Error Analysis regarding the calculation of NLFF Field

Abstract: Field extrapolation is an alternative method to study chromospheric and coronal magnetic fields. In this paper, two semi-analytical solutions of force- free fields (Low and Lou, 1990) have been used to study the errors of nonlin- ear force-free (NLFF) fields based on force-free factor alpha. Three NLFF fields are extrapolated by approximate vertical integration (AVI) Song et al. (2006), boundary integral equation (BIE) Yan and Sakurai (2000) and optimization (Opt.) Wiegelmann (2004) methods. Compared with the first semi-analytical field, it is found that the mean values of absolute relative standard deviations (RSD) of alpha along field lines are about 0.96-1.05, 0.94-1.07 and 0.46-0.72 for AVI, BIE and Opt. fields, respectively. While for the second semi-analytical field, they are about 0.80-1.02, 0.63-1.34 and 0.33-0.55 for AVI, BIE and Opt. fields, respectively. As for the analytical field, the calculation error of hjRSDji is about 0.1 {\guillemotright} 0.2. It is also found that RSD does not apparently depend on the length of field line. These provide the basic estimation on the deviation of extrapolated field obtained by proposed methods from the real force-free field.