Optimal Fitting of the Freidberg Solution to In Situ Spacecraft Measurements of Magnetic Clouds

TL;DR

This paper presents an optimization method for fitting a 3D magnetic cloud model, called the Freidberg solution, to in situ spacecraft measurements, achieving high accuracy and correlation in a case study.

Contribution

The paper introduces a least-squares optimization approach for fitting the Freidberg 3D magnetic cloud model to spacecraft data, including uncertainty estimates.

Findings

Achieved reduced chi-squared less than 1 in fitting.

Obtained 0.89 correlation coefficient between model and measurements.

Validated the model with a case study from 2007.

Abstract

We report, in detail, an optimization approach for fitting a three-dimensional (3D) magnetic cloud (MC) model to {\em in situ} spacecraft measurements. The model, dubbed the Freidberg solution, encompasses 3D spatial variations in a generally cylindrical geometry, as derived from a linear force-free formulation. The approach involves a least-squares minimization implementation with uncertainty estimates from magnetic field measurements. We present one case study of the MC event on 22 May 2007 to illustrate the method and demonstrate the satisfying result of the minimum reduced $\chi^2\lesssim 1$, obtained from the STEREO B (STB) spacecraft measurements. In addition, since the ACE spacecraft at Earth crossed the STB solution domain with an appropriate separation distance, the result from the optimally fitted Freidberg solution along the ACE spacecraft path is compared with the actual measurements of magnetic field components. A correlation coefficient of 0.89 is obtained between the two sets of data.