A Method for Analysis of Spatial Uncertainty in Image Based Surface Velocimetry - Schweitzer, Seth A.; Cowen, Edwin A. (Frontiers in Water, 2022)
The use of image-based velocimetry methods for field-scale measurements of river flow and discharge has become increasingly widespread in recent years. These methods are able to measure over large areas with high spatial and temporal resolution, without requiring contact with the water. However, there is a lack of tools to understand the spatial uncertainty in these methods and, particularly, its sensitivity to parameters that can be controlled. We present a tool specifically developed to assess spatial uncertainty in remotely sensed images used in surface velocimetry techniques, and results from measurements that illustrate the tool’s capabilities. The software tool is freely available online. Uncertainty exists in the coordinate transformation between pixel array coordinates (2D) and physical coordinates (3D) because of the uncertainty of each input to the transformation, and since the transformation itself is calculated in a least-squares sense from an overdetermined system of equations. We perform a Monte Carlo simulation, perturbing the inputs to the algorithm used to find the coordinate transformation, and observe the effect on transformations between pixel- and physical- coordinates. This perturbation is performed independently a large number of times with values selected from the input parameter space, creating a set of inputs 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 perturbed transformations, and quantify the sensitivity of the transformation to changes in each of the inputs. 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. 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.