Modeling Inner Boundary Values at 18 Solar Radii During Solar Quiet time for Global Three-dimensional Time-Dependent Magnetohydrodynamic Numerical Simulation
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The solar wind speed plays a key role in the transport of CME out of the Sun and ultimately determines the arrival time of CME-driven shocks in the heliosphere. Here, we develop an empirical model of the solar wind parameters at the inner boundary (18 solar radii, Rs) used in our global, 3D MHD model (G3DMHD) or other equivalent ones. The model takes solar magnetic field maps at 2.5 Rs (which is based on the Potential Field Source Surface, PFSS model) and interpolates the solar wind plasma and field out to 18 Rs using the algorithm of Wang and Sheeley [1990a]. A formula V_{18Rs} = V1 + V2 fs^α is used to calculate the solar wind speed at 18 Rs, where V1 is in a range of 150-350 km/s, V2 is in the range of 250-500 km/s, and fs is an expansion factor, which was derived from the Wang and Sheeley (WS) algorithm at 2.5 Rs. To estimate the solar wind density and temperature at 18 Rs, we assume an incompressible solar wind and a constant total pressure. The three free parameters are obtained by adjusting simulation results to match in-situ observations (Wind) for more than 54 combination of V1, V2 and α during a quiet solar wind interval, CR2082. We found V18Rs = (150 +/- 50) + (500 +/- 100) fs^-0.4 km/s performs reasonably well in predicting solar wind parameters at 1 AU not just for CR 2082 but other quiet solar period. Comparing results from the present study with those from WSA [Arge et al. 2000; 2004] we conclude that i) Results of using V_{18Rs} with the full rotation data (FR) as input to drive G3DMHD model is better than the results of WSA using FR, or daily updated. ii) When using a modified daily updated 4-day-advanced solar wind speed predictions WSA performs slightly better than our G3DMHD. iii) When using V_{18Rs} as input, G3DMHD model performs much better than the WSA formula. We argue the necessity of the extra angular width (θb) parameter used in WSA.
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