Experimental data indicate that in a sloped area, the value of β abruptly changes before and after a given source arrives at the closest point of approach to the hydrophone, which has not been previously reported. The adiabatic approximation is employed to explain the above abrupt change in β, and it is found that the azimuthal variance in the sound path is the reason for this phenomenon. Simulations are performed to confirm the model and experimental data, and perfect agreement is achieved. This work suggests that β should be carefully set in related applications in a sloped area.