Preliminary Field Tests to Determine the Soil Water Content Using Resistivity Measurements

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ScienceDirect Procedia Environmental Sciences 25 (2015) 158 – 165

7th Groundwater Symposium of the International Association for Hydro-Environment Engineering and Research (IAHR)

Preliminary field tests to determine the soil water content using resistivity measurements C. Miracapilloa* and H. Morel-Seytouxb a b

Universty of Applied Sciences of Northwestern Switzerland, 4132 Muttenz, Switzerland Hydroprose International Consultant, 328 Beech Avenue, Santa Rosa, CA 95409, USA

Abstract Preliminary field tests were carried out in the protected area of Langen Erlen in Basel in order to find a correlation between variations of soil resistivity and variations of the soil water content. The experimental set up is described and the accuracy of the data is evaluated. Data are interpreted using a conceptual physical model in order to determine the infiltration patterns. An inverse relationship between the variations of soil resistivity and the variations of soil water content is used. © by Elsevier B.V. This an open access © 2015 2015Published The Authors. Published by isElsevier B.V. article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of the IAHR Groundwater Symposium 2014. Peer-review under responsibility of the Scientific Committee of the IAHR Groundwater Symposium 2014 Keywords: unsaturated zone; water content; resistivity values

1. Introduction In soil sciences, hydrology and agricultural sciences, water content plays an important role regarding groundwater recharge, agriculture, soil chemistry and ecology. The interest in modeling soil water dynamics in the unsaturated zone and in soil moisture variations has been increased in the last 30 years [1] [2] [3] [4] [5]. A wide range of techniques for field estimation of the water content have been improved and their accuracy tested [6].

* Corresponding author. Tel.: +41 61 361 2470 E-mail address: [email protected]

1878-0296 © 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of the IAHR Groundwater Symposium 2014 doi:10.1016/j.proenv.2015.04.022

C. Miracapillo and H. Morel-Seytoux / Procedia Environmental Sciences 25 (2015) 158 – 165

The purpose of this study is to provide the order of magnitude of soil resistivity in an area of Basel and their variations under permanent and transient conditions. This study is part of a project, which focuses on soil moisture measurements using the Electrical Impedance Spectrometry Method. The investigations made on the real part of the impedance are summarized in this article, while the investigations on the imaginary part are the content of a future article. The modeling approach is based on soil water balance [7], on a rectangular shaped water front and on an inverse relationship between the variations of soil resistivity and the variations of soil water content. 2. Test description a data interpretation Test 1 and test 2 were both carried out under constant conditions (no water supply at the soil surface) respectively at experimental site1 and at experimental site 2. Both experimental sites are located in the groundwater recharge area of the „Lange Erlen“ in Riehen, close to Basel (Fig.1). Experimental site 1 is on a cultivated field, while experimental site 2 is on a artificial groundwater recharge basin “Verbindungsweg”. Test 3 was carried out at experimental site 2.

Site2

Site1

Fig. 1. The „Lange Erlen“ with its artificial recharge basins and the location of the two experimental sites

The following devices were used to measure the electrical resistivity of the soil: - Data Logger with Panel (8 boards, each with 16 channels, giving a total of 128 channels) - Personal computer with Z-Meter und software - Battery (12 Volt, 40 Ampere) - Converter (12-220 Volts) - Three pairs of probes 1.5m, 3.0m, 4.5m long with point. The probes are composed of Electrodes in fine steel 1.4404 (produced by C.C.T. inox S.p.A. in Italy) and plastic pieces in Polyamid PA Ertalon 6 SA Natural (produced by Quadrant in Belgium).

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The probes are built by modules. Each module is composed of a plastic piece (insulation) and an electrode. The probes were installed using a ramming technique with a weight falling per gravity on the top of the last module [8]. 2.1. Test 1 The distance between the electrodes on a horizontal level varies (Fig.2, left). The vertical distance between the electrodes of a probe is 50 cm (Fig.2, right). There 4 probes (each with 2 electrodes) were installed to a depth of 67 cm.

Sonde 1 10 cm

L1

Level 1

Sonde 2 Electrode

25 mm 40 cm

10 cm 7 cm

Insulation

Level 2 point

Fig. 2. Position of the probes (left) and vertical section of the probes (right)

The values of the electrical resistivity (Ω) are deduced from measurements of electrical current in the soil column in a horizontal direction from one electrode (source) to the other one (reception). At each investigated profile (with horizontal distance between electrodes being approximately half a meter) a value of electrical resistivity was measured. The values were normalised with respect to the distance between the electrodes (Ω/cm), taking into account the precise length of the profile (Tab.1). The mean value, the standard deviation and the coefficient of variation were calculated for each level. Level 1 is 5 cm below the surface soil and level 2 is 65 cm below the surface soil. Comparison of the data shows that the mean value Ω, the standard deviation σ, the coefficient of variation Cv are relatively close. The resistivity value – as is well known- varies with the soil matrix and with the amount of water in the soil. Since the coefficients of variation Cv are practically identical, it seems realistic to assume that the soil matrix is uniform (or has the same degree of heterogeneity). This would mean that the soil characteristics and the water content are distributed uniformely. If this is the case, the difference between the average values of the resistivity at the two levels implies different water content at different levels, or more precisely, at different depths. The fact that the difference between the average values of the resistivity at the two levels is little could mean that the difference in water content in level 1 and level 2 is little too, which is probably the case.

C. Miracapillo and H. Morel-Seytoux / Procedia Environmental Sciences 25 (2015) 158 – 165

The analysis of data between the levels has shown almost a perfect correlation (correlation factor=0.9875). This might imply that the pattern of water flow is essentially vertical everywhere in the investigated area, since there is significant variation in the horizontal direction but not in the vertical one. 2.2. Test 2 Test 2 was carried out at experimental site 2. This is located in an artificial recharge basin, “Verbindungsweg”. There 2 probes (each with 4 electrodes) were rammed to the depth of 117 cm (Fig.3).The vertical distance between the electrodes is 50 cm und the horizontal distance 52.5 cm. 10 cm

40 cm

L=

10 cm

Level 1

Electrode

25 mm 40 cm

10 cm

Level 2

40 cm

10 cm

Level 3

7 cm

Fig. 3. Vertical section of the probes (site 2)

After measuring, the cables were wrapped and signalized. The mean values of the resistivity at different levels show a trend : they decrease with the depth (as in Test 1), which means that, if there is no variability of the soil characteristic, the variability of the resistivity refers to the variability of the water content. According to the expectation based on the meteorological conditions of the previous hours, the upper levels could have a higher water content, as the data in terms of mean values show. Table 1. Measured values of the resistivity for different profiles at sites 1 and 2

Depth cm

5 65 105

Site 1 Ω / cm

Site 2 Ω / cm

1-2

1-3

2-4

3-4

1-4 (d)

2-3 (d)

20.14 21.23 -

22.7 23.23 -

14.95 16.87 -

21.74 22.08 -

14.95 15.27 -

13.82 14.5 -

5.49 5.84 8.81

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The coefficient of variation within one level varies between 1‰ and 3% at different levels. These values are extremely small. This indicates that measurement errors are very small. At level 1, where the coefficient of variation is higher than in the other 2 levels, some variation of the ambient conditions might have caused some additional fluctuation of the electrical response. Given such low coefficients of variability at each level, the confidence limit for the mean values in each level would not overlap. Therefore, the difference in the mean values can give information about differences in water content. Given the very low values of the coefficients of correlation between two levels and the fact that there are so few data points, these values are not significantly different from zero. Therefore, one can infer that the measurement error noise in the levels are independent. 2.3. Test 3 Test 3 occurred at site 2. Measurements were made under flooding conditions. The water volume, which was poured where the electrodes were placed, was 50 liter. The flooding period and the observed period were approximately 3 and 5 min respectively. By pouring water (50 l at different intervals during 3 min) the simultaneous behaviour of four pair of electrodes could be observed. The upper electrodes were in the air. Three pairs of electrodes were in the soil at different depths respectively 5, 55 and 105 cm below the bottom of the recharge basin. Within the monitored time (5 min) the electrodes located at a depth of 5 cm reacted almost instantaneously. During the first flooding (most of the total amount of water was poured over the soil at the beginning of the simulation) these electrodes measured a change of resistivity from 5.25 to 4 Ω/cm (Fig.4). The total flooding period is 200 seconds as the graph in Fig.4 shows. After this period the resistivity values remain constant in time. The measurements of the resistivity of the soil below the bottom of the artificial basin under mostly drainage conditions (upward trend) were interpreted using a simple conceptual model. This model is based on Darcy’s law for unsaturated flow and assumes a rectangular shape for the water content profile. A postulated relation between water content and resistivity was used, based on the physical fact that resistivity and water content vary inversely. The hydraulic properties of the soil were not available and thus values were inferred from the knowledge of the type of soil existing in that area. Consequently the water content values cannot be considered absolute and have merit only in a relative sense (no validating measurements of water content were performed during the experiment). It can also be noticed that the water poured over the surface of the soil was not applied at a uniform rate. This is the major reason for the random fluctuations shown in the observations. 5.500 5.300 5.100

R (Ω/cm)

4.900 4.700 4.500 4.300 4.100 3.900 3.700 3.500 0.0

50.0

100.0

150.0

200.0

250.0

Time (s)

Fig. 4. Resistivity values under flooding conditions at depth= 5 cm below the soil surface (site 2)

300.0

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3. Modeling Only test 3 shows sufficient variability of the resistivity to be used for this analysis. Since the history of the supply rate was not known with accuracy, rates of water application at the soil surface were calibrated on the data, making sure that the total infiltrated volume of water was equal to the volume of water poured over the surface, namely 50 liters. Using the current understanding of unsaturated flow in porous media, approximate equations for the evolution of water content with time were derived. The basic approximation consist of assimilating the water content profile as a rectangle with the water content being uniform from the surface to the wetting front downstream which propagates further into the assumed initially uniform and rather dry profile [9] [10]. This approximation of a rectangular profile is especially valid down into the column once the wetting front has passed it. This must have happened around time 6.4 when resistivity is particularly low, in fact has the lowest value of the test. Let us define

~

water content, θ water content at natural saturation, θ r residual water content, θ i ~ initial water content, r the supply rate at the soil surface and K the hydraulic conductivity at natural ~ * saturation, r/ K = normalized supply rate r , k rw the relative permeability.

a few symbols:

θ

The normalized water content is

θ −θ θ* = ~ r (θ − θ r )

(1)

A superscript o refers to an old value, the value at the beginning of a time step and t is time. Time step is:

Δt = t − t 0 . The velocity at which the wetting front propagates is given by the equation: dz f dt

=

~ Kkrw θ − θi

(2)

The cumulative infiltration depth W within the rectangular profile by mass conservation must be:

W = z f (θ − θ i )

(3)

One can combine these equations to obtain a differential equation in terms of normalized water content:

W d (θ * − θi* ) ~ + Kkrw = r (θ * − θi* ) dt

(4)

This differential equation can be rewritten in terms of relative permeability as the unknown using a power law for the relative permeability as a function of normalized water content with exponent p, yielding:

dk rw * i

−

1 p

*

krw[1 − θ (krw ) ](r − krw )

~ pKdt = W

(5)

The difficulty for the integration of this equation lies primarily with the term:

(krw )

−

1 p

However due to

the smallness of the exponent it does not have a great influence on the solution and one can evaluate it at the beginning of the time step. W varies linearly with time. It was evaluated at the end of the time step, none of the time steps being very long. Having defined:

ko rw E C= o k − r* rw

p[1 − θ * (k o ) i rw W E=e

−

1 p

]rΔt

(6)

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C. Miracapillo and H. Morel-Seytoux / Procedia Environmental Sciences 25 (2015) 158 – 165

The solution is :

k rw =

C r* C −1

(7)

Once the relative permeability determined the water content is obtained as:

~

θ = θ r + (θ − θ r )(krw )

1 p

(8)

A slightly different equation holds if the supply rate is zero, namely: 1

− 1 1 ~ o = o + pK [1 − θi* (krw ) p ]Δt krw krw

(9)

The pattern of supply rate at the soil surface is shown in Tab.2 . Table 2. Supply rates

Period 1 2 3 4 5 6 7 8 9 10 11 12

The soil parameters are:

~

θ

Time at the beginning 0.0 6.4 8.0 20.0 40.0 65.6 83.2 84.0 89.6 90.4 118.4 120.0

= 0.4,

θr

= 0.2,

θi

Time at the end 6.4 8.0 20.0 40.0 65.6 83.2 84.0 89.6 90.4 118.4 120.0 180.0

Normalized supply rate In the period 2.0 0.88 0.4 0.67 0.8 0.0 9.5 0.0 6.0 0.0 10.0 0.0

~ = 0.2, K = 0.0062 cm/s.

As resistivity has to increase if water content decreases, an inverse relationship was postulated.

~ ε ~ ( Rr − R ) ~ (θ − θ r + ε ){1 − ~ } R= R+ ~ θ −θ + ε (θ − θ r )

~

(10)

~

For θ = θr then R = Rr =4.35 and for θ = θ then R = R = 3.9 . The value of the parameter ε is – 0.05. An overview of observed and calculated data is shown in Fig. 5. 4. Conclusions Preliminary field tests were carried out in the protected area of Langen Erlen in Basel in order to find a correlation between variations of soil resistivity and variations of the soil water content. The accuracy of the data is evaluated. A variability study of the results has shown that the noise during the electrical measurements is irrelevant. In addition to that, under realistic assumptions, based on the inverse relationship between resistivity and water content, the results could be easily interpreted.

C. Miracapillo and H. Morel-Seytoux / Procedia Environmental Sciences 25 (2015) 158 – 165

Fig. 5. Observed and simulated resistivity and water content with time.

Acknowledgements This work was done in the framework of two Eureka projects. The first author would like to acknowledge the financial support of the Swiss partners, Roche, HydroCosmos, BBL Basler Baulabor and IWB Industrielle Werke Basel. Their contribution was essential for the development of the projects. References [1] Haverkamp, R., Vauclin, M.,Touma, J., Wierenga, P.J., Vachaud G. A comparison of numerical simulation models for onedimensional infiltration. Soil Science Soc. Am. J. 1977, 41, 2, p. 285 [2] Feddes, R.A., Kabat, P., Van Bakel, P.J.T., Bronswijk, J.J.B., Halbertsma, J. Modelling soil water dynamics in the unsaturated zone – State of the art. Journal of Hydrology 1988, 100, 1-3, p. 69-111 [3] Gandolfi, G., Facchi A., Maggi D. Comparison of 1D models of water flow in unsaturated soils. Environmental Modelling and Software 2006, 21, p. 1759-1764 [4] Heiß, V.I., Neuweiler, I., Ochs, S., Färber, A. Experimental investigation on front morphology for two-phase flow in heterogeneous porous media. Water Resources Research Journal 2011, Vol. 47 [5] Letha, J., Elango, K. Simulation of mildly unsaturated flow, Journal of Hydrology 1994, 154: 1-17 [6] IAEA Report. Field estimation of soil water content, soil and water Management & Crop Nutrition Section, 2008, International Atomic Energy Agency, Vienna [7] Morel-Seytoux, H.J., Miracapillo, C. Prediction of infiltration, mound development and aquifer recharge from a spreading basin or an intermittent stream. Hydrowar Reports Division, 1988, Hydrology Days Publications, Fort Collins, Colo. [8] Miracapillo, C. Field Tests in Basel using the EIS Method. Proceedings of the 5th Working Session, EUREKA Projekt E!3838, 2009, ISBN 978-80-214-3969-6, p. 53-68 [9] Morel-Seytoux, H.J., Billica, J.A. A two-phase numerical model for prediction of infiltration: application to a semi-infinite soil column. Water Resources Research Journal 1985, 21, (4), p. 607-615 [10] Morel-Seytoux, H.J., Khanji, J. Derivation of an equation of infiltration, Water Resources Research Journal 1974, Vol.10, (4), p.795-800

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