The increasing volume and velocity of science data necessitate the frequent movement of enormous data volumes as part of routine research activities. As a result, limited wide-area bandwidth often leads to bottlenecks in research progress. However, in many cases, consuming applications (e.g., for analysis, visualization, and machine learning) can achieve acceptable performance on reduced-precision data, and thus researchers may wish to compromise on data precision to reduce transfer and storage costs. Error-bounded lossy compression presents a promising approach as it can significantly reduce data volumes while preserving data integrity based on user-specified error bounds. In this paper, we propose a novel data transfer framework called Ocelot that integrates error-bounded lossy compression into the Globus data transfer infrastructure. We note four key contributions: (1) Ocelot is the first integration of lossy compression in Globus to significantly improve scientific data transfer performance over wide area network (WAN). (2) We propose an effective machine-learning based lossy compression quality estimation model that can predict the quality of error-bounded lossy compressors, which is fundamental to ensure that transferred data are acceptable to users. (3) We develop optimized strategies to reduce the compression time overhead, counter the compute-node waiting time, and improve transfer speed for compressed files. (4) We perform evaluations using many real-world scientific applications across different domains and distributed Globus endpoints. Our experiments show that Ocelot can improve dataset transfer performance substantially, and the quality of lossy compression (time, ratio and data distortion) can be predicted accurately for the purpose of quality assurance.