Simulations are currently an essential tool to develop and test wireless sensor networks (WSNs) protocols and to analyze future WSNs applications performance. Researchers often simulate their proposals rather than deploying high-cost test-beds or develop complex mathematical analysis. However, simulation results rely on physical layer assumptions, which are not usually accurate enough to capture the real behavior of a WSN. Such an issue can lead to mistaken or questionable results. Besides, most of the envisioned applications for WSNs consider the nodes to be at the ground level. However, there is a lack of radio propagation characterization and validation by measurements with nodes at ground level for actual sensor hardware. In this paper, we propose to use a low-computational cost, two slope, log-normal path-loss near ground outdoor channel model at 868 MHz in WSN simulations. The model is validated by extensive real hardware measurements obtained in different scenarios. In addition, accurate model parameters are provided. This model is compared with the well-known one slope path-loss model. We demonstrate that the two slope log-normal model provides more accurate WSN simulations at almost the same computational cost as the single slope one. It is also shown that the radio propagation characterization heavily depends on the adjusted model parameters for a target deployment scenario: The model parameters have a considerable impact on the average number of neighbors and on the network connectivity.