Evapotranspiration (ET) links the water and carbon cycles in the atmosphere, hydrosphere and biosphere. Models based on energy-balance principles have been widely used to estimate ET and its spatio-temporal pattern. Many uncertainties remain, however, in particular because of incomplete understanding of stomatal regulation. Here we evaluate an ET modelling framework embodying the hypothesis that canopy conductance acclimates to plant growth conditions according to the least-cost hypothesis, that is, minimizing the combined costs of maintaining carboxylation and transpiration capacities. Coupled with an a priori productivity model, the P model, based on the principle of co-limitation between light- and Rubisco-limited photosynthesis, this approach allows canopy conductance to be modelled with no need for plant type- or biome-specific parameters.
In our approach, we use the Fick’s Law to describe the canopy conductance as:
Gs = 1.6 * GPP / Ca ( 1 – K)
where 1.6 is the ratio of the molecular diffusivities of water and CO2, is the ambient atmospheric CO2 partial pressure (Pa).
K (which is the ratio of leaf-internal to external CO2 concentration) is retrieved using P Model (Wang et al., 2017). GPP is the gross primary production, which is calculated using P Model V1.0, with the consideration of water stress and the temperature effect on intrinsic quantum yield of photosynthesis (Stocker et al., 2020)
Total evapotranspiration is divided into the contribution by biotic transpiration (T) and abiotic evaporation (E, from soil and canopy interception). We use a Penman-Monteith equation to estimate transpiration, and an empirical approach to estimate the ratio of T/ET considering this ratio is only affected by environment. Result shows our approach performs a satisfied accuracy compared with flux observation (from 20 sites with 245 years observation) at weekly scale (see Fig. 1), and with parameter-based conductance approaches (see Fig. 2).
Fig. 1. Scatterplots of weekly modelled ET against observed ET. The solid black line is the fitted regression line; the dashed black line is the 1:1 line.
Fig. 2. Sensitivity analysis of canopy conductance and daily ET towards variant air temperature (a and b), ambient CO2 concentration (c and d) and VPD (e and f). Other input variables were set to the average condition at site DK-SOR.USO refers to the model of Medlyn et al. (2011); Jarvis to Jarvis (1976); BWB to Ball et al. (1987); BBL to Leuning (1995). The black line shows the result of our method (the P Model). All ET results are all calculated using PM equation. We referred to the result of required parameters of other methods from existing research. Abiotic evaporation is retrieved using the empirical relationship in our research. Dashed black lines represent current values. Black points in (b, d and f) represents averaged ET at DK-SOR from 2005 to 2010.
Reference
Ball J T, Woodrow I E, Berry J A. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions[M]//Progress in photosynthesis research. Springer, Dordrecht, 1987: 221-224.
Jarvis P G. The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field[J]. Philosophical Transactions of the Royal Society of London. B, Biological Sciences, 1976, 273(927): 593-610.
Leuning R. A critical appraisal of a combined stomatal‐photosynthesis model for C3 plants[J]. Plant, Cell & Environment, 1995, 18(4): 339-355.
Medlyn B E, Duursma R A, Eamus D, et al. Reconciling the optimal and empirical approaches to modelling stomatal conductance[J]. Global Change Biology, 2011, 17(6): 2134-2144.
Stocker B D, Wang H, Smith N G, et al. P-model v1. 0: an optimality-based light use efficiency model for simulating ecosystem gross primary production[J]. Geoscientific Model Development, 2020, 13(3): 1545-1581.
Wang H, Prentice I C, Keenan T F, et al. Towards a universal model for carbon dioxide uptake by plants[J]. Nature Plants, 2017, 3(9): 734-741.