The probabilistic forecasting method described in this study is devised to leverage spatial and temporal dependency of urban traffic networks, in order to provide predictions accurate at short term and meaningful for a horizon of up to several hours. By design, it can deal with missing data, both for training and running the model. It is able to forecast the state of the entire network in one pass, with an execution time that scales linearly with the size of the network. The method consists in learning a sparse Gaussian copula of traffic variables, compatible with the Gaussian belief propagation algorithm. The model is trained automatically from an historical dataset through an iterative proportional scaling procedure, that is well suited to compatibility constraints induced by Gaussian belief propagation. Results of tests performed on two urban datasets show a very good ability to predict flow variables and reasonably good performances on speed variables. Some understanding of the observed performances is given by a careful analysis of the model, making it to some degree possible to disentangle modeling bias from the intrinsic noise of the traffic phenomena and its measurement process.