Spatially resolved root water uptake determination using a precise soil water sensor.

To answer long-standing questions about how plants use and regulate water, an affordable, non-invasive way to determine local root water uptake is required. Here, we present a sensor, the Soil Water Profiler (SWaP), which can determine local soil water content (θ) with a precision of 6.10-5 cm3cm-3, an accuracy of 0.002 cm3cm-3, a temporal resolution of 24 minutes and a one-dimensional spatial resolution of 1 cm. The sensor comprises two copper sheets, integrated into a sleeve and connected to a coil, thereby forming a resonant circuit. A vector network analyzer, inductively coupled to the resonant circuit, measures the resonance frequency, against which θ was calibrated. The sensors were integrated into a positioning system, which measures θ along the depth of cylindrical tubes. When combined with modulating light (4-hour period) and resultant modulating plant transpiration, the SWaP enables quantification of the component of root water uptake distribution that varies proportionally with total plant water uptake, and distinguishes it from soil water redistribution via soil pores and roots. Additionally, as a young, growing maize (Zea mays) plant progressively tapped its soil environment dry, we observed clear changes in plant-driven root water uptake and soil water redistribution profiles. Our SWaP setup can measure the root water uptake and redistribution of sandy soil water content with unprecedented precision. The SWaP is therefore a promising device offering new insights into soil-plant hydrology, with applications for functional root phenotyping in non-saline, temperature controlled conditions, at low cost.

Plant water use depends on multiple shoot and root traits and their interaction with environmental conditions. Aboveground, the most important environmental factors influencing plant water use are light, vapor-pressure deficit, and temperature (Vadez et al., 2014). Belowground, the spatial distribution of soil water content (u), soil hydraulic conductivity (K[u]), and soil osmotic potential are the most influential environmental factors for plant water uptake (Chapman et al., 2012;York et al., 2016). Plant factors determining water use include leaf area, root system length, root and shoot architecture, and the associated root, shoot and stomatal conductance (Caldeira et al., 2014;McAusland et al., 2016). Under well-watered conditions, most of the root system is redundant for water uptake. However, in drying soil, root traits such as length, distribution, diameter, age, level of suberization, expression levels of active aquaporins, xylem number and diameter, number and presence of root hairs become increasingly important for maintaining transpiration rates (Chaumont and Tyerman, 2014;Lobet et al., 2014;Lynch et al., 2014;Carminati et al., 2017;Gleason et al., 2019) as stomata will close when water supply is limited (Rodriguez-Dominguez and Brodribb, 2020). In the field, competition for limited resources makes root performance even more critical for capturing sufficient water. Studying the abovementioned traits is useful because they are under genetic control, and considerable breeding effort goes into improved survival and yield of crops under drought (Lynch et al., 2014). Complementary research focuses on water conservation management and irrigation strategies, like partial root zone drying (Sepaskhah and Ahmadi, 2012), to achieve target yields with minimal water use (Bourzac, 2013). The need for drought-tolerant cultivars and efficient water use in agriculture is outlined in several articles (Blum, 2009;Tardieu, 2012;Wasson et al., 2012). Despite many years of research, there is still considerable uncertainty as to what the important plant traits and combinations thereof are for plant water use. In part, research is hampered by lack of affordable technology for measuring spatial and temporal distribution of root water uptake (RWU), especially in relation to the z U p z; t ð Þdz 5 U tot t ð Þ, cm 3 h 21 , which includes soil water used for transpiration and growth). A second component additive to U p adjusts RWU distribution to total soil water potentials, which is the sum of soil matric and gravitational potentials. We refer to it as "soil-driven root water uptake redistribution," also normalized by soil layer volume, U s , cm 3 $ cm 23 h 21 , typically called "compensatory" (Couvreur et al., 2012) or "compensation" RWU (Jarvis, 1989). It relies on soil water potential heterogeneity and spatially integrates to zero as per definition. Note that here U s , U p , and U tot are defined negative when removing water from the soil. Only in limited cases (locally 2U s , U p ) is hydraulic lift observed (Caldwell and Richards, 1989). The impact of these simultaneous processes on the observed u-profile can be modeled employing an extended one-dimensional (1D) Richards equation following Couvreur et al. (2014aCouvreur et al. ( , 2014b: ∂uðz; tÞ ∂t 5 U p ðz; tÞ þ U s ðz; tÞ þ ∂ ∂z Kðuðz; tÞÞ 3 ∂hðz; tÞ where K (cm h 21 ) is the soil unsaturated hydraulic conductivity, h (cm) is the soil matric potential, and E s (cm 3 $ cm 23 h 21 ) is the soil surface water evaporation rate per unit soil layer volume (pr 2 $ Dz, with r as the inner pot radius in centimeters). Many of the parameters and variables in Equation 1A are difficult to determine. Specifically, soil hydraulic conductivity is difficult to measure and is often derived theoretically with considerable uncertainty (Baroni et al., 2010). Root architecture and hydraulic conductivity data, which could be used to estimate U p and U s terms, are also hardly accessible experimentally, although some are available in the literature (Doussan et al., 2006;Ahmed et al., 2018). Yet, root conductivity may change with environmental conditions and can have a circadian rhythm (Sakurai-Ishikawa et al., 2011;Caldeira et al., 2014;Chaumont and Tyerman, 2014).
From a simpler perspective, the divergence of soil water capillary flow rates and U s are both driven by-and tend to reduce-soil water potential heterogeneity, while being instantaneously independent of U tot . Therefore, we gather them under the term "soil water redistribution," S r (s 21 , equal to U s ðzÞ þ ∂ where V equals total soil volume, the normalized variableÛ^p z ð Þ 5 Up z ð Þ U tot $V (positive, and Furthermore, S r values are null when the total soil water potential is spatially uniform, and by definition R z S r ðz; tÞdz 5 0. The relevant processes are schematically presented in Supplemental Figure S1. In this study, we present a sensor of soil water content, the soil water profiler (SWaP), and propose a method to estimate the vertical distribution of the plantdriven RWU distribution as demonstrated for maize (Zea mays). Assuming that on an hourly timescale, U p ðzÞdoes not vary, e.g. no substantial growth and S r evolves linearly with small variations of h (soil matric potential only), then relatively fast light-induced modulations of U tot generate variations of the profile of du(z)/dt directly proportional toÛ p ðzÞ. Measuring such small variations of du(z)/dt requires unprecedented precision, which can only be reached with the new SWaP device presented in this article. The idea of using day-night fluctuations of transpiration to separate RWU from soil water flow using synthetic data has been previously proposed (Guderle and Hildebrandt, 2015). However, our approach is to perform it on considerably shorter timescales with experimental laboratory data.

Sensor Characteristics
We constructed a sleeve-like sensor with two opposing copper sheets (internal diameter of 9 cm, sheet area of 537 cm 2 ) that function as a capacitor (Fig. 1A) with a pot (9-cm diameter, 50-cm length) standing free within the sensor. When the sleeve with copper plates is connected to a coil this yields a resonant circuit whose resonance frequency (f) depends on the capacitance (C) as follows: f ; 1/=C. This circuit is coupled inductively, via a second, identical coil with 2-mm spacing, to a vector network analyzer (VNA) working in input reflection mode (S 11 ) to determine the resonance frequency (an example is shown in Fig. 1B). The resonance frequency depends on the average permittivity between the copper plates (see "Materials and Methods") and can therefore be used to determine u(z) using a calibration curve (Fig. 1D). The system has been multiplexed to four sensors using a PIN diode switch, with all four sensors being shifted longitudinally by a stepper motor along a linear axis. This construction forms our SWaP.
The four independent sensors have an average resonance frequency of 250.4 MHz (SD 5 1.4 MHz) when unloaded, which drops to 156.9 6 1.3 MHz when our soil is water-saturated (u 5 0.32). The deviations of the resonance frequencies under climate chamber conditions equaled 3 kHz. The relative electric field (E-field) vertical distributions of each of the sensors are displayed in Figure 1C, expressed in frequency shifts relative to the unloaded resonance frequency (f 0 ; Sydoruk et al., 2016). Each data point represents four individual resonance frequency measurements. Additionally, the simulated E-field distribution of a sensor as calculated on the platform Comsol (https://www.comsol.com/) is added to Figure 1C (see "Materials and Methods"). The simulated and measured E-field distributions agree to a very large extent that gives confidence that the simulation model can also be used to predict other features of our setup. Whereas the total E-field depth (in z-direction) covers 12 cm, 95% of the summed field strength, corresponding to its sensitivity, occurs with the inner 8 cm. The simulated horizontal field distribution is presented in Supplemental Figure S2.
Because the electric permittivity is also temperaturedependent and the climate-chamber lamps cause small variations in temperature, the influence of temperature on the resonance frequency was determined. Across the temperature range of 16°C to 24°C, we recorded a 12 6 4 kHz°C 21 temperature-drift coefficient. Furthermore, we verified the dependency of the resonance frequency on different nutrition solution strengths, tested up to 7 mS cm 21 , but observed no influence on the resonance frequency in the tested range.
The sensitivity of each of the sensors to known soil water content, determined gravimetrically, was determined in stationary mode that yielded the calibration curves, plotted in Figure 1D. The calibration curves could be fitted with a second-order polynomial with an average 95% confidence interval (CI) of 0.003 cm 3 $cm 23 and an average initial slope of 2.67 MHz cm 3 $ cm 23 . We excluded from the calibration those samples that were very wet (u between 0.16 and 0.32), as in our sandy soils such wet samples were very sensitive to handling. These wet samples compacted easily and built up nonlinear soil water content gradients quickly. At full saturation, measured with a closed base, no soil water content gradients occur, so this point could also be measured reliably.
In addition to the calibration at known soil water contents, the sensor's response to soil-filled tubes was simulated using a physical model of the sensor using the platform Comsol. The results of these simulations are also presented in Figure 1D (solid line), showing good agreement with the measured data with a root mean square error of 0.68 MHz.

Scanning Mode Validation
Given the good results for homogeneous samples, we tested the SWaP in scanning mode on nonhomogeneous samples. Such scans were performed automatically to measure u-profiles for four 45-cm soil columns with and without maize plants every 24 min. Two steps were required before profiles of u or du/dt could be determined: deconvolution over space, and conversion of resonance frequency data to u. Deconvolution is a procedure that corrects for the fact that our sensor is sensitive over a length (z9) of 12 cm instead of the desired resolution of 1 cm. Each 1-cm layer contributes to the capacitance weighted with the relative electrical field strength at that position. This contribution can be Figure 1. Schematic drawing of the SWaP, the raw data it generates, and relevant curves to calculate soil water content (u) profiles. A, Drawing of the SWaP without casing, showing the copper sheets (brown areas, one marked with Cu) that function as capacitor. B, The two radio frequency (R.F.) coils inductively coupling the sensor to a VNA that generates input reflection (S 11 ) data. a.u., Arbitrary units. C, The relative E-field distribution, expressed in frequency shifts relative to the unloaded resonance frequency (f 0 ), E(z9) of each sensor (represented by different symbols) and the simulated E-field using the platform Comsol (black line). D, Calibration curves of the soil water content (u) against the resonance frequencies for all sensors (represented by different symbols). Black line represents the predicted sensor response (see "Materials and Methods").
retrieved by measuring at several z-positions and undoing the sensors' convolution or blending using a deconvolution procedure. The deconvolution and calibration procedures are described in more detail in "Materials and Methods." First, we demonstrate how the model-constrained deconvolution method performs under realistic circumstances, including the presence of a plant. In Figure 2A, a typical resonance frequency profile (solid circles), the fitted model of the data before deconvolution (f(z), solid red line) r 2 . 0.99, and the deconvoluted model (g(z), dashed blue line) are presented for a soil column close to water holding capacity. As expected, the deconvoluted model deviates significantly from the raw data at the edges, because the permittivity outside the soil columns has very different values and is blended with those inside the soil column owing to the sensor's sensitivity profile. Because of the very low noise of our sensor, an equidistant three-point time derivative of the scanning data can be made for each z-position. Figure 2B presents the change of the resonance frequency profile with time for 45 z-positions for two different cases: one with a transpiring maize plant during daytime (solid circles), and one with a maize plant at night (gray squares). Here too, the modeled, convoluted polynomials, df(z)/dt (solid red line) and r 2 . 0.99 (magenta line), follow the data quite well. The deconvoluted model, dg(z)/dt, is presented by dashed blue or cyan lines. Both g(z) and dg(z)/dt can be converted to u(z) and du(z)/dt, respectively, using the calibration curve.
Second, we compared u(z) obtained using the SWaP with two types of measurements.
Type I: After a SWaP scan, small quantities of soil were excavated (10 to 20 cm 3 ) at known positions, for which the local water content was determined gravimetrically. These values were compared to u(z) measurements with the SWaP in scan mode. The results and fit (y 5 0.0013 1 0.997x) are plotted in Figure 2C with the 95% CI as dashed lines. At the bottom of the soil Figure 2. Typical frequency profiles along soil-filled columns, the time derivatives thereof, and some validation data. A, Profile of resonance frequency, f(z) (black dots); the fit results (red lines); and the deconvoluted frequency profile g(z) (dashed blue line). B, Profile of time derivative of the frequency profile, df(z)/dt for soil column with maize plant during daytime, df(z)/dt (black dots), fit results (red line), and dg(z)/dt, the deconvoluted time derivative (dashed blue line); and during night-time, df(z)/dt (black squares), fit results (magenta line), and dg(z)/dt (dashed cyan line). C, Gravimetrically determined soil water content (u versus u) obtained with SWaP and the fit (y 5 0.0013 1 0.997x) with the 95% CI (dashed lines). D, Change of soil column water amount versus sequential additions of 20 mL of water including fit (black line) and the CI (dashed lines). column, where u is largest, we observe a reduced accuracy of ;0.005 cm 3 $ cm 23 -probably due to deviations of the E-field distribution close to sharp edges. Moreover, at the edges, both at the top and the bottom, noise is enhanced because these slices were measured less frequently.
Type II: We added known amounts of water to the soil columns and monitored the change of the integrated amount of water as determined by the SWaP. The smallest amount of repeatedly added water we could detect was 20 mL for our 2.4-L soil columns. These results are presented in Figure 2D. We found a slope of 1.1 (r 2 5 0.993; CI 5 8 mL).

Quantification of Plant Water Uptake and Redistribution in Soil Columns
Soil water depletion measurements in cylindrical pots with growing maize seedlings started after the shoot emerged from the soil, 4 d after sowing (DAS). At the three-leaf stage (11 DAS), oscillations of the soil water depletion rate caused by the light-induced, modulating transpiration rate of the maize plant were sufficiently large to distinguish them from temperaturerelated oscillations on a local (z) level, but insufficient to perform a reliable analysis. After a few more days, an increasing shoot size caused increased soil waterdepletion rates and more pronounced modulations thereof, which is exemplified in Figure 3. Figure 3A depicts two soil water-content curves measured over a 3-d period at a relatively low depth (z 5 8 cm) relative to the surface. The combined noise and temperature drift of these curves was as low as 6 310 25 cm 3 $ cm 23 . The blue data points were acquired starting at nine DAS and the black data points at 15 DAS. The time derivatives of these traces, the soil water-depletion rates, are plotted in Figure 3B. Additionally, the sum of the soil water depletion rates of the whole column Þ) starting at 15 DAS is plotted (red line), scaled down by a factor of 10 for visual comparison. Soil water depletion was clearly faster during daytime (orange blocks at the bottom of Fig. 3B). Within each day, three oscillations of U tot synchronous with high-and low-light levels in the chamber are visible (range annotated by arrow labeled "M"; low daytime U tot annotated by arrow labeled "NM"). We also note that during the night, while the column is still losing water (red line), the zone at z 5 8 cm shows some positive values for du/dt at night, indicative of a form of redistributive water flow.
Disentangling the U p component of RWU from soil water redistribution (S r ; see Eq. 1B) required the estimation of U tot and E s , as well as the simplifying assumption that within a 12-h window, S r is well described by a linear regression: S r (z,t) 5 p 1 (z) 1 p 2 (z) $ t. This is the simplest model for S r that is physically sensible, as we know that RWU induces changes of h(z), driving variations of soil water redistribution over time (see further below for supportive data). The fact that U tot , S r , andÛ p vary on different timescales (see further below) allowed the use of clearly distinct functions to fit the du/dt data.
Based on Equation 1B and the simplifying assumption of S r , the local soil water depletion rate at any given position (z) within a 12-h window was thus modeled as Evaporation was determined independently by monitoring soil water depletion in a column without a plant, and subtracted from evapotranspiration, which is estimated as the spatial integral of the soil water depletion rates, to yield U tot . The remaining unknownsÛ p ðzÞ, p 1 ðzÞ, and p 2 ðzÞ were fitted by least-square regression of du/dt, e.g. dashed blue lines and black data points in Figure 3, C and D, respectively, for each z-position independently. The modulation amplitude of du/dt relative to M in Figure 3B is sufficient to determinê U p . U p (z,t) was then calculated by multiplyingÛ p ðzÞ and U tot (t). Even though the parameterization was completed independently for each depth, the vertical integrals ofÛ p ðzÞ and of p 1 ðzÞ þ p 2 ðzÞ$t always converged to 1 and 0 with accuracies of 10 25 and 10 27 , respectively. In Figure 3, C and D, soil water depletion rate data at two depths is presented for two different maize plants with different rooting depths, as evidenced by magnetic resonance imaging (MRI) data, with t 5 0 h when the lights are switched on. Figure 3C depicts du/dt data collected from a well-watered, shallow-rooted maize plant in a well-rooted zone (z 5 8 cm, black circles) and a nonrooted zone (z 5 21 cm, gray squares) a few centimeters below the deepest root. High light periods are denoted by yellow blocks at the bottom of Figure 3D. The plant-driven component of RWU normalized by the soil layer volume was isolated based on Equation 2 (red line; z 5 8 cm, dashed magenta; z 5 21 cm). Its summation with S r adequately fits the measured du(t)/dt data at z 5 8 cm, represented by the blue dashed line, r 2 5 0.95. In the nonrooted zone (Fig. 3C, z 5 21 cm) we find no evidence of RWU (see magenta dot-dashed line for U p ), but we do observe soil water depletion owing to vertical soil capillary flow. Here, squares and cyan line present measured and modeled du(z,t)/dt, respectively, which follows our simple model S r (t) 5 p 1 1 p 2 $ t. The same type of data and its model results are presented in Figure 3D for a wellwatered, deeper-rooted plant, but with a higher root length density (RLD) at z 5 8 cm (black circles) than at z 5 21 cm (gray squares, r 2 5 0.95).
Plant-driven water uptake distribution and soil water redistribution were calculated as described above for each layer. The corresponding profiles are plotted in Figure 4, A and B. Additionally, the RLD distribution (RLD[z]) obtained from MRI root images and subsequent analysis with NMRooting (van Dusschoten et al., 2016) is presented using black squares, and inverted for easy visual comparison. U p (t 5 8 h) is represented by the solid red lines for a shallow-rooted maize plant in Figure 4A and a deep-rooted maize plant in Figure 4B. A strong correlation between plant-driven RWU and the RLD distribution was observed for all four maize plants whenever the soil column was close to its waterholding capacity, as it was watered the day before and had a rather uniform soil water matric potential. See, as an example, the lower line in Supplemental Figure S4; the maximum difference between the bottom and top of the soil column is 23 kPa in matric potential. The Pearson correlation coefficient between RLD(z) and U p (z) ranged between 0.89 and 0.95, for four plants at seven different instances, with a minimum modulation in uptake rate amplitude of 0.3 cm 3 h 21 . The dotted magenta line represents the soil water depletion rate (t 5 8 h), and only roughly follows RLD(z), with a Pearson correlation coefficient of 0.6. Note that, at the bottom, the soil water depletion rate (t 5 8 h) turns positive, owing to earlier watering from the top and subsequent, downward movement of this water.
Our analysis also yields soil water redistribution profiles that we assume are linearly dependent on time within each 12-h window, as a first-order approximation. To validate this assumption, we compared the measured soil water depletion rates at night (represented by red and blue dots in Fig. 4C) for deep-and shallow-rooted plants, respectively. Here, plant water uptake is minimal, so that we approximatively measured S r (z), with extrapolated S r (z) based on our model (see red and blue curves in Fig. 4C). The measured and model-based, extrapolated S r (z) agreed reasonably well (r 2 . 0.9 for both plants). This suggests that our linear model for S r is a reasonable assumption. . Soil water depletion curves of soil columns with maize plants. A, Three-day period time series of soil water content, u(z 5 8 cm) with a transpiring maize plant starting at 9 DAS (blue data points) and 15 DAS (black data points). B, Same data but now soil water depletion rate du(z 5 8 cm)/dt. Added is a U tot 1E s curve (evapotranspiration rate), scaled down for visual comparison (red squares). Orange squares at the bottom denote daytime. The relative amplitude of the U tot modulation is indicated by the lengths of the arrows labeled "M" and "NM" (nonmodulated transpiration). C, Time series of soil water depletion rate, du/dt for shallow-rooted maize plant over 12-h period after lights were switched on (15 DAS). Yellow blocks at the bottom indicate high light. Black dots are du(z)/dt; red line is plant-driven RWU, U p (z 5 8 cm); dashed blue line includes soil water redistribution. Gray squares are du(z)/dt, magenta dash dots are U p (z 5 21 cm), dashed cyan line includes soil water redistribution. D, Time series of a deeper-rooted maize plant. See C for explanation.
For the above analysis, we assume thatÛ p ðzÞ is timeinvariant during the 12-h experimental time window. This can be verified by reducing the time window for the analysis to 4 h and performing the analysis for three subsequent time periods on 1 d. We performed this check for 12 different whole-day measurement series (three plants on four different days each) and found low SDs among the three 4-h time-periodsÛ p ðzÞ values for each plant during the 12-h periods (average SD , 0.0075). This confirmed that in these experimentsÛ p ðzÞ was sufficiently stable during the day (Supplemental Fig. S3).

Proof of Concept ofÛ p ðzÞ Retrieval Using In Silico Observations
To verify if known plant-driven RWU rates could be accurately estimated from the soil water depletion rate under modulating plant transpiration rate, we used numerical simulation of soil-plant hydrodynamics to generate in silico observations of soil water depletion rate profiles, and then applied Equation 2 to retrievê U p ðzÞ. The results of these in silico experiments are presented in Supplemental Figure S5 with a more extensive description. The main findings are thatÛ p ðzÞ is retrieved most reliably when the modulation period is short, at maximum six hours, otherwiseÛ p ðzÞ is smeared out over 5 cm or more. Also,Û p ðzÞ is retrieved more reliably when soil conductivity is lower in the sense that less smearing occurs.
From the comparison between our imposed and re-trievedÛ p profiles, we conclude that the proposed approach of soil water depletion rate profile monitoring under modulating transpiration rate is a reliable method to separate profiles of plant-driven RWU from soil water redistribution, given the sufficient sensitivity of the SWaP device.

RWU in Drying Soils
In conditions close to soil water-holding capacity, the investigated maize plants showed a higher RWU rate near the soil surface (Fig. 4B), closely related to the higher RLD there. In consequence, water depletion was more pronounced in the upper half of the profile, generating substantial vertical gradients in u and soil water potential over timescales of several days. Under such conditions, we observed increasing rates of soil water content change lower in the profile. Disentangling U p (z) from S r (z) with Equation 2 allowed us to interpret that this trend was caused by a net downward trend of U p (z) on four consecutive days, as depicted in Figure 5A. Here data are presented always 4 h after the light was switched on. On the fourth day (26 DAS) after watering, the maize plant reduced its transpiration rate considerably after 4:00 PM, so these data were excluded from the analysis as presented here. The soil water matric potential data for these measurement days is given in Supplemental Figure S4. The difference in soil water potential between the top and the bottom consecutively reached 3, 15, 80, and 430 kPa during these 4 d. Figure 5B depicts a comparison between two instances, one with high, the other with lower light, for U p (z), red and blue lines respectively, and the concurrent soil water depletion rates, the red and blue circles, on 25 DAS, which is 3 d after watering. The differences between U p (z) and the soil water depletion rates are caused by soil water redistribution (S r ), which is nearly identical for both instances (reduction of ,5.10 25 cm 3 $ cm 3 h 21 during 2 h). The data shows clearly that at high light, the soil water depletion rate profile better approximates U p (z) than at lower light, where the depletion rate has a completely different profile and is nearly flat.
In Figure 5C, the ratio of U p (z) to RLD(z) is used to color an MRI image of a root system, which approximates the RWU per unit length of root when redistributive water uptake (U s ) is minimal because of the small soil matric potential difference (3 kPa) at this time. Figure 5D presents the same ratio under a vertical difference of 430 kPa, with u ranging from 0.07 to 0.025 cm 3 $ cm 23 from bottom to top of the column. To determine the correct soil water content numbers, MRI data were used to correct for the root mass, which is also detected by the SWaP and cannot be distinguished from soil water. Especially when the soil is dry this correction is important because the amount of water in the roots (;1% volume at the top) is comparable to the soil water content, being in the range of 2.5%. Ignoring this contribution leads to a considerable underestimation of h(z). This error is typical for sensors that depend on the electrical permittivity to determine soil water content, like TDR. The changes of the root lengths over the 4-d period are clearly not mimicked by the ratio of U p (z) to RLD(z), which suggests that root hydraulic properties may have been altered between the wet and dry conditions.

DISCUSSION
Our results show that we successfully developed an accurate (0.002 cm 3 $ cm 23 ) and especially highly precise (6.10 25 cm 3 $ cm 23 ) soil water content sensor adapted to soil columns in climate chambers, more than an order-of-magnitude more precise than commonly available tools like TDR and frequency domain reflectometry (Cooper, 2016). Furthermore, the sensor's 1D spatial resolution theoretically reaches 1 cm, and its continuous nature also allows spatial integration of u(z) to track a soil column's total water content dynamically for multiple columns simultaneously. We determined local soil water content depletion rates and their variations as induced by transpiring maize plants. At an hourly timescale, modulating transpiration with varying light intensities allowed decoupling of the plantdriven RWU from the soil water redistribution signals quantitatively.

The SWaP Sensor Specificity
Because resonance frequencies can be determined very accurately, we build the soil water-content sensor as a resonant circuit. Also, we placed the copper plates that form a capacitor outside of our medium such that a more homogeneous E-field is generated, especially in the horizontal plane. Compared to TDR or frequency domain reflectometry sensors (Bore et al., 2016), this gave a better weighing of the different regions within or around the sensor (see Supplemental Fig. S2). As we demonstrated in the results, our design with inductive coupling and shielding results in a sensor with a very high, usable dynamic range factor of 20,000.
The gain in accuracy is also very good although not as high, because water distribution in larger volumes is not a priori known relative to the E-field distribution. Therefore, calibration was not possible between 16% and 32% because of rapid downward water mobility, causing a gradient in water distribution, and thereby soil compaction, which may be a limiting factor for accuracy. During scanning, at the edges of the soil column, the E-field distribution is distorted and errors in the range of 0.5% to 1.0% may be expected, and in our validation we never found deviations . 1% (see Fig. 2). This means that scanning does not introduce additional errors except for close to the soil column edges. We obtained confirmation for the quality of the scanning data when we added water volumes, down to 20 mL, at the top of the soil column and were able to detect the change with sufficient accuracy (see Fig. 2D). This experiment was performed under laboratory conditions, otherwise temperature fluctuations would have masked the small frequency changes caused by adding such small amounts of water to a large column. Temperature sensitivity of the sensor can pose a problem when temperature is not precisely controlled. Despite the above limitations, the overall performance of the SWaP offers a considerable improvement in soil water content profiling, especially in regard to the simplicity and cost of the equipment. This ability to determine soil water content profiles by itself is very useful and important, as it provides a rapid method to determine the soil water content profile in relation to plant performance, like growth and transpiration related to soil water distribution.
The variations in du(z)/dt were detectable at a very early stage when the leaf area was ;20 to 30 cm 2 . At 8 cm below the surface we initially only observed the indirect effect of surface evaporation on soil water depletion, which is slightly higher with light than without (Fig. 3, A  and B). In an earlier implementation of the SWaP where the resonance frequency was simply approximated by the frequency showing minimal reflection, noise levels limited our precision to 0.1% to 0.2% cm 3 $ cm 23 , comparable to high-end TDRs (Gong et al., 2003). These noise levels were still ;10 times too high to detect the light-induced variations in du(z)/dt (e.g. compare with Fig. 3B). Even for plants with a leaf area of 400 cm 2 , which deplete soil water in a few days, noise levels of 0.1% cm 3 $ cm 23 are not low enough to observe varying uptake rates, with typical modulation amplitudes of du/dt of ,0.002 cm 3 $ cm 23 h 21 , when light levels change between 400 and 700 mE $ m 2 s 21 . It requires very high precision u-measurements to be able to observe the effects that we described here, which explains why it is not described elsewhere. Once the plants were sufficiently large, the modulation patterns in the soil became usable for further analysis.
The temporo-spatial water content profiles that our sensor collects may also be compared to those obtained with NT. NT offers higher dimensionality (mostly 2D) and spatial resolution, but is a very expensive technique not generally available to plant biologists or hydrologists. The very precise soil water sensors that we showed here are rather easy to build, and come at low cost; our current prototype with four sensors cost ;1,500 € to build, is portable (can be used in climate chambers) and is completely harmless to the plant. A combination with a fully programmable water-cooled LED panel should be profitable as it minimizes thermal influences and should help with resolving lightdependent and light-independent RWU rates. This then constitutes a new, versatile tool to probe RWU profiles in relation to water management strategies and genotype-specific responses.

From Water Depletion Rate to Uptake and Redistribution Profiles
We presented a simple model to quantify the fraction of local RWU that varies proportionally to the plant transpiration rate, or plant-driven RWU distribution by layer-wise fitting soil water depletion rate data to Equation 2 using total water uptake U tot as independent parameter. Measured U p (z) should closely approximate RWU when the profile of soil water potentials is uniform (Couvreur et al., 2012). When it is not, the only difference between U p (z) and du(z)/dt is the soil water redistribution S r (z; through soil and roots). This profile can be estimated with a methodology also described by Guderle and Hildebrandt (2015), provided that S r variations remain nonmodulating (owing to soil water capacitance) during the light modulations.
By observing layers just below the lowest roots, information that we can glean from MRI data, we could verify experimentally that S r does not fluctuate there and also changes approximately linearly with time. An example of the absence of modulations in the soil water depletion rate is given in Figure 3C, but can be seen to persist farther away from the roots as well (see Fig. 4A). Additionally, our forward simulation studies (see Supplemental Fig. S5) confirm that the effect of the plant-driven RWU modulations on the soil water depletion rate dampens out in the soil within a few centimeters when these modulations occur within 6 h, even when the simulated U p (z) has a sharp front. These simulations therefore suggest this does not work well on a day-night timescale. The combination of these findings indicates that under the conditions we are working with, S r (z,t) should not show considerable modulations.
In drying soil with a considerable vertical water potential gradient (25 DAS), modulating transpiration rate using moderate and higher light intensity levels (400 and 700 mmol m 2 s 21 , respectively) was key to show the independence between soil water redistribution S r (z) and U p (z) profiles, as demonstrated theoretically by Couvreur et al. (2012). In contrast, Figure 5B shows that their shapes differ significantly (see blue and red circles du(z)/dt under moderate and high light, respectively). Hence, in drying conditions RWU(z) is a mix of independent shoot-and soil-driven water flow dynamics, U p and U s , respectively. It also demonstrates the importance of light intensity when studying plant drought stress, as water-depletion zones will develop quite differently under high as compared to low transpiration rates.

The Plant-Driven Water Uptake Distribution as a Proxy for RLD
Our results in soil close to its water-holding capacity support experimentally the common assumption that overall U p and RLD profiles scale proportionally (r 2 5 0.95; Feddes et al., 2001;Lobet et al., 2014;Albasha et al., 2015), here for young maize plants. The original underlying hypotheses are that root axial conductivity is high while root radial conductivity is relatively uniform across roots (Steudle and Peterson, 1998), even though some studies suggest this need not hold always (Ahmed et al., 2018). Alternatively, a limiting axial root conductivity combined with a higher radial conductivity deeper in the soil could yield the same results. The correlation between RLD and du(z)/dt is also significant (r 2 . 0.6), but clearly lower than between RLD(z) and U p (z), because the causal relation between du(z)/dt and RLD(z) is obscured by soil water redistribution.
Through the estimation of the "proxy" U p (z), the transpiration modulation method, combined with the SWaP sensor, can therefore also offer a simple way to estimate the relative RLD profile in soil columns close to their water-holding capacity as a first-order approximation at least for maize. In the case U p (z) equals zero, this is a good indicator of the absence of roots or at the least active roots when plant water uptake is large enough to be quantified.
However, plant-driven water-uptake profile and relative RLD do not always match. The data in Figure 5A indicates that the U p (z) peak shifts to deeper soil layers over time, while the soil column is drying out. This is not caused by inhomogeneous root growth, as otherwise Figure 5D would still show a single color, nor by passive adjustments of water uptake in response to soil water potential heterogeneity, as U s is not included in U p . Although for a given root system architecture U p (z) only varies with the system hydraulic properties, this phenomenon most likely results from a reduction of the hydraulic conductivity in the drier, upper half of the column between the bulk soil and root surface (Schroeder et al., 2008), at soil-root interfaces (Carminati and Vetterlein, 2013), and/or across root tissues (Hachez et al., 2012). Such reduced hydraulic conductivities would prevent both the uptake and the release of water by roots in the driest parts of the soil profile, as confirmed by isotopic experiments (Meunier et al., 2017b;Couvreur et al., 2020). Furthermore, the soil-plant hydraulic conductance would as well be reduced, which was also recently confirmed (Hayat et al., 2019), using a pressure chamber. All these studies are in line with our observation of decorrelation between U p (z) and RLD(z) resulting from changing hydraulic conductivities in the soil-plant system.
Perspectives to Disentangle Soil Water Redistributive Terms, through Soil and Roots used to determine RWU(z), but rely heavily on modeling (Kühnhammer et al., 2020). NT clearly provides more detailed information along a limited set of roots, but heavy water must be added to the system to obtain this information, thereby changing the uptake pattern along all roots, especially in heterogeneously wetted soil. Neither of the last two methods can be applied to a large number of plants in a normal climate chamber setting, whereas the SWaP can be. The SWaP and the proposed light modulation methodology therefore offer a considerable improvement in the toolbox of plant physiologists interested in plant water usage, and should provide new insights in RWU in realistic soil environments.

SWaP, Further Details on Hardware
The sensor part of the SWaP is a circular polyvinyl chloride (PVC) sleeve where two sheets of copper (735 cm 2 ) are glued on the inside, 9-cm apart on opposite sides (Fig. 1A). These are connected via a 2-cm-wide coil, thus forming a resonant circuit. The resonance frequency of this circuit can be determined via the so-called input reflection mode (S 11 ) of a VNA (DG8SAQ VNWA3; SDR-Kits). The VNA performs a frequency sweep (here between 150 and 220 MHz) and at the same time measures the reflected radio frequency-signals of the sensor. The minimum reflection occurs at resonance, which was extracted by a straightforward fit using a Lorentzian with a "skewed" baseline as a model, and which yields our "raw" data in the form of resonance frequencies (Fig. 1B). We linked the VNA to the sensor by means of a second single-turn coil, 2-mm apart from the coil that is part of the sensor itself, by means of inductive coupling. Inductive coupling works like a balun to the resonant circuit and, because the plates are also symmetrical, creates a symmetrical electrical field distribution throughout the object of interest. Also, cable capacitance is reduced on the sensor side, increasing dynamic range and reducing influences of parasitic capacitances, e.g. to electrical ground. The sensor was screwed into an aluminum socket (dimensions: outside diameter 5 17 cm; height 5 12 cm; internal diameter 5 9 cm), further improving stability and noise.
The system has been multiplexed to four sensors, using a PIN diode switch (catalog no. SP4T, CDS0624; Daico Industries), with all four sensors being shifted longitudinally by a stepper motor on a linear axis (controlled via an Arduino Nano combined with an A4988 driver, programmed via the software AVR Studio 4 using the language C; https://atmega32-avr.com/). A Python script controlled the VNA and the stepper motor and performed a fit to the frequency spectra (Lorentzian and first-order polynomial) to extract the resonance frequencies of each of the four sensors at 45 vertical positions along the tubes.

SWaP, Further Details on Data Analysis
The resonance frequency, f(z), of our sensor depends on the permittivity distribution relative to the E-field distribution, E(z9), of the sensor. We do not measure a local resonance frequency from which we would calculate a local u, but instead we can determine the contribution, g(z), of a slice of soil to the resonance frequency by repeatedly measuring the resonance frequencies at well-defined positions along the tube, e.g. in 1-cm steps in the z-direction, and perform a deconvolution afterward. For the deconvolution step, the relative local E-field strength has to be known, which we obtained by moving a 1-cmthick, 9-cm-wide PVC disk within the sensor at 12 different z9 positions (25, 24,. 0.5, 6 cm, where 0 5 middle of sensor) while measuring the resulting resonance frequency (see also further below). The local contribution to the resonance frequency at a given position can now be obtained via a deconvolution step by solving f(z) 5 E(z9)*g(z), where the asterisk denotes convolution. Ideally, a deterministic deconvolution is applied to determine g(z), but noise and small deviations of E(z9) compared to the measured one, at the edges of the soil column, would cause distortions after deconvolution even on locations where deviations of E(z9) do not occur. We therefore performed a modelconstrained deconvolution, by assuming that u and therefore g(z) is relatively smooth and can be approximated by a high (seventh) order polynomial, f ðzÞ 5 Eðz 9 Þ * ½gðzÞ 5 ∑ 7 k 5 0 a k z k . When we use this to model f(z), a k values can be adjusted to minimize the squared differences with the measured resonance frequency profile. This approach requires that the resonance frequencies beyond the soil edges are known, which can easily be measured separately. Furthermore, the permittivity jumps at the soil edges should be minimized to limit perturbations of E(z9) at these edges. This was achieved by adding slightly wetted soil to the otherwise hollow stand for each of the four tubes and placing five water-filled 25-mL vials next to the plants on top of the soil. The described procedure then yields g(z), the deconvoluted resonance frequency profile. The same procedure can also be followed to determine dg(z)/dt, with the advantage that the resonance frequency changes beyond the soil edges can be set to zero.
To convert g(z) to u(z), we need to calibrate our sensors. Therefore we filled fourteen 12-cm high pots (0.6 L) with oven-dried soil (loamy sand mix with twothirds coarse sand; see van Dusschoten et al., 2016) to which known amounts of water were added to achieve the desired u such that the average u in the pot was between residual and saturated water content. We carefully mixed the soil shortly before measuring to achieve a homogeneous distribution of water. Each of the 14 pots was measured with the soil profiler in static mode four times. Above 16% of soil water content, gravity causes water to flow downward, which causes nonuniform water distributions. Also, upon handling, the risk of soil itself flowing downward exists. Both factors prevent the use of very wet soil being used for calibration, as resonance frequency shifts over time, and after the containers are lifted out, or lowered into, the sensors. At full saturation, soil water flows are absent, and compression can be reverted by carefully turning the closed container upside down. The values u(z,t) and du(z,t)/dt can now be calculated using the calibration curve via a straightforward root-finding procedure. Summation of u (cm 3 $ cm 23 ) and multiplication with volume yields total amount of water of the soil column, which includes root water when a plant is present. MRI measurements of root systems can be used to correct for this error (see below).

Physical Modeling of Sensor
We simulated the complete structure of the SWaP using the platform Comsol (COMSOL Multiphysics). The simulation was used to calculate the E-field distribution of the sensor and its response to loading it with a PVC tube filled with wetted soil. Wetted soil was approximated with artificial material having a dielectric permittivity, « soil 5 3, 5, 10, 15, and which was virtually placed in between the SWaP's plates. The results were then fitted to the Landau-Lifshitz/ Looyenga equation (Nelson, 2005) relating u to soil permittivity, after minor rewriting: where 4:36 , « SiO2 , 4:58 and, « H2O 5 81:7 (at 150 MHz and 20°C), are the dielectric constant of quartz and water respectively, r soil is the density of a soil (here r soil 5 1:71 g$cm 2 3 ), and r SiO2 5 2:65 g$cm 2 3 is the (particle) density of SiO 2 .
The vertical E-field distribution for the SWaP depends on the permittivity gradient within the sample. Whereas normally u is smooth, this is not so at the edges where we expect distortions of the E-field. However, the E-field distribution needs to be sufficiently stable to perform deconvolution of the frequency data. Using Comsol, we simulated the effect of considerable jumps in permittivity. In our simulated physical model we inserted a dielectric cylinder, having dielectric constant « insert , with a diameter equal to the outer pot diameter at the bottom edge of the pot and simulated this structure when it is placed at different z-positions from the center of the SWaP. The simulated resonance frequency distributions were compared with ones based on the assumption that the E-field is unmodified by sharp changes, and the residuals were calculated as a function of « insert . For 2 , « insert , 4, the E-field distribution had the smallest deviations from the assumed E-field distribution. Therefore we increased the E-field distribution stability at the edges of the SWaP by filling the hollow foot on which our PVC pots stand with wetted loamy soil and placing five 2.5-cm-wide vials filled with water on top of the column.

Simulations of Soil Water Flows Based on the Extended Richards Equation
To solve the extended Richards equation for our sandy soil, it is necessary to determine the soil water retention curve and obtain the van Genuchten parameters of this soil. Furthermore, the hydraulic conductivity, K(u) or K(h), needs to be calculated for our soil using Mualem's theorem (Mualem, 1976), i.e. hydraulic conductivities K(u) are calculated by numerical approximation of the Mualem Integral because we use a van Genuchten curve with variable parameter m (van Genuchten, 1980) implemented in Python (Bittelli et al., 2015). Here we used the same shape of K(u) but with various K s values (the soil conductivity for saturated soils) ranging from 2.5 to 20 cm h 21 .
Input RWU(z,t) was modeled using a sine-function with a DC offset that prevents positive values. The resulting gradients in soil water content and potential drive the S r . From the simulated u-values, we computedÛ p ðzÞ in the same way we do with the experimental data.
An artificialÛ p profile was constructed (a simple step function, with sum of 1) as a vector over space (45 layers) and multiplied component-wise with the total transpiration vector (entries in time direction). In this manner we obtain an imposed RWU matrix in space and time, which is then used as input for the numerical solution of the Richards equation. The 1D finite volume method is supplied with an initial u(z,0). After this simulation of soil water content propagation, we get a discrete soil water content gradient in time and we can use the identical multiple linear regressions as discussed above to obtainÛ p ðzÞ and S r (z,t).

MRI
Three-dimensional images of the maize (Zea mays) roots were acquired using a 4.7-T wide bore (310 mm) magnet (Magnex) equipped with a gradient coil (internal diameter 5 205 mm) with gradients up to 300 mT m 21 . A Varian console was used for control of the MRI experiments. Root lengths were calculated using the software NMRooting (van Dusschoten et al., 2016). Root mass density profiles were determined using a Spin Echo Multiple Slice sequence with reduced resolution (0.75 3 0.75 3 4 mm 3 , compared to 0.5 3 0.5 3 1 mm 3 for the normal imaging), which facilitates a shorter echo time (TE 5 4 ms instead of 9 ms), thereby minimizing the potential artifact caused by air-filled intercellular spaces. The root mass density is required to correct u as measured with the SWaP, because root mass cannot be discriminated from soil water based on permittivity. Especially for making correct calculations of the soil water potential, this is required. These MRI measurements were performed on regular intervals.
For a comparison of RWU profiles between 2 d, it is useful to correct for root growth, e.g. dividing RWU(z) by RLD(z) for the relevant days. RLD(z)'s values for 22 and 26 DAS (days of SWaP measurements) were interpolated values based on the MRI root images taken on 21 and 27 DAS. In this manner, maps in Figure 5C were calculated

Water Potential Measurements
For determination of the pF-curve, we used two approaches. To determine the water retention close to soil water saturation, we filled a cylinder with 45 cm of soil and wetted it from above, making sure that water was draining from the bottom. This soil column was scanned with the SWaP continuously for 8 d until no further changes in the soil water profile were detected and residual water droplets were still visible at the bottom. In that case, the water head is identical to the soil water content of these 45 cm (starting with h 5 0 cm at the bottom). At the dry end of the pF-curve, we used a polymer tensiometer.

Plants and Growing Conditions
Four maize plants were grown in a climate chamber with 14-to 10-h daylight/night rhythm. Air temperature at night was set to 16°C, with 22°C during daytime. Air relative humidity at night was at 55% 6 2% and during the day at 43% 6 2%. During the day, lights were switched between 400W HPI lamps (Philips) and 400W SON-T lamps (Philips) every 2 h, resulting in a difference of light intensity between 250 and 350 and 600 to 700 mmol • m 2 s 21 and also 0.5°C to 1°C difference in temperature. Owing to the large temperature jump when lights are switched on the first time, the first 2 h after daybreak were not used.
Maize seeds were inserted into a soil mix (two-thirds coarse sand and onethird loamy sand from a field site near Kaldenkirchen, Germany), which was wetted close to field capacity. Seeds were left to germinate in the climate chamber. The soil was covered by a perforated piece of plastic that reduced soil water evaporation. Once the plant was longer than 4 cm, five small watercontaining vials used to minimize permittivity jumps at the soil edge were placed on top of the soil. Plants were watered weekly to prevent the plants from wilting.
The soil water-content profile of each potted plant was measured every 24 min during a 3-d period and a 4-d period, each after watering, for the data analysis described here; each profile consists of 45 measurements at different depth positions (z 5 0 at the soil surface). All profiles were independently deconvoluted, resulting in 60 profiles g(z) per day. Thirty-one of these profiles, during the 12 h of light switching, were used to calculate the 45 U p (z) and S r (z) values on each of the 7 d that data were acquired for all four plants. For determination of the correlation between RLD(z) andÛ p ðzÞ, one plant on one of the 2 d that the soil water potential was flat (,3 kPa difference) experienced dripping water from the climate chamber ceiling so its data were rejected. Therefore, seven instances (four plants on two separate days minus one instance) could be used for the correlation. Other relevant data presented here describes results of single 12-h measurement periods of single plants (45 z-positions at 31 different time points).

Data and Code Availability
The data that support our findings of this study are available from http:// www.fz-juelich.de/ibg/ibg-2/SWaP and code required to analyze the data are available at the same location.

Supplemental Data
The following supplemental materials are available.
Supplemental Figure S1. Schematic representation of relevant soil water depletion processes.
Supplemental Figure S2. E-field distribution map of a sensor.
Supplemental Figure S4. Water head of soil water columns with growing maize plant.
Supplemental Figure S5. Simulation results from soil water depletion rates with modulated plant transpiration rates.