Quantifying Below-Water Fluvial Geomorphic Change: The Implications of Refraction Correction, Water Surface Elevations, and Spatially Variable Error

Much of the geomorphic work of rivers occurs underwater. As a result, high resolution quantification of geomorphic change in these submerged areas is important. Currently, to quantify this change, multiple methods are required to get high resolution data for both the exposed and submerged areas. Remote sensing methods are often limited to the exposed areas due to the challenges imposed by the water, and those remote sensing methods for below the water surface require the collection of extensive calibration data in-channel, which is time-consuming, labour-intensive, and sometimes prohibitive in difficult-to-access areas. Within this paper, we pioneer a novel approach for quantifying above- and below-water geomorphic change using Structure-from-Motion photogrammetry and investigate the implications of water surface elevations, refraction correction measures, and the spatial variability of topographic errors. We use two epochs of imagery from a site on the River Teme, Herefordshire, UK, collected using a remotely piloted aircraft system (RPAS) and processed using Structure-from-Motion (SfM) photogrammetry. For the first time, we show that: (1) Quantification of submerged geomorphic change to levels of accuracy commensurate with exposed areas is possible without the need for calibration data or a different method from exposed areas; (2) there is minimal difference in results produced by different refraction correction procedures using predominantly nadir imagery (small angle vs. multi-view), allowing users a choice of software packages/processing complexity; (3) improvements to our estimations of water surface elevations are critical for accurate topographic estimation in submerged areas and can reduce mean elevation error by up to 73%; and (4) we can use machine learning, in the form of multiple linear regressions, and a Gaussian Naive Bayes classifier, based on the relationship between error and 11 independent variables, to generate a high resolution, spatially continuous model of geomorphic change in submerged areas, constrained by spatially variable error estimates. Our multiple regression model is capable of explaining up to 54% of magnitude and direction of topographic error, with accuracies of less than 0.04 m. With on-going testing and improvements, this machine learning approach has potential for routine application in spatially variable error estimation within the RPAS-SfM workflow.