Nowadays, many devices in wireless sensor networks are provided with energy harvesting capability to allow for their continuous operation over long periods of time. In principle, the energy level within each sensor should be managed optimally to ensure the best performance. Network engineers, however, often consider optimality under the idealized assumption of perfect knowledge about the State-of-Charge (SOC) of the device. This information is not always realistic or accurate. In our previous work , we showed that optimal policies for sensing, transmission, and battery usage should rather consider uncertainty on the SOC of the device. In this paper, we extend that investigation, therein performed in the idealized scenario of i.i.d. energy arrivals, by considering a correlated energy generation process. We show that the knowledge of the SOC and that of the energy generation process are useful in a complementary manner, that is they can be traded for each other. Moreover, the knowledge on the state of the energy generation process can obviate the need for acquiring accurate SOC information. This investigation paves the road for a new line of research in wireless sensor networks, allowing a tighter interaction between the designers of energy harvesting and battery storage mechanisms on the one hand, and the engineers of network operation and control policies on the other.