Atmospheric turbulence in free space affects communication links, leading to a deterioration of the frequency stability of frequency-transmission systems. We establish a relation between the effect of phase fluctuations induced by atmospheric turbulence and the instability of frequency transmission in free space. Considering the optical coupling efficiency as an intermediary between the frequency-transmission system and atmospheric turbulence, we analyze the transfer behavior of frequency stability under varying turbulence conditions, combined with the Gamma-Gamma channel statistical model. In this study, we experimentally validate the model over a 1 km free-space link. Frequency stabilities of $4.1\times {10}^{-12}$ at 1 s and $4.7\times {10}^{-15}$ at 1000 s are demonstrated. The observed optical power fluctuations and the system Allan deviation (ADEV) are in excellent agreement with the simulation results, fully confirming the model’s accuracy and applicability in assessing the degradation effects of atmospheric turbulence. This work provides a theoretical tool for quantitatively analyzing the limits of frequency transmission in complex atmospheric environments and offers important guidance for optimizing the design of urban free-space optical frequency transfer systems.

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• Atmospheric fluid dynamics
• Laser applications
• Space science
• Time & frequency standards
• Turbulence modeling
• Wireless communication networks
• Radio frequency techniques
• Statistical methods