The wireless sensor network (WSN), is a type of self-organized distribution system without complex infrastructure requirement. However, WSN's independence and un-attended usage limit its power supply and life expectancy. These become a critical issue for any WSN implementation. The in-network processing which, intends to minify data volume locally can greatly reduce the energy consumption of data delivery over a long distance to the sink. However, open problems are still remain with in-network processing, such as how to carry out in-network processing, and how to combine routing scheme to the sink (e.g. the long distance delivery). For any WSN application, the following pre-assumption is vital. There exists a physical signal field which bridges physical events to the sensors of WSN, otherwise WSN does not work. In fact, the physical signal field can be depicted by sensory data of all the nodes, and can even be used for local data convergence (e.g. in-network processing). An immediate solution which we propose is that, sensory data of the nodes can be converged to local extremes of the physical signal field along its gradient direction. Furthermore, the physical signal field is integrated with the cost field routing scheme. The cost field routing is in charge of delivering data to the sink. During the in-network processing, the delivery direction is derived by combining linearly the gradient directions of the cost field and physical signal field. Also simulation results show that the proposed schemes are robust, adaptable, and reliable to the variation of physical events.