In the event of a single-phase arcing ground fault in the distribution network, the geometric parameters of the arc path dynamically change due to factors such as electric field strength, environment, and temperature. Therefore, establishing an accurate arc model is fundamental for analyzing fault characteristics, locating, and isolating faults. This article first analyzes the physical mechanisms of arc generation and development, Subsequently, an improved arc model based on the dynamic changes of arc length and radius is proposed. This model incorporates the arc radius into the power constant, demonstrating that dynamic arc radius directly influences the characteristics of arc ignition and extinction. To account for the effects of external environmental factors, a randomly varying arc length is also introduced into the arc time constant. Comparing the improved arc model with simulated experimental data, the voltage and current waveforms are found to be in good agreement, with a deviation of 2% for the arc ignition voltage. By changing the inter-electrode spacing of the arc, the model can reflect the voltage characteristics of the arc at different spacings; In summary, the proposed arc model can accurately reflect the actual characteristics of the arc, providing precise descriptions of the ignition voltage, extinction voltage, stable burning arc voltage, and the “zero current” phenomenon in the AC arc ignition process.