TELIATNIKOV Ivan S. (1), McBRATNEY, Alex B. (1,2), TRIANTAFILIS John (2)

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1 Scientific registration n 623 Symposium n : 17 Presentation: poster Proximal sensing and profile reconstruction technique for use in quantitative soil survey Télédétection proche et techniques de construction de profil au service de l étude pédologique quantitative TELIATNIKOV Ivan S. (1), McBRATNEY, Alex B. (1,2), TRIANTAFILIS John (2) (1) Department of Agricultural Chemistry and Soil Science, The University of Sydney Ross St Building A03 NSW 2006, Australia. (2) CRC for Sustainable Cotton Production Australian Cotton Research Institute, P.O. Box 59, Narrabri NSW, 2390 Australia. Introduction The use of frequency-domain electromagnetic induction techniques to study subsurface soil properties has become increasingly popular since the introduction of an instrument specifically designed to measure apparent electrical conductivity (ECa) of the soil material within the first two meters. The instrument is also known by its commercial name as the EM-38. The instrument was developed to overcome the disadvantages of the traditional resistivity techniques and therefore to increase both speed and accuracy of soil conductivity surveys. Since its development it has been extensively used in different areas such as: groundwater recharge investigations (Cook et al, 1992), estimation of field scale leaching rates (Slavich and Young, 1988), soil salinity mapping (Cannon et al, 1994), and estimation of herbicide partition coefficients (Janes et al, 1995). Despite the comment made by the designer of the EM-38 (McNeill, 1983) that the instrument was not specifically built for the detailed vertical sounding of variation of conductivity, there have been numerous attempts to use the instrument to determine vertical trends in the profile conductivity. Rhoades and Corwin (1981) demonstrated that bulk soil electrical conductivity could be determined for discrete depth intervals of soil if the measurements are made at the successive heights above the ground - multiple coefficient approach, and using only two readings one each in horizontal and vertical and the horizontal mode - established coefficient approach (Rhoades and Corwin, 1982, 1984). The latter was used with a large calibration set to yield a better ECa prediction than had been previously reported (Rhoades et al, 1989). The disadvantage of both methods is that they are both site specific, thus a large calibration set is required for each new location where prediction is to be attempted. Slavich (1987) modelled the EM-38 response to ECa profiles of different shapes and developed relationships to predict an average ECa to a specified depth. This method 1

2 was applied to a set of temperature-corrected EM data (Slavich and Petterson, 1990). A more elegant approach to finding the optimal solution of relative responses from soil above a specified depth was derived by Cook and Walker (1990). This method unlike all pre-existing techniques was not site specific and did not require calibration. The logistic coefficient approach was developed by Laslett (1995) and reported to yield more accurate prediction when it was compared with the established-coefficients (Triantafilis,1996) method. Significant improvement in the quality of interpretation of electromagnetic data was achieved by mathematical inversion using a layered-earth model and the linear model of the instrument response (Borchers et al., 1997 ). In this new approach a system of linear equations was first constructed by taking readings at a number of heights above the soil surface. The system was then solved for each discrete layer using a special mathematical technique, known as Tikhonov regularisation, that enables minimisation of errors associated with finding the solution of an ill-posed linear system. It should be noted that an attempt to solve a system of linear equations described by Borchers (1997) was previously conducted (Rhoades and Corwin, 1980), but was unsuccessful. The main objectives of this work were to investigate the reliability of the new profile reconstruction method for monitoring the soil apparent electrical conductivity in the agricultural environment, and to assess its potential for detecting changes in soil ECa caused by change in soil moisture. Methods The experiments were undertaken at the Myall Vale Cotton Research Institute located near Narrabri, NSW. The study area was a small experimental field situated on a flat middle terrace of the Namoi river. Sites were located on the uncultivated and cultivated parts, respectively. According to the field's history, the uncultivated part had been used for pasture and the cultivated one had been managed as a fallow for the last three years. The soil profile is a Vertosol (Isbell, 1996) formed on fine alluvial sediment and clay. Following Borchers et al (1997), the experimental sites were selected where soil apparent electrical conductivity as measured by EM-38, was lower than 100 ms/m. This step was necessary in order to satisfy the assumption incorporated into the linear response model described by McNeill (1980). Soil apparent electrical conductivity was measured with an EM-38 apparatus (with Digital Readout). The instrument was set to zero with in-phase nulling adjusted as described in the operating manual. At each site a set of measurements in vertical and horizontal dipole orientation were taken starting from the surface to the height of 1.6 m with 0.05 m increment. At each height three readings were taken and the average is obtained. This procedure was repeated three times to obtain a representative data set, which was later used to compute the conductivity profile. Soil samples were taken to obtain an independent measurement of ECa in the laboratory. A hydraulic push tube was used to extract a soil core of 0.04 m diameter. The first core was taken to a maximum depth of 1.2 m. The soil core was taken from the push tube, cut into pieces of 0.05 m lengths to represent ECa at a particular depth. After the initial ECa readings and the soil core were taken, an approximately 0.2 m 3 of water was sprayed evenly over the soil surface. Soil was covered with straw and left to equilibrate for 48 h. After equilibration, a second set of EM measurements and a second 2

3 core were extracted using the same method. This procedure was conducted on both cultivated and uncultivated parts of the field. The following procedures were used in soil laboratory analysis: Hydrometer method (Day, 1965) was used for particle-size analysis; EC 1:5 (soil:water) extract (Loveday,1965) to measure electrical conductivity. Modification of the Core Method (Black, 1965) was used to determine bulk density of each sample. The modification consisted in the use of a hydraulic core sampler was used to extract the soil core. When pushed into the soil, the sampler cuts the core without changing soil volume, thus, it can be used for bulk density sampling. Relations between soil properties and soil apparent electrical conductivity. A model of electrical current flow in soil (Rhoades et al., 1988a) was used to predict the soil ECa from the soil properties. According to this model current flows in the soil through three elements acting in parallel: large pores filled with electrolyte (continuous pathway 'wc'); small discontinuous pores (series-coupled pathway 'ws') and surface of soil particles in direct contact with one another. The same author showed that the soil ECa can be related to soil physical and chemical properties as follows: ECa = (θs+ θws)2 ECwsECs + (θw θws)ecws (1) Rhoades1988a,1990) (θs)ecws + (θws)ecs θs - volumetric fraction of soil solid [m 3 /m 3 ]. This is equivalent to θs = ρ ρ b s, where ρ b and ρ s are bulk density and average density of soil solids [m 3 /m 3 ]. θw- volumetric water content of soil [m 3 /m 3 ]. θws - volumetric content of water in small discontinuous pores [m 3 /m 3 ]. θws = θw [m 3 /m 3 ]. θwc - volumetric water content in large continuous pores [m 3 /m 3 ]. ECs-electrical conductivity of solid phase [S/m]. ECws and ECwc are EC of the soil solution in θws and θwc respectively. [S/m] ECw = ( EC 1:5 SP p b 6.5 ) 100 θ w, where SP = 0.76 % Clay (saturation percentage) Since it is not possible to obtain independent measurements of ECws and ECwc, it was assumed following Rhoades (1989) that ECws=ECwc and from ECwθw = ECwsθws + ECwcθwc it follows that ECws = ECws = ECw. This model was used to obtain an independent estimate of ECa of the profile under investigation. Following (Borchers, et al., 1997) a system of linear equations of the from b = Ax, where constructed x represents the vector of conductivities for each discrete layer, b is a vector of instrument readings at a number of heights, and A is a matrix of the instrument responses coming from different depths as measured at different heights above the surface. The system was then solved using Tikhonov regularisation in the standard form: 2 2 min Ax b + λ 2 x (2) (Hansen, 1993), 2 2 and modified Tikhonov regularisation: Ax b min, subject to x > 0, (3) (Borchers,1997), λlx 3

4 where L is a discrete approximation of the derivative operator. Tikhonov regularization with L approximating the kth derivative operator is referred to as kth-order regularisation (Borchers et al., 1997) To find solutions of the equations 2 and 3 the "Tikhonov" procedure in "Regularization Tools for Matlab" (Hansen, 1993), and modified "NNLS" procedure in Matlab 5 with non-negativity constraint were used respectively. Matlab's implementations of L-curve, Global Optimum Criteria and Generalised Cross Validation algorithms were used to compute the regularisation parameter λ (Hansen,1993) ( for more details on the reconstruction method see Borchers et.al., 1997) Results and Discussion When used to compute the regularisation factor, both Global Optimum Criteria (GOC) and General Cross Validation (GCV) algorithms failed to produce meaningful results, while the L-curve method yielded satisfactory results and therefore it was used for further computation. Standard Tikhonov regularisation. lambda = 0.1, 0.05, 0.02; 0 uncultivated field, before application of water. Standard Tikhonov regularisation. lambda = 0.1,0.05,0.02; uncultivated field, after application of water Measured ECa profile -0.5 Predicted ECa profile A1-1 A1 A2 A3-1 A2 A3 Measured ECa profile ECa (ms/m) Figure 1 Results of the profile ECa reconstruction using Tikhonov regularisation in standard form for λ = 0.1 (A 1); λ= 0.05 (optimal (A 2)); λ= 0.02 (A 3). U ncultivated f ield bef ore application of w ater ECa (ms/m) Figure 2 Results of the prof ile ECa reconstruction using Tikhonov regularisation in standarad f orm f or λ = 0.1 (A 1); λ= 0.05 (optimal (A 2)); λ= 0.02 (A 3) U ncultivated f ield af ter application of w ater. Figure 1 presents the results of the reconstruction using Tikhonov regularisation in standard form for different λ values along with the measured conductivity profiles. While the optimum λ was equal to 0.05 two other solutions were computed with larger and smaller λ to illustrate the effect of different λ values on reconstruction quality. The reconstruction predicts general trend in the ECa, however, it gives slightly underestimated values when compared with ECa computed from equation 1. The difference however is small and may be due to the fact that EM-38 measures conductivity of a much greater volume of soil than the amount of soil used in the sampling. Figure 2 shows the results of the reconstruction using the same method upon the data collected from the uncultivated site after the application of water. The reconstruction has detected the increase in conductivity at the near surface layers, however it failed to account for the variation in EC along the profile. The optimum lambda (λ=0.05) was found to be the similar for both dry and moist conditions. 4

5 Modified Tikhonov-NNLS, L order = 1, 2; lambda = 0.3, 0.1, A11 A2 B1 A3 Measured ECa profile Reconstructed profiles ECa (ms/m) Figure 3 shows the results of the reconstruction using Modified Tikhonov-NNLS method upon data collected on uncultivated field before application of water. A1, A2, A3 solutions were computed with 1st-order regularisation, B1,B2,B3 were computed by 2nd-order regularisation for lambda = 0.3, 0.1, and 0.05, respectively. B2 B3 Results of the reconstructed ECa using Modified Tikhonov NNLS algorithm are shown in Figure 3. Reconstructed profiles do not agree with the ECa predicted from soil parameters using Equation 1, with the exception of reconstruction A2 for which λ=0.3 is large and not optimal. This contradicts the results reported by Borchers et at., (1997), in which modified Tikhonov-NNLS method yielded excellent prediction values. Figure 3 also shows what effect different regularisation orders and regularisation parameters have on the nature of the solution. It can be seen from Figure 3 that the smaller the regularisation order and the larger lambda, the more penalties are applied to the solution, thus less rapid changes between different layers are permitted. Both reconstruction algorithms have failed to predict ECa profile conductivity for the data collected in the cultivated field, and for both data sets before and after the inundation. Poor reconstruction results observed on the cultivated field are more likely to be explained by the violation of an assumption that instrument response comes from a layered earth. This complication is a very difficult to overcome since there is no simple method which can be used in the field to verify that the conductivity layers exists parallel before EM data are taken. The only instrument which can be potentially used for this purpose is a ground-penetrating radar for it is capable of tracking the lateral changes in vertical distribution of soil ECa, however its application is limited to specific field situation (Collins and Doolittle, 1987, Vellidis et al., 1990, Habbard et at., 1990) and the instrument is rarely available to a soil scientists because of its very high cost. Conclusions For the experimental data sets used in the study we concluded that: 1. Tikhonov regularisation in standard mode yielded better prediction than the modified Tikhonov-NNLS algorithm. 2. The L-curve method was found to be superior to both the Quasi-optimality criterion and Cross-validation methods for computing the regularisation parameter λ. 3. The results also indicate that although the reconstruction algorithms can be used for the reconstruction of the soil ECa the quality of the prediction appears 5

6 insufficient for the monitoring of changes associated with the rapid change in water content due to irrigation or rain. This requires further investigation. 4. The quality of the reconstruction can very significantly from on site to another, probably due to violation of the model assumption that the instrument response comes from a horizontally stratified earth. Further research is needed to find methods that could be used to check that this assumption holds before the measurement are taken. References Black, C.A. (1974) Bulk density. In Black, C.A. Ed. Physical and mineralogical properties, including statistic of measurement and sampling. Methods of soil analysis. Part 1. American Society of Agronomy. p 374. Borchers, B., T. Uram., J.M., Hendrickx. (1997). Tikhonov regularization of electrical conductivity depth profiles in field soils. Soil Sci. Soc. Am. J. 61. pp Cannon, M.N., R.C. McKenzie, and G. Lachapelle. (1994) Soil salinity mapping with electromagnetic induction and satellite based navigation method. Can. J. Soil Sci. 74. pp Collins, M.L., J.A. Doolittle. (1987) Using ground penetrating radar to study soil microvariability. Soil. Sci. Soc. Am. J. 51: pp Cook, P.G., G.P. Walker. (1992) Depth profiles of electrical conductivity for linear combination of electromagnetic induction measurements. Soil Sci. Soc. Am. J. 56. pp Cook, P.G., G.R. Walker, G. Buselli, I. Potts and A.R. Dodds. (1992) The application of electromagnetic techniques to groundwater recharge investigations. Journal of Hydrology, 130. pp Corwin, D.L., J.D. Rhoades. (1982) An improved technique for determining soil electrical conductivity - depth relationships from above ground electromagnetic measurements. Soil. Sci. Soc. Am J. 46. pp Corwin, D.L., J.D. Rhoades. (1984) Measurements of inverted electrical conductivity profiles using electromagnetic induction. Soil Sci. Soc. Am. J. 48 pp Day, R.D. (1974). Particle fraction and particle size. In Black C.A. Ed. Physical and mineralogical properties, including statistic of measurement and sampling. Methods of soil analysis. Part 1. American Society of Agronomy. pp Hansen, P.C. (1993) Regularization tools: a Matlab package for the analysis and solution of discrete ill-posed problems. Danish Computing Center for Research and Education, Building 305, Technical University of Denmark, DK-2800, Denmark. Hubbard, R.K, E.L. Asmussen, and H.F.Perkins. (1990) Use of ground-penetrating radar on upland Coastal Plan soils. Journal of Soil and Water Conservation. 45. pp Isbell, R.F. (1996). The Australian soil classification. CSIRO Publishing, Collingwood. Janes, D.B., J.M. Novak, T.B. Moorman, and C.A. Camberdella. (1995) Estimating herbicide partition coefficients from electromagnetic induction measurements. J. Env. Qual. 24. pp Laslett, G.M. (1995). A calibration model for prediction of soil electrical conductivity form electromagnetic measurements. CSIRO Division of Mathematics and Statistics. Report N0. DMS-95/97 6

7 Loveday, J. (Ed) (1974) Methods for analysis of irrigated soils. Commonwealth Agricultural Bureaux. 100 pp. McNeill J.D. (1983) EM34-3 survey interpretation techniques. Technical note TN-8. McNeill, J.D. (1980). Electromagnetic terrain conductivity measurement at low induction numbers. Technical Report TN-6, Geonics Limited. McNeill, J.D. (1990). Geonics EM38 ground conductivity meter: operating manual. Geonics Limited, 1745 Meyerside Drive, Unit 8 Mississauga, Ontario Canada L5T1C6 Rhoades, J.D., B.L. Waggoner, P.J. Shouse, and W.J Alves (1989). Determining soil salinity for soil and soil-paste electrical conductivities: sensitivity analysis of models. Soil. Sci. Soc. Am. J. 53, pp Rhoades, J.D., D.L. Corwin. (1981) Determining soil electrical conductivity-depth relationship using an inductive electromagnetic soil conductivity meter. Soil Sci. Soc. Am. J. 45. pp Rhoades, J.D., N.A. Manteghi, P.J., P.J. Souse, W.J. Alves, (1988a). Soil electrical conductivity and soil salinity: new formulations and calibrations. Soil Sci. Soc. Am. J. 53 pp Slavich, P.G., G.H. Petterson. Estimating average root zone salinity form electromagnetic induction (EM-38) measurements. Aust. J. Soil Res. 28. pp Slavich, P.G., J. Yang. (1988) Estimation of field scale leaching rates from chloride mass balance and electromagnetic induction measurements. Irrig. Sci. 11. pp Triantafilis. J. (1996) Quantitative assessment of soil salinity in Lower Namoi valley. PhD thesis. Department of Agricultural Chemistry and Soil Science The University of Sydney, New South Wales, Australia. Vellidis, G., M.C.Smith, D.L. Tomas and L.E. Asmussen. (1990). Detecting wetting front in a sandy soil with ground penetrating radar. Am. Soc. Agr. Eng. 33. pp Keywords: apparent electrical conductivity, profile reconstruction, EM-38, tikhonov regularisation Mots clés : conductivité électrique apparente, reconstruction de profil, EM-38, régularisation de tikhonov 7