A framework for modeling connections between hydraulics, water surface roughness, and surface reflectance in open channel flows

This paper introduces a framework for examining connections between the flow field, the texture of the air-water interface, and the reflectance of the water surface and thus evaluating the potential to infer hydraulic information from remotely sensed observations of surface reflectance. We used a spatial correlation model describing water surface topography to illustrate the application of our framework. Nondimensional relations between model parameters and flow intensity were established based on a prior flume study. Expressing the model in the spatial frequency domain allowed us to use an efficient Fourier transform-based algorithm for simulating water surfaces. Realizations for both flume and field settings had water surface slope distributions positively correlated with velocity and water surface roughness. However, most surface facets were gently sloped and thus unlikely to yield strong specular reflections; the model exaggerated the extent of water surface features, leading to underestimation of facet slopes. A ray tracing algorithm indicated that reflectance was greatest when solar and view zenith angles were equal and the sensor scanned toward the Sun to capture specular reflections of the solar beam. Reflected energy was concentrated in a small portion of the sky, but rougher water surfaces reflected rays into a broader range of directions. Our framework facilitates flight planning to avoid surface-reflected radiance while mapping other river attributes, or to maximize this component to exploit relationships between hydraulics and surface reflectance. This initial analysis also highlighted the need for improved models of water surface topography in natural rivers.