Airborne light detection and ranging (LIDAR) technology now makes it possible to sample the Earth's surface with point spacings well below 1 m. It is, however, time consuming, costly, and technically challenging to directly use very high resolution LIDAR data for hydraulic modeling because of the computational requirements associated with solving fluid dynamics equations over complex boundary conditions in large data sets. For high relief terrain and urban areas, using coarse digital elevation models (DEMs) can cause significant degradation in hydraulic modeling, particularly when artificial obstructions, such as buildings, mask spatial correlations between terrain points. In this paper we present a strategy to reduce the computational complexity in the estimation of surface water discharge through a decomposition of the DEM data, wherein features have different characteristic spatial frequencies. Though the optimal DEM scale for a particular application will ultimately be decided by the user's tolerance for error, we present guidelines to choose a proper scale by balancing computer memory usage and accuracy. We also suggest a method to parameterize man-made structures, such as buildings in hydraulic modeling, to efficiently and accurately account for their effects on surface water discharge.
The multiscale Kalman smoother (MKS) is a globally optimal estimator for fusing remotely sensed data. The MKS algorithm can be readily parallelized because it operates on a Markov tree data structure. However, such an implementation requires a large amount of memory to store the parameters and estimates at each scale in the tree. This becomes particularly problematic in applications where the observations have very different resolutions and the finest scale data are sparse or aggregated. Such cases commonly arise when fusing data to capture both regional and local structure. In this work, we develop an efficient MKS algorithm and apply it to the fusion of topographic and bathymetric elevation data.