Estimating the uncertainty of video-based flow velocity and discharge measurements due to the conversion of field to image coordinates

Video-based hydrometry continues to develop for contactless discharge measurements, automated flood gauging stations and the use of crowd-sourced flood videos for discharge reconstruction. Irrespective of the velocimetry algorithm used (LSPIV, STIV, PTV…), orthorectification of the images is necessary beforehand, so that each pixel has the same known physical size. Most times, the orthorectification transformation is a plane-to-plane projection from the water surface to the camera sensor. Two approaches are typically used to compute the coefficients of this transformation: their calibration from ground reference points (GRPs) with known image and real-world coordinates (“implicit calibration”) or their calculation from the values of the intrinsic (focal length, sensor size) and extrinsic (position, angles) parameters of the camera (“explicit calibration”). In this paper, we develop a Bayesian method which makes it possible to combine the implicit and explicit approaches in a probabilistic framework. The Bayesian approach can be used from situations suitable for the implicit approach (plenty of GRPs) to situations propitious to the explicit approach (well-known camera parameters). The method is illustrated using synthetic views of a typical streamgauging scene with known true values of the parameters and GRP coordinates. We show that combining observational and prior information is generally beneficial to get precise estimates. Further tests carried out with a real scene of the Arc River at Randens, France, in flood conditions illustrate the impact of the number, uncertainty and spatial distribution of GRPs on the final uncertainty of flow velocity and discharge.