Process-based models (PBMs) provide a mechanistic foundation for simulating complex genotype, environment, and management interactions across multiple scales. Integrating PBMs with agent-based models (ABMs), machine learning (ML), and advanced model coupling strategies (sequential, loose, tight, and framework-based) enables more comprehensive representations of agricultural systems. ABMs capture the adaptive behaviours of individual farmers, while ML techniques efficiently approximate nonlinear physiological processes or act as surrogates for computationally expensive submodules and reveal data-driven patterns, collectively enhancing the simulation of G × E × M interactions under variable climate scenarios. Digital twins (DTs), defined as systems that dynamically synchronize virtual models with real-time sensor data, extend coupled PBM–ABM–ML systems by enabling bidirectional feedback between computational models and farm operations. However, the implementation of DTs remains constrained by challenges such as data integration across heterogeneous sources, computational scalability, and semantic/technical interoperability making them appropriate only where continuous decision support and real-time feedback outweigh complexity and cost. This review evaluates the function of PBMs as the mechanistic core of DT architectures, surveys model integration techniques, and outlines the IT infrastructure required for operationalization. We conclude that digital twins are best deployed when real-time feedback is essential, whereas PBM–ABM–ML couplings suffice for research and policy applications requiring long-term scenario analysis.

A plant's development is strongly linked to the water and carbon (C) flows in the soil-plant-atmosphere continuum. Ongoing climate shifts will alter the water and C cycles and affect plant phenotypes. Comprehensive models that simulate mechanistically and dynamically the feedback loops between water and C fluxes in the soil-plant system are useful tools to evaluate the sustainability of genotype-environment-management combinations that do not yet exist. In this study, we present the equations and implementation of a rhizosphere-soil model within the CPlantBox framework, a functional-structural plant model that represents plant processes and plant-soil interactions. The multi-scale plant-rhizosphere-soil coupling scheme previously used for CPlantBox was likewise updated, among others to increase the accuracy and stability of the model outputs. The model was implemented to simulate the effect of dry spells occurring at different plant development stages, and for different soil kinetic parameterisations of microbial dynamics in soil. We could observe diverging results according to the date of occurrence of the dry spells and soil parameterisations. For instance, earlier dry spells (from 11th to the 18th day of growth) led to a lower cumulative plant C release, while later dry spells (from 18th to the 25th day of growth) led to higher C input to the soil. For more reactive microbial communities (higher maximum C uptake rate and (de)activation rates), this higher C input caused a strong increase in CO2 emissions. For the same weather scenario, we observed lower microbial CO2 emissions with less reactive communities. This model can be used to gain insight into C and water flows at the plant scale, and the influence of soil-plant interactions on C cycling in soils.

To assess the impact of agricultural practices on water and carbon cycles within specific Genome-Environment-Management combinations, understanding the interactions across the Soil-Plant-Atmosphere continuum (SPAC) is crucial.Indeed, soil water conditions influence carbon concentration and transport, impacting soil carbon physical and biochemical reactions.The soil water and carbon status affect, in turn, the plant water and carbon dynamics directly via the plant-to-soil water or carbon gradient, and indirectly via plant water status, influencing its inner balance of water (uptake, transpiration and flow) and carbon (assimilation, usage for maintenance and growth, storage, respiration, rhizodeposition, and transport).Reciprocally, plant water and carbon balances affect the soil carbon cycle in the short term through root water uptake and rhizodeposition. Those rhizodeposits are, for the most part, made of exudates and mucilage. Root exudates are low molecular weight organic compounds that are mainly passively diffused, while mucilage is a fluid made of polymers with high molecular weight created from starch via an active process.Modelling plant and soil water and carbon processes, along with their interactions, can help to understand better and represent the effects of the underlying feedback loops. In this study, we therefore coupled the Functional Structural Plant Model (FSPM) CPlantBox with the rhizosphere model TraiRhizo, implemented using the porous medium flow and transport solver DuMux.The overall coupled model and multiscale framework includes a module of 3D plant architecture development, and modules to represent flow and transport within the plant, the soil and the perirhizal zone around each root segment. Flows between compartments are solved implicitly via fixed-point iteration, using parallel computation for both the 3D soil and rhizosphere models.We present a case study in which we simulated the growth of a C3 monocot and observed how changes in soil water content, due to root water uptake, influenced dissolved carbon concentration and (de)activation of the soil microbial communities during a dry spell.In the future, the model will be applied to assess the impact of small dry spells at various stages of plant development against a baseline scenario. In time, this model could support plant breeding efforts to find root traits that aim for more drought-resistant plants in specific pedoclimatic environments.

The subsoil, commonly defined as the soil beneath the tilled or formerly tilled soil horizon, contains large amounts of nutrients and water. Large fractions of these subsoil resources are not readily available to agricultural crops due to compacted layers of high bulk density. Although there are conventional methods for loosening compacted subsoils (e.g., mechanical subsoiling and deep ploughing), their effects are often quickly reversed or can even be harmful to the soil structure. Eventually, the brief enhancement in subsoil access for crops is often insufficient to justify the considerable expenses associated with the methods. To facilitate a more efficient use of subsoil resources, the Soil³ project for sustainable subsoil melioration derived a novel approach, which is carried out in a single crossing of the field. First, the top soil of a 30 cm wide strip is excavated and deposited on the soil surface beside the strip, creating a furrow. The subsoil in this furrow (30-60 cm depth) is then loosened and intermixed with organic material (e.g., compost). After mixing, the excavated topsoil is lead back into the furrow, thus closing it again. The method therefore preserves the natural soil structure by not mixing the top and subsoil substrates, while the loosened subsoil structure is stabilized by incorporating organic material. Additionally, the operating costs are kept reasonable by only loosening the soil in a strip-wise manner.Here, we use and extend the 3D functional-structural plant model CPlantBox to investigate the impact of the Soil³ method on root growth. On the soil side, we employ pedo-transfer functions to model the evolution of soil bulk density (soil setting) and the resulting changes in soil hydraulic properties in time. The pedo-transfer functions are parameterized based on data of the Soil³ field trials and are solved for different soil depths, as well as for the soil layers on and beside the melioration strips. In our model, we account for the time-dependent changes in soil hydraulic properties of all soil layers by implementing the usage of variable Van-Genuchten parameter sets within a single simulation run. Based on the parameterized soil domain, we simulate root growth and root water uptake from the different soil layers. Experimental data is used to parameterize general root growth parameters (e.g., root length density, planting density, transpiration). The explicit 3D root system architecture, however, is a result of the model, and its growth is modeled as a function of bulk density, water content and penetration resistance. By performing virtual replications of the field trials over multiple consecutive years, we can evaluate the impact and longevity of the subsoil melioration on root growth and its underlying processes.

Root water uptake strongly affects soil water balance and plant development. It can be described by mechanistic models of soil–root hydraulics based on soil water content, soil and root hydraulic properties, and the dynamic development of the root architecture. Recently, novel upscaling methods have emerged, which enable the application of detailed mechanistic models on a larger scale, particularly for land surface and crop models, by using mathematical upscaling. In this study, we explore the underlying assumptions and the mathematical fundamentals of different upscaling approaches. Our analysis rigorously investigates the errors introduced in each step during the transition from fine-scale mechanistic models, which considers the nonlinear perirhizal resistance around each root, to more macroscopic representations. Upscaling steps simplify the representation of the root architecture, the perirhizal geometry, and the soil spatial dimension and thus introduces errors compared to the full complex 3D simulations. In order to investigate the extent of these errors, we perform simulation case studies, spring barley as a representative non-row crop and maize as a representative row crop, using three different soils. We show that the error introduced by the upscaling steps strongly differs, depending on root architecture and soil type. Furthermore, we identify the individual steps and assumptions that lead to the most important losses in accuracy. An analysis of the trade-off between model complexity and accuracy provides valuable guidance for selecting the most suitable approach for specific applications.

Abstract. A plant's development is strongly linked to the water and carbon (C) flows in the soil-plant-atmosphere continuum. Ongoing climate shifts will alter the water and C cycles and affect plant phenotypes. Comprehensive models that simulate mechanistically and dynamically the feedback loops between water and C fluxes in the soil-plant system are useful tools to evaluate the sustainability of genotype-environment-management combinations that do not yet exist. In this study, we present the equations and implementation of a rhizosphere-soil model within the CPlantBox framework, a functional-structural plant model that represents plant processes and plant-soil interactions. The multi-scale plant-rhizosphere-soil coupling scheme previously used for CPlantBox was likewise updated, among others to include an implicit time-stepping. The model was implemented to simulate the effect of dry spells occurring at different plant development stages, and for different soil biokinetic parametrisations of microbial dynamics in soil. We could observe diverging results according to the date of occurrence of the dry spells and soil parametrisations. For instance, an earlier dry spell led to a lower cumulative plant C release, while later dry spells led to higher C input to the soil. For more reactive microbial communities, this higher C input caused a strong increase in CO2 emissions, while, for the same weather scenario, we observed a lasting stabilisation of soil C with less reactive communities. This model can be used to gain insight into C and water flows at the plant scale, and the influence of soil-plant interactions on C cycling in soil.

Root water uptake strongly affects soil water balance and plant development. It can be described by mechanistic models of soil-root hydraulics based on soil water content, soil and root hydraulic properties, and the dynamic development of the root architecture. Recently, novel upscaling methods have emerged (Vanderborght et al. 2023, 2021), which enable the application of detailed mechanistic models on a larger scale, particularly for land surface and crop models, by using mathematical upscaling.In this study, we explore the underlying assumptions and the mathematical fundamentals of the upscaling approach. Our analysis rigorously investigates the errors introduced in each step during the transition from fine-scale mechanistic models, which considers the nonlinear perirhizal resistance around each root, to more macroscopic representations. Upscaling steps simplify the representation of the root architecture, the perirhizal geometry, and the soil spatial dimension and thus introduces errors compared to the full complex 3D simulations. In order to investigate the extent of these errors, we perform simulation case studies: spring barley as a representative non-row crop and maize as a representative row crop, and using three different soils.We show that the accuracy of the upscaled modeling approach strongly differs, depending on root architecture and soil type. Furthermore, we identify the individual steps and assumptions that lead to the most important losses in accuracy. An analysis of the trade off between model complexity and accuracy provides valuable guidance for selecting the most suitable approach for specific applications. References Vanderborght, J., Couvreur, V., Meunier, F., Schnepf, A., Vereecken, H., Bouda, M., and Javaux, M. (2021). From hydraulic root architecture models to macroscopic representations of root hydraulics in soil water flow and land surface models. Hydrology and Earth System Sciences, 25(9):4835–4860.Vanderborght, J., Leitner, D., Schnepf, A., Couvreur, V., Vereecken, H., and Javaux, M. (2023). Combining root and soil hydraulics in macroscopic representations of root water uptake. Vadose Zone Journal, e20273.

Root systems of trees are obviously much larger than those of herbaceous plants. Considering a root length of 30 km of roots below a surface area of 1m2 in a forest and considering that the root system of a single tree extends over a horizontal area of 10 m², this would mean that a root system of one tree is 300 km long. To simulate the water flow in the root system, the root system is typically discretized in 1cm long root segments and a set of flow equations is setup and solved to derive the water potential and flux in each segment of the 3D root hydraulic architecture. For a system with n root segments and n+1 nodes at which segments are connected, this results in a set of n equations that need to be solved. Solving this set of equations corresponds with inverting an n by n matrix. For the root system of a tree, the size of this matrix would be 3 107 by 3 107. The linear equation matrix is sparse and could be solved using equation solvers that do not calculate the inverse matrix. But, also these solutions might still be too expensive so that an upscaled and reduced set of equations is needed. We developed an approach to upscale flow equations in root hydraulic architectures (Vanderborght et al., 2021), which were subsequently coupled to non-linear flow equations that account for resistance to flow in the soil around root segments (Vanderborght et al. 2023). But, these upscaling approaches require an inversion of the linear equation matrix. In order to address this problem, we developed an inversion method that uses the hierarchical structure of the root network to divide the inversion into a set of smaller inversion problems that can be solved in parallel. In this presentation, we outline the principle of the inversion method and demonstrate it for large root systems of trees. ReferencesVanderborght, J., et al. (2021) From hydraulic root architecture models to macroscopic representations of root hydraulics in soil water flow and land surface models. Hydrol. Earth Syst. Sci., 25(9), 4835-4860. https://doi.org/10.5194/hess-25-4835-2021 Vanderborght, J., et al. (2023). Combining root and soil hydraulics in macroscopic representations of root water uptake. Vadose Zone Journal, n/a(n/a), e20273. https://doi.org/https://doi.org/10.1002/vzj2.20273

Plant development strongly depends on the water and nutrient uptake by the evolving root system, the carbon uptake and assimilation in the leaves, as well as the water, solute and carbon transport inside the plant. The mechanistic functional-structural plant model CPlantBox enables simulations of the dynamic plant and soil systems, and therefore the analysis of feedback loops between water and carbon fluxes as well as root-soil interface processes such as water and solute uptake or rhizodeposition. Such models are a crucial tool to evaluate the sustainability of future phenotype-environment-management combinations, as well as to enhance plant breeding efforts and to analyze the impact of future climate scenarios. Therefore, CPlantBox serves as a powerful platform for advancing sustainable agricultural management strategies .The open-source model CPlantBox has been developed over the last fifteen years starting from a pure structural root model (Leitner et al. 2010) developing to a functional-structural root architecture model (Schnepf et al. 2018), towards a more holistic functional structural plant model (Giraud et al. 2023, Zhou et al. 2020). Today, CPlantBox includes multiple functional modules describing water and carbon fluxes within the plant, including a photosynthesis model, as well as various dynamic rhizosphere modules that are described by 1D axisymmetric systems of partial differential equations (PDE) around root segment that interact with 1D, 2D or 3D macroscopic soil models. The PDEs are solved with the open-source finite volume solver DuMux (Koch et al. 2021). In this work we describe CPlantBox by state-of-the art examples from various research projects specifically focusing on its functional modules, and presenting its modelling framework which facilitates further model development. ReferencesGiraud M., Gall S.L., Harings M., Javaux M., Leitner D., Meunier F., Rothfuss Y., van Dusschoten D., Vanderborght J., Vereecken H., Lobet G., and Schnepf A. (2023). CPlantBox: a fully coupled modelling platform for the water and carbon fluxes in the soil–plant–atmosphere continuum. in silico Plants 5 (2), diad009Koch T., Gläser D., Weishaupt K., Ackermann S., Beck M., Becker B., ... & Flemisch B. (2021). DuMux 3–an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling. Computers & Mathematics with Applications, 81, 423-443.Leitner D., Klepsch S., Bodner G, and Schnepf A. (2010). A dynamic root system growth model based on L-Systems: Tropisms and coupling to nutrient uptake from soil. Plant and soil 332: 177-192.Schnepf A., Leitner D., Landl M., Lobet G., Mai T.H., Morandage S., Sheng C., Zörner M., Vanderborght J., Vereecken H. (2018). CRootBox: a structural–functional modelling framework for root systems. Annals of botany 121 (5), 1033-1053.Zhou X.R., Schnepf A., Vanderborght J., Leitner D., Lacointe A., Vereecken H., and Lobet G. (2020) CPlantBox, a whole-plant modelling framework for the simulation of water-and carbon-related processes. in silico Plants 2 (1), diaa001.

The subsoil, commonly defined as the soil beneath the tilled or formerly tilled soil horizon, contains large amounts of nutrients and water. Large fractions of these subsoil resources are not readily available to agricultural crops due to compacted layers of high bulk density. Although there are conventional methods for loosening compacted subsoils (e.g., mechanical subsoiling and deep ploughing), their effects are often quickly reversed or can even be harmful to the soil structure. Eventually, the brief enhancement in subsoil access for crops is often insufficient to justify the considerable expenses associated with the methods. To facilitate a more efficient use of subsoil resources, the Soil³ project for sustainable subsoil melioration derived a novel  approach, which is carried out in a single crossing of the field. First, the top soil of a 30 cm wide strip is excavated and deposited on the soil surface beside the strip, creating a furrow. The subsoil in this furrow (30-60 cm depth) is then loosened and intermixed with organic material (e.g., compost). After mixing, the excavated topsoil is lead back into the furrow, thus closing it again. The method therefore preserves the natural soil structure by not mixing the top and subsoil substrates, while the loosened subsoil structure is stabilized by incorporating organic material. Additionally, the operating costs are kept reasonable by only loosening the soil in a strip-wise manner.Here, we use and extend the 3D functional-structural plant model CPlantBox to investigate the impact of the Soil³ method on root growth. On the soil side, we employ pedo-transfer functions to model the evolution of soil bulk density (soil setting) and the resulting changes in soil hydraulic properties in time. The pedo-transfer functions are parameterized based on data of the Soil³ field trials and are solved for different soil depths, as well as for the soil layers on and beside the melioration strips. In our model, we account for the time-dependent changes in soil hydraulic properties of all soil layers by implementing the usage of variable Van-Genuchten parameter sets within a single simulation run. Based on the parameterized soil domain, we simulate root growth and root water uptake from the different soil layers. Experimental data is used to parameterize general root growth parameters (e.g., root length density, planting density, transpiration). The explicit 3D root system architecture, however, is a result of the model, and its growth is modeled as a function of bulk density, water content and penetration resistance. By performing virtual replications of the field trials over multiple consecutive years, we can evaluate the impact and longevity of the subsoil melioration on root growth and its underlying processes.

Abstract Water uptake by plant roots is an important component of the soil water balance. Predicting to what extent potential transpiration from the canopy, that is, transpiration demand, can be met by supply of water from the soil through the root system is crucial to simulate the actual transpiration and assess vegetation water stress. In models that simulate the dynamics of vertical soil water content profiles as a function of water fluxes and soil water potential gradients, the root water uptake (RWU) distribution is represented by macroscopic sink terms. We present RWU functions that calculate sink terms based on a mechanistic model of water flow in the soil–root system. Based on soil–root hydraulics, we define α‐supply functions representing the maximal uptake by the root system from a certain soil depth when the root collar water potential equals the wilting point, ω‐supply factors representing the maximal supply from the entire root system, and a critical ωc factor representing the potential transpiration demand. These functions and factors are subsequently used to calculate RWU distributions directly from potential transpiration or demand and the soil water potentials. Unlike currently used approaches, which define α‐stress functions and ω factors representing ratios of actual uptake to uptake demand, the supply‐based formulations can be derived directly from soil and root hydraulic properties and can represent processes like root hydraulic redistribution and hydraulic lift.

Abstract Plant water uptake and plant and soil water status are important for the soil water balance and plant growth. They depend on atmospheric water demand and the accessibility of soil water to plant roots, which is in turn related to the hydraulic properties of the root system and the soil around root segments. We present a simulation model that describes water flow in the soil–plant system mechanistically considering both root and soil hydraulic properties. We developed an approach to upscale three‐dimensional (3D) flow in the soil toward root segments of a 3D root architecture to a model that considers one‐dimensional flow between horizontal soil layers and radial flow to root segments in that layer. The upscaled model couples upscaled linear flow equations in the root system with an analytical solution of the nonlinear radial flow equation between the soil and roots. The upscaled model avoids simplifying assumptions about root hydraulic properties and water potential drops near roots made in, respectively, soil‐ and root‐centered models. Xylem water potentials and soil–root interface potentials are explicitly simulated and show, respectively, large variations with depth and large deviations from bulk soil water potentials under dry soil conditions. Accounting for hydraulic gradients in the soil around root segments led to an earlier but slower reduction of transpiration during a drought period and a better plant water status with higher nighttime plant water potentials.

Understanding root system architecture (RSA) is essential for improving crop resilience to climate change, yet assessing root systems of woody perennials under field conditions remains a challenge. This study introduces a pipeline that combines field excavation, in situ 3-dimensional digitization, and transformation of RSA data into an interoperable format to analyze and model the growth and water uptake of grapevine rootstock genotypes. Eight root systems of each of 3 grapevine rootstock genotypes ("101-14", "SO4", and "Richter 110") were excavated and digitized 3 and 6 months after planting. We validated the precision of the digitization method, compared in situ and ex situ digitization, and assessed root loss during excavation. The digitized RSA data were converted to root system markup language (RSML) format and imported into the CPlantBox modeling framework, which we adapted to include a static initial root system and a probabilistic tropism function. We then parameterized it to simulate genotype-specific growth patterns of grapevine rootstocks and integrated root hydraulic properties to derive a standard uptake fraction (SUF) for each genotype. Results demonstrated that excavation and in situ digitization accurately reflected the spatial structure of root systems, despite some underestimation of fine root length. Our experiment revealed significant genotypic variations in RSA over time and provided new insights into genotype-specific water acquisition capabilities. Simulated RSA closely resembled the specific features of the field-grown and digitized root systems. This study provides a foundational methodology for future research aimed at utilizing RSA models to improve the sustainability and productivity of woody perennials under changing climatic conditions.

A plant’s development is strongly linked to the water and carbon flows in the soil-plant-atmosphere continuum. Expected climate shifts will alter the water and carbon cycles and will affect plant phenotypes. Comprehensive models which simulate mechanistically and dynamically the feedback loops between a plant’s three-dimensional development and the water and carbon flows are useful tools to evaluate the sustainability of genotype-environment-management combinations which do not yet exist. In this study, we present the latest version of the open-source three-dimensional Functional-Structural Plant Model CPlantBox with PiafMunch and DuMu x coupling. We simulated semi-mechanistically the development of generic C3 monocots from 10 to 25 days after sowing and undergoing an atmospheric dry spell of one week (no precipitation). We compared the results for dry spells starting on different days (day 11 or 18) and with different climates (wetter and colder against drier and warmer atmospheric and initial soil conditions). Compared with the wetter and colder climate, the dry spell with the drier and warmer climate led to a lower instantaneous water use efficiency. Moreover, the lower symplasm turgor for the drier and warmer climate limited the growth, which made the sucrose available for other processes, such as maintenance respiration. Both of these effects were stronger for the later dry spell compared with the early dry spell under the drier and warmer climate. We could thus use CPlantBox to simulate diverging emerging processes (like carbon partitioning) defining the plants’ phenotypic plasticity response to their environment.

Simulation software and results for "Phloem anatomy constraints root system architecture development: theoretical clues from in silico experiments"

Schnepf et al., (2020) defined benchmark scenarios for root growth models, soil water flow models, root water flow models, and for water flow in the coupled soil-root system. All benchmarks and corresponding reference solutions were published in the form of Jupyter Notebooks on the GitHub repository https://github.com/RSAbenchmarks/collaborative-comparison. Several groups of functional-structural model developers have joined this benchmarking activity and provided the results of their individual implementations of the different scenarios. The focus of this contribution is on water uptake from a drying soil by a static root architecture. The numerical solutions of the different participating simulators as compared to the provided reference solution. The participating simulators are CPlantBox, DuMux, R-SWMS, OpenSimRoot and SRI. They have in common that they simulate water flow in the 3D soil domain, water flow inside the root system that is represented as a mathematical tree graph, and the coupling between the two domains in form of a volumetric sink term that describes the transfer of water between the two domains. The simulators differ in the numerical schemes used for solving the water flow equations in roots and soil domains, as well as in the way the sink term is formulated, in particular in the way the possibly increased rhizosphere resistance to water flow is accounted for. The results to the water flow in soil benchmarks show how the different simulators perform against the analytical solution to a problem of infiltration into an initially dry soil, as well as a problem of evaporation from initially moist soil. All of the simulators could accurately predict the infiltration front in different soil types as well as the actual evaporation curves. The coupled problem of root water uptake by a static root architecture from an initially already dry soil posed a bigger challenge to the different simulators and revealed some diversity between the different solutions. The Benchmark with an initially rather dry soil defined a potential transpiration that immediately induced water stress of the plant. The simulators had to simulate the consequent rhizosphere drying and associated increase in rhizosphere resistance. All of the soil simulators smoothed the gradients in the rhizosphere at the soil grid size such that root water uptake was significantly overestimated unless the rhizosphere resistance was explicitly accounted for in the root water uptake model. As a result, all simulators came close to the reference solution (that itself is a numerical solution, see Schnepf et al. 2020 for details). In this study, we showed that all simulators are generally able to solve the benchmark problems but minor differences occur amongst the simulators when simulating different soil types. Benchmarking led to model improvements and helped interpret model results in a more informed way. The availability of “reference solutions“ made modellers aware of the range of validity of their numerical solution and encouraged them to improve either their numerical solution or to introduce new processes Future efforts may aim to extend the benchmarks from water flow to further processes, such as solute transport or rhizodeposition. Schnepf et al., 2020, Front. Plant Sci.

<p>To describe plant transpiration in drying soil, several models use ‘α-stress functions’, which represent the ratio of the maximal possible water uptake when the plant reaches the wilting point to the transpiration demand or potential transpiration, as a function of the soil water potential. Water potentials vary within the root zone, and the plant ‘senses’ with its root system an average root zone water potential and redistributes the uptake from drier to wetter zones in the root zone. This redistribution or root water uptake compensation is accounted for using an average stress index, ω, which is a weighted average of the local stress indices α at different depths in the root zone, and a critical stress index ω<sub>c </sub>(Jarvis, 2011; Simunek & Hopmans, 2009). When ω > ω<sub>c</sub>, root water uptake is equal to the potential root water uptake or the energy limited potential transpiration. The α-ω approach refers to a mechanistic description of water fluxes in the soil-root system but remains semi-empirical missing a direct link with soil and, especially, root hydraulic properties. In this contribution, we derive the α-ω approach starting from a mechanistic description of water flow in a hydraulic root architecture assuming that resistance to flow in the soil towards the soil-root interface can be neglected. In a second step, we include the non-linear soil resistance.</p> <p>For relatively wet soil conditions and neglecting the soil resistance, root water uptake functions can be cast in a form that is identical to the α-ω approach that was derived by Jarvis (2011), but for opposite conditions, i.e., Jarvis neglected the root resistance compared to soil resistance. Following Jarvis, the α-function should be interpreted as the ratio of the maximal possible uptake by the root system for a certain soil water potential to the maximal possible uptake by the system when the soil is fully saturated, which differs from its common interpretation. This means that the α-function is just a linear function that ranges from zero when the soil water potential is equal to the wilting point to 1 when the soil water potential is zero and that it is independent of the transpiration rate. Another outcome is that the critical stress level ω<sub>c</sub> is inverse proportional to the hydraulic conductance of the root system and is not a constant but a variable parameter that is proportional to the transpiration rate. For dry soil conditions, when soil resistance is important, we find that α and ω are non-linear functions of the soil water potential. Using α and ω functions that are derived from soil and root hydraulic properties, the uptake distributions can be calculated directly from the soil water potentials without solving a non-linear equation with iterations to derive water potentials in the plant. But, this approach is based on a simplification, which requires further testing.</p> <p>Jarvis, N. J. (2011). <em>Hydrology and Earth System Sciences, 15</em>(11), 3431-3446. doi:10.5194/hess-15-3431-2011</p> <p>Simunek, J., & Hopmans, J. W. (2009). <em>Ecological Modelling, 220</em>(4), 505-521. doi:10.1016/j.ecolmodel.2008.11.004</p>

A plant's development is strongly linked to the water and carbon flows in the soil-plant-atmosphere continuum. Expected climate shifts will alter the water and carbon cycles and will affect plant phenotypes. Comprehensive models that simulate mechanistically and dynamically the feedback loops between a plant's three-dimensional development and the water and carbon flows are useful tools to evaluate the sustainability of genotype-environment-management combinations which do not yet exist. In this study, we present the latest version of the open-source three-dimensional Functional-Structural Plant Model CPlantBox with PiafMunch and DuMu(X)coupling. This new implementation can be used to study the interactions between known or hypothetical processes at the plant scale. We simulated semi-mechanistically the development of generic C3 monocots from 10 to 25 days after sowing and undergoing an atmospheric dry spell of 1 week (no precipitation). We compared the results for dry spells starting on different days (Day 11 or 18) against a wetter and colder baseline scenario. Compared with the baseline, the dry spells led to a lower instantaneous water-use efficiency. Moreover, the temperature-induced increased enzymatic activity led to a higher maintenance respiration which diminished the amount of sucrose available for growth. Both of these effects were stronger for the later dry spell compared with the early dry spell. We could thus use CPlantBox to simulate diverging emerging processes (like carbon partitioning) defining the plants' phenotypic plasticity response to their environment. The model remains to be validated against independent observations of the soil-plant-atmosphere continuum.

Functional-structural root architecture models have evolved as tools for the design of improved agricultural management practices and for the selection of optimal root traits. In order to test their accuracy and reliability, we present the first benchmarking of root water uptake from soil using five well-established functional-structural root architecture models: DuMux, CPlantBox, R-SWMS, OpenSimRoot and SRI. The benchmark scenarios include basic tests for water flow in soil and roots as well as advanced tests for the coupled soil-root system. The reference solutions and the solutions of the different simulators are available through Jupyter Notebooks on a GitHub repository. All of the simulators were able to pass the basic tests and continued to perform well in the benchmarks for the coupled soil-plant system. For the advanced tests, we created an overview of the different ways of coupling the soil and the root domains as well as the different methods used to account for rhizosphere resistance to water flow. Although the methods used for coupling and modelling rhizosphere resistance were quite different, all simulators were in reasonably good agreement with the reference solution. During this benchmarking effort, individual simulators were able to learn about their strengths and challenges, while some were even able to improve their code. Some now include the benchmarks as standard tests within their codes. Additional model results may be added to the GitHub repository at any point in the future and will be automatically included in the comparison.

Soil hydraulic conductivity (ksoil) drops significantly in dry soils, resulting in steep soil water potential gradients (ψs) near plant roots during water uptake. Coarse soil grid resolutions in root system scale (RSS) models of root water uptake (RWU) generally do not spatially resolve this gradient in drying soils which can lead to a large overestimation of RWU. To quantify this, we consider a benchmark scenario of RWU from drying soil for which a numerical reference solution is available. We analyze this problem using a finite volume scheme and investigate the impact of grid size on the RSS model results. At dry conditions, the cumulative RWU was overestimated by up to 300% for the coarsest soil grid of 4.0 cm and by 30% for the finest soil grid of 0.2 cm, while the computational demand increased from 19 s to 21 h. As an accurate and computationally efficient alternative to the RSS model, we implemented a continuum multi-scale model where we keep a coarse grid resolution for the bulk soil, but in addition, we solve a 1-dimensional radially symmetric soil model at rhizosphere scale around individual root segments. The models at the two scales are coupled in a mass-conservative way. The multi-scale model compares best to the reference solution (−20%) at much lower computational costs of 4 min. Our results demonstrate the need to shift to improved RWU models when simulating dry soil conditions and highlight that results for dry conditions obtained with RSS models of RWU should be interpreted with caution.