Limitations of temporally linearized soil–water flux gradients in estimating root water uptake

In a recent article, Rickard et al. (2025) proposed a novel approach to estimate root water uptake in field-grown plants by integrating soil moisture dynamics with root hydraulic traits. Their effort to bridge soil physical processes and plant hydraulic functioning represents a timely and important contribution to plant ecohydrology. Burks & Tumber-Dávila (2025) commented that this is a ‘promising framework for scaling spatiotemporal root water uptake estimations’, providing a simple and scalable approach to track root hydraulic adjustments under fluctuating soil moisture conditions. We fully acknowledge the innovation of using a soil–water mass balance framework to infer root water uptake in situ. This method offers a promising alternative to traditional tracer-based approaches and demonstrates how temporal changes in soil–water content can be quantitatively linked to root physiological responses. However, upon reviewing their derivation of root water uptake from soil–water balance equations, we identified a potentially important inconsistency in the approximation of spatial water flux gradients. Specifically, Eqn 3 in their paper appears to involve a conceptual inconsistency, as it approximates the spatial derivative of soil–water flux (∂Q/∂z) from its temporal variations. This implicitly assumes that ∂Q/∂z changes linearly with time at a given depth, an assumption that lacks clear physical justification under real soil conditions. Since this approximation directly informs the estimation of root water uptake (their Eqn 4) and further affects the calculation of root water potential and radial permeability (their Eqns 7, 8), any systematic error in ∂Q/∂z could bias the entire hydraulic inference framework. In this Correspondence article, we aim to clarify this issue, demonstrate its potential impact using numerical simulations, and discuss the implications for interpreting root water uptake from soil–water content time series. Rickard et al. (2025) derived the daytime root water uptake density (denoted as S) from the soil–water mass balance ∂ Θ ∂ t = − ∂ q ∂ z − S $$ \left(\frac{\partial \varTheta }{\partial t}=-\frac{\partial q}{\partial z}-S\right) $$ , under the assumption that plant transpiration occurs only during the daytime and is negligible at night (Fig. 1). The derivation of Eqn 3 relies on the key assumption that the vertical water flux profile (∂Q/∂z) changes linearly over time (Eqn 2), implying temporal smoothness and continuity between the two consecutive nights and the intervening daytime period. The assumption for approximating ∂Q2/∂z (Eqn 2) may not hold in real field conditions. Soil–water profiles are often subject to abrupt changes caused by various boundary fluxes such as intense precipitation and evaporation, making the temporal variation of ∂Q/∂z highly nonlinear. As a result, the linear interpolation in Eqn 2 may introduce significant errors, especially during dynamic hydrological events. In Case 1, the MARE of Eqn 2 is 0.04 during the early non-steady evaporation phase (Fig. 2a). Once a steady-state evaporation regime was established, the MARE is drastically reduced to 0.001 (c. 40-fold reduction, Fig. 2a). This validates our hypothesis that the temporal linearization of ∂Q/∂z is only valid under steady-state conditions. By contrast, under field conditions where precipitation varies dynamically, the MARE of Eqn 2 in estimating ∂Q/∂z reaches 4.45. These rapid atmospheric variations induce nonlinear changes in soil–water fluxes, confirming that the linear approximating ∂Q/∂z using Eqn 2 can introduce substantial errors when soil–water dynamics deviate from steady-state. Additionally, error peaks coincide with precipitation events, indicating that Eqn 2 estimates are highly sensitive to rapid soil–water changes. This is expected, as rainfall amplifies temporal variation and violates the steady-state assumption of Eqn 2. Overall, while Eqn 2 may be suitable under controlled or steady-state conditions, it is inappropriate for real-world, nonstationary soil–plant–atmosphere systems with inherently nonlinear dynamics. Theoretically, transpiration rates estimated using Eqn 3 should fall between Tupper and Tlower (Eqns 5, 6). However, Rickard et al. (2025) frequently reported values outside these bounds, with 38.5% in grassland and 36.3% in wheat plots exceeding the physically plausible range, typically after rainfall events (Fig. 3). This strongly highlights substantial errors introduced by Eqn 2 under non-steady-state conditions, consistent with our simulations. Notably, as these bounds are already conservative, the actual proportion of implausible estimates may be even higher. In most cases, the vertical profile of root water uptake (S) is not known. Therefore, a nonparametric representation is preferred, as it does not assume any fixed functional form (shape free). This approach provides greater flexibility to capture complex or multimodal uptake patterns that cannot be adequately represented by simple analytical functions. By contrast, parametric representation assumes a predefined mathematical shape (such as an exponential decay), which can be applied when the actual uptake profile is relatively simple. For example, this is the case when root distribution is shallow and concentrated near the top-soil layer and soil–water availability is not strongly limiting. Eqn 8 also enables coupling with Bayesian inference, integrating the prior distribution of the sink term (e.g. parametric or nonparametric forms) with observed soil–water changes to infer the most likely root water uptake profile. Such approaches are conceptually similar to continuous isotope mixing models (Fu et al., 2024) but further incorporate soil–water mass balance constraints. We believe this offers a more rigorous and generalizable framework for quantifying in situ root water uptake, respecting soil–water physics and allowing probabilistic uncertainty quantification. In summary, while we fully acknowledge the scientific value and innovation of Rickard et al. (2025), we believe clarifying the mathematical foundations of their approach is warranted. Ensuring consistency between physical meaning, method limitations, and numerical approximations is essential for robust root water uptake estimation. We offer these remarks in the spirit of constructive dialogue and hope they support further refinement of integrated ecohydrological models and encourage broader collaborations to advance quantitative understanding of root–soil–water interactions. This research was supported by the National Key R & D Program of China (2022YFD1500100), the Outstanding Youth Fund of Heilongjiang Province (JQ2024D002), China Agriculture Research System of MOF and MARA (CARS04), National Natural Science Foundation of China (42507413). Special thanks to the Electronic Rothamsted Archive (e-RA) for providing the daily meteorological data of the Rothamsted site in Fig. 3. None declared. HF, BS and WZ designed the research; HF performed numerical simulation, analysis, and visualization and completed the initial draft; all authors participated in manuscript writing and editing. The MOIST source code is publicly available in Fu et al. (2025) (doi: 10.1029/2024WR037068). Field data used in this study are publicly available from Rickard et al. (2025) (doi: 10.1111/nph.70013) and Stumpp et al. (2012) (doi: 10.2136/vzj2011.0075). The New Phytologist Foundation remains neutral with regard to jurisdictional claims in maps and in any institutional affiliations.