Identifying Potential Leakage Zones in an Irrigation Supply Channel by Mapping Soil Properties Using Electromagnetic Induction, Inversion Modelling and a Support Vector Machine

: The clay alluvial plains of Namoi Valley have been intensively developed for irrigation. A condition of a license is water needs to be stored on the farm. However, the clay plain was developed from prior stream channels characterised by sandy clay loam textures that are permeable. Cheap methods of soil physical and chemical characterisations are required to map the supply channels used to move water on farms. Herein, we collect apparent electrical conductivity (EC a ) from a DUALEM-421 along a 4-km section of a supply channel. We invert EC a to generate electromagnetic conductivity images (EMCI) using EM4Soil software and evaluate two-dimensional models of estimates of true electrical conductivity ( σ —mS m − 1 ) against physical (i.e., clay and sand—%) and chemical properties (i.e., electrical conductivity of saturated soil paste extract (EC e —dS m − 1 ) and the cation exchange capacity (CEC, cmol( + ) kg − 1 ). Using a support vector machine (SVM), we predict these properties from the σ and depth. Leave-one-site-out cross-validation shows strong 1:1 agreement (Lin’s) between the σ and clay (0.85), sand (0.81), EC e (0.86) and CEC (0.83). Our interpretation of predicted properties suggests the approach can identify leakage areas (i.e., prior stream channels). We suggest that, with this calibration, the approach can be used to predict soil physical and chemical properties beneath supply channels across the rest of the valley. Future research should also explore whether similar calibrations can be developed to enable characterisations in other cotton-growing areas of Australia.


Introduction
The vertosols that characterise the extensive clay alluvial plains of Namoi Valley, New South Wales (NSW) make this a highly productive agricultural area. Up until the 1960s, their versatility enabled dryland wheat, sheep and beef cattle production [1]. The construction of Keepit Dam in the late 1960s provided water for irrigation, and today, Namoi Valley has been extensively developed for irrigated cotton farming. In the lower Namoi, this is mostly dependent on water supplied from Keepit Dam via the river. Moreover, a condition of an irrigation license is that the water needs to be stored on a farm. This requires supply channels and water storages. Between Narrabri and Wee Waa, many supply channels were constructed and traverse the plain from south to north. However, the clay plains

Study Site
The study area is located within a corporate farm (204 m above sea level; 30 • 19 60 S, 149 • 66 76 E), which is in the lower Namoi Valley of New South Wales, Australia (Figure 1a). The climate is semi-arid, with means an annual rainfall of 643 mm and potential evaporation over 1800 mm. The rainfall is summer-dominant, with a mean maximum in January (79.8 mm) and minimum in August (37.5 mm).
The farm was developed for irrigated cotton production in the 1960s. To supply water for irrigation, a large earthen channel was constructed. It extends from the Namoi River in the south toward a large water reservoir some 10 km away to the north. Herein, we investigate the first 4 km of the channel. Figure 1b shows the location of the channel relative to the Kamilaroi Highway and a floodway, which cuts across the southern and northern thirds of the channel, respectively.
In a reconnaissance soil survey of this part of the lower Namoi Valley, Stannard and Kelly (1977) [2] identified four physiographic units. Figure 1c shows the location of these physiographic units, including the clay plain, prior stream formation, coarse-textured dissected flood plain and Pilliga Scrub Complex. The clay plain is the largest and is characterised by uniform topography, where the uppermost sediments are fine-textured, upon which a self-mulching clay soil has developed. In the Australian soil classification [12], these fall under the sub-order of grey or black vertosols.  (13), (c) physiography of the lower Namoi valley (after Stannard and Kelly, 1968 [14]) and (d) general shallow stratigraphy near prior stream channels nearby Gwydir Valley (after Pietsch, 2006 [13]).
The prior stream formations occur mostly in continuous belts of slightly elevated and undulating lands. Figure 1d shows that the uppermost materials, in prior stream channels in the nearby Gwydir Valley, are coarser and can be as wide as 300 m [13]. The prior stream channels can generally be distinguished from levees with the channels underlain by coarse sediments and gravels. The prior stream channels are usually found in low-lying areas and act as preferential paths for floodwaters (i.e., floodways). They are identifiable from normal effluents by wide meander belts and broad and shallow channels.
In some locations, migrational channel deposits (palaeochannels) underlie these prior stream channels, and because they are also characterised by coarse sands and gravels [14], the deep draining water passing beyond the soil in the prior stream channel can be recharged to ground water via the palaeochannels.
The EC a from a DUALEM-421 was collected inside the channel (Figure 1b) starting from the northern end, with the last measurements logged adjacent to the Namoi River in the south where the pumps pump the water into the channel. The survey was conducted on 15 October 2019. The instrument was mounted on plastic wheels, approximately 0.2 m above the ground and aligned in the orientation of the channel (north-south). The EC a data were geo-referenced in latitude and longitude using a NovAtel SMARTV1 GPS (NovAtel Inc., Hexagon Calgary, Alberta, Canada) antenna. The coordinates were later converted into easting and northing (UTM 84). Both the EC a and GPS data were collected using a Panasonic Toughbook CF-19 and logged using HGIS (v. 10.5) Software (StarPal Inc., Fort Collins, CO, USA).

Soil Sampling and Laboratory Analysis
To evaluate the inversion modelling results, soil samples were collected. Figure 1b shows the soil sample locations selected and spaced, on average, approximately 0.3 km apart along the transect. In total, 13 sampling sites were selected and chosen to cover a wide range of EC a . At each sampling site, the first sample was taken from the surface (0 m). From there, soil samples were taken at 0.5-m increments to a maximum depth of 6 m. In total, 169 samples were collected. The samples were collected on 22 October 2019. The samples were collected from south to north and numbered from 1 to 13, accordingly, as shown in Figure 1b.
The samples were air-dried, ground and passed through a 2-mm sieve. The samples were oven-dried (60 • C) for 48 h. Laboratory analysis involved determination of the soil physical properties, including soil particle size fractions (e.g., clay, silt and sand-%) and based on the hydrometer method [16]. Various chemical properties were also determined, including the pH from a 1-part soil to 5-part water extract (pH 1:5 ). The soil electrical conductivity was similarly determined from this extract (EC 1:5 -mS m −1 ). Subsequently, the EC e (dS m −1 ) was estimated from the EC 1:5 using conversion factors for various soil textures determined from the Australian soil texture triangle [17]. The conversion was adopted from Slavich and Petterson (1993) [18] and recommended by the Department of Primary Industries as follows: clay (EC 1:5 × 6.7), clay loam (8.6) and sandy clay loam (9.5). Tucker's (1974) [19] method was used to determine the CEC (cmol(+) kg −1 ) using a mechanical leaching device. Briefly, samples were washed with 60% ethanol to remove any soluble salts, followed by extraction with 1-M NH4Cl. The extracts were analysed using an inductively coupled plasma optical emission spectrometry (ICP-OES). The exchangeable cations determined were summed to estimate the CEC.

Inversion Modelling Using EM4Soil
To invert the DUALEM EC a , the EM4Soil software package [20] was used. The algorithm works for EC a at low induction numbers [21]. Primarily, the software generates electromagnetic conductivity images (EMCI) and specifically estimates the σ by inverting EC a obtained from EM instruments [22]. The estimates of σ are constrained by neighbouring sites using a 1-dimensional laterally constrained approach [23] where 2-dimensional smoothness constraints are imposed. To generate various EMCI to compare, we changed the following parameters: (i) Forward modelling-forward calculations and derivatives consider two functions: The cumulative function (CF) is satisfactory if the EC a is measured at low induction numbers; however, the full-solution (FS) would be preferred when the EC a is acquired over conductive terrain (i.e., >100 mS m −1 ). The latter, therefore, better accounts for nonlinearity. (ii) Inversion algorithms-include S1 and S2, whereby the latter constrains EMCI variations around a reference model. It generally produced smoother EMCI than S1. Both are variations of Occam regularisation. (iii) Damping factor (λ) and iterations-as λ increases, it tends to smooth the EMCI. Herein, we considered λ = 0.07, 0.3 and at 0.3 increments thereafter, to a maximum of 3.0. A similar effect occurs when choosing the number of iterations. We selected 10.
Our aim was to determine the optimal combination of inversion parameters (i.e., λ or S1 or S2, CF or FS) for the quasi-2D inversion of DUALEM-421 EC a . We determined this by looking for the largest coefficient of determination (R 2 ) between the σ and the soil physical properties (i.e., clay or sand) and chemical properties (i.e., EC e and CEC). We did this by obtaining the σ from the EMCI and correlating these with the measured soil properties at the same depths the σ was estimated.

Establishing a Calibration Model between the σ and Various Soil Properties
To develop a mathematical model between estimates of the σ and various soil physical and chemical properties, a support vector machine (SVM) model was chosen. This is because we anticipate that the EM instruments' response in the soil would be a function, potentially, of four separate soil properties (i.e., clay content and mineralogy, salinity and moisture), and the relationship of each of these and the σ would also be nonlinear. We also have a limited number of soil cores.
In these circumstances, an SVM can perform well on problems that are nonlinear, sparse and are highly dimensional. This is because an SVM uses kernel functions to project the data onto a new hyperspace where complex nonlinear patterns can be simply represented [24,25]. SVM predictions are calculated using the following function: where f(x) is the target soil physical (e.g., clay) or chemical (e.g., EC e ) property; α * i and α i are the weights (Lagrange multipliers); K x i , x j is a user-defined kernel function (i.e., linear, polynomial, radial and sigmoid) and an error parameter c, which is calculated from the best model, where x is the feature vector (i.e., σ from inversion).
The kernel function used herein is an isotropic Gaussian radial basis function: with the bandwidth parameter γ. The α * i and α i are weights (Lagrange multipliers), which determine the influence of each point in the model and are obtained from the solution of a quadratic programming optimisation problem [26,27] of the form: The constraints are given as follows: subject to where ε is the non-negative content specified, and C defines the trade-off between training error and model complexity (i.e., flatness of f(x)) and is a regularisation parameter. Herein, and using trial and error, 5 and 0.1, respectively, were the best parameters for C and γ obtained using the training data.
In this work, we applied the SVM from the "e1071" and "caret" packages [28] in R.
In order to improve the performance of the SVM, we selected the best parameters for the model with different couples of epsilons (ε) and cost parameters using the tune function in R. In our study, we trained models with ε = 0, 0.1, 0.2, ..., 1 and cost = 21, 22, 23, ..., 2100, which means it will train 1100 models. We successfully tuned the SVM model, with the best model having values of ε = 0.3 and cost = 4.

Validation and Evaluating Prediction Accuracy, Bias and Concordance
Herein, a leave-one-site-out cross-validation is used to validate our predictions of various soil physical and chemical properties. This was done owing to a limited number of sample sites. Specifically, we removed a whole site, including all depths. A model was fitted using the remaining calibration dataset of 12 sites and applied to the site removed. This was done 13 times.
Several indices, including the root mean square error (RMSE) and mean error (ME), were considered, with the former a measure of prediction accuracy and the later bias, respectively. The RMSE is a frequently used measure of prediction accuracy and is calculated as follows [29]: and describes the difference between measured and predicted data. The smaller a RMSE value, the greater prediction accuracy. Moreover, if the RMSE is less than half the standard deviation (SD) of the measured data, the prediction model is considered to produce satisfactory results [30]. The mean error (ME) is calculated as follows [31]: For an unbiased prediction, their values should be near zero. The Lin's concordance correlation coefficient (LCCC) is also used, herein, as a measure of the agreement between measured and predicted soil properties. That is, how close predictions fall along a 45-degree line from the origin to the measured data [32]. It is a determinant of both accuracy and precision of the predictions and is calculated using following equation: where y andŷ are measured and predicted soil properties, ρ is the correlation coefficient of the measured and predicted data, σ y and σŷ are equivalent variances and µ y and µŷ are the average of the measured and predicted data, respectively. The agreement can then be considered in terms described by McBride (2005) [33] of almost perfect (>0.9), substantial (0.8-0.9), moderate (0.65-0.8) and poor (<0.65). Table 1 shows the summary statistics of EC a collected along the channel. The mean of the 1mHcon (62 mS m −1 ) was approximately twice as large as the 1mPcon (32 mS m −1 ). It also shows that, while the difference between the mean of the 2mHcon (91 mS m −1 ) and 2mPcon (61 mS m −1 ) was large, the mean of the latter was like that of the 1mHcon. The mean of the 4mHcon (95 mS m −1 ) and 4mPcon (89 mS m −1 ) were equivalent to the 2mHcon. Table 1 also shows that summary statistics of the EC a at 13 calibration sites were equivalent and, therefore, were a good representation and valid to use for calibration/validation.  Figure 2a shows that the measured DUALEM-421 EC a of 1mHcon (100 mS m −1 ) and 1mPcon (50 mS m −1 ) were largest within 600 m of the southern (sites 2 and 3) and northern (site 11) ends. Conversely, 1mHcon (20 mS m −1 ) and 1mPcon (10 mS m −1 ) were smallest closest to Namoi River (site 1) at the southern end and near the floodway (site 10). Figure 2b shows equivalent patterns for the 2mHcon and 2mPcon. Whereas the 2mHcon was generally larger along the entire transect than either the 1mHcon or 1mPcon, the 2mPcon was equivalent to the 1mHcon. As indicated in Table 1, Figure 2c shows that the 4mHcon and 4mPcon were essentially equivalent to each other and the 2mHcon.  Table 2 shows the summary statistics of measured soil physical properties at the 13 soil sampling sites. The clay ranged from small (4%) to large (77.3%), with a mean clay (44.2%) akin to a soil texture approximating a medium clay. The sand was similarly variable, with the minimum (5.9%) and maximum (92.4%) showing a larger range with a smaller mean (35.54%) than clay. The standard deviation (SD) for clay (14.1%) and sand (18.3%) were comparable. Table 2. Summary statistics of measured soil properties. Note: soil salinity of the saturated soil paste extract (EC e -dS m −1 ) estimated from the measured electrical conductivity from a 1-part soil to 5-parts water extract (EC 1:5 ), cation exchange capacity (CEC-cmol(+) kg −1 ) and pH of a 1-part soil to 5-parts water extract (pH 1:5 ).  Table 2 also shows summary statistics of the chemical properties. The EC e minimum (0.1 dS m −1 ) and mean (1.7 dS m −1 ) were non-saline (<2 dS m −1 ), with the maximum (3.99 dS m −1 ) slightly saline (2-4 dS m −1 ). The CEC ranged between small (1.31 cmol(+) kg −1 ) and large (47.7 cmol(+) kg −1 ), which represented good shrink-swell behaviour, and, on average, the soil had a mean CEC (24.4 cmol(+) kg −1 ), which indicated channel sediments that have shrink-swell behaviour. The SD of the EC e (0.9 dS m −1 ) and CEC (8.43 cmol(+) kg −1 ) were small. The pH 1:5 ranged between strongly acidic (4.5) and very strongly alkaline (9.65), with a mean of moderate alkalinity (8.5). Except for the pH 1:5 (−1.16), the data were not skewed. Figure 3 shows contour plots generated using JMP Software 13.2 (SAS Institute, Cary, NC, USA) of measured soil physical and chemical properties with depths and at the 13 calibration sites. Figure 3a shows clay was largest (≥50%) at the northern (11 to 13) end and in the middle of the transect (site 7) in the root (0-2 m) and vadose zone (2-6 m). This was similarly the case at the southern end (sites 2 and 3). In this regard, the 1mHcon was generally above 100 mS m −1 .

Soil
Beyond 2 m, clay was variable and generally decreased, however, to intermediate-small (20-30%) clay. At the southern-most site 1, adjacent to Namoi River, clay was uniformly intermediate-small beyond the root zone, where it was small (<20%). This was also the case in the centre of the transect (sites 5 and 6) in the deeper vadose zone (4-6 m) and in the floodway (9 and 10). At these locations, the 1mHcon was smaller and generally below 40 mS m −1 . Figure 3b shows the spatial distribution of sand. For the most part, it was the inverse of clay. Specifically, at the southern end (sites 2 and 3) where clay was large, sand was small (<20%). Conversely, where clay was small, sand was large (≥50%), at the southernmost end (site 1) next to the river just to the south of the centre (sites 5 and 6) and where the channel intersects the northern part of the floodway (site 10). At these sites, large sand indicates the location of the current Namoi River, a prior stream channel and an active floodway, respectively. At these sites, we note that poorly sorted gravels were also present at various depths, particularly between 4-6 m. This indicates the presence of previous migrational channels or palaeochannels.
We also note that, at the last three sites (sites 5, 6 and 10), the location of coarser sediments was overlain in the topsoil (0-0.5 m) by intermediate clay (40-50%), which masks their presence. This was consistent with Stannard and Kelly (1977) [2], who indicated that prior stream channels in low-lying areas relative to the plain are characterised by coarse channel sediments where upper sediments were of a fine texture. Silt (data not shown) did not vary as much as clay and sand, with a narrow range (10-30%). The largest silt (20-30%) was found at most depths at the southern end (sites 2-4) but also just to the north of the centre (sites 5-7) but at deeper depths (>4 m).  Figure 3c shows distribution of the EC e , which was non-saline (i.e., <2 dS m −1 ). Relatively speaking, it was large (i.e., >2.0 dS m −1 ) in the subsoil (>2 m) and in various parts of the channel where clay was large (e.g., sites 3, 7 and 11). In the areas where sand was large, the EC e was small (<0.5 dS m −1 ). This suggests these areas were recharge areas and where water drains freely. Figure 3e shows the CEC was similarly distributed as a function of clay. Of note was that, at the northern end, the CEC was large (>30 cmol(+) kg −1 ) and most likely to have shrink-swell properties and indicate the location of vertosols. pH 1:5 (data not shown) was slightly alkaline in the sandy areas (<7.5) but moderately (8-8.5) to strongly alkaline (≥8.5) in the areas with more clay of the channel. Figure 3e shows the spatial distribution of the soil texture groups. We calculated this using the Australian textural soil classification based on the laboratory measured particle size fractions of the soil samples. Essentially, the transect was characterised by three soil texture groups but, for the most part, was predominantly clay. However, next to the river (site 1) and south of the centre (i.e., sites [4][5][6] and in the floodway (sites 9 and 10), the dominant texture was a sandy clay loam, with clay loams sub-dominant. What is again worth pointing out is that, in low-lying areas to the south of the centre and in the narrow floodway in the north, the veneer of finer-texture soil (clay) overlies and masks the coarser (sandy clay loam) soil associated with the prior stream formations.

Relationship between the σ and Soil Variables
The values of the σ were estimated from the inversion of all EC a measured using the DUALEM-421 instrument. By comparing various parameters (described in Section 2.4), we determined that the best correlations coefficient between the σ and soil physical and chemical properties were achieved by estimating the σ using either the CF forward model, S2 inversion algorithm and λ = 0.3 or λ = 1.8. Figure 2 shows the EMCI from passing the DUALEM-421 EC a through EM4Soil and using the CF forward model and S2 inversion algorithm. Figure 2d shows the EMCI using a λ = 0.3, and Figure 2e shows the EMCI using λ = 1.8. For all intents and purposes, and for both EMCI, the top 1 m was uniformly small in estimates of the σ (45 mS m −1 ). In the areas associated with the parts of the channel with more clay, the σ increased steadily to large values (>175 mS m −1 ) at a depth of 1.5 m, which persisted until a depth of around 4 m, when λ = 0.3 and to 6 m, when λ = 1.8. Conversely, in the sandier parts of the channel, the σ increased to intermediate (132-175 mS m −1 ) values before decreasing again to small values. Table 3 shows the best correlation coefficient (R 2 ) between the σ and soil physical properties of clay and sand and that the chemical property of the CEC was best with the CF, S2 and λ = 0.3. All relationships, while small, were statistically significant (*** p < 0.001). The CF, S2 and λ = 1.8 produced the largest R 2 (0.39) between the σ and EC e . There was also a statistically significant (*** p < 0.001) correlation between the σ and pH 1:5 (0.32), with estimates of the σ from the CF, S2 and λ = 1.8. Unlike in the study by Khongnawang et al. (2019) [11], where a good R 2 was achieved between the σ with clay (0.65) and the CEC (0.68) when the EM38h0 and EM38v0 EC a were inverted, this was not the case here, with either of the estimates of the σ inverted from the DUALEM-421 EC a data available.
To understand the lack of correlation further, Figure 4 shows the plots of the σ, derived from the EMCI, against their respective physical and chemical properties. Figure 4a shows the plot of the σ and clay. It shows that there was linearity between the σ and clay at depths of 1-6 m. This was similarly the case with sand, EC e and CEC (Figure 4b-d, respectively). We attribute this to the σ being jointly a function of the interrelationship between clay and the CEC with EC e , whereby the salts in the subsoil accumulate as a function of aeolian and cyclical deposition over time in this semi-arid landscape.
However, this was not the case in the near surface. Specifically, samples from the surface (0 m) and subsurface (0.5 m). We attribute this to the fact that the large σ appears to be a function of the more reactive clay veneer (CEC > 25 cmol(+) kg −1 ) above the prior stream and floodways and along the channel, because the EC e herein was non-saline. Hence, the smaller values of the σ relative to the subsoil clay which had relatively larger amounts of salts but the same clay content and CEC. Table 3. Coefficient of determination (R 2 ) between selected estimates of true electrical conductivity (σ-mS m −1 ) and various soil properties. Note: soil salinity of saturated soil paste extract (EC e -dS m −1 ) estimated from measured electrical conductivity from a 1-part soil to 5-parts water extract (EC 1:5 ), cation exchange capacity (CEC-cmol(+) kg −1 ) and pH of a 1-part soil to 5-parts water extract (pH 1:5 ). CF-cumulative function, p-statistical significance (p-value).

Measured Versus Predicted Soil Properties
Owing to the poor linear relationships and small R 2 , and the inability to develop a linear or multiple linear regression model, we explored the potential to develop various SVM models between the various soil physical (i.e., clay and sand) and chemical (EC e and CEC) properties and estimates of the σ. We also considered depth in each SVM model. Figure 5 shows the leave-one-site-out cross-validation between measured and predicted soil properties using the SVM models.  Figure 5a shows the predicted clay was in good agreement (Lin's = 0.85) with the measured clay, with the prediction precision (RMSE = 6.85) and bias (ME = 0.20) both being small and close to zero, respectively. Given the RMSE was less than half the SD for the measured clay (7.07%), we can consider these predictions of clay overall as satisfactory [30]. They were also unbiased (ME = 0.20). Figure 5b shows a comparable result achieved for sand, and while the concordance (Lin's = 0.81) was smaller than clay, the predicted sand was still in good agreement. Prediction precision (RMSE = 9.71%) was also larger than clay; nevertheless, the prediction is still considered satisfactory, because the predicted sand was close to half the SD for the measured sand (9.15%).
With respect to the chemical properties of interest, similar conclusions can be drawn regarding their prediction using the leave-one-site-out cross-validation results. In terms of salinity, Figure 5c shows for the EC e there was good concordance (Lin's = 0.86). Again, not only were the predictions precise (RMSE = 0.44 dS m −1 ) and unbiased (ME = −0.03 dS m −1 ), the precision was satisfactory given they were less than half the SD of the measured EC e (0.45 dS m −1 ). Figure 5d shows that, for the CEC, equivalent results were achieved with predictions showing good concordance (Lin's = 0.83), with precise (4.28 cmol(+) kg −1 ) and unbiased (0) predictions.

Mapping Soil Properties with Depth and Along the Channel
To understand the results from a pedological, geomorphological, soil and water use and management standpoint, we plotted the predicted physical and chemical properties beneath the channel. We did this by applying the SVM using the EMCIs generated from the various EC a data, using the CF and S2, with maximum iteration of 10 and λ = 0.3 (Figure 2d) for clay and sand and the CEC and λ = 1.8 for the EC e (Figure 2e). Figure 6a shows that, for the most part, the pattern of predicted clay was consistent with measured clay (Figure 3a). What was evident was the uniform nature of the predicted clay (40-50%) in the surface (0 m) and subsurface (0.5 m) along most of the supply channel. We note that the clay was slightly underpredicted in the central-north part of the channel, however, where the heavy clay plain was evident (sites 7-10). Nevertheless, the heavy clay (>50%) of the plain in the northern part (sites 11-13) was well-predicted. So too was the veneer of intermediate-large (40-50%) clay, which overlied the prior stream channel in the centre and to the south (sites 4-6).
The location of a paleochannel, which commonly underlies the clay plain herein at a depth of around 5-6 m where the clay (<30%) was intermediate-small, was also well-resolved. These indicate places where previous migrational channel deposits (palaeochannels), characterised by coarse sands and gravels (Stannard and Kelly, 1968), shown in Figure 1c can be found. Figure 6b shows this more succinctly due to the large sand (>50%) evident (4.5-6 m) in the area of the prior stream channel just south of the centre (sites 4-6) and also the area of the floodway in the northern third of the channel (near sites 9 and 10). Figure 6c shows that the predicted EC e was consistent with the slightly saline (2-4 dS m −1 ) nature of the vertosols, which characterise the clay plain. The non-saline (<2 dS m −1 ) and highly leached nature of the prior stream formations and the coarser sandy clay loam textures of the dermosols were also well-discerned. Figure 6d helps further explain these results, as it shows where the clay was most reactive and reinforces the notion that the clays with larger CEC (30 cmol(+) kg −1 ) will be more reactive in terms of their shrink and swell and most likely help form a seal in the channel and hold the water sufficiently to enable its conveyance most efficiently along the northern section of the channel.
Conversely, the less reactive parts of the channel (<20 cmol(+) kg −1 ) indicates where the shrink-swell behaviour would be poor and where losses can be expected. This aligns well with the sandy clay loam soil textures, which characterise the prior stream channels and floodway (see Figure 6e). This idea is generally supported by the generally non-saline nature of the soil and vadose zone, thereby indicating where recharge occurs along the channel. We note that the prior stream channel clay content was less than 40%, and this was consistent with where research in the nearby lower Gwydir Valley showed that these clay contents were susceptible to excess deep drainage at the field [34] and district scale [4].
The results described herein have implications for the remaining lower Namoi Valley, where many other supply channels remain unsurveyed. This is because a similar approach can be used by an increasingly large number of consultants who commonly conduct EM surveys using the more popular Geonics EM38 or smaller versions of the DUALEM range of instruments, including DUALEM-1. In this regard, further research could be conducted to see if equivalent calibrations can be developed to predict the physical and chemical properties described herein but only using a smaller number of EC a values. The transect studied herein could act as a calibration location. We also recommend that a similar approach can be used to develop equivalent calibrations to enable predictions in other cotton growing-areas of Australia. Moreover, the results described herein indicate that, in a section of the supply channel which extends some 300 m across a prior stream channel, future work needs to be undertaken to determine engineering solutions to seal the areas where the clay was predicted to be small (<40%) and were indicative of where more permeable dermosols were likely to exist.

Conclusions
Using a DUALEM-421, we have shown where soil samples sites can be located to characterise the soil types beneath a supply channel based on the measured EC a . Using EM4Soil inversion software, we also demonstrated how estimates of the σ can be derived from an inversion of EC a from a DUALEM-421. Moreover, we showed how these estimates of the σ were correlated with the soil physical properties of clay and sand and chemical properties of the CEC when they were estimated using the CF, S2 and λ = 0.3 and the EC e using the CF, S2 and λ = 1.8. While these relationships were statistically significant (*** p < 0.001), the correlations were not strong (R 2 < 0.4). We attribute these poor correlations to the fact that the DUALEM-421 EC a response was a function of four separate soil properties (i.e., clay content and mineralogy, salinity and moisture), and the relationship of each of these and the σ was nonlinear. This was particularly the case for the topsoil (0 and 0.5 m) samples.
Given we also have a limited number of soil cores, we found that, by using an SVM, we could establish a model between the σ and clay and EC e and CEC using the same EMCI. To validate the SVM, we used a leave-one-site-out cross-validation, which produced a good 1:1 agreement with clay (0.85), sand (0.81), EC e (0.86) and CEC (0.83). Our interpretation of the predicted EC e suggests the approach can identify recharge (non-saline) areas. These aligned with where the clay (<40%) was relatively small and in areas associated with prior stream channels that were typically underlain by migrational palaeochannels.
We attribute our success to the ability of the SVM to perform well on datasets that are nonlinear, sparse and are highly dimensional. The results have practical implications for the farmer and where future work should be focused-in particular, along a 300-m section of the supply channel where a prior stream channel was masked by a thin veneer of clay alluvium. Herein, future work needs to be undertaken to determine a suitable engineering solution to seal areas like this, where the clay was predicted to be too small (<40%) and susceptible to deep drainage.
We suggest that, with this calibration, the approach can be used to predict the soil physical and chemical properties within the supply channels across the rest of the valley. Future research should also explore whether similar calibrations can be developed to enable characterisations in other cotton-growing areas of Australia.
Author Contributions: Conceptualisation and investigation, E.Z. and J.T.; formal analysis, data curation, visualisation and resources, E.Z.; writing-original draft preparation, E.Z. and J.T.; software and validation, E.Z., N.L., T.K. and M.F. and supervision, J.T. All authors have read and agreed to the published version of the manuscript.
Funding: This research was financially supported by the Australian Federal Governments Cotton Research and Development Corporation (CRDC) through a research project entitled "Where does the water go?" The first author also acknowledges an Australian Federal Government Research Training Program Scholarship and a top-up scholarship from the CRDC.