Estimation of daily apple tree transpiration in the Loess Plateau region of China using deep learning models

Quantitatively characterizing and accurately predicting plant transpiration are of great significance, but directly measuring transpiration is impractical, time-consuming, and labor-intensive. This study compared the transpiration estimation performance of multiple linear regression (MLR), modified Jarvis–Stewart (MJS), and Shuttleworth–Wallace (S-W) with deep belief network (DBN), long short-term memory recurrent neural network (LSTM-RNN), and LSTM-RNN improved with multiple restricted Boltzmann machines (R-L-RNN) using 31 input combinations comprising complete subsets of Vapor pressure deficit (VPD), Net solar radiation (Rn), Average air temperature (Ta), Soil water content (SWC), and Leaf area index (LAI) observations collected at Wuwei, Changwu and Taigu stations on the Loess Plateau in China. The results showed that R-L-RNN obtained the most accurate estimations in the partial canopy stage, dense canopy stage, and whole growth stage, compared to MLR, MJS, S-W, DBN, and LSTM-RNN. The accuracy of the deep learning models (DNN) increased exponentially as the number of input variables increased, and the importance of the input variables followed the orders of: LAI > VPD > Rn > Ta > SWC in the partial and whole canopy stage, and VPD > Rn > Ta > LAI > SWC in the dense canopy stage. The apple tree transpiration models were more accurate in the partial and dense canopy stages than the whole growth stage. The coefficient of determination and Nash-Sutcliffe efficiency coefficient for the R-L-RNN model increased by 8.1–13.1% and 11.2–25.4% in the partial canopy stage, respectively, and by 2.6–6.9% and 14.7–20.1% in the dense canopy stage, whereas the relative root mean square error decreased by 8.7–28.6% and 17.3–38.2%. Overall, R-L-RNN is the most recommended model for estimating the apple tree transpiration, because it is such a simple method that agricultural water managers can easily determine the water consumption of apple trees using limited accessible observational data.