Integration of flux footprint and physical mechanism into convolutional neural network model for enhanced simulation of urban evapotranspiration

Estimating urban evapotranspiration (ET) is of great significance for urban water resource allocation and assessing the urban heat island effect. However, most current urban ET models are based on the energy balance theory to estimate urban ET. These models lead to significant errors in urban ET simulation due to the surface heterogeneity and the existence of anthropogenic heat fluxes in urban areas. To solve this issue, this study proposes a modified machine learning-based urban ET method that can estimate urban ET at the site and regional scales. To better characterize the heterogeneity of urban surfaces, the flux footprint of in-situ ET and physical mechanism of ET process are integrated into the convolutional neural network (CNN) model. The modified CNN model is tested in a fast-developing city: Shenzhen, China based on two Eddy Correlation (EC) observations. The verification results indicated that coupling flux footprint and physical mechanism into the CNN model could effectively improve the accuracy of urban ET simulation at the site scale. The modified CNN model significantly reduced the root-mean-square-error (RMSE) of 25.8 W/m2 and increased the determination coefficient (R2) of 0.17 compared to the CNN-O model (The CNN-O model is defined as the CNN model do not integrate flux footprint and physical mechanism of ET). Further analyses suggested that fusing flux footprint data into a machine learning model helps enhance ET estimation in regions with high heterogeneity and highly variable wind directions. Moreover, the integration of physical mechanisms significantly enhanced the model capability to simulate extreme ET events. The modified CNN model is further applied to map the spatial distribution of urban ET and reconstruct long-term urban ET changes. The spatial pattern of urban ET exhibited large spatial variability, where the urban ET in water bodies (mean λET larger than 480 W/m2) and vegetation-covered areas (mean λET larger than 260 W/m2) are substantially higher than the impervious surfaces (mean λET less than 30 W/m2). Long-term trend analyses demonstrated that urbanization resulted in decline in urban ET. The average decreasing rate of urban ET is 1.61 mm/yr (P < 0.05), with a 18 % decrease relative to the long-term ET average. The leading causes for the decline of urban ET are the increased impervious surfaces and the decreased radiation. This study improved the simulation accuracy of urban ET and revealed the response of urban ET to urbanization.