Internal tides (ITs) are sub-surface gravity waves that generate significant sea surface height (SSH) signals detectable with satellite altimetry. The Surface Water Ocean Topography (SWOT) mission is capturing ocean surface data at an unprecedented spatial resolution of 2 km. Accurately identifying these IT signals is crucial for effectively monitoring other non-tidal oceanic signals. We use data-assimilative forecast system based on the HYbrid Coordinate Ocean Model (HYCOM) to identify both coherent and incoherent ITs and compared its performance with the state-of-the-art IT correction model (High Resolution Empirical Tide, HRET8.1). HYCOM demonstrated a 9% greater variance removal for coherent IT compared to HRET8.1 and eliminated an additional 14.6% of incoherent IT. Specifically, at the M2 frequency, HYCOM removed 40-60% of coherent IT variance and 10-20% of incoherent IT variance. Ocean forecast models like HYCOM enhance our understanding of IT dynamics and serve as alternative tools for IT mapping and altimetry correction.