This paper proposes a monocular geometric 3D reconstruction framework to be applied to image-based river velocimetry. Image-based river surface velocity estimation methods in the literature require both planar river surface assumption and Ground Reference Points (GRPs) locations. These two elements are then used to create ortho-rectified images with uniform spatial resolution. The motion estimation is thus applied directly to the transformed set of images. In this paper, the water surface planarity assumption is exploited further to create minimal 3D representations of river sites. Ortho-images are not needed; instead, the reconstructed 3D points will have a direct relationship with their corresponding 2D image points such that any 2D displacement could be reprojected back to 3D. The proposed modeling framework is based on an orthogonality assumption between the planar river surface and a plane located on any of the banks, and visible in the images. The reconstruction is then scaled to the correct physical scale if the height of the camera with respect to the river surface is known. Otherwise, the scale could be computed if any object of a known size could be located on any of the two planes. Applications of this new method are presented and discussed both in controlled lab environment and in the field. The proposed framework significantly reduces the field work required for GRPs deployment. Under simple assumptions, raw amateur videos can be processed without ever going to the site.