Monitoring environmental phenomena by distributed sensor sampling confronts the challenge of unpredictable variability in the spatial distribution of phenomena often coupled with demands for a high spatial sampling rate. The introduction of actuation-enabled robotics sensors permits a system to optimize the sampling distribution through runtime adaptation. However, such systems must efficiently dispense sampling points or otherwise suffer from poor temporal response. In this paper we propose and characterize an active modeling system. In our approach, as the robotic sensor acquires measurement samples of the environment, it builds a model of the phenomenon. Our algorithm is based on an incremental optimization process where the robot supports a continuous, iterative process of 1) collecting samples with maximal coverage in the design space, 2) building the environmental model 3) predicting sampling point locations that contribute the greatest certainty regarding the phenomenon 4) and sampling the environment based on a combined measure of information gain and navigation and sampling cost. This can provide significant reductions in the magnitude of field estimation error with a modest navigational trajectory time. We evaluate our algorithm through a simulation, using a combination of static and mobile sensors sampling light illumination field.