Apple tree transpiration estimated using the Penman-Monteith model integrated with optimized jarvis model

Accurate estimates of plant transpiration (Tsf) are essential to maximizing the efficient use of water. When only considering the surface canopy resistance (rc), the Penman-Monteith (PM) model is commonly used in Tsf modeling. However, the rc is difficult to measure but it can be accurately estimated using the Jarvis canopy resistance model (JA). Our objectives were to evaluate the rc of apple trees calculated with an inverted PM model integrated with different versions of the JA model for different growth stages and to compare their accuracy using four optimization algorithms, the least squares method (LSM), genetic algorithm (GA), quantum particle swarm optimization (QPSO), and the mind evolutionary algorithm (MEA). We explored the effect of environ-mental constraint functions and parameter optimization of three environmental variables, vapor pressure deficit (VPD), net irradiance (Rn), and air temperature (Ta), and of soil water content (theta a) on the accuracy of JA sub -models to calculate apple tree rc and Tsf. In our analysis, we used rainfed data from experiments on an apple orchard conducted during 2008-2010 at Wuwei City on the Loess Plateau of China. We compared 81 segmented JA sub-models (by canopy growth stage), comprising of the combination of the environmental constraint functions that were used to calculate rc. Moreover, the JA sub-models were optimized and results were compared to improve the accuracy of Tsf estimates with five empirical rc models, combined with the PM model. The results showed that sub-model JA3322, i.e., the third constraint for VPD, the third constraint for Rn, the second constraint for Ta, and the second constraint for theta a attained the best estimate of rc with a coefficient of determination (R2 = 0.71), a Nash-Sutcliffe efficiency coefficient (NSE = 0.65), root mean squared error (RMSE = 1257.4 s m-1), and global performance indicator (GPI = 1.0) for the whole growth stage. The equivalent values for the partial canopy stage were 0.78, 0.72, 1203.3 s m-1 and 0.99, and the values for the dense canopy stage were 0.78, 0.77, 445.6 s m-1 and 0.97, respectively. Segmented JA models based on the leaf area index threshold significantly improved the accuracy of rc estimation, where the median R2 and NSE were improved by 7.1 % and 12.4 % in the partial canopy stage and by 12.2 % and 13.4 % in the dense canopy stage. Despite pointing out the best envi-ronmental constraint functions of the JA model in the different growth stages, results indicated that the MEA yielded the most accurate estimates of rc, followed by QPSO, GA, and LSM. Moreover, the JA model with environmental constraints was the most accurate method to estimate the apple tree Tsf, and MEA was the most suitable parameter optimization algorithm. Overall, the findings of this study provide accurate actual water consumption information of apple trees using easily accessible meteorological data for the effective day-to-day water management decision-making of rain-fed apple tree orchards on the Loess Plateau of China previously.