Modeling spatio-temporal distribution of soil moisture by deep learning-based cellular automata model

Soil moisture content (SMC) is a key hydrological parameter in agriculture, meteorology and climate change, and understanding of spatio-temporal distributions of SMC in farmlands is important to address the precise irrigation scheduling. However, the hybrid interaction of static and dynamic environmental parameters makes it particularly difficult to accurately and reliably model the distribution of SMC. At present, deep learning wins numerous contests in machine learning and hence deep belief network (DBN), a breakthrough in deep learning is trained to extract the transition functions for the simulation of the cell state changes. In this study, we used a novel macroscopic cellular automata (MCA) model by combining DBN to predict the SMC over an irrigated corn field (an area of 22 km²) in the Zhangye oasis, Northwest China. Static and dynamic environmental variables were prepared with regard to the complex hydrological processes. The widely used neural network, multi-layer perceptron (MLP), was utilized for comparison to DBN. The hybrid models (MLP-MCA and DBN-MCA) were calibrated and validated on SMC data within four months, i.e. June to September 2012, which were automatically observed by a wireless sensor network (WSN). Compared with MLP-MCA, the DBN-MCA model led to a decrease in root mean squared error (RMSE) by 18%. Thus, the differences of prediction errors increased due to the propagating errors of variables, difficulties of knowing soil properties and recording irrigation amount in practice. The sequential Gaussian simulation (sGs) was performed to assess the uncertainty of soil moisture estimations. Calculated with a threshold of SMC for each grid cell, the local uncertainty of simulated results in the post processing suggested that the probability of SMC less than 25% will be difference in different areas at different time periods. The current results showed that the DBN-MCA model performs better than the MLP-MCA model, and the DBN-MCA model provides a powerful tool for predicting SMC in highly non-linear forms. Moreover, because modeling soil moisture by using environmental variables is gaining increasing popularity, DBN techniques could contribute a lot to enhancing the calibration of MCA-based SMC estimations and hence provide an alternative approach for SMC monitoring in irrigation systems on the basis of canals.