Spatio-temporally varying Strickler coefficient: A calibration approach applied to a Danish river using in-situ water surface elevation and UAS altimetry

Hydraulic roughness (e.g., expressed in terms of Manning's or Strickler's coefficient) is an essential input to numerical hydrodynamic models. One way to estimate roughness parameters is by hydraulic inversion, using observed water surface elevation (WSE) collected from gauging stations, satellite platforms, or Unmanned Aerial System (UAS) altimeters. Specifically, UAS altimetry provides close to instantaneous observations of longitudinal profiles and seasonal variations of WSE for various river types, which are helpful for calibrating roughness parameters. However, it is computationally expensive to run high-resolution hydrodynamic models thousands to millions of times as required for the global optimization of distributed parameter sets (e.g., spatio-temporally varying river roughness). This study presents an efficient calibration approach for hydrodynamic models using a simplified steady-state hydraulic solver, UAS altimetry datasets, and in-situ observations. The calibration approach minimized the weighted sum of a misfit term, spatial smoothness penalty, and an a-priori sinusoidal temporal variation constraint. The approach was first demonstrated for several synthetic calibration experiments, and the results indicated that the global search algorithm accurately recovered the variations of Strickler coefficient (K_s) for short river reaches in temporal (due to the seasonal growth cycle of the aquatic vegetation) and spatial (e.g., due to spatially variable density of submerged vegetation) scales. Subsequently, the calibration approach was demonstrated for a real WSE dataset collected at a Danish test site (Vejle Å). In this river, friction is dominated by submerged vegetation growing in the stream and shows strong seasonal and longitudinal variations due to the plant growth cycle and variable vegetation density and species composition. Results indicated that spatio-temporal variation of K_s was required to fit in-situ observations and UAS altimetry accurately. This study illustrates how UAS altimetry and hydrodynamic modeling can be combined to achieve an improved understanding and better parameterization of small and medium-sized rivers, where river channel conveyance is controlled by vegetation growth and other spatio-temporally variable factors.