Water Resources Research
Supporting Information for
Impact of switching crop type on water and solute fluxes in deep vadose zone
T. Turkeltaub1,2*, D. Kurtzman2, E. E. Russak3 and O. Dahan1
1
Dept. of Hydrology & Microbiology, Zuckerberg Institute for Water Research,
Blaustein Institutes for Desert Research, Ben Gurion University of the Negev, Sede
Boqer Campus 84990, Israel, 2Institute of Soil, Water and Environmental Sciences,
The Volcani Center, Agricultural Research Organization, PO Box 6, Bet Dagan
50250, Israel, 3Geological and Environmental Sciences, Ben-Gurion University of the
Negev, Beer Sheva, Israel
Contents of this file
This file includes a detailed description on the vadose zone monitoring system
installation, operation and the components that composed it and concise explanation
on the optimization approach.
The need for real-time information on the quality of percolating water led to the
development of a vadose-zone monitoring system (VMS). The VMS is designed to
provide in-situ continuous measurements of the hydraulic and chemical properties of
the percolating water across the entire vadose zone, from land surface to the water
table. The monitoring system is composed of a flexible sleeve made of thin polyvinyl
chloride (PVC) line, hosting several customized FTDR probes, for water content
tracking, and vadose zone pore-water sampling ports (VSPs) for sediments pore-water
sampling (Figure 1).
Installation: The monitoring systems are installed in incased, small-diameter (15.24
cm or 6"), slanted boreholes (305°). The FTDR probes and VSPs are aligned along
the borehole’s upper side wall facing the undisturbed sediment column, which extends
from the probe location on the borehole wall to the land surface. Immediately after
inserting the sleeve into the borehole, it is filled with a mixture of concrete that
solidifies in the borehole shortly after its application. The hydrostatic pressure
generated by the high-density filling material within the sleeve causes its expansion
and ensures that it fills the entire void of the borehole. As a result, the FTDR probes
and VSPs are pushed against the borehole’s upper side wall with sufficient force to
achieve good contact with the sediments. Therefore, any potential preferential flow
along the borehole wall is eliminated [Rimon et al., 2011].
Flexible TDR (FTDR): The FTDR probes are designed to provide information on the
infiltrating water via temporal variations in the vadose zone water content. The FTDR
probes are made of flexible waveguides and are attached to a flexible PVC sleeve.
After the filling of the sleeve with the aforementioned material and its expansion, the
waveguides are forced against the borehole walls and follow its roughness,
undulations, and diameter irregularities. The FTDR waveguides are shielded by a
thick dielectric insulation to prevent potential impact of the concrete from within the
sleeve on the water content measurement of the sediment outside the sleeve. The
FTDR operates with Campbell Scientific data acquisition and logging instruments
including TDR100, SDM50X and AM16/32 multiplexers, and CR10X data loggers.
All waveguides are connected to an acquisition system using a highquality RG-58
coax cable (shielding factor >95%). Due to the known effect of cable length on TDR
waveform, a linear relationship between apparent and cable length is implemented
and cable length corrections are established as follows [Rimon et al., 2007]:
Corrected La/L = measured La/L - cable L × 0.016
Finally, a calibration curve for volumetric water content measurements by FTDR
probes is established for several different soils [Rimon et al., 2007]. The calibration
showed a linear correlation between the TDR signals (the calculated apparent length
[La] divided by the real length [L]) and the volumetric water content (Figure 1).
Figure 1. Calibration curve for water content measurements by FTDR probes for
three different soils. FTDR output presented as apparent length/actual rod length
[Rimon et al., 2007].
Vadose one pore-water sampling port (VSP): The VSP enables frequent sampling
of the vadose zone pore-water and therefore can attain the chemical transformation of
the percolating water. The VSP are based on a structural modification of standard
tensiometers and suction cups and are made from a customized ceramic tip, embedded
in sand matrix which is attached to an inner sampling cell. The physical mechanism
that allows sampling of the vadose zone pore water by the VSP is based on creating
hydraulic continuity between the sediment pore water and the sampling cell.
Hydraulic continuity between the VSP and the coarse sediments on the borehole
sidewall is achieved through an unconsolidated agent made of a soft and flexible sand
pillow. For frequent sampling of sediments pore-water the VSP is operated through a
set of small-diameter access pipes (i.d. 1<mm) and control valves. Once hydraulic
continuity between the sediment pore water and the VSP is achieved, a low pressure
(vacuum) is applied to the sampling cell to draw the sediment pore water to the
sampling cell. The water sample is then retrieved using pressurized gas (N2) to push
the water sample to the surface. Finally, the sampling efficiency, as expressed by the
water flux into the sampling cell, is controlled by the sediment water content.
Rimon, Y., O. Dahan, R. Nativ, and S. Geyer (2007), Water percolation through the
deep vadose zone and groundwater recharge: Preliminary results based on a new
vadose zone monitoring system, Water Resour. Res., 43, W05402, doi:
10.1029/2006WR004855.
Rimon, Y., R. Nativ, and O. Dahan (2011), Physical and chemical evidence for porescale dual-domain flow in the vadose zone, Vadose Zone J., 9, 1–10,
doi:10.2136/vzj2009.0113.
The Marquardt-Levenberg optimization approach [Hopmans et al., 2002]:
The inverse estimation was conducted by minimizing the objective function:
k
n

 ; b | c    v j  w ji g *j (ti )  g j (ti , b | c)
j 1

2
i 1
where kj is the number of different sets of measurements and ni is the number of
observations for the jth measurement set, b|c is the vector b containing the unknown
parameters estimated given the fixed and known parameters in vector c (non-sensitive
parameters), g*j (ti) is the measured variable at time ti for the jth measurement set, gj
(ti, b|c) is the corresponding model prediction and vj and wi,j are weights associated
with a particular measurement set or point, respectively. In this study, all wi,j were
equal to 1 and vj was given by:
vj 
1
m 2
where σ2j is the measurement variances for the jth measurement set.
The parameter uncertainty is limited to measurement errors only under the assumption
that solution converges to a global minimum and model error is negligible. Prior to
the calculation of the confidence interval, the approximate estimate of the standard
error is implemented based on the Cramer-Rao theorem, defining an estimate of the
lower bound of the parameter covariance matrix:
C  H 1
where H is the Hessian matrix and C is the parameter covariance matrix.
Nevertheless, this solution of standard error is for linear regression analysis and
therefore it only approximately holds for non-linear problems. Under the
aforementioned assumptions, the parameter covariance matrix C can be estimated
from the variance of the residuals, s2e (e =g* - g):
( e T e)
s 
nm
2
e
where n is the number of observations and m is the number of parameters. The
combination of these two equations gives:
C  s e2 ( H 1 )
An approximate solution of the Hessian matrix is calculated according to the Gauss–
Newton method which assumes that H can be approximated by a matrix N using only
first order derivatives:
N  J wT J w
where Jw is the derived from the Jacobian matrix J:
[ gi*  gi (  )]
g (  )
J ij 
 i
 j
 j
From here, the standard error of the parameter βj can be determined from the diagonal
elements of C by:
sj 
C jj
The confidence interval is estimated from the Student's t distribution:
 j ,max   j  v,1 / 2 s j
 j ,min   j  v,1 / 2 s j
where β is the parameter j, α is the interval, v is the degrees of freedom (number of
observations (n) – number of optimized parameters (m)) and sj is the standard
deviation of the parameter βj.
Hopmans, J. W., J. Šimůnek, N. Romano, and W. Durner (2002), Simultaneous
determination of water transmission and retention properties—Inverse methods,
in Methods of Soil Analysis: Part 4, Physical Methods, SSSA Book Ser. vol. 5,
edited by J. H. Dane and G. C. Topp, pp. 963 – 1008, Soil Sci. Soc. of Am.,
Madison, Wis.