Improvement of sap flow estimation by including phenological index and time-lag effect in back-propagation neural network models

Abstract Sap flow is an important indicator reflecting water transport in a soil-plant-atmosphere continuum system. Therefore, identifying the effects of different factors on sap flow is imperative for understanding its physiological responses to environmental conditions and other associated ecological processes. However, conventional statistical methods have produced unsatisfactory results due to the complex and nonlinear relationship between sap flux density ( v s ) and its driving factors. This study illustrated the utility of the back-propagation (BP) neural network method for sap flow estimation and compared the performance of BP models with the multiple-linear regression (MLR) technique. Based on the measured sap flow of Pinus massoniana in the field, three-layer BP models trained by the Levenberg-Marquardt algorithm were developed with an architecture of 4-10-1, corresponding to four, ten and one nodes in the input, hidden and output layers, respectively. The BP models were trained and validated in the MATLAB environment with four different combinations of air temperature ( T a ), relative humidity ( RH ), average net radiation ( ANR ) and the phenological index. High degrees of correlation were observed between the measured and simulated results by BP, and the coefficients of determination ( R 2 ) and fitting accuracies ( Acc ) (greater than 0.9 and 80%, respectively) were higher than the corresponding values from the MLR (0.78 and 69%, respectively). Furthermore, the performance of the BP models could be greatly improved by including the phenological index and a time-lag effect, thereby suggesting that these two factors were crucial variables in modelling v s by BP approaches. The BP models were also tested with cross-validation method and 50% of the collected data that were not used in model development. We conclude that the BP model had a higher degree of accuracy in predicting sap flow due to its superior performance for complicated, nonlinear and uncertain processes, especially with inclusion of the phenological index and time-lag effect.