Improving the representation of stomatal responses to CO2 within the Penman–Monteith model to better estimate evapotranspiration responses to climate change

Abstract

An increase in atmospheric CO2 concentration (CO2) affects stomatal conductance (gs). Since gs is an important parameter in the Penman–Monteith model (P-M), an accurate estimate of gs can improve the accuracy of the estimation of evapotranspiration (ET) by P-M when CO2 increases. This paper identifies three models of the relationship between gs and CO2 (the linear model, L, the hyperbolic model, H, and the modified hyperbolic model, MH), and compares their estimations of ET when they are incorporated into P-M. A two-year experiment which included four levels (400, 550, 700, and 900 μmol mol−1) and three levels (400, 550, and 700 μmol mol−1) of CO2 in 2015 and 2016, respectively, was conducted in order to obtain validation data. Fifty papers that had studied the effect of increased CO2 on gs, over a 45-year period, were analyzed to obtain calibration data. After being calibrated and validated, each of the three models was in turn included as a component of P-M to estimate ET under increased CO2, followed by the comparison between estimated and observed ET. The sensitivity of P-M to the parameters in three models was also analyzed. Our results show that gs decreased and the reduction rate gradually lessened as CO2 increased. Of the three models, MH gave the best estimate of gs, having the largest values of the coefficient of determination (R2), 0.97, the Nash–Sutcliffe efficiency coefficient (NSE), 0.96, and the modified affinity index (d), 0.93, and the smallest values of the root mean square error (RMSE), 0.03, and the Akaike information criterion (AIC), −47.48. Each of the three models gave different ET results for different levels of CO2 when used as a component of P-M. The MH had better ET estimations than L and H when compared to observed ET across all CO2 concentration levels, with the highest R2, NSE, and d, and the lowest RMSE and AIC. The sensitivity of P-M to the empirical parameters varied among the three models, for instance, ±40 and ±20% changes of parameter p in L, gsmaxp and Cs0 in H, and b in MH resulted in −15 to 4%, −13 to 7%, −9 to 4%, and −3 to 3% changes in predicted ET, respectively. Thus, changes of parameter b in MH had minimum effect on predicted ET, indicating greater stability of P-M in ET estimation by incorporating MH. Therefore, using MH to model the response of gs to increased CO2 when incorporated into P-M to estimate ET not only represents a more appropriate stomata physiological reaction to higher CO2, but also results in a more accurate estimate of ET, and making the model more broadly applicable.