Five Root Models Compete in Benchmarking Challenge

Functional-structural root architecture models (FSRMs) can be used to select root traits that optimize plant performance under specific environmental conditions. Current simulators differ in the way they (1) represent the way the processes are captured and translated into mathematical equations; (2) solve mathematical problems by their choice of analytical or numerical approaches, numerical scheme, or programming technique; and (3) couple and represent the exchange between the root and soil domains. These differences can result in varying levels of accuracy and reliability.

Andrea Schnepf led the first ever effort to benchmark root water uptake from soil using FSPMs that allows quantitative comparison of the outputs of different simulators with reference solutions and with each other.

This effort began with a call for participation FOR collaborative benchmarking from Schnepf and colleagues. As a result, five research groups that developed the root FSPMs DuMu^x, CPlantBox, R-SWMS, OpenSimRoot, and SRI contributed to an in silico Plants article describing the benchmarking.

The five simulators were benchmarked using a multi-step approach with growing levels of complexity. Accuracy was based on comparison to reference solutions and existing literature values.

For the first challenge, the validity of single domain modules (i.e., root OR soil) was tested. The scenarios were simple, and the goal was to build trust in the accuracy of the individual modular parts of the simulators and to help interpret potentially diverging results of the coupled benchmark challenges.

CHALLENGE 1: MODULAR

These challenges considered the infiltration front and root water pressure head. Water applied to the soil surface enters the soil through the process of infiltration. This is mainly controlled by water supply and soil type. In this case, the infiltration front is measured as the depth to which water infiltrates dry soil at specific timepoints in relation to the volumetric water content (the ratio of the volume of water to the unit volume of soil).

Pressure heads are a measure of water potential. Root water uptake is computed according to the water pressure head difference between the xylem and the soil water pressure head at the soil-root interface. In this case, the model described the root water head pressure distribution in the xylem over soil depth.

Benchmark A – The module accurately represents the infiltration front of water into dry soil for three soil types (sand, loam and clay).

Results: DuMu^x, R—SWMS, and OpenSimRoot were all in agreement for sand, loam and clay. SRI was in agreement with the reference for sand and loam, but deviated for clay, but still within the range of other simulators in the benchmark of Vanderborght et al. (2005).

Benchmark B – The module accurately represents soil evaporation for three soil types.

Results: DuMu^x, R—SWMS, OpenSimRoot, and SRI were all in agreement for sand, loam and clay.

Benchmark C:  The module accurately describes the root water pressure head distribution in the xylem of a single vertical root segment for three soil types.

Results: DuMu^x, R—SWMS, OpenSimRoot, and SRI were all in agreement for sand, loam and clay.

Benchmark D: The module accurately describes the root water pressure head distribution in the xylem of a root system for three soil types.

Results: DuMu^x, R—SWMS, OpenSimRoot, and SRI were all in agreement with the reference for sand, loam and clay.

The positive results of the modular challenge built trust in all the simulators. While the authors found a difference between SRI and the reference solution for the infiltration front of water into dry soil in the clay, the results were within the order of magnitude of other simulators.

The authors explain the two factors that drive this deviation. “Water flow is caused by gradients in water potential. Directly at the infiltration front there is a sharp change in soil water potential, that can only be accurately captured if the spatial resolution is fine enough. If too coarse, as was the case with SRI, the actual gradient will appear smeared.” The second factor is the strong nonlinearity of the soil hydraulic functions. “Unsaturated hydraulic conductivity refers to a measure of soil’s water-retaining ability when soil pore space is not saturated with water. This factor determines the magnitude of the flow, which is a highly nonlinear function. That means a small inaccuracy in the water potential may lead to a large error in hydraulic conductivity. Very dry soils represent a particular challenge, and most simulators have some kind of regulation.”

Grid size (spatial resolution), convergence criteria (at what point a model is considered to be “accurate” and can no longer be improved), and the method of evaluating the soil hydraulic conductivities strongly influence the results.

CHALLENGE 2: COUPLED SINGLE ROOT

For the second challenge of benchmarking, the validity of the simulators for the coupled root-soil models was tested. The focus of this benchmark was the development of water potential gradients around a single vertical root. “As the soil only and root only modules were solved well by the different simulators, any differences in the results of the most challenging benchmark can be mainly attributed to the coupling approaches and how well the soil water potential gradients that develop around the roots are recognized,” explained Schnepf.

For this challenge, DuMu^x was used in two ways:

1. DuMu^x was used to represent both the soil and the root domains, and the resulting problem was solved in a coupling approach in which the interpolated value of soil water potential at the root perimeter was used (DuMu^x_CYL); and
2. DuMu^x was used to represent the soil while the root subproblem and the coupling were solved by CPlantBox. For this method, the averaged value of soil water potential at the root perimeter was used (DuMu^x_CPlantBox).

SRI did not participate in this challenge due to time constraints, but they did participate in challenge 3.

Benchmark E1: The coupled model accurately describes the soil water pressure head distribution as a result of radial water flow towards a single vertical root for three soil types.

Results: DuMu^x_CYL and DuMu^x_PBox were in agreement with the reference for sand and loam, but deviated for clay. R—SWMS and OpenSimRoot were in agreement with the reference for sand and clay, but deviated for loam. SRI had a bye for this challenge.

Benchmark E2 The coupled model accurately describes the time of soil water stress onset as a result of radial water flow towards a single vertical root for three soil types.

All of the models performed similarly for this challenge. Discrepancies in soil water pressure head distribution as a result of radial water flow towards a single vertical root between the DuMu^x variations and R—SWMS & OpenSimRoot were due to differences in the numerical technique used to divide the soil into discrete spatial units.

CHALLENGE 3: COUPLED ROOT SYSTEM

For the third, and most difficult challenge, the validity of the simulators for the coupled root-soil models with root systems were tested.

For this challenge, DuMu^x was used in two ways:

1. DuMu^x was used to represent both the soil and the root domains and using the kernel support method the represent the rhizosphere resistance to water flow (DuMu^x-ks); and
2. the soil module of DuMu^x was coupled to CPlantBox as above. In addition, 1D radially symmetric rhizosphere models, also based on DuMu^x, were solved around each root segment to determine the water potential at the root-soil interface.

Benchmark F: The coupled model accurately describes root system water uptake from a drying soil and the resulting transpiration over time.

Results: All the models performed similarly for the final challenge. It was found that all of them needed to explicitly consider the additional resistance to water flow in the drying soil to avoid large overestimated the root water uptake. The different simulators used quite different approaches to do so. While R-SWMS and SRI still slightly overestimated transpiration, all of the simulators got the order of magnitude correct.

From this benchmarking, the authors were able to conclude that the simulators did not have other bugs or mistakes that could have rendered their solutions inaccurate. Insights gained from this challenge, and the participation of users and developers of the models, can lead to further model improvements.

READ THE ARTICLE:

Andrea Schnepf, Christopher K Black, Valentin Couvreur, Benjamin M Delory, Claude Doussan, Adrien Heymans, Mathieu Javaux, Deepanshu Khare, Axelle Koch, Timo Koch, Christian W Kuppe, Magdalena Landl, Daniel Leitner, Guillaume Lobet, Félicien Meunier, Johannes A Postma, Ernst D Schäfer, Tobias Selzner, Jan Vanderborght, and Harry Vereecken. Collaborative benchmarking of functional-structural root architecture models: Quantitative comparison of simulated root water uptake, in silico Plants, 2023; diad005, https://doi.org/10.1093/insilicoplants/diad005

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All the benchmarks and corresponding reference solutions were published in the form of Jupyter Notebooks on the GitHub repository https://github.com/RSA-benchmarks/collaborative-comparison.

This manuscript is part of in silico Plant’s newest Functional Structural Plant Model special issue.