Time-effective and accurate source localization with mobile robots is crucial in safety-critical scenarios, e.g. leakage detection. This becomes particular challenging in realistic cluttered scenarios, i.e. in the presence of complex current flows or wind. Traditional methods often fall short due to simplifications or limited onboard resources.We propose to combine source localization with a Gaussian Markov Random Field (GMRF). This allows to improve source localization hypotheses by building on the GMRF's concentration and flow field belief that are continuously updated by gathered measurements. We introduce the upstream source proximity (USP) as a natural metric that exploits the joint knowledge represented in the field belief's concentration and flow field, i.e. predicting sources upstream. As a result, our method yields a computationally efficient source localization and field belief module providing substantially more stable gradients than conventional concentration gradient-based methods.We demonstrate the suitability of our approach in a series of numerical experiments covering complex source location scenarios. With regard to computational requirements, the method achieves update rates of 10Hz on a RaspberryPi4B.