Soil root systems play a pivotal role in the many soil hydrological functions. Soil–plant interactions are complex, time dependent, scale dependent, species dependent and spatially heterogeneous. Special attention shall be paid to plant roots. It is therefore important to have techniques allowing us to assess root system properties at the appropriate support scale.

Noninvasive methods can provide spatially extensive, high-resolution information that, supported by traditional local data, helps complete the complex picture of subsoil structure and dynamics. Among noninvasive methods, Grote et al. (2010) discussed the use of the ground-penetrating radar (GPR) for water estimation in a vineyard. However, the scope of the investigation of GPR is often limited by the soil type and is difficult to apply in clayed soil, and resolution is constrained by available wavelengths. A more developed approach is electrical resistivity imaging (ERI) – also called electrical resistivity tomography (ERT) – which can be particularly informative regarding soil water content. In most soil types, electrical resistivity (ER) can be described as a function of porosity, saturation of electrolyte, its pH and mineralization within the pores (Archie, 1942), clay content (and generalized Archie's laws) and temperature (e.g., Campbell et al., 1949). Water content could be derived from the measured ER using pedotransfer functions such as the well-known Archie's law or other approaches (e.g., Rhoades et al., 1976; Waxman and Smits, 1968). Since absolute soil moisture content is of limited interest for researchers and professionals which are focused on the soil water availability for the plant, several studies relate the application of the variation of ERT or the fraction of electrical resistivity variation (FERV) introduced by Brillante et al. (2016) as a predictor of the fraction of transpirable soil water (FTSW) and related variables.

Amato et al. (2008) tested the capability of 3-D ERT to quantify root biomass on herbaceous plants using resistivity root correlation and calibration. Electrical methods have been also used to identify root water uptake (RWU – e.g., Cassiani et al., 2012; Garré et al., 2011; Michot et al., 2003; Srayeddin and Doussan, 2009) and demonstrated the match between soil water content variations and temporal changes in electrical resistivity. Cassiani et al. (2016) monitored the electrical resistivity in an apple orchard under external forcing conditions (irrigation- and plant-driven evaporation) and showed that the increase in resistivity is located in the subsoil region where active roots are present. Electrical and electromagnetic methods have been also used to identify root water uptake (e.g., Cassiani et al., 2015). Werban et al. (2008) performed an interesting ERT study on lupine roots and showed that rooted soil differs from bare soil in terms of the pedophysical model. Several studies related to soil–root systems have shown that the measured root mass density statistically correlates with the electrical conductivity (EC) data obtained from ERT (Amato et al., 2008). Nevertheless, in some cases, the ranges of electrical resistivity of soil and roots overlap. The amplitude of contrasts varies according to the soil resistivity and tree species (Zanetti et al., 2011; Mary et al., 2016), to the water content and the decay state of the wood itself (Martin, 2012), and to variations in soil water content (Garré et al., 2011; Beff et al., 2013; Cassiani et al., 2015; Mary et al., 2016). The problem would complicate further the correlation with root mass considering heterogeneous soil properties and moisture, as well as the electrical anisotropy caused by the root system, i.e., the root connectivity and root structure as further described in Rao et al. (2018).

Recent studies have shown a correlation between bulk electrical resistivity and root mass density, but an understanding of the contribution of the segments of the root system (by its own properties, with no interaction with soil) to that bulk signal is limited to only a few studies describing wood electrical properties. Gora et al. (2015) reviewed the literature describing electrical properties of stems noting large differences between trees and vine plants' resistivity values (200 % higher for trees), suggesting that there is a phylogenetic basis for variation of the ER that reflects the influence of anatomy and physiology. Observations from stems are directly transposable to roots. The range of electrical resistivity of roots depends on their nature. Typically, coarse roots, because of the heartwood and the isolative layer of bark, are considerably more resistive than fine roots (Hagrey, 2007). Electrical resistivity is also linked to the physiological state of the roots. Depending on the season, roots carry electrical charges as sap composition is variable and sap flows vary in intensity and direction. Wood composition and physical properties also change with root decay, which implies a variation of electrical properties (Martin, 2012; Martin and Günther, 2013; Weller et al., 2006). Very recently, Rao et al. (2018) produced an interesting study aiming at understanding bulk electrical conductivity on individual root segments, incorporating the impact of roots in the pedophysical relations to better infer the real soil water content.

Finally, root water uptake and the release of different exudates by fine roots change soil water content and resistivity at several temporal scales (York et al., 2016): on a daily basis (night vs. day, sunny vs. cloudy days) and seasonally (growth period vs. winter or drought season). In conclusion, roots might have a considerable impact on ERT signals, but this may not be directly measurable: ERT thus is an indirect determination of root presence.

Other bioelectrical phenomena can contribute to a more effective characterization of root properties. Plant water uptake generates a water circulation and a mineral segregation at the soil–roots interface, thus inducing an ionic concentration gradient which generates an electrical potential of a few mV. This can be measured in terms of a passive distribution of voltage in the soil (Boleve, 2009). Gora et al. (2017) provide a framework for studying the ecological effects of lightning in the context of electrical properties of trees. Also, Gibert et al. (2006) and Le Mouël et al. (2010) measured natural variations of electrical potential using electrodes in the stem. They respectively measured 25 mV due to daily variations of sap flow and 10 to 50 mV caused by the flow of thunderstorms, which would produce soil charges and give rise to a current circulating through the roots and the tree stem. In theory, by analyzing the voltage distribution in the soil, it is possible to find the characteristics of the sources (depth and extension) causing the voltage anomaly (Saracco et al., 2004). In practice, these sources are too low in generally noisy environments. But one may think about taking advantage of these results to build an active method producing current flow and potential distribution into the soil.

In this study, we aim at investigating the feasibility of the mise-à-la-masse (MALM) method in the context of plant root mapping. MALM is an electrical resistivity method originally developed to delineate conductive ore bodies for mining exploration purposes (e.g., Schlumberger, 1920; Parasnis, 1967). An electrical current is injected into a conductive body and the resulting voltage values are measured at the ground surface or in boreholes; the shape of equipotential contour lines is informative about the extent and orientation of the conductive body in the subsoil.

In the plant stem and roots, electrical current is transmitted through active electrical layers, in the xylem and phloem (on either side of the cambium), where sap flow processes take place. Our main assumption is to consider that, thanks to the quasi-infinite fine root connections and their mycorrhiza at the interface between roots and soil, current tends to run out uniformly from the roots to the soil. In the context of MALM applications, the tree root system can thus be viewed as the conductive body to be imaged, with some important caveats: current may be carried within the roots but is likely to be released into the soil only at the points where fine roots emerge from the woody root structure. As fine roots are the active ones, this would be of major interest for the plant science community. Note that this is not necessarily proven for non-woody plant species. For instance, Anderson and Higinbotham (1976) showed that maize roots have significantly lower electrical resistance in the radial compared to the axial direction (thus being anisotropic), thus allowing current to exit laterally from the entire root length.

In practice, for MALM applied to root prospection, the current is to be injected directly into the tree stem with one electrode, while the other current electrode is placed in the soil at some distance from the tree. Voltage is measured at the soil surface and in boreholes with respect to a second, remote reference voltage electrode.

It must be noted that soil and root conductivity depends, among other parameters, on seasonal variations, water content or even salinity of the soil, making the interpretation potentially complex. In contrast, the sensitivity of MALM to water content makes the monitoring of plant water uptake occurring near roots possible and strengthens interpretation of their location.

Some knowledge gaps exist concerning root electrical properties. However, several theories have been proposed in the scientific literature in this respect, all confirming that each root may act as a current source in the MALM configuration above:

Dalton (1995) analyzed the root–soil circuit and proposed a conceptual model with an electrical analog composed of resistance R and capacitance C (the ability of a system to store an electric charge). In that model, the internal fluid (xylem and phloem) of the plant roots constitutes a duct of low resistance which is separated from a low-resistance external medium (soil) by insulating root membranes (Ozier-Lafontaine et al., 2005). These membranes, in addition to being insulating, accumulate charges on the surface. Observation from Dalton and subsequent theories are fully consistent with the use of MALM for plants, even though the capacitance part is not exploited in these measurements. A benchmarking of the experimental approaches supporting the subsequent theories is proposed in Postic et al. (2016).

Given the review of current knowledge on electrical properties of roots, in this paper we hypothesize that the mise-à-la-masse method can be a viable tool to locate active roots under in situ conditions. The paper has the following aims:

define a viable field protocol that uses jointly MALM and ERT to map active tree vine roots,

A discussion of the results will be provided in light of biological assumptions.

The field study was carried out in a vinery of the Château La Louvière appellation contrôlée, located in Pessac-Léognan (Fig. 1a) near Bordeaux (Gironde, France). The climate of the region is oceanic with an average annual air temperature of 13.7 ∘C and total annual rainfall of 811 mm (André et al., 2012). According to the meteorological station near the experimental plot (200 m), the study period was wet after rainfall, with an air temperature of 11 ∘C. The topography of the plot is mostly convex with an average slope of about 10 % but less than this value at the location of the experimental plot, thus inducing small surface water runoff.

The 3-D ERT setup was originally developed by Boaga et al. (2013) and subsequently improved and adapted at different sites to obtain successful results regarding soil–plant interactions, for example, in salt marsh environments (Boaga et al., 2014) and in apple and orange orchards (Cassiani et al., 2015, 2016; Consoli et al., 2017; Vanella et al., 2018). The apparatus was adapted again and applied for the first time in a vineyard for this study. Figure 2 shows the geometry of the electrode system: four micro-boreholes define a rectangular domain, 1 m along the vineyard direction (y) and 1.2 m in the perpendicular direction. Each borehole houses 12 electrodes with 0.1 m vertical spacing. In addition, 24 surface electrodes define a regular grid. Such disposition allowed us to conduct high-resolution measurements around the selected vine plant (Fig. 2). Field measurements were conducted in March 2017, using a 10-channel resistivity meter (Syscal Pro Switch 72, IRIS Instruments). For the 3-D scheme of ERT, a complete skip-two dipole–dipole scheme was adopted and produced some 5000 measurements, including reciprocal measurements used to estimate and reject bad data quality (Binley et al., 1995; Daily et al., 2004). A pulse duration of 250 ms for each measurement cycle and a target of 50 mV for potential readings were set as criteria for the current injection. The R3t code (Binley, 2013) was used for data inversion.

Figure 6 shows the solution of the inversion from the 3-D ERT data acquisition. The pulse duration was 250 ms per measurement cycle, and the target voltage was 50 mV for the current injection. The result of a measure corresponds to the mean of between three and six stacks with a relative difference between two stacks of 5 % on the resistivity term. Contact resistances were good during the acquisition: by accepting a threshold equal to 5 % for reciprocity error, only 12 % of the measurements were rejected. Electrical resistivity ranges from 100 to 250 Ω⋅m with significant lateral and vertical spatial variations (Fig. 6). Soil texture is expected to be rather homogeneous with depth, except at the very top where the soil tillage can induce also electrical resistivity changes. A profile taken at 0.2 m depth (Fig. 6a) shows two distinct peaks of resistivity, with the first peak corresponding to the highest value of ER (250Ω⋅m) located at y=0.78 m, close to the plant stem position but with some slight shift. In the 3-D visualization (Fig. 6c) the high-resistivity peak corresponds to an extended anomaly around the plant.

When considering the electrical resistivity profile with depth below the stem (Fig. 6b), a maximum region between 0.2 and 0.4 m depth is clearly visible. A horizontal profile at 0.4 m depth (Fig. 6a) confirms a maximum around y=0.7 m, which is not far from the stem location. At larger depths no noteworthy features are apparent since neither soil tillage nor plant roots seem to act on the electrical resistivity of the soil.

As discussed above, we acquired direct and reciprocal measurements also for the MALM data. A comparison between direct and reciprocal resistances allows us to, in ERT, quantify the data quality, remove outliers and define the error level to be adopted in the data inversion procedure. However, the reciprocity theorem holds only in case of linearity (Parasnis, 1988). In the MALM case at hand, linearity may be violated when current is injected into the tree stem (by accepting a threshold equal to 5 % for reciprocity error, only 10 % of the measurements were rejected for the stem injection while 7 % of the measurements were for the soil injection). And indeed the differences between direct and reciprocal data (Fig. A1) seem to be systematic and linked to the region around the stem. In the following we will refer to the MALM results obtained by injecting current into the stem. Figure 7 shows a comparison between normalized voltage data obtained by injecting current into the stem and into the soil. At a very first glance, the spatial distributions of the voltage caused by stem and soil injection results appear very similar, with the striking exception of the voltage absolute values, with the stem injection leading to much lower normalized voltage values (maximum is 200 V/A versus 500 V/A for the soil injection) especially close to the stem. This is an indication that current is indeed not injected at the ground surface, but emerges at some point(s) below ground. Note that also the gradients along the ground surface are much steeper for the soil injection than for the stem injection, confirming the hypothesis just presented.

Figure 7 also shows borehole results, which appear to be more complex and harder to interpret in terms of actual current distribution. Normalized voltages range between roughly 20 V/A at 0.1 m depth to nearly zero at 1.3 m depth. For both stem and soil injections, the voltage decreases regularly from 0.6 to 1.3 m. Slight differences in the decay slope and between boreholes are only visible for the shallow region (0–0.6 m depth). In particular, in the presence of stem injection, the voltage is nearly constant from 0 to 0.3 m depth, while for soil injection the slope is slightly larger. This pattern is observed in each borehole. Borehole 4 shows some irregular behavior (one electrode is abnormally low, possibly because of bad contact with the soil. On average, voltages resulting from soil injection are higher than from stem injection.

Figure 8 shows the spatial distribution of the F1 function, where the spatial dependence is implicitly accounted for by the index i (ith node in the mesh) in Eq. (1). Each individual source was forwarded to produce a tentative normalized voltage at electrodes also as a function of the resistivity distribution reconstructed by ERT inversion of field data. Obviously, Fig. 8 shows that none of the single source positions is capable of fitting all data perfectly – the misfit range reproduced by F1 values in Fig. 8 is between 10 % and 50 %. Nevertheless, the fit is not too low, and the F1 spatial distribution is a clear indication of the regions where distributed sources shall be placed to reproduce field data. For both injection schemes, in stem and soil, F1 values decrease with depth, but with different rates. In the case of injection into the soil, the source locations with a 20 % misfit are very close to the ground surface (within 0.05 m depth). In the case of stem current injection, the same misfit level extends to a 0.3 m depth (Fig. 8c).

Considering a single punctual source is, of course, a very rough approach in trying to identify the distribution of current sources that generate the observed MALM voltage distributions. Thus, we used the results of the section above only as a first approach to guide the identification of distributed current sources. The objective function in Eq. (2) – named F2 – was used for inversion of sources during stem current injection. Function F2 reflects the L2-norm (least squares) of the differences between the measured data and the sum of the sources weighted by a coefficient α that is accounting for the fraction of total current pertaining to that source. The vector of α values is the target of the inversion, while the locations of candidate sources are defined by the nodes of the finite element mesh used for forward modeling. Given the very large number of nodes, most of which are located in regions that are very unlikely to host active roots, and thus MALM current sources, we constrained the candidate locations on the basis of the results of the F1 inversion (see section above): only locations that would contribute in a substantial manner to reducing the F1 misfit (to 17 %) are used as candidate locations in the F2 minimization – about 200 locations were used (see Fig. 8c). The corresponding values of optimized F1 are used, after their sum is normalized to 1, as initial guesses for α values to start the inversion. Individual α values are allowed to vary in the 1×10-4 to 0.1 range. Current conservation was respected since the sum of the weight was equal to 1 at the end of the inversion iterations.

The result of the F2 minimization is shown in Fig. 9, where it is apparent how the region where distributed current sources are located is no deeper than about 0.3 m and has a lateral extent between 0.5 and 0.9 m. This is likely to be the extent of the plant active roots.