Downscaling Images with Trends Using Multiple-Point Statistics Simulation: An Application to Digital Elevation Models

Remote sensing and geophysical imaging techniques are often limited in terms of spatial resolution. This prevents the characterization of physical properties and processes at scales finer than the spatial resolution provided by the imaging sensor. In the last decade, multiple-point statistics simulation has been successfully used for downscaling problems. In this approach, the missing fine-scale structures are imported from a training image which describes the correspondence between coarse and equivalent fine-scale structures. However, in many cases, large variations in the amplitude of the imaged physical attribute, known as trends, pose a challenge for the detection and simulation of these fine-scale features. Here, we develop a novel multiple-point statistics simulation method for downscaling coarse-resolution images with trends. The proposed algorithm relies on a multi-scale sequential simulation framework. Trends in the data are handled by an inbuilt decomposition of the target variable into a deterministic trend component and a stochastic residual component at multiple scales. We also introduce the application of kernel weighting for computing distances between data events and probability aggregation operations for integrating different support data based on a distance-to-probability transformation function. The algorithm is benchmarked against two-point and multiple-point statistics simulation methods, and a deterministic interpolation technique. Results show that the approach is able to cope with non-stationary data sets and scenarios in which the statistics of the training image differ from the conditioning data statistics. Two case studies using digital elevation models of mountain ranges in Switzerland illustrate the method.