$$\beta$$-plane correction for eddy detection and the drivers of eddy activity heterogeneity in a semi-closed maritime continent basin

The Indonesian seas, located within the Maritime Continent, are characterized by complex topography, narrow straits, and some of the warmest sea surface temperatures (SSTs) globally. Eddy activity in this region is strongly influenced by monsoonal winds, the Indonesian Throughflow (ITF), Intertropical Convergence Zone (ITCZ), and local bathymetry, producing seasonal patterns that differ from those of the open Pacific and Indian Oceans. Most existing eddy detection methods, however, were designed for mid-latitude regions and neglect equatorial corrections to the Coriolis parameter. This study introduces a localized β-plane correction to improve Coriolis parameter estimation for eddy detection in equatorial waters, applied to three decades (1993-2022) of satellite-derived sea level anomaly data. Using a modified Winding Angle (WA) method, we identified 8,435 anticyclonic eddies (AEs) and 8,126 cyclonic eddies (CEs), with 7,656 AEs and 7,415 CEs confirmed as persistent features based on the Okubo-Weiss (OW) parameter. Eddy sizes were predominantly 60-80 km, with mesoscale eddies concentrated in the northern sector of the domain and along its eastern and southern boundaries. Seasonal variability was evident: AEs peaked during the southeast monsoon (June-August), while CEs dominated during the northwest monsoon (December-February) with stable size. During the eddy-minimum season, high-vorticity CEs formed at lower latitudes than AEs. Regionally, the Java Sea and North Natuna Sea hosted the most energetic eddies during the southeast monsoon, whereas the Sulu, Celebes, Maluku, and Banda Seas emerged as key eddy formation zones. Although eddies were generally short-lived (21-28 days), they contributed substantially to regional energy variability. The spatio-temporal heterogeneity of eddy activity reflects the combined influence of monsoonal wind forcing, SST gradients, and bathymetric constraints, which jointly regulate eddy generation, propagation, and decay. Eddy occurrence also exhibits a hemispheric asymmetry that coincides with ITCZ displacement. These results underscore the coupled atmosphere-ocean processes shaping mesoscale variability in one of the world's most dynamic tropical marine environments.