Hydraulic resistance of submerged rigid vegetation derived from first‐order closure models

Abstract

The past decade witnessed rapid developments in remote sensing methods that now permit an unprecedented description of the spatial variations in water levels ( H w ), canopy height ( h c ), and leaf area density distribution ( a ) at large spatial scales. These developments are now renewing interest in effective resistance formulations for water flow within and above vegetated surfaces so that they can be incorporated into simplified water routing models driven by such remote sensing products. The first generation of such water routing models linked the bulk velocity to gradients in H w via a constant diffusion velocity that cannot be inferred from canopy properties ( a and h c ). The next generation of such hydrologic models must preserve the nonlinear relationship between the resistance value, canopy attributes (e.g., a and h c ), and H w without compromising model simplicity. Using a simplified scaling analysis on the depth‐integrated mean momentum balance and a two‐layer model for the bulk velocity, the Darcy‐Weisbach friction factor ( f ) was shown to vary with three canonical length scales that can be either measured or possibly inferred from remote sensing products H w , h c , and the adjustment length scale L c = ( C d a ) −1 , where C d is the drag coefficient (of order unity). The scaling analysis proposed here reveals that these length scales can be combined in two dimensionless groups, H w / h c and L c / h c . The dependence of f on these two functional groups was then explored using a combination of first‐order closure modeling and 130 experimental runs derived from a large number of flume experiments carried out for rigid and flexible vegetation. The results from the data and the model show a nonlinear decrease in f with increasing H w / h c at a given L c / h c and the nonlinear increase in f with decreasing L c / h c . Furthermore, both model and data results did not exhibit any dependence on the bulk Reynolds number.