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Accurate simulation and analysis of wireless protocols and systems is inherently dependent on an accurate model of the underlying channel. In this paper, we show that residual MAC layer wireless sensor network (WSN) channels cannot be characterized using the commonly-used high-order Markov channel models. Instead, we demonstrate that 2-Tier models, in which a high-level (tier 1) frame-level model excites a lower-level (tier 2) bit-error model, are needed to accurately characterize WSN residual channels. We compare the modeling accuracy of 1-Tier and 2-Tier models using residual bit-error traces collected over an operational 802.15.4 network. We first analyze error traces collected over different setups to investigate the amount of bit-level memory present in wireless sensor network channels. We then validate the accuracy of the proposed models using information divergence measures. We show that 2- Tier models have significantly and consistently better accuracy than 1-Tier models. Finally, we demonstrate that the wrong choice of a channel model can result in grossly inaccurate simulation results. This claim is substantiated by simulating three important metrics: (i) recovery ratio for an abstract Forward Error Correction (FEC) scheme, (ii) frame goodput of an unreliable protocol over a multihop network, and (Hi) number of retransmissions per packet for a reliable protocol.