Free-space optical (FSO) channels can be characterized by random power fluctuations due to atmospheric turbulence, which is known as scintillation. Weak coherent source based FSO quantum key distribution (QKD) systems suffer from the scintillation effect because during the deep channel fading the expected detection rate drops, which then gives an eavesdropper opportunity to get additional information about protocol by performing photon number splitting (PNS) attack and blocking single-photon pulses without changing QBER. To overcome this problem, in this paper, we study a large-alphabet QKD protocol, which is achieved by using pulse-position modulation (PPM)-like approach that utilizes the time-frequency uncertainty relation of the weak coherent photon state, called here TF-PPM-QKD protocol. We first complete finite size analysis for TF-PPM-QKD protocol to give practical bounds against non-negligible statistical fluctuation due to finite resources in practical implementations. The impact of scintillation under strong atmospheric turbulence regime is studied then. To overcome the secure key rate performance degradation of TF-PPM-QKD caused by scintillation, we propose an adaptation method for compensating the scintillation impact. By changing source intensity according to the channel state information (CSI), obtained by classical channel, the adaptation method improves the performance of QKD system with respect to the secret key rate. The CSI of a time-varying channel can be predicted using stochastic models, such as autoregressive (AR) models. Based on the channel state predictions, we change the source intensity to the optimal value to achieve a higher secret key rate. We demonstrate that the improvement of the adaptation method is dependent on the prediction accuracy.