Correlation scales of digital elevation models in developed coastal environments

Author Posting. © The Author(s), 2014. This is the author's version of the work. It is posted here by permission of Elsevier for personal use, not for redistribution. The definitive version was published in Remote Sensing of Environment 159 (2015): 80-85, doi:10.1016/j.rse.2014.11.031.Accuracy of digital elevation models (DEMs) often depends on how features of different spatial scales are represented. Scale dependence is particularly important in low gradient coastal environments where small vertical errors can affect large areas and where representation of fine scale topographic features can influence how DEMs are used for modeling inundation. It is commonly observed that different types of DEMs represent larger, coarse-scale topographic features similarly, but differ in how they represent smaller, finer-scale features. Spatial scale dependence of DEM accuracy can be quantified in terms of the correlation scale (λc); the spatial wavelength above which models agree with spectral coherency > 0.5 and below which they differ. We compare cross spectral analyses of the GDEM2 and SRTM global DEMs with 14,572 LiDAR derived elevations along transects in diverse coastal environments of New York City. Both global DEMs have positive bias relative to LiDAR ground elevations, but bias (μ) and uncertainty (σ) of GDEM2 (μ: 8.1 m; σ: 7.6 m) are significantly greater than those of SRTM (μ: 1.9 m; σ: 3.6 m). Cross-spectral coherency between GDEM2 and the LiDAR DEM begins to roll-off at scales of λ < ~3 km, while coherency between SRTM and the LiDAR DEM begins to roll-off at scales of λ < ~1 km. The correlation scale below which coherency with LiDAR attains a signal to noise ratio of 1 is ~1 km for GDEM2 and ~ 0.5 km for SRTM; closely matching the divergence scales where the surface roughness of the land cover exceeds the roughness of the underlying terrain.This research was supported by the Office of Naval Research (grant N000-14-11-1-0653 to C.S.)