Measuring soil surface water content using full- wave inversion of off-ground GPR data

Sébastien Lambot(1,2), Evert Slob(3)

Diana Chavarro(4), Maciek Lubczynski(4)

(1)Université

catholique de Louvain (Belgium)(2)Forschungszentrum Jülich (Germany)

(3)Delft

University of Technology (The Netherlands)(4)ITC, The Netherlands

Sustainable and optimal management of soil and water resources is required to preserve our environment and sustain increasing societal demands

Human activities, but also natural processes, lead to soil degradation worldwide:erosion, compaction, pollution, desertification, sealing, salinization, nutrient depletion

Surface water content is a key hydrological variable, controlling infiltration and runoff, evaporation, and energy exchanges between the soil and the atmoshere.

Management strategies and decision support

Observation: characterizing and monitoring the environment

Process understanding and modeling

GPR is promising to characterize surface water content at the field scale

InnaccessibilityHeterogeneity

Electromagnetic contrasts

GPR basic principles

GPR operates by transmitting microwave electromagnetic energy down into the ground through an antenna. The transmitted energy is reflected from various electromagnetic interfaces. An antenna then receives the reflected signal.

• Dielectric permittivity ε

• Electric conductivity σ

• Magnetic permeability µ

wave velocity

Tx Rx

ε1

, σ1

, µ1

Radar system

electronics

ε2

, σ2

, µ2

ε3

, σ3

, µ3

wave attenuation

reflection and refraction

Common GPR surface ground wave

txv =

2

⎟⎠⎞

⎜⎝⎛=

vc

rε

• GPR contact with the soil• Identification of the ground wave• Large antenna separation• Strong EM simplifying assumptions

Limitations

Common GPR surface reflection coefficient method

with

⇔

ε1

ε2

ε1

PECσ→∞

• Reference PEC measurements, at same h!• Strong EM symplifying assumptions

Limitations

Ei Ei EsEs

Advanced GPR forward and inverse modeling

• Parameter retrieval capabilities are limited

• Error in the estimates are inherently introduced

• Expert user is needed and techniques may be cumbersome

Common techniques

• SFCW radar with a VNA

→ UWB, international standard

• Directive horn antenna

→ to be used off the ground

• Monostatic

mode

→ accurate and efficient forward modeling

Low-cost and handheld radar

GPR system

(Lambot et al., IEEE TGRS, 2004)Antenna equation in the frequency domain

Time domain illustration

Antenna

at

≠

heights

above

a PEC

Antenna equation

h

Time domain illustration

Antenna

at

≠

heights

above

a PEC

Antenna equation

Linear time gain

*

h

• 3-D

multilayered

medium

• Dirac electric source/receiver

Exact solution of Maxwell’s equations

3D Green’s function

Frequency domain Time domain

Configuration ≠

θ

Model validation

Inverse problem for the particular case of surface dielectric permittivity retrieval

tmin

h

εσ ≅ 0

tmax

zmax

with

Surface roughness: hmax

<λ/8

(Lambot et al., WRR, 2006b)

(Lambot et al., WRR, 2006a)

min

Advantages compared to the ground-wave or common reflection methods

Issues to take care of

• Effect of surface roughness (hmax

<λ/8)

• Effect of vegetation

• VNA measurements are an international standard

• 3-D

solution of Maxwell’s equations

• Antenna effects are filtered

• No time-zero and reflection time issues

• Reference PEC measurements are not needed

• Antenna height should not be known

• No need to identify the ground wave using multiple measurements

• Possibility to include effects of soil layering and high σ

• Fully automated

1-2 GHz

0.1-0.9 GHz

Effect of electric conductivity: numerical experiments

Effect of shallow layering: numerical experiments

≠

d1

≠

θ

1

2

std FD = 8×10-3

std TD = 2×10-2

Validation in laboratory conditions

Field experiment: Selhausen test site

Water content

dry

Saturated

Aquiferex project: Tunisia

Measurements in different irrigated plots (Gabes):

36 measurements over 17 plots

Topp’s

model

Topp’s

model

Results

GPR TDR

(gravimetric) (gravimetric)

GPRSoil

specific

model

TDR

Results taking into account electric conductivity during inversion of GPR data

r=0.94Soil

specific

modelr=0.93

→ Microvariability→ Measurement scale→ Surface roughness

(gravimetric) (gravimetric)

1-2 GHz 0.1-0.9 GHz

Extending the frequency range towards lower frequencies is required to estimate σ

z θ

x

Surface GPR TDR

Sample Remote sensingMeasurement scales

• Gravimetric

• Theta-probe

• Off-ground GPR

Transect

Olive trees

Measurements over a transect in Ben Gardane:

65

measurements

Dielectric permittivity and water content over the transect

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0 10 20 30 40 50 60 70

Measurement

Wat

er c

onte

nt

0,00

1,00

2,00

3,00

4,00

5,00

6,00

0 10 20 30 40 50 60 70

Measurement

Die

lect

ric c

onst

ant 687119mE 3672243mN

688533mE 3670591mN

• Dry

• Small variation range

• Some spatial correlation

Observations

Integrated hydrogeophysical inversion for vertical profile reconstruction

EM model

Modeled signals

Measured signalsError

function

Optimization algorithm

Dielectric and electric profiles

G↑xx

(f,t)

ε(z,t)σ(z,t)

z

θ

t (min)

BC

∞

unknowns

EM model

Modeled signals

Measured signalsError

function

Optimization algorithm

Hydraulic properties

Hydrodynamic model

Modeled water content

Petrophysical relationships

Dielectric and electric profiles

0 20 40 60 80 100 120 140 160 180 200

0.15

0.2

0.25

0.3

Wat

er c

onte

nt (m

3 m-3

)

Time (min)

G↑xx

(f,t)

ε(z,t)σ(z,t)

θ(z,t)

?

P Time lapse

Constraint

(Lambot et al., GRL, 2006)

Integrated hydrogeophysical inversion

Simulated infiltration in a sandy soil

Hydrodynamic model configuration

• Hydraulic properties: Mualem-van Genuchten’s

model

0 20 40 60 80 100 120 140 160 180 200

0.15

0.2

0.25

0.3

Wat

er c

onte

nt (m

3 m-3

)

Time (min)

θr

= 0.00θs

= 0.357Ks = 8.24 cm/minα

= 0.0278 cm-1

n = 7.02λ

= 2.89

• 1-D Richard’s equation: WAVE

Precipitation

Water table

30 cmSimulation domain

• Boundary conditions unknowns

Initial condition:Hydrostatic equilibrium

(Lambot et al., WRR, 2002)

Water content profiles as f(t) Pedotransfer functions

Model of Ledieu

Model of Rhoades

2

⎥⎦⎤

⎢⎣⎡ −

=a

br

θε

( ) swba σσθθσ +′+′= 2

Electromagnetic model configuration and radar data

ε(z,t)σ(z,t)

S0.15 m

Δz=0.005 m

0.30 m

⎟⎠⎞

⎜⎝⎛

10minλ

(Thanks to Oliver Bucker, ZAM)

t

(min) t

(min)

JUMP: 1312 CPUs, 8.9 TFLOPSJUBL: 16384 CPUs, 45.8 TFLOPS

Objective function

( )2* ),(),(∑∑ ↑↑ −=Φ

f txxxx tftf GGb

Least squares

Optimization algorithm

Global multilevel

coordinate

search

(GMCS) algorithm

+

Nelder-Mead simplex (NMS) algorithm

91 frequencies

25 observation times

t

(min)

Well-posedness of the inverse problem

Response surface analysis

No convergence

θr

= 0.00θs

= 0.357Ks = 8.24 cm/minα

= 0.0278 cm-1

n = 7.02λ

= 2.89

unknown

known

Successful

(~450 iterations)

θr

= 0.00θs

= 0.357Ks = 8.24 cm/minα

= 0.0278 cm-1

n = 7.02λ

= 2.89

unknown

known

Successful

(~800 iterations, ~8 hours, 16 CPUs)

3p 4p

Enough information is contained in the time-lapse GPR measurements

Optimization results

Other soil types

Coarse Fine

Successful Successful

Parameter space constraints

A priori knowledge,

other sources of information

• UWB, dynamic range• EMI, seismic/acoustic

• BC• IC• Structure Computation

time

Petrophysical parameters, σw

A priori knowledge

Spatial correlation

Laboratory experiment (preliminary results)

(TNO facilities, The Netherlands)

Measured Green’s function Modeled Green’s function

Very

fine

Very

fineFine

Fine

Medium fine

Medium fineMedium

Medium

Coarse

Coarse

Estimated

Estimated

Water retention curve Hydraulic conductivity function

(HYPRES)

•

Full-wave

GPR

data inversion presents considerable theoretical and practical advantages for surface water content mapping

•

The proposed method is operational and fully automated

•

We are exploring methods to extend its applicability in high conductive and strongly layered soils, and better define characterization scale

Soil

moisture

mapping

and monitoringSoil

hydraulic

properties

mapping

Conclusions and perspectives

References

-Lambot, S., E.C. Slob, I. van den Bosch, B. Stockbroeckx, and M. Vanclooster, Modeling

of ground-penetrating

radar for accurate

characterization

of subsurface

electric

properties, IEEE Transactions on Geoscience

and Remote

Sensing, 42, 2555-2568, 2004.

-

Lambot, S., L. Weihermüller, J.A. Huisman, H. Vereecken, M. Vanclooster, and E.C. Slob, Analysis

of air-launched

ground-penetrating

radar techniques to measure

the soil

surface water content, Water Resources

Research, 42, W11403, doi10.1029/2006WR005097, 2006.

-

S. Lambot, E. C. Slob, M. Vanclooster, and H. Vereecken, "Closed loop GPR data inversion for soil hydraulic and electric property determination," Geophysical Research Letters, vol. 33, pp. L21405, doi:10.1029/2006GL027906, 2006.