This paper reveals and explores the flow characteristics of airport surface network on both mesoscopic and macroscopic levels. We propose an efficient modeling approach based on the cell transmission model for simulating the spatio-temporal evolution of flow and congestion on taxiway and apron networks. The existence of link-based fundamental diagram that expresses the functional relationship between link density and flow is demonstrated using empirical data collected in Guangzhou Baiyun airport. The proposed CTM-based network model is shown to be an efficient and accurate method capable of supporting air traffic prediction and decision support. In addition, using both CTM-based simulation and empirical data, we further reveal the existence of an aggregate relationship between traffic density and runway throughput, which is referred to as macroscopic fundamental diagram (MFD) in the literature of road traffic. The MFD on the airport surface is analyzed in depth, and utilized to devise several robust off-block control strategies under uncertainties, which are shown to significantly outperform existing off-block control methods.