Time-lapse monitoring of root water uptake using electrical resistivity

This paper presents a time-lapse application of electrical methods (Electrical Resistivity Tomography – ERT – and 10 Mise-à-la-Masse – MALM) for monitoring plant roots and their activity (root water uptake) during a controlled infiltration 11 experiment. The use of non-invasive geophysical monitoring is of increasing interest as these techniques provide time-lapse 12 imaging of processes that otherwise can only be measured at few specific spatial locations. The experiment here described was 13 conducted in a vineyard in Bordeaux (France) and was focused on the behaviour of two neighbouring grapevines. The joint 14 application of ERT and MALM has several advantages. While ERT in time-lapse mode is sensitive to changes in soil electrical 15 resistivity and thus to the factors controlling it (mainly soil water content, in this context), MALM uses DC current injected in 16 a tree stem to image where the plant-root system is in effective electrical contact with the soil at locations that are likely to be 17 the same where root water uptake (RWU) takes place. Thus, ERT and MALM provide complementary information about the 18 root structure and activity. The experiment shows that the region of likely electrical current sources produced by MALM does 19 not change significantly during the infiltration time in spite of the strong changes of electrical resistivity caused by changes in 20 soil water content. Ultimately, the interpretation of the current source distribution strengthened the hypothesis of using current 21 as a proxy for root detection. This fact, together with the evidence that current injection in the soil and in the stem produce 22 totally different voltage patterns, corroborates the idea that this application of MALM highlights the active root density in the 23 soil. When considering the electrical resistivity changes (as measured by ERT) inside the stationary volume of active roots 24 delineated by MALM, the overall tendency is towards a resistivity increase during irrigation time, which can be linked to a 25 decrease in soil water content caused by root water uptake. On the contrary, when considering the soil volume outside the 26 MALM-derived root water uptake region, the electrical resistivity tends to decrease as an effect of soil water content increase 27 caused by the infiltration. The use of a simplified infiltration model confirms at least qualitatively this behaviour. The 28 monitoring results are particularly promising, and the method can be applied to a variety of scales including the laboratory 29 scale where direct evidence of roots structure and root water uptake can help corroborate the approach. Once fully validated, 30 the joint use of MALM and ERT can be used as a valuable tool to study the activity of roots under a wide variety of field 31 conditions. 32


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(i.e., a configuration where the current dipoles and potential dipoles are three times larger than the minimal electrode spacing). 164 The total dataset includes three types of measurements: 430 surface-to-surface, 2654 surface-to-borehole and 4026 in-hole 165 measurements. 166 In addition to acquiring ERT data, we also acquired MALM data. MALM acquisition was logistically the same as ERT and 167 was support by the same device, but used a pole-pole scheme (with two remote electrodes). Borehole and surface electrodes 168 composing the measurement setup were used as potential electrodes, while current electrode C1 was planted directly into the 169 stem, 10 cm from the soil surface, with an insertion depth of about 2 cm, in order to inject current directly into the cambium 170 layer. The two remotes electrodes C2 (for current) and P2 (for voltage) were placed approximatively at 30m distance from the 171 plot, in opposite directions. Note that for MALM (unlike than for ERT), one corner surface electrode was put near the stem in 172 order to refine the information at the centre of each rectangle. 173 Each MALM acquisition was accompanied by a companion MALM acquisition where the current electrode C1 was placed 174 directly in the soil next to the stem rather than in the stem itself. In this way the effect of the plant stem-root system in conveying 175 current can be evidenced directly comparing the resulting voltage patterns resulting from the two MALM configurations. 176 For both ERT and MALM, we acquired both direct and reciprocal configurations (that swap current and voltage electrode 177 pairs), in order to assess the reciprocal error as an estimate of measurement error (see e.g. Cassiani et al., 2006). Note that for 178 the MALM case, reciprocals may not be the best solutions to estimate data quality as it has been shown in Mary et al. (2018), 179 possibly because of non-linearity caused by current injection in the stem. 180 We adopted a time-lapse approach, conducting repeated ERT and MALM acquisitions over time in order to assess the evolution 181 of the system's dynamics under changing moisture conditions associated with the infiltration experiment. We conducted 182 repeated measurements starting on 19 June 2017 at 10:20 LT, and ending the next day at about 17:00 LT. The schedule of the 183 acquisitions and the irrigation times is reported in Table 1. 184

Forward hydrological model and comparison with geophysical results 185
Hydrus 1D (Simunek, J. et al., 1998) was used to simulate cumulative infiltration and water content distributions for plant B 186 (the larger one). The result from geophysical data acquisition were used to feed the hydrological model initial conditions. 187 Boundary conditions were set for the column respectively as an atmospheric BC with surface run off (observed during the 188 experiment) and triggered irrigation for the upper part, and free drainage for the lower part (see Figure 2). We assumed that 189 the retention and hydraulic conductivity functions can be represented by the Mualem-van Genuchten model (MVG, Mualem, 190 1976;van Genuchten, 1980). Soil hydraulic parameters were directly inferred using grain size distribution and the pedo- The link between the forward hydrological and the geophysical model is a petrophysical relation which transforms electrical 199 resistivity distributions into the corresponding simulated water content (θERT) distributions. There are several petrophysical 200 models of varying complexity to relate water content with electrical resistivity (e.g. Archie, 1942; Waxman and Smits, 1968; 201 6 transformation and reduction by averaging to 1D the ER values obtained during background time T0. We obtained a non-205 homogeneous initial water content for the hydrological simulation varying from 0.1 to 0.27 cm3.cm-3 (Fig. 2a). In order to 206 compare the model results with the geophysical data, we used control points at 0, 0.2, 0.4, 0.6, 0.8m depth. 207

Micro-ERT time lapse analysis 209
The inversion of ERT data was conducted using the classical Occam's approach (Binley and Kemna, 2005). We conducted 210 both absolute inversions and time-lapse resistivity inversions, as done in other papers (e.g. Cassiani et al., 2015, 2016). We 211 used for inversion only the data that pass the 10% reciprocal error criterion at all measurement times. A large percentage of 212 the data had reciprocity errors below this threshold. We inverted the data using the R3t code (Binley, 2019) adopting a 3-D 213 mesh with very fine discretization between the boreholes, while larger elements were used for the outer zone. Most of the 214 inversions converged after fewer than 5 iterations, and the final RMS errors respect the set convergence criteria (Table 1)

MALM modelling and source inversion 219
The MALM processing applied to a plant is thoroughly described in Mary et al (2018). Here we only recall the mathematical 220 background on which the method relies on and some advances compare to the previous approach described by Mary et al. 221 (2018). 222 In MALM, we measure the voltage (with respect to the remote electrode) at N points, corresponding to the N electrodes 223 locations, x1, x2, …, xN. Voltage depends on the density of current sources C according to Poisson's equation: 224 where is the conductivity of the medium, here assumed to be defined by the conductivity distribution obtained from ERT 226 data inversion. The main idea behind the source inversion is to identify the distribution of M current sources C(x,y,z)in 227 practice located at the mesh nodes =[ 1 , 2 , … , ]that produce the measured voltage V distribution in space. Given a 228 distribution of current sources, and once  (x,y,z) is known from ERT inversion, the forward problem is uniquely defined and 229 consists in the calculation of the resulting V field. Conversely, the identification of C(x,y,z) distribution given V(x,y,z) and 230 proposed a linearized form of the problem. In this case, the cost function F2 consists of error-weighted data misfit Φ and 246 model roughness Φ containing model relative smallness and smoothness both weighted by the regularization parameter λ: 247 Given a set of N voltage measurements, minimization of the objective function, 2 , given by eq. (3), produces a vector of M 250 current sources densities Cj ( j = 1,2,…,M), where d is the data vector, ( ) is the forward model that relates the model m to 251 the resistances, is a smoothness operator, is an error weighting matrix, and λ is a regularization parameter that 252 determines the amount of smoothing imposed on m during the inversion. An L-curve analysis is used to identify the optimal 253 regularisation parameter λ. In the revised algorithm all candidate current sources are kept during the inversion. Thus, there is 254 no more a need to identify a threshold for which some sources are rejected. However, the misfit of F1 is transformed into a 255 normalized initial model (m0) of current density via the inverse (1/ 1 ) transformation. During the inversion of the current 256 density, we adopted a relative smallness regularisation as a prior criterion for the inversion i.e. the algorithm minimizes ||m -257 m0 || 2 , where m0 is a reference model to which we believe the physical property distribution should be close. 258 8 measurement were taken overnight, and the acquisition time match with the start of the increase of ET and mean air 283 temperature. No increase was observed on plant A (Fig. B1). After T3, no positive change in ER was observed.  Figure 6 shows the iso-surfaces of fitness index (or misfit) F1 (Eq. 2) for the background (pre-irrigation) conditions of plant B 316 (plant A in appendix C3) and for current injection in the soil and in the stem at all-time steps listed in Table 1. In all cases, 317 Figure 6 shows the iso-surface corresponding to the value F1= 7V corresponding to the 25% misfit index (value selected after 318 analysing the evolution of the L-curve of sorted misfit F1. The same threshold is fixed for all the time steps thus the images the other during the irrigation experiment (or for different seasons) may vary, so the distribution of the misfit and ultimately and in the soil. Current injection in the soil produces a voltage distribution that, albeit corresponding to a heterogeneous 324 resistivity distribution and thus different from the predictions of a simpler model such as Eq. (3), collapses effectively to one 325 point, i.e. the point where current was effectively injected in the ground. On the contrary, when current is injected in the stem, 326 the region of possible source locations in the ground is much wider, and depicts a volume that is likely to correspond to the 327 contact points between roots and soil, i.e. the volume where roots have an active role in the soil especially in terms of RWU. 328

Inversion of virtual current sources to estimate roots extents 315
While this latter interpretation remains somewhat speculative, at least in the present experimental context, nevertheless the 329 different results between soil and stem injection can only find an explanation in the role of roots and their spatial structure. 330 The most interesting feature shown by Figure 6 is that the likely source volumes do not change with time during irrigation 331 distributions. We assimilated the root distribution, derived the geophysical data, into the hydrological model. Attempts in this 403 direction are very promising to describe the root functioning in the framework of continuum physics, i.e. the one endorsed by 404 SPAC. The integration of modelling and data has proven a key component of this type of hydro-geophysical studies, allowing 405 us to draw quantitative results of practical interest. For example, in our study it is apparent that although infiltration occurred 406 during the peak of evapotranspiration (between 1pm and 3pm), very small RWU was observed before the second day. 407 Nevertheless, after a certain time, RWU is observed while infiltration is still ongoing. Smaller RWU observed for the small 408 plant A compared to plant B is also observed. 409

Recommendation for future experiments 410
In this field case study, we had very little available quantitative information that could allow the validation of the geophysical 411 data in terms of the volume of soil affected by RWU. The final objective of this study was then to discuss issues for obtaining 412 suitable validation data using existing methods and propose some recommendation for future experiments: 413 Validation through destructive methods has numerous potential pitfalls. As roots are underground, and thus 414 invisible in their space-time evolution, and are also fragile, especially in their fine structure, the monitoring of 415 their structure and activity using destructive methods such as trenches or air spade presents various limitations. 416 In such approaches, even in the best case where fine roots may be sufficiently preserved and described, it is 417 impossible to know where the active roots actually are. Active roots may be located only in one part of the whole 418 root system. Destructive methods may help to validate the confidence area determined by F1 but are not 419 appropriated methods to validate the F2 inversion. 420 spacing as well as on other factors that are difficult to assess a priori, such as resistivity contrasts and signal to noise ratio. 439 Thus similar experiments can also be used in the laboratory, where more direct evidence of root distribution can be used to 440 further validate the method. 441