ESS 261 Topics in magnetospheric physics Space weather forecast models ____ the prediction of solar wind speed April 23, 2008

Methods Empirical methods Interplanetary scintillation (IPS) techniques Interplanetary scintillation (IPS) of cosmic radio signals has been employed to deduce the solar wind in regions beyond the ecliptic plane and near the sun, where spacecrafts have no access. IPS observations are performed at a frequency of 327 MHz using four radio telescopes at Toyokawa, Fuji, Sugadaira, and Kiso. This four-antenna system is able to observe the solar wind at distances of 0.1-1 AU from the sun. 12/2/2018 ESS 261

Potential field source surface (PFSS) model Principle: the more slowly a coronal flux tube expands in areal cross-section, the higher the asymptotic wind speed along that flux tube. (The physical basis for this inverse correlation is the rapid increase in the mass flux density at the coronal base ___ hence decrease in the energy per particle ___ with increasing areal divergence rate.) The flux tube divergence rates will be calculated by applying a potential-field source-surface (PFSS) extrapolation to the observed photospheric flux distribution, in the form of monthly synoptic maps from the Wilcox Solar Observatory (WSO). In the PFSS model, the magnetic field is assumed to be curl-free in the region between the solar surface and a spherical “source surface”, where the tangential field components are constrained to vanish. 12/2/2018 ESS 261

Expansion factor For a flux tube that passes through a given point on the source surface, which is the factor by which the flux tube expands in solid angle between its footpoint location and the source surface. The expansion factor equals to 1 if the bundle of open field lines diverges as r2, but exceeds 1 if (as usually the case) the flux diverges more rapidly than r2. 12/2/2018 ESS 261

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A modification to the PFSS model Arge et al. have applied a modification to the Wang-Sheeley model. The modification consists of deriving an empirical relationship between fs and solar wind speed at 2.5 Rs rather than L1. This empirical function was found by iteratively testing various mathematical relationships between fs and vsw, using it to assign the solar wind speed at the source surface, propagating the wind out to L1, and then comparing the results with observations. The procedure was repeated until a best fit was found. A simple 1-D modified kinematic (1-DMK) model, which included an ad hoc method to account for stream interactions, was used to transport the wind to L1. 12/2/2018 ESS 261

Solar wind observations made at L1 must be mapped back to the Sun to compare with photospheric and coronal field parameters. WIND spacecraft observations was mapped from 1995 back to 0.1 AU (i.e., 21.5 Rs) assuming constant flow speed, neglecting stream interactions, but accounting for solar rotation. 12/2/2018 ESS 261

Schatten current sheet (SCS) model Representing the field configuration of the outer corona between 2.5 and 21.5 Rs. Others? 1-D modified kinematic model (1-DMK) Using this model rather than MHD model is mainly for simplicity For this particular study, the 1-DMK code is preferred over a more advanced 3-D MHD code, as it significantly reduces the time required for each new trial run. 12/2/2018 ESS 261

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Parameters Expansion factor fs evaluated at 2.5 Rs; Photospheric (or footpoint) field strength (Bph); The minimum (spherical) angular separation between an open field footpoint and Sub-earth point; Current sheet; Nearest coronal hole boundary. 12/2/2018 ESS 261

Fourth, directly compare predicitons with observations. First, search for patterns between solar wind speed and the above five photospheric/coronal parameters; Second, deduce and empirical relationship for vsw involving one or more these parameters; Third, assign vsw at the outer boundary of the SCS model, and then, for each daily updated map from 1995, propagate the solar wind out to Earth using a 1-D modified kinematic (1-DMK) code; Fourth, directly compare predicitons with observations. 12/2/2018 ESS 261

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To be continued by Morrisa