Effects of Various Bipolar Approximations of Active Regions on Solar Surface Magnetic Field Simulations

The evolution of solar surface magnetic fields is essential for understanding solar activity and the underlying dynamic process. The surface flux transport (SFT) model is a widely used and effective tool for simulating this evolution. Active regions are incorporated as magnetic flux sources of the SFT model, but their configurations are usually simplified as symmetric or asymmetric bipolar magnetic regions (BMRs). Here, we aim to quantitatively and systematically assess how such flux source approximations affect SFT results and explore improved approximation methods using our recently developed SFT code. By comparing simulations that incorporate realistic active region configurations from solar cycle 23 through the ongoing cycle 25, we show that approximating active regions as symmetric BMRs leads to a systematic overestimation of the axial dipole strength at solar minimum. This result is independently confirmed using an algebraic quantification that evaluates the axial dipole contribution of individual active regions. The overestimation can be partially reduced by monotonically decreasing the size of the approximated BMRs, but it cannot be fully eliminated. When active regions are instead represented by morphologically asymmetric BMRs, the simulated axial dipole strength exhibits a strong and nearly linear negative dependence on the size ratio between the following and leading polarities. Based on these results, we propose a combination of BMR size and polarity size ratio that yields an axial dipole evolution comparable to that obtained with fully incorporated realistic active region configurations. This study provides a new quantitative constraint for improving future simulations with approximated BMRs.