Table 2.

Description of benchmark scenarios to be implemented in 3D functional-structural root architecture models^a.

	Benchmark problem	Domain	Initial conditions	Boundary conditions	Evaluation	Remarks
RSA	M1.1: RSA calibration	tsim = 11 (8) for lupine (maize)	Seed position (0,0,−3)	n.a.	Comparison against the measured root systems provided—traits and persistent homology (PH)	Model parameters are determined from calibration against traced images provided in the github repository in RSML format in the folder in M1.1 RSA calibration/M1.1 Reference data; 100 realizations for each model setup
	M1.2: RSA simulation	tsim = 60	Seed position (0,0,−3)	n.a.	No reference solution, comparison amongst models—traits, PH, RLD	RSA model parameters from M1.1; 10 realizations for each model setup
Soil	M2.1: Infiltration	l × w × d = 10 × 10 × 200, tsim = 1	ψs,i = −400	at $\begin{array}{l}z=0\{\begin{array}{l}{J}_s=-100\text{ if}{\psi }_s<0\hfill \\ {\psi }_s=0\text{ else}\hfill \end{array},\\ \frac{\partial {\psi }_s}{\partial z}{|}_{z=200}=1\end{array}$, no-flux at the sides	Analytical solution, Equation (4)	Sand, loam, clay (Table 3)
	M2.2: Evaporation	l × w × d = 10 × 10 × 100, tsim = 10	ψs,i = −40 for sand and −200 for all other scenarios	at $z=0\{\begin{array}{l}{J}_s=J_{s,ref}\text{if }{\psi }_s>-10,000\hfill \\ {\psi }_s=-10,000\text{ else}\hfill \end{array},$ no-flux at all other boundaries	Analytical solution, Equation (5)	Scenario 1: sand,Js,ref = 0.1, scenario 2: loam,Js,ref = 0.1, scenario 3: loam,Js,ref = 0.3, scenario 4: clay,Js,ref = 0.3
Xylem	M3.1: Single root	1 vertical root, L = 50	n.a.	ψx|collar = −1000, Qx|tip = 0	Analytical solution, Equation (7)	kx = 0.0432, kr=1.73 × 10−4, ψs = −200
	M3.2: Root system	14-days old root system	n.a.	ψx|collar = −500, Qx|tips = 0	Hybrid analytical solution (Meunier et al., 2017)	Root hydraulic properties in scenario (a): Table 4, (b): Figure 7, ψs = −200, static RSA given in the root_grid folder of this benchmark
Coupled 1	C1.1: Single RWU	1D radially symmetric, rroot = 0.02, rout = 0.6, tsim = 20	ψs,i = −100	at $r=r_{root}\{\begin{array}{l}{q}_r=q_{root},\text{if}{\psi }_s>-15,000\hfill \\ {\psi }_s=-15,000\text{ else}\hfill \end{array}{q}_r{|}_{r=r_{out}}=0$	Analytical solution, Equations (11) and (12)	Sand, loam, clay (Table 3), scenarios 1–3: qroot = 0.1, scenarios 4–6: qroot=0.05
	C1.2: RWU, static RSA	static 8-days old root system, soil: l × w × d = 8x8x15, tsim = 3	ψs,i = −659.8−z	$\begin{array}{l}\{\begin{array}{l}{Q}_x{|}_{collar}=6.4\text{if}{\psi }_x{|}_{collar}>-15,290\hfill \\ {\psi }_s=-15,290\text{ else}\hfill \end{array},\\ Q_x{|}_{tips}=0,\end{array}$no-flux at all soil faces	Reference solution: explicit 3D simulation	Loam (Table 3), static RSA given in the root_grid folder of this benchmark, root hydraulic properties in scenario (a): Table 4, (b): Figure 7
Coupled 2	C2.1: RWU, dynamic RSA	Growing root system, soil: l × w × d = 25 × 25 × 100, tsim = 60	ψs,i = −200	$\{\begin{array}{l}{Q}_x=0.5·re{l}_{LAI}\text{if }{\psi }_x>-15,000\hfill \\ {\psi }_x{|}_{collar}=-15,000\text{ else}\hfill \end{array},Q_x{|}_{tips}=0,$no-flux at all soil faces	No reference solution, comparison amongst models	Loam (Table 3), kx=0.0432, kr = 1.73 × 10−4, RSA parameters from M1.1, relLAI scales the potential transpiration

^aAll paths are relative to the github repository https://github.com/RSA-benchmarks/collaborative-comparison.git. For other abbreviations and units see Table 1.