Reply [to “Comment on ‘Modeling the magnetosphere for northward interplanetary magnetic field: Effects of electrical resistivity’ by Joachim Raeder”]

Abstract

In their comment, Gombosi et al. [this issue] (hereinafter referred to as GPL99) claim that the conclusions reachedby Raeder [1999] (hereinafter referred to as R99) are not correct and not supported by their simulations. Specifically, they raise the issues of (1) results from other codes for northward interplanetary magnetic field (IMF), (2) the inherent numerical resistivity of different schemes, (3) mesh convergence, and (4) the diffusion of the bow shock in the highresistivity cases. Each of these issues warrants clarification.GPL99 essentially claim that their model is more accurate than anyone else' s. This assertion is based on the notion of "mesh convergence." As I shall discuss below, mesh convergence is at most necessary, but not sufficient for validating a simulation. GPL99 do not offer any physical explanation for their results, that is, why there should be a closed magnetosphere with a 50 R• short tail as a result of a moderately northward IME Neither do they show any conclusive experimental evidence to support their assertion. They do, however, present a simulation based on the first-order accurate and highly diffusive Rusanov scheme (as I do in this reply) which shows a closed magnetosphere. These simulations corroborate the main result of R99, namely, that large values of resistivity produce a closed magnetosphere for northward Numerical ResistivityGPL99 point out correctly that any discrete numerical scheme to solve the MHD equations will lead to diffusion and that these artificial effects are difficult to quantify. It is an unfortunate reality of computational physics that there is no method to solve hyperbolic equations, such as the ideal MHD equations, numerically without introducing numerical diffusion and dispersion when discontinuities are present in the solution [Sod, 1985]. The quest has always been to minimize these effects. While schemes with no diffusion can be constructed (for example, central second-order spatial differences with leap-frog time stepping), they suffer from excessive numerical dispersion which makes them useless for computations that involve shocks and discontinuities. The Zalesak, 1979;van Leer, 1973van Leer, , 1974van Leer, , 1977 Harten and Zwas, 1972;Harten, 1983Harten, , 1984Sweby, 1984;Yee, 1985Yee, , 1987 try to achieve monotonicity with high global accuracy by blending high order fluxes with low order fluxes, using so-called "flux limiters" or "smoothness monitors." In essence, these schemes are of high order every-13,149

Relation of polar auroral arcs to magnetotail twisting and IMF rotation: a systematic MHD simulation study

“…It has been proposed by Raeder (1999) that the tail length during northward IMF depends strongly on the rate of numerical diffusion. A high diffusion rate results in a partial decoupling between magnetic flux tube motion and plasma convection, leading to a short closed field line region in the tail (see also the following discussion by Gombosi et al, 2000;Raeder, 2000). Figure 11 shows the B y B z vector components of the total magnetic field in tail cross sections at x=−10, −15 and −30 R E after a 2 h run with a constant pure IMF B y field of 5 nT.…”

Unusual shrinkage and reshaping of Earth’s magnetosphere under a strong northward interplanetary magnetic field

“…Although the previous simulation suggested that the magnetotail length could vary with the reciprocal of the IMF B Z component (1/B Z ) 17,18,27 , and attempted to explained HCA appearance or polar cap disappearance due to dual-lobe reconnections 24,28 , there are still some controversy, e.g. 17,25,26,29,30 and neither study had provided a complete picture or explanation of all observed features.…”

What sustained multi-disciplinary research can achieve: The space weather modeling framework

“…The criticism culminated in a paper by Raeder (2000) that tried to discredit the 8-wave scheme. The subsequent comment and reply exchange (Gombosi et al, 2000;Raeder, 2000) stopped the open criticism, but the underlying skepticism from some competitors still lingers even today.…”