The signal-to-noise ratio (SNR) of communication system is variable with channel status and circuits noise. We analyze the turbulence index and irradiance variance, and then establish the relationship between Rytov index of the atmospheric turbulence and SNR of intensity modulation free space optical communication (FSO) system. Firstly, the multiplicative noise induced by irradiance is analyzed. The relationship between irradiance variance and SNR of the FSO system is introduced. Then two common noise models are introduced to simulate the multiplicative noise. The relationship among Rytov index, irradiance variance and SNR of FSO system is derived. At last, the experimental measurement data under different weather conditions are used to prove the simulation results. The results show that there is a linear relationship between Rytov index and variance of intensity in weak turbulent weather. SNR of FSO system relatively decreases as the Rytov index increases. While in medium to strong turbulent weather, variance of intensity converges towards saturation, and SNR tends to a stable value.