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For the first time, a functional–structural root-system model is validated by combining a tracer experiment monitored with magnetic resonance imaging and three-dimensional modeling of water and solute transport.

1 functional-structural root architecture models. 2 The case of root water uptake. Abstract 35Three-dimensional models of root growth, architecture and function are becoming im-36 portant tools that aid the design of agricultural management schemes and the selection of 37 beneficial root traits. However, while benchmarking is common in many disciplines that use 38 numerical models such as natural and engineering sciences, functional-structural root archi-39 tecture models have never been systematically compared. The following reasons might induce 40 disagreement between the simulation results of different models: different representation of 41 root growth, sink term of root water and solute uptake and representation of the rhizosphere. 42Presently, the extent of discrepancies is unknown, and a framework for quantitatively com-43 paring functional-structural root architecture models is required. We propose, in a first step, 44 to define benchmarking scenarios that test individual components of complex models: root 45 architecture, water flow in soil and water flow in roots. While the latter two will focus mainly 46 on comparing numerical aspects, the root architectural models have to be compared at a con-47 ceptual level as they generally differ in process representation. Therefore defining common 48 inputs that allow recreating reference root systems in all models will be a key challenge. In 49 a second step, benchmarking scenarios for the coupled problems are defined. We expect that 50 the results of step 1 will enable us to better interpret differences found in step 2. This bench-51 marking will result in a better understanding of the different models and contribute towards 52 improving them. Improved models will allow us to simulate various scenarios with greater 53 confidence and avoid bugs, numerical errors or conceptual misunderstandings. This work will 54 set a standard for future model development. 55 1 Introduction 56 A growing number of different modelling techniques and software libraries are now available to 57 build functional-structural root architecture models. Different available models of root architec-58 ture and functions have been discussed and qualitatively compared in Dunbabin et al. (2013). 59The available models differ in the way they represent different processes such as root growth, wa-60 ter flow, solute transport are captured and translated into mathematical equations (process-level 61 differences); in how they solve mathematical problems by their choice of analytical or numerical 62 approach, numerical scheme, programming technique (solution-level differences); and in how they 63 couple the different processes to the full model (coupling-level differences). However, the extent of 64 discrepancies is currently unknown. Thus, a framework for quantitatively comparing functional-65 structural root architecture models is required. In addition to the explanatory or predictive power 66 of a model, it is also important to understand the performance of these models, e.g. in terms of 67 ac...

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<p>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 <em>https://github.com/RSAbenchmarks/collaborative-comparison</em>. Several groups of functional-structural model developers have joined this benchmarking activity and provided the results of their individual implementations of the different scenarios.</p> <p>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.</p> <p>The participating simulators are CPlantBox, DuMu<sup>x</sup>, 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. </p> <p>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.</p> <p>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). </p> <p>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.</p> <p> </p> <p>Schnepf et al., 2020, <em>Front. Plant Sci.</em> 11</p>