A surrogate modeling method for distributed land surface hydrological models based on deep learning

Abstract

Surrogate modelling methods have been used to estimate spatially distributed parameters of land surface hydrological models due to their computational efficiency. However, traditional surrogate techniques have trouble in modelling high-dimensional input–output maps. In addition, their applications to a distributed model over large spatial and temporal domains are very unlikely to produce consistent spatial pattern and dynamic relationship of model input and output, leading to unbalanced model performance across different spatiotemporal domains. To address these issues, we employ a deep autoregressive neural network to construct an accurate and reliable surrogate system of distributed dynamic model outputs. The network uses a deep convolutional encoder-decoder architecture to take full advantage of the deep convolutional layers in high-dimensional image processing and spatial feature extraction. Moreover, the autoregressive strategy makes the network good at handling dynamic relationship between the time-varying model input and output. We apply this deep learning (DL) network to building a surrogate model of the Variable Infiltration Capacity (VIC) model simulated soil moisture over the Huaihe river basin of China. The results show that the adopted deep autoregressive neural network can provide an accurate surrogate model of the high-dimensional dynamic relationship between 15 input fields and 1 output field, each covering 408 grids, over multiple years. This surrogate model significantly outperforms the popular long short-term memory (LSTM) model, achieving an average mean squared error (MSE) of 0.26 and an average R2 of 0.76 using the test datasets. The surrogate's MSE and R2 performance represents an average improvement of 43% and 33%, respectively, compared to the LSTM model. In addition, it shows better spatial performance than the LSTM model, demonstrating its superior performance in approximating spatial patterns of VIC simulated soil moisture. The accuracy of this surrogate method and its ability to handle high-dimensional data is promising for advancing parameter uncertainty quantification of distributed land surface hydrological models, which usually have high dimensionality due to the large number of variables involved, including distributed parameters, input forcing variables, and output variables.