Accurate estimation of Zenith Tropospheric Delay (ZTD) is essential for mitigating atmospheric effects in radio astronomical observations and improving the retrieval of precipitable water vapor (PWV). In this study, we first analyze the periodic characteristics of ZTD at the NanShan Radio Telescope site using Fourier transform, revealing its dominant seasonal variations, and then investigate the correlation between ZTD and local meteorological parameters, to better understand atmospheric influences on tropospheric delay. Based on these analyses, we propose a hybrid deep learning Gated Recurrent Units-Long Short-Term Memory model, incorporating meteorological parameters as external inputs to enhance ZTD forecasting accuracy. Experimental results demonstrate that the proposed approach achieves a Root Mean Squared Error of 7.97 mm and a correlation coefficient R of 96%, significantly outperforming traditional empirical models and standalone deep learning architectures. These findings indicate that the model effectively captures both short-term dynamics and long-term dependencies in ZTD variations. The improved ZTD predictions not only contribute to reducing atmospheric errors in radio astronomical observations but also provide a more reliable basis for PWV retrieval and forecasting. This study highlights the potential of deep learning in tropospheric delay modeling, offering advancements in both atmospheric science and geodetic applications.