Operational weather forecasting models have advanced for decades on both the explicit numerical solvers and the empirical physical parameterization schemes. However, the involved high computational costs and uncertainties in these existing schemes are requiring potential improvements through alternative machine learning methods. Previous works use a unified model to learn the dynamics and physics of the atmospheric model. Contrarily, we propose a simple yet effective machine learning model that learns the horizontal movement in the dynamical core and vertical movement in the physical parameterization separately. By replacing the advection with a graph attention network and the convection with a multi-layer perceptron, our model provides a new and efficient perspective to simulate the transition of variables in atmospheric models. We also assess the model's performance over a 5-day iterative forecasting. Under the same input variables and training methods, our model outperforms existing data-driven methods with a significantly-reduced number of parameters with a resolution of 5.625 deg. Overall, this work aims to contribute to the ongoing efforts that leverage machine learning techniques for improving both the accuracy and efficiency of global weather forecasting.