In P-model, β(θ) is a soil moisture stress function based on empirical results from Stocker et al. (2018). Here, θ is the soil water available for plant growth, expressed as a fraction of field capacity. β(θ) can be calculated as
where θ* is a threshold set to 0.6 (Wang et al. 2017). And sensitivity parameter q is related to the mean aridity.
While in the version of Stocker et al. (2020), he carelessly assumed that the wilting point was zero, which may lead to the estimation error of β(θ). Therefore, we refer to the parameterization of β(θ) in the land surface model and verify it at flux tower sites on the Tibetan Plateau. And β(θ)is calculated as
where θ* is a threshold set to 0.75, and θ is set as:θ=(soil moisture-min(soil moisture))/(max(soil moisture)-min(soil moisture)).
The comparison with the observation shows that the latter parameterization scheme of β(θ) is suitable.
Fig.1 The comparison of predicted GPP and observed GPP at three flux tower sites on the Tibetan Plateau. The orange line is the predicted GPP considering soil moisture limitation and the blue solid line shows the predicted GPP assuming no soil moisture limitation.
Stocker, B. D., J. Zscheischler, T. F. Keenan, I. C. Prentice, J. Peñuelas & S. I. Seneviratne (2018) Quantifying soil moisture impacts on light use efficiency across biomes. New Phytologist, 218, 1430-1449.
Wang, H., I. C. Prentice, T. F. Keenan, T. W. Davis, I. J. Wright, W. K. Cornwell, B. J. Evans & C. Peng (2017) Towards a universal model for carbon dioxide uptake by plants. Nat Plants, 3, 734-741.
Stocker, B., H. Wang, N. Smith, S. Harrison, T. Keenan, D. Sandoval, T. Davis & I. Prentice (2020) P-model v1.0: an optimality-based light use efficiency model for simulating ecosystem gross primary production. Geoscientific Model Development, 13, 1545-1581.