Quantifying errors in 3D CME parameters derived from synthetic data using white-light reconstruction techniques

(Shortened version) Current efforts in space weather forecasting of CMEs have been focused on predicting their arrival time and magnetic structure. To make predictions, methods have been developed to derive the true CME speed, size and position, among others. Difficulties in determining input parameters for CME forecasting arise from the lack of direct measurements of the coronal magnetic fields and uncertainties in estimating the CME 3D geometric and kinematic parameters. White-light coronagraph images are usually employed by a variety of CME reconstruction techniques. We explore how subjectivity affects the 3D CME parameters that are obtained from the GCS reconstruction technique. We have designed two different synthetic scenarios where the ``true'' geometric parameters are known in order to quantify such uncertainties for the first time. We explore this as follows: 1) Using the ray-tracing option from the GCS model software, and 2) Using 3D MHD simulation data from the MAS code. Our experiment includes different viewing configurations using single and multiple viewpoints. CME reconstructions using a single viewpoint had the largest errors and error ranges for both synthetic GCS and simulated MHD white-light data. Increasing the number of viewpoints to two, the errors decreased by about 4$^\circ$ in latitude, 22$^\circ$ in longitude, 14$^\circ$ in tilt, and 10$^\circ$ in half-angle, pointing towards a need for at least two viewpoints. We found the following CME parameter error bars as a starting point for quantifying the minimum error in CME parameters from white-light reconstructions: $\Delta\theta$ (latitude)=${6^\circ}$, $\Delta\phi$ (longitude)=${11^\circ}$, $\Delta\gamma$ (tilt)=${25^\circ}$, $\Delta\alpha$ (half-angle)=${10^\circ}$, $\Delta h$ (height)=$0.6 R_{\odot}$, and $\Delta\kappa$ (ratio)=$0.1$.