Robust Estimation of Absorbing Root Surface Distributions From Xylem Water Isotope Compositions With an Inverse Plant Hydraulic Model

Abstract

The vertical distribution of absorbing roots is one of the most influential plant traits determining plant strategy to access below ground resources. Yet little is known of natural variability in root distribution since collecting field data is challenging and labor-intensive. Studying stable water isotope compositions in plants could offer a cost-effective and practical solution to estimate the absorbing root surfaces distribution. However, such an approach requires developing realistic inverse modeling techniques that enable robust estimation of rooting distributions and associated uncertainty from xylem water isotopic composition observations. This study introduces an inverse modeling method that supports the assessment of the root allocation parameter (β) that defines the exponential vertical decay of a plants’ absorbing root surfaces distribution with soil depth. The method requires measurements obtained from xylem and soil water isotope composition, soil water potentials, and sap flow velocities when plants’ xylem water is sampled at a certain height above the rooting point. In a simulation study, we show that the approach can provide unbiased estimates of β and its associated uncertainty due to measuring errors and unmeasured environmental factors that can impact the xylem water isotopic data. We also recommend improving the accuracy and power of β estimation, highlighting the need for considering accurate soil water potential and sap flow monitoring. Finally, we apply the inverse modeling method to xylem water isotope data of lianas and trees collected in French Guiana. Our work shows that the inverse modeling procedure provides a robust analytical and statistical framework to estimate β. The method accounts for potential bias due to extraction errors and unmeasured environmental factors, which improves the viability of using stable water isotope compositions to estimate the distribution of absorbing root surfaces complementary to the assessment of relative root water uptake profiles.

Introduction

The absorbing root surfaces distribution (A_R), i.e., those surfaces of a plants’ root system that support water uptake, is a pivotal plant characteristic that determines the plant species’ nutrient and water acquisition strategy. Investments in competitive advantage usually imply maximizing the upper soil layer’s exploitation, where the concentration of nutrients is generally highest (Jobbagy and Jackson, 2001). However, this comes at the cost of drought tolerance since upper layers are generally more drought-prone than deeper soil layers with more stable water reserves (Fogel, 1985). Accurate measures of A_R are thus needed to characterize specific plant competitive strength and drought response.

Unfortunately, data on root distributions in general—and on A_R in specific—is scarce, and little is known about the intra- and interspecific variability in A_R across different environments (Böhm, 2012). This paucity is caused in part by the available techniques to study root distributions of individual plants, which are often destructive, expensive, and labor intensive (Cabal et al., 2021). Root excavation, for example, holds the highest promise of most accurately characterizing a plant’s natural root distribution (Böhm, 2012). However, the associated workload limits its practical application to small sample sizes and small habitus plants, e.g., annual plants, crops, and young trees. As an illustration, Preston (1942) estimated that one laborer requires approximately 5 weeks to fully excavate and examine the root system of single 15-year-old lodgepole pine. These time and labor disadvantages have led to the development of many other direct and indirect in situ techniques, such as rhizotron systems, acoustic and electromagnetic tomography, the auger method, or the use of non-radioactive tracers (reviewed in Cabal et al., 2021). However, while these techniques provide a less invasive alternative to root excavation, they generally fall short in the level of details they can provide on the distribution of the individual absorbing root surfaces.

A relatively straightforward technique to relate relative root water uptake (RWU, which is inextricably linked toA_R) with soil depth is using stable water isotope composition as non-radioactive tracers. Ehleringer and Dawson (1992) described the simplicity of the technique, which lies in a direct relationship between the isotopic composition of the xylem sap (δ_xyl) and the isotopic composition observed in soil water (δ_soil) along with a soil depth profile. Common approaches assume that xylem water is a proportional mixture of δ_soil from the various depths at which roots absorb water (Phillips and Gregg, 2003). The approach requires: (i) the occurrence of a natural isotopic gradient in the soil generated by topsoil water evaporation (Beyer et al., 2018); and (ii) the absence of processes that alter the xylem water isotope composition while entering the plant or during transport along the plant hydraulic system (Wershaw et al., 1966; Zimmermann et al., 1967; White et al., 1985; Dawson and Ehleringer, 1991; Walker and Richardson, 1991; Dawson et al., 2002; Zhao et al., 2016). Requirements (i) and (ii) generally limit the technique to lignified plants and implementation during rain-free periods after sufficient soil evaporation has occurred. However, these conditions still allow strong flexibility and usability across multiple temporal and spatial scales (Dawson et al., 2002). Its moderate labor and time investment allows sampling of more and larger plant species far beyond what is possible with root excavation.

However, the robustness of stable water isotope techniques has been recently questioned (Penna et al., 2018; von Freyberg et al., 2020). An increasing number of studies discuss a potential mismatch between available water sources and isotopically depleted compositions in xylem water. Hypothetical discrepancies have resulted from: isotopic discrimination at root-level (Allison et al., 1983; Vargas et al., 2017) or by associated mycorrhizae (Poca et al., 2019), and by internal mixing of xylem water with isotopically depleted water reserves stored in stem tissue (Barbeta et al., 2020; Knighton et al., 2020). The link between source water and the isotopic composition of xylem water (δ_xyl) can be further obscured by pronounced water-transport lags (Meinzer et al., 2006; Gaines et al., 2016; Magh et al., 2020; Marshall et al., 2020; Mennekes et al., 2021) or possible excessive intra-individual variance in δ_xyl due to variable RWU dynamics caused by fluctuating biophysical factors, frequently overlooked in isotopic studies (e.g., soil water potentials, vapor pressure deficits and sap flow dynamics) (De Deurwaerder et al., 2020). This growing body of literature suggests that standard sampling methods may deliver biased estimates of RWU profiles while simultaneously underestimating uncertainty among species, biomes, or seasonality. Therefore, a real need exists to develop methods that accurately estimate A_R and associated uncertainty in the face of unmeasured biophysical factors that affect δ_xyl.

Coupling stable isotope measurements to biophysical models (e.g., RAPID algorithm) could support the inverse reconstruction of absorbing root surfaces distribution, A_R, and the assessment of their active contribution to RWU (Ogle et al., 2004). Such a coupled technique has enormous potential to build a fundamental understanding of spatial and temporal variability in water competition strategy amongst and within plant species. To the best of our knowledge, only one previous study endeavored to develop such a tool (Ogle et al., 2004). However, it did not account for unmeasured biophysical factors that affect δ_xyl potentially leading to biased estimates. Here we adopt a mechanistic model for uptake and transport of stable water composition through plants (De Deurwaerder et al., 2020) and use simulations to show that this inverse modeling method offers estimates of β, the allocation parameter which defines the exponential vertical decay of a plants’ A_R while (1) accounting for the xylem water isotopic variance within plants, as well as (2) uncertainties in isotopic measurements and (3) biophysical parameters, e.g., sap flow dynamics. We further provide guidelines to improve sampling design in future studies. Finally, we show how the model can validate previous results by re-analyzing a case study in French Guiana for tree and liana growth forms. This study suggests that previous methods underestimated the uncertainty in mean xylem water δ²H and δ¹⁸O provided by De Deurwaerder et al. (2018). The applied inverse method is provided as an open-source code (see GitHub repository HannesDeDeurwaerder/iSWIFT).

Materials and Methods

The SWIFT model links xylem water isotope compositions (δ_xyl) to an allocation parameter β, that defines the exponential vertical decay of A_R with soil depth. We give a brief overview of the model in box 1, restricted to key equations expressed for the hydrogen isotope composition in xylem and soil water (δ²H_X and δ²H_S). Subsequently, we describe the numerical inversion needed to generate estimates of β from δ_xyl and δ_soil. Here, we evaluate how increased levels of variable range restrictions improve estimates of β, followed by a power analysis to inform to which extent β should differ between groups of plants subject to similar edaphic conditions to observe statistical differences in δ_xyl. Both analyses can help guide future study design optimization. Finally, we introduce a practical case study in French Guiana. We maintain the following notation in the subscripts of presented variables: the medium through which water travels is indicated by uppercase fonts, while lowercase fonts highlight the units of time and distance: X for xylem, R for root, S for soil, h for stem height, t for time, and i for the corresponding soil layer. A complete overview of variables, definitions and units is given in Supplementary Table 1, and details on the SWIFT model can be found in Supplementary Appendix A and De Deurwaerder et al. (2020).

Inverse SWIFT: Numerical Model Inversion and Likelihood Estimation

The goal is to estimate the relative shape of absorbing root surfaces distribution by numerical inversion of the allocation parameter β, given a set of measured δ_xyl collected from plants in the field (Figure 1). We start with a vector C consisting of paired δ²H_x and δ¹⁸O_x observations, and assume C to be a bi-variate random variable with a conditional probability density function P(C|β_true,χ_true) determined by the “true” allocation parameter, β_true, and natural occurring variance in the local set of biophysical variables, χ_true (Figure 1A).

FIGURE 1

Subsequently, we consider Equations 1–3 (Box 1) to generate distributions of synthetic δ_xyl values that correspond to a wide range of biophysical parameters (χ) which prior distributions are user-specified or measured (Supplementary Table 2) and given a specific value of β (Figure 1B). These distributions are defined as conditional probability density distributions where P(δ_xyl|β,χ) represents the range of possible δ_xyl values generated by the SWIFT model (hereafter “Synthetic δ_xyl”), given a specific β and uncertainty in χ. We then vary the parameter β, generating new distributions associated with each considered β-value, P(δ_xyl|β,χ), until we find the distribution that maximizes the likelihood of observing the field samples C (Figure 1C). This maximum likelihood estimate of β (hereafter indicated as ) is then assumed to be the best approximation of β_true. The distribution of each biophysical variable in χ can be based on prior measurements of the studied system or set as uninformative uniform distributions when no prior knowledge is available. A schematic workflow of this Inverse SWIFT approach is provided in Figure 1.

Likelihood and Model Optimization

The inversion procedure starts by numerically generating a vector of paired values (see Equation S1) for a given value of β, with other parameters drawn by q Monte-Carlo simulations from the user assigned or measured distributions of each biophysical variable χ. Here, we set q to 250, and the distributions of χ are given in Supplementary Table 2. The conditional density probability distributions P(δ_xyl|β,χ) are computed using a bi-variate kernel density estimator (i.e., the kde function of the “ks” R-package, Duong, 2007). The likelihood of observing C, the paired δ_xyl values from field data of k samples (j = 1, 2, …, k), is then defined as:

The β of the P(δ_xyl|β,χ) which minimizes the sum of the negative log-likelihood function, given the observed C, is then considered as the best estimate of β_true, i.e., .

The search of β values is restricted to the range 0.905–0.995, according to the global analysis in Jackson et al. (1996). A one-dimensional general-purpose optimization method was used to find minima for Equation 2 (“brent” method in the “stats” package optim function, R Core Team, 2017).

Bias Evaluation in the Inversion Procedure

To quantify how the three distinct parameter sets defined earlier–physical, biological, and sampling (Box 1)–influence the likelihood, bias, and power, we generated sets of synthetic δ_xyl data (C_SYN) with known values of β (β_true and χ_true; β_true set at 0.966. The selected value is representative for temperate deciduous forest rooting profiles after Jackson et al. (1996; see Table 1 and Supplementary Table 2) and then inversely estimated and associated likelihood profiles. During this procedure, the following four scenarios of increasing variable restriction of χ are considered and represent different levels of prior knowledge on the parameter set χ.

Scenario A: No variable range restrictions. This scenario assumes no prior knowledge of the system, except for δ_Soil and soil water potential (Ψ_S) profiles with soil depth. This corresponds to the most common study conditions (Rothfuss and Javaux, 2017). Ideally, well-characterized δ_Soil-profiles from homogeneous soils yield the best results but in natural settings, soil heterogeneity can lead to high spatial variability which causes large random sampling errors. Therefore, we start from clearly defined empirical δ¹⁸O_S and Ψ_S profiles, hereafter the “true profiles” (illustrated by those obtained by Meißner et al. (2012)) and sample more uncertain “observed” soils profiles (using ± 3 standard deviation from the true δ¹⁸O_S and Ψ_S, profiles see functions Supplementary Table 2)—hereafter “heterogeneous profiles.” As we assume equilibrium conditions δ²H_S profiles are deduced from δ¹⁸O_S using the local meteoric water line (LMWL) (for details see Supplementary Appendix B).

Scenario B: Variable range restriction of the soil heterogeneity. Here the Ψ_S and δ_Soil-profiles are assumed to be characterized with higher precision. The input parameterization now considers narrow variance ranges, i.e., mean ± 1 standard deviation of the Ψ_S and δ¹⁸O_S true profiles. Yet again, δ²H_S profiles are calculated from δ¹⁸O_S using the LMWL.

Scenario C: Variable range restriction by sampling strategy. Restricting sampling of δ_xyl–values to periods that correspond to maximum RWU activity may decrease bias (see De Deurwaerder et al., 2020). In this scenario, we assumed that the sampling strategy was optimized in timing (t) and the height of sampling (hos) targeting representative δ_xyl values representative for peak RWU. Specifically, the height of sampling is set at 1.3 m, which corresponds to the general practice of sampling trees at breast height. Subsequently, we define the sampling time by the moment the δ_xyl–values that correspond to the plant’s peak water uptake of the plant passes the 1.3 m sampling height, which depends on the plant’s sap flow velocity.

Scenario D: Variable range restriction of biophysical plant traits. Knowledge of natural variance in plant-specific input variables can be used to restrict the model. In practice this can be done via direct in situ measurement or through literature information. In this scenario, we consider the sapwood area (A_SAPWOOD), the lumen fraction (LF), the effective root radial conductivity (k_R) and the instantaneous sap flow (SF) known to a much better degree allowing restriction of their range and distribution (provided in Table 1 and Supplementary Table 2).

Bias in the was calculated as . We calculated the bias for different sample sizes (C_SYN with 5, 25 and 50 samples) and all scenarios. Per scenario and sample size, we randomly assign aβ_true, inversely estimate and calculate bias for 500 independent simulations per scenario (with q = 250). The latter reveals which combination of sample size and set of variable restrictions (physical, biological, or sampling) yields the largest considerable estimation accuracy improvement.

Power Analysis

A power analysis quantifies the ability to distinguish between plant groups with different relative A_R–profiles (as determined by β). Here we generate two sets of synthetic δ_xyl values which correspond to distinct plant groups which have similar χ, but differ in β. By inverse modeling, we computed the corresponding and via the inverse model approach as it would be done in actual study conditions. The power analysis consists of two parts. First, we quantified the minimal detectable difference (d), being the smallest statistical detectable difference between groups for each scenario. Here, d is the difference in and where the mean of one conditional density probability distributions P(δ_xyl|β,χ) is outside the 95% quantile of the other. Hence, we generated P() and P() for each scenario as described above (see section “Likelihood and Model Optimization”). Secondly, we calculated how often a significant difference would be detected for a different combination of β values under each scenario. We maintained the standard power level of 0.80 as a validation level for different sample sizes (i.e., 5, 25, and 50).

Case Study: Estimation of the Generic Rooting Depths for Trees and Lianas in French Guiana

In the case study, we examine two growth forms, lianas and trees, that strongly differ in traits that could bias RWU depth estimation, i.e., hydraulic properties and sap flow dynamics (Chen et al., 2015). We also evaluate differences in sampling strategy where a standard approach is compared to a setup where Ψ_S profiles were measured in Laussat, French Guiana, in 2017 (Supplementary Figures 3, 4). The two setups allow us to quantify the impact of different degrees of parameter restriction in the inverse model procedure.

Sampling Strategy Field Data

Setup A applies a standard setup that ignores soil properties, e.g., Ψ_S profile, and plant physiological processes that increase variance in δ_xyl. The latter is similar to the sampling strategy applied in De Deurwaerder et al. (2018). This standard method ignores uncertainty in the biophysical variables and uncertainty introduced by sampling. For instance, stem cores were taken at breast height for trees, while for lianas, sampling was done at various heights, which depended on branch accessibility for the climber. Sampling at different heights requires correction for the expected lag in transport (see Box 1), and not correcting for sampling height can lead to underestimation of uncertainty (De Deurwaerder et al., 2020). Here, insights in sap flow velocities and related biophysical variables (i.e., lumen area and root radial conductivity) would govern insights in daily variance in plant water potentials. The latter drives RWU dynamics, hence the incoming mixture of isotope compositions of tapped soil water sources. Such sap flow measurements would also support the characterization of the transportation lag essential for correctly matching δ_xyl with the driving abiotic conditions at the time of uptake. Hence, we expect that ignoring unmeasured biophysical variables and the sampling design can lead to an underestimation of the error in mean δ_xyl compared to using the inverse SWIFT method.

Setup B differs from A in that representative Ψ_S profiles were obtained from soil water potential sensors installed at the Paracou field station (French Guiana, period 15/09-15/10 2017, 3 setups of MPS-6 dielectric water potential sensors, Decagon Devices, Inc. Washington, United States). Given its similarities in edaphic and environmental conditions, the in situ Ψ_S monitored in Paracou is considered representative for the Laussat study site. Pooling all the data per monitoring depth (i.e., 15, 30, 45, 60, and 90 cm) provided Ψ_S averages and variance, allowing the construction of a representative Ψ_S profile for inverse SWIFT.

For both setups A and B, we estimated the uncertainty in mean δ_xyl values, tested whether significant differences were observed between lianas and trees which informs RWU depth and evaluated the influence of improved monitoring to restrict the unknown parameter space of our inverse model. In line with De Deurwaerder et al. (2018), we assume more inter- than intra growth form differences in rooting distributions. All samples were therefore clustered according to their growth form, and model parameterization was guided by growth form specific empirical data from literature. Further details on the study site, sampling strategy and extraction protocols are provided in Supplementary Appendix C.

Applying the Inverse Model

In both case study setups, we consider a moderately constrained version where various biophysical SWIFT input variables are obtained by reasoned assumptions from literature and measurements collected under similar conditions (Supplementary Table 3). In Supplementary Appendices B–D, we supply descriptions of the dual-isotope plots (Supplementary Figures 3, 4), applied data collection and processing which account for the observed δ²H offset (after Barbeta et al., 2019), as well as detailed information concerning datasets used for inverse SWIFT parameterization of both setups (Supplementary Table 3). This case study is restricted to clay plots as no representative Ψ_S data is available for sand plots needed to enable qualitative assessment of β. The lack of a Ψ_S profile obscures the link between absorbing root surfaces distribution and the water uptake activity and rates per soil layer, hence imposing a bias in which we are unable to quantify. Finally, the inverse SWIFT approach was performed for 10 independent iterations to quantify bias, where the average of all iterations represents the generic of the studied liana and tree communities.

Results

Model Simulation With Synthetic Field Data

The minima of log-likelihood profiles for each simulation showed a close to β_true. Robust and unbiased will require some restrictions in the variable ranges and measurement uncertainty. In most cases, simulations show that log-likelihood curves tend to be flatter when little restrictions were applied (Figures 2, 3 and Supplementary Figure 2), implying significant uncertainty. The log-likelihood curves were generally steeper when soil heterogeneity (Sc. B) and an optimized sampling strategy (Sc. C) were considered. Interestingly, an increase in sample size had only a moderate effect on decreasing uncertainty (Figure 3) compared to applying other restrictions (Figures 2, 3 and Supplementary Figure 2), indicating that effort in reducing uncertainty in biophysical variables should be a priority. Bias was greatest with no variable range restrictions (scenario A), resulting in underestimation compared to β_true (Figure 3), since the generated P(δ_xyl|β,χ) were skewed to more negative signatures (Figure 4B). The peak of P(δ_xyl|β,χ) narrows with increased scenario restrictions resulting in an improved ability to distinguish different datasets (Figure 4). Restriction of the soil heterogeneity reduced the width of P(δ_xyl|β,χ), albeit a distinct tail toward more depleted isotope compositions remained (Figure 4B). An optimized sampling strategy overcame this skewness (Figure 4C) and hence provided an improved which was no longer biased toward overestimation. As expected, the greatest restriction of the biophysical plant variables (Sc. D) yielded the lowest bias, although improvements from scenario C were modest (Figures 2–4).

FIGURE 2

FIGURE 3

FIGURE 4

The power analysis showed that the minimal detectable difference in β-values increased as plants became shallower rooted (Figure 5, see example in panel C), allocating most of their absorbing root surface in the upper soil layers (i.e., when β of the focal plant is lower). A larger difference in β, or more variable range restrictions, will be needed when studying shallow-rooted plants. A significant difference in the average δ_xyl can be detected earlier when plants are more deeply rooted (larger β). In all cases, increased sample size resulted in additional power, but the greatest improvement was obtained by restricting the parameter space with prior knowledge, measurements, or study design (Figure 5).

FIGURE 5

Practical Case Study

We observed a shallower shape of the absorbing root surfaces distribution, i.e., smaller , for lianas (0.657, i.e., half of A_R in the upper 2 cm soil layer) than for their co-occurring trees (0.954, i.e., half of A_R in the upper 15 cm soil layer) (Figure 6; parameterization Supplementary Table 3). However, as setup A ignored all biophysical parameters, uncertainty in the estimates is much larger and showed a non-robust difference between lianas and trees (Figure 6A and Table 2). This considerable uncertainty resulted from the poor characterization of Ψ_S profile. Applying inverse SWIFT for scenario B, with field measurements of the Ψ_S, resulted in a much more conspicuously difference in mean δ²H for trees and lianas and a substantial reduction in uncertainty, i.e., an uncertainty range improvement of ∼ 4.0 (Figure 6 and Table 2). The latter highlights the uncertainty underestimation by De Deurwaerder et al. (2018), which used a standard approach due to unmeasured biophysical parameters.

FIGURE 6

TABLE 2

The standard error confidence intervals (i.e., 2.5 and 97.5 percentiles) and corresponding mean (±1SD) of inverse SWIFT simulated conditional density probability distributions, i.e., P(), of xylem water isotope composition of lianas and trees for Laussat, French Guiana.

Setups differ in considered restriction in soil water potential gradients (Ψ_S). Setup A: ignores restriction in Ψ_S. Setup B: improved characterization of Ψ_S. Parameterization of the inverse SWIFT procedure is provided in Supplementary Table 3. Significant (*) and non-significant (ns) differences are indicated.

Discussion

This study introduces a parametric method to estimate A_R with stable isotope data. The main benefit of the inverse SWIFT approach is that it provides a more realistic quantification of uncertainty, as well as improved accuracy (Figure 3). Simulations suggest that will likely be systematically overestimated and uncertainty considerably underestimated when ignoring field conditions. Both uncertainty and estimation bias can be significantly reduced by (1) improved characterization of soil heterogeneity (i.e., by accurate characterization of Ψ_S andδ_Soil) in combination with (2) optimized sampling that accounts for RWU and sap flow dynamics (De Deurwaerder et al., 2020). The former implies a study setup that monitors δ_Soil and Ψ_S in different soil layers and locations, and our simulation suggest that this should be prioritized above increasing the number of δ_xyl samples. The latter involves the application of a study design where sampling targets the δ_xyl corresponding to peak RWU, which results in a more pronounced V-shaped log-likelihood curve (Figure 2), i.e., less skewness inP(δ_xyl|β,χ) and hence far less uncertainty.

Case Study Findings

De Deurwaerder et al. (2018) reported significantly enriched δ_xyl for lianas compared to co-occurring trees during the dry season in Paracou (French Guiana) which suggests shallower root systems for lianas (as also shown elsewhere: Johnson et al., 2013; Carvalho et al., 2016; Smith-Martin et al., 2019, 2020). However, De Deurwaerder et al. (2018) approach ignored soil properties and many plant physiological processes that increase variance in δ_xyl. As our case study for Laussat shows, the lack of relevant biophysical information results in underestimating uncertainty in the mean δ_xyl. The latter implies that the findings of De Deurwaerder et al. (2018) can be explained by factors other than rooting depth, and should in hindsight have been interpreted with more caution than initially reported. Next, we applied an improved sampling setup in Laussat with a better representation of Ψ_S, which resulted in a strong drop in uncertainty and while still suggesting that a shallower absorbing root surface distribution for lianas is required to explain the differences in δ_xyl at least when only considering the confounders included in the current model (see “Recommendations and Future Directions” below). The results of these case study are also in line with our power analysis (Figure 5), which show that better quantification of Ψ_S should yield an improved ability to detect robust differences between these two growth forms. This highlights the importance of optimizing data collection and sampling strategy.

Recommendations and Future Directions

De Deurwaerder et al. (2020) showed that many biophysical variables could contribute to the intra-individual variance in δ_xyl. In the present study, we discussed how a power-analysis using mechanistic plant hydrological models could help optimize study designs and help restrict confounding parameters by identifying the most important biophysical variables to monitor. The latter could be invaluable to optimize sample sizes to maximize the efficient use of labor, resources, and time. Our simulations and analysis suggest that monitoring of soil heterogeneity (i.e., Ψ_S, δ¹⁸O_S, and δ²H_S profiles) and sap flow dynamics contribute to increased power in the detection of differences between plants in their distribution of absorbing root surfaces (A_R), especially when targeted sample sizes are small.

The use of stable water isotopes offers a scalable, time and labor efficient alternative for root excavation. When this is combined with models such as inverse SWIFT, we show that the A_R (as defined by β) can be assessed indirectly with high accuracy and power. This technique is not only unique in its ability to simultaneously assess A_R and RWU; but its less intrusive nature also supports repetitive sampling to study temporal dynamics. However, intra-individual variance in δ_xyl may be impacted by physiological plant processes or soil properties currently not considered. The robustness of the inverse approaches such as the one used here might therefore benefit from further improvements. The latter will require applying both (i) a more realistic modeling and improved theory; and (ii) more experimental and empirical work that monitors the impact of relevant physiological plant processes or soil properties on variance in δ_xyl. Essential considerations include temporal and spatial soil dynamics, fractionation at the root level, and storage tissue and phloem enrichment (see also De Deurwaerder et al., 2020).

Inverse SWIFT provides a robust tool to estimate β for plants which A_R approximates a power-law distribution. The latter is a basic representation of root systems in the current SWIFT model. A promising starting point for improvement would be the representation of roots to include more details as in models such as R-SWMS (Javaux et al., 2008) or SPACSYS (Wu et al., 2007). Such detail may be required to account for temporal and spatial soil and root dynamics properly, and in extension their impact on δ_xyl. Moreover, such approaches would support an improved representation of the flow path length within the rooting system allowing a more realistic propagation of isotopic composition from soil to the stem base (Seeger and Weiler, 2021).

The implementation of mycorrhizal colonization as an integral component of the water uptake process may present an additional perspective for future model improvement. While their direct contribution to RWU remains unclear (Ruth et al., 2011), various studies have highlighted an increased root hydraulic conductivity because of mycorrhizal colonization (Gianinazzi-Pearson and Gianinazzi, 1983; Augé, 2001; Aroca et al., 2007). Hence, as long as mycorrhizal colonization is relatively uniformly distributed over the rooting system, the impact of mycorrhizae on the inverse SWIFT assessment can be resolved indirectly by altering k_R. However, inverse SWIFT may become prone to biased assessment when colonization is not uniform and the proportional contribution of water influx via mycorrhizae is substantial. Indeed, future endeavors to implement a more dynamic A_R and which can account for mycorrhizal colonization are encouraged.

Besides, many unknowns hamper model development. For instance, the extent to which fractionation during root water uptake or within the plant arises needs to be quantified before implementation. Here, root membrane (Lin and Sternberg, 1993; Zhao et al., 2016; Vargas et al., 2017) and mycorrhizal fractionation (Poca et al., 2019) present pathways that may introduce additional uncertainty. Also, stable water isotopes studies generally assume no alteration in δ_xyl once contained within the plant’s conduit system. We encourage evaluation of this assumption, as δ_xyl enrichment via storage tissue or phloem is not unreasonable (Barbeta et al., 2020; Knighton et al., 2020), which would pose additional model interpretation complexities.

Conclusion

Root excavation can only provide a snapshot, a one-time-only measure due to its destructive nature. A stable water isotopes approach is advantageous for upscaling root attributes in space and time. Stable water isotope approaches can be applied over a wide range of edaphic and environmental conditions (Zhao et al., 2016). New developments in high temporal resolution monitoring of xylem water isotope composition would enable quantification of absorbing root surfaces distributions over time. This all can provide invaluable insights for understanding drought strategy and water competition among different plant species. However, this exciting prospect is only possible when techniques are unbiased under different edaphic or physiological conditions between plant species and sites. Our work here highlights a key role for mechanistic inverse plant model to help guide the research agenda for the critical zone and water stable isotope work.

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