Meshing workflows for multiscale hydrological simulations: Wavelet-based
approach improves model accuracy
The high computational cost of large-scale, process-based hydrological
simulations can be approached using variable resolution meshes, where
only the region around significant topographic features is refined.
However, generating quality variable resolution meshes from digital
elevation data is non-trivial. In literature, usually a slope or
curvature-based criterion is defined to detect regions of refinement.
These techniques often involve a number of free parameters that control
the finest and coarsest resolutions, and the transition between fine
resolution to coarse resolution. The influence of these parameters on
the resulting mesh is usually not well-understood. In order to overcome
the large number of free parameters involved, we propose to carry out
the Mallat decomposition of the digital elevation data using the Haar
wavelet. This gives a nested multilevel representation of the elevation
data, split into average coefficients and detail coefficients. Applying
hard-thresholding to these detail coefficients assigns a required level
of refinement to each data point. This reduces the number of free
parameters to exactly one: the acceptable error threshold. In this
presentation, we focus on identifying which geomorphometric parameter(s)
should be used to steer mesh refinement. We compare zero-inertia model
simulation runs on meshes generated by decomposing elevation and slope.
We hypothesize that because of the form of the Haar wavelet, the first
mesh refinement essentially is using the gradient information, while the
latter is using the curvature as refinement criterion. Our results
suggest that in high-elevation catchments the curvature of the
topography is a far better indicator for refinement than the slope.
Using the Mallat decomposition on the tensor of the first derivative of
the bed elevation (i.e., bed slope) for mesh refinement yields better
agreement in the hydrograph compared to the decomposition of the bed
elevation. We present surface runoff results for the Lower Triangle
catchment, CO, USA, to illustrate the performance of the wavelet-based
local mesh refinement.