Locally adaptive gridding of noisy high resolution topographic data

Topography plays a fundamental role in modulating land surface and atmospheric processes across a wide range of spatial scales (Hutchinson 2008). Thus digital elevation models (DEMs) have provided a key role in supporting mesoscale representations of surface climate as well as supporting finer scale representations of surface hydrology and catchment processes. The usual means of supporting these representations is a regular grid elevation model interpolated from a variety of data sources. The ANUDEM locally adaptive elevation gridding procedure (Hutchinson 2007) is commonly used to calculate these elevation models. Two key features of the method are its computational efficiency, allowing it to be applied to very large data sets, and a drainage enforcement algorithm that attempts to maintain connected drainage structure in the interpolated DEM, a key necessity for hydrological applications. The ANUDEM procedure has been steadily upgraded over the last two decades to process a wide range of topographic data and to improve the quality of its underlying algorithms. In particular, the drainage enforcement algorithm has undergone considerable revision. Traditional data sources include point elevation data and stream line data. These have been augmented by contour elevation data, coastline data, cliff line data, stream distributaries and lake boundary data. All of these have been used to calculate Version 3 of the national 9 second digital elevation model, recently jointly released by the ANU Fenner School of Environment and Society and Geoscience Australia (2008). Until recently the source elevation data have been relatively sparse and essentially error free, apart from coding errors. The ANUDEM procedure has applied an efficient multi-grid algorithm to underpin the basic interpolation of these sparse data according to a variety of roughness penalties that can be tuned to the different data sources. Thus sparse point elevation data has been interpolated using a roughness penalty composed of surface curvature and potential. This has been particularly effective in eliciting surface drainage structure from relatively sparse surface specific elevation data points. Contour data have been effectively interpolated using a minimum curvature roughness penalty augmented by a locally adaptive minimum profile curvature penalty. In both cases initialisation of elevations on data streamlines has relied on the error free nature of the source elevation data. Recent elevation data sources are airborne and spaceborne platforms using laser and radar techniques. They differ from the traditional data sources in two fundamental ways. The data typically have high spatial resolution, less than 1 metre for airborne laser data, and all have significant elevation errors. The errors can be both systematic, as particularly evident in data obtained by spaceborne platforms, such as SRTM data, and sporadic. Sporadic errors are associated with surface features such as vegetation cover and man-made structures. This paper describes key modifications to the ANUDEM procedure to effectively process these noisy, high resolution data sources. The multi-grid interpolation procedure is still effective in stably interpolating high resolution data. This is important in enabling effective application of drainage enforcement to the interpolated grid. The different errors in the source data can be specifically accommodated by smoothing the data according to the differing magnitudes of the variances of the errors of the source elevation data. This is particularly appropriate when the data have been subject to pre-processing. Finally, revision of the initialization of heights on data streamlines is required to prevent corruption of stream heights by noisy elevation values and to improve the computational efficiency of the initialization of distributary streamlines in the presence of dense source elevation data. Both are facilitated by the underlying stable multi-grid interpolation method.