Untitled Field measurements of topsoil moisture profiles by vertical TDR probes Roberto Greco *, Andrea Guida Dipartimento di Ingegneria Civile, CIRIAM – Centro Interdipartimentale di Ricerca in Ingeg[.]
Journal of Hydrology (2008) 348, 442– 451 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jhydrol Field measurements of topsoil moisture profiles by vertical TDR probes Roberto Greco *, Andrea Guida Dipartimento di Ingegneria Civile, CIRIAM – Centro Interdipartimentale di Ricerca in Ingegneria Ambientale, ` di Napoli, Via Roma 29, 81031 Aversa (CE), Italy Seconda Universita Received 27 July 2006; received in revised form 27 July 2007; accepted 10 October 2007 KEYWORDS Time domain reflectometry; Moisture profiles; Inverse problems; Infiltration; Evaporation; Field monitoring A recently developed inverse method for the estimation of water content profiles from single time domain reflectometry (TDR) waveforms in laboratory has been adapted and applied to field measurements of topsoil moisture profiles in a pyroclastic sandy loam Three metallic probes of the lengths of 30 cm, 45 cm and 60 cm were vertically installed in an experimental field for the measurement of vertical water content profiles One 15 cm long probe was inserted vertically into soil surface and five 10.5 cm long probes were buried horizontally at various depths for the measurement of local values of mean water content by means of the classical TDR approach The experimental campaign lasted 28 days, during which daily rainfall heights and daily maximum and minimum temperatures were measured at the experimental field TDR waveforms acquisition was carried out twice a day The agreement between local volumetric water content measurements and vertical profiles was in general satisfactory, although some of the vertical profiles failed in detecting a layer with systematically smaller water content values indicated by the horizontal probe buried at the depth of 30 cm below soil surface Such small water content values could be probably ascribed to the presence of a large amount of pumice stones in the soil around that depth, affecting the water content measured by TDR probes and thus increasing estimated moisture spatial variability ª 2007 Elsevier B.V All rights reserved Summary Introduction Time domain reflectometry (TDR) has been widely used in the last decades for monitoring topsoil water content Indeed, TDR provides easy and cheap water content estima* Corresponding author E-mail address: Roberto.Greco@unina2.it (R Greco) tions with relatively small disturbance to the investigated soil TDR measurement of soil water content, based on the strong correlation observed between relative dielectric permittivity of wet soil and its volumetric water content h (Campbell, 1990), consists of measuring travel time Tp of an electromagnetic pulse along a metallic waveguide of known length Lp inserted into the soil The volume averaged value of soil relative dielectric permittivity er, affecting the 0022-1694/$ - see front matter ª 2007 Elsevier B.V All rights reserved doi:10.1016/j.jhydrol.2007.10.013 Field measurements of topsoil moisture profiles by vertical TDR probes velocity of propagation of electromagnetic waves along the metallic waveguide, is given by (Topp et al., 1980) 2 c0 T p : 1ị er ẳ 2Lp In Eq (1) c0 is the propagation velocity of electromagnetic waves in the vacuum space Several expressions of the relationship between er and h have been proposed, empirically stated (Topp et al., 1980) as well as based on semi-analytical approach to dielectric mixing models (Roth et al., 1990; Whalley, 1993; Heimovaara et al., 1994) So far, TDR field applications suffered the limitation due to the capability of the technique of estimating only the mean water content in the volume investigated by the probe Whereas the knowledge of non-homogeneous vertical water content profiles was needed, it was necessary to install either several vertical probes of different length or several horizontal probes placed in the soil at different depths, in both cases strongly increasing soil disturbance as well as the complexity of the measurements For the sake of brevity, from now on the TDR measurements techniques providing the volume averaged water content will be referred to as ‘classical’ TDR approach Several studies have been recently dedicated to the development of inversion methods aimed to extract more information from TDR waveforms, in some cases concerning soil dielectric properties (Heimovaara, 2001; Weerts et al., 2001; Lin, 2003), in others dealing with estimating non-homogeneous moisture profiles along the probe axis A common feature of all these methods is that the electromagnetic transient through the wet soil along the metallic probe is mathematically modeled, assuming that the unknown soil properties correspond to the best agreement between simulated and measured waveforms In some cases the soil is modeled as a series of small layers with different dielectric properties, and the waveform is obtained as the result of the superposition of multiple reflections arising from impedance discontinuities between the layers (Nguyen et al., 1997; Todoroff et al., 1998; Heimovaara, 2001; Moret et al., 2006) Other methods consider the dielectric properties of the soil as smoothly variable along probe axis (Greco, 1999; Schlaeger et al., 2001; Oswald et al., 2003; Greco, 2006) So far, the retrieval of non-homogeneous water content profiles along TDR probes has been successfully applied only under controlled laboratory conditions Aim of this paper is testing the applicability to field measurements of an inverse method for the estimation of water content profiles along vertical TDR waveguides, recently applied in laboratory to a sample of homogeneous soil with hydraulic boundary conditions leading to monotonic moisture distributions (Greco, 2006) In this paper, the inverse method has been adapted and applied to measurements of vertical water content profiles in an experimental field where non-monotonic moisture profiles could be observed in the topsoil Materials and methods Soil moisture inverse profiling by TDR The inverse method for retrieving moisture profiles along TDR probes by Greco (2006) is here briefly described The 443 propagation of the electromagnetic pulse along a one dimensional transmission line may be expressed in terms of electric voltage V(x, t) and electric current i(x, t) by means of the so-called telegraph equations (Ramo et al., 1994): < @i ỵ @V ỵ Rxị i ẳ 0; @t Lxị @x Lxị 2ị : @V ỵ @i ỵ Gxị V ẳ dx x~ịẵ1 expbtị: Cxị @t Cxị @x In Eq (2), R, L, G and C represent, respectively, resistance, inductance, transverse conductance and capacitance of transmission line unit length; the forcing term at RHS of the second equation represents the voltage transient imposed by the generator, with parameter b depending on emitted pulse rise time; the Dirac function d locates the forcing term at the abscissa x~ representing transmission line origin In TDR applications to soil moisture determination, the transmission line along which the electromagnetic pulse propagates is typically constituted by a coaxial cable and a metallic probe buried into the soil At frequencies mostly contributing to TDR waveforms, roughly ranging between 20 kHz and 1.5 GHz (Heimovaara, 1994), R and L may be assumed constant along a metallic probe of given geometry, while C(x) and G(x) depend, respectively, on relative dielectric permittivity er(x) and electrical conductivity r(x) of the soil, both in turn depending on water content distribution h(x) The retrieval of the unknown moisture profile along TDR probe implies the resolution of the inverse problem, consisting in finding the coefficients C(x) and G(x) for which the integration of Eq (2) gives rise to simulated voltage at a generic abscissa x, Vðx; tÞ, closest to a given experimental waveform Vexp(t) This issue is achieved by minimizing the objective function W defined as a measure of the distance between simulated and experimental waveforms: Wẵhxị ẳ (R T exp ẵV exp tị Vẵx; t; Chxịị; Ghxịị2 dt R T exp V exp ðtÞ2 dt )1=2 : ð3Þ For the laboratory application, the unknown moisture profile was parameterized according to a monotonic functional form with four parameters to be determined Therefore, the retrieval of the unknown moisture profile reduced to the identification of four parameters of the chosen functional form In this paper, the above described inverse method has been applied to the retrieval of water content profiles in a pyroclastic soil subject to natural infiltration and evaporation transients in the field In this case, a monotonic functional form for describing moisture distribution could not be a priori assumed Therefore, in order to let the unknown moisture profile to be freely determined without imposing any predefined functional form, water content distribution has been schematized with a broken line formed by N segments of length Dx = L/N, the parameters being the values hi assumed in N + equidistant vertices With this choice, whereas a too large number N of segments is chosen, the inverse problem may likely turn to be ill-posed, with multiple minima of the objective 444 R Greco, A Guida function, which would hamper unknown moisture profile retrieval However, the length Dx of a segment has to be larger than the effective spatial resolution of the TDR instrument, in turn related to the frequency content of the voltage pulse A rough estimate of the spatial resolution can be made by considering signal rise time tr, usually defined as the time for the signal to rise from 10% to 90% of its final value (Oswald et al., 2003): Dx ¼ c0 tr 4e1=2 r ð4Þ : Energy dissipations, due either to electrical conductivity or to dielectric relaxation, mainly reduce signal power at high frequencies (Robinson et al., 2003), smoothing the front of the voltage pulse propagating along the probe: the rise time of 200 ps of the pulse emitted by Tektronix 1502C cable tester used for the experiments extends up to nearly ns for the pulse reflected at the end of the longer metallic probe in wet conditions Therefore, Dx = 5.0 cm has been chosen, sensibly larger than the spatial resolution, whatever the water content could be This choice, as it will be clarified in Section ‘‘Sensitivity analysis’’, also prevents the problem to be ill-posed, since the simulated waveform results sensible to the variation of even only one of the hi values The minimization of the objective function has been carried out with a genetic algorithm (Holland, 1975; Goldberg, 1989) Such an evolutionary algorithm allows easily to introduce constraints to parameters variability, at the same time avoiding local minima by introducing random parameters vectors at each generation 0.25 m and 0.35 m is characterized by of a large amount of pumice stones with dimensions ranging between few millimeters and some centimeters The presence of pumice stones may affect the volumetric water content measured by TDR Soil physical characterization, consisting in the determination of dry soil bulk density, particle size distribution, saturated water content and saturated hydraulic conductivity, was carried out on seven undisturbed samples taken at various locations and depths in the experimental field Fig shows the particle size distribution curves measured for three of the samples, all falling within sandy loam limits according to USDA standards Table summarizes the measured soil physical parameters The relationships linking volumetric water content, measured gravimetrically, with soil dielectric permittivity and electrical conductivity were determined on two undisturbed cylindrical soil samples, with diameter of 10 cm and height of 12 cm, taken at soil surface To this aim, a TDR metallic probe of the length of 12 cm, with three rods of the diameter of 1.5 mm and external spacing of 20 mm was inserted into the samples After immersion in water, with electrical conductivity of 0.1 S/m at 20 °C, for 24 h, the samples were placed on an electronic balance Precisa Instrument Ltd XB4200C with an accuracy of 0.01 g and evaporation took place for 10 days, with air temperature ranging between 18° and 21° and relative humidity between 45% and 55% The weights of the samples were recorded at regular time intervals during evaporation and, at the same time, TDR Table Field experiments and soil characterization The above described method was applied to the measurement of topsoil water content vertical profiles in an experimental field located in S Arpino (CE) The field belongs to the volcanic area north west of Napoli, where pyroclastic deposits characterize the upper soil layer Soil physical characteristics not vary significantly up to a depth of 2.0 m below soil surface The soil layer between the depths Physical characteristics of the investigated soil Sampling depth (m) cdry (g/cm3) hsat ksat (cm/min) 0.00 0.00 0.00 0.00 0.20 0.75 2.00 1.06 1.13 0.94 1.07 – 1.06 0.92 0.556 0.547 0.578 0.509 0.547 0.589 0.641 0.06 0.15 0.20 0.17 0.15 0.20 0.17 100 90 80 weight % 70 60 50 40 30 20 10 0.0001 0.001 0.01 0.1 10 d [mm] z=0.2 m Figure z= 0.75 m z=2.0 m Particle size distribution curves of the investigated soil 100 Field measurements of topsoil moisture profiles by vertical TDR probes 445 5.5 ε r 1/2 R2 = 0.975 4.5 0.2 0.25 0.3 0.35 0.4 0.45 0.5 θ [m3/m3] Figure Experimental soil bulk dielectric permittivity vs water content relationship: (d) experimental data; (—) best fit by Eq (5) 0.06 0.05 R2 = 0.8355 σ [S/m2] 0.04 0.03 0.02 0.01 0.2 0.25 0.3 0.35 0.4 0.45 0.5 θ [m /m ] Figure Experimental soil bulk electrical conductivity vs water content relationship: (d) experimental data; (—) best fit by Eq (6) with the parameters given in Eq (7) waveforms were acquired At the end of the evaporation experiment, the samples were oven dried at 105 °C for 24 h and then weighed for the measurement of the dry weight Soil dielectric permittivity was determined from TDR waveforms with ‘classical’ approach by Eq (1) Bulk soil electrical conductivity was determined from the waveforms with the following expression (Dalton et al., 1984): p er Vt rẳ : 5ị ln Vr 120pLp In Eq (5) Vt and Vr represent respectively incident and reflected voltage at the beginning of the probe The (e, h) and (r, h) experimental points are respectively plotted in Figs and 3, together with the relevant best fitting curves A linear relationship between h and the square root of er showed the best performance for fitting the er(h) experimental data: e0:5 2:1301 : 6ị hẳ r 8:1366 The relationship proposed by Rhoades et al (1976) was adopted for fitting the r(h) data: r ẳ rs ỵ rw hah þ bÞ: ð7Þ In the above equation, rs represents dry soil electrical conductivity; rw is soil solution electrical conductivity; a and b are fitting parameters related to tortuosity of electric current flow paths From experimental data fitting, it resulted rs ¼ 0:0086 S=m; a ¼ 1:752; b ¼ 0:176: ð8Þ 446 R Greco, A Guida Table Geometrical characteristics of the TDR probes used for field water content measurements Rods diameter (mm) Rods spacing (mm) Probe length (mm) S1 S2 S3 S4 H1 H2 H3 H4 H5 3 3 3 3 32 32 32 32 32 32 32 32 32 300 600 150 450 105 105 105 105 105 S2 S4 S1 15 cm Probe S3 H2 45 cm 60 cm H1 30 cm 15 cm H3 H4 - H5 Vertical Section S1 Since soil water electrical conductivity in the field is not known and probably variable during infiltration/evaporation processes, rw turns to be an additional fitting parameter of the inverse water content retrieval method The soil surface in the experimental field is nearly flat horizontal and the groundwater table lays approximately 20 m deep below soil surface TDR water content measurements were carried out with Tektronix 1502C cable tester, connected alternately via coaxial cable to three rods metallic probes of various dimensions After removing the grass covering, four probes of various lengths ranging between 15 cm and 60 cm were inserted vertically from soil surface; a 60 cm deep trench was dug for the installation of five 10.5 cm long probes; such probes were inserted horizontally into the wall of the trench at various depths The geometric characteristics of the probes are given in Table Fig shows a sketch of the experimental field with the locations of the probes The experimental apparatus was completed by a rain gauge for the measurement of daily rainfall heights and a thermometer for the measurement of daily maximum and minimum air temperatures The experimental activities lasted from 15 March 2007 to 11 April 2007 During the entire period, rainfall height was measured every day at 12.00 a.m.; with few exceptions, TDR waveforms were acquired twice a day, in the morning between 9.00 a.m and 11.00 a.m and in the afternoon between 2.00 p.m and 4.00 p.m In total, around 40 waveforms for each installed probe were acquired during the experimental campaign 20 cm 50 cm Sensitivity analysis S3 S2 15 cm 15 cm 15 cm H1 - H2 - H3 - H4 H5 S4 40 cm Plan View Figure Sketch of the experimental field with the locations of the TDR probes Identifiability of the parameters of a model is difficult to state rigorously, but it always requires model output to show high sensitivity to parameters variations (Chavent, 1987; Sun, 1994) The non-uniqueness of the solution may also be avoided by imposing constraints to parameters values variability deduced by their physical meaning In the present case model parameters are constituted by N + water content values hi in the vertices of the profile and 1.50 V /V 1.25 θ7=0.05 θ7=0.15 θ7=0.3 θ7=0.45 θ7=0.6 1.00 0.75 0.50 t [ns] Figure Effect of the change of the water content h7 in the middle of the 60 cm long probe on simulated TDR waveforms Field measurements of topsoil moisture profiles by vertical TDR probes 447 1.50 σ w=0.001S/m σ w=0.005S/m σ w=0.01S/m 1.25 σ w=0.02S/m V /V σ w=0.05S/m 1.00 σ w=0.1S/m 0.75 0.50 10 t [ns] Effect of the change of soil water electrical conductivity rw on simulated TDR waveforms Figure by soil water electrical conductivity rw, which have been subjected to the following constraints: 0:05 hi 0:6 m3 =m3 ; 0:001 rw 0:1 S=m: ð9Þ A sensitivity analysis has been carried out to show the effects on the simulated waveform obtained by integrating Eq (2) due to a change of a single parameter The waveforms refer to the case of a 60 cm long probe along which the soil water content profile is represented as a broken line with 12 segments Waveform sensitivity to variations of a single hi is studied by changing the water content in the middle of the probe, h7, over the entire range of variability given in the first of Eq (9) The other hi values are all equal to 0.3 Some of the obtained waveforms are plotted in Fig Fig shows the waveforms corresponding to a constant water content profile with h = 0.3 and different values of soil water electrical conductivity rw, covering all the interval of variability given in the second of Eq (9) In both cases the waveforms are significantly affected by parameters changes Since the chosen objective function W is a measure of the area between experimental and simulated waveforms, it looks clear that its value is certainly affected even by the change of a single parameter Results and discussion During the observation period, the total recorded rainfall height was 95.0 mm, with 10 rainy days (daily rainfall height above 1.0 mm) Fig shows the histogram of daily rainfall height and the observed minimum and maximum daily temperatures The large amount of precipitation and the high level of air relative humidity during the dry periods caused relatively slow evaporation form topsoil surface, determining in most cases wet soil conditions within the entire inves- 30 T [˚C] h [mm] 20 10 15/03/07 Figure 22/03/07 29/03/07 05/04/07 Histogram of daily rainfall heights and time history of daily minimum and maximum temperatures 448 R Greco, A Guida 0.5 probe S3 z