Bernacchi 2013, Plant Cell Environ.

The Bernacchi 2013 model is a review-and-synthesis presentation of the Farquhar, von Caemmerer & Berry (FvCB) biochemical model of C₃ photosynthesis, tracing how the same steady-state framework is used from the chloroplast all the way up to the ecosystem scale. Net CO₂ assimilation is expressed as the minimum of three potential rates: Rubisco-carboxylation-limited ( $W_{c}$ ), RuBP-regeneration (electron-transport)-limited ( $W_{j}$ ), and triose-phosphate-utilization-limited ( $W_{p}$ ), each written as a function of intercellular CO₂ ( $C_{i}$ ), photosynthetically active photon flux density (PPFD), and the enzyme capacities $V_{c ma x}$ , $J_{ma x}$ and TPU. The GreenSloth implementation follows this classical formulation directly: the light-limited electron transport rate $J$ is obtained from a non-rectangular hyperbola of absorbed light and $J_{ma x}$ , and $A_{n}$ is the minimum of the three limiting rates minus day respiration $R_{d}$ .

Beyond restating the biochemistry, the paper's contribution is showing how the model's parameters ( $V_{c ma x}$ , $J_{ma x}$ , $Γ^{*}$ , $K_{c}$ , $K_{o}$ ) can be scaled with temperature and how the resulting leaf-level $A$ – $C_{i}$ curves feed into canopy and land-surface models used for ecosystem- and global-scale predictions of carbon uptake. In GreenSloth it serves as a standard, well-parameterized FvCB-type reference model alongside FvCB 1980 and Johnson 2021, against which extensions of the classical Rubisco-limited/RuBP-regeneration-limited switching can be compared.

Analysis

Model definition

Parameters

Symbol	ID	Value
	Ci	275
	PPFD	1500
	Vcmax	100
	Jmax	200
	TPU	12
	Rd	1.5
	Gamma_star	42.75
	Kc	404.9
	Ko	278.4
	O	210
	alpha	0.24
	theta	0.7

Derived quantities

Symbol	ID	Equation
	absorbed
	Ci_safe
	J
	Wc
	rubisco
	rubp
	tpu
	an

Curation

July 2026: Maintenance by Marvin van Aalst
July 2025: Initial implementation by Tanvir Hassan

This model was validated by reproducing the following figures of the original publication.

Figures

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