Abstract: The aerial photogrammetry of shallow water bottoms has the potential to be an efficient high-resolution survey technique for shallow water topography, thanks to the advent of convenient UAV and automatic image processing techniques Structure-from-Motion (SfM) and Multi-View Stereo (MVS)). However, it suffers from the systematic overestimation of the bottom elevation, due to the light refraction at the air-water interface. In this study, we present an empirical method to correct for the effect of refraction after the usual SfM-MVS processing, using common software. The presented method utilizes the empirical relation between the measured true depth and the estimated apparent depth to generate an empirical correction factor. Furthermore, this correction factor was utilized to convert the apparent water depth into a refraction-corrected (real-scale) water depth. To examine its effectiveness, we applied the method to two river sites, and compared the RMS errors in the corrected bottom elevations with those obtained by three existing methods. The result shows that the presented method is more effective than the two existing methods: The method without applying correction factor and the method utilizes the refractive index of water (1.34) as correction factor. In comparison with the remaining existing method, which used the additive terms (offset) after calculating correction factor, the presented method performs well in Site 2 and worse in Site 1. However, we found this linear regression method to be unstable when the training data used for calibration are limited. It also suffers from a large negative bias in the correction factor when the apparent water depth estimated is affected by noise, according to our numerical experiment. Overall, the good accuracy of refraction correction method depends on various factors such as the locations, image acquisition, and GPS measurement conditions. The most effective method can be selected by using statistical selection (e.g. leave-one-out cross validation).
Abstract: A methodology is proposed for estimating the optical
attenuation and proportional depth variation of shallow inland water.
The process is demonstrated with EO-1 Hyperion hyperspectral and
IRS-P6 LISS-3 multispectral images of Kolkata city nearby area
centered around 22º33′ N 88º26′ E. The attenuation coefficient of
water was found to change with fine resolution of wavebands and in
presence of suspended organic matter in water.
Abstract: A water surface slope limiting scheme is tested and
compared with the water depth slope limiter for the solution of one
dimensional shallow water equations with bottom slope source term.
Numerical schemes based on the total variation diminishing Runge-
Kutta discontinuous Galerkin finite element method with slope
limiter schemes based on water surface slope and water depth are
used to solve one-dimensional shallow water equations. For each
slope limiter, three different Riemann solvers based on HLL, LF, and
Roe flux functions are used. The proposed water surface based slope
limiter scheme is easy to implement and shows better conservation
property compared to the slope limiter based on water depth. Of the
three flux functions, the Roe approximation provides the best results
while the LF function proves to be least suitable when used with
either slope limiter scheme.