A two-stage downscaling hydrological modeling approach via convolutional conditional neural process and geostatistical bias correction

Hydrological modeling plays an indispensable role in many practical applications, such as hydrology, water resources assessment, and environmental survey. Downscaling approach is able to obtain high-resolution hy-drological models according to a prior reference model. In this work, we propose a downscaling hydrological modeling approach based on convolutional conditional neural processes (ConvCNP) and a novel geostatistical bias correction, named ConvCNP-GBC. A two-stage downscaling modeling workflow is presented. In the model building stage, to reduce the training consumption of the ConvCNP, low-resolution conditioning data are used for training. In the model generating stage, the ConvCNP is used to reconstruct coarse-scale realizations based on upscaling sampled conditioning data and to generate high-resolution realizations by downscaling. Besides, a geostatistical bias correction strategy is presented to refine large-scale realizations with high-resolution condi-tioning data constraints. The experimental results confirm that ConvCNP-GBC can reproduce heterogeneous patterns by using coarse-scale conditioning data and characterize hydrological structures. The downscaled re-alizations also have a high spatial correspondence with the coarse-scale realizations, which provide fine sub-surface heterogeneous structures. The proposed method can be easily extended to reservoir modeling, geophysical inversion, etc.