In video-based dynamic point cloud compression (V-PCC), 3D point clouds are projected onto 2D images for compressing with the existing video codecs. However, the existing video codecs are originally designed for natural visual signals, and it fails to account for the characteristics of point clouds. Thus, there are still problems in the compression of geometry information generated from the point clouds. Firstly, the distortion model in the existing rate-distortion optimization (RDO) is not consistent with the geometry quality assessment metrics. Secondly, the prediction methods in video codecs fail to account for the fact that the highest depth values of a far layer is greater than or equal to the corresponding lowest depth values of a near layer. This paper proposes an advanced geometry surface coding (AGSC) method for dynamic point clouds (DPC) compression. The proposed method consists of two modules, including an error projection model-based (EPM-based) RDO and an occupancy map-based (OM-based) merge prediction. Firstly, the EPM model is proposed to describe the relationship between the distortion model in the existing video codec and the geometry quality metric. Secondly, the EPM-based RDO method is presented to project the existing distortion model on the plane normal and is simplified to estimate the average normal vectors of coding units (CUs). Finally, we propose the OM-based merge prediction approach, in which the prediction pixels of merge modes are refined based on the occupancy map. Experiments tested on the standard point clouds show that the proposed method achieves an average 9.84\% bitrate saving for geometry compression.