A Method for Analysis of Spatial Uncertainty in Image Based Surface Velocimetry

Abstract

The use of image based velocimetry methods for field-scale measurements of river surface flow and river discharge have become increasingly widespread in recent years, as these methods have several advantages over more traditional methods. In particular, image based methods are able to measure over large spatial areas at the surface of the flow at high spatial and temporal resolution without requiring physical contact with the water. However, there is a lack of tools to understand the spatial uncertainty in these methods and, in particular, the sensitivity of the uncertainty to parameters under the implementer's control. We present a tool specifically developed to assess spatial uncertainty in remotely sensed, obliquely captured, quantitative images, used in surface velocimetry techniques, and selected results from some of our measurements as an illustration of the tool's capabilities. The developed software is freely available via the public repository GitHub. Uncertainty exists in the coordinate transformation between pixel array coordinates (2D) and physical coordinates (3D) because of the uncertainty related to each of the inputs to the calculation of this transformation, and additionally since the transformation itself is generally calculated in a least squares sense from an over determined system of equations. In order to estimate the uncertainty of the transformation, we perform a Monte Carlo simulation, in which we perturb the inputs to the algorithm used to find the coordinate transformation, and observe the effect on the results of transformations between pixel- and physical- coordinates. This perturbation is performed independently a large number of times over a range of the input parameter space, creating a set of inputs to the coordinate transformation calculation, which are used to calculate a coordinate transformation, and predict the physical coordinates of each pixel in the image. We analyze the variance of the physical position corresponding to each pixel location across the set of transformations, and quantify the sensitivity of the transformation to changes in each of the inputs across the field of view. We also investigate the impact on uncertainty of ground control point (GCP) location and number, and quantify spatial change in uncertainty, which is the key parameter for calculating uncertainty in velocity measurements, in addition to positions. This tool may be used to plan field deployments, allowing the user to optimize the number and distribution of GCPs, the accuracy with which their position must be determined, and the camera placement required to achieve a target level of spatial uncertainty. It can also be used to estimate the uncertainty in image-based velocimetry measurements, including how this uncertainty varies over space within the field of view.