Shallow roots of different crops have greater water uptake rates per unit length than deep roots in well-watered soil

Commonly, root length distributions are used as a first approximation of root water uptake profiles. In this study we want to test the underlying hypothesis of a constant water uptake rate per unit root length over depth. Root water uptake profiles were measured using a novel sensor technology. Root length was measured with MRI and by scanning harvested roots. Experiments were performed with pot-grown barley (Hordeum vulgare), maize (Zea mays), faba bean (Vicia faba), and zucchini (Cucurbita pepo). For barley, maize, and faba bean, we found that roots in the top 15 cm had significantly greater water uptake rates per unit length than roots in the bottom 30 cm. For zucchini, the trend was similar but not significant. Therefore, variation of root water uptake rates with depth could be explained only partly (61–71%) by a variation of root length with depth. The common approximation of root water uptake profiles by root length distributions relies on constant water uptake rates per unit root length. This hypothesis does not hold in our study, as we found significantly greater water uptake rates per unit length in shallower than in deeper roots. This trend was consistent among species, despite the partly strong variation in physiological parameters. We suggest that this is caused by a decreasing axial transport conductance with depth. This might result in a general underestimation of water uptake rates in shallow soil layers when they are approximated by the root length distribution.


Introduction
Spatial information on root water uptake rates is often required to describe soil-plant water relations. Since root water uptake profiles are challenging to measure, they are commonly approximated by the distribution of root length with depth, especially in macroscopic water uptake models (Coppola et al. 2015(Coppola et al. , 2019Feddes et al. 2001;Wu et al. 1999). This approximation implies constant root water uptake rates per unit root length with depth. At the single root scale, however, uptake rates per unit root length vary with root branching order (Rewald et al. 2012), root type (Ahmed et al. 2016, distance from the root tip (Ahmed et al. 2016Meunier et al. 2018;Steudle and Peterson 1998), root cortical senescence (Schneider et al. 2017) and root age (Schneider et al. 2020). Most of these parameters are related to root age, which is usually distributed along a vertical gradient, with older roots in shallow layers and younger roots in deeper layers (Koebernick et al. 2014). Therefore, one could expect a systematic variation in water uptake rates per unit root length with depth. Nevertheless, empirical studies, operating at a vertical resolution between 10 and 20 cm, generally suggest a good correlation between profiles of water uptake rates and root length (Ehlers et al. 1991;Sharp and Davies 1985;Shein and Pachepsky 1995), which supports the common assumption in macroscopic models. It needs to be considered, however, that usually, a homogenous soil water potential distribution is a prerequisite for a reasonable comparison between root length distributions and water uptake profiles. This is highlighted by studies in which the strength of the correlation between root length and water uptake profiles varied among different soil water conditions (Dara et al. 2015;Sharp and Davies 1985;Shein and Pachepsky 1995). Since a homogeneous water potential distribution is difficult to achieve in experiments with natural soil substrates, approximating water uptake profiles by root length distributions still comes with uncertainty.
Generally local root water uptake rates (RWU) are determined by the radial root conductance (K R ) and the water potential gradient between soil (Ψ soil ) and the root xylem (Ψ X ). Focusing on the vertical axis with depth z, this writes: In our study, we measure a component of the water uptake profile which is independent of Ψ soil . This is achieved by measuring the short-term response of RWU to a change in light intensity which alters Ψ X but not Ψ soil , and thus, according to Eq. 1, only depends on K R and Ψ X . The theoretical framework for deriving a component of RWU which is independent of the soil water distribution has been developed by Couvreur et al. (2012). In their study, the authors show that local root water uptake rates (RWU) can be disentangled into two terms which we call plantdriven root water uptake distribution (U P ) and soildriven root water uptake redistribution (U S ): U P (z) is determined by the spatial arrangement of root hydraulic conductance which depends on the distribution of intrinsic hydraulic conductivities and root length. U P (z) integrates to the total root water uptake rate (U tot ) across the whole root system. U S (z) additionally depends on the distribution of soil water potential (Ψ soil ) and can be interpreted as a redistributive water flow through the root system from relatively wet soil layers into relatively dry soil layers. Across the whole root system, U S (z) integrates to zero (Fig. 1A). Using the hydraulic network presented in Online Resource 1, we show in Appendix 1 that in a simplified form (compare Couvreur et al. (2012)), U P and U S can be expressed as: In Eq. 3 we used the total water uptake rate (U tot ), the total root conductance (K tot ), and the plant sensed soil water potential (Ψ seq ). Note that K tot and Ψ seq are not measured in our study but are introduced here, to describe the meaning of U P and U S . In case of a homogeneous distribution of soil water potential (Ψ soil (z) = Ψ seq , in all layers), U S becomes zero throughout. Therefore, U P reflects the distribution of water uptake rates in a soil with uniform water potential distribution (corrected for gravity). Deviations from a uniform soil water distribution are considered by U S . Fig. 1 A Scheme of different water flow patterns in the soil root system, separated into vertically stacked layers. Local root water uptake rates (RWU) are the sum of the plant driven root water uptake distribution (U P ) and the soil driven root water uptake redistribution (U S ). U P is the local fraction of the total root water uptake rate, determined by the local root conductance (K R ). Direct water flow from wetter to drier soil layers is called redistributive soil water flow (rSWF). B Overview of the measured parameters and the tested hypotheses. Normalized root water uptake profiles ( Û P ) were determined with the SWaP, normalized root length profiles ( L ) were determined with MRI. Based on these profiles we calculated the water uptake rates per unit root length (A) over depth. We tested the null hypothesis (H 0 ) that A is constant over depth, and the alternative hypothesis of systematic deviations of A with depth (H 1 or H 2 ) Due to its independence of the soil water distribution, U P is better suited than RWU to analyze how well water uptake profiles can be approximated by root length distribution. Recently, a method was introduced to measure U P without actually depending on a uniform soil water distribution, using a highly precise soil water sensor in combination with a fluctuating light intensity . With this technology, we test the null hypothesis that root water uptake rates per unit root length (A) are constant with depth: As alternative hypothesis, we test whether water uptake rates per root length vary systematically with depth, indicating a spatial gradient of root conductivity. Figure 1B gives an overview over the analyzed parameters and the tested hypotheses. Root system architecture potentially affects our hypothesis, since a simulation study predicted less variation in water uptake rates per root length for taproot compared to fibrous root systems (Javaux et al. 2013). We therefore tested whether H 0 is true across four different crop species: two monocots with a fibrous root system, barley and maize, and two dicots with a taproot system, zucchini, and faba bean. We performed the following analysis for each of the four species: In a first step, we analyzed to what extent the variation of U P with depth is explained by a variation of L with depth and to what extent by a variation of A with depth. In a next step, we evaluated H 0 by testing for significant differences between water uptake rates per root length in shallow (upper third of the pots) and deeper layers (lower two thirds). Potential deviations from H 0 would indicate a variation of root conductivity. Since root conductivity is closely linked to root diameter (Ahmed et al. 2016;Frensch and Steudle 1989;Huang and Eissenstat 2000), we checked in a third step, whether variations of A(z) can be explained by root diameter distributions over depth.

Plant growing conditions
We grew four different plant species: the monocots barley (Hordeum vulgare), and maize (Zea mays), and the dicots faba bean (Vicia faba), and zucchini (Cucurbita pepo cylindrica). Seeds were germinated for 2-3 days in the dark on moistened germination paper. Seedlings were transferred into soil-filled PVC pipes (50 cm high, Inner Diameter: 8.1 cm), suitable for both MRI and SWaP measurements. We used a sandy loam, collected in Kaldenkirchen, Germany with 73.3% sand, 23.1% silt, 3.6% clay, (Pohlmeier et al. 2009) mixed with 20% (v) coarse sand (0.7-1.4 mm). Water saturation was reached at volumetric soil water content (θ) of 40.7%. The soil type was selected because it wets easily and uniformly within half a day after rewatering. Additionally, its water retention curve is relatively flat in the wet regime, making it easier to avoid large vertical soil water potential gradients. Note that even though our measurement of U P is independent of the soil water potential distribution, vertical soil water flows would introduce noise during the analysis process. Furthermore, the soil type used leads to a good image quality of the MRI measurements which is related to the low silt, clay, and ferromagnetic content (Pflugfelder et al. 2017). The pots were filled with soil to a height of 45 cm, resulting in a total substrate volume of 2.32 l. Pots were filled under gentle shaking to promote uniform compaction, achieving a bulk density of 1.47 kg/l. Four plants per species were grown in the prepared pots in a climate chamber providing a controlled temperature of 21.5 °C ± 0.2 °C and a VPD air of 1.49 kPa. Plants were watered from the top every 2 nd or 3 rd day to keep them well-watered at an average θ of above 20% (v/v). Before and during water uptake measurements, plants were not watered for approximately 24 h to minimize spatial gradients of soil water potential during the measurement, as confirmed by our measurements (Fig. 3). For fertilization, NPK nutrient salt (Hakaphos Red; Compo Expert; 8% N, 12% P, 24% K), diluted in water at 0.3% (v/v) was given to the plants once a week. The total amount of fertilized water supplied to the plants depended on the actual water use and varied between 30 ml (1 st week) and up to 200 ml (4 th week). We used a water-cooled LED panel (3200 K, 5 × 5 LEDs á 20 W) for illumination. During the day, two levels of light intensity alternated in periods of two hours for 14 h in total (three low light periods and four high light periods) for the full growing and measurement period. Photosynthetically active radiation of the lower level was 500 µmol m −2 s −1 , that of the higher level 1000 µmol m −2 s −1 . The light intensity sums up to a daily light integral of 39.6 mol m −2 d −1 . This light fluctuation was required for the derivation of root water uptake profiles as described below. Twenty-eight days after germination, we measured the root water uptake profiles with the SWaP and the root length distribution with MRI of each individual plant. Within one day, we could measure all four replicates of one species. Below, we describe the SWaP and MRI measurements in detail.

SWaP measurement of Û P z i
We measured Û P with a recently developed soil water profiler (SWaP) . The sensors of the SWaP basically consist of two opposing copper plates (7 × 5 cm 2 ) in a 12 cm high PVC sleeve, shielded with aluminum. The sensors partially enclose the pots with soil columns and are movable along the z-axis. The copper plates form a capacitor which is connected to a coil, forming a resonator circuit. The resonance frequency of the circuit is a function of the electrical permittivity of the material in between the copper plates, which is largely determined by the soil water content θ. Thus, measuring the resonance frequency allows determination of θ as described below. A vector network analyzer (DG8SAQ, VNWA3, SDR-Kits, UK) was used to determine the resonance frequency of the circuit by applying a frequency sweep between 150 and 220 MHz. The sensors move vertically along the pots and measure the resonance frequency in equidistant steps of 1 cm. A complete scan of four pots with 45 cm high soil columns simultaneously took around 12 min. To synchronize with light fluctuations, scans were started every 15 min. For conversion of the resonance frequency into θ, we measured a calibration curve. To this end, we filled 12 cm high PVC pots with soil at a defined bulk density (1.47 kg/l, as used for plant growth) and a defined θ ranging from 2 to 30% and measured the resulting resonance frequency with the SWaP. The data were fitted using a second order polynomial (Online Resource 2). This procedure enabled us to measure the vertical θ profiles of our soil columns in 1-cm steps.
For our analysis, we interpreted the 45 cm high soil column as 45 stacked layers each of 1 cm height and uniform θ. The layers were indexed i = 1 (top layer),…, 45 (bottom layer) with the top of each layer at depth z i = 0 cm,…, 44 cm. Given the 12 cm height of the SWaP sensors, the measurement at each 1-cm layer is not the precise θ value in that layer, but a convolution of (1) the electrical field strength between the copper plates and (2) the 12 soil layers enclosed by the sensor. To achieve a spatial resolution of 1 cm, a deconvolution was applied. This procedure requires measuring the exact θ-values at the pot borders and the profile of the electrical field strength. Given these values we performed a numerical deconvolution. As this amplifies errors, we constrained the deconvoluted result by a regularization term which reduces fluctuations of the profile.
Given the deconvolved θ profiles over time we could, in a next step, derive the profiles of water uptake rates. For that, we calculated the rate of change in water content over time ( t ) in each layer. A change in water content in layer i is caused by local RWU, redistributive soil water flow (rSWF) between adjacent layers, and evaporation in the top layer E s (t): Using Eq. 2 we can express RWU as the sum of U P and U S with Neither U S nor rSWF contribute to U tot but sum up to zero across the whole pot. We summarize these two terms as soil water redistribution through soil and roots ( S r ) and write Eq. 5 as: To determine Û P from Eq. 6, we make use of the light intensity fluctuating between a lower and a higher level at a period of two hours. The alternating light intensity induces a fast response of the transpiration rate, via stomatal regulation, and thus U tot . Note that the transpiration rate and U tot are almost similar, and only differ by the shoot growth rate. The response of U P to a change of U tot is much faster than the response of S r , as it takes time to generate water potential gradients within the soil which drive both rSWF and Us. Therefore, U P and S r can be separated based on their response rate to fluctuating light intensity. Biologically, this can be understood as follows: A greater local root conductance leads to a greater (5) change in the water uptake rate when the light intensity changes. Therefore, the stronger the local (t) t responds to a change in light intensity, and thus in U tot , the greater the local root conductance, and thus U P . Mathematically, Û P can be derived as slope of a linear regression between (t) t and U tot (t) according to Eq. 6 (Online resource 3). Such a regression was performed in each layer separately, using the data acquired during a 12 h period (7.00 am to 7.00 pm) covering three high and low light intensity periods of two hours each.

Determination of soil water potential and conductance
The soil water retention curve was measured using the evaporation method (Peters and Durner 2008) with the HYPROP setup (METER Group, Munich, Germany). The characteristic parameters of the water retention curve were obtained by fitting a Brooks-Corey model (Brooks and Corey 1964) to the measured data of the pressure head h (cm) for varying θ: with saturated water content θ s , residual water content θ r , air entry pressure head α −1 (cm), and a dimensionless pore size index λ. To obtain the soil water potential Ψ soil , a gravity component was added to the pressure head: MRI measurement and processing of root length Roots were non-invasively imaged using MRI. For logistical reasons, MRI measurements were either shortly before or after the SWaP measurements. Since plants were not under controlled conditions during MRI, scanning was preferably conducted during the night. The MRI setup consisted of a 4.7 T vertical wide bore (310 mm) magnet (Magnex, Oxford, UK) and a gradient coil (ID 205 mm (MR Solutions)) providing gradients up to 400 mT/m. The MRI experiments were controlled Harvest and root scanning To include the fine root fraction below the detection limit of MRI, roots were harvested after the MRI or SWaP measurement respectively. Since we were interested in the vertical distribution of root traits, soil columns were taken out of the pots and cut into five blocks of 9 cm height each. The roots were isolated from the soil using sieves with different mesh sizes (0.3 mm to 2.0 mm) and stored in a solution of 70% water and 30% ethanol. Roots of each block were scanned separately. We used WinRHIZO software (Regent Instruments, Ottawa, Canada) to analyze total root length and root length in 20 equidistant diameter classes ranging from 0.0 mm to 2.0 mm (last class included all roots thicker than 2.0 mm) for all 5 blocks per plant separately. Using the distribution of harvested roots, we calculated correction factors for each 9 cm high soil block. The MRI measured root distribution was corrected accordingly. Finally, we applied the same convolution and deconvolution procedure to the root length profile as to Û P to achieve a similar degree of smoothing caused by this procedure. Normalized, corrected, and deconvolved root length profile is called L . Leaf area and shoot fresh weight were also determined at harvest.

Quantitatively explaining the variation in UP(z)
Here we use a concept which has been developed to relate how important the variation of each of two factors of a product is to explain the variation of the product (Poorter and Nagel, 2000). For that we write U P as product of L and A: Vol.: (0123456789) and apply an ln transformation: which can be written as: Given the U P , L, and A profiles of a plant or species, each consisting of 45 values, we thus linearly fitted the ln of the 45 U P values against the ln of the 45 L or A values respectively. Then the two terms on the right-hand side of Eq. 11 were determined as the slopes of the linear fits. According to Eq. 11, these two slopes add up to one, and are a measure for the (9) U P = L ⋅ A (10) ln(U P ) = ln( ⋅ ) relative importance of L, and A in explaining variation in U P .

Characteristic plant and soil parameters
Maize and zucchini had significantly greater shoot fresh weight than barley and faba bean (14-50 g) (Fig. 2). In barley, also the leaf area was significantly smaller than in maize and zucchini (199-576 cm 2 ). The total root length of faba bean (27 m) was significantly smaller than that of the other species (82-94 m). During the 12 h measurement period, zucchini took up significantly more water (95 ml) than Fig. 2 Characteristic parameters of the species at the day of measurement: A shoot fresh weight, B leaf area, C total root length, D total root water uptake rate, E Water uptake rate per unit root length, F water uptake rate per leaf area, and G rootto-shoot ratio, expressed as leaf are per root length. Height of the bars are species averages (n = 4), error bars are standard errors of the mean. Differences between species were considered significant if p-values of a Student's t-test were < 0.05. Significant differences between groups are indicated by different letters the other species (40 -48 ml). The total water uptake rate per unit length was significantly greater in faba bean (1.7 ml d −1 m −1 ) and zucchini (1.1 ml d −1 m −1 ) than in barley and maize (both 0.5 ml d −1 m −1 ). However, water uptake per unit leaf area was significantly greater in barley (0.20 ml d −1 cm −2 ) than in maize and faba bean (0.11 -0.15 ml d −1 cm −2 ). Shoot to root ratio, expressed as leaf area per root length, was significantly different among all species. It was lowest in barley, followed by maize and zucchini and highest in faba bean (2.5 -11.3 cm 2 m −1 ). For all species, we generally measured a vertical gradient in Ψ soil with more negative values at the top and less negative values at the bottom (Fig. 3). This gradient was more pronounced at the end compared to the start of the measurement. At start, the average Ψ soil with depth ( Ψ soil ) was similar (-9 to -11 kPa) among the four species. At the end of the measurement, Ψ soil for zucchini (-21 kPa) was significantly more negative than for barley (-12 kPa) and faba bean (-13 kPa). For maize (-14 kPa), Ψ soil was not significantly different from the other species. Ψ soil profiles of each individual plant are shown in Online Resource 4.
Root length distribution explains 61 -71% of variation in water uptake profiles Due to the higher abundance of roots in shallow soil layers, water uptake profiles and root length were both generally high in top layers and declined with depth (Fig. 4). In maize, both profiles dropped rather sharply within the top 10 cm but declined smoother in barley and faba bean. In zucchini, both profiles were generally flatter compared to the other species. In barley, maize, and faba bean, Û P was consistently Fig. 3 Distribution of Ψ soil at start (filled circles) and end (empty squares) of the SWaP measurements as species averages (n = 4). Error bars are standard errors of the mean. Mean values over depth ( Ψ soil ) at start and end of the measurement are given in the legend higher than L in the top layers but lower towards the bottom. Û P and L profiles of each individual plant are shown in Online resource 5. We evaluated to what extent variation in U P (z) is determined by variation in L(z) and A(z) respectively using Eqs. 9-11. This analysis was performed for each individual plant separately. Table 1 shows the results as species averages with standard errors of the mean. Between 61 and 71% of variation in U P (z) were explained by a variation in L(z), 29-39% were explained by a variation in A(z) without any significant differences among species.
Shallow roots show significantly greater uptake rates per unit length than deeper roots The findings reported in Table 1 indicate a variation of water uptake rates per root length over depth, which implies deviations from our null hypothesis, H 0 , of constant uptake rates per unit root length with depth. In a next step, we analyzed whether these deviations in A(z) followed a spatial pattern (Fig. 5A). The vertical orange lines in Fig. 5A are the mean values over depth and represent H 0 . In all four species, we observed that water uptake rates per root length in the top 15 cm (blue lines in Fig. 5A) were higher than in the bottom 30 cm (red lines), indicating a systematic deviation. Profiles of A(z) of each individual plant are shown in Online resource 6. To quantify this trend of higher uptake rates per unit root length in top layers, we compared A(z) between the top 15 cm and bottom 30 cm in each individual plant, and calculated the species averages (Fig. 5B). In barley, faba bean and maize, water uptake rates per root length were significantly higher in the top 15 cm compared to the bottom 30 cm. Except for one faba bean plant, this trend was found in each single plant (Online resource 6). In zucchini, there Table 1 Relative importance of L and A in explaining variation in U P with depth, determined as slopes of the linear fits between ln(L) and ln(U P ), and ln(A) and ln(U P ) Values shown are mean values with standard error of the mean among the four replicates of each species. There were no significant differences between species as tested by a one-way ANOVALÂ barley 0.70 ± 0.01 0.30 ± 0.01 maize 0.61 ± 0.08 0.39 ± 0.08 faba bean 0.71 ± 0.12 0.29 ± 0.12 zucchini 0.67 ± 0.14 0.33 ± 0.14

Fig. 4 Û P (blue) and L
(red) as species averages (n = 4). Horizontal error bars are standard errors of the mean in each layer. For total water uptake rate and total root length see Fig. 2 was no significant difference, and two individual plants had higher, two had lower uptake rates per length in top layers (Online resource 6). Among all 16 plants from the four different species, shallow roots had a significantly higher water uptake rate per root length than deeper roots (Fig. 5B).
Does the distribution of root diameter explain the variation of water uptake per root length?
The observed deviations from the null hypothesis indicate a vertical gradient in root conductivity with higher conductivity in shallow roots and lower conductivity in deeper roots. In a next step, we analyzed whether this pattern is reflected by the distribution of root traits (Fig. 6). Figure 6A exemplary shows an image of a root system from each species, acquired with MRI. Barley and maize have a fibrous root system with thicker (yellowish and reddish pseudo colors) seminal and nodal roots from which thinner (blueish pseudo colors) lateral roots emerge. In both species, the seminal and nodal roots were thinner in deeper layers compared to shallower layers. Faba bean and zucchini both have a taproot system with one main root growing vertically and lateral roots emerging from it. In faba bean, laterals in the upper soil layers appear as thick as the taproot. The laterals preferably grew horizontally and started spiraling downwards when they reached the pot borders. In zucchini, there was a clear trend of generally thicker roots in deeper layers compared to shallower layers for both, the main root and laterals. Note that the MRI had a detection limit between 200 µm and 300 µm. The color-coded diameter in Fig. 6A suggests that, except for faba bean and deep layers of zucchini, a diameter of 0.5 mm is a reasonable threshold to distinguish between lateral roots and main roots. To quantify the distribution of laterals, we therefore analyzed the fraction of fine roots with a diameter below 0.5 mm over depth, using data from harvested and scanned roots (Fig. 6B). In barley, there was a continuous, significant decrease of this fine root fraction from 94% in the top soil layer to 69% in the bottom layer. In maize, the fine root fraction was greatest in the second layer (88% at a depth between 9 and 18 cm) and also decreased towards the bottom. In the deepest soil layer, it was significantly lower (66%) than in the second layer. In zucchini the decrease was even more pronounced, ranging from 92% in the top layer to only 30% in the bottom layer. Note, however that due to the general root thickening in the bottom layers of zucchini, a diameter-based distinction between laterals and main roots is difficult (Fig. 6A). In contrast to the other species, the fine root fraction in faba bean significantly increased from around 10% in the top 30 cm to 30% in the bottom layer. As mentioned above, the distinction based on root diameter in faba bean is questionable as laterals were comparably thick as the main root (Fig. 6A). Additionally, we analyzed the average root diameter over depth which revealed a similar picture (Online resource 7). For barley, maize and zucchini, the average diameter was almost constant in the top half of the pot and increased towards the bottom. Such a root thickening in deeper layers is typical for sandy soils (Lippold et al. 2021;Qin et al. 2005) and might be related to an increased ethylene concentration which reportedly induced root thickening in compacted soil layers (Pandey et al. 2021;Vanhees et al. 2022). For faba bean, however, average root diameter was lower in shallow than in deep soil layers.

Discussion
In the present study, we analyzed the common approximation of root water uptake profiles ( Û P ) by the distribution of root length ( L ) in 4 weeks old pot-grown crop plants. For that, we tested the hypothesis of a constant root water uptake rate per unit root length (A) with depth. We observed that only 61-71% of the variation in U P with depth were explained by a variation of L with depth. 39-29% were explained A Complete A(z) profiles. Colored vertical lines are mean values over depth (n = 4) for the whole pot (orange), top 15 cm only (blue), bottom 30 cm only (red). Note that the orange line represents the null hypothesis of constant water uptake rates per unit root length. Data points are averages among species, error bars are standard errors of the mean. Layers with a root length below 10 cm caused considerable scatter of uptake rates per root length and thus were dropped for this and the following figure. This only concerned the bottom 5 cm of faba bean. B A(z) separated into the top 15 cm and bottom 30 cm of the pot. Height of the error bars are mean values among species (n = 4), error bars are standard deviations of the mean. For each species, and all replicates we tested for significant differences between the top 15 cm and bottom 30 cm using a Student's t-test. Significant differences with a p-value below 0.05, 0.01, or 0.001 are indicated by *, **, or *** respectively ◂ by a variation in A with depth. The hypothesis of a constant A(z) did not hold as we found significantly greater water uptake rates per unit root length in the top 15 cm than in the bottom 30 cm of the pots in barley, maize and faba bean. Also in these three species, the fraction of lateral roots appeared to decrease towards the bottom.
Since spatial data on root hydraulic traits are rarely available, the approximation of root water uptake profiles by root length distributions was established in macroscopic water uptake models (Coppola et al. 2015(Coppola et al. , 2019Feddes et al. 2001;Wu et al. 1999). Our data suggest that this approximation comes with limitations as only 61-71% (without significant differences between species) of variation in U P could be explained by a variation in L (Table 1). These values are generally lower than those reported by the few quantitative, empirical studies on this topic (70-100% in oat and faba bean (Ehlers et al. 1991), 91-100% in oat and horse bean (Shein and Pachepsky 1995)). One major difference between these studies and our approach is that we measure a component of the root water uptake profile, namely Û P , which reflects the distribution of root hydraulic conductance and is independent of the soil water potential distribution. This was realized by measuring the fast response of local water depletion rates to a changing light intensity. The change in light intensity induces a change in the root xylem suction while the soil water potential at first stays constant. Therefore, how strong a change in xylem suction affects the local water depletion rate only depends on the distribution of root hydraulic conductance (see Eq. 1), and thus Û P . Typically, as in our measurements (Fig. 3), the soil water potential is lower (more negative) in upper layers than in deeper layers. This causes a redistributive water flow from lower to upper soil layers through the roots. Therefore, U S usually is in opposite direction to U P in upper soil layers and in the same direction in deeper layers (Fig. 1A). According to Eq. 2 this results in RWU exceeding U P in top layers and falling below it in bottom layers. Thus, if we had measured RWU instead of U P the water uptake profiles (blue lines in Fig. 4) would have been closer to the root length profiles (red lines in Fig. 4). From this we conclude, that in studies measuring RWU instead of U P , the predictive power of water uptake profiles by root length distributions is artificially increased by the impact of vertical soil water potential gradients on RWU. Approximating root water uptake profiles by root length distributions is equivalent to hypothesizing a constant water uptake rate per unit root length with depth. We observed that water uptake rates per root length were significantly greater in shallow roots compared to deeper roots (Fig. 5), emphasizing that the hypothesis does not hold. Two previous studies using neutron radiography to measure water fluxes into upper and lower parts of lupine root systems reported similar trends (Dara et al. 2015;Zarebanadkouki et al. 2013). Such a systematic deviation of water uptake rates per root length over depth is problematic for the common approximation of root water uptake profiles by root length distributions since it leads to a systematic underestimation of water uptake by roots in top layers and an overestimation in bottom layers. The trend of greater water uptake rates per root length in top layers was consistently observed for barley, maize and faba bean plants ( Fig. 5 and Online resource 6). Note, that different physiological parameters, such as shoot size, root length, shoot-root ratio, and total water uptake rate per unit root length and leaf area (Fig. 2) varied, partly significantly, among these species. We therefore suggest that the trend of greater water uptake rates per root length in shallow roots is valid for a wider range of species and plants of different sizes and should be considered when water uptake profiles are approximated by root length distributions.
This leads us to the question of what caused the greater water uptake rates per root length in shallow roots. One potential reason is the impact of pot dimensions, which are known to constrain root growth (Poorter et al. 2012). However, since root length densities were greatest in shallow soil layers in our experiments (Figs. 4, 6A) we would also expect the strongest constrains in these layers. However, Fig. 6 Distributions of characteristic root system traits measured with MRI and by scanning harvested roots. A Images of the different species' root systems and diameters acquired with MRI and analyzed with NMRooting. Exemplary, the image of one replicate per species is shown. Color code is root diameter ranging from blue (0 mm) to red (1.5 mm). Column size was 80.5 mm in diameter and 450 mm in height. B Fraction of fine roots with diameter below 0.5 mm over depth, derived by scanning of harvested roots. Horizontal bars are species averages, error bars are standard errors of the mean. Differences among depth were considered significant if p-values of a Student's t-test were < 0.05. Significant differences between different layers are indicated by different letters, starting with 'a' for the greatest value ◂ water uptake rates per root length were greater in upper soil layers compared to deeper layers (Fig. 5). This emphasizes that potential consequences of constrained pot dimensions, such as saturation effects or limited root functioning, did not result in measurable impairment of water uptake rates.
Mathematically, local root water uptake rates are the product of the local radial root conductance and the water potential difference between the root xylem and the soil (Eq. 1). The radial root conductance depends on the radial root conductivity, an intrinsic hydraulic property, and root length. Therefore, uniform soil water potential distribution, uniform radial conductivity, and sufficiently high axial conductance to provide uniform water potentials in the root xylem are requirements for constant uptake rates per unit root length throughout the root system (Javaux et al. 2013). Given that U P is independent of the soil water potential distribution, the difference in A(z) between shallow and deep roots must be caused by differences in the hydraulic parameters (i.e. radial root conductivity and xylem water potential) between the top and bottom part of the root system. As summarized by (Vetterlein and Doussan 2016), root radial conductivity depends on several root anatomical traits changing with root age, such as apoplastic barriers, cortex thickness, or aquaporin density. Towards the root tip, there usually is a lower degree of suberization (Huang and Eissenstat 2000;Steudle 1994;Steudle and Peterson 1998), thinner cell walls (McCormack et al. 2015;Steudle and Peterson 1998) and higher aquaporin expression (Gambetta et al. 2013), all of which results in a greater radial conductivity. This contributes to the generally high radial conductivity in lateral roots (Ahmed et al. 2016) or roots with a low branching order (Rewald et al. 2012). Our analysis suggests a greater fraction of fine lateral roots with a diameter below 0.5 mm in shallower than in deeper soil layers for barley, maize, and zucchini (Fig. 6B). If this fine root fraction indeed had a relatively high radial conductivity, it might have contributed to the greater water uptake rates per unit root length in shallow soil layers. However, as argued above, the anatomical features causing greater radial root conductivity usually appear towards the root tip. Therefore, we would expect a greater radial conductivity in deeper layers, where roots are generally younger (Koebernick et al. 2014). We can only speculate here, whether the effect of an increased root diameter, and thus, a longer radial pathway outweighed the age-effect of a lower suberization and greater aquaporin expression in deeper roots. Note that for faba bean this quantitative analysis of root type distribution was not possible since lateral roots and main roots had a comparable diameter (Fig. 6A). Additionally, the general thickening of roots towards bottom layers (Online resource 7) could have obscured the distinction of lateral and main roots based on root diameter.
Another possibility is a less negative xylem water potential (less water suction) in deeper roots due to an insufficient axial conductance. The axial conductivity increases with increasing number and diameter of conducting xylem vessels. In addition, the axial conductance increases with increasing length of the hydraulic pathway (Frensch and Steudle 1989). In crops, both number and diameter of xylem vessels usually decrease towards the root tip, and thus with depth (Bramley et al. 2009;Clément et al. 2022;Frensch and Steudle 1989;Steudle and Peterson 1998;Watt et al. 2008). Note that in contrast, trees usually have a greater number and diameter of conducting root xylem in deeper layers (McElrone et al. 2004;Pate et al. 1995;Wang et al. 2015). For crops however, the root xylem anatomy, together with the long hydraulic pathway, lead to a decreasing axial conductance Zarebanadkouki et al. 2016), and finally to a less negative xylem water potential in deeper roots . In maize, the maturation of the late metaxylem in the main root was shown to occur around 25 cm from the root tip (Steudle and Peterson 1998) leading to increased axial conductance. This is spatially correlated to the rather sharp drop in A(z) that we observed within the top 15 cm in maize (Fig. 5A). In summary, the greater water uptake rates per unit root length in shallow roots in barley, maize and faba are most likely explained by a less restricted axial water transport as compared to deeper roots. This might be accompanied by the greater fraction of lateral roots, potentially leading to greater radial conductivity in shallow soil layers (Fig. 7).
In the field, greater water uptake efficiencies of shallow roots could be beneficial regarding the competition for rainwater in shallow soil layers. Our study, as well as those two studies reporting similar results (Dara et al. 2015;Zarebanadkouki et al. 2013), were performed with pot-or container-grown plants and, straightforwardly transferring the results to field-grown plants is difficult. Only limited data on water uptake rates per root length from field experiments are available in the literature, probably because soil water conditions are barely controllable in the field, making a reliable measurement of water uptake profiles even more challenging. Two recent field studies in wheat suggest that root length and water uptake rates are asymptotically related due to a saturation of water uptake in upper soil layers with great root length densities (Gao et al. 2022;Zhang et al. 2020), which is opposite to our findings. It is possible that the restricted horizontal root growth in our pots led to a stronger vertical gradient in root system traits compared to field conditions, which might have contributed to the reduced uptake per root length in deeper layers. Further experiments are required to determine the distribution of root hydraulic traits in field-grown plants, which is, however limited by the current technologies for measuring root water uptake patterns.

Concluding remarks
In the present study we tested the hypothesis of constant root water uptake rates per unit root length with depth to answer how reliably profiles of root water uptake rates can be approximated by root length distributions. We consistently found that in well-watered soil, water uptake rates per unit root length were significantly higher in shallower compared to deeper roots. Since this higher root activity in top soil layers was consistently observed among species which differed significantly in Fig. 7 Schematic evaluation of our hypothesis. Shallow roots generally have greater water uptake rates per unit root length (A(z)) than deeper roots. This is probably explained by a less negative xylem water potential in deeper layers due to an incomplete maturation of xylem vessels. Additionally, radial conductivity in shallow soil layers might be greater due to a higher fraction of fine lateral roots various physiological parameters, it seems to be an universal trend. We suggest that it is explained by a limiting axial conductance of deeper roots. The greater uptake rates per unit root lengths of shallow roots need to be taken into account when water uptake profiles are used to estimate root length distribution or vice versa.
At this point, we assume that K X (z i ) is much higher than K R (z i ) and therefore Ψ X (z i ) is well approximated by Ψ collar . Note that this assumption is not required for the separation of RWU in U P and U S as shown by Couvreur et al. (2012), but used here to keep the derivation concise. With this, Eq. 12 writes: Using Eq. 15 to replace Ψ collar in Eq. 16 gives after rewriting: In Eq. 17, RWU is expressed as sum of two terms, of which the first one is independent of the soil water potential distribution.
We define U P (z i ) = K R (z i ) ⋅ U tot K tot and write Eq. 17 as: Note that under the assumption K X (z i ) > > K R (z i ), K tot simplifies to the sum of the radial conductance of all layers: K tot = ∑ i K R (z i ) . Therefore, U P can be normalized by division by U tot : Without the assumption K X (z i ) > > K R (z i ), Û P (z i ) would additionally depend on the axial and radial conductance of other layers and thus on the overall root hydraulic architecture. Nevertheless, it would still be independent of Ψ soil (z i ).