Quasi 3D Image Construction of Infiltration Processes in the Vadose Zone byCombining Inter Borehole Radar Data and Numerical Simulation of Water
Flow in Soils
Seiichiro Kuroda(1), Hirotaka Saito(2), Takehiko Okuyama(1) Mutsuo Takeuchi(1),Jiri Šimůnek (2) and Martinus TH. Van Genuchten(3)
(1)

(3)

(2)
National Institute for Rural Engineering, Japan.
University of California, Riverside, USA.
G.E. Brown Jr. Salinity Laboratory, USDA, ARS,Riverside, CA.

ABSTRACT
A study to clarify the hydrological processes in thevadose zone by using a time-laps geophysicalmethodology has been performed. Recently, estimationof soil hydraulic parameters, such as the hydraulicconductivity, using geophysics data has increasingly
received attention. We report the study characterizing
hydraulic parameters of the vadose zone using interborehole radar data obtained from artificial ground water
recharge test at the infiltration pit. A numerical study
was carried out to obtain inversely the hydraulicparameters, such as soil water retention curve model
parameters and hydraulic conductivity function using
HYDRUS-2D. The forward simulation of soil water flowusing obtained parameters could be used to construct thequasi 3D image of water flow in the vadose zone.
KEY WORDS: Ground Penetrating Radar (GPR),
cross-borehole radar, soil hydrology, vadose zone,
parameterization
INTRODUCTION
Recently many studies have tried to characterize
the hydrological processes by monitoring time-lapsgeophysical methodologies. Inter-borehole radar, which
has an advantage in quantitatively estimatiing watercontents in a variety of spatial resolutions, has been oneof the most useful geophysical tools for analyzinghydrological processes, especially in the vadose zone(Hubbard, et al., 1997; Parkin, et al., 2000; Binley, et al.,
2001; Rucker and Ferré, 2003). Recently the soil
hydraulic properties were theoretically estimated from
borehole GPR data (Rucker and Ferré, 2003).
This paper presents the study characterizing
hydraulic parameters of the vadose zone using interborehole radar data obtained from artificial ground water
recharge test at the infiltration pit. A numerical study
was carried out to obtain inversely the hydraulicparameters, such as soil water retention curve model
parameters and hydraulic conductivity function using
HYDRUS-2D. The forward simulation of soil water flowusing obtained parameters could be used to construct thequasi 3D image of water flow in the vadose zone.
FIELD TEST DATAInter-borehole radar data to characterize hydraulicparameters in the vadose zone were obtained bymonitoring the artificial groundwater recharge test
conducted in Nagaoka City in Niigata Prefecture, Japan.
Figure 1(a) shows the schematics of the test site and thespatial arrangement of the infiltration pit and boreholes.
The top 2-m surface soil was loam, and the subsoil wasgravel. The water table was located about 10 m below
the surface. The infiltration pit was a 2 × 2 m square andits bottom, at which infiltration into the soil occurred,
was located at 2.3 m from the surface (z=–2.3 m). Twoboreholes were located on opposite sides of the pit.
While the length of the borehole T (Fig. 1(a)) was 11 m,
the borehole R was only 5.7 m long because of an
unexpected machine trouble at the field. The distance
between the two boreholes was 3.58 m. The target
ponding depth in the infiltration pit was set at 50 cm. It
took about 40 min for the ponding depth to reach its
target value.
All ground penetrating radar data were collectedby a GSSI SIR10 system with borehole antennae at thedominant frequency 110 MHz. The transmitter wasplaced in T borehole, while the receiver antenna wasplaced in R borehole (Fig. 1(a)).
In this test, instead of using time-consuming
multi-offset gathering (MOG) and tomography analysis,
repetitive zero-offset gathering (ZOG) was adopted as
the main measurement methodology because we wereparticularly interested in vertical water flow. Rapid water
migration into the gravel layer was expected on the basisof hydraulic conductivity data obtained by a series ofpumping tests. ZOG measurements were made at z=–2.3
and –2.55 m, and at every 0.1-m between z=–2.8 and –5.0 m.
The volumetric water content at each measurement
depth was estimated as follows. First, the propagation
velocity of the electromagnetic wave V in the soil wascalculated by V = D/t, assuming ray-path linearity, whereD is the distance between the boreholes, and t is thetravel time between the two boreholes measured withZOG. Next, the apparent dielectric constant Ka wasobtained by the following equation:
Ka = (C/V)2,
where C is the electromagnetic velocity in free space.
Finally, volumetric water content was estimated bysubstituting the calculated Ka value into Topp's equation(Topp et al., 1980).

Figure 1 : Schematics of artificial recharge test and water content change in the vadose zone
obtained by cross-hole GPR
SIMULATION OF SOIL WATER FLOW IN THE
VADOSE ZONE AND CHARACTERIZATION OF
HYDRAULIC PROPERTIES

Figure 1(b) shows the vertical profile oftraveltimes (or calculated water contents) and theirchange with time. Wetting front movement and theinfiltration process in the vadose zone are clearlyobserved. As can be seen, the initial water content in theupper zone (around 2.5-3.5m depth) is greater than thelower zone (around 4.5m depth). The spatial distributionof the final water content (105-107 min.) has a similar
trend. This difference is therefore due to the difference inhydraulic characteristics of soils: the soil in the upper
layer has finer texture higher water retentivity comparedto the soil in the lower layer, resulting higher initialwater contents. On the other hand, because the finer andless permeable upper layer limits the amount of
infiltration, the lower layer with higher permeability is
kept unsaturated and at a low volumetric water content.
Such a feature suggested that it is not appropriate toconsider a uniform vadose zone. The characterization of
hydraulic properties in the next chapter was conducted inconsideration of the feature mentioned above.

Simulation of water flow in the vadose zone andits parameterization were conducted using HYDRUS-2D(Simunek, et al., 1999). It was based on the DarcyRichard’s equation. The water movement around theinfiltration pit was assumed axisymmetric and wassimulated within cylindrical 2 dimensional coordinates.
The pore size distribution model of Mualem(1976) was used to predict the unsaturated hydraulicconductivity function, K(h), from the saturated hydraulicconductivity Ks and the van Genuchten’s (1980) model
parameters of the soil water retention curve%" s # "r'" r +n m'h<01+ $h" ( h) = &[''(][K ( h ) = K sSel 1# (1# S1/e m )where

m=1-1/n, n>1!

h)0"sm 2]

!

and " (h) is soil water retention curve, which describes
the functional relationship between the volumetric watercontent θ at a pressure head h.
The simulation zone is simply divided into two
regions above and blow the 3.5m depth, following thefeature described in the previous section (Table .1). The
initial volumetric water content "ini was 0.19 in the upper
region and 0.18 in the lower region, referring to themeasurement value. The same values for θr and θs wereused for both regions.
Other parameters, " , n, and!
saturated soil hydraulic conductivity Ks were inversely
obtained using the Levenberg-Marquardt nonlinear
minimization method (details can be found in Simunek,!
et al., 1999).
Fig.2 shows the break through curves of watercontent measured by inter-borehole radar at 5 depths andtheir fitting curves using estimated parameteres listed inTable.1. Fitting curves reproduce the observed values
and the feature of soil water flow described in theprevious section well.
Fig.3 shows the simulated quasi 3D (cylindrical2D) water flow in the vadose zone under the infiltration
pit using parameters obtained. It only shows the righthand side of the axis. Although the original data were on
dimensional obtained by zero offset profiling of interborehole radar, the fusion with numerical simulation ofwater flow enables a creation of a quasi-3D dynamic
image of water infiltration processes.
CONCLUSIONSThe simulation of water flow in soils based on
the Darcy-Richards equation and the van Genuchten
model has flexibility in estimating hydraulic properties
by fitting to the actual field data of inter-borehole radar.
The hydraulic parameters inversely obtained using thenonlinear least-squares approach enable to describe theinfiltration process into the vadose zone from theartificial ground water recharge pit observed by interborehole radar. The hydraulic parameters obtained
enable to create a quasi 3D dynamic image of theinfiltration process.
In the future, the radiation pattern, the propagation
path, and the resolution of the electromagnetic wave
must be considered.

REFERENCES
Binley, A., P. Winship, R. Middleton, M. Pokar, J. West,
2001, High-resolution characterization of vadose zone
dynamics using cross-borehole radar, Water Resour.
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Rucker,D.F. and Ferré,Ty P. A., 2002, Measuring theadvance of a wetting front using cross-borehole GPR,
Proceedings of SPIE,Volume 4758,Ninth International
Conference on Ground Penetrating Radar, Steven
Koppenjan, Hua Lee, Editors, 176-179

Rucker,D.F. and Ferré,Ty P. A., 2004, Parameter
Estimation for Soil Hydraulic Properties Using ZeroOffset Borehole Radar: Analytical Method, Soil Sci.
Soc. Am. J.68: 1560-1567.
Hubbard, S.S., Peterson, Jr, J.E., Majer, E.L,Zawislanski, P.T., Williams, K.H., Roberts, J. andWobber, F., 1997, Estimation of permeable pathways
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LEADING EDGE, Vol.16,1623 -1628
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Asano, Yoshinori Todoroki, and Michiaki Konno.
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Table 1: Parameters for vadose zone water flow simulation
Zone

DepthαnKsl

Region1~3.5m

0.19 0.178 0.282 5.33

4.44

6.12E-05

0.5Region2 3.5m~
0.18
4.85
" ini : Volumetric water content in the initial condition
Italic figures were parameters given by inversion

2.784.07E-04

inir!

Figure 2 : Comparison between simulation results and GPR data

Depth0s

1,500s2,000s2,500s3,000s4,000s5,000s6,000s9,000s

12,000s

2.3m3.5m-

6.0m2.3m3.5m-

6.0m-

Figure 3 : Infiltration image by vadose zone simulation based on GPR data fitting