Super-resolution of digital elevation models by using multiple-point statistics and training image selection

Super-resolution (SR), also called downscaling, has been widely explored in hydrology, climate, and vegetation distribution models, among others. Digital elevation model (DEM) SR aims to reconstruct terrain at a finer resolution than available measurements. The raw terrain data are often non-stationary and characterized by trends, while terrain residuals are generally stationary in geomorphologically heterogeneous areas. Here, we develop a multiple-point statistics approach that decomposes the target low-resolution DEM into a deterministic low-frequency trend component and a stochastic high-frequency residual component. Our simulation is focusing on the residual component. A training image selection process is applied to determine locally appropriate high-resolution residual training images. The high-resolution residual of the target DEM is simulated with an open-source multiple-point statistics (MPS) framework named QuickSampling. The residual of the low-resolution target DEM is used as conditioning data to ensure local accuracy. The deterministic trend component is then added to obtain the final downscaled DEM. The proposed algorithm is compared with the bicubic interpolation, a convolutional neural network(CNN), a generative adversarial network (GAN), a modified super-resolution residual network (MSRResNet), and geostatistical area-to-point-kriging. The results show that the proposed approach maintains the statistical properties of the fine-scale DEM with its spatial details, and can be easily extended to other fields such as the super-resolution/downscaling of precipitation, temperature, land use/cover, or satellite imagery. •DEM super-resolution is considered with both MPS and DL.•This is the first formal comparison between MPS and DL.•We use a multi-training image selection scheme for efficient MPS.•We use a detrending strategy that performs well for both MPS and DL.