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KnowledgeFusionSoilWaterDynamics fromMonitoring InfiltrationwithGPR
Lisa Hantschel1,2 and Kurt Roth1
1Institute of Environmental Physics, Heidelberg University, Heidelberg2Heidelberg Graduate School of Fundamental Physics, Heidelberg University, Heidelberg
1. IntroductionUnderstanding infiltration in dry heterogeneous sandy soils is a key issue with water resources insemi-arid areas. It includes a number of challenging soil-water phenomena that range from thestrong non-linearity through mulitscale heterogeneity, all the way to non-equilibrium phenomenalike fingering. We aim to represent the processes based primarily on GPR-measurements and inparticular aim for the quantification of effective soil hydraulic properties.
2. Infiltration in sandy soilsPhysics of Infiltration
Soil water dynamics is commonly represented by the Richards equation, describing thedevelopment of water content θ in dependence of hydraulic conductivity K and matricpotential Ψm
∂θ
∂t= −~∇ · [K[~∇Ψm − ρ~g]] (1)
For the representation of the subscale physics we use the Mualem and van-Genuchtenparametrization:
Θ(hm) = (1 + (αhm)n)−1+1/n , hm =Ψm
ρg(2)
K(hm) = K0(1 + (αhm)n)−τ(1−1/n)[1− (αhm)n−1(1 + (αhm)n)−1+1/n
]2(3)
Sensitivity of hydraulic parameters on infiltration characteristics
weiçelinieweiçelinieweiçelinieweiçelinieweiçelinieweiçelinieTo show the sensitivity of shape and water distribu-tion within an infiltration pulse several infiltrationswere simulated while always one parameter wasvaried in a physical reasonable range. All otherparameters are fixed using standard hydraulicparameters of sand after [5]. As a result thedependency of the size and shape of the volume ofthe infiltration pulse as well as different gradientsof the water content at the pulse edge can benoted. Therefore the determination of hydraulicsoil parameters seems quite promising on the basisof infiltration processes. Following figures showsimulated water content distributions colorcodedfrom blue (wet) to yellow (dry).
Influence of hydraulic conductivity
An increasinghydraulic con-ductivity leadsto a much largervolume theinfiltration pulse
is spread into. For low hydraulic conductivitiesthe potential difference to the surroundingarea has to be much larger to realize the sameinflux determined by the boundary condition.Therefore the gradient of the potential aswell as of the water content at the pulseedge is much larger for low conductivities.The pulse shape is horizontally wider for lowconductivities, because due to the slowerpropagation velocity capillary forces are morerelevant.
Influence of parameter n
The parameter n determines the sharpness ofthe capillary fringe, where large n produce avery sharp fringe. Thus for potentials aroundthe capillary fringe a small variation of the po-tential leads to a major change in water content.The potential within the volume of the infiltra-tion pulse is nearly constant for the shown sim-ulations. The water content variation for largen is larger within the pulse volume due to thelarger gradient of θ(hm). This can be seen inthe smoother pulse boundary for larger n.
Influence of scale factor α p
Increasing the parameter α leads to a decreasingcapillarity of the simulated soil material. There-fore the capillary fringe, which is analogous tothe largest gradient of the function θ(h), occursfor larger potentials for increasing α. Infiltrationof water with a certain flux rate creates a gra-dient of the potential from the infiltration areato the dry surrounding. Depending on α thisrange of potentials can produce different gradi-ents of θ. Therefore the smoothness of the pulseboundary varies for varying parameter α.
behavior at layer boundaries
A sudden change of hydraulic properties at layer boundaries deformsinfiltration pulses. Water accumulates if the infiltration front entersa material with lower hydraulic conductivity. This leads to a broad-ening of the infiltration pulse above the layer boundary. Differentporosities of the materials can produce different water contents inthe materials. The amount of water of an infiltration pulse withsaturated water content has to be distributed in a larger soil vol-
ume, if it enters a material with lower porosity which leads to a broadening of the pulse below the layer boundary.
3. Monitoring Infiltration with GPRGround Penetrating Radar is a method to monitor subsurface processes with electromagnetic waves. It mea-sures travel time, phase and amplitude of an electromagnetic pulse between two antennas. These quantitiesare determined by the permittivity of the soil and the pathway of the rays, e.g. reflections at permittivityjumps in different depth. Soil permittivity is strongly related to the soil water content. Two measurementsare commonly used for local GPR measurements: CMP measurements where both emitter and receiver aremoving symmetrically away from one common midpoint. Here a number of reflections at the same point ismeasured with different angles. WARR measurements are realized by moving the receiver over the infiltrationarea, while the emitter stays at a fixed position. Thus the reflection point moves with varying antenna sepa-ration. The measurement radargrams show color coded amplitude in dependence of travel time and antennaseparation. The development of the signal travel time due to varying permittivity on the ray path can be seen.
Raypath from GPR measurements above infiltration
CMP For CMP- measure-ments over infiltra-tions the signal dif-fers, if the antennasare on the infiltra-tion area (a), close toit (b) or far enoughto enable a reflec-tion around the infil-tration pulse throughcompletely dry soil(c). The correspond-ing development ofthe signal travel time
can be found in radargrams below.
WARR WARR mea-surements overinfiltration ar-eas include ameasurement incompletely drysoil (a), a mea-surement with thereceiver on the in-filtration area andtherefore parts ofthe raypaths inwet soil (b), anda measurement
with angles large enough to enable a reflection aroundthe infiltration pulse (c).
Simulated radargrams above infiltration
CMP Dashed arrowsmark the signalof the reflectionat the edge ofthe infiltrationpulse, while solidarrows showthe direct signalin air (shortesttravel time) andthe groundwave.Dashed-pointedarrows show thebottom reflection.
This signal shows a jump in travel time, when areflection in completely dry soil is possible (c). Thegradient of travel time of all signals decreases, whenthe antennas leave the wet infiltration area with highpermittivity (b).
WARR The gradientof the traveltime increaseswhen the re-ceiver enters theinfiltration areadue to higherpermittivity (b).It decreases afterentering thedry area again(c). Dashedarrows mark thesignal of the
bottom reflection, while solid arrows show the directsignal in air (smallest travel time) and the ground-wave propagating directly under the soil-air-interface.weiçelinieweiçelinieweiçelinieweiçelinieweiçelinieweiçelinie
Quantification of infiltration from radargrams
Evaluation of CMP-radargramsPermittivity of infiltration pulse from bottom reflec-tion when infiltration reaches this boundary :
εwet =
(tBRc0√a2 + 4d2
)2
(4)
Depth of infiltration pulse from reflection at pulseboundary:
dinfilt =1
2
√t2IRc
20
εwet− a2 (5)
Width w of infiltration pulse at upper boundary fromfit at measured groundwave traveltime:
tGW(a) =
{ac0
√εwet a < w
wc0
√εwet +
a−wc0
√εdry a ≥ w
(6)
Evaluation of WARR-RadargramsPermittivity of dry soil from bottom reflection withboth antennas before infiltration area:
εdry =
(tBRc0√a2 + 4d2
)2
(7)
Estimation of edge of infiltration pulse due to geo-metric considerations:1. total length of ray path of bottom reflection
s =√a2 + 4d2 = swet + sdry (8)
2. travel time of bottom reflection
tBR =sdry√εdry
c0+swet√εwet
c0(9)
3. coordinates of pulse edge
xwet = a− swet cos(arctan
(2d
a
))(10)
ywet = swet sin
(arctan
(2d
a
))(11)
Estimation of infiltration volume from width at upperboundary calculated from ground wave and depthcalculated from reflection at lowest boundary of the
infiltration pulse in CMP-measurement
Estimation of infiltration volume from geometricraypath considerations with the assumption of
constant εdry and εwet
- ε electric permittivity, a antenna separation, c0 speed oflight- tBR, tGW, tIR signal travel time of bottom reflection, ofground wave and of reflection at edge of infiltration pulse- d, dinfilt depth of bottom reflector and of of edge ofinfiltration pulse
4. Summary
Automated GPR-scanner at ASSESS site [P. Klenk]
Infiltration processes are highly depen-dent on the properties and architectureof the soil. Especially the single param-eters commonly used to characterize soilwater dynamics can influence the shapeand water distribution of an infiltrationpulse. GPR measurements can moni-tor the temporal evolution of infiltrationprocesses, as the signals are delayed andreflected by infiltrated water. Already
simple ray geometrics indicates that while the GPR data will contain quantitative information onsoil hydraulic properties, their determination is not straightforward. This is further corroboratedby the simulated radargrams. High-precision measurements, as they become feasible with thebuilt GPR-scanner, in conjunction with knowledge fusion (see posters by Hannes Bauser andDaniel Berg) appears as a promising route to gaining a consistent and quantitative representationof the sites soil hydrology in a truly noninvasive way.
References[1] All simulations of soil water content are done with µφ, a numerical solver of the Richards equation by Olaf Ippisch. For
further information see: O. Ippisch, H-J. Vogel, P. Bastian, Validity limits for the van Genuchten- Mualem model andimplications for parameter estimation and numerical simulation, 2006, Advances in Water Resources
[2] All simulated radargrams are created with meepGPR, a development of Jens Buchner based on the numerical solver ofthe Maxwell equations meep. For further information see: J. Buchner, U. Wollschläger, K. Roth, Inverting surface GPRdata using FDTD simulation and automatic detection of reflections to estimate subsurface water content and geometry,2012, Geophysics
[3] L. A. Richards, Capillary conduction of liquids through porous mediums, 1931, Journal of Applied Physics
[4] M. Th. van Genuchten, A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils, 1980,Soil Sci. Soc. Am. J.
[5] J. C. van Dam, J. N. M. Stricker, P. Droogers, Inverse method for determining soil hydraulic functions from one-stepoutflow experiments, 1992, Soil Sci. Soc. Am. J.
AcknowledgmentThis research is founded by Deutsche Forschungsgemeinschaft (DFG) through project RO 1080/12-1
