different dielectric

properties, and the waveform is obtained as the result of

the superposition of multiple reflections arising from

imped-ance discontinuities between the layers (Nguyen et al., 1997;

Todoroff et al., 1998; Heimovaara, 2001; Moret et al., 2006)

Other methods consider the dielectric properties of the soil as

smoothly variable along probe axis (Greco, 1999; Schlaeger

et al., 2001; Oswald et al., 2003; Greco, 2006)

So far, the retrieval of non-homogeneous water content

profiles along TDR probes has been successfully applied only

under controlled laboratory conditions Aim of this paper is

testing the applicability to field measurements of an inverse

method for the estimation of water content profiles along

vertical TDR waveguides, recently applied in laboratory to

a sample of homogeneous soil with hydraulic boundary

con-ditions leading to monotonic moisture distributions (Greco,

2006) In this paper, the inverse method has been adapted

and applied to measurements of vertical water content

pro-files in an experimental field where non-monotonic moisture

profiles could be observed in the topsoil

Materials and methods

Soil moisture inverse profiling by TDR

The inverse method for retrieving moisture profiles along

TDR probes by Greco (2006)is here briefly described The

propagation of the electromagnetic pulse along a one dimensional transmission line may be expressed in terms

of electric voltage V(x, t) and electric current i(x, t) by means of the so-called telegraph equations (Ramo et al.,

1994):

@i

@tþ 1 LðxÞ

@V

@xþRðxÞLðxÞi ¼ 0;

@V

@tþ 1 CðxÞ @x@iþGðxÞCðxÞV ¼ dðx  ~xÞ½1  expðbtÞ:

8

<

:

ð2Þ

In Eq.(2), R, L, G and C represent, respectively, resistance, inductance, transverse conductance and capacitance of transmission line unit length; the forcing term at RHS of the second equation represents the voltage transient im-posed by the generator, with parameter b depending on emitted pulse rise time; the Dirac function d locates the forcing term at the abscissa ~x representing transmission line origin

In TDR applications to soil moisture determination, the transmission line along which the electromagnetic pulse propagates is typically constituted by a coaxial cable and

a metallic probe buried into the soil At frequencies mostly contributing to TDR waveforms, roughly ranging between

20 kHz and 1.5 GHz (Heimovaara, 1994), R and L may be as-sumed constant along a metallic probe of given geometry, while C(x) and G(x) depend, respectively, on relative dielec-tric permittivity er(x) and electrical conductivity r(x) of the soil, both in turn depending on water content distribution h(x)

The retrieval of the unknown moisture profile along TDR probe implies the resolution of the inverse problem, consist-ing in findconsist-ing the coefficients C(x) and G(x) for which the integration of Eq.(2)gives rise to simulated voltage at a generic abscissa x, Vðx; tÞ, closest to a given experimental waveform Vexp(t) This issue is achieved by minimizing the objective function W defined as a measure of the distance between simulated and experimental waveforms:

W½hðxÞ ¼

RT exp

0 ½VexpðtÞ  V½x; t; CðhðxÞÞ; GðhðxÞÞ2dt

RTexp

0 VexpðtÞ2dt

: ð3Þ For the laboratory application, the unknown moisture pro-file was parameterized according to a monotonic functional form with four parameters to be determined

Therefore, the retrieval of the unknown moisture profile reduced to the identification of four parameters of the cho-sen functional form

In this paper, the above described inverse method has been applied to the retrieval of water content profiles in a pyroclastic soil subject to natural infiltration and evapora-tion transients in the field In this case, a monotonic func-tional form for describing moisture distribution could not

be a priori assumed Therefore, in order to let the unknown moisture profile to be freely determined without imposing any predefined functional form, water content distribution has been schematized with a broken line formed by N seg-ments of length Dx = L/N, the parameters being the values

hiassumed in N + 1 equidistant vertices

With this choice, whereas a too large number N of segments is chosen, the inverse problem may likely turn

to be ill-posed, with multiple minima of the objective

function, which would hamper unknown moisture profile

retrieval

However, the length Dx of a segment has to be larger

than the effective spatial resolution of the TDR instrument,

in turn related to the frequency content of the voltage

pulse A rough estimate of the spatial resolution can be

made by considering signal rise time tr, usually defined as

the time for the signal to rise from 10% to 90% of its final

va-lue (Oswald et al., 2003):

Dxmin¼ c0tr

4e1=2r

Energy dissipations, due either to electrical conductivity or

to dielectric relaxation, mainly reduce signal power at high

frequencies (Robinson et al., 2003), smoothing the front of

the voltage pulse propagating along the probe: the rise time

of 200 ps of the pulse emitted by Tektronix 1502C cable

tes-ter used for the experiments extends up to nearly 1 ns for

the pulse reflected at the end of the longer metallic probe

in wet conditions

Therefore, Dx = 5.0 cm has been chosen, sensibly larger

than the spatial resolution, whatever the water content

could be This choice, as it will be clarified in Section

‘‘Sen-sitivity analysis’’, also prevents the problem to be ill-posed,

since the simulated waveform results sensible to the

varia-tion of even only one of the hivalues

The minimization of the objective function has been

car-ried out with a genetic algorithm (Holland, 1975; Goldberg,

1989) Such an evolutionary algorithm allows easily to

intro-duce constraints to parameters variability, at the same time

avoiding local minima by introducing random parameters

vectors at each generation

Field experiments and soil characterization

The above described method was applied to the

measure-ment of topsoil water content vertical profiles in an

exper-imental field located in S Arpino (CE) The field belongs to

the volcanic area north west of Napoli, where pyroclastic

deposits characterize the upper soil layer Soil physical

characteristics do not vary significantly up to a depth of

2.0 m below soil surface The soil layer between the depths

0.25 m and 0.35 m is characterized by of a large amount of pumice stones with dimensions ranging between few milli-meters and some centimilli-meters The presence of pumice stones may affect the volumetric water content measured

by TDR

Soil physical characterization, consisting in the determi-nation of dry soil bulk density, particle size distribution, sat-urated water content and satsat-urated hydraulic conductivity, was carried out on seven undisturbed samples taken at var-ious locations and depths in the experimental field.Fig 1

shows the particle size distribution curves measured for three of the samples, all falling within sandy loam limits according to USDA standards.Table 1summarizes the mea-sured soil physical parameters

The relationships linking volumetric water content, mea-sured gravimetrically, with soil dielectric permittivity and electrical conductivity were determined on two undisturbed cylindrical soil samples, with diameter of 10 cm and height

of 12 cm, taken at soil surface To this aim, a TDR metallic probe of the length of 12 cm, with three rods of the diame-ter of 1.5 mm and exdiame-ternal spacing of 20 mm was inserted into the samples After immersion in water, with electrical conductivity of 0.1 S/m at 20 °C, for 24 h, the samples were placed on an electronic balance Precisa Instrument Ltd XB4200C with an accuracy of 0.01 g and evaporation took place for 10 days, with air temperature ranging between 18° and 21° and relative humidity between 45% and 55% The weights of the samples were recorded at regular time intervals during evaporation and, at the same time, TDR

0 10 20 30 40 50 60 70 80 90 100

z=0.2 m z= 0.75 m z=2.0 m

d [mm]

Figure 1 Particle size distribution curves of the investigated soil

Table 1 Physical characteristics of the investigated soil Sampling depth (m) cdry(g/cm3) hsat ksat(cm/min)

waveforms were acquired At the end of the evaporation

experiment, the samples were oven dried at 105 °C for

24 h and then weighed for the measurement of the dry

weight

Soil dielectric permittivity was determined from TDR

waveforms with ‘classical’ approach by Eq (1) Bulk soil

electrical conductivity was determined from the waveforms

with the following expression (Dalton et al., 1984):

r¼

ffiffiffiffi

er

p

120pLp

ln Vt

Vr

In Eq.(5)Vtand Vrrepresent respectively incident and

re-flected voltage at the beginning of the probe The (e, h)

and (r, h) experimental points are respectively plotted in

Figs 2 and 3, together with the relevant best fitting curves

A linear relationship between h and the square root of er

showed the best performance for fitting the er(h) experi-mental data:

h¼e

0:5

r  2:1301

The relationship proposed by Rhoades et al (1976) was adopted for fitting the r(h) data:

In the above equation, rsrepresents dry soil electrical con-ductivity; rwis soil solution electrical conductivity; a and b are fitting parameters related to tortuosity of electric cur-rent flow paths From experimental data fitting, it resulted

rs¼ 0:0086 S=m;

a ¼ 1:752;

b ¼ 0:176:

ð8Þ

R2= 0.975

4 4.5 5 5.5 6

θ[m3/m3]

εr

Figure 2 Experimental soil bulk dielectric permittivity vs water content relationship: (d) experimental data; (—) best fit by Eq.(5)

R2= 0.8355

0 0.01 0.02 0.03 0.04 0.05 0.06

θ[m3/m3]

Figure 3 Experimental soil bulk electrical conductivity vs water content relationship: (d) experimental data; (—) best fit by Eq. (6)with the parameters given in Eq.(7)

Since soil water electrical conductivity in the field is not known and probably variable during infiltration/evaporation processes, rwturns to be an additional fitting parameter of the inverse water content retrieval method

The soil surface in the experimental field is nearly flat horizontal and the groundwater table lays approximately

20 m deep below soil surface TDR water content measure-ments were carried out with Tektronix 1502C cable tester, connected alternately via coaxial cable to 9 three rods metallic probes of various dimensions After removing the grass covering, four probes of various lengths ranging be-tween 15 cm and 60 cm were inserted vertically from soil surface; a 60 cm deep trench was dug for the installation

of five 10.5 cm long probes; such probes were inserted hor-izontally into the wall of the trench at various depths The geometric characteristics of the probes are given inTable

2.Fig 4shows a sketch of the experimental field with the locations of the probes

The experimental apparatus was completed by a rain gauge for the measurement of daily rainfall heights and a thermometer for the measurement of daily maximum and minimum air temperatures

The experimental activities lasted from 15 March 2007 to

11 April 2007 During the entire period, rainfall height was measured every day at 12.00 a.m.; with few exceptions, TDR waveforms were acquired twice a day, in the morning between 9.00 a.m and 11.00 a.m and in the afternoon be-tween 2.00 p.m and 4.00 p.m In total, around 40 wave-forms for each installed probe were acquired during the experimental campaign

Sensitivity analysis

Identifiability of the parameters of a model is difficult to state rigorously, but it always requires model output to show high sensitivity to parameters variations (Chavent,

1987; Sun, 1994) The non-uniqueness of the solution may also be avoided by imposing constraints to parameters val-ues variability deduced by their physical meaning In the present case model parameters are constituted by N + 1 water content values hi in the vertices of the profile and

Table 2 Geometrical characteristics of the TDR probes

used for field water content measurements

Probe Rods diameter

(mm)

Rods spacing (mm)

Probe length (mm)

0.50 0.75 1.00 1.25 1.50

t [ns]

θ 7=0.05

θ 7=0.15

θ 7=0.3

θ 7=0.45

θ 7=0.6

Figure 5 Effect of the change of the water content h in the middle of the 60 cm long probe on simulated TDR waveforms

Vertical Section

S4

S1

S3 S2

H1 H2 H3 H4 - H5

S3 S1 S4

S2

Plan View

15 cm

H5

H1 - H2 - H3 - H4

15 cm

50 cm

40 cm

15 cm

Figure 4 Sketch of the experimental field with the locations

of the TDR probes

by soil water electrical conductivity rw, which have been

subjected to the following constraints:

0:05 6 hi60:6 m3=m3;

A sensitivity analysis has been carried out to show the

ef-fects on the simulated waveform obtained by integrating

Eq (2)due to a change of a single parameter The

wave-forms refer to the case of a 60 cm long probe along which

the soil water content profile is represented as a broken line

with 12 segments

Waveform sensitivity to variations of a single hiis studied

by changing the water content in the middle of the probe,

h7, over the entire range of variability given in the first of

Eq (9) The other hi values are all equal to 0.3 Some of

the obtained waveforms are plotted inFig 5

Fig 6shows the waveforms corresponding to a constant

water content profile with h = 0.3 and different values of

soil water electrical conductivity rw, covering all the inter-val of variability given in the second of Eq.(9)

In both cases the waveforms are significantly affected by parameters changes Since the chosen objective function W

is a measure of the area between experimental and simu-lated waveforms, it looks clear that its value is certainly af-fected even by the change of a single parameter

Results and discussion During the observation period, the total recorded rainfall height was 95.0 mm, with 10 rainy days (daily rainfall height above 1.0 mm).Fig 7shows the histogram of daily rainfall height and the observed minimum and maximum daily tem-peratures The large amount of precipitation and the high level of air relative humidity during the dry periods caused relatively slow evaporation form topsoil surface, determin-ing in most cases wet soil conditions within the entire

inves-0.50 0.75 1.00 1.25 1.50

t [ns]

σw=0.001S/m

σ

w =0.05S/m

σw=0.02S/m

σw=0.01S/m σ

w =0.005S/m

σ

w =0.1S/m

Figure 6 Effect of the change of soil water electrical conductivity rwon simulated TDR waveforms

0 10 20 30

Figure 7 Histogram of daily rainfall heights and time history of daily minimum and maximum temperatures

tigated soil profile Only the topsoil water content, affected

by evaporation, showed more variability Fig 8 gives the

mean water contents measured, with classical TDR

ap-proach, with 15 cm long vertical probe installed at soil

sur-face and with four 10.5 cm long horizontal probes buried at

various depths

The water content at the depth of 30 cm resulted always

much smaller than what was measured at the other

investi-gated depths This was probably due to the presence of

pumice stones inside the volume investigated by the TDR

probe buried at that depth

The local mean values of water content provided by

clas-sical TDR approach have been compared with the profiles

retrieved with the inverse profiling TDR method applied to

30 cm, 45 cm and 60 cm long vertical probes installed at soil

surface The optimization procedure for water content

pro-file estimation always provided low values of the objective

function W, between 0.033 and 0.042, indicating that very

good agreement between simulated and acquired TDR

waveforms was achieved (Fig 9)

Soil water electrical conductivity values obtained by the minimization of W resulted in all cases between 0.019 S/m and 0.031 S/m, with a mean value of rw= 0.023 S/m The agreement between mean volumetric water content measurements and h(z) profiles is in general satisfactory, with a mean difference between local value of water con-tent provided by classical TDR approach and by inverse pro-filing method of 0.011 m3/m3, with a standard deviation of 0.060 m3/m3 The standard deviation of the differences is mainly due to the values of water content provided by the two approaches at 30 cm depth At that depth, in fact, vol-umetric water content measured by TDR presents a partic-ularly high spatial variability due to the presence of pumice stones inside the volume investigated by the probe

If the water content data at 30 cm depth are removed, the standard deviation of the differences between the two ap-proaches becomes 0.007 m3/m3

Figs 10–12give some examples of the obtained agree-ment between local water content values and retrieved pro-files In particular,Fig 10is representative of extremely wet

0.2 0.3 0.4 0.5

3 /m

probe S3 z<15cm probe H1 z=15cm probe H2 z=30cm

0.3 0.35 0.4 0.45

3 /m

probe H3 z=45cm probe H4 z=60cm probe H5 z=60cm

Figure 8 Time history of mean local water content at various depths estimated with classical TDR approach

0.5 0.75 1 1.25 1.5

t [ns]

Figure 9 Example of the agreement between experimental (dots) and simulated (continuous line) waveforms: S2 probe on 04.04.2007 morning (W = 0.037)

0

10

20

30

40

50

60

θ[m3/m3]

vertical 30cm probe vertical 45cm probe vertical 60cm probe horizontal probes vertical 15cm probe

Figure 11 Vertical water content profiles and mean local values observed on 03.04.2007 afternoon: (d) mean values from horizontal probes; (– –) mean value from vertical 15 cm long probe; (

0

10

20

30

40

50

60

θ[m3/m3]

horizontal probes vertical 15cm probe vertical 30cm probe vertical 45cm probe vertical 60cm probe

Figure 10 Vertical water content profiles and mean local

values observed on 04.04.2007 morning: (d) mean values from

horizontal probes; (– –) mean value from vertical 15 cm long

probe; (

conditions, since the plotted data refer to the measurements

carried out on 04.04.2007 afternoon, when 27 mm of

precipitation had been recorded by the rain gauge.Figs 11

and 12 refer, respectively, to the measurements made on

03.04.2007 afternoon, when only 5 mm of rain height had

been measured during the previous 9 days, and to the

after-noon of 11.04.2007, after 6 dry days with brilliant sunshine

and high maximum temperatures, representing two of the

driest conditions encountered during the experimental

campaign

In all the showed examples, the three vertical profiles are

in good agreement, either mutually or with the mean local

values In most cases, the profiles show the presence of a

layer with smaller water content, although not exactly

around the depth of 30 cm as it is indicated by the horizontal

probe H2 buried at that depth Such result may be ascribed to

different depths of the pumice stones affecting the water

content detected by the TDR probes Such hypothesis seems

to be confirmed by the fact that the vertical probe predicting

the dryer layer closer to the depth of 30 cm is the probe S2,

which is the closest to the horizontal ones

Conclusions

An inverse method for the measurement of soil water

con-tent profiles along TDR probes, already successfully tested

in laboratory experiments (Greco, 2006), has been adapted and applied to field measurements of topsoil moisture pro-files in a pyroclastic sandy loam The adaptation to field measurements consisted in removing the a priori assumed monotonic water content profile functional form, substi-tuted with a broken line shaped water content profile with unconstrained values in the vertices

Before applying the method, a preliminary physical char-acterization of the investigated soil was carried out on undisturbed samples taken at the experimental field In particular, the relationships linking soil volumetric water content with dielectric permittivity and electrical conduc-tivity were experimentally determined

For the field application of the inverse profiling method, three TDR metallic probes (30 cm, 45 cm and 60 cm long) were vertically inserted into topsoil surface of a pyroclastic sandy loam soil One 15 cm long probe vertically inserted into topsoil surface and five horizontal 10.5 cm long probes horizontally buried at various depths were also installed for the measurement of mean values of water content with the classical TDR method

TDR waveforms acquisition was carried out twice a day for 28 days During the same period daily rainfall heights and daily minimum and maximum temperatures were also measured with a rain gauge and a thermometer installed

at the experimental field

The reliability of the vertical water content profiles esti-mated from the waveforms acquired with the three longer vertical probes was tested by comparing them with the mean local values of soil water content provided by the ver-tical 15 cm long probe and by the five horizontal probes A satisfactory agreement was observed during the entire per-iod, although the estimated water content at the depth of

30 cm resulted strongly variable, probably because mea-surements results were affected by the presence of pumice stones inside the volumes investigated by some of the probes at that depth

The obtained results indicate that the proposed TDR based soil water content inverse profiling technique is suit-able for field applications, although the presence of heter-ogeneous soil layers may hamper the reliability of the retrieved water content profiles However, the developed technique looks as a promising tool for infiltration and evap-oration monitoring in the field

References

Campbell, J.E., 1990 Dielectric properties and influence of conductivity in soils at one to fifty megahertz Soil Sci Soc.

Am J 54, 332–341.

Chavent, G., 1987 Identifiability of parameters in the output least square formulation In: Walter, E (Ed.), Identifiability of Parametric Models Pergamon, New York.

Dalton, F.N., Herkelrath, W.N., Rawlins, D.S., Rhoades, J.D., 1984 Time domain reflectometry: simultaneous assessment of the soil water content and electrical conductivity with a single probe Science 224, 989–990.

Goldberg, D.E., 1989 Genetic Algorithms in Search, Optimization and Machine Learning Addison-Wesley, Reading, Massachussets Greco, R., 1999 Measurement of water content profiles by single TDR experiments In: Feyen, J., Wiyo, K (Eds.), Modelling of Transport Processes in Soils Wageningen Pers, Wageningen, the Netherlands, pp 276–283.

0

10

20

30

40

50

60

θ [m3/m3]

horizontal probes vertical 15cm probe vertical 30cm probe vertical 45cm probe vertical 60cm probe

Figure 12 Vertical water content profiles and mean local

values observed on 11.04.2007 morning: (d) mean values from

horizontal probes; (– –) mean value from vertical 15 cm long

probe; (—) vertical water content profiles.

Greco, R., 2006 Soil water content inverse profiling from single

TDR waveforms J Hydrol 317, 325–339.

Heimovaara, T.J., 1994 Frequency domain analysis of time domain

reflectometry waveforms 1 Measurements of complex

dielec-tric permittivity of soils Water Resour Res 30, 189–199.

Heimovaara, T.J., 2001 Frequency domain modelling of TDR

waveforms in order to obtain frequency dependent dielectric

properties of soil samples: a theoretical approach In: TDR 2001

– Second International Symposium on Time Domain

Reflecto-metry for Innovative Geotechnical Applications Northwestern

University, Evanston, Illinois, pp 19–21.

Heimovaara, T.J., Bouten, W., Verstraten, J.M., 1994 Frequency

domain analysis of time domain reflectometry waveforms 2 A

four component complex dielectric mixing model for soils.

Water Resour Res 30, 201–209.

Holland, J.H., 1975 Adaptation in Natural and Artificial Systems.

MIT Press, Cambridge.

Lin, C.-P., 2003 Analysis of nonuniform and dispersive time domain

reflectometry measurement system with application to the

dielectric spectroscopy of soils Water Resour Res 39 (1), 1012.

Moret, D., Arru ´e, J.L., Lo ´pez, M.V., Gracia, R., 2006 A new TDR

waveform analysis approach for soil moisture profiling using a

single probe J Hydrol 321, 163–172.

Nguyen, B.L., Bruining, J., Slob, E.C., 1997 Saturation profiles from

dielectric (frequency domain reflectometry) measurements in

porous media In: Proceedings of International Workshop on

characterization and Measurements of the Hydraulic Properties of

Unsaturated Porous Media, Riverside, California, pp 363–375.

Oswald, B., Benedickter, H.R., Ba ¨chtold, W., Flu ¨hler, H., 2003.

Spatially resolved water content profiles from inverted time

domain reflectometry signals Water Resour Res 39 (12), 1357.

Ramo, S., Whinnery, J., Van Duzer, T., 1994 Fields and Waves in

Communication Electronics J Wiley and Sons, New York.

Rhoades, J.D., Raats, P.A.C., Prather, R.J., 1976 Effects of liquid-phase electrical conductivity, water content, and surface conductivity on bulk soil electrical conductivity Soil Sci Soc.

Am J 40, 651–655.

Robinson, D.A., Jones, S.B., Wraith, J.M., Or, D., Friedman, S.P.,

2003 A review of advances in dielectric and electrical conduc-tivity measurement in soils using time domain reflectometry Vadose Zone J 2, 444–475.

Roth, K., Schulin, R., Fluhler, H., Attinger, W., 1990 Calibration of time domain reflectometry for water content measurement using a composite dielectric approach Water Resour Res 26, 2267–2273.

Schlaeger, S., Huebner, C., Scheuermann, A., Gottlieb, J., 2001 Development and application of TDR inversion algorithms with high spatial resolution for moisture profile determination In: TDR 2001 – Second International Symposium on Time Domain Reflectometry for Innovative Geotechnical Applications North-western University, Evanston, Illinois, pp 236–248.

Sun, N.-Z., 1994 Inverse Problems in Groundwater Modeling Kluwer Academic Publishers, Dordrecht.

Todoroff, P., Lorion, R., Lan Sun Luk, J.-D., 1998 L’utilisation des

ge ´ne ´tiques pour l’identification de profils hydriques de sol a ` partir de courbes re ´flectome ´triques CR Acad Sci Paris, Sciences de la terre et des plane `tes 327, 607–610.

Topp, G.C., Davis, J.L., Annan, A.P., 1980 Electromagnetic determination of soil water content: measurement in coaxial transmission lines Water Resour Res 16, 574–582.

Weerts, A.H., Huisman, J.A., Bouten, W., 2001 Information content of time domain Reflectometry waveforms Water Resour Res 37 (5), 1291–1299.

Whalley, W.R., 1993 Considerations on the use of time domain reflectometry (TDR) for measuring soil water content J Soil Sci.

44, 1–9.