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SCOPE addresses the computational bottlenecks and data scarcity of high-resolution digital elevation model (DEM) reconstruction by learning continuous implicit terrain representations strictly from coarse-resolution training pairs. The framework decouples latent coefficient prediction on low-resolution grids from output query density by evaluating reusable local Fourier residual functions with geometry-guided ensemble fusion. Across global land and ocean benchmarks, it maintains near-supervised accuracy at 3× unseen upsampling factors and cuts RMSE by 19% over implicit baselines, while a 9× increase in query grid density incurs only a 2% increase in multiply–accumulate operations.
Terrain grids can be super-resolved to 9× continuous output density at an arithmetic overhead of just 2% by decoupling latent coefficient prediction from local Fourier basis evaluation.
High-resolution digital elevation models (DEMs) support Earth observation applications, but paired training references are often available only at coarser output resolutions. Reconstructing finer terrain grids therefore requires both effective transfer beyond the supervised scale and control of dense-query computation. To address this problem, SCOPE learns a continuous terrain representation from coarser-resolution pairs. It predicts a latent coefficient field on the low-resolution grid and reuses local Fourier residual functions through basis evaluation and geometry-guided ensemble fusion. This separates high-dimensional coefficient prediction from output-grid construction. Experiments on geographically distributed land--ocean samples assess supervised reconstruction, unseen-scale inference, cross-domain generalization, and theoretical computation. SCOPE leads the compared methods across six metrics in the main supervised-scale evaluation. At an unseen factor three times the training factor, land reconstruction reduces RMSE and MAE by approximately 12\% relative to bicubic interpolation, with errors close to target-scale fine-tuning. Ninefold output density increases counted multiply--accumulate operations by only about 2\%. Frozen-model validation on held-out external marine regions reduces RMSE relative to the DEM-specific implicit baseline EBCF-CDEM by approximately 19\% under self-downsampling and 2\% with cross-product inputs, while also yielding lower RMSE than LIIF-MS in both settings. These results demonstrate the value of reusable coefficient fields for accurate reconstruction beyond the supervised resolution with low incremental arithmetic cost.