In the paper we formulate the WSNs with a two-tier architecture

where the cluster head nodes partitioned into the upper tier are studied

and the routing problem is analyzed with the time-varying data rate

then a time-varying bit rate routing algorithm based on data fusion(TBRRDF) is proposed. If the mean value of varying data rate at a specific cluster head is known a priori

then the routing solution obtained by the proposed algorithm achieves maximal network lifetime. Further

we prove that the routing solution is optimal by applying the bit rate routing algorithm

and the simulation results validate the effectiveness.