Climate change is believed to increase the amount of dissolved organic matter in surface water, as a result of the release of bulk organic matter, which make difficult to achieve a high quality of drinking water via conventional water treatment techniques. Therefore, the natural water treatment techniques, such as managed aquifer recharge (MAR), can be proposed as a alternative method to improve water quality greatly. Removal of bulk organic matter using managed aquifer recharge system is mainly achieved by biodegradation. Biodegradable dissolved organic carbon (BDOC) and assimilable organic carbon (AOC) can be used as water quality indicators for biological stability of drinking water. In this study, we compared the change of BDOC and AOC with respect to pretreatment methods (i.e., ozone or peroxone). The oxidative pretreatment can transform the recalcitrant organic matter into readily biodegradable one (i.e., BDOC and AOC). We also investigated the differences of organic matter characteristics between BDOC and AOC. We observed the decreases in dissolved organic carbon (DOC) and the tryptophan-like fluorescence intensities. Liquid chromatographic - organic carbon detection (LC-OCD) analysis also showed the reduction of the low molecular weight (LMW) fraction (15% removed, less than 500 Da), which is known to be easily biodegradable, and the biopolymers, high molecular weight fractions (66%). Therefore, BDOC consists of a broad range of organic matter characteristics with respect to molecular weight. In AOC, low molecular weight organic matter and biopolymers fraction was reduced by 11 and 6%, respectively. It confirmed that biodegradation by microorganisms as the main removal mechanism in AOC, while BDOC has biodegradation by microorganism as well as the sorption effects from the sand. $O_3$ and $O_3+H_2O_2$ were compared with respect to biological stability and dissolved organic matter characteristics. BDOC and AOC were determined to be about 1.9 times for $O_3$ and about 1.4 times for $O_3+H_2O_2$. It was confirmed that $O_3$ enhanced the biodegradability by increasing LMW dissolved organic matter.